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Methods for investigating the properties of polycrystalline silicon P-N junction solar cells

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Title:
Methods for investigating the properties of polycrystalline silicon P-N junction solar cells
Creator:
Mazer, Jeffrey Alan, 1948- ( Dissertant )
Neugroshcel, Arnost ( Thesis advisor )
Lindholm, Fredrik A. ( Reviewer )
Fossum, Jerry G. ( Reviewer )
Holloway, Paul H. ( Reviewer )
Varma, Arun K. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1981
Language:
English
Physical Description:
vii, 144 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Approximation ( jstor )
Capacitance ( jstor )
Diodes ( jstor )
Electric current ( jstor )
Grain boundaries ( jstor )
Mesas ( jstor )
Phosphorus ( jstor )
Photovoltaic cells ( jstor )
Pn junctions ( jstor )
Silicon ( jstor )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Solar batteries ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
Experimental and analytical methods are developed for investigating the properties and performance-degrading mechanisms of poly-crystalline silicon p-n junction solar cells. The degrading effects of areal inhomogeneity are demonstrated by means of a parallel-subcell equivalent circuit model. It is shown that it is the area of the poor-quality material in a silicon p-n junction solar cell that dominates in determining the overall cell performance. An experimental method is developed for assessing the validity of the shifting approximation for solar cells made from polysilicon and other material. The experimental data suggest that the shifting approximation is valid for a variety of polysilicon solar cells in which the intragrain base minority carrier diffusion length is smaller than or equal to the average giant diameter. The current components associated with the grain boundaries of diffused p-n junction polysilicon solar cells made on Wacker substrates are analyzed and experimentally identified. The analysis shows that the dominant current component at small bias levels (0-300 mV) is the recombination current component at the grain boundary within the p-n junction space-charge region. At high bias levels (V≈Voc≈500-600 mV), both this current component and the current component due to recombination at that part of the grain boundary which is adjacent to the quasi-neutral base region are important. New electrical methods for determining the presence or absence of preferential diffusion along the grain boundaries and for determining the average doping density of preferentially diffused regions along the grain boundaries are described. A small-signal admittance method is developed for the determination of the grain-boundary surface-state distribution in the energy gap for that part of a grain boundary which has been preferentially diffused with phosphorus. various experimental attempts at suppressing the grain-boundary dark recombination current are described. It is shown that the large leakage currents of small polysilicon p-n junction mass diodes cause the measured I-V characteristics of those diodes to be of questionable value in analyzing the grain boundary component of the current.
Thesis:
Thesis (Ph. D.)--University of Florida, 1981.
Bibliography:
Includes bibliographic references (leaves 139-143).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Jeffrey Alan Mazer.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
000296280 ( ALEPH )
08055623 ( OCLC )
ABS2641 ( NOTIS )

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METHODS FOR INVESTIGATING THE PROPERTIES OF
POLYCRYSTALLINE SILICON P-N JUNCTION SOLAR CELLS








BY

JEFFREY ALAN MAZER


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1981

















ACKNOWLEDGEMENTS


The author sincerely thanks the chairman of his supervisory

committee, Dr. Arnost Neugroschel, and the co-chairman,

Dr. Fredrik A. Lindholm, for their help and guidance during the course

of the research presented in this dissertation. The author also thanks

the other members of his supervisory committee, Dr. Jerry G. Fossum,

Dr. Paul H. Holloway, and Dr. Arun K. Varma for their friendly

assistance.

Appreciation is extended to the author's colleagues and friends for

stimulating discussions: Shing C. Pao, J. Ignacio Arreola,

Franklin N. Gonzalez, Dersun Lee, and Phillip E. Russell. Appreciation

is also extended to Raymond Wilfinger, William Axson, Dean Schoenfeld,

Bruce Chovnick, and William Wagner for technical assistance during the

fabrication of devices.

The author gratefully acknowledges the financial support and

technical assistance of the U.S. Department of Energy and the Solar

Energy Research Institute during the course of this research.

Last, but not least, the author thanks his parents for their

frequent support and encouragement throughout his graduate school

career.

















TABLE OF CONTENTS

PAGE

ACKNOWLEDGMENTS . . . . ... .... ii

ABSTRACT . . . . ... . ... vi

CHAPTER

1 INTRODUCTION . . . . .. 1

2 DEGRADATION OF SOLAR-CELL PERFORMANCE
BY AREAL INHOMOGENEITY . . . . 3

2.1 Introduction . . . .... .. 3
2.2 Type 1 Areal Inhomogeneity . . . 5
2.3 Type 2 Areal Inhomogeneity . . .. 11
2.4 Discussion . . . .... 12

3 A METHOD FOR EXPERIMENTAL ASSESSMENT OF THE SHIFTING
APPROXIMATION, WITH APPLICATION TO POLYSILICON SOLAR
CELLS . . . . ... .. ... 14

3.1 Introduction .... . . . .... 14
3.2 Method for Analyzing the Measured I-V Curves 15
3.3 Experimental Procedure . . ... 21
3.4 Experimental Results . . . ... 24
3.5 Discussion . . . .... 24

4 EFFECTS OF GRAIN BOUNDARIES ON THE CURRENT-VOLTAGE
CHARACTERISTICS OF POLYSILICON SOLAR CELLS . .. 33

4.1 Introduction . . . . ... 33
4.2 Fabrication of Devices and Evaluation of Prefer-
ential Grain-Boundary Diffusion . ... 36
4.3 Analysis of the I-V Curves . . ... 45

4.3.1 Space-Charge Region Current Components
(n+-p diodes) . . ... .. 48
4.3.2 Quasi-Neutral Region Current Components
(n+-p diodes) ..... .. . . 53

4.3.2.1 IGB . . . 55
4.3.2.2 IB and GB Passivation .... 55
QNE
4.3.2.3 IGB . . .. 57
B











PAGE


4.3.3 Illuminated I-V Curves (n -p diodes). 58
4.3.4 Grain-Boundary Passivation by
Hydrogenation Treatment . .. 62
4.3.5 I-V Characteristics (p+-n diodes) . 65
4.3.6 Grain-Boundary Shunt Resistance
RG . . . . 67
Sh

4.4 Comparison of Mesa Diode and Planar Diffused
Diode I-V Curves . . . .. 70
4.5 Discussion . . . . 71

5 SMALL-SIGNAL ADMITTANCE METHOD FOR DETERMINING THE
SURFACE-STATE DISTRIBUTION AT THE PREFERENTIALLY
DIFFUSED PART OF THE GRAIN BOUNDARY . ... 77

5.1 Introduction . . . .... 77
5.2 Small-Signal Equivalent Circuit Model of
a Diode with a Preferentially Diffused
Grain Boundary . . . ... 78
5.3 An Admittance Method for Determining N . 87
ss
5.4 Inversion along the GB in the p-Type Bulk .. 92
5.5 Experimental Procedure and Results ...... 92
5.6 Conductance Method for Determining N .. 101
ss
5.7 Discussion . . . . 103

6. DESCRIPTION OF SEVERAL METHODS INTENDED TO SUPPRESS
THE GRAIN-BOUNDARY DARK RECOMBINATION CURRENT . 108

6.1 Introduction . . . ... 108
6.2 Low-Temperature-Enhanced Preferential Diffusion
of Phosphorus . . . ... 108
6.3 Low-Temperature-Enhanced Preferential Diffusion
of Boron . . . .... ... 110
6.4 Grain-Boundary Passivation by Hydrogen Plasma
Treatment . ......... ............ 111
6.5 Preferential Etching of Grain Boundaries to
Enhance Performance . . . ... 112
6.6 Discussion .... . . .. . 113

7 DISCUSSION . . . . . 114

APPENDIX

I FORTRAN PROGRAMS FOR SIMULATING THE EFFECT OF AREAL
INHOMOGENEITY IN AN n+-p SILICON SOLAR CELL ... 117

II FORTRAN PROGRAM FOR PROJECTING THE PERFORMANCE OF
A SOLAR CELL GIVEN THE EMPIRICAL PARAMETER VALUES
OF THE SUBCELLS . . . . ... 121

III DERIVATION OF A SIMPLIFIED EXPRESSION FOR THE SPACE-
CHARGE REGION RECOMBINATION CURRENT . .. 124











PAGE


IV GROOVE AND STAIN EXPERIMENT TO DETERMINE THE
EXTENT OF STAINING . . . ... 126

V STANDARD WAFER CLEANING AND POLISHING PROCEDURES 128

VI FABRICATION SCHEDULES FOR RUNS 4P4, 6P1, 7P, 8P1,
13P3 and 13P4. . . . .... .129

VII FABRICATION SCHEDULE FOR RUNS 22P and 25P. . ... 132

VIII FABRICATION SCHEDULES FOR RUNS 34P, 36P, AND 37P 133

IX FABRICATION SCHEDULES FOR RUNS 39P AND 40P . .. .135

X COMMENTARY ON THE RELIABILITY OF GROOVE AND STAIN
RESULTS IN CHAPTERS 4 AND 5. . . ... 137

REFERENCES . . . . . . 139

BIOGRAPHICAL SKETCH . . . .... .144

















Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy

METHODS FOR INVESTIGATING THE PROPERTIES OF
POLYCRYSTALLINE SILICON P-N JUNCTION SOLAR CELLS

By

Jeffrey Alan Mazer

August 1981



Chairman: Dr. Arnost Neugroschel
Co-Chairman: Dr. Fredrik A. Lindholm
Major Department: Electrical Engineering

Experimental and analytical methods are developed for investi-

gating the properties and performance-degrading mechanisms of poly-

crystalline silicon p-n junction solar cells.

The degrading effects of areal inhomogeneity are demonstrated by

means of a parallel-subcell equivalent circuit model. It is shown that

it is the area of the poor-quality material in a silicon p-n junction

solar cell that dominates in determining the overall cell performance.

An experimental method is developed for assessing the validity of the

shifting approximation for solar cells made from polysilicon and other

material. The experimental data suggest that the shifting approximation

is valid for a variety of polysilicon solar cells in which the intra-

grain base minority carrier diffusion length is smaller than or equal to

the average grain diameter. The current components associated with the

grain boundaries of diffused p-n junction polysilicon solar cells made on











Wacker substrates are analyzed and experimentally identified. The

analysis shows that the dominant current component at small bias

levels (0-300 mV) is the recombination current at the grain boundary

within the p-n junction space-charge region. At higher bias levels

(V = V0C 500-600 mV), both this current component and the current

component due to recombination at that part of the grain boundary

which is adjacent to the quasi-neutral base region are important.

New electrical methods for determining the presence or absence of

preferential diffusion along the grain boundaries and for determining

the average doping density of preferentially diffused regions along

the grain boundaries are described. A small-signal admittance method

is developed for the determination of the grain-boundary surface-state

distribution in the energy gap for that part of a grain boundary which

has been preferentially diffused with phosphorus. Various experimen-

tal attempts at suppressing the grain-boundary dark recombination

current are described. It is shown that the large leakage currents

of small polysilicon p-n junction mesa diodes cause the measured I-V

characteristics of these diodes to be of questionable value in

analyzing the grain boundary component of the current.


vii
















CHAPTER 1

INTRODUCTION


Recent attention has been focused on polycrystalline silicon solar

cells because of their potential low cost. The anticipated advantage

of low cost is offset by the fact that polycrystalline solar cells

have displayed efficiencies that are much less than those of the

corresponding single-crystal devices [1,2,3]. This lower efficiency

is caused, to varying degrees, by the presence of dark recombination

currents associated with the grain boundaries, by the degrading effects

of areal inhomogeneity, by a low short-circuit current density, and

by a low shunt resistance. In this dissertation, we develop methods

for investigating the properties and performance-degrading mechanisms

of polysilicon p-n junction solar cells.

In Chapter 2, we demonstrate the degrading effects of areal inhomo-

geneity by means of a parallel-subcell equivalent-circuit model.

Chapter 3 describes an experimental method for assessing the validity

of the shifting approximation. These two chapters are applicable to

single-crystal as well as to polycrystalline solar cells.

Most of the experimental devices used in this research were

fabricated on Wacker polysilicon substrates. Wacker material (both p

and n-type) was chosen because it has large enough grain diameters

(~1 mm) to conveniently enable the fabrication of devices that contain

either zero, or at most a few, grain boundaries. By comparing the data

(e.g., capacitance, current-voltage characteristic) on a device










containing a few grain boundaries with the corresponding data on a

similarly fabricated grain-boundary-free (GBF) device, the grain-

boundary (GB) component of the data could be isolated and accurately

analyzed provided that the surface and edge leakage currents were

adequately suppressed. The fabrication of GBF devices also enabled

the determination of some of the intragrain material parameters,

e.g., the intragrain base minority carrier diffusion length. This

fabrication and measurement strategy was used frequently in the

research described in chapters 4, 5, and 6.

In Chapter 4, the current components associated with the grain

boundaries are analyzed and experimentally identified. New electrical

methods for determining the presence or absence of preferential

diffusion along the grain boundaries and for determining the average

doping density of preferentially diffused regions along the grain

boundaries are described.

Chapter 5 describes a small-signal admittance method for the determina-

tion of the grain-boundary surface-state distribution in the energy

gap for that part of a grain boundary which has been preferentially

diffused with phosphorus.

Chapter 6 describes various experimental attempts at suppressing

the grain-boundary dark recombination current. Many of these experi-
+
ments were done on 50-mil n -p mesa diodes. Such experiments were

inconclusive because of the presence of large surface and edge leakage

currents. The subsequent awareness of this fact motivated the fabrica-
+ +
tion of the 30-mil n -p and p -n dark diodes and solar cells used for

the research described in Chapter 4.















CHAPTER 2

DEGRADATION OF SOLAR-CELL PERFORMANCE
BY AREAL INHOMOGENEITY


2.1 Introduction

Areal inhomogeneity refers to the spatial variation of material

properties across the area of a solar cell. Unavoidable statistical

fluctuations in doping concentration across the area always occur. In

addition to this, fabrication procedures can sometimes result in large

areal fluctuations in recombination rates. For polycrystalline cells,

preferential diffusion of impurities down the grain boundaries and the

non-uniform spatial distribution of these grain boundaries can result in

drastic changes in the recombination rates across the area of the

cell [1-3]. The intent here is to quantitatively indicate the limita-

tions on silicon p-n junction solar-cell performance that can be caused

by areal inhomogeneity.

To deal with the areal inhomogeneity, a solar cell can be modeled

as the parallel combination of as many one-dimensional diodes [4] as are

needed to approximate the spatial distribution of the material proper-

ties. Resistive coupling of the diodes is then used to represent

interdiode paths for the recombination and shunt currents (Fig. 2.1).

The use of one-dimensional diodes in this modeling scheme is a first

approximation for polycrystalline solar cells having columnar grains in

which the grain diameter greatly exceeds the minority carrier diffusion

length in the base. This equivalent circuit representation of an illumi-

nated solar cell assumes the validity of the shifting approximation that






























IL,l Sh,l IL,n RSh,n








RSB,1 SB,n





BASE -..


Figure 2.1 Parallel-subcell model of a p-n junction silicon solar cell with areal inhomogeneity.
RSE is series resistance in the emitter, RSB is series resistance in the base, RSh is

shunt resistance, IL is photogenerated current; and, ISCR and IQN are the dark recom-
bination currents in the space-charge region and quasi-neutral region, respectively.


m M










illuminated current is equal to the dark current shifted by the short-

circuit photocurrent [5].

We consider a simple ideal case in which only two subcells are used;

one subcell represents the good-quality material part of the cell, and

the other represents the poor-quality material part of the cell. The

series and shunt resistances are neglected, and the current in each

subcell is assumed to be one-dimensional (Fig. 2.2). For this simple

+
case, two types of areal inhomogeneity for an n -p Si solar cell are

considered. We define AG and Ap to be the areas of the good and poor

regions of the cell, respectively. Then the areal quality factor is

defined to be AQF = AG/A, where A = AG + A is the total solar cell area.


2.2 Type 1 Areal Inhomogeneity

For this type of areal inhomogeneity, the non-illuminated (or dark)

quasi-neutral current densities of the good-quality and poor-quality

diodes, JQNG and JQNP' respectively, are allowed to differ by several

orders of magnitude. For both diodes, the recombination currents are

dominated by recombination in the quasi-neutral regions rather than in

the space-charge regions. Both diodes have the same short-circuit

current density JSC. This type of areal inhomogeneity could occur if the

quasi-neutral emitter dark recombination current density JQNE experiences

drastic areal variations due, for example, to impurity clusters or

variations in the surface recombination velocity in the heavily doped

emitter. For these variations in JQNE to be important, JQNE must be the

dominant component of JQNP. To increase the likelihood of this, we will

17 -3
assume a high base doping concentration: N = 10 cm We assume

further a long base diode for which the short-circuit current density
JSC 25 mAcm2, and the base minority carrier diffusion length
J = 25 mA/cm and the base minority carrier diffusion length


















I
+ AI





POOR AREA


Figure 2.2


Two-diode modeling of areal inhomogeneity in a solar cell, assuming the validity of the
shifting approximation, and neglecting the series and shunt resistances.










L n 100 pm. By the shifting approximation, the illuminated current of

the solar cell is


S= ISC DARK

AG[(JSC)G JQNGOexp(qV/kT)] + Ap[(Js)P JQNPOexp(qV/kT)]

= A {JSC -[exp(qV/kT)][(AQF)JQNGO + (1-AQF)JQNPO]}. (2.1)


In (2.1), JQNGO and JQNPO are the dark saturation quasi-neutral current

densities of the good and poor areas of the cell, respectively. In the

good portion of the cell we are assuming that JQNE is negligible compared
G102 -13
toJ Thus, J J qn D/LN 4.4 x A/cm2 at 250 C,
QNB' QNGO QNBO nn
where JQNBO is the dark saturation current density of the quasi-neutral

base as derived in [6], and D is the electron diffusivity in the base.

In the poor portion of the cell we are assuming that JQNB is negligible

compared to JQNE; thus JQNPO JQNE By defining JR = JQNPO QNGO'

(2.1) may be rewritten as


I = A {JSC -[exp(qV/kT)]JQNGO[AQF + (1-AQF)JR]}. (2.2)


From (2.2), we calculate [Appendix I] and plot the open-circuit voltage

VOC, the fill-factor FF, and the power conversion efficiency n as a

function of AQF with JR as a parameter in Figs. 2.3, 2.4, and 2.5,

respectively. These figures show that even a small poor-material area,

for example 5% (corresponding to AQF = 0.95) of the total solar cell

area, can drastically decrease the overall performance of the solar cell.
2 +
The parameter value JR = 10 corresponds to a silicon n -p thin-junction

solar cell with negligible recombination in the space-charge region,

JSCR JQN. The surface of the good-quality subcell is covered by a
SCR UiM


I










I I I I I I I.
1.0
1.0

TYPE 1 .- -

0.9 0.1/=^ L =LR
102= jQNO)POOR/Q NO GOOD =JR
TYPE 2 /
x 0.7 -


> 0.6

> 0.5


0.4 -

0.3


0.2 Z 0.01

0.1

0 II I I I I I I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

A GOOD /A TOTAL AQF


Figure 2.3 Normalized open-circuit voltage vs. areal quality factor.



















0.8-

0.7


0.6


1.0TYPE 1


102 QNO POOR/( N ) D =--- I

0.1 = Lp /LGoo= DLRT 2
POOR GOOD TYPE 2


- -


A- - -L


0.5 <
0.01


I I


0.4


0.7


A OOD /AT TOTAL =AQF


Figure 2.4 Normalized fill-factor vs. areal quality factor.


0.4


0.3


0.2

0.1


0-.-












1.0 1.0
TYPE 1
0.9 -

0.8 '
102 =(NO POOR /(NO)GOOD =JR .
0 / 7


TYPE 2


0.1= LPOOR/LGOOD = DLR


/
/


7
7
7
7


0.1
.-.


-- 0.01


- -- I I I I


0.4


0.7


0.8


GOOD TOTALL =AQF


Figure 2.5 Normalized power conversion efficiency vs. areal quality factor.


0.6-

0.5-


0.3

0.2-


0.9










passivating thermal SiO2, which yields a low surface recombination

velocity; and the surface of the poor-quality subcell is covered by an

ohmic contact.


2.3 Type 2 Areal Inhomogeneity

In this type of areal inhomogeneity, the p-type base lifetime Tn and

diffusion length L vary across the area of the cell for either of two

reasons: (i) as a result of large variations in the bulk recombination-

center density; or (ii) as a result of the presence of grain boundaries,

in which case T is an effective lifetime. The dark current J K comes
n DARK
mainly from the junction space-charge region (SCR) and from the quasi-

neutral base (QNB), whereas the short-circuit current JSC comes mainly

from the QNB. The shifting approximation then gives the illuminated

current density in each of the two subcells as


J = JSC DARK (2.3)


= JSC JQNB[exp(qV/kT) 1] JSCRO[exp(qV/mkT) 1] (l

in which the expression for JDARK is derived in [7]. A simplified form

of (2.3), which follows from the Sah-Noyce-Shockley treatment of the SCR

recombination current [8] is


J = JC JQNBO[exp(qV/kT) 1] JsCRO[exp(qV/2kT) 11, (2.4)


where


JC qn.W Dn/2L2. (2.5)
SCRO i SCR n n


The details are given in Appendix III. The total illuminated current of

the solar cell is then






12

I = AQF {(JS (JQNBO)G[exp(qV/kT) 1] (JSCRO)G[ex(qV/2kT) 1]}

+ (1 AQF) {(JSC)- (JQNBO)[exp(qV/kT) 1]

(JSCRO)[exp(qV/2kT) 1]}. (2.6)


To demonstrate this type of areal inhomogeneity, we let
16 -3
NAA = 10 cm and, for the good portion of the cell, let
2
(L)G = 100 pm and (JSC)G = 25 mA/cm We assume that at any point on

the cell area JSC"log(Ln), where the constant of proportionality is that

found in both experimental [9,10] and numerical [11] studies for

1 pm L L 100 pm. We define the diffusion length ratio to be

DLR = (Ln)p/(Ln)G. From (2.6), we plot VOC, FF, and n as a function of

AQF with DLR as a parameter in Figs. 2.3, 2.4, and 2.5, respectively.

Again, we notice that it is the poor-quality area of the solar cell that

-2
dominates the overall cell performance. The case for DLR = 10- corre-

sponds to empirical observations by Schwuttke [12] that the generation

lifetime of silicon ribbon material (and thus the related defect density)

varies in a random fashion across the area of the ribbon by between four

and five orders of magnitude.


2.4 Discussion

The above treatment assumes several idealities: resistance and

fringing effects are neglected; the good and poor-material is concen-

trated into two single-connected regions; the current flow in each region

is assumed to be one-dimensional. We now consider the effect of series

resistance on the illuminated solar cell.

In a solar cell with an adequate grid geometry, the dominant

component of series resistance will be that contributed by the bulk

material. This bulk component resists the current of majority carriers









that flow in from the contacts to support recombination with minority

carriers. In the poor-region of the cell, the recombination rate is

very high. Consequently, it is in the poor-region of the solar cell

where majority carrier currents, and thus series resistance effects, will

be most important. The series resistance must be included in the

parallel-subcell model if it causes a voltage drop which is a signifi-

cant fraction of the terminal voltage. A two-parallel subcell model

that includes the series resistance has been considered [4,13]. The

significant finding in [4,13] is that the inclusion of the series

resistance has the effect of decoupling the subcells. This is because

the series resistance tends to suppress the currents flowing between

subcells. The result of this is that the degradation of solar-cell

performance is not as severe as that predicted when the series resis-

tances are neglected. Estimation of the series resistance is given

in [4].

The idealization of two single-connected regions can be removed by

extending the two-parallel subcell model into an n-subcell model, where

n is sufficiently large to accurately describe the variation of material

properties across the area. A computer program that predicts the overall

performance of the solar cell when provided with the empirical parameters

of the subcells is given in Appendix II. A discussion of fringing

effects on the two-parallel subcell model is given in [4].
















CHAPTER 3

A METHOD FOR EXPERIMENTAL ASSESSMENT OF THE SHIFTING
APPROXIMATION, WITH APPLICATION TO POLYSILICON SOLAR CELLS


3.1 Introduction

The shifting approximation that the illuminated current of a solar

cell is equal to the dark current shifted by the short-circuit photocur-

rent is discussed in detail in [5,14]. We report here the results of an

experimental investigation of the validity of the shifting approximation

for four types of polycrystalline Si solar cells.

A solar cell may be thought of as a system with two inputs and two

outputs. The inputs are the optical generation rate in the base and the

excess minority carrier concentration at the edge of the space-charge

region in the base (if the recombination current in the quasi-neutral

emitter is negligible); the corresponding outputs are the short-circuit

photocurrent and the dark recombination current, respectively. It is

shown in [5] that the shifting approximation is valid if this system is

linear; in [14] it is shown that the shifting approximation may remain

practically valid despite some nonlinearity in the system. In a poly-

silicon solar cell, if the shifting approximation is not valid, it is

most likely because the system has been rendered nonlinear by the depen-

dence of the material properties (e.g., the effective minority carrier

lifetime) on the illumination level or by the existence of a large series

or small shunt resistance. Recent data on the majority-carrier Hall

mobility in polysilicon material [15] indicate that the grain-boundary

potential barrier under illumination vanishes almost completely. This

14







15

suggests one possible origin of a dependence on illumination of the

effective minority carrier lifetime. Such a dependence would tend to

invalidate the shifting approximation.

The equivalent circuit diagram of a solar cell is shown in

Fig. 3.1. The shunt resistance RSh is assumed to be large enough so that

the shunt current may be neglected. The combination of the current

generator and the dark diode constitute the intrinsic system [5] of the

solar cell. Even though the series resistance RS may be large enough so

as to invalidate the shifting approximation for the overall solar cell,

it may nevertheless be the case that the shifting approximation is valid

for the intrinsic system of the cell. The approach taken here is to

measure the dark and illuminated I-V curves and then to compare these

curves after separating out the influence of RS. (Shunt resistance for

these cells was determined to be large.) If, after the correction for

RS, the dark and illuminated I-V curves are identical except for being

shifted or translated by the short-circuit current ISC, then the

shifting approximation is valid for the intrinsic system of the solar

cell. It is this sense of the shifting approximation that we are

concerned with in this chapter. The validity of the shifting approxima-

tion for a given solar cell considerably simplifies the theoretical

understanding of the performance of the cell, because then the dark I-V

characteristic and ISC can be considered separately [5].


3.2 Method for Analyzing the Measured I-V Curves

In Fig. 3.1, the voltage V across the terminals differs from the

voltage across the intrinsic system VIS by a voltage drop across the

series resistance RS. In the dark V = VIS + IDRS, whereas under illumi-

nation V = VS ILRS. In Fig. 3.2, we illustrate qualitatively the













F --- -------I




I I
I I '
I I

I I





II
I I
I I


I I
I I


L___-____i__-St
Intrinsic System


Figure 3.1


Equivalent circuit diagram of a solar cell. The dashed lines denote the intrinsic
system of the solar cell.




























































Figure 3.2(a)


Schematic representation of the current-voltage depen-
dencies of a solar cell.


















(ISC)maxi


7


VOLTAGE (Arbitrary Units)


Figure 3.2(b)


Schematic representation of the current-voltage depen-
dencies of a solar cell with all curves shown in the
same quadrant.










dependencies ID V, IL V, and ISC VC for a solar cell. (IScmax

and (Voc)max are the short-circuit current and open-circuit voltage at

the maximum illumination level of the ISC V dependence. Note that

the ideal (reciprocal slope = 1) ISC V0C dependence is the I-V depen-

dence of the intrinsic cell system, since ISC = IS[exp(qV0C/kT) 1] =

IS[exp(qVIS/kT) i], where IS is the dark saturation current of the

cell. This is valid if RS is small enough so that the externally

measured ISC is equal to the short-circuit current of the current gener-

ator in Fig. 3.1. In general, the current-voltage dependencies will have

the following two properties: (i) the ISC VC dependence will be

negligibly influenced by RS; and (ii) the series resistance will shift

the IL V and ID V curves to the left and right of the ISC VC

curve, respectively.

It follows from the above discussion that the shifting approximation

will be valid if the series resistance RS is independent of the illumina-

tion level, and if the IL V and ID V curves are symmetrically shifted

with respect to the ISC VC curve. By symmetrically shifted we mean

that at any given current I (ISC)max, the distance AV1 between the

ID V and ISC VC curves when the ISC VOC curve is shifted into the

first quadrant is the same as the distance AV2 between the IL V and

ISC VOC curves when these two curves are rotated about the V-axis into

the first quadrant. This test for symmetry is shown in Fig. 3.3. Note

that the ISC V0C curves cross at (ISC)max/2 and, if symmetry holds,

then AV1 = AV2 = AV at (ISC)max/2. The series resistance of the solar

cell can then be calculated [16] as


RS = AV/[(IS)max/2] = 2AV/[(IS)max].


I





















S about V axis AV AV

2 7 -
/D v
6
Z (1 )/2- -I V rotated AV--AV
r 5 5 about V axis



3 -\ \
4-


/ v
3-,

2-



0 1 2 3 4 5 6 (Voc)max

VOLTAGE (Arbitrary Units)



Figure 3.3 Illustration of the test for symmetry in the measured
I-V curves. The ISC-VOC curves cross at (ISC)max/2.
If the I-V curves are symmetric, then AV =AV2 at any
given current I < (ISC)max and AV, = AV2 = AV at
I= (IS) max/2.
Sc max










To determine whether RS is independent of the illumination level, we must

perform a second test which involves an independent determination of RS

in the dark. This is done by a method employing small-signal admittance

measurements [17] at a frequency of 4 MHz with zero de-bias. We then

compare this measured value of RS with the value of RS obtained from the

displacement of the curves. If the calculated and measured values of RS

agree, then this would indicate that (i) RS is independent of the

illumination level, and (ii) RS is the only reason for the voltage

displacement of the curves in Fig. 3.3.


3.3 Experimental Procedure

The ID V, IL V, and ISC VOC dependencies at 25.0C were

measured for the seven solar cells listed in Table 3.1. The illuminated

curves were obtained as tracings on an X-Y recorder by continuously

varying (with a helipot) the external load across the solar cell while

the cell was being illuminated by an Oriel solar simulator equipped with

an AMO filter. The level of illumination was varied from exactly 1 sun

intensity, which produced (ISC)max, to about 1/3 sun intensity. Calibra-

tion was accomplished by using a single-crystal standard solar cell

(device No. 7) calibrated at the NASA Lewis Research Center. The dark

I-V curves at 25.00C were obtained by varying the dark diode current with

a digital current source and measuring the corresponding voltage across

the diode terminals. The experimental setup for both the dark and

illuminated measurements (Fig. 3.4) used a four-point probe technique

so as to eliminate the effects of the contact resistance between the cell

and the measuring probes on the top, and between the cell and the vacuum

chuck on the bottom.













Table 3.1 The seven experimental solar cells for which the I-V dependencies were measured.


Device No.


Description


Total Area
(cm2)


Grain Diameter
milss)


4
(25P4)


5
(36P#28-L2)





6
(36P#3-L1)


+
n -p 50 pm thick epi-layer grown on Dow
Corning grade 2P polysilicon substrate.


SnO2 on n-type Wacker polysilicon
substrate.


Indium-Tin-Oxide on 0.1 0.3 Q-cm p-type
polysilicon substrate.


Phosphorus diffused on 5 0-cm Wacker
polysilicon p-type substrate.


Phosphorus diffused on 5 --cm Wacker
silicon p-type substrate. One grain bound-
ary goes through the cell. This solar cell
is 30 mils in diameter and has an MOS guard
ring.


Same as No. 5, but with five grain bound-
aries.


4.45


4.0


10 150


20 70


20 50


20 70


RCA



Exxon


Colorado
State Univ.


UF


4.6 x 10-3






4.6 x 10-3


Diffused n -p single-crystal control. 2.0
Diffused n -p single-crystal control. 2.0


Source


Sandia
















hv from solar simulator


Digital
Current Source


Figure 3.4 Four-point probe experimental setup for investigating the
validity of the shifting approximation.
(a) Setup for measuring IL-V and ISC-VOC
(b) Setup for measuring ID-V.
In both setups, X and Y are the voltage and current axes on
an X-Y recorder. The chuck is connected to a circulating
water bath. The temperature of the chuck is controlled by
the water bath and is measured by a thermocouple inside of
the chuck.










The small-signal admittance measurement for determining the value of

RS at zero de-bias in the dark was accomplished with an HP 4275A LCR

meter. The ac-signal was 10 mV. The values of the series resistance

determined by the small-signal admittance method and by the method of

comparing the dark and illuminated I-V curves are shown in Table 3.2.


3.4 Experimental Results

The symmetries exhibited in the I-V curves, Figs. 3.5 3.9, along

with the corresponding data on the series resistance, suggest that the

shifting approximation is valid for all of the devices measured. From

Table 3.2, note that the values of RS for devices No. 5 and 6 are much

higher than those for the other devices. This is primarily because

devices No. 5 and 6 are much smaller in area than the other devices. If

we approximate the current flow as one-dimensional, then the value of RS
2
for these two devices normalized to an area of 2 cm would be about

0.07 Q.


3.5 Discussion

As mentioned in Section 3.1, it is possible in polysilicon material

that the effective minority carrier lifetime will depend on the illumina-

tion level. The likelihood of this dependency is increased if (i) the

illumination-induced lowering of the grain-boundary potential barrier

significantly changes the effective surface recombination velocity at the

grain boundary, and (ii) the intragrain base minority carrier diffusion

length L is greater than or equal to the average grain diameter dG.

Thus, it is particularly interesting to investigate the validity of the

shifting approximation in polysilicon solar cells where L dG. All six

of the polysilicon devices in Table 3.1 have relatively large grain








Values of series resistance by the small-signal admittance
method and by the method of comparing the dark and illumi-
nated I-V curves.


RS by small-signal
admittance method
(Q)


0.43

0.42


by comparison
the I-V curves
(2)


0.51

0.29

0.30

0.55


0.56


0.05


Table 3.2


Device No.


0.05































E 100
I-
z
w

80




60-

IL -V


40 -




20-



0 I I i i
250 300 350 400 450

VOLTAGE (mV)


Figure 3.5 I-V curves for device No. 1.












140


I
120 T = 25.00C
A = 4.0 cm2
Isc141mA 1 SunAMO
Voc = 539mV I
100 \ -
\ l
I VI


40 I- -
280
z

I.I
l ID.v
60






40 IL ---- \ ---- --V--- l --- ----
I
Iv-
40 ~II

I

20 I
I


0
300 350 400 450 500 550 600

VOLTAGE (mV)


Figure 3.6 I-V curves for device No. 2.


























































375 400 425

VOLTAGE (mV)


Figure 3.7 I-V curves for device No. 3.


< 20

I-
w
cc

o 15





10


450


5-





0 -
350

























Z 20
E
\ /
w

- 15-
/

I-v // \
10 I I




5




450 475 500
VOLTAGE (mV)


Figure 3.8 I-V curves for device No. 4.



























































Figure 3.9


Curve tracer photographs of the dark and illuminated I-V
curves for device No. 6. The symmetry of these curves is
displayed in this fashion rather than in the fashion of
Fig. 3.3 because the voltage displacement of the curves
is very small. ISC = 60 pA, V0C = 467 mV.
(a) Dark I-V curve.
(b) Illuminated I-V curve.










diameters except device No. 6 (see Fig. 3.10) for which L = dG. L was

determined by applying the method of [7] to the dark I-V dependence of a

small grain-boundary-free device and was found to be about 130 Um. For

the small grain-boundary-free device, ISC = 62 pA and VC = 497 mV;

whereas, for device No. 6, ISC = 60 pA and VOC = 467 mV. The 30 mV

decrease in V0C resulting from the presence of the grain boundaries

corresponds to approximately a threefold increase in the dark recombi-

nation current. These data show the degrading effect that the grain

boundaries have on the performance of device No. 6. We note, however,

that the shifting approximation remains valid for device No. 6 in spite

of the very strong influence of the grain boundaries on VOC.

Though no general conclusions can be drawn from these experimental

results, they suggest that the nonlinearities introduced by illumination

levels of one sun are insufficient to invalidate the shifting approxima-

tion in polysilicon solar cells. If this is true, then the simplifica-

tions afforded to solar cell theory by the shifting approximation remain

intact for polysilicon. We emphasize that the experimental method

described here provides a general technique for assessing the validity

of the shifting approximation for solar cells made from polysilicon and

other material, including single crystal, polycrystalline, and highly

disordered semiconductors.





















































Figure 3.10 Microphotograph showing a top view of device No. 6. The
device is 30 mils in diameter and has five grain bound-
aries going through it. The five small white circles
are the top ohmic contacts, and the white annulus is an
MOS guard-ring gate that overlaps the p-n junction dif-
fusion edge.
















CHAPTER 4

EFFECTS OF GRAIN BOUNDARIES ON THE CURRENT-VOLTAGE
CHARACTERISTICS OF POLYSILICON SOLAR CELLS


4.1 Introduction

The performance of polycrystalline solar cells is limited by the

effects of the grain boundaries (GB's) on the current-voltage (I-V)

characteristics. The I-V characteristics determine the efficiency of a

solar cell. Several theoretical models of the GB's and their influence

on the recombination currents have been published [18-23]. The purpose

here is to experimentally investigate the effects of the GB's on the

dark and illuminated I-V characteristics of polysilicon p-n junction

solar cells. The analysis of the experimental I-V characteristics, with

the help of the theoretical models [18-23], will lead to a determination

of the parameters which govern the recombination at the GB's. It will

also lead to a determination of the dominant GB current components.

Most experimental studies on polycrystalline solar cells have been

done on large area (~ 1 cm2) devices which, in general, contain hundreds

of GB's. Due to nonuniform distribution of the GB's and nonuniform grain

geometries, it is difficult to obtain reproducible results on such cells;

thus, an evaluation of the effects of the GB's and different fabrication

procedures on the performance of the cells is difficult. Moreover, poly-

crystalline solar cells usually exhibit large leakage currents which can

mask the contribution of the GB's.










To overcome these difficulties, most of the work reported here was

done on small-area (30 mil in diameter) diodes which contain at most a

few GB's. On such devices the total length and the area of the GB's can

be found, and comparison among the devices can be easily made. The

length and area of the GB's have to be exactly known in order to derive

quantitative results concerning their parameters from the data. Large

area devices containing many GB's can be used mostly for qualitative

studies only.

To assure that the surface and edge currents are suppressed, the

diodes were fabricated with a thermally-grown silicon dioxide on the top

surface and an MOS guard-ring gate overlapping the edge of the diffused

layer, as shown in Fig. 4.1. The surface recombination current compo-

nents, including the surface inversion channel current and the recombina-

tion current through the surface states at the periphery and at the GB's

intersecting the edge of the diode, are suppressed by applying a suit-

able gate voltage to the MOS guard-ring. The remaining current compo-

nents are then only the bulk intragrain and grain-boundary components.

An additional and very important advantage of using small-size diodes is

the possibility of placing diodes inside of grains. This grain-boundary-

free (GBF) diode will then allow us to measure the properties of the

bulk of the grain and will serve as a reference diode for comparison

with a nearby diode containing GB's.

Diffusion of impurities into the polycrystalline material is

expected to proceed preferentially down the GB's [24-26]. The width and

average doping density of this enhanced grain-boundary diffusion region

is determined for the case of phosphorus dopant. Also, the current

components associated with the enhanced grain-boundary diffusion will be

discussed and analyzed here for thefirst time.










Gate


SiO2


Figure 4.1


+
(a) Cross section of the 30 mil in diameter n -p solar cell
with MOS guard ring showing one columnar grain boundary
crossing through the middle.

(b) Top view showing five metal contact circles (5 mil in
diameter) and one grain boundary crossing the cell. The
total metal coverage is 20%.


xi Jn-


Grain Boundary


P type


- -1 1










4.2 Fabrication of Devices and Evaluation of Preferential Grain-Boundary
Diffusion
+ + +
Both n -p and p -n diodes were studied. The n -p diodes were

fabricated on 5 0-cm p-type Wacker polycrystalline silicon substrates.

The phosphorus emitter was predeposited at 900C for 30 minutes followed

by a drive-in diffusion at 1050C for 40 minutes. Wet oxide about
0
3000 A thick was grown on the top surface during the drive-in step. The

junction depth xj was 1.8 pm and the sheet resistance was 8 n/square.
+
The p -n diodes used 0.3 Q-cm n-type Wacker substrates. The boron was

predeposited at 900C for 25 minutes. The drive-in was done at 10000C

for 120 minutes resulting in a junction depth of 0.8 pm and sheet

resistance of 800 0/square. The top surface was passivated by an Si02

layer, about 3000 X thick, grown during the drive-in step.

In Fig. 4.2(a), a grooved and stained section [27,28] of an n -p

diode shows a preferential diffusion of phosphorus down the GB's [24-26].

A copper staining solution was used. The preferential diffusion spike is

about 6 pm deep and is uniformly about 2.3 pm wide. (We refer to a

longitudinal cross-section of a preferentially diffused grain-boundary

region as a diffusion spike.) It was determined by an investigation of

the cross-sections of the 15 mil thick substrate wafers that the GB's go

all the way through the material at an angle between 200 and 450 to the

normal [29]. This angle is referred to as a in Fig. 4.2(b). The GB

also cuts the groove at another angle which is referred to as @ in

Fig. 4.2(b). Both of these angles were considered in calculating the

depth of the n-spike. No phosphorus preferential diffusion spikes were

observed after the 30 minute 900C predeposition step; however, we

measured 5-10 pm spikes after 48 hours heating at 600C after the

predeposition. For the p -n diodes, no preferential diffusion spikes of


















4


I -
'A.

II

'Ir
U

N
*,4V~


Figure 4.2(a)


Grooved and stained section of the n -p junction showing preferential
phosphorus diffusion along the grain boundary. A copper staining solu-
tion was used. The junction depth is about 1.8 pm; the depth of the
preferential diffusion is about 6 pm. A commentary on the reliability
of groove and stain results appears in Appendix X.


























































Figure 4.2(b)


Diagram of a groove and stain sample showing the two
angles, a and a, that define the orientation of the
GB-plane with respect to the substrate wafer. The spike
depth d = d/cos a, where d is the depth for the plane
with a = 0; the angle 8 does not influence d .
n










boron were observed for various diffusion schedules employing 900-1000C

for 20-120 minutes. In order to remove the uncertainties in delineating

the very narrow diffusion spikes by the groove and stain method, we have

developed an electrical measurement procedure which can positively

identify the presence or absence of a preferential diffusion down the

GB's. This electrical measurement will also yield an average doping

density within the preferentially diffused region.

A test structure for determining the presence of preferential GB
+
diffusion is demonstrated for the case of n -p mesa diodes made from a

wafer that received a 30 minute 900C phosphorus predeposition followed

by a 40 minute 10500C drive-in. As stated previously, for this diffusion
GB
schedule x. = 3x. in the bulk. The mesa structures are formed by
J J
masking small dots on the top of the diffused wafer with wax or photo-

resist and then etching off about a 2 pm layer of silicon. The etch

depth is just slightly in excess of x.. This leaves about a 4 pm depth
J
of preferentially diffused GB's around the mesa diodes. Figure 4.3 shows

four mesa diodes, the top two of which are GBF, and the bottom two of

which are connected by a GB.

Two tests can be made on these mesa diodes. The first test, alluded

to above, is the measurement of conductance between the top two diodes

and between the bottom two diodes. The top two diodes represent back-to-
+
back n -p junctions, and very little current will flow between them when

a bias is applied. The bottom two diodes, which are connected by the

diffused GB, constitute a structure similar to a JFET and will show a

current which is dependent on the conductance of the diffused GB channel.

For the second test, reverse-biased capacitance is measured between the

n -diffusion layer and the p-type substrate. The capacitance measured















































Figure 4.3 Test structures for determining the presence of a prefer-
ential diffusion in the GB. The top two mesa diodes are
GBF; the bottom two mesa diodes are connected by a prefer-
entially diffused GB conducting channel.










between one of the top two diodes and the substrate is merely the

capacitance of the GBF diode. The capacitance measured between the small

diode in the bottom pair and the substrate will be equal to the sum of

the capacitances of the two diodes on the bottom plus the capacitance

contributed by the diffused GB channel. Figure 4.4 shows the capacitance

of a 10-mil GBF diode and the capacitance of a 10-mil GB diode which is

connected by a diffused GB channel to a much larger GB diode.

Two conclusions can be made based on Fig. 4.4. First, the capaci-

tance of the 10-mil GB diode is much larger than the capacitance of a

10-mil GBF diode at VR = 0 V. This indicates that the diffusion sched-

ule used in the fabrication of these devices (30 minute 900C predeposi-

tion followed by a 40 minute 10500C drive-in) resulted in a preferential

diffusion of phosphorus down the GB's. Such devices that share a common

GB will be electrically connected by that diffused GB. The 6 pm deep

preferential diffusion will increase the p-n junction area of the 10-mil

GB diode by only a few percent. This slight increase in the area cannot

account for the large value of capacitance at VR = 0 V, which is due

mainly to the contribution from the larger GB diode. Secondly, at

VR 3 V, the capacitance of the 10-mil GB diode drops to the level of

the 10-mil GBF diode, and the two curves are identical for VR Z 3 V.

The reason for this capacitance dependence on reverse bias is a widening

of the depletion layer in the channel by the reverse bias until the

channel is completely depleted. The GB-connected diodes thus become

electrically disconnected due to a depleted nonconducting channel.
+
This capacitance experiment also was done on n -p devices made by a

30 minute diffusion at 900C and on the p -n diodes. No capacitance

difference comparable to that exhibited in Fig. 4.4 was observed. This
















































0 1 2


REVERSE BIAS VOLTAGE (V)


Figure 4.4


Capacitance versus reverse bias measured on the test struc-
tures of Fig. 4.3. The insert shows the measured conduc-
tance of the JFET-like channel between the two bottom GB
diodes of Fig. 4.3 as a function of voltage between the
diodes.











indicates that no inversion layer was created at the intersection of

the GB's with the silicon surface or along the GB's in the p-type bulk;

such an inversion layer could also lead to results shown in Fig. 4.4.

The stained width of the diffusion spike, Fig. 4.2(a) is about

2.3 pm. Based on a series of experiments (see Appendix IV) on both
+ +
n -p and p -n junctions, we concluded that the stained region using the

copper stain solution includes the p-n junction space-charge-region

(SCR) from both sides of the diffusion spike. Inside the spike, a GB

potential barrier is created due to the GB surface states [18,19]. The

reverse bias, VR, required to deplete the channel of width W (Fig. 4.5)
n
will have to push the edge of the p-n junction SCR to the edge of the

grain-boundary SCR. By using a linearly-graded junction approximation

for the p-n junction, we estimated that the average channel doping den-
16 -3
sity is approximately NDD 1 x 10 cm and W = 0.5 pm. We assume

as a first approximation, that the width of the grain-boundary SCR is

independent of the reverse bias VR.

The conductance test described above using the simple structure

created by black wax masking, which results in large spacing between

the GB diodes ( 10 mil), will yield rather small channel current. It

was difficult to separate this channel current from the reverse leakage
16 -3
current of the mesa diodes for the device with NDD 10 cm The

conductance method is demonstrated here for another, more heavily doped,

structure diffused at 1050C for one hour which resulted in a preferen-

tially diffused region 11 pm deep; the stained width of the n-spike was

about 3.6 pm and W = 1 pm. The insert of Fig. 4.4 shows the measured
n
channel current of this JFET-like structure versus the applied voltage.

The existence of a large conductance confirms the occurrence of a
















Z &e


Figure 4.5


WSCR


+
Section of an n -p diode with a columnar GB and a preferen-
tially diffused n-spike with depth d The broken lines
indicate the edges of the p-n junction SCR and the edges of
the GB potential barrier within the n-spike. For the polar-
GB GB
cities indicated, I IB and IB are negative currents.
QNB 1B QNB
The p-n junction along the preferentially diffused GB is
modeled, as a first approximation, as having a square-well
shape with a one-sided step junction at the bottom of the
square well. A more accurate model for the diffusion pro-
file along the GB is one in which the p-n junction appears
wedge-shaped with phosphorus dopant extending below the a-
pex of the wedge. In such a model, the phosphorus concentra-
tion below the apex gradually diminishes to zero.










preferential diffusion. In addition, we can calculate the value of NDD

from the linear portion of the channel current-voltage dependence and

geometry [30]:


NDD = GPGB/qA = 2 x 1017 cm-


-3
where G = 1 x 10-3 mhos is the conductance of the linear portion of the

-4
channel I-V dependence, GB = 23 x 10 cm is the length of the channel,

P = 400 cm2/V-sec is the estimated electron mobility in the channel, and
-7 2
A = 2.2 x 10 cm is the cross-sectional area of the channel. The gate

voltage between the p-type substrate and one of the GB diodes (source)

can be used to modulate the channel conductance and thus to study the

diffusion profile within the preferentially diffused region. NDD also

can be estimated from the reverse gate bias required to deplete the

channel and decrease the channel current to zero; this was not possible

in this device because of the large NDD and the wide channel.


4.3 Analysis of the I-V Curves

A solar cell under illumination is forward biased; the external

current is given by the photogenerated short-circuit current ISC minus

the dark current ID, providing that the superposition principle is

valid [5]. In the following discussion we will concentrate on the open-

circuit voltage VOC of the cell, and also on the dark current ID, since

for many cells, VOC is degraded much more by the GB's than is ISC [31,32].

The illuminated I-V characteristics will be considered in more detail in

Section 4.3.3.

In order to analyze the I-V characteristics of GB diodes, we first

define and describe all current components. Figure 4.5 shows a cross-

section of a portion of the n-p diode showing one columnar grain
section of a portion of the n -p diode showing one columnar grain










boundary with the n-diffusion spike. We assume that the GB is perpen-

dicular to the top surface. The presence of the GB and the diffusion

spike will result in dark current components in addition to those present

in the GBF device. All these additional components, shown in Fig. 4.5,

are designated by a superscript "GB"'. The total dark current is equal to

the sum of all current components:


GB GB GB GB GB GB GB
D QNB + QNE +SCR SCR +SCR' +B QNB + QN + h. (4.1)


The dark current of the GBF diode is given by


ID = IQNB + QNE + ISCR + V/RSh. (4.2)


The current components in (4.1) and (4.2) are defined as follows: IQNB

and IQNE are the recombination currents within the quasi-neutral base
+
and emitter, respectively, and orginate from the lateral n -p junction.
GB
I and ISG are the recombination components due to the carrier
SCR SCR
recombination in the bulk space-charge region (SCR) adjacent to the

lateral n -p junction, and adjacent to the n-diffusion spike, respec-

tively. IGB is the recombination current at the GB within the
SCR
SCR [23]; 1GB is the recombination current at the grain boundary adjacent
G
to the quasi-neutral base (QNB) region; INB is the current component
QNB

injected from the diffusion spike and recombining within the QNB region;

IGB is the current injected from the substrate into the emitter diffu-
QNE
sion spike and recombining within the spike and at the GB surface; and
GB
RS and RGB are the shunt resistances of the GBF and GB diodes, respec-
Sh Sh
tively. The components IQNB IQNE and ICR in (4.1) and (4.2) are

nearly equal in a special case. Their equality requires that the

fundamental kinetic parameters (recombination-center density, capture










cross-sections, etc.) describing recombination in the bulk of the GBF

diode are the same as those relating to the bulk (as opposed to the GB

surface) of the GB diode under study. Additionally, (a) for ISCR

equality, the volume of the SCR straddling the lateral n -p metallurgical

junction must be nearly the same for the GB and the GBF diodes; (b) for

IQNB equality, the electron diffusion length in the quasi-neutral base

of a GB diode containing one GB must be much smaller than the diode

diameter d; and (c) for IQNE equality, the effective hole diffusion

length (which includes the influence of drift) in the quasi-neutral

emitter of a diode containing one GB must be much smaller than the diode

diameter.

The presence of current components associated with the GB will

result in a complicated two-dimensional current flow inside the diode.

The problem can be greatly simplified using an empirical relationship for

the measured I-V curve [7] which expresses the measured I-V dependence of

the GB diode as a sum of three terms:


GB GB GB GB GB
ID = I[exp(qV/mX kT) 1] + IQN[exp(qV/kT) 1] + V/RSh, (4.3)


where IB is the lumped SCR saturation current component and ~B is the
GB
reciprocal slope factor of that component. IQN is the lumped saturation
QNO
current of all quasi-neutral current components, which have a reciprocal
GB
slope factor m = 1.0. The IB is generally a function of injection level

in low injection [23], and its reciprocal slope factor m can be different

from m = 1.0. However, for very large surface recombination velocity

SGB at the GB, which is the case for our devices as will be shown later,

GB
m = 1.0, and the IB can then be lumped together with the other QN










components. Equation (4.3) is strictly valid only if one of the SCR

components in (4.1) is dominant or if all SCR components in (4.1) have

the same reciprocal slope factor.

Similarly for the GBF diode:


ID = IX[exp(qV/mkT) 1] + IQN[exp(qV/kT) 1] + V/RSh. (4.4)


All I-V curves of diodes investigated in this work are described by (4.3)

or (4.4).


4.3.1 Space-Charge Region Current Components (n -p diodes)

Figure 4.6 shows the measured dark I-V characteristics for five
+
representative n -p diodes chosen from over 100 devices containing

either zero or a few grain boundaries. A summary including the total

length of the GB's and the parameters defined in (4.3) and (4.4) for

each of these diodes is shown in Table 4.1. A comparison of the data

for the GB diodes with the data for the GBF diode No. 1 shows the strong

effect of the GB's on the I-V characteristics. This is true even for

device No. 3 which had only one GB. The ratio of currents at 160 mV for

diodes No. 3 and No. 1 is about 40.
+
We now analyze the current components in the n -p GB diodes by

comparing the I-V curves of these diodes with the I-V curve of a GBF

diode, Fig. 4.6. The GB component of IB can be obtained by subtracting

the measured current of the GBF diode from the measured current of the
GB
GB diode, i.e., I ID. However, we observe that the GB components

dominate the current at small biases, below about 300 mV. In this range
GB
mX m 1.8; therefore we can write:

GB GB GB GB
I (100 300 mV) = ISCR + ISCR' + V/R h. (4.5)
D SCR SCR' Sh*













































0 .1 .2 .3 .4 .5


VOLTAGE (V)




+
Figure 4.6 Measured dark I-V curves for five n -p solar cells: a GBF
cell (No. 1), a cell containing twins only (No. 2), and
three GB cells (No. 3, 4, and 5).












Parameter values for devices No. 1-8.


T = 25.0C, A = 4.6 x 10-3 cm2


Device No.


Type


Description


kGB
milss)


GB
I I0
XO' XO
(A)


GB GB
mX, mX QNO' QNO
(A)


1
(36P#13-L2)

2
(36P#4-L1)

3
(36P#28-L2)

4
(36P#25-L1)

5
(36P#3-L1)

6
(34P#4-L2)

7
(34P#1-D1)

8
(34P#1-L1)


+
n -p

+
n -p

+
n -p

+
n -p

+
n -p

+
p -n

+
p -n

+
p -n


GBF


twins only


one GB


several GB's


several GB's


GBF


twins only


several GB's


Table 4.1


SGB
(cm/sec)


2.1


4.8


4.0


9.9


5.7


1.1


1.8


7


x 1012


x 10-12

x 10-0



x-10


x 1010


x 109


x 1010


x 0-10
x 10


1.18


1.29


1.83


1.84


1.76


2.0


1.88


1.94


10-14


10-13


10-13
10-13



10-13



1-14


10-14


10-14


65


3.4 x 104


2.5 x 10


8.2 x 103


9.7


1.6


2.5


2.4


3.4


5.1


2.0


3









GB
The recombination in the SCR adjacent to the n-diffusion spike I was
SCR
analyzed by Sah-Noyce-Shockley [8] and is, in fact, just an extension of

the ISCR of the GBF diode. The area of the n-spike is A = 2kGBdn where

GB is the total length of the GB's in a diode and d is the GB
GB n
preferential diffusion depth. For the GB diodes No. 2-5 in Table 4.1,
2 -3 2
An << A, where A = rd /4 = 4.6 x 10-3 cm is the top area of a 30-mil
GB
diode, and thus ISCR' can be neglected. This component could be impor-

tant in solar or metallurgical grade material where the impurities can

be segregated at the GB's resulting in a very short lifetime in the SCR
GB
adjacent to the n-spike and a large ISC'. The recombination current at
SCR,.
the GB within the SCR can be expressed as [20,23]


GB GB GB (4.6)
SCR ASCR qiSGBexpqVm kT), (4.6)


where SGB is the GB surface recombination velocity at that part of the

GB adjacent to the bulk, Bm 2.0, and ASG 2 WSCR is the approxi-

mate area over which the GB recombination current is described by
GB
(4.6) [23]. WSR is the SCR width of the GB barrier [18,19]. This cur-

rent component is proportional to n.. Such a current will have an acti-
GB
vation energy of one-half of the bandgap (EG/2). ID was measured for

the GB devices in the temperature range from 2220K to 2860K. The slope

factor mX was almost constant in this temperature range. Figure 4.7
GB
shows the ID versus 1/T plot yielding activation energy

Ea= 0.59 eV = E/2. This result very strongly suggests that IGB is

the dominant GB recombination component at small biases below about

300 mV. The theoretical analysis [23] of IS R, based on idealizations,
SCR,
predicts mB = 2.0. Our data give mX mB = 1.76 1.84 at 250C with
GB
most of the devices having mX 1.8. By using (4.6) and an estimate of





















10-9 -


Ea = 0.59 eV


10-11'


10-1r I I I I


3.4


3.6 3.8


1000/T (K-')


Figure 4.7


The dark current of a GB diode measured at 150 mV versus
1/T showing an activation energy Ea = 0.59 eV EG/2.
a. G


10-1o
z
w
C-)


1 I I










WsGB = 0.5 pm, we can calculate the approximate values of SGB. The

results in Table 4.1 indicate that electrically active GB's do not have

a uniform SG. By using the values for IGB = IRGB where
S GB X SCRO
ISRO = ASCR qnSGB, we can calculate the average current per unit

GB -13
length of GB, ISCRG 4.6 x 10 A/pm, with the average slope factor
GB
S mS = 1.81. These two average values can then be used to predict

the behavior of the I-V curves for different grain sizes. The average

GB recombination velocity for devices No. 3-5 is SGB = 2.2 x 104 cm/sec.

The device No. 2 which contains only twin boundaries is almost identical

to the GBF device.


4.3.2. Quasi-Neutral Region Current Components (n -p diodes)
GB
Each value of IQNO, Table 4.1, which includes the QN components
GB
plus the IB from (4.1), is an increasing function of kGB' as expected.

IQNO for the GBF diode is a function of only the doping density in the

p-type substrate and the minority electron diffusion length. The IQNE

can be neglected because of the low doping density in the base

NAA = 3 x 101 cm-3 [7]. The diffusion length L = 130 pm in the GBF
AA n
diode was obtained from the QNB component of the dark current [7]. In

the small area devices, such as the 30 mil diodes used in this work, the

two-dimensional spreading effects will be important if the radius d/2 is

comparable to the diffusion length L [331. For the GBF diode, the

radius of the diode is d/2 = 380 Pm > Ln, which will assure almost one-

dimensional current flow; but for the 30 mil diodes with several GB's,

the grain size could be comparable to the electron diffusion length and

the injected electrons will combine within the grain and at the GB's.

The recombination current in the device can then be described by

Shockley's filament theory [34]:







54


IQN= (AGqn /NAA)[Dn/T(eff)] exp(qV/kT), (4.7)


where AG is the grain area and Tn(eff) is the effective electron life-

time [34] which includes recombination within the grain and at the GB's.

The effective lifetime can be calculated exactly from (4.7) for columnar

grains with rectangular or cylindrical geometry [34]. This is not the

case for the Wacker polycrystalline silicon material. We can, however,
GB
estimate an average effective electron diffusion length L in the poly-
n

crystalline material by measuring the X-ray induced current [35] on a

large area polycrystalline cell and then comparing this current to the

response of a single-crystal cell with known diffusion length. The
2 +
experiment used a 2 cm polycrystalline n -p cell with average grain
GB
size of 500-1000 pm and yielded L = 70 pm which is smaller than

L = 100-130 pm for the GBF diode. This result demonstrates that the
n
+
effect of the GB's on the electrons injected from the top n -p junction

in diodes No. 2-5 cannot be neglected. In addition, the GB's will

contribute to the I QN because of the preferentially diffused n-region

which increases the total area of the p-n junction and contributes

additional current components, as was discussed in Section 4.3.1. The
GB
separation of IQN0 as defined in (4.3) into components for the general

case requires solution of a two-dimensional boundary value problem which

is beyond the scope of this work. We can, however, approximately

accomplish this for our devices by considering the components separately
GB
and identifying the dominant one. Neglecting RSh, there are three quasi-
GB
neutral current components associated with the grain boundary: IQNB,
GB GB
IQNE, and I We now consider each of these components.









GB
4.3.2.1 I
QNB
GB
The IQNB component is due to the electrons injected from the prefer-

entially diffused vertical GB region with an area A into the base.
n
This current component, coupled with the electron current injected from

the top lateral junction with an area A, will result in a two-dimensional

current flow in the base. An accurate solution of such a two-dimentional

problem is not presently available. If, however, A << A, then IGB can
n QNB
be neglected. Considering our n -p devices from Fig. 4.6 and Table 4.1,

the ratio An/A is largest for device No. 5 and is only about 0.1. Thus,

as a first approximation, we will neglect IQB in further analysis of
QNB
GB
our devices. IQ will be important for devices with large depths of

preferential diffusion in the GB.


GB
4.3.2.2. I and GB Passivation
QNE
GB
INE is due to the holes injected from the p-type substrate into the

preferentially diffused region of the GB and recombining inside that

region. The current transferred through the narrow n-spike, Fig. 4.5,

can be treated in a way similar to the current transferred through a

narrow emitter region of a solar cell. A detailed investigation of this

problem was done by Shibib et al. [36]. The recombination current in

the n-spike will be a function of the hole lifetime T in the bulk of
P
the spike, the hole transit time Tt through the spike, and the surface

recombination velocity SGB at the GB inside the spike. The transit time

can be expressed as [36]



T (W2/2D ) + (W /SGB (4.8)
t n p n p(eff)










where D is the average diffusion coefficient corresponding to the

average doping density NDD in the preferentially diffused GB region, W
'D n
GB
is the width of the QN region of the n-spike, and S Gf is the effec-
p(eff) i
tive recombination velocity for holes at the edge of the GB SCR in the

n-spike [18,23]. We will assume now that T << T and check later for
t P
self-consistency. For Tt << Tp, the n-spike will be transparent to the

injected minority holes and the saturation current of the holes

recombining at the GB surface is [36]


GB 2- GB
IQNEO = (Aqni /NDD) [/[(/Sp(eff) ) + (Wnp) (4.9)


This current has to be separated from two other IQN components:
GB GB
IQNB and IB We approach this problem by calculating IN from (4.9).
GB n
This requires a knowledge of SGB Let us assume that S inside of
p(eff)" GB
the n-spike is equal to the surface recombination velocity at that part
GB
of the GB adjacent to the bulk, SB. SG is obtained from IX in
GB GB XO
Table (4.1). From [18,23]:

GB n
Sp(eff) SGB exp(q/kT), (4.10)


where cB is the barrier height of the GB-SCR. By using the estimate

GB 6
S p( ) = 1 x 10 cm/sec. By using this value in (4.9), along with the
p(eff)
16 -3 2
values NDD 1 x 10 cm D 11 cm /sec, and W = 0.4 pm, we obtain
GB -13
IQNO = 2 x 10 A for the device No. 5. This value is close to the
QNEO
GB
measured value of I (see Table 4.1), which implies that I can
QNO QNE
dominate the dark current of the GB diodes if the preferentially

diffused GB regions are lightly doped and SGB is large.
GB







57

GB GB
Note, however, that I EGO exp(qV/kT) is a one-dimensional
QNE QNEO
current linearly dependent on the total length of the GB's in the diode,
GB GB +
since A = 2k d .Therefore, if I dominates the I of the n -p
n GB n QNEO QNO
GB
devices in Fig. 4.6 and Table 4.1, then I should be a linear function
QNO
GB
of kGB. The measured IQNO is, however, much less than linearly depen-

dent on GB; compare, for example, diodes No. 3 and No. 4 in Table 4.1.
GB GB
This implies that the IQN is dominated by IQNB and I We can thus
QN QNB B
make a reasonable estimate that IGB 0.1 IGB Then for device
QNEO QNO.
No. 5, (4.9) implies that S GB ) 4 x 10 cm/sec, and (4.10) implies
p(eff)
that SGB 400 cm/sec. This suggests that the recombination velocity of

the GB was lowered by the diffusion of phosphorus into the GB. Similar

conclusions are also valid for other devices investigated.
GB
We now use the above calculated value for S in (4.8) and
p(eff)
obtain T < 0.1 psec. Thus, our assumption that Tt << T is reasonable
t t p
16 -3
for a relatively low doped n-spike, such as NDD 10 cm found in our

devices.


GB
4.3.2.3. IB
B

IB is the electron current recombining at the GB adjacent to the

QN base. This component will not be linearly proportional to GB due to

the two-dimensional nature of the electron current flow injected from
GB
the top junction. The importance of IB will depend on the grain size

dG, the electron diffusion length Ln, and the surface recombination

velocity SGB. Its influence on the total quasi-neutral current, IQN,

as defined in (4.3) and (4.7) can best be demonstrated by the dependence

of Tn(eff) on these parameters. For our devices with large

SGB ~ 10 cm/sec, we can write [23,37]:










/nef) = (/)[ + 2r 2(L /d )]. (4.11)
n(eff) n n G


For dG >> L Tn(eff) T and IQNB dominates; for small dG, Tn(eff) < T
G n n(eff) n QNB G n(eff) n
and I becomes important. For device No. 5 with diameter d = 760 pm

and five GB's, the approximate grain size is dG = 150 pm and

Tn(eff) 0.9 psec. This value is to be compared to Tn = 6 psec,
GB
corresponding to L = 130 pm for the GBF diode No. 1. For IB to be
n B
important, the intragrain base electron diffusion length, Ln, has to be

larger than the preferential diffusion depth d = 4 pm. From our
GB
experiment we found L = 130 pm >> d The effect of IB will obviously
n n B
increase with decreasing d .
n


4.3.3. Illuminated I-V Curves (n -p diodes)

Table 4.2 shows the summary of results of measurements on illumi-

nated diodes. The short circuit current ISC is almost constant except

for device No. 5, but VOC decreases slightly with increasing RGB. This

is consistent with previous results [31,32] and also with a recently

proposed model [38] for devices with grain size dG > L The decrease
G n
in VO is due to increased ISCR which is directly proportional to kGB'
GB
and also due to increased I The slight decrease in IS for device

No. 5 is because, in this device with five GB's within the 760 pm diode,

the average grain size is comparable to L = 130 pm; thus, some of the

light-generated electrons will recombine at the GB's and will not

contribute to the external measured ISC.

The preferentially diffused n-regions can contribute to the ISC if

d ~ L For the devices studied, d << L and no increase in ISC is
n n n n SC
observed for the GB diodes. The fill factor decreases with kGB as

expected due to the increasing importance of IX with mX > 1.0.










Table 4.2 Parameter values
illumination. T



Device No.


for devices No. 1-8 while under 1 Sun AMO
-3 2
250C, A = 4.6 x 10 cm


ISC
(PA)


VOC
(mV)


497

497

489

485

467

494

480

496


0.81

0.80

0.78

0.75

0.77

0.78

0.78

0.78










Another important consideration for the preferentially diffused

n-regions is the possibility of pinching-off the narrow-n-channel due to

the current passing through it. The detailed description of current flow

through the n-region, both in the dark and under illumination, is very

complicated; but we can roughly estimate the current required for pinch-

off. As a first approximation we will assume that the current leaves or
+
enters the n-region at a distance d /2 from the top n -p junction, i.e.,
n
in the middle of the n-region. We can then treat this n-region as the

channel of a JFET with floating drain and calculate the saturation

current of the n-region channel for our geometry and parameters [30].

This approximation gives Isat = 2mA. The available ISC for 1-sun AMO

conditions for the 30 mil diameter device is only about 0.14 mA [31].

This indicates that the preferentially diffused n-region will not be

pinched-off at 1-sun, even if the entire photogenerated current is

collected by this region. The n-region, however, could be pinched-off

at high concentrations of illumination or in devices which have narrower

Wn or lower NDD Isat also can be directly measured by using the

conductance method on suitable structures shown in Fig. 4.3. This

measurement is demonstrated in the insert of Fig. 4.4.

The device No. 2 which contains only twins has about the same VC

and ISC as the GBF diode.
+
The n -p diodes in Tables 4.1 and 4.2 are representative illumi-

nated diodes (solar cells) from Run 36P. Parameter values for additional

diodes in Run 36P are presented in Tables 4.3 and 4.6. The fabrication

schedule for Run 36P is presented in Appendix VIII.


I













Table 4.3


Description


Parameter values for additional diodes in Run 36P
GB GB -3 2
ICRO IX. T = 25.0C, A = 4.6 x 10 cm

GB GB GB
GB XO' X mX,' X QNO' QNO
milss) (A) (A)


GBF


twins only

one GB


several GB's

several GB's

several GB's


one GB


several GB's


Averages for GB diodes including
the GB diodes in Table 4.1:


64 5.2 x 10 0 1.76


Diode


SGB
(cm/sec)


36P#10-D1


36P#4-D1

36P#14-D2


36P#9-D1

36P#1-D2


36P#34-D1


36P#8-L1


36P#9-L2


8.2


4.7


1.9


2.4

2.6


7.4


6.1


1.4


4.1


1.9

2.4

1.9


10-13


10-12

10-

10-10


10-10

10-10




1010


10-10


10-14


10-13

10-13


10-13


10-13


10-13


1.17

1.32


1.64


1.71


1.70

1.80



1.73


1.81


8.4

1.0


9.2


8.8


2.4


x 101

x 104


x 103

x 103


x 104


1.4 x 1013


2.2 x 10-13


2.6 x 104


3.0 x 10


10-13 4
2.5 x 10 2.0 x 10










4.3.4 Grain-Boundary Passivation by Hydrogenation Treatment
+
Tables 4.4 and 4.6 present parameter values for the n -p diodes in

Run 37P. The Run 37P diodes underwent the same fabrication schedule as

the Run 36P diodes, except for an additional processing step [39] that

was intended to tie up dangling bonds along the grain boundaries with

monoatomic hydrogen [39,40]. After the 37P wafer had undergone the

drive-in step, the oxide grown during the drive-in was covered with a

6000 X layer of vacuum-evaporated aluminum. The wafer was then sintered

at 450C for 12 hours in dry N2. The aluminum was then removed by

chemical etchant and the processing of the wafer was continued as in

Run 36P. This additional processing step is known to tie up dangling

bonds at the Si-SiO2 interface in MOS devices by the generation of some

form of active hydrogen at the Si02-Al interface [41]. By following

this procedure, we were able to use the diodes of Run 36P as a control

group for determining the effect of the hydrogenation step on the diodes

of Run 37P. The 37P wafer was not sintered after the ohmic contacts were

formed so as to avoid out-diffusion of the hydrogen from the GB's [39].

A comparison of the values of SGB for Run 37P in Table 4.4 with

the values of SGB for Run 36P in Table 4.3 shows that the hydrogenation

step has a negligible effect on SGB. By applying both the method of [7]

and the method of [35] to several GBF diodes in Run 37P, it was deter-

mined that the hydrogenation step lowers the intragrain base minority

carrier diffusion length L from about 130 pm to about 90 ilm. This

lowering of Ln is reflected in the I-V characteristics shown in Fig. 4.8.

In agreement with the data reported in [39], Table 4.6 indicates that

the hydrogenation treatment slightly increases VOC. This conclusion is

not firm though, because the increase observed averaged only 11 mV and

the spread of values of VOC was large.













Table 4.4 Parameter values for diodes in Run 37P. T = 25.0C, A =


Description


GB(
milss)


GB
XO' XO

(A)


GB
mx, m"


GB
SCRO
(A)


-3 2
4.6 x 10 cm.


GB GB
SCR QNO' QNO
(A)


37P#11-D2

37P#12-D1

37P#2-D2

37P#1-D1

37P#5-D2

37P#9-D2

37P#10-D1


37P#2-L1

37P#6-L1

37P#8-L1

37P#11-L1


1.3 x 10-10

2.5 x 10-10

5.8 x 10-10

8.5 x 10-11

1.8 x 10-10


6.9 x 10-11

1.9 x 10-9

3.6 x 109

3.9 x 10-10


79 7.4 x 1010 1.78 8.0 x 1010


1.85 3.8 x 1013 2.2 x 104


Diode


GBF

GBF


SGB

(cm/sec)


several

several

several

several

one GB


one GB

several

several

several


4.0

7.5

1.3

2.4

5.4

8.0

1.7


6.7

1.8

3.5

3.6


GB's

GB's

GB's

GB's


GB's

GB's

GB's


x 10-12

x 10-12

x 10-10

x 10-11


x 10-10
x 10-11

x 10-10


10-11

10-9


10-9

10-10


140

75

35

90

20


80

68

150

50


1.19

1.30

1.63

1.69

1.94

1.59

1.61


1.57

2.03

2.01

1.93


x 103

x 103

x 104

x 103

x 104


1.3

8.1

4.1

4.3

2.9

2.3

4.0


4.8

3.1

3.8

4.8


x 10-13

x 10-14

x 10-13

x 10-13

x 10-13

x 10-13

x 10-13


x 10-13

x 10-13

x 10-13

x 10-13


1.67

1.75

2.02

1.71

1.67


1.69

2.08

2.05

2.03


2.0

7.2

3.6

2.0

1.9


1.8

6.0

5.2

1.7


Averages for GB diodes:





















































.1 .2 .3 .4 .5 .B


VOLTAGE (V)


Figure 4.8


Measured dark I-V curves of two GBF n -p solar cells
showing the effect of the hydrogenation treatment on the
intragrain base minority carrier diffusion length, L .
n
The solar cells had identical fabrication schedules ex-
cept that the cell represented by the upper curve under-
went the hydrogenation treatment. This treatment lowered
L from about 130 pm to about 90 pm.
n


1E-04




1E-05




1E-06




IE-07




1E-08


1E-09




1E-10


1E-11










Figure 4.8 also displays the effect that the absence of sintering

of the ohmic contacts had on the series resistance of the 37P diodes:

the extra series resistance of the 37P diode causes the I-V curve of

that diode to bend to the right and cross the I-V curve of the 36P

diode.


4.3.5 .I-V Characteristics (p -n diodes)

Figure 4.9 shows the measured I-V curves for two representative

p -n diodes; device No. 6 is a GBF diode; device No. 8 is a GB diode. A

summary of parameters for these two diodes and for diode No. 7 which

+
contains only twins is in Tables 4.1 and 4.2. In contrast to the n -p

diodes, the effect of the GB's on diode No. 8 is very small. This is

evident both from Fig. 4.9 and Tables 4.1 and 4.2. The intragrain hole

diffusion length for the GBF p -n diode No. 6, obtained from the dark

I-V curve [7], is Lp 35 pm. Thus, for the GB diode No. 8, dG >> L ,

GB
and the effect of the GB's on I QN is negligible. At small bias levels
QNO
the SCR recombination currents are dominated by the recombination in
+ GB
the SCR adjacent to the top p -n junction, IR, and ISCR is negligible.
SCR' SCR
With several ideal assumptions (Appendix III), the Sah-Noyce-Shockley

theory [8] allows ISCR to be written as
SCR


ISCR [AqWSCRn /(2TSCR)]exp(qV/mkT), (4.12)


where TSCR is the time constant controlling the recombination in the

SCR at small bias levels, and m = 2.0. Using (4.12) we find
+
TSCR 0.2 psec for the p -n GBF device No. 6 and TS 100 psec for
+
the n -p GBF device No. 1. This comparison of values for TSCR and also

a comparison of L with L explains the insensitivity of parameters in
p n















1 E-04


0 .1 .2 .3 .4 .5


VOLTAGE (V)


Figure 4.9


+
Measured dark I-V curves for two p -n solar cells: No. 6
is a GBF cell, No. 8 is a GB cell.










GB +
Tables 4.1 and 4.2 (including IXO and V C) to the GB's in the p -n

diodes. The grain size of p -n diodes would have to be comparable to

L = 35 pm in order to observe the effects of the GB's on the I-V curves.
p
+ +
The other important difference between the n -p and p -n diodes is

that no preferential diffusion of dopant impurity (boron) was observed
+
in the p -n diodes. The differences in the values for IX and IN0 for
XO QNO
+
the p -n devices in Table 4.1 are due mainly to the measured variations
16 -3 16 -3
in the base doping density (NDD = 1.3 x 1016 2.6 x 106 cm-3).

Notice also that the device No. 7 containing only twins is very similar

to the other two p -n diodes. Values for ISC are slightly higher for
+ +
the p -n diodes than for the n -p diodes because of the shallower

p -junction depth of 0.8 pm compared to 1.8 pm for the n -junction depth.
+
The p -n diodes in Tables 4.1 and 4.2 are representative diodes

from Run 34P. Parameter values for additional diodes in Run 34P are

presented in Tables 4.5 and 4.6. The relative scattering of values for

these diodes (as opposed to the Run 36P n -p diodes) is attributed mainly

to the measured variation in base doping density.

GB
4.3.6 Grain-boundary Shunt Resistance RSh

The shunt resistance effects on the I-V curve will be most effective

at very small biases. An analysis of the I-V curves in the voltage
+ +
range of about 0-300 mV for both the n -p and p -n GBF and GB diodes

shows that the measured curves can be described by Icexp[(qV/nmkT) 1],

i.e., they follow exactly an exponential dependence for a certain

constant slope factor mX. This indicates that the V/RG term in (4.3)
GB GB
and (4.5) can be neglected and GSh = 1/RSh = 0. This is an important

conclusion regarding the shunt resistance. The effects of RSh on I-V

curves can be confused with the effects of IGB or the edge effects.
SCR













Table 4.5 Parameter values for additional diodes in Run 34P. T = 25.0C, A = 4.6 x 10-3 cm2 .


Description


GB
milss)


GB
IXO IX
(A)


GB
x, "mx


GB
QNO' QNO
(A)


GBF

GBF


twins only

one GB


several GB's

several GB's


several GB's


several GB's


several GB's



several GB's


Averages for GB diodes including
the GB diode in Table 4.1:


5.3

5.5


70 1.3


90 1.2


40 2.8


50 5.7


55 3.0


30 3.0


40 7.3


34P#4-D1

34P#9-D1


34P#1-D1


34P#11-D2


34P#1-D2

34P#3-D1


34P#3-D2


34P#5-D1


34P#6-D2



34P#1-L2


1.91 3.4 x 1014


Diode


2.9 x 10-10


10-11

10-10

10-10

10-10


10-10


10-10

10-10


10-10


10-10


1.58


1.93


1.88


1.74


2.06

1.72


1.90


1.79

2.19



1.97


10-15


10-14

10-14

10-14


10-14

10-14

10-14


10-14

10-14


1.4 x 10-14


50 4.1 x 10 10













Summary of IS and V for
T = 25.0C, A = 4.6 x 10-3


Number of
Diodes
Measured


VOC spread
(mV)


all 30-mil diameter
2
cm 1 Sun AMO.


VOC average
(mV)


solar cells.


ISC spread
(PA)


ISC average

(1A)


471 522

451 558



478 504

466 491


494
480
496


495
496
481


73 76

66 84


61 75

59 74


64 82 70


Table 4.6


Type


34P





36P





37P


GBF
Twins
GB



GBF
Twins
GB



GBF
Twins
GB


+
p -n





+
n -p





+
n -p


468 502 492









However, the use of a structure with an MOS guard ring and the careful

analysis described above shows that the GB's in diffused p-n junction

polycrystalline solar cells made on Wacker material do not cause notice-

able leakage effects due to the GB shunt resistance. This conclusion

is also supported by measuring the I-V curve in the reverse direction

which shows negligible current between zero and about IV of reverse

bias.


4.4 Comparison of Mesa Diode and Planar Diffused Diode I-V Curves

Prior to the fabrication of the 30-mil n -p and p -n planar diffused

diodes described in this chapter, we fabricated (Appendix VI) 50-mil n -p

dark mesa diodes and attempted to isolate the GB-component of IB by

the method of subtracting I from IGB. The I-V measurements on these

mesa diodes tended to be instable and unreliable because of the surface

and edge leakage currents described in Section 4.1. In particular,

the leakage currents caused the measured values for the current densi-
GB
ties JD and JD in the low voltage range (0-300 mV) to be as much as

three orders of magnitude higher for the mesa diodes than for the planar

diffused diodes. The mesa diodes also tended to have higher measured
GB
values of mX and mX (often approximately 2.0) than did the planar

diffused diodes. Since, for the 50-mil mesa diodes, the measured current

in the low voltage range (0-300 mV) was predominately leakage current,

it was not possible to isolate and accurately analyze the GB-component

of IB for these diodes. As described in Section 4.1, the surface and

edge leakage currents are suppressed in the planar diffused diodes by

the use of an oxide on the top surface and an MOS guard-ring gate over-

lapping the edge of the diffused layer.










Figures 4.10 and 4.11 show the effect of leakage current on the J-V
+
characteristics of 50-mil n -p mesa diodes. The leakage current of the
GB
GB mesa diode in Fig. 4.11 causes the measured value of IX,G and conse-

quently, the calculated value for SGB, to be erroneously high. By the

method of Section 4.3.1, SGB is calculated to be 1.5 x 10 cm/sec. This
+
value exceeds the corresponding values for all of the n -p diodes in

Tables 4.1 and 4.3 by more than a factor of four. Though SGB can vary

significantly from diode to diode (Tables 4.1 and 4.3), the above

comparison demonstrates the questionable value of I-V measurements on
GB
small mesa diodes in analyzing the GB-component of ID Some researchers

have failed to notice this point [42]. In Fig. 9 of [42], for example,
GB
the I-V curves of 50-mil mesa diodes display values of mB > 2.0, which

indicates that the current at low bias levels is dominated by recombina-

tion at the surface around the perifphery of the diode [43]; and,

consequently, these I-V data are of little analytical use.

Surface leakage current is proportional to the circumference, and

thus to the radius r of the diode; whereas, the current of a leakage-
2
free diode is proportional to the area of the diode, and thus to r

Consequently, in a mesa diode, the relative contribution of the surface

leakage current to the total measured current will increase as r

decreases. As seen in Fig. 4.10, for a mesa diode with r 25 mils,

the leakage current can dominate the total measured current at low bias

levels (0-300 mV).


4.5 Discussion

This chapter has described and analyzed the effects of GB's on the

performance of polysilicon p-n junction solar cells.








72 -


VOLTAGE (V)


Figure 4.10


Measured dark J-V characteristics of GBF mesa and planar
diffused diodes showing the effect of leakage current on
the low-voltage current density and on the reciprocal
slope mX of the mesa diode. Diode 4P2-1,3,f is a mesa

diode; diode 36P#10-D1 is a planar diffused diode with
an MOS guard ring.


1E-03




1E-04




1E-05




IE-06




1E-07


1E-0e




1E-09
















1E-01




1E-02




1E-03




1E-04




1E-05


1E-07l /
0







Figure 4.11


VOLTAGE (V)


Measured dark J-V characteristics of GB mesa and planar
diffused diodes showing the effect of leakage current
on the low-voltage current density and on the reciprocal
GB
slope mX of the mesa diode. Diode 4P2-4,8,f is a mesa
diode with 300 mils of GB's; diode 36P#1-D2 is a planar
diffused diode with an MOS guard ring and has 65 mils of
GB's. The leakage current of the mesa diode causes the
GB
measured value of IXO and consequently, the calculated
value for S to be erroneously high.
IxD










In order to obtain quantitative results about the GB-recombination

currents in the bulk of the cell, care must be exercised to eliminate

surface and edge-leakage currents. In our devices (30-mils in diameter)

this was accomplished by fabricating the diodes with a thermally-grown

SiO2 on the top surface and an MOS guard-ring gate overlapping the edge

of the diffused layer.

Diffusion of phosphorus into polysilicon material results in a

preferential diffusion along the GB's. The preferential diffusion can

be directly observed by using a groove and stain procedure. This proce-

dure was found to be unreliable, though, because the time and conditions

required to clearly delineate the very narrow preferentially diffused GB

region (spike) varied with the stain solution used and the doping

concentration in the spike. In Section 4.2 we described two new

electrical methods which can positively identify the presence or absence

of a preferentially diffused region. Once the preferentially diffused

region is identified, we may use a suitable groove and stain procedure

to measure the depth of the preferential diffusion and use electrical

methods to determine the average doping concentration in the region.

Our results show that a phosphorus predeposition at 9000 for 30 minutes

followed by a drive-in at 1050C for 40 minutes will preferentially

diffuse the GB's in p-type Wacker material to a depth d of about 4 pm

and will yield an average doping concentration in the diffused GB
16 -3
regions of NDD = 1 x 10 cm The substrate doping was
15 -3
NAA = 3 x 10 cm A predeposition at 1050C for 30 minutes followed

by a drive-in at 1050C for 30 minutes yields dn = 9 m, and
- 2 17 -3
DD 2 x 107 cm The quasi-neutral width W of the preferentially

diffused n-region is about 0.5 pm for the first case and about 1.0 pm










for the second case. On the other hand, a diffusion at 900C for

30 minutes did not result in the creation of a p-n junction along the

GB's.

No preferential diffusion of boron was observed either by the groove

and stain method or by the electrical methods for various diffusions at

900 1000C for 20 120 minutes in n-type Wacker substrate with
16 -3
N D 2 x 101 cm3
DD
Both the GB and the preferentially diffused region along the GB

will have recombination-current components associated with them. These

current components were identified by comparing the I-V characteristics

of the GB devices with the I-V characteristics of devices that were

grain-boundary-free (GBF). A first order analysis of the I-V curves of

the GB diodes, and separation of the total measured current into compo-

nents, was done in Section 4.3. This analysis has shown that the

dominant current component in the GB diodes at small bias levels

(0-300 mV) is the recombination current at the GB within the p-n junction
GB GB
SCR, ISCR. At higher bias levels (V = VC = 500-600 mV), both I and

the recombination current at that part of the GB which is adjacent to
GB
the quasi-neutral base region, IB are important. Both of these
GB
components cause degradation in V and I ; ISR also degrades FF. It
OC SC SCR
was also observed that twin GB's have very little effect on the I-V

characteristics of solar cells.

The preferentially diffused region along the GB increases the area

of the p-n junction. This will result in additional carriers injected
GB
from this region into the base, IQNB, and also in additional carrier

GB
injection from the base into the region, IQNE. A first order analysis

of these currents was done here for the first time.










This analysis suggests some important conclusions regarding the

effects of the preferential GB diffusion on the solar cell I-V curves.

(i) The surface recombination velocity at the GB within the preferen-

tially diffused n-region is about two orders of magnitude smaller than

outside this region. This suggests that a phosphorus diffusion into the

GB's does indeed passivate the GB's. (ii) The preferentially diffused
1018 -3 GB
regions should be heavily doped with NDD = 10 cm to suppress IQNE
n GB
even for large SGB and large d (iii) If IQNE can be suppressed, then
GB n' QNE
the depth of the preferential diffusion should be made comparable to the
GB
base diffusion length, i.e., d = L so as to minimize I (iv) The
n n B
preferentially diffused regions will aid in collection of the photogen-

erated carriers, thus increasing ISC. (v) Increased area of the p-n
GB
junction will increase the IQNB dark current component. However, the
QNB
total dark current will not increase proportionally to the total junction

area because of a two-dimensional coupling between IQNB injected from the
GB
QNB
currents tend to oppose each other.

Another important conclusion of this chapter is that the GB's do not

cause any measurable shunt resistance effects in diffused p-n junction

cells made on Wacker polysilicon material.


















CHAPTER 5

SMALL-SIGNAL ADMITTANCE METHOD FOR DETERMINING
THE SURFACE-STATE DISTRIBUTION AT THE PREFERENTIALLY
DIFFUSED PART OF THE GRAIN BOUNDARY


5.1 Introduction

Lattice mismatch at the grain boundaries (GB's) of polysilicon

solar cells causes the formation of energy levels (surface states) in

the energy gap that serve as recombination centers. Surface states

can be either donor-type or acceptor-type. Those surface states that

are near the center of the energy gap will afford the highest recombina-

tion rates [44] and, thus, will be the most efficient recombination

centers.

For an n -p polysilicon diode, methods for calculating the sur-

face recombination velocity SGB at that part of a GB which is adjacent

to the quasi-neutral p-type bulk and for estimating the surface recom-

bination velocity SGB at that part of a GB which is in a preferential-

ly diffused n-region have been demonstrated in sections 4.3.1 and

4.3.2.2, respectively. With the assumption of a uniform distribution

of surface states in the energy gap, the GB surface-state density N
SS
can be calculated [45] for both the diffused and undiffused sections

of the GB:

N s= S/ vh (5.1)
ss th '

where, S, c, and vth are the surface recombination velocity, capture

cross-section, and thermal velocity for minority carriers at the GB,


1











respectively. The above assumption is generally invalid and, con-

sequently, (5.1) at best gives an estimate of N In order to de-
SS

termine the feasibility of preferential diffusion as a means of GB

surface-state passivation and, subsequently, as a means of lowering

the dark recombination current and increasing VOC and n, a more ac-

curate method for determining Nss must be developed. In this chapter,
ss

we develop a small-signal admittance method that enables the determina-

tion of Nss in the energy gap for that part of the GB which is in a
ss
preferentially diffused n region. The method, in principle, can

yield the determination of all of the fundamental kinetic parameters

in the energy gap at the GB surface: Nss(E), ET, Cn(ET), c (ET) en(ET),

and e (E ). In addition, the method can yield the GB barrier height,

and the doping and mobility in the preferentially diffused region.


5.2 Small-Signal Equivalent Circuit Model of a Diode with a Prefer-
entially Diffused Grain Boundary
+
We consider again the n -p diode with a preferentially diffused

n-region along the GB shown in Fig. 4.5. (The preferentially diffused

n-region of the GB, seen from the perspective of Fig. 4.5, is sometimes

referred to as the n-spike.) The equilibrium band diagram for that

part of the diode that is in the proximity of the preferentially

diffused GB is shown in Fig. 5.1. We assume that the region immediate-

ly next to the GB is depleted due to the presence of the surface

states at the GB [18,19]. The band bending due to those surface states
GB
is q#GB. The narrow depletion region of width WSCR on both sides of

the GB is similar to the surface channel of an MOS transistor in the

depletion regime; and the GB with its surface states is similar to the

Si-Si02 interface of that surface channel. Consequently, the simplified
























































Figure 5.1


+
(a) Cross-section of an n -p polysilicon diode showing the
preferentially diffused n-region of a GB.

(b) The corresponding thermal equilibrium band diagram. The
GB is located at x = 0. The width of the GB space-charge
region is WD; the width of the quasi-neutral n-region
in the n-spike is Wn; the band-bending at the GB is

94GB*











equilibrium small-signal transmission-line equivalent circuit model

of the preferentially diffused n-region shown in Fig. 4.5 will be

similar to the circuit model of the surface channel of an MOS tran-

sistor [46]. This simplified model is shown in Fig. 5.2. By consider-

ing the two-dimensional current flowing through the preferentially

diffused n-region, this model can be derived from the general small-

signal transmission-line equivalent circuit model developed by Sah [47]

for any two-terminal one-dimensional semiconductor device.

The circuit parameters in Fig. 5.2 are defined as follows:

pn is the per-unit-length resistance of the quasi-neutral n-region

in C/cm;

C is the capacitance of the p-n junction space-charge region

along the n-spike in F/cm2

CD is the capacitance of the GB space-charge region in the n-spike

in F/cm2;

G is the electron capture conductance of the GB surface states
ns
2
in mhos/cm ;
2
C is the storage capacitance of the GB surface states in F/cm ;
ss
C GBF is the capacitance of the lateral p-n junction space-charge
GBF
region in F/cm2; and,

Z is the length (into the plane of the paper) of the preferen-

tially diffused n-region.

In Fig. 5.2., we have neglected the electron and hole storage

capacitances in the quasi-neutral regions, and we have assumed the

simple case of a single level of surface states at the GB. The

capacitive coupling between the n-spike and the substrate at the bot-

tom of the spike is neglected on the grounds that the volume of the

























































Figure 5.2 Simplified equilibrium small-signal transmission-line
+
equivalent circuit model of a polysilicon n -p diode with
a preferentially diffused GB.










space-charge region at the bottom of the spike is small compared to the

volume of other regions that contribute capacitance. The resistive

coupling between the n-spike and the substrate through the GB can also

be neglected since it was determined in Section 4.3.6 that G s = 1/RG
Sh Sh
0. The Shockley-Read-Hall recombination through the deep trap levels

in the quasi-neutral bulk is also neglected. The equivalent circuit

model obtained by lumping the circuit elements from both sides of the

GB is shown in Fig. 5.3(a). The transmission line is open-circuited be-
GB +
cause GS 0. This model is also applicable to an n -p diode contain-
Sh
ing more than one GB, because the GB's are all electrically connected

to each other by the lateral n layer on the top.

We now assume, for the circuit shown in Fig. 5.3(a), that small-

signal admittance measurements will be made at frequencies that are

much less than the transmission-line characteristic frequency f [46].

With this assumption, the pn circuit elements can be shorted. The re-

sult is the circuit shown in Fig. 5.3(b). The corresponding simple one-

lump circuit model is shown in Fig. 5.3(c). This model is valid for the

depletion and weak inversion regimes, i.e., for EF(0) 3 Ei(0), where

the GB is located at x = 0.

The input admittance for the circuit of Fig. 5.3(c) is

Yin = Gin + Cin' (5.2)

where

Gin = 2T CssC/[W 2 T (CD + C)2 + (Css + CD + CW) 21 (5.3)

Cin = [wr2C CD (CD + C ) + CW (Css + CD)(Css + CD + CW)]/

[2 2(CD + C W)2 + (Css + CD + CW)2] + CGBF, (5.4)




















Pndy
c -----


CD ZAyzy
-: lCoZ,' !


CGBF C ZA

T ~tCW Zdy
0 --- i ------- i ---------------------o


Figure 5.3(a)


The equivalent circuit model obtained from Fig. 5.2
by lumping the circuit elements from both sides of
the GB.














































Figure 5.3(b) The equivalent circuit model obtained by shorting the
Pn circuit elements in Fig. 5.3(a).






























No in


Figure 5.3(c)


The one-lump equivalent circuit model obtained from
Fig. 5.3(b). Here CD, CW, Css, and CGBF are in farads,
and G is in mhos.
ns











T =/W = C /G (5.5)
ss ss ns
Both (5.3) and (5.4) are dependent on C ; therefore, we can use
ss
either Gi or Ci to obtain information about the surface states.

Experimentally, it is found that the surface states at an Si-Si02

interface [48], and also the surface states at silicon GB's [22], are

continuously distributed in the energy gap rather than existing at a

single energy level. These continuously distributed surface states

can be represented in the circuit model of Fig. 5.3(c) as a parallel

array of Gns Css circuit elements, each element representing surface
ns ss
states at a certain energy level. The capacitance of a G C cir-
ns ss
cuit element is proportional to Nss at the given energy level, and Gs
ss ns
reflects the time constant of the surface states at the given energy

level. The problem of calculating the surface-state capacitance C
ss
for an MOS capacitor with a continuous distribution of surface states

has been considered by Sah [49]. In [49] it is shown that, for the

case of an MOS capacitor with a small-signal current flow, the net C
ss
for distributed states can be obtained by summing the contribution to

Css from all the energy levels between EV and EC referenced to a single

Fermi level. The net Css is determined by those states within about

kT of the Fermi level at the Si surface. Since the equivalent circuit

of a preferentially diffused GB at zero-bias is similar to that of an

MOS capacitor in the depletion regime, the results of [49] may be ex-

tended to include the preferentially diffused GB's of our devices.

Consequently, the circuit model of Fig. 5.3(c) is applicable to the

realistic case of a preferentially diffused GB with a continuous dis-

tribution of surface states.










5.3 An Admittance Method for Determining N
ss

We now describe a small-signal admittance method in which we

use Ci to obtain information about the surface states at that part

of a GB which has been preferentially diffused with phosphorus.

Figure 5.3(c) shows that the zero-bias small-signal capacitance

associated with the preferentially diffused region of the GB's in a

GB diode, C, is equal to the measured terminal capacitance C. of the
in
GB diode minus the measured terminal capacitance of the corresponding

GBF diode:

C = C CGBF (5.6)

The capacitance GGBF is frequency-independent until f ~ 1 GHz. For

sufficiently low frequency, f << f = G /21TC the G can be
ss ns ss ns
short-circuited, and the equivalent circuit will reduce to that shown

in Fig. 5.3(d). From (5.4) and (5.6), the low-frequency limit for C

is then

CLF = Cw(Css + CD)/(Css + CD + CW) (5.7)

For sufficiently high frequencies, f >> f the surface states can-
ss
not follow the signal and the C can be short-circuited. With the
ss
provision that the frequency f is less than the characteristic fre-

quency fo, the equivalent circuit model shown in Fig. 5.3(c) then

reduces to that shown in Fig. 5.3(e); and (5.4) and (5.6) yield the

high-frequency limit for C:

CHF = CWCD/(C + CD). (5.8)

From (5.7) and (5.8), we obtain an expression for Css in terms of CLF

and CHF [50]:

Css = Cw[(CLF/C )/( CLF/CW) (CHF/C)/(1 CHF/CW)]. (5.9)




























Css


Figure 5.3(d)


CGBF


----Yin


The equivalent circuit model obtained from Fig. 5.3(c)
for the low-frequency case, i.e., for f << f .
ss






















-CGBF


iC w

T_


Figure 5.3(e)


The equivalent circuit model obtained from Fig. 5.3(c)
for the high-frequency case, i.e., for f << f << f .
ss o


----Yin










The surface-state density along the preferentially diffused part of

the GB's is then given by

N = Css/qAGB (5.10)

where AGB= d Z is the total area of the preferentially diffused part

of the GB's.

We assume as a first approximation that the preferentially dif-

fused n-region is uniformly doped. In Fig. 5.1(b), it is seen that

the position of the Fermi level for the preferentially diffused part

of the GB's is given by

E (0) E.(0) = E (0)/2 qn q GB (5.11)
F g n GB
where the GB is located at x = 0. In order to determine the position

of the Fermi level for the preferentially diffused part of the GB's,

qpn and q4GB must be calculated.

With the use of the Boltzmann relation [51] for a nondegenerate

semiconductor in thermal equilibrium, the band diagram in Fig. 5.1(b)

shows that

q n = E (0)/2 kT In (N /ni). (5.12)

The values of E (0) and n. as a function of the temperature T are
g 1
found in [52].

The band bending q4GB which is due to the surface states at the

GB can be approximately determined by the method of [46]. In [18], it

is assumed that Nss is uniformly distributed in the energy gap and
ss
that there exists a "neutral level" qqo at approximately E (0)/3 such

that, for EF (0) = q#0, the net charge in the GB surface states is

zero. The assumption concerning the energy gap position of qco is

supported by [53]. With these assumptions, the requirement of overall










charge-neutrality in the n-region of the GB, and the band diagram in

Fig. 5.1(b), yield the following system of equations:

qG = q2Nss 2 [EF(0) q] 1/8EoNDD (5.13)
^GB ss F o o DD (5.13)

EF(00)= E (0 q qGB (5.14)

where po = EV(0)/q + E (0)/3q, and EV(0) is arbitrarily taken to be

zero. This system of equations can be solved for q GB to yield:

qGB =[(23 + 1) 1 (4aB + 1) 1 /2a, (5.15)

where a = qN 2 /8KS N and 3 = 2E (0)/3 [kT In(N /N )].
ss o DD g C DD

In establishing (5.15), it is assumed that N is uniformly dis-
ss
tribute in the energy gap. This generally invalid assumption can

lead to an error in the calculation of q GB. With the assumption of

a one-sided depletion region at the GB, a more accurate expression

for the band bending at the GB is given by


qGB = q () s(E)dE) 2/8 DD (5.16)
Jq
o0

The determination of q GB by (5.16) requires a knowledge of the distri-

bution of Nss between qdo and EF(0) and is only obtainable by means

of iterative calculations. To avoid the laborious nature of the cal-

culations associated with (5.16) while at the same time improving

upon the accuracy that would be afforded by (5.15) if one value of

N were used in (5.15), we have chosen to calculate qGB by using an
ss
average value for Nss in (5.15).
ss
With the calculation of qPn and q GB' EF(0) may be calculated

for various temperatures from (5.11). Thus, by measuring the small-

signal admittance at various temperatures, we can use (5.10) and

(5.11) to determine Nss vs. [E (0) E.(0)].
ss F 1










5.4 Inversion along the GB in the p-Type Bulk

We now consider that part of the GB which is adjacent to the

p-type bulk. Equation (5.13) shows that, with the assumption of a

uniform distribution of surface states in the energy gap, the band

2
bending at the GB is proportional to N For sufficiently large
ss
N E (0) > E (0) where E. is the intrinsic Fermi level, and the
SS F I
region next to the GB becomes inverted. It is of interest to deter-

mine the value of Nss necessary for the formation of an inversion lay-
ss
er along that part of the GB which is adjacent to the p-type bulk.

In Fig. 5.4, it is seen that the onset of inversion occurs when

EF(0) E (0) = q GB = E (0)/2. By substituting these relationships

into (5.13) with NDD replaced by NAA and with o = E (0)/3q, we may

solve for the value of Ns necessary for the onset of inversion:

(N )v = (12/q)[K NAA /E (0)]1/2 (5.17)
ssny o AA g

Since Nss is, in fact, not uniformly distributed in the energy gap,

(5.17) provides only an estimate of the value of Nss necessary for the
SS
onset of inversion. In Section 4.2, an argument based on experimental

data was presented to show that there does not exist an inversion layer

about the GB in the bulk. Consequently, (N ss)in represents an esti-

mate of the upper limit of Nss along that part of the GB which is ad-
ss
jacent to the p-type bulk.


5.5 Experimental Procedure and Results

To demonstrate the above method for determining Nss, two runs
+
(39P and 40P) of n -p mesa diodes were fabricated on 5 --cm Wacker

polysilicon p-type substrates (Appendix IX). The mesa diodes were

made by the method of wax-masking a small dot on a chip that had been


















p-type bulk


( 4.B


S Ev



--GRAIN BOUNDARY

x=0


Figure 5.4 Thermal equilibrium band diagram for that part of a GB
+
which is adjacent to the p-type bulk of an n -p poly-
silicon diode.


Y




Full Text
119
Type 2 Areal Inhomogeneity
C VOC, FF, AND EFF ARE CALCULATED AS FUNCTIONS OF QF WITH DLR AS A
C PARAMETER.
C QF = AGOOD/ATOTAL IS THE AREAL QUALITY FACTOR.
C DLR = BDL/GDL IS THE DIFFUSION LENGTH RATIO.
C GDL IS THE BASE DIFFUSION LENGTH IN THE GOOD PORTION OF THE CELL
C BDL IS THE BASE DIFFUSION LENGTH IN THE POOR PORTION OF THE CELL
C JSCG IS THE SHORT CIRCUIT CURRENT DENSITY IN THE GOOD PORTION OF
C CELL.
C JSCB IS THE SHORT CIRCUIT CURRENT DENSITY IN THE POOR PORTION OF
C CELL.
C USE NAA = 1.0E16/CC, WSCR = 3.37E-5 CM, NI = 1.33E10/CC,
C D = 25.6 CM2/SEC, T = 300 DEG KELVIN, GDL = 100 UM, JSCG = 0.025
C A/CM2.
C
C
C
REAL JSCG,JSCB,JO1G,J02G,J01B,J02B,J01,J02,JSC
REAL JR,JSCR,ISC,I01,I02,KT,IMP
COMMON M,N,EP1,EP2,I01,I02,ISC
KT = 4.14E-21
Q = 1.602E-19
GDL = 100.0E-4
JSCG = 0.025
DO 10 N = 1,20
QF = N*0.05
WRITE(6,2)
2 FORMAT(1H1)
WRITE(6,3) QF
3 FORMAT(5X,FOR QUALITY FACTOR:',F5.2)
4 DO 20 M = 1,10
DLR = 0.01*M
BDL = GDL*DLR
JSCB = ((ALOGIO(BDL*1.0E4))/ALOGIO(GDL*1.0E4)))*JSCG
J01G = (7.25E-14)/GDL
J02G = (9.19E-13)/(GDL**2)
J01B = (7.25E-14)/BDL
J02B = (9.19E-13)/(BDL**2)
J01 = J01G + J01B
J02 = J02G + J02B
JSC = JSCG + JSCB
JR = J02/J01
JSCR = JSCB/JSCG
ISC = (JSCG*QF) + ((1-QF)*JSCB)
101 = (J01G*QF) + ((1-QF)*J01B)
102 = (J02G*QF) + ((1-QF)*J02B)
K = 1
5 VMP = 0.0500 + K*0.0005
CALL FCTVAL(VMP,D7)
FX = D7
K = K + 1
VMP = 0.0500 + K*0.0005


74
In order to obtain quantitative results about the GB-recombination
currents in the bulk of the cell, care must be exercised to eliminate
surface and edge-leakage currents. In our devices (30-mils in diameter)
this was accomplished by fabricating the diodes with a thermally-grown
SO2 on the top surface and an MOS guard-ring gate overlapping the edge
of the diffused layer.
Diffusion of phosphorus into polysilicon material results in a
preferential diffusion along the GB's. The preferential diffusion can
be directly observed by using a groove and stain procedure. This proce
dure was found to be unreliable, though, because the time and conditions
required to clearly delineate the very narrow preferentially diffused GB
region (spike) varied with the stain solution used and the doping
concentration in the spike. In Section 4.2 we described two new
electrical methods which can positively identify the presence or absence
of a preferentially diffused region. Once the preferentially diffused
region is identified, we may use a suitable groove and stain procedure
to measure the depth of the preferential diffusion and use electrical
methods to determine the average doping concentration in the region.
Our results show that a phosphorus predeposition at 900C for 30 minutes
followed by a drive-in at 1050C for 40 minutes will preferentially
diffuse the GBs in p-type Wacker material to a depth dn of about 4 ym
and will yield an average doping concentration in the diffused GB
16 ~3
regions of 1 x 10 cm The substrate doping was
15 -3
- 3 x 10 cm A predeposition at 1050C for 30 minutes followed
by a drive-in at 1050C for 30 minutes yields dn = 3 ym, and
17 -3
Ndd 2 x 10 cm The quasi-neutral width Wn of the preferentially
diffused n-region is about 0.5 ym for the first case and about 1.0 ym


76
This analysis suggests some important conclusions regarding the
effects of the preferential GB diffusion on the solar cell I-V curves.
(i) The surface recombination velocity at the GB within the preferen
tially diffused n-region is about two orders of magnitude smaller than
outside this region. This suggests that a phosphorus diffusion into the
GBs does indeed passivate the GBs. (ii) The preferentially diffused
18 -3 GB
regions should be heavily doped with 10 cm to suppress Iq^j.
n GB
even for large S^g and large d^. (iii) If I^g can be suppressed, then
the depth of the preferential diffusion should be made comparable to the
base diffusion length, i.e., dn Ln> so as to minimize Ig (iv) The
preferentially diffused regions will aid in collection of the photogen
erated carriers, thus increasing Ig^,. (v) Increased area of the p-n
GB
junction will increase the I g dark current component. However, the
total dark current will not increase proportionally to the total junction
area because of a two-dimensional coupling between I^g injected from the
GB
top lateral area and I,.-T_ injected from the vertical area. These two
currents tend to oppose each other.
Another important conclusion of this chapter is that the GBs do not
cause any measurable shunt resistance effects in diffused p-n junction
cells made on Wacker polysilicon material.


60
Another important consideration for the preferentially diffused
n-regions is the possibility of pinching-off the narrow-n-channel due to
the current passing through it. The detailed description of current flow
through the n-region, both in the dark and under illumination, is very
complicated; but we can roughly estimate the current required for pinch-
off. As a first approximation we will assume that the current leaves or
enters the n-region at a distance d^/2 from the top n+-p junction, i.e.,
in the middle of the n-region. We can then treat this n-region as the
channel of a JFET with floating drain and calculate the saturation
current of the n-region channel for our geometry and parameters [30].
This approximation gives I 2mA. The available I for 1-sun AMO
SSL DL*
conditions for the 30 mil diameter device is only about 0.14 mA [31].
This indicates that the preferentially diffused n-region will not be
pinched-off at 1-sun, even if the entire photogenerated current is
collected by this region. The n-region, however, could be pinched-off
at high concentrations of illumination or in devices which have narrower
W or lower I also can be directly measured by using the
conductance method on suitable structures shown in Fig. 4.3. This
measurement is demonstrated in the insert of Fig. 4.4.
The device No. 2 which contains only twins has about the same
and Igc as the GBF diode.
The n+-p diodes in Tables 4.1 and 4.2 are representative illumi
nated diodes (solar cells) from Run 36P. Parameter values for additional
diodes in Run 36P are presented in Tables 4.3 and 4.6. The fabrication
schedule for Run 36P is presented in Appendix VIII.


56
where is the average diffusion coefficient corresponding to the
average doping density DD in the preferentially diffused GB region, Wn
is the width of the QN region of the n-spike, and is the effec
tive recombination velocity for holes at the edge of the GB SCR in the
n-spike [18,23]. We will assume now that xt << and check later for
self-consistency. For xt x the n-spike will be transparent to the
injected minority holes and the saturation current of the holes
recombining at the GB surface is [36]
GB
QNEO
2
GB
WV^^^pCeff)) + W]1-
(4.9)
This current has to be separated from two other I components:
T A XGB
XQNB and XB
GB
We approach this problem by calculating from (4.9).
IjJNrjO
GB ti
This requires a knowledge of Bp(ef£)* Let us assume that inside of
the n-spike is equal to the surface recombination velocity at that part
of the GB adjacent to the bulk, S
Table (4.1). From [18,23]:
GB*
GB
is obtained from I_, in
vjJo A
Sp(eff) SGB exP(q^g/kT),
(4.10)
where (¡>B is the barrier height of the GB-SCR. By using the estimate
<}>B 0.12 V for a forward-biased diode at 25C, we obtain
GB 6
S (eff) 1 x 10 cm/sec. By using this value in (4.9), along with the
16 -3 2.
values __ 1 x 10 cm D 11 cm /sec, and W 0.4 ym, we obtain
DD p 7 n
GB -~13
IqNeq ~ 2 x 10 A for the device No. 5. This value is close to the
GB
measured value of I^NQ (see Table 4.1), which implies that I^NE can
dominate the dark current of the GB diodes if the preferentially
diffused GB regions are lightly doped and Sa is large.


25
Table 3.2 Values of series resistance by the small-signal admittance
method and by the method of comparing the dark and illumi
nated I-V curves.
Device No. Rg by small-signal
admittance method
(fi)
Rg by comparison
of the I-V curves
1
2
3
4
5
6
7
0.43
0.42
0.56
27
30
0.05
0.51
0.29
0.30
0.55
30
~50
0.05


110
for a total time of 130 minutes. The 6P1 wafer received the additional
treatment of a 48 hour 600C drive-in, in dry N in between the 900C
predeposition and the final 900C drive-in steps. The purpose of the
low-temperature step was to enhance the preferential diffusion of
phosphorus along the GB's [54,55], and thereby tie up dangling bonds
along the GB's. It has been reported that the intragain diffusivity
decreases faster with decreasing temperature than does the GB diffus
ivity [54]; and, at 600C, the preferential diffusion of phosphorus
along the GB's was anticipated to dominate the diffusion of phosphorus
into the intragrain bulk [54,55]. Zero-bias capacitance measurements
confirmed that the 600C treatment enhanced the preferential diffusion
of phosphorus along the GB's.
When it became clear to us that the measured currents of these
mesa diodes were dominated by leakage currents, we fabricated (Appen
dix VI) two runs of planar diffused diodes with MOS guard rings (Runs
13P3 and 13P4), one of which underwent a 48 hour 600C drive-in, in dry
in between the predeposition and final high-temper ature drive-in.
By using the subtraction method described in Section 6.1, it was de
termined that the low-temperature treatment had a negligible effect
on the GB component of the dark recombination current.
6.3 Low-Temperature-Enhanced Preferential Diffusion of Boron
In Run 8P1 (Appendix VI), n+-p mesa diodes were fabricated with a
diffusion schedule that included a 1 hour predeposition of boron at
1050C followed by a 48 hour boron drive-in at 600C. The boron doped
top Si layer was then removed and phosphorus was diffused to form the
top n -p junction. The low-temperature step was intended to enhance


136
Run 4OP
Same as Run 39P but with the following changes:
Step 2. Predeposition: 30 minutes at 900C; pg = 288 tifu.
Step 5. Drive-in: 40 minutes at 1050C; p =63 ft/.
s
Step 12. The Si etching requires 60 seconds in 1 HF : 6 HNO^ : 1 CH^COOH
solution.


38
(b)
Figure 4.2(b) Diagram of a groove and stain sample showing the two
angles, a and 3, that define the orientation of the
GB-plane with respect to the substrate wafer. The spike
depth dn = d/cos a, where d is the depth for the plane
with a = 0; the angle 3 does not influence d^.


40
P- type
GB Conducting Channel
Figure 4.3 Test structures for determining the presence of a prefer
ential diffusion in the GB. The top two mesa diodes are
GBF; the bottom two mesa diodes are connected by a prefer
entially diffused GB conducting channel.


32
Figure 3.10 Microphotograph showing a top view of device No. 6. The
device is 30 mils in diameter and has five grain bound
aries going through it. The five small white circles
are the top ohmic contacts, and the white annulus is an
MOS guard-ring gate that overlaps the p-n junction dif
fusion edge.


39
boron were observed for various diffusion schedules employing 900-1000C
for 20-120 minutes. In order to remove the uncertainties in delineating
the very narrow diffusion spikes by the groove and stain method, we have
developed an electrical measurement procedure which can positively
identify the presence or absence of a preferential diffusion down the
GB*s. This electrical measurement will also yield an average doping
density within the preferentially diffused region.
A test structure for determining the presence of preferential GB
diffusion is demonstrated for the case of n+-p mesa diodes made from a
wafer that received a 30 minute 900C phosphorus predeposition followed
by a 40 minute 1050C drive-in. As stated previously, for this diffusion
GB
schedule x. 3x. in the bulk. The mesa structures are formed by
J J
masking small dots on the top of the diffused wafer with wax or photo
resist and then etching off about a 2 pm layer of silicon. The etch
depth is just slightly in excess of x ^ This leaves about a 4 pm depth
of preferentially diffused GBs around the mesa diodes. Figure 4.3 shows
four mesa diodes, the top two of which are GBF, and the bottom two of
which are connected by a GB.
Two tests can be made on these mesa diodes. The first test, alluded
to above, is the measurement of conductance between the top two diodes
and between the bottom two diodes. The top two diodes represent back-to-
back n+-p junctions, and very little current will flow between them when
a bias is applied. The bottom two diodes, which are connected by the
diffused GB, constitute a structure similar to a JFET and will show a
current which is dependent on the conductance of the diffused GB channel.
For the second test, reverse-biased capacitance is measured between the
n+-diffusion layer and the p-type substrate. The capacitance measured


82
space-charge region at the bottom of the spike is small compared to the
volume of other regions that contribute capacitance. The resistive
coupling between the n-spike and the substrate through the GB can also
GB GB
be neglected since it was determined in Section 4.3.6 that G^, = 1/Ri
Dll bn
- 0. The Shockley-Read-Hall recombination through the deep trap levels
in the quasi-neutral bulk is also neglected. The equivalent circuit
model obtained by lumping the circuit elements from both sides of the
GB is shown in Fig. 5.3(a). The transmission line is open-circuited be-
GB
cause Ggk 0. This model is also applicable to an n -p diode contain
ing more than one GB, because the GB's are all electrically connected
to each other by the lateral n+ layer on the top.
We now assume, for the circuit shown in Fig. 5.3(a), that small-
signal admittance measurements will be made at frequencies that are
much less than the transmission-line characteristic frequency f [46].
With this assumption, the circuit elements can be shorted. The re
sult is the circuit shown in Fig. 5.3(b). The corresponding simple one-
lump circuit model is shown in Fig. 5.3(c). This model is valid for the
depletion and weak inversion regimes, i.e., for Ep(0) ~ E^(0), where
the GB is located at x = 0.
The input admittance for the circuit of Fig. 5.3(c) is
(5.2)
where
G.
C.
m
in
(5.3)
(5.4)


21
To determine whether R is independent of the illumination level, we must
D
perform a second test which involves an independent determination of Rg
in the dark. This is done by a method employing small-signal admittance
measurements [17] at a frequency of 4 MHz with zero dc-bias. We then
compare this measured value of Rg with the value of Rg obtained from the
displacement of the curves. If the calculated and measured values of Rg
agree, then this would indicate that (i) Rg is independent of the
illumination level, and (ii) Rg is the only reason for the voltage
displacement of the curves in Fig. 3.3.
3.3 Experimental Procedure
The ID V, Ip V, and IgC VQp dependencies at 25.0C were
measured for the seven solar cells listed in Table 3.1. The illuminated
curves were obtained as tracings on an X-Y recorder by continuously
varying (with a helipot) the external load across the solar cell while
the cell was being illuminated by an Oriel solar simulator equipped with
an AMO filter. The level of illumination was varied from exactly 1 sun
intensity, which produced (I ) to about 1/3 sun intensity. Calibra-
b O THcL2C
tion was accomplished by using a single-crystal standard solar cell
(device No. 7) calibrated at the NASA Lewis Research Center. The dark
I-V curves at 25.0C were obtained by varying the dark diode current with
a digital current source and measuring the corresponding voltage across
the diode terminals. The experimental setup, for both the dark and
illuminated measurements (Fig. 3.4) used a four-point probe technique
so as to eliminate the effects of the contact resistance between the cell
and the measuring probes on the top, and between the cell and the vacuum
chuck on the bottom.


75
for the second case. On the other hand, a diffusion at 900C for
30 minutes did not result in the creation of a p-n junction along the
GB's.
No preferential diffusion of boron was observed either by the groove
and stain method or by the electrical methods for various diffusions at
900 1000C for 20 120 minutes in n-type Wacker substrate with
Ndd 2 x 1016 cm-3.
Both the GB and the preferentially diffused region along the GB
will have recombination-current components associated with them. These
current components were identified by comparing the I-V characteristics
of the GB devices with the I-V characteristics of devices that were
grain-boundary-free (GBF). A first order analysis of the I-V curves of
the GB diodes, and separation of the total measured current into compo
nents, was done in Section 4.3. This analysis has shown that the
dominant current component in the GB diodes at small bias levels
(0-300 mV) is the recombination current at the GB within the p-n junction
GB PTC
SCR, lgCR At higher bias levels (V = VQC 500-600 mV), both IgCR and
the recombination current at that part of the GB which is adjacent to
GB
the quasi-neutral base region, I^ are important. Both of these
D
GB
components cause degradation in VAO and I ; I^ also degrades FF. It
Ut> bL dCK
was also observed that twin GB*s have very little effect on the I-V
characteristics of solar cells.
The preferentially diffused region along the GB increases the area
of the p-n junction. This will result in additional carriers injected
GB
from this region into the base, Irt_TT), and also in additional carrier
Jt>
GB
injection from the base into the region, Iq^r. A first order analysis
of these currents was done here for the first time.


47
cross-sections, etc.) describing recombination in the bulk of the GBF
diode are the same as those relating to the bulk (as opposed to the GB
surface) of the GB diode under study. Additionally, (a) for I_
bCK
equality, the volume of the SCR straddling the lateral n+-p metallurgical
junction must be nearly the same for the GB and the GBF diodes; (b) for
Iq^B equality, the electron diffusion length in the quasi-neutral base
of a GB diode containing one GB must be much smaller than the diode
diameter d; and (c) for I ^ equality, the effective hole diffusion
length (which includes the influence of drift) in the quasi-neutral
emitter of a diode containing one GB must be much smaller than the diode
diameter.
The presence of current components associated with the GB will
result in a complicated two-dimensional current flow inside the diode.
The problem can be greatly simplified using an empirical relationship for
the measured I-V curve [7] which expresses the measured I-V dependence of
the GB diode as a sum of three terms:
rGB
rGB
GB.
Ij" = lJo[exp(qV/mpcT) 1] + I[exp(qV/kT) 1] + V/Rg", (4.3)
GB
GB GB
where 1^ is the lumped SCR saturation current component and m^ is the
GB
reciprocal slope factor of that component. *s t*ie lumPe current of all quasi-neutral current components, which have a reciprocal
GB
slope factor m = 1.0. The Ig is generally a function of injection level
in low injection [23], and its reciprocal slope factor m can be different
from m = 1.0. Hcwever, for very large surface recombination velocity
Sgg at the GB, which is the case for our devices as will be shown later,
GB
m = 1.0, and the Ig can then be lumped together with the other QN


11
passivating thermal SiC>2> which yields a low surface recombination
velocity; and the surface of the poor-quality subcell is covered by an
ohmic contact.
2.3 Type 2 Areal Inhomogeneity
In this type of areal inhomogeneity, the p-type base lifetime and
diffusion length vary across the area of the cell for either of two
reasons: (i) as a result of large variations in the bulk recombination-
center density; or (ii) as a result of the presence of grain boundaries,
in which case T is an effective lifetime. The dark current JL4T1T, comes
n DARK
mainly from the junction space-charge region (SCR) and from the quasi
neutral base (QNB), whereas the short-circuit current Jg^, comes mainly
from the QNB. The shifting approximation then gives the illuminated
current density in each of the two subcells as
J JSC JDARK
(2.3)
= Jsc JQNB0[exp(qV/kT) 1] JSCR0[exp(qV/mkT) 1] (l in which the expression for J is derived in [7]. A simplified form
DARK
of (2.3), which follows from the Sah-Noyce-Shockley treatment of the SCR
recombination current [8] is
J = Jsc JQNB()[exp(qV/kT) 1] JSCR0[exp(qV/2kT) 1], (2.4)
where
SCRO
(2.5)
The details are given in Appendix III. The total illuminated current of
the solar cell is then


i2a
130 CONTINUE
GO TO 190
140 VMP = P2(1P1)
IMP = ILOAD
WRITE(6,150)
150 FORMAT(1HO)
WRITE(6,160) P2(IP1),IMP
160 FORMAT(5X,VMP IS:' ,F7.4,5X,'IMP IS:',E9.4.//)
FF = (VMP*IMP)/(VOC*ISC)
EFF = VOC*ISC*FF
WRITE(6,170)
170 FORMAT(1H1)
WRITE(6,180) VOC,ISC,VMP,IMP,FF,EFF
180 FORMAT(5X,'VOC=',E12.5,3X,'ISC=',E12.5,3X,VMP=,E12.5,3X,
FIMP=',E12.5,3X,'FF=E12.5,3X,EFF=,E12.5,//)
GO TO 210
190 WRITE(6,200)
200 FORMAT(5X,RLOAD FOR VMP, IMP HAS NOT BEEN FOUND',//)
210 CONTINUE
WRITE(6,220) KKDUMM
220 FORMAT(5X,KKDUMM=,13,//)
STOP
END
C
C
SUBROUTINE CALFUN(NP,XP,FP)
DIMENSION XP(1),FP(1)
REAL IL(2),MX(2), 1X0(2),IQNO(2),RS(2),RSH(2),ISC,ILOAD
COMMON IL,MX,IXO,IQNO,RS,RSH,RLOAD
QKT = 38.61
Al (XP(l)-XP(3))/RS(1)
A2 = (XP(2)-XP(3))/RS(2)
B1 = IXO(1)*(EXP(QKT*XP(1)/MX(1))-1.0)
B2 = IXO(2)*(EXP(QKT*XP(2)/MX(2))-1.0)
Cl = IQNO(1)*(EXP(QKT*XP(1))-1.0)
C2 = IQNO(2)*(EXP(QKT*XP(2))-1.0)
FP (1) = IL (1) -Bl-Cl- (XP (1) /RSH (1) ) -A1
FP(2) = IL(2)-B2-C2-(XP(2)/RSH(2))-A2
FP(3) = A1+A2-(XP(3)/RLOAD)
RETURN
END


143
54. T. H. DiStefano and J. J. Cuomo, "Enhancement of carrier collec
tion efficiency in polycrystalline silicon solar cells," NSF-RANN
Report on National Workshop on Low-Cost Polysilicon Solar Cells,
pp. 230-245, May 1976.
55. T. H. DiStefano and J. J. Cuomo, "Reduction of grain-boundary
recombination in polycrystalline silicon solar cells," Appl. Phys.
Lett., vol. 30, pp. 351-353, April 1977.
56. J. R. Hauser and P. M. Dunbar, "Minority carrier reflecting
properties of semiconductor high-low junctions," Solid State
Electronics, vol. 18, pp. 715-716, July 1975.
57. C. H. Seager and D. S. Ginley, "Improvement of polycrystalline
silicon solar cells with grain-boundary hydrogenation techniques,"
Appl. Phys. Lett., vol. 36, pp. 831-833, May 1980.
58. G. H. Schwuttke, private communication, 1979.
59. F. N. Gonzalez and A. Neugroschel, "Design of quasi-grain-boundary-
free (QGBF) polycrystalline solar cells," IEEE Electron Device
Lett., vol. EDL-2, pp. 141-143, June 1981.
60. R. M. Burger and R. P. Donovan, Fundamentals of Silicon Integrated
Device Technology, vol. I, pp. 313-314, Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1967.


CHAPTER 6
DESCRIPTION OF SEVERAL METHODS INTENDED TO SUPPRESS
THE GRAIN-BOUNDARY DARK RECOMBINATION CURRENT
6.1 Introduction
Prior to the fabrication of the planar diffused diodes discussed in
Chapter 4, we investigated several fabrication procedures that were
intended to suppress the grain-boundary (GB) component of the dark
recombination current. The experimental devices were 10-, 20-, and
+ +
50-mil n -p mesa diodes; 10-, 20-, and 50-mil n -p planar diffused
2 +
diodes with MOS guard rings; and large area (~1 cm ) n -p solar cells.
The substrates for these devices came from the same lot of 5 fi-cm p-type
wafers as did the substrates for the n+-p devices discussed in
Chapter 4. Table 6.1 presents a summary of the experimental runs
incorporating the special fabrication procedures. For the mesa and
planar diffused diodes, we attempted to isolate the GB component of the
dark recombination current by the method of subtracting the I-V
characteristic of a grain-boundary-free (GBF) diode from the I-V charac
teristic of a similarly fabricated diode containing a few GB's. As
mentioned in Chapter 1 and Section 4.4, the experimental results for
the small mesa diodes were inconclusive due to the presence of large
leakage currents.
6.2 Low-Temperature-Enhanced Preferential Diffusion of Phosphorus
In Runs 4P4 and 6P1 (Appendix VI), n -p mesa diodes were fabricated
on wafers that had undergone a 900C predeposition and a 900C drive-in
108


Table 5.2
Additional parameter values for the diodes listed in Table 5.1. The capacitance
is calculated from the expression for C^, equation (5.8). The doping density
Np^(O) is calculated from the depletion approximation expression for C^.
Diode
uu
T
(K)
CD
(pF)
, -3.
(cm )
D
5dd from
Chapter 4
(cm 3)
39P//2
93
151
2 x 1017
39P#2
145
180
It
39P#2
198
204
It
40P#3
93
50
15
9.4 x 10
1 x 1016
40P#3
145
55
1.0 x 1016
II
40P#3
198
65
1.3 x 1016
If


2
containing a few grain boundaries with the corresponding data on a
similarly fabricated grain-boundary-free (GBF) device, the grain
boundary (GB) component of the data could be isolated and accurately
analyzed provided that the surface and edge leakage currents were
adequately suppressed. The fabrication of GBF devices also enabled
the determination of some of the intragrain material parameters,
e.g., the intragrain base minority carrier diffusion length. This
fabrication and measurement strategy was used frequently in the
research described in chapters 4, 5, and 6.
In Chapter 4, the current components associated with the grain
boundaries are analyzed and experimentally identified. New electrical
methods for determining the presence or absence of preferential
diffusion along the grain boundaries and for determining the average
doping density of preferentially diffused regions along the grain
boundaries are described.
Chapter 5 describes a small-signal admittance method for the determina
tion of the grain-boundary surface-state distribution in the energy
gap for that part of a grain boundary which has been preferentially
diffused with phosphorus.
Chapter 6 describes various experimental attempts at suppressing
the grain-boundary dark recombination current. Many of these experi
ments were done on 50-mil n+-p mesa diodes. Such experiments were
inconclusive because of the presence of large surface and edge leakage
currents. The subsequent awareness of this fact motivated the fabrica
tion of the 30-mil n+-p and p+-n dark diodes and solar cells used for
the research described in Chapter 4.


40
35
a.
t
CJ
CD
O
C
cD
30
H
a
C
p-
aj
U
25
CD
ti
e
s-i
H
20
15
10
Frequency (Hz)
Figure 5.7
Measured terminal capacitance C. as a function of frequency for the n -p mesa diode 40P#3.
V£5


FF/FF
O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Aq o o D ^TO T A L = AQF
Figure 2.4 Normalized fill-factor vs. areal quality factor.


125
Since n = n + An, the net recombination rate of excess electrons and
o
holes is
U U = where Uq is the thermal equilibrium recombination rate of electrons and
holes. We also assume that the quasi-fermi levels for majority carriers
are nearly flat across the quasi-nertral regions and nearly flat across
the SCR. This implies that n = p = n^exp(qV/2kT) so that
U Uq (n/2To)[exp(qV/2kT) 1]. (A5)
Finally, we assume that Dn = = Dq throughout the SCR, so that
U U (n.D /2L 2)[exp(qV/2kT) 1]. (A6)
o in n
The SCR current is then Jcn q(U U )Wor, -
bLK O bLK
(qn.W^^D /2L 2)[exp(qV/2kT) -1], where Wc is the width of the SCR.
i oLK n n
Equation (2.3) may then be rewritten as
J JgC JQNBQ[exp(qV/kT) 1] JSCR()[exp(qV/2kT) -1], (A7)
where the SCR saturation current is
JSCRO <

116
base; (iv) an investigation of the validity of the shifting approxi
mation for polysilicon solar cells under high-injection conditions and
for polysilicon solar cells in which the average grain size is smaller
than the base diffusion length; and (v) the demonstration of the con
ductance method discussed in Sections 5.6 and 5.7.


PAGE
4.3.3 Illuminated I-V Curves (n -p diodes). . 58
4.3.4 Grain-Boundary Passivation by
Hydrogenation Treatment 62
4.3.5 I-V Characteristics (p+-n diodes) .... 65
4.3.6 Grain-Boundary Shunt Resistance
4.4 Comparison of Mesa Diode and Planar Diffusd
Diode I-V Curves 70
4.5 Discussion 71
5 SMALL-SIGNAL ADMITTANCE METHOD FOR DETERMINING THE
SURFACE-STATE DISTRIBUTION AT THE PREFERENTIALLY
DIFFUSED PART OF THE GRAIN BOUNDARY 77
5.1 Introduction 77
5.2 Small-Signal Equivalent Circuit Model of
a Diode with a Preferentially Diffused
Grain Boundary 78
5.3 An Admittance Method for Determining N .... 87
s s
5.4 Inversion along the GB in the p-Type Bulk .... 92
5.5 Experimental Procedure and Results 92
5.6 Conductance Method for Determining N ..... 101
5.7 Discussion ?S 103
6. DESCRIPTION OF SEVERAL METHODS INTENDED TO SUPPRESS
THE GRAIN-BOUNDARY DARK RECOMBINATION CURRENT .... 108
6.1 Introduction 108
6.2 Low-Temperature-Enhanced Preferential Diffusion
of Phosphorus 108
6.3 Low-Temperature-Enhanced Preferential Diffusion
of Boron 110
6.4 Grain-Boundary Passivation by Hydrogen Plasma
Treatment Ill
6.5 Preferential Etching of Grain Boundaries to
Enhance Performance 112
6.6 Discussion ..... 113
7 DISCUSSION 114
APPENDIX
IFORTRAN PROGRAMS FOR SIMULATING THE EFFECT OF AREAL
INHOMOGENEITY IN AN n+-p SILICON SOLAR CELL 117
IIFORTRAN PROGRAM FOR PROJECTING THE PERFORMANCE OF
A SOLAR CELL GIVEN THE EMPIRICAL PARAMETER VALUES
OF THE SUBCELLS 121
IIIDERIVATION OF A SIMPLIFIED EXPRESSION FOR THE SPACE-
CHARGE REGION RECOMBINATION CURRENT 124
iv


113
The improvement of solar cell performance by fabrication techniques
involving the preferential etching of the GB's is a topic of on-going
research [59].
6.6 Discussion
The n+-p solar cells of Runs 7P, 22P, and 25P were large-area
2
devices (~1 cm ) that had their edges etched in a solution of
3HF : 5HN0g : 3CHgC00H for 10 minutes. Consequently, leakage currents
did not dominate the measured dark recombination currents of these
devices. This edge-etching technique has been used successfully in
our laboratory for both single-crystal and polycrystalline Si solar
cells.
As previously mentioned, the intragrain base minority carrier
diffusion length in the p-type Wacker substrates has been determined
-f.
to be about 130 ym. The average grain diameter for the n -p solar
cells in Runs 7P, 22P, and 25P was about 1000 ym. The large ratio of
average grain diameter to base diffusion length tended to minimize the
effects that the special fabrication procedures may have had on the
GB component of the dark recombination current.


70
However, the use of a structure with an MOS guard ring and the careful
analysis described above shows that the GB's in diffused p-n junction
polycrystalline solar cells made on Wacker material do not cause notice
able leakage effects due to the GB shunt resistance. This conclusion
is also supported by measuring the I-V curve in the reverse direction
which shows negligible current between zero and about IV of reverse
bias.
4.4 Comparison of Mesa Diode and Planar Diffused Diode I-V Curves
Prior to the fabrication of the 30-mil n -p and p -n planar diffused
diodes described in this chapter, we fabricated (Appendix VI) 50-mil n+-p
GB
dark mesa diodes and attempted to isolate the GB-component of 1^ by
GB
the method of subtracting IQ from 1^ ., The I-V measurements on these
mesa diodes tended to be instable and unreliable because of the surface
and edge leakage currents described in Section 4.1. In particular,
the leakage currents caused the measured values for the current densi-
GB
ties Jp and in the low voltage range (0-300 mV) to be as much as
three orders of magnitude higher for the mesa diodes than for the planar
diffused diodes. The mesa diodes also tended to have higher measured
GB
values of m^. and m^ (often approximately 2.0) than did the planar
diffused diodes. Since, for the 50-mil mesa diodes, the measured current
in the low voltage range (0-300 mV) was predominately leakage current,
it was not possible to isolate and accurately analyze the GB-component
GB
of I for these diodes. As described in Section 4.1, the surface and
edge leakage currents are suppressed in the planar diffused diodes by
the use of an oxide on the top surface and an MOS guard-ring gate over
lapping the edge of the diffused layer.


CURRENT (Arbitrary Units)
18
Figure 3.2(b) Schematic representation of the current-voltage depen
dencies of a solar cell with all curves shown in the
same quadrant.


CHAPTER 7
DISCUSSION
The main contributions of this dissertation are:
(A) the development and analysis of a parallel-subcell equivalent-
circuit model to quantitatively indicate the limitations on
silicon p-n junction solar-cell performance that can be caused
by areal inhomogeneity (Chapter 2);
(B) the development of an experimental method for assessing the
validity of the shifting approximation for solar cells made
from polysilicon and other material (Chapter 3);
(C) the analysis and experimental identification of the current
components associated with the grain boundaries in polysilicon
diodes (Chapter 4);
(D) the development of new electrical methods for determining the
presence or absence of preferential diffusion along the grain
boundaries and for determining the average doping density of
preferentially diffused regions along the grain boundaries
(Chapter 4); and,
(E) the development of a small-signal admittance method for determining
the grain-boundary surface-state distribution in the energy gap
for that part of a grain boundary which has been preferentially
diffused with phosphorus (Chapter 5).
Approximations used in the interpretation of measurements in
Chapters 4 and 5 do not, in all instances, yield highly accurate
numerical values for the parameters involved. We emphasize again that
the intent of this dissertation is the development of experimental and
analytical methods for investigating the properties and performance
degrading mechanisms of polycrystalline silicon p-n junction solar
cells. The detailed statistical evaluation of a large number of
empirical data was not investigated in this work. The methods we have
114


86
T = 1/co = C /G .
ss ss ns
(5.5)
Both (5.3) and (5.4) are dependent on C ; therefore, we can use
s s
either G. or C. to obtain information about the surface states,
m m
Experimentally, it is found that the surface states at an Si-SiO^
interface [48], and also the surface states at silicon GBs [22], are
continuously distributed in the energy gap rather than existing at a
single energy level. These continuously distributed surface states
can be represented in the circuit model of Fig. 5.3(c) as a parallel
array of G C circuit elements, each element representing surface
IIS s s
states at a certain energy level. The capacitance of a G C cir-
ns ss
cuit element is proportional to N at the given energy level, and G
ss ns
reflects the time constant of the surface states at the given energy
level. The problem of calculating the surface-state capacitance C
s s
for an MOS capacitor with a continuous distribution of surface states
has been considered by Sah [49]. In [49] it is shown that, for the
case of an MOS capacitor with a small-signal current flow, the net C
ss
for distributed states can be obtained by summing the contribution to
C from all the energy levels between and E referenced to a single
SS V C
Fermi level. The net C is determined by those states within about
ss
kT of the Fermi level at the Si surface. Since the equivalent circuit
of a preferentially diffused GB at zero-bias is similar to that of an
MOS capacitor in the depletion regime, the results of [49] may be ex
tended to include the preferentially diffused GBs of our devices.
Consequently, the circuit model of Fig. 5.3(c) is applicable to the
realistic case of a preferentially diffused GB with a continuous dis
tribution of surface states.


101
temperatures, f approaches f which makes determination of C (and
ss o ss
thus N ) difficult; and also, because the low frequency measurements
s s
on the admittance bridges that we used (HP LCR meters) tended to be
very noisy at the higher temperatures.
For Runs 39P and 40P, (N ). was calculated from (5.17) to be
ss xnv
about 2 x 10^2 cm ^eV
5.6 Conductance Method for Determining N
ss
An alternative to the above capacitance method for determining
the distribution of N in the energy gap is a conductance method
SS
[48,50], In the conductance method, the parallel branch of the lumped
equivalent circuit shown in Fig. 5.3(c) is converted into a capacitance
Cp in parallel with a conductance as shown in Fig. 5.8. In Fig.
5.8, we have assumed the simple case of a single level of surface
states at the GB. The values of C and G are given by
P P
C = Cn + C /(I + o)2x2),
p D ss
G = C w2t/ (1 + 0)2T2) .
p ss
(5.18)
(5.19)
By measuring the zero-bias small-signal admittance of the diode
= G^ + jcoC^ as a function of frequency, the dependence G^/co vs.
a) can be plotted. The plot of G^/co vs. co goes through a maximum at
a) = 1/t. The value of G /u at the maximum is G /2. Thus, from the
p ss
plot of Gp/w vs. co, we can directly determine the values of both T
and C Then, by using (5.10) and (5.11), we can determine the dis-
s s
tribution of N in the energy gap.
s s
For a continuous distribution of surface states in the energy gap,
the conductance expression (5.19) must be modified [48,50]. This


51
GB
The recombination in the SCR adjacent to the n-diffusion spike I was
bCR
analyzed by Sah-Noyce-Shockley [8] and is, in fact, just an extension of
the I._ of the GBF diode. The area of the n-spike is A = 2iL,TJd where
SCR r n GB n
is the total length of the GB's in a diode and d is the GB
preferential diffusion depth. For the GB diodes No. 2-5 in Table 4.1,
2 -3 2
An A, where A = ird /4 4.6 x 10 cm is the top area of a 30-mil
GB
diode, and thus I0 can be neglected. This component could be impor-
bGR
tant in solar or metallurgical grade material where the impurities can
be segregated at the GB's resulting in a very short lifetime in the SCR
GB
adjacent to the n-spike and a large Ig ,. The recombination current at
the GB within the SCR can be expressed as [20,23]
tGB ^ .GB / GB. v
XSCR ASCR (lniSGBeXp^qV/,II1X kT^
(4.6)
where S is the GB surface recombination velocity at that part of the
UD
GB
.GB
21 is the approxi-
GB adjacent to the bulk, m^. 2.0, and AgCR GB"SCR
mate area over which the GB recombination current is described by
(4.6) [23]. is the SCR width of the GB barrier [18,19]. This cur
rent component is proportional to n.. Such a current will have an acti-
GB
vation energy of one-half of the bandgap (E /2). l!f was measured for
(jr D
the GB devices in the temperature range from 222K to 286K. The slope
factor m^ was almost constant in this temperature range. Figure 4.7
GB
shows the IR versus 1/T plot yielding activation energy
GB
E 0.59 eV Ep/2. This result very strongly suggests that I is
a. bGR
the dominant GB recombination component at small biases below about
PT
300 mV. The theoretical analysis [23] of Icor>, based on idealizations,
bLK
GB PR
predicts m^. =2.0. Our data give m^. m^. = 1.76 1.84 at 25C with
GB
most of the devices having 1.8. By using (4.6) and an estimate of


36
4.2 Fabrication of Devices and Evaluation of Preferential Grain-Boundary
Diffusion
+ + +
Both n -p and p -n diodes were studied. The n -p diodes were
fabricated on 5 fi-cm p-type Wacker polycrystalline silicon substrates.
The phosphorus emitter was predeposited at 900C for 30 minutes followed
by a drive-in diffusion at 1050C for 40 minutes. Wet oxide about
O
3000 A thick was grown on the top surface during the drive-in step. The
junction depth x^ was 1.8 ym and the sheet resistance was 8 ii/square.
The p+-n diodes used 0.3 i2-cm n-type Wacker substrates. The boron was
predeposited at 900C for 25 minutes. The drive-in was done at 1000C
for 120 minutes resulting in a junction depth of 0.8 ym and sheet
resistance of 800 i)/square. The top surface was passivated by an SO2
layer, about 3000 thick, grown during the drive-in step.
In Fig. 4.2(a), a grooved and stained section [27,28] of an n+-p
diode shows a preferential diffusion of phosphorus down the GB's [24-26],
A copper staining solution was used. The preferential diffusion spike is
about 6 ym deep and is uniformly about 2.3 ym wide. (We refer to a
longitudinal cross-section, of a preferentially diffused grain-boundary
region as a diffusion spike.) It was determined by an investigation of
the cross-sections of the 15 mil thick substrate wafers that the GB's go
all the way through the material at an angle between 20 and 45 to the
normal [29]. This angle is referred to as a in Fig. 4.2(b). The GB
also cuts the groove at another angle which is referred to as 3 in
Fig. 4.2(b). Both of these angles were considered in calculating the
depth of the n-spike. No phosphorus preferential diffusion spikes were
observed after the 30 minute 900C predeposition step; however, we
measured 5-10 ym spikes after 48 hours heating at 600C after the
predeposition. For the p+-n diodes, no preferential diffusion spikes of


Table 4.4 Parameter
values
for diodes in Run
37P.
T = 25
.0C, A
= 4.6 x 10 3
2
cm .
Diode
Description
GB
Ixo1
GB
XO
GB
V x
]
.GB
SCRO
GB
mSCR
IQN0
GB
QNO
SGB
(mils)
(A)
(A)
(A)
(cm/ sec)
37P#11-D2
GBF
4.0
,n-12
x 10
1.19
1.3 x
io"13
37P#12-Dl
GBF
7.5
m12
x 10
1.30
8.1 x
io-14
37P#2-D2
several GB's
140
1.3
in10
x 10
1.63
1.3
X
lo"10
1.67
4.1 x
io-13
2.0 x
io3
37P#1-Dl
several GB's
75
2.4
ln-ll
x 10
1.69
2.5
X
lo"10
1.75
4.3 x
io13
7.2 x
io3
37P#5-D2
several GB's
35
5.4
in"10
x 10
1.94
5.8
X
lo"10
2.02
2.9 x
io-13
3.6 x
io4
37P#9-D2
several GB's
90
8.0
in-n
x 10
1.59
8.5
X
io-11
1.71
2.3 x
10-13
2.0 x
10 3
37P//10-D1
one GB
20
1.7
in"10
x 10
1.61
1.8
X
10-10
1.67
4.0 x
io-13
1.9 x
io4
37P//2-L1
one GB
80
6.7
x 10-11
1.57
6.9
X
io"11
1.69
4.8 x
io-13
1.8 x
io3
37P#6-L1
several GB's
68
1.8
x 10-9
2.03
1.9
X
10-9
2.08
3.1 x
10-13
6.0 x
10 4
37P#8-L1
several GB's
150
3.5
x 10-9
2.01
3.6
X
10-9
2.05
3.8 x
io-13
5.2 x
io4
37P#11-L1
several GB's
50
3.6
in"10
x 10
1.93
3.9
X
io-10
2.03
4.8 x
io-13
1.7 x
io4
Averages :
for GB diodes:
79
7.4
in"10
x 10
1.78
8.0
X
io-10
1.85
3.8 x
io-13
2.2 x
io4


Terminal Capacitance C.
io2 io3 io4 io5 io6 io7
Frequency (Hz)
Figure 5.6 Measured terminal capacitance as a function of frequency for the n+-p mesa diode 39P#2.
The capacitance of a GBF diode in Run 39P, normalized to the top area of the GB diode, is
shown for the temperature 145 K.


Voc/Voc
Figure 2.3 Normalized open-circuit voltage vs. areal quality factor.


46
boundary with the n-diffusion spike. We assume that the GB is perpen
dicular to the top surface. The presence of the GB and the diffusion
spike will result in dark current components in addition to those present
in the GBF device. All these additional components, shown in Fig. 4.5,
are designated by a superscript "GB''. The total dark current is equal to
the sum of all current components:
TGB _ T tGB tGB 4- 4- 4- T 4- V /t>^ (L 1 'S
ID XQNB + XQNE + ISCR + ISCR + ISCR' + *B + XQNB + XQNE + V/RSh* (4,1)
The dark current of the GBF diode is given by
ID IQNB + IQNE + ISCR + V/,RSh*
(4.2)
The current components in (4.1) and (4.2) are defined as follows: IqNB
and are the recombination currents within the quasi-neutral base
QNE ^
and emitter, respectively, and orginate from the lateral n+-p junction.
GB
I and E are the recombination components due to the carrier
SCR SCR
recombination in the bulk space-charge region (SCR) adjacent to the
lateral n -p junction, and adjacent to the n-diffusion spike, respec-
GB
tively. E is the recombination current at the GB within the
SCR
GB
SCR [23]; 1^ is the recombination current at the grain boundary adjacent
GB
to the quasi-neutral base (QNB) region; is the current component
injected from the diffusion spike and recombining within the QNB region;
is the current injected from the substrate into the emitter diffu-
QNE J
sion spike and recombining within the spike and at the GB surface; and
GB
R, and R, are the shunt resistances of the GBF and GB diodes, respec-
Sh Sh
tively. The components I^g, '*'QNE an<^ ''"SCR an(^ (^.2) are
nearly equal in a special case. Their equality requires that the
fundamental kinetic parameters (recombination-center density, capture


43
indicates that no inversion layer was created at the intersection of
the GB's with the silicon surface or along the GB's in the p-type bulk;
such an inversion layer could also lead to results shown in Fig. 4.4.
The stained width of the diffusion spike, Fig. 4.2(a) is about
2.3 pm. Based on a series of experiments (see Appendix IV) on both
f* f
n -p and p -n junctions, we concluded that the stained region using the
copper stain solution includes the p-n junction space-charge-region
(SCR) from both sides of the diffusion spike. Inside the spike, a GB
potential barrier is created due to the GB surface states [18,19]. The
reverse bias, V required to deplete the channel of width W (Fig. 4.5)
will have to push the edge of the p-n junction SCR to the edge of the
grain-boundary SCR. By using a linearly-graded junction approximation
for the p-n junction, we estimated that the average channel doping den-
16 3
sity is approximately 1 x 10 cm and Wn 0.5 pm. We assume
as a first approximation, that the width of the grain-boundary SCR is
independent of the reverse bias V .
R
The conductance test described above using the simple structure
created by black wax masking, which results in large spacing between
the GB diodes (~ 10 mil), will yield rather small channel current. It
was difficult to separate this channel current from the reverse leakage
current of the mesa diodes for the device with N ~ 10 cm The
conductance method is demonstrated here for another, more heavily doped,
structure diffused at 1050C for one hour which resulted in a preferen
tially diffused region 11 pm deep; the stained width of the n-spike was
about 3.6 pm and W 1 pm. The insert of Fig. 4.4 shows the measured
channel current of this JFET-like structure versus the applied voltage.
The existence of a large conductance confirms the occurrence of a


Table 5.1 Parameter values for representative mesa diodes of Runs 39P and 40P. The values of C
Lr
and C are the low and high frequency measured values corrected for the GBF capacitance.
HF
The area of the preferentially diffused section of the GB's is A = £d .
GB n
Diode
T
A
CLF
CHF
cw
C
ss
E (O)-E.(O)
r 1
N
ss
(K)
( 2\
(cm )
(pF)
(pF)
(pF)
(pF)
(eV)
(eV)
/ 2 -1N
(cm eV )
39P//2
93
3.1 x 10"3
66
58
94
66
1.3 x 1011
39 P# 2
145
It
72
63
97
96
11
2.0 x 10
39P//2
198
II
79
68
102
134
2.7 x 1011
40P#3
93
9.2 x 10-4
23
18
28
78
-0.289
-0.25
5.3 x 1011
40P#3
145
II
25
19
29
122
-0.268
-0.23
8.3 x 1011
40P//3
198
It
28
21
31
213
-0.243
-0.20
12
1.4 x 10


87
5.3 An Admittance Method for Determining N
ss
We now describe a small-signal admittance method in which we
use C. to obtain information about the surface states at that part
in
of a GB which has been preferentially diffused with phosphorus.
Figure 5.3(c) shows that the zero-bias small-signal capacitance
associated with the preferentially diffused region of the GBs in a
GB diode, C, is equal to the measured terminal capacitance of the
GB diode minus the measured terminal capacitance of the corresponding
GBF diode:
C in ~ CGBF
(5.6)
The capacitance Gnr¡T, is frequency-independent until f ~ 1 GHz. For
OJjr
sufficiently low frequency, f f = G /27rC the G can be
ss ns ss ns
short-circuited, and the equivalent circuit will reduce to that shown
in Fig. 5.3(d). From (5.4) and (5.6), the low-frequency limit for C
is then
CLF-CW(CSa + S)/(Css + S + For sufficiently high frequencies, f f the surface states can-
ss
not follow the signal and the C can be short-circuited. With the
ss
provision that the frequency f is less than the characteristic fre
quency fQ, the equivalent circuit model shown in Fig. 5.3(c) then
reduces to that shown in Fig. 5.3(e); and (5.4) and (5.6) yield the
high-frequency limit for C:
cHr W(CH + V-
(5.8)
From (5.7) and (5.8), we obtain an expression for C in terms of CT_
SS Lr
and CHF [50]:
Css CW[<-CLF/CW^/(1 ~ LF^V ^HF^W^1 ^F^V-*'
(5.9)


80
equilibrium small-signal transmission-line equivalent circuit model
of the preferentially diffused n-region shown in Fig. 4.5 will be
similar to the circuit model of the surface channel of an MOS tran
sistor [46']. This simplified model is shown in Fig. 5.2. By consider
ing the two-dimensional current flowing through the preferentially
diffused n-region, this model can be derived from the general small-
signal transmission-line equivalent circuit model developed by Sah [47]
for any two-terminal one-dimensional semiconductor device.
The circuit parameters in Fig. 5.2 are defined as follows:
is the per-unit-length resistance of the quasi-neutral n-region
in fi/cm;
is the capacitance of the p-n junction space-charge region
2
along the n-spike in F/cm ;
is the capacitance of the GB space-charge region in the n-spike
in F/cm^;
G is the electron capture conductance of the GB surface states
ns
in mhos/cm^;
2
C is the storage capacitance of the GB surface states in F/cm ;
s s
C is the capacitance of the lateral p-n junction space-charge
(jr
2
region in F/cm ; and,
Z is the length (into the plane of the paper) of the preferen
tially diffused n-region.
In Fig. 5.2., we have neglected the electron and hole storage
capacitances in the quasi-neutral regions, and we have assumed the
simple case of a single level of surface states at the GB. The
capacitive coupling between the n-spike and the substrate at the bot
tom of the spike is neglected on the grounds that the volume of the


81
Figure 5.2 Simplified equilibrium small-signal transmission-line
+
equivalent circuit model of a polysilicon n -p diode with
a preferentially diffused GB.


31
diameters except device No. 6 (see Fig. 3.10) for which L d L was
determined by applying the method of [7] to the dark I-V dependence of a
small grain-boundary-free device and was found to be about 130 lim. For
the small grain-boundary-free device, I = 62 yA and V^ = 497 mV;
whereas, for device No. 6, IQ = 60 yA and V = 467 mV. The 30 mV
decrease in VQC resulting from the presence of the grain boundaries
corresponds to approximately a threefold increase in the dark recombi
nation current. These data show the degrading effect that the grain
boundaries have on the performance of device No. 6. We note, however,
that the shifting approximation remains valid for device No. 6 in spite
of the very strong influence of the grain boundaries on V. .
ULi
Though no general conclusions can be drawn from these experimental
results, they suggest that the nonlinearities introduced by illumination
levels of one sun are insufficient to invalidate the shifting approxima
tion in polysilicon solar cells. If this is true, then the simplifica
tions afforded to solar cell theory by the shifting approximation remain
intact for polysilicon. We emphasize that the experimental method
described here provides a general technique for assessing the validity
of the shifting approximation for solar cells made from polysilicon and
other material, including single crystal, polycrystalline, and highly
disordered semiconductors.


APPENDIX IX
FABRICATION SCHEDULES FOR RUNS 39P AND 40P
All runs were fabricated on 5 i2-cm p-type Wacker polysilicon sub
strates.
Run 39P
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Phosphorus predeposition. 30 minutes at 1050C in an atmosphere of
90 cc/min ^ bubbling through POCl^ at 30C, 170 cc/min dry O2
1500 cc/min N9 carrier gas; p = 3 fi/o.
z s
3. Etch phosphosilicate glass in 10% HF solution for 10 seconds.
4. Rinse in deionized water.
5. Drive-in: 30 minutes at 1050C in 1500 cc/min ^5 pg = 2 Q/o.
6. Remove n+-layer from backside by lapping with SiC slurry.
7. Standard wafer cleaning.
8. Metallization with Al.
9. Anneal: 10 minutes at 400C in 400 cc/min
10. Dice into 90 mil x 90 mil squares.
11. Wax dot masking to define a mesa diode on each square.
12. Etch in Al and Si etches to form mesa diodes. This step removes
the top (lateral) p-n junction around the mesa diode without
significantly etching the preferentially diffused grain boundaries.
The Si etching requires 70 seconds in 1 HF : 6 HNO^ : 1 CH^COOH
solution.
135


84
Figure 5.3(b) The equivalent circuit model obtained by shorting the
circuit elements in Fig. 5.3(a).


IV
PAGE
GROOVE AND STAIN EXPERIMENT TO DETERMINE THE
EXTENT OF STAINING 126
VSTANDARD WAFER CLEANING AND POLISHING PROCEDURES . 128
VIFABRICATION SCHEDULES FOR RUNS 4P4, 6P1, 7P, 8P1,
13P3 and 13P4 129
VIIFABRICATION SCHEDULE FOR RUNS 22P and 25P 132
VIIIFABRICATION SCHEDULES FOR RUNS 34P, 36P, AND 37P . 133
IXFABRICATION SCHEDULES FOR RUNS 39P AND 4OP 135
XCOMMENTARY ON THE RELIABILITY OF GROOVE AND STAIN
RESULTS IN CHAPTERS 4 AND 5. . 137
REFERENCES 139
BIOGRAPHICAL SKETCH 144
v


100
follow the signal at frequencies of f > f is clearly visible. It
s s
is also seen that the value of f (the first break-point) moves to the
s s
right with increasing temperature. This is in agreement with theor
etical prediction [48].
The characteristic frequency f can be used in estimating the
electron mobility and the doping density in the preferentially diffused
region of the GB's [46]. In Fig. 5.6, the frequency dependence of the
input capacitance of a GBF diode, normalized to the top area of the GB
diode, has been plotted. It is seen that at a given temperature, 145K
for example, the capacitance of the GBF diode is essentially frequency-
independent (as expected), and the capacitance of the GB diode asymp
totically approaches the capacitance of the GBF diode for frequencies
£
beyond the second break-point (- 10 Hz). This strongly suggests that
the second break-point in the C vs. f curve indicates the character
istic frequency f for the GB diode. This idea is strengthened by the
observation that, for frequencies beyond the second break-point, the
1/2
vs. f curve drops with a slope of about w in agreement with the
theoretical work of [46].
The purpose of Figs. 5.6 and 5.7 and Table 5.1 is to demonstrate
that the above method can be used to profile the GB surface-state dis
tribution in the energy gap for E (0) > E (0). We note in Table 5.1
r
that the values of E (0) corresponding to the temperatures at which
F
C. was measured are about midway between E. and E By making meas-
in x C
urements at higher temperatures (up to about 400K) we could, in
principle, scan the energy gap down to E E^(0). In Figs. 5.6 and
5.7, it is seen that we have not included measurements of C. vs. f
at these higher temperatures. This is mainly because, at higher


CHAPTER 4
EFFECTS OF GRAIN BOUNDARIES ON THE CURRENT-VOLTAGE
CHARACTERISTICS OF POLYSILICON SOLAR CELLS
4.1 Introduction
The performance of polycrystalline solar cells is limited by the
effects of the grain boundaries (GB's) on the current-voltage (I-V)
characteristics. The I-V characteristics determine the efficiency of a
solar cell. Several theoretical models of the GB's and their influence
on the recombination currents have been published [18-23]. The purpose
here is to experimentally investigate the effects of the GB's on the
dark and illuminated I-V characteristics of polysilicon p-n junction
solar cells. The analysis of the experimental I-V characteristics, with
the help of the theoretical models [18-23], will lead to a determination
of the parameters which govern the recombination at the GB's. It will
also lead to a determination of the dominant GB current components.
Most experimental studies on polycrystalline solar cells have been
2
done on large area (~ 1 cm ) devices which, in general, contain hundreds
of GB's. Due to nonuniform distribution of the GB's and nonuniform grain
geometries, it is difficult to obtain reproducible results on such cells;
thus, an evaluation of the effects of the GB's and different fabrication
procedures on the performance of the cells is difficult. Moreover, poly
crystalline solar cells usually exhibit large leakage currents which can
mask the contribution of the GB's.
33


27
Figure 3.6 I-V curves for device No. 2.


115
developed can be used by other researchers who need detailed statistical
evaluations of large quantities of empirical data.
Although Chapters 4 and 5 deal with polysilicon solar cells and
mesa diodes, the work of these chapters used concepts from JFET and
MOSFET theory to develop methods for determining N^, Ngg (E), c^ (E^),
e (E} etc., for phosphorus diffused polysilicon diodes. In light
n 1
of the growing importance of polysilicon in the integrated-circuit
technology, the methodology developed in Chapters 4 and 5 may find
application to the device physics of integrated circuits.
Most of the devices measured (and, in particular, all of the
devices in Chapters 4 and 5), were fabricated from Wacker Silso poly-
silicon material. For both p and n-type Wacker material, the average
grain diameter was significantly larger than the base minority carrier
diffusion length and only one substrate doping concentration was avail
able. Wacker material is cast polysilicon supplied as 15 mil thick
wafers. Polysilicon solar cells of the future may be made from small-
grain thin-film material.
Several topics associated with the concepts presented in this
dissertation which might be the subject of future research include the
following: (i) a detailed statistical study correlating grain-boundary
crystallographic orientation with the extent of GB preferential diffusion,
with the GB fundamental kinetic parameters, and with the various carrier
recombination velocities; (ii) a study of the effects of deep preferen
tial diffusions in small-grain thin-film polysilicon material on short-
circuit current and open-circuit voltage; (iii) the development of a
methodology for determining the GB surface-state distribution in the
energy gap for that part of the GB which is adjacent to the quasi-neutral


CURRENT DENSITY (A/cm )
73
Figure 4.11 Measured dark J-V characteristics of GB mesa and planar
diffused diodes showing the effect of leakage current
on the low-voltage current density and on the reciprocal
GB
slope m^ of the mesa diode. Diode 4P2-4,8,f is a mesa
diode with 300 mils of GBs; diode 36P//1-D2 is a planar
diffused diode with an MOS guard ring and has 65 mils of
GBs. The leakage current of the mesa diode causes the
GB
measured value of I and consequently, the calculated
xo
value for S to be erroneously high.
GB


130
Run 7P
Steps:
1. Same as step 1 in Run 4P4.
2. Same as step 2 in Run 4P4.
3. Drive-in: 100 minutes at 900C in 100 cc/min dry 0
4. Same as step 4 in Run 4P4.
5. Same as step 5 in Run 4P4.
6. The wafers sent to Sandia were exposed to H+-plasma at 350C and
2 Torr for 18 hours.
7. Remove n+-layer on backside by lapping with SiC slurry.
8. Standard wafer cleaning.
9. Metallization. Front: Ti, Ag. Back: Ti, Ag.
10. Photolithography and etching to form solar cell grid.
11. Etch wafer edges in a solution of 3 HF : 5 HNO^ : 3 CH^COOH for
10 minutes.
Run 8P1
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Boron predeposition (BN-1150 solid source): 60 minutes at 1050C
in 200 cc/min ^.
Drive-in: 48 hours at 600C in 1500 cc/min N2.
3. Remove boron doped top Si layer with 3 HF : 5 HNO^ : 3 CH^COOH
solution.
4. Phosphorus predeposition. 20 minutes at 900C in an atmosphere
of: 90 cc/min N2 bubbled through POCl^ at 30C, 170 cc/min dry
0^ 1500 cc/min ^ carrier gas.
5-10. Same as steps 6-11 in Run 4P4.


Table 4.3
Parameter values for additional
^RO XX0- T = 25*C A 4
diodes in Run
-3 2
.6 x 10 cm .
36P
Diode
Description
£gb
(mils)
I IGB
xo xo
(A)
GB
V x
I IGB
QNO QNO
(A)
SGB
(cm/sec)
36P#10-D1
GBF
-13
8.2 x 10
1.17
6.1 x
lo"14
36P#4-D1
twins only
100
4.7 x 10-12
1.32
1.4 x
io-13
8.4 x 10'
36P#14-D2
one GB
45
1.9 x 10_1
1.64
4.1 x
10"13
1.0 x 10
36P//9-D1
several GB's
45
2.4 x 10-1
1.71
1.9 x
io-13
9.2 x 10
36P#1-D2
several GB's
65
2.6 x 10-1
1.70
2.4 x
10-13
8.8 x 10
36P#34-Dl
several GB's
65
7.4 x 10_1
1.80
1.9 x
io-13
2.4 x 10
36P#8-L1
one GB
30
3.8 x 10-1
1.73
1.4 x
io-13
2.6 x 10
36P#9-L2
several GB's
65
9.2 x 10_1
1.81
2.2 x
io-13
3.0 x 10
Averages for
the GB diodes
GB diodes including
in Table 4.1:
64
c o ,n-10
5.2 x 10
1.76
2.5 x
10-13
2.0 x 10


12
I AQF {USC)G (JQNBO^eXp^qV/,kT^ ^ ^JSCRO^G^eXp^qV//2kT^
+ (1 AQF) {(Jsc)p (JQNB0)p[exp(qV/kT) 1]
- (JSCR0)p[exp(qV/2kT) 1]}. (2.6)
To demonstrate this type of areal inhomogeneity, we let
3
=10 cm and, for the good portion of the cell, let
2
(L ). s 100 pm and (J__)= 25 mA/cm We assume that at any point on
no be u
the cell area Jc logCL ), where the constant of proportionality is that
bu XI
found in both experimental [9,10] and numerical [11] studies for
1 pm ^ L ^ 100 pm. We define the diffusion length ratio to be
n
DLR = (Ln)p/(Ln)g. From (2.6), we plot V^, FF, and q as a function of
AQF with DLR as a parameter in Figs. 2.3, 2.4, and 2.5, respectively.
Again, we notice that it is the poor-quality area of the solar cell that
_2
dominates the overall cell performance. The case for DLR = 10 corre
sponds to empirical observations by Schwuttke [12] that the generation
lifetime of silicon ribbon material (and thus the related defect density)
varies in a random fashion across the area of the ribbon by between four
and five orders of magnitude.
2.4 Discussion
The above treatment assumes several idealities: resistance and
fringing effects are neglected; the good and poor-material is concen
trated into two single-connected regions; the current flow in each region
is assumed to be one-dimensional. We now consider the effect of series
resistance on the illuminated solar cell.
In a solar cell with an adequate grid geometry, the dominant
component of series resistance will be that contributed by the bulk
material. This bulk component resists the current of majority carriers


105
In Table 5.1, the calculated values for q and E (0) E.(0)
GB F i.
have not been Included for Run 39P because these values were highly un
reliable. This is because the value of q much greater than the values obtained from (5.15). We attribute this
large difference in the calculated values for to inaccuracies in
the model of [18]. The uncertainty in the energy gap position of the
surface states does not affect the determination of N
ss
The values of N in Table 5.1 suggest that N does not vary
SS ss
rapidly with position in the energy gap.
In Table 5.2, is calculated (5.8) from the high-frequency
capacitance measurement. The doping density at the preferentially
diffused part of the GB, NDD(0)> is calculated using (5.20). Values
of for Run 39P are not listed because of the unreliability of
the calculated values of q4> for that run. Table 5.2 also shows the
values of the average doping density in the preferentially diffused
n-region, N^, as determined in Section 4.2. In general, N^(0) will
not be exactly the same as because the diffusion process creates
a doping profile in the preferentially diffused n-region.
The conductance method has two main advantages over the capaci
tance method. Firstly, unlike the capacitance method, the conductance
method does not depend on C^. Secondly, the relative change of G^/to
vs. w in the conductance method is much greater than the relative change
of C. vs. to in the capacitance method [48], These two advantages
xn
enable the conductance method to yield a more accurate value for C
ss
than the capacitance method.
In our measurements of the devices in Runs 39P and 40P, we did not
observe a peak in the plot of G /to vs. to; and, consequently, we were


APPENDIX I
FORTRAN PROGRAMS FOR SIMULATING THE EFFECT OF AREAL
INHOMOGENEITY IN AN n+-p SILICON SOLAR CELL
Type 1 Areal Inhomogeneity
C VOC, FF, AND EFF ARE CALCULATED AS FUNCTIONS OF QF WITH JR AS A
C PARAMETER.
C QF = AGOOD/ATOTAL IS THE AREAL QUALITY FACTOR.
C JR = J01P/J01G IS THE DARK SATURATION CURRENT DENSITY RATIO.
C J01G = 4.42E-13 A/CM2 IS THE DARK SATURATION CURRENT DENSITY OF THE
C GOOD PORTION OF THE SOLAR CELL.
C JSC = 0.025 A/CM2 IS THE SHORT CIRCUIT CURRENT DENSITY.
C THE BASE DOPING DENSITY IS 1.0E17/CC. NI = 1.33E10/CC. THE ELEC-
C TRON DIFFUSIVITY IN THE BASE IS 15.6 CM2/SEC. THE ELECTRON
C DIFFUSION LENGTH IN THE BASE IS 100 UM. T = 300 DEGREES KELVIN.
C
C
C
REAL KTQ, KT, JSC, J01G, J01B, ISC, IMP, JR
COMMON M, N, VOC, KTQ, ISC
KT 4.14E-21
Q = 1.602E-19
KTQ = 0.02584
JSC = 0.025
ISC = 0.025
J01G = 4.42E-13
DO 10 N = 1,20
QF = N*0.05
WRITE(6,2)
2 FORMAT(1H1)
WRITE(6,3) QF
3 FORMAT(5X,'FOR QUALITY FACTOR:',F5.2)
DO 20 M = 1,9
J01B = (10**(M-1))*J01G
JR = J01B/J01G
VOC = KTQ*ALOG(JSC/((QF*J01G)+((1-QF)*J01B)))
K = 1
5 IMP = 0.0100 + K*0.0001
CALL FCTVAL(IMP,FILF)
FX = FILF
K = K+l
IMP = 0.0100 + K*0.0001
CALL FCTVAL(IMP,FILF)
GX = FILF
DIF = GX-FX
117


57
GB GB
Note, however, that ^g^gg expC^V/kT) is a one-dimensional
current linearly dependent on the total length of the GB's in the diode,
GB GB
since A = 2JL,T)d Therefore, if I- dominates the Inxrn of the n -p
n GB n QNEO QNO
GB
devices in Fig. 4.6 and Table 4.1, then IqNQ should be a linear function
GB
of The measured IzL^ is, however, much less than linearly depen-
GB QNO
dent on compare, for example, diodes No. 3 and No. 4 in Table 4.1.
GB
GB GB
This implies that the 1^ is dominated by Ig^g and We can thus
-GB
rGB
make a reasonable estimate that ~ 0.1 I_.T_.
QNEO QNO
B *
Then for device
PR A
No. 5, (4.9) implies that Sp(eff) ~ 4 x 10 cm/sec, and (4.10) implies
that sJL 400 cm/sec. This suggests that the recombination velocity of
the GB was lowered by the diffusion of phosphorus into the GB. Similar
conclusions are also valid for other devices investigated.
GB
We now use the above calculated value for S in (4.8) and
p(eff)
obtain T. ~ 0.1 ]isec. Thus, our assumption that T T is reasonable
t t p
16 3
for a relatively low doped n-spike, such as NQD ~ 10X cm found in our
devices.
4.3.2.3.
I
GB
B
Ig is the electron current recombining at the GB adjacent to the
QN base. This component will not be linearly proportional to due to
GB
the two-dimensional nature of the electron current flow injected from
GB
the top junction. The importance of Ig will depend on the grain size
dp, the electron diffusion length L and the surface recombination
ij n
velocity Sgg. Its influence on the total quasi-neutral current, Iqjj>
as defined in (4.3) and (4.7) can best be demonstrated by the dependence
f Tn(eff) on these parameters. For our devices with large
4
S ~ 10 cm/sec, we can write [23,37]:
GB


104
Aside from the error introduced by the calculated value for C ,
w
the accuracy in the determination of N and q ,, will depend on the
ss GB
accuracy of the physical models that are used. In particular, it is
to be noted that the model of [ 183 used to calculate q (5.15) is
highly simplistic. The simplicity of this model, coupled with the
great sensitivity of ql,, to the calculated value of CTT, tends to make
GB W
the calculated value of q<[> less reliable than the calculated value
GB
for N
ss
The depletion approximation expression for CD affords an alternate
expression for q GB
q*GB q2KEo %(0)/[2(CD/An)2] (5.20)
where N^CO) and C^/A^ are the doping density and depletion capacitance
per unit area, respectively, at the preferentially diffused part of the
GB. The area A is given by A = 2 d and the capacitance C_ can
n n n GB D
be calculated from C and C (5.8). Consequently, if an independent
rir W
measurement of N^(0) is available, (5.20) provides an alternate method
for determining q(t This alternate method is sensitive to the error
in C^, but has the advantage of being independent of the highly re
strictive model of [18].
If the electron capture cross-section cr at the GB is known, the
surface-state position E^(0) E^(0) can be directly determined from
the measured C vs. f dependence by the relation [48]
ss = an Vth ni exp{CEF() Ei(0)]/kT} (5.21)
where v ^ is the thermal velocity for electrons. The accuracy of this
method for determining E (0) E,(0) is limited by the accuracy of the
F i
value for o .
n


91
charge-neutrality in the n-region of the GB, and the band diagram in
Fig. 5.1(b), yield the following system of equations:
q*GB A* 2 [EF(0) *o]2/8|CEoNDD (5-13)
VO) Eg(0) q*n q*GB (5.14)
where 4>Q = Ey(0)/q + E^(0)/3q, and E^(0) is arbitrarily taken to be
zero. This system of equations can be solved for qcft to yield:
GB
qGB = [(2ot0 + 1) + (4a0 + l)1/2]/2a, (5.15)
where a = q2N 2 /8ke N and 0 = 2E (0)/3 [kT ln(N /N )].
SS o DD g C DD
In establishing (5.15), it is assumed that N is uniformly dis-
SS
tributed in the energy gap. This generally invalid assumption can
lead to an error in the calculation of qcf> With the assumption of
a one-sided depletion region at the GB, a more accurate expression
for the band bending at the GB is given by
The determination of q GB
bution of N between qd> and E(0) and is only obtainable by means
of iterative calculations. To avoid the laborious nature of the cal
culations associated with (5.16) while at the same time improving
upon the accuracy that would be afforded by (5.15) if one value of
N were used in (5.15), we have chosen to calculate q^ by using an
SS GB
average value for N in (5.15).
ss
With the calculation of qcj> and q n GB F
for various temperatures from (5.11). Thus, by measuring the small-
signal admittance at various temperatures, we can use (5.10) and
(5.11) to determine N vs. [E (0) E.(0)].
ss F i


CAPACITANCE (PF)
42
Figure 4.4 Capacitance versus reverse bias measured on the test struc
tures of Fig. 4.3. The insert shows the measured conduc
tance of the JFET-like channel between the two bottom GB
diodes of Fig. 4.3 as a function of voltage between the
diodes.


28
VOLTAGE (mV)
Figure 3.7 I-V curves for device No. 3.


CURRENT (Arbitrary Units)
17
Figure 3.2(a) Schematic representation of the current-voltage depen
dencies of a solar cell.


Wacker substrates are analyzed and experimentally identified. The
analysis shows that the dominant current component at small bias
levels (0-300 mV) is the recombination current at the grain boundary
within the p-n junction space-charge region. At higher bias levels
(V c V ^ z 500-600 mV), both this current component and the current
component due to recombination at that part of the grain boundary
which is adjacent to the quasi-neutral base region are important.
New electrical methods for determining the presence or absence of
preferential diffusion along the grain boundaries and for determining
the average doping density of preferentially diffused regions along
the grain boundaries are described. A small-signal admittance method
is developed for the determination of the grain-boundary surface-state
distribution in the energy gap for that part of a grain boundary which
has been preferentially diffused with phosphorus. Various experimen
tal attempts at suppressing the grain-boundary dark recombination
current are described. It is shown that the large leakage currents
of small polysilicon p-n junction mesa diodes cause the measured I-V
characteristics of these diodes to be of questionable value in
analyzing the grain boundary component of the current.
vii


I 1
Intrinsic System
Figure 3.1 Equivalent circuit diagram of a solar cell. The dashed lines denote the intrinsic
system of the solar cell.


Device No
1
(36P//13-L2)
2
(36P/M-L1)
3
(36P#28-L2)
4
(36P25-L1)
5
(36P#3-L1)
6
(34P#4-L2)
7
(34P#1-D1)
8
(34P#1-L1)
Table 4.1
Parameter values
for devices
No. 1-
-8. T =
25.0C, A =
4.6 x 10 ^ cm2.
Type
Description
£gb
(mils)
I i
xo xo
(A)
GB
V x
I I^B
QNO QNO
(A)
SGB
(cm/sec)
+
n -p
GBF
0
2.1 x
10 12
1.18
9.7 x 10-14
+
n -p
twins only
160
4.8 x
lo"12
1.29
-13
1.6 x 10
65
+
n -p
one GB
25
4.0 x
io"10
1.83
2.5 x IO-13
3.4 x 10
+
n -p
several GB's
85
9.9 x
10-10
1.84
2.4 x IO-13
2.5 x 10'
+
n -p
several GB's
150
5.7 x
io-10
1.76
-13
3.4 x 10
8.2 x 10
+
p -n
GBF
0
1.1 X
io-9
2.0
5.1 x IO-14
+
p -n
twins only
75
1.8 x
io"10
1.88
-14
2.0 x 10
+
p -n
several GB's
60
7 x
io-10
1.94
3 x IO-14


2?GLtH
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AUTHOR: Mazer, Jeffrey
TITLE: Methods for Investigating the Properties of Polycrystalline
Silicon...
PUBLICATION 1981
DATE:
I, JEFFREY A. MAZER, as copyright holder for the aforementioned dissertation,
hereby grant specific and limited archive and distribution rights to the Board of Trustees
of the University of Florida and its agents. I authorize the University of Florida to digitize
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26
Figure 3.5 I-V curves for device No. 1.


23
hv from solar simulator
.. ,
r >'
> Y
Solar Cell J <
Chuck
y
y v
(a)
(b)
Figure 3.4 Four-point probe experimental setup for investigating the
validity of the shifting approximation.
(a) Setup for measuring I -V and I -V p.
J-i bC O'-*
(b) Setup for measuring I^-V.
In both setups, X and Y are the voltage and current axes on
an X-Y recorder. The chuck is connected to a circulating
water bath. The temperature of the chuck is controlled by
the water bath and is measured by a thermocouple inside of
the chuck.


78
respectively. The above assumption is generally invalid and, con
sequently, (5.1) at best gives an estimate of N In order to de-
s s
termine the feasibility of preferential diffusion as a means of GB
surface-state passivation and, subsequently, as a means of lowering
the dark recombination current and increasing V and n5 a more ac-
UL
curate method for determining N must be developed. In this chapter,
ss
we develop a small-signal admittance method that enables the determina
tion of N in the energy gap for that part of the GB which is in a
ss
preferentially diffused n region. The method, in principle, can
yield the determination of all of the fundamental kinetic parameters
in the energy gap at the GB surface: N (E), E c (E ), c (E ) e (E ),
ss ini pi n i
and e (Em). In addition, the method can yield the GB barrier height,
P T
and the doping and mobility in the preferentially diffused region.
5.2 Small-Signal Equivalent Circuit Model of a Diode with a Prefer
entially Diffused Grain Boundary
We consider again the n+ -p diode with a preferentially diffused
n-region along the GB shown in Fig. 4.5. (The preferentially diffused
n-region of the GB, seen from the perspective of Fig. 4.5, is sometimes
referred to as the n-spike.) The equilibrium band diagram for that
part of the diode that is in the proximity of the preferentially
diffused GB is shown in Fig. 5.1. We assume that the region immediate
ly next to the GB is depleted due to the presence of the surface
states at the GB [18,19]. The band bending due to those surface states
GB
is qcj>_,,. The narrow depletion region of width W on both sides of
the GB is similar to the surface channel of an MOS transistor in the
depletion regime; and the GB with its surface states is similar to the
Si-SiC^ interface of that surface channel. Consequently, the simplified


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
METHODS FOR INVESTIGATING THE PROPERTIES OF
POLYCRYSTALLINE SILICON P-N JUNCTION SOLAR CELLS
By
Jeffrey Alan Mazer
August 1981
Chairman: Dr. Arnost Neugroschel
Co-Chairman: Dr. Fredrik A. Lindholm
Major Department: Electrical Engineering
Experimental and analytical methods are developed for investi
gating the properties and performance-degrading mechanisms of poly
crystalline silicon p-n junction solar cells.
The degrading effects of areal inhomogeneity are demonstrated by
means of a parallel-subcell equivalent circuit model. It is shown that
it is the area of the poor-quality material in a silicon p-n junction
solar cell that dominates in determining the overall cell performance.
An experimental method is developed for assessing the validity of the
shifting approximation for solar cells made from polysilicon and other
material. The experimental data suggest that the shifting approximation
is valid for a variety of polysilicon solar cells in which the intra
grain base minority carrier diffusion length is smaller than or equal to
the average grain diameter. The current components associated with the
grain boundaries of diffused p-n junction polysilicon solar cells made on
vi


112
6.5 Preferential Etching of Grain Boundaries to Enhance Performance
In Runs 22P and 25P (Appendix VII), the GB's of p-type wafers
2
(~1 cm ) were preferentially etched with Sirtl Etch (50 g CrO^, 100 ml
H^O, 100 ml HF) in an ultrasonic bath for 10 minutes. The wafers were
then diffused with phosphorus and fabricated into n+-p solar cells.
The Sirtl Etch removed 23 ym from the intragrain top and bottom surfaces,
while at the same time preferentially etching the GB's to an average
depth of 15 ym below the intragrain top and bottom surfaces. The pur
pose of the Sirtl Etch treatment was to preferentially remove part of
the GB's. In each run, some of the wafers were fabricated into solar
cells without receiving the Sirtl Etch treatment, and those cells were
used as controls. Unlike the wafers of Run 22P, the wafers of Run 25P
were polished with a solution of 2 HF : 15 HNO^ : 5 CH^COOH
(Appendix V) for 10 minutes at the beginning of the wafer processing.
This polishing removed 27 ym from the top and bottom intragrain surfaces
and was only slightly preferential to the GB's.
In Run 22P, the measured at 1 sun AMO was between 60 and 70 mV
higher for the cells that had received the Sirtl Etch treatment than
for the control cells; but, in Run 25P, the Sirtl Etch cells and the
control cells displayed a negligible difference in V^. Also, the dark
I-V curves for the Sirtl Etch cells and the control cells in Run 25P
were essentially identical. These data strongly suggest that the
improvement in V for the Sirtl Etch cells of Run 22P was due to the
removal of saw damage by the Sirtl Etch and not to the preferential
etching of the GB's. The data are consistent with an observation by
Schwuttke that the saw damage in Wacker wafers extends into the material
to a depth of about 25 ym [58].


15
suggests one possible origin of a dependence on illumination of the
effective minority carrier lifetime. Such a dependence would tend to
invalidate the shifting approximation.
The equivalent circuit diagram of a solar cell is shown in
Fig. 3.1. The shunt resistance is assumed to be large enough so that
the shunt current may be neglected. The combination of the current
generator and the dark diode constitute the intrinsic system [5] of the
solar cell. Even though the series resistance Rg may be large enough so
as to invalidate the shifting approximation for the overall solar cell,
it may nevertheless be the case that the shifting approximation is valid
for the intrinsic system of the cell. The approach taken here is to
measure the dark and illuminated I-V curves and then to compare these
curves after separating out the influence of Rg. (Shunt resistance for
these cells was determined to be large.) If, after the correction for
R the dark and illuminated I-V curves are identical except for being
O
shifted or translated by the short-circuit current Ig^,, then the
shifting approximation is valid for the intrinsic system of the solar
cell. It is this sense of the shifting approximation that we are
concerned with in this chapter. The validity of the shifting approxima
tion for a given solar cell considerably simplifies the theoretical
understanding of the performance of the cell, because then the dark I-V
characteristic and Ig^ can be considered separately [5].
3.2 Method for Analyzing the Measured I-V Curves
In Fig. 3.1, the voltage V across the terminals differs from the
voltage across the intrinsic system V^.g by a voltage drop across the
series resistance Rg. In the dark V = V^g + I^Rg, whereas under illumi
nation V = V^-g I^Rg. In Fig. 3.2, we illustrate qualitatively the


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Paul H. Holloway
Associate Professor of Materials
Science and Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Arun K. Varma
Professor of Mathematics
This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
August 1981
'tdzl.
Dean, College of Engineering
Dean for Graduate Studies and Research


APPENDIX X
COMMENTARY ON THE RELIABILITY OF GROOVE AND
STAIN RESULTS IN CHAPTERS 4 AND 5.
In chapters 4 and 5, we report the average values for the prefer
ential diffusion depth d for several diffusion schedules. These
n
values were determined by the method of groove and stain. For the
diffusion schedule consisting only of a 30 minute 900C predeposition
of phosphorus into p-type material, and for the diffusion schedules
consisting of boron diffusion into n-type material at 900-1000C for
20-120 minutes, the groove and stain method did not detect any preferen
tial GB diffusion. Published theoretical and experimental results al
luded to in Sections 4.2 and 6.2 lead us to presume that the above
diffusion schedules did produce some degree of preferential GB diffusion,
and that, the groove and stain method did not have adequate sensitivity
to detect the preferential GB diffusion.
For each diffusion schedule for which the groove and stain method
did detect preferential GB diffusion (Sections 4.2 and 5.5), it was the

case that some GB's (as much as 50%) did not stain. We attribute this
phenomenon to some unknown property or parameter of the groove and stain
method. It was nevertheless the case that all GB diodes fabricated by
such diffusion schedules showed greater zero-bias capacitance than the
corresponding GBF diodes. For those diffusion schedules for which the
groove and stain method did detect preferential GB diffusion, the cal
culated values for d were scattered by as much as + 15%. Because it
n -
is reasonable to believe that GB's with different crystallographic
137


APPENDIX III
DERIVATION OE A SIMPLIFIED EXPRESSION FOR
THE SPACE-CHARGE REGION RECOMBINATION CURRENT
For a forward-biased p-n junction, the steady-state net recombina
tion rate for electrons or holes in nondegenerate material is given by
Equation (6) in reference [8] as
U = (pn ni2)/Tno[P + niexp[(Ei Et)/kT]] (Al)
+ TpQ[n + nexp[(Et E)/kT]]},
where Tno and XpQ are the low-injection level minority-carrier lifetimes
for electrons and holes, respectively; E^ is the energy level of the
recombination-generation centers; and E^ is the intrinsic Fermi level.
If we assume that there is a spatially-uniform monoenergetic distribution
of recombination-generation centers located at the middle of the bandgap
and T = T = T then (Al) may be written as
no po o ^
U = (pn ni2)/[Xo(p + n + 2n)]. (A2)
2
Because of forward bias, pn m and p + n 2m. Thus,
U pn/[TQ(p + n)]. (A3)
We further assume that U = U throughout the SCR. This implies that
max r
p = n throughout the SCR, so that
U n/2TQ. (A4)
124


Ill
the preferential diffusion of boron along the GB's. It was hypothesized
that such a preferential diffusion could result in a lowering of the GB
component of the dark recombination current either by the formation of
a high-low (p+-p) junction along the GB's or by the compensation of
dangling bonds along the GB's. A high-low junction [56] would decrease
the effective surface recombination velocity of minority carrier elec
trons flowing into the GB's. Due to large leakage currents, I-V meas
urements were inconclusive. It is suggested that this GB passivation
technique, repeated with planar diffused diodes, might be the subject
of future research.
6.4 Grain-Boundary Passivation by Hydrogen Plasma Treatment
In Run 7P (Appendix VI), phosphorus diffused p-type wafers
2
(~1 cm ) were sent to Sandia National Laboratories to receive a hydrogen
plasma treatment similar to that described in [40,57], This treatment
was intended to cause the preferential transport of monoatomic hydrogen
along the GB's, and thereby passivate the GB's by tying up dangling
bonds. Several n+-p wafers were kept at the University of Florida as
controls. After the sample wafers were returned from Sandia, both sam
ples and controls were fabricated into solar cells. This fabrication
used only low-temperature techniques (~ 130C) to avoid any out-gassing
of the hydrogen from the GB's. Dark and illuminated measurements on
these solar cells showed that the hydrogen plasma treatment had a negli
gible effect on the measured dark recombination current, short-circuit
current, and open-circuit voltage.


METHODS FOR INVESTIGATING THE PROPERTIES OF
POLYCRYSTALLINE SILICON P-N JUNCTION SOLAR CELLS
BY
JEFFREY ALAN MAZER
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1981


134
Runs 36P and 37P
Substrate: 5 Q-cm p-type Wacker polysilicon.
Steps:
1-4. Same as steps 1-4 in Run 34P.
5. Phosphorus predeposition. 30 minutes at 900C in an atmosphere of
90 cc/min N2 bubbled through POCl^ at 30C, 170 cc/min dry 02,
1500 cc/min N2 carrier gas.
6. Remove phosphosilicate glass and thin oxide down to 3200 with
BOE etchant, p =20 Q/O.
s
7. Drive-in at 1050C in 1700 cc/min 02: 15 minutes in dry 02,
20 minutes in wet 02 bubbled through deionized water at 95C,
O
5 minutes in dry 02> New oxide thickness = 3000 A. pg = 7.7 ti/o.
x. = 1.8 ym.
3
8. For Run 37P only: deposit 6000 A1 on front surface; anneal at
450C for 12 hours in 400 cc/min N2; remove A1 with A1 etchant.
9. Remove n+-layer from back side by lapping with SiC slurry.
10. Solvent cleaning.
11. Photolithography to open holes for metal contacts.
12. Solvent cleaning.
13. Metallization: A1 front and back.
14. Photolithography to define top contact and MOS guard ring.
15. Solvent cleaning.
16. Anneal (36P only): 10 minutes at 400C in 400 cc/min N2.


67
GB j-
Tables 4.1 and 4.2 (including I and V ) to the GBs in the p -n
Xu oc*
diodes. The grain size of p+-n diodes would have to be comparable to
1.^ 35 ]im in order to observe the effects of the GBs on the I-V curves.
4 *4*
The other important difference between the n -p and p -n diodes is
that no preferential diffusion of dopant impurity (boron) was observed
in the p+-n diodes. The differences in the values for and I_. for
XO QNO
the p"*-n devices in Table 4.1 are due mainly to the measured variations
16 -.3 15 3
in the base doping density (N^ 1.3 x 10 cm 2.6 x 10 cm J).
Notice also that the device No. 7 containing only twins is very similar
to the other two p -n diodes. Values for Ig^ are slightly higher for
the p+-n diodes than for the n+-p diodes because of the shallower
p+-junction depth of 0.8 ym compared to 1.8 ym for the n+-junction depth.
The p+-n diodes in Tables 4.1 and 4.2 are representative diodes
from Run 34P. Parameter values for additional diodes in Run 34P are
presented in Tables 4.5 and 4.6. The relative scattering of values for
these diodes (as opposed to the Run 36P n -p diodes) is attributed mainly
to the measured variation in base doping density.
4.3.6 Grain-boundary Shunt Resistance R
GB
Sh
The shunt resistance effects on the I-V curve will be most effective
at very small biases. An analysis of the I-V curves in the voltage
+ +
range of about 0-300 mV for both the n -p and p -n GBF and GB diodes
shows that the measured curves can be described by Iaexp[(qV/m^kT) 1]
i.e., they follow exactly an exponential dependence for a certain
p-D
constant slope factor n^. This indicates that the V/Rgh term in (4.3)
GB GB
and (4.5) can be neglected and Ggh = l/R^ 0. This is an important
Sh
conclusion regarding the shunt resistance. The effects of R01 on I-V
bn
curves can be confused with the effects of I^L or the edge effects.
SCR


Table 3.1 The seven experimental solar cells for which the I-V dependencies were measured.
Device No.
Description
Total Area
(cm2)
Grain Diameter
(mils)
Source
1
n+-p 50 ym thick epi-layer grown on Dow
Corning grade 2P polysilicon substrate.
4.45
10 150
RCA
2
SnO^, on n-type Wacker polysilicon
substrate.
4.0
20 70
Exxon
3
Indium-Tin-Oxide on 0.1 0.3 fi-cm p-type
polysilicon substrate.
2.0
20 50
Colorado
State Un:
4
(25P4)
Phosphorus diffused on 5 ii-cm Wacker
polysilicon p-type substrate.
1.4
20 70
UF
5
(36P#28-L2)
Phosphorus diffused on 5 Q-cm Wacker
silicon p-type substrate. One grain bound
ary goes through the cell. This solar cell
is 30 mils in diameter and has an MOS guard
ring.
4.6 x 10-3
"15
UF
6
(36P#3-L1)
Same as No. 5, but with five grain bound
aries .
4.6 x 10-3
~6
UF
Diffused n -p single-crystal control.
7
2.0
Sandia


138
orientations will have different rates of preferential diffusion, the
variation in the calculated values for d is attributed to variations
n
in the individual GB diffusion rates. The reported value for d for a
n
given diffusion schedule was based on the observation of at least ten
GB's that showed preferential diffusion as a result of the given dif
fusion schedule.


24
The small-signal admittance measurement for determining the value of
R at zero dc-bias in the dark was accomplished with an HP 4275A LCR
b
meter. The ac-signal was 10 mV. The values of the series resistance
determined by the small-signal admittance method and by the method of
comparing the dark and illuminated I-V curves are shown in Table 3.2.
3.4 Experimental Results
The symmetries exhibited in the I-V curves, Figs. 3.5 3.9, along
with the corresponding data on the series resistance, suggest that the
shifting approximation is valid for all of the devices measured. From
Table 3.2, note that the values of Rg for devices No. 5 and 6 are much
higher than those for the other devices. This is primarily because
devices No. 5 and 6 are much smaller in area than the other devices. If
we approximate the current flow as one-dimensional, then the value of Rg
2
for these two devices normalized to an area of 2 cm would be about
0.07 .
3.5 Discussion
As mentioned in Section 3.1, it is possible in polysilicon material
that the effective minority carrier lifetime will depend on the illumina
tion level. The likelihood of this dependency is increased if (i) the
illumination-induced lowering of the grain-boundary potential barrier
significantly changes the effective surface recombination velocity at the
grain boundary, and (ii) the intragrain base minority carrier diffusion
length L is greater than or equal to the average grain diameter d .
Thus, it is particularly interesting to investigate the validity of the
shifting approximation in polysilicon solar cells where L d_. All six
of the polysilicon devices in Table 3.1 have relatively large grain


APPENDIX IV
GROOVE AND STAIN EXPERIMENT TO DETERMINE THE EXTENT OF STAINING
To accurately measure the stained width of a preferential diffusion
spike in a grooved and stained sample, it is necessary to know which
parts of the p-n junction SCR are stained by the staining solution. To
determine the extent of staining by the copper solution referred to in
Section 4.2 and by the commonly used HF solution, we compared the values
of the p-n junction depth x^ obtained [28] by using these two solutions
on two sample wafers. The copper solution was Philtec Company Stain
No. 2. The HF solution consisted of HNO^ : HF : ^0 = 1 : 10 : 89,v/v.
The sample wafers were p+-n and n+-p single-crystal wafers. It is known
that the HF solution will stain only the quasi-neutral p-region in a
grooved sample [60]; the copper solution will stain n-type material.
Table A1 presents the average calculated values for x^ obtained
with the two solutions and the two sample wafers. For each wafer, the
Stain solutions yield approximately the same values for x^. This
suggests that the copper solution stains both the quasi-neutral n-region
and the entire p-n junction SCR in a grooved sample.
126


85
in
Figure 5.3(c) The one-lump equivalent circuit model obtained from
Fig. 5.3(b). Here C C C and C are in farads,
D W SS (jJ5r
and G is in mhos,
ns


88
Figure 5.3(d) The equivalent circuit model obtained from Fig. 5.3(c)
for the low-frequency case, i.e., for f f .
s s


19
dependencies Ip V, IT V, and ISf, Vnf, for a solar cell. (Isr,)
SC OC
SC max
and (V) are the short-circuit current and open-circuit voltage at
the maximum illumination level of the Ig V^ dependence. Note that
the ideal (reciprocal slope = 1) Ig^, dependence is the I-V depen
dence of the intrinsic cell system, since Ig^ = I,, [exp(qVnfl/kT) 1] =
OC'
I [exp(qVTC/kT) 1], where I is the dark saturation current of the
o Jld o
cell. This is valid if Rg is small enough so that the externally
measured I is equal to the short-circuit current of the current gener-
bu
ator in Fig. 3.1. In general, the current-voltage dependencies will have
the following two properties: (i) the Ig^ V^ dependence will be
negligibly influenced by Rgj and (ii) the series resistance will shift
the I-V and Ip V curves to the left and right of the Ig^ V^c
curve, respectively.
It follows from the above discussion that the shifting approximation
will be valid if the series resistance R is independent of the illumina-
b
tion level, and if the I-V and I-V curves are symmetrically shifted
Li JJ
with respect to the Ig^, V^ curve. By symmetrically shifted we mean
that at any given current I ^ (I ) t^ie distance AV., between the
ID V and IgC VQC curves when the IgC VQC curve is shifted into the
first quadrant is the same as the distance AV£ between the 1.^ V and
Ic V curves when these two curves are rotated about the V-axis into
the first quadrant. This test for symmetry is shown in Fig. 3.3. Note
that the Ic Vn curves cross at (Ic ) /2 and, if symmetry holds,
dLi ol> max
then AV- = AV = AV at (I_) /2. The series resistance of the solar
1 / SC max
cell can then be calculated [16] as
Rg ^/[^scPmax/2] 2AV/[ ^SC^ax^ *


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Arnost Neugroschel, Chairman
Associate Professor of Electrical
Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
v
Fredrik A. Lindholm, Co-Chairman
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
' -
Fossum
cofessor of Electrical Engineering


EMITTER
Parallel-subcell model of a p-n junction silicon solar cell with areal inhomogeneity.
Rgg is series resistance in the emitter, is series resistance in the base, R^ is
shunt resistance, I is photogenerated current; and, I and I are the dark recom-
L SCR ON
bination currents in the space-charge region and quasi-neutral region, respectively.
Figure 2.1


55
4.3.2.1 I
GB
QNB
-GB
The IqjjB component is due to the electrons injected from the prefer
entially diffused vertical GB region with an area into the base.
This current component, coupled with the electron current injected from
the top lateral junction with an area A, will result in a two-dimensional
current flow in the base. An accurate solution of such a two-dimentional
PR
problem is not presently available. If, however, An A, then IqNB can
be neglected. Considering our n+-p devices from Fig. 4.6 and Table 4.1,
the ratio A^/A is largest for device No. 5 and is only about 0.1. Thus,
GB
as a first approximation, we will neglect in further analysis of
GB
our devices. *q^b will be important for devices with large depths of
preferential diffusion in the GB.
PR
4.3.2^2. Xand GB Passivation
QNE
GB
IqNE "^S ^Ue t0 t^ie k^-es injected from the p-type substrate into the
preferentially diffused region of the GB and recombining inside that
region. The current transferred through the narrow n-spike, Fig. 4.5,
can be treated in a way similar to the current transferred through a
narrow emitter region of a solar cell. A detailed investigation of this
problem was done by Shibib et al. [36]. The recombination current in
the n-spike will be a function of the hole lifetime T in the bulk of
P
the spike, the hole transit time t through the spike, and the surface
recombination velocity S^B at the GB inside the spike. The transit time
can be expressed as [36]
T (W2/2D ) + (W /SG
t n p n p(eff)
(4.8)


141
26. R. S. Barnes, "Diffusion of copper along the grain boundaries of
nickel," Nature, Lond., vol. 166, pp. 1032-1033, Dec. 1950.
27. W. L. Bond and F. M. Smits, "The use of an interference microscope
for measurement of extremely thin surface layers," Bell Syst. Tech.
J., vol. 35, pp. 1209-1221, Sept. 1956.
28. B. McDonald and A. Goetzberger, "Measurement of the depth of
diffused layers in silicon by the grooving method," J. Electrochem.
Soc., vol. 109, pp. 141-144, Feb. 1962.
29. P. H. Holloway, private communication, 1979.
30. S. M. Sze, Physics of Semiconductor Devices, Chap. 7, J. Wiley &
Sons, New York, 1969.
31. H. J. Hovel, Semiconductors and Semimetals vol. 11: Solar Cells,
Academic Press, New York, 1975.
32. H. J. Hovel, "Photovoltaic materials and devices for terrestrial
solar energy applications," Tech. Digest 1979 International Electron
Devices Meeting, pp. 3-8, Dec. 1979.
33. A Neugroschel, P. J. Chen, S. C. Pao, and F. A. Lindholm, "Forward-
bias capacitance measurements for determining the base and emitter
lifetime in p-n junction solar cells," Record of 13th IEEE Photovol
taic Specialists Conf., pp. 70-75, June 1978.
34. W. Shockley, Electrons and Holes in Semiconductors, Chap. 12,
Van Nostrand, Princeton, NJ, 1950.
35. W. Rosenzweig, "Diffusion length measurement by means of ionizing
radiation," Bell Syst. Tech. J., vol. 41, pp. 1573-1588, Sept. 1962.
36. M. A. Shibib, F. A. Lindholm, and F. Therez, "Heavily doped trans
parent-emitter regions in junction solar cells, diodes, and
transistors," IEEE Trans. Electron Devices, vol. ED-26, pp. 959-965,
June 1979.
37. J. G. Fossum, A. Neugroschel, F. A. Lindholm, and J. A. Mazer, "The
influence of grain boundaries on recombination in polysilicon p-n
junction solar cells," Record of 14th IEEE Photovoltaic Specialists
Conf., pp. 184-190, Jan. 1980.
38. J. G. Fossum and F. A. Lindholm, "Effects of grain boundaries in
the junction space-charge region of polycrystalline solar cells,"
IEEE Electron Device Lett., vol. EDL-1, pp. 267-269, Dec. 1980.
39. R. Janssens, R. Mertens, and R. Van Overstraeten, "Passivation of
grain boundaries in polysilicon solar cells," preprint of paper
intended for publication, 1980.
40. C. H. Seager and D. S. Ginley, "Passivation of grain boundaries in
polycrystalline silicon," Appl. Phys, Lett., vol. 34, pp. 337-340,
March 1979.


CURRENT (A)
52
Figure 4.7 The dark current of a GB diode measured at 150 mV versus
1/T showing an activation energy E = 0.59 eV E /2.


CURRENT DENSITY (A/cm )
72
VOLTAGE (V)
Figure 4.10 Measured dark J-V characteristics of GBF mesa and planar
diffused diodes showing the effect of leakage current on
the low-voltage current density and on the reciprocal
slope m^. of the mesa diode. Diode 4P2~l,3,f is a mesa
diode; diode 36P//10-D1 is a planar diffused diode with
an MOS guard ring.


53
GB
^SCR ~ we can calculate the approximate values of S^g. The
results in Table 4.1 indicate that electrically active GB's do not have
GB
a uniform S. By using the values for 1^ Ior,n, where
GB*
SCRO
rr GB
K = Ac qn.S T3, we can calculate the average current per unit
bGKU bGK 1 GB
GB *"13
length of GB, 4.6 x 10 A/ym, with the average slope factor
oGK
GB
m^ nigQ^ 1.81. These two average values can then be used to predict
the behavior of the I-V curves for different grain sizes. The average
GB recombination velocity for devices No. 3-5 is S,,,, 2.2 x 10 cm/sec.
GB
The device No. 2 which contains only twin boundaries is almost identical
to the GBF device.
4.3.2. Quasi-Neutral Region Current Components (n*~-p diodes)
GB
Each value of Iq^q> Table 4.1, which includes the QN components
GB
plus the Ig from (4.1), is an increasing function of £^g, as expected.
Iqnq fr the GBF diode is a function of only the doping density in the
p-type substrate and the minority electron diffusion length. The I^g
can be neglected because of the low doping density in the base
Naa 3 x 1015 cm ^ [7], The diffusion length Ln 130 ym in the GBF
diode was obtained from the QNB component of the dark current [7]. In
the small area devices, such as the 30 mil diodes used in this work, the
two-dimensional spreading effects will be important if the radius d/2 is
comparable to the diffusion length Ln [33]. For the GBF diode, the
radius of the diode is d/2 = 380 ym > L^, which will assure almost one
dimensional current flow; but for the 30 mil diodes with several GBs,
the grain size could be comparable to the electron diffusion length and
the injected electrons will combine within the grain and at the GBs.
The recombination current in the device can then be described by
Shockley's filament theory [34]:


CURRENT (Arbitrary Units)
20
Figure 3.3 Illustration of the test for symmetry in the measured
I-V curves. The In curves cross at (I__) /2.
SC OC SC max
If the I-V curves are symmetric, then Aat any
given current I < (Isc)max >
1 (IscW2- "
and AV,
AV
AV at
9


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45
preferential diffusion. In addition, we can calculate the value of DD
from the linear portion of the channel current-voltage dependence and
geometry [30]:
NDD = G£GB/qUA 2 X 1017 cm"3
-3
where G 1 x 10 mhos is the conductance of the linear portion of the
-4
channel I-V dependence, 23 x 10 cm is the length of the channel,
2
U 400 cm /V-sec is the estimated electron mobility in the channel, and
-7 2
A 2.2 x 10 cm is the cross-sectional area of the channel. The gate
voltage between the p-type substrate and one of the GB diodes (source)
can be used to modulate the channel conductance and thus to study the
diffusion profile within the preferentially diffused region. also
can be estimated from the reverse gate bias required to deplete the
channel and decrease the channel current to zero; this was not possible
in this device because of the large and the wide channel.
4.3 Analysis of the I-V Curves
A solar cell under illumination is forward biased; the external
current is given by the photogenerated short-circuit current Ig^, minus
the dark current 1^, providing that the superposition principle is
valid [5], In the following discussion we will concentrate on the open-
circuit voltage Vq£ of the cell, and also on the dark current 1^, since
for many cells, V^ is degraded much more by the GBs than is Ig^, [31,32].
The illuminated I-V characteristics will be considered in more detail in
Section 4.3.3.
In order to analyze the I-V characteristics of GB diodes, we first
define and describe all current components. Figure 4.5 shows a cross-
section of a portion of the n"*"-p diode showing one columnar grain


79
Figure 5.1 (a) Cross-section of an n -p polysilicon diode showing the
preferentially diffused n-region of a GB.
(b) The corresponding thermal equilibrium band diagram. The
GB is located at x = 0. The width of the GB space-charge
region is W^; the width of the quasi-neutral n-region
in the n-spike is W^; the band-bending at the GB is


30
(b)
Figure 3.9 Curve tracer photographs of the dark and illuminated I-V
curves for device No. 6. The symmetry of these curves is
displayed in this fashion rather than in the fashion of
Fig. 3.3 because the voltage displacement of the curves
is very small. Ig^ = 60 yA, = 467 mV.
(a) Dark I-V curve.
(b) Illuminated I-V curve.


TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS . ii
ABSTRACT vi
CHAPTER
1 INTRODUCTION 1
2 DEGRADATION OF SOLAR-CELL PERFORMANCE
BY AREAL INHOMOGENEITY 3
2.1 Introduction 3
2.2 Type 1 Areal Inhomogeneity 5
2.3 Type 2 Areal Inhomogeneity 11
2.4 Discussion 12
3 A METHOD FOR EXPERIMENTAL ASSESSMENT OF THE SHIFTING
APPROXIMATION, WITH APPLICATION TO POLYSILICON SOLAR
CELLS 14
3.1 Introduction 14
3.2 Method for Analyzing the Measured I-V Curves ... 15
3.3 Experimental Procedure 21
3.4 Experimental Results 24
3.5 Discussion 24
4 EFFECTS OF GRAIN BOUNDARIES ON THE CURRENT-VOLTAGE
CHARACTERISTICS OF POLYSILICON SOLAR CELLS 33
4.1 Introduction 33
4.2 Fabrication of Devices and Evaluation of Prefer
ential Grain-Boundary Diffusion 36
4.3 Analysis of the I-V Curves 45
4.3.1
4.3.2
Space-Charge Region Current Components
(n+-p diodes) 48
Quasi-Neutral Region Current Components
(n+ -p diodes) 53
4.3.2.1
4.3.2.2
4.3.2.3
rGB
3NB
55
tGB and GB Passivation 55
QNE
lgb
B
57
iii


Table 4.5
Parameter values
for additional diodes
in Run 34P. T
= 25.0C, A = 4.6
x 10-3 cm2.
Diode
Description
GB
(mils)
T IGB
XO* XO
(A)
GB
V x
I IGB
QNO QNO
(A)
34P#4-Dl
GBF
5.3 x 10-11
1.58
3.0 x 10-15
34P#9-D1
GBF
5.5 x 10-10
1.93
-14
5.1 x 10
34P//1-D1
twins only
70
.10
1.3 x 10
1.88
-14
2.0 x 10
34P#11-D2
one GB
90
1.2 x 10-1
1.74
-14
7.0 x 10
34P//1-D2
several GB's
40
2.8 x 10_1
2.06
-14
2.8 x 10
34P//3-D1
several GBs
50
5.7 x 10-10
1.72
2.4 x 10-14
34P//3-D2
several GB's
55
3.0 x 10"10
1.90
-14
3.2 x 10
34P//5-D1
several GB's
30
3.0 x 10_1
1.79
-14
1.8 x 10
34P#6-D2
several GB's
40
7.3 x 10-1
2.19
-14
5.4 x 10
34P#1-L2
several GB's
35
2.9 x 10-1
1.97
-14
1.4 x 10
Averages for GB diodes including
the GB diode in Table 4.1:
50
4.1 x 10_1
1.91
-14
3.4 x 10


140
13. J. R. Davis, A. Rohatgi, R. H. Hopkins, P. D. Blais,
P. Rai-Choudhury, J. R. McCormick, and H. C. Mollenkopf, "Effects
of impurities and processing on silicon solar cells," Thirteenth
Quarterly Report for DOE Contract No. 954331, Jan. 1978.
14. N. G. Tarr and D. L. Pulfrey, "The superposition principle for
homojunction solar cells," IEEE Trans. Electron Devices, vol. ED-27,
pp. 771-776, April 1980.
15. H. P. Maruska, A. K. Ghosh, A. Rose, and T. Feng, "Hall mobility of
polycrystalline silicon," Appl. Phys. Lett., vol. 36, pp. 381-382,
March 1980.
16. M. Wolf and H. Rauschenback, "Series resistance effects on solar
cell measurements," Advanced Energy Conversion, vol. 3, pp. 455-479,
April-June 1963.
17. P. J. Chen, S. C. Pao, A. Neugroschel, and F. A. Lindholm, "Measure
ment of series resistance in p-n junction diodes and solar cells,"
IEEE Trans. Electron Devices, vol. ED-25, pp. 386-388, March 1978.
18. H. C. Card and E. S. Yang, "Electric processes at grain boundaries
in polycrystalline semiconductors under optical illumination,"
IEEE Trans. Electron Devices, vol. ED-24, pp. 397-402, April 1977.
19. L. L. Kazmerski, "The effects of grain boundary and interface
recombination on the performance of thin-film solar cells," Solid
State Electronics, vol. 21, pp. 1545-1550, Nov.-Dec. 1978.
20. C. T. Sah and F. A. Lindholm, "Characteristics of solar cells on
granular semiconductors," Record of 12th IEEE Photovoltaic
Specialists Conf., pp. 93-95, Nov. 1976.
21. C. H. Seager and T. G. Castner, "Zero-bias resistance of grain
boundaries in neutron transmutation doped polycrystalline silicon,"
Record of 13th IEEE Photovoltaic Specialists Conf., pp. 1220-1231,
June 1978.
22. C. H. Seager and G. E. Pike, "Grain boundary states and varistor
behavior in silicon bicrystals," Appl. Phys. Lett., vol. 35,
pp. 709-711, Nov. 1979.
23. J. G. Fossom and F. A. Lindholm, "Theory of grain-boundary and
intragrain recombination currents in polysilicon p-n junction solar
cells," IEEE Trans. Electron Devices, vol. ED-27, pp. 692-700,
April 1980.
24. H. J. Queisser, I. Hubner, and W. Shockley, "Diffusion along small-
angle grain boundaries in silicon," Phys. Rev., vol. 123,
pp. 1245-1254, Aug. 1961.
25. R. T. P. Whipple, "Concentration contours in grain boundary diffu
sion," Philosophical Mag., vol. 45, pp. 1225-1236, 1954.


89
Y
in
Figure 5.3(e) The equivalent circuit model obtained from Fig. 5.3(c)
for the high-frequency case, i.e., for f << f fQ.


34
To overcome these difficulties, most of the work reported here was
done on small-area (30 mil in diameter) diodes which contain at most a
few GB's. On such devices the total length and the area of the GB's can
be found, and comparison among the devices can be easily made. The
length and area of the GB's have to be exactly known in order to derive
quantitative results concerning their parameters from the data. Large
area devices containing many GB's can be used mostly for qualitative
studies only.
To assure that the surface and edge currents are suppressed, the
diodes were fabricated with a thermally-grown silicon dioxide on the top
surface and an MOS guard-ring gate overlapping the edge of the diffused
layer, as shown in Fig. 4.1. The surface recombination current compo
nents, including the surface inversion channel current and the recombina
tion current through the surface states at the periphery and at the GB's
intersecting the edge of the diode, are suppressed by applying a suit
able gate voltage to the MOS guard-ring. The remaining current compo
nents are then only the bulk intragrain and grain-boundary components.
An additional and very important advantage of using small-size diodes is
the possibility of placing diodes inside of grains. This grain-boundary-
free (GBF) diode will then allow us to measure the properties of the
bulk of the grain and will serve as a reference diode for comparison
with a nearby diode containing GB's.
Diffusion of impurities into the polycrystalline material is
expected to proceed preferentially down the GB's [24-26]. The width and
average doping density of this enhanced grain-boundary diffusion region
is determined for the case of phosphorus dopant. Also, the current
components associated with the enhanced grain-boundary diffusion will be
discussed and analyzed here for the first time.


CURRENT (A)
49
Figure 4.6 Measured dark I-V curves for five n -p solar cells: a GBF
cell (No. 1), a cell containing twins only (No. 2), and
three GB cells (No. 3, 4, and 5).


Terminal Capacitance C. (pF)
Figure
Terminal Conductance G. ( x 10 mhos)
m


102
GBF
in
Figure 5.8
The one-lump equivalent circuit model used in the conduc
tance method for determining the surface state distribu
tion in the energy gap. This model is obtained by convert
ing the parallel branch of the circuit model in Fig. 5.3(c)
into a capacitance C in parallel with a conductance G .


REFERENCES
1. H. Fischer and W. Pschunder, "Low-cost solar cells based on large-
area unconventional silicon," IEEE Trans. Electron Devices,
vol. ED-24, pp. 438-442, April 1977.
2. M. A. Green, "Photocurrent loss within the depletion region of
polycrystalline solar cells," Solid State Electronics, vol. 21,
pp. 1139-1144, 1978.
3. S. I. Soclof and P. A. lies, "Grain boundary and impurity effects
in low cost silicon solar cells," Record of 11th IEEE Photovoltaic
Specialists Conf., pp. 56-61, May 1975.
4. F. A. Lindholm, J. A. Mazer, J. R. Davis, and J. I. Arreola,
"Degradation of solar cell performance by areal inhomogeneity,"
Solid State Electronics, vol. 23, pp. 967-971, Sept. 1980.
5. F. A. Lindholm, J. G. Fossum, and E. L. Burgess, "Application of
the superposition principle to solar cell analysis," IEEE Trans.
Electron Devices, vol. ED-26, pp. 165-171, March 1979.
6. W. Shockley, "The theory of p-n junctions in semiconductors and p-n
junction transistors," Bell Syst. Tech. J., vol. 28, pp. 435-489,
July 1949.
7. A. Neugroschel, F. A. Lindholm, and C. T. Sah, "A method for deter
mining the emitter and base lifetimes in p-n junction diodes,"
IEEE Trans. Electron Devices, vol. ED-24, pp. 662-671, June 1977.
8. C. T. Sah, R. N. Noyce, and W. Shockley, "Carrier generation and
recombination in p-n junctions and p-n junction characteristics,"
Proc. IRE, vol. 45, pp. 1228-1243, Sept. 1957.
9. J. M. Denny, R. G. Downing, S. R. Lackman, and J. W. Oliver,
"Estimate of space-radiation effects on satellite solar-cell power
supplies," IRE Trans. Military Electronics, vol. MIL-6, pp. 14-20,
Jan. 1962.
10. W. Cooley and R. Janda, Handbook of Space-Radiation Effects on
Solar Cell Power Supplies, NASA publication SP-3003, p. 7, 1963.
11. J. G. Fossum, private communication, 1978.
12. G. Schwuttke, private communication, 1978.
139


65
Figure 4.8 also displays the effect that the absence of sintering
of the ohmic contacts had on the series resistance of the 37P diodes:
the extra series resistance of the 37P diode causes the I-V curve of
that diode to bend to the right and cross the I-V curve of the 36P
diode.
4.3.5 I-i-V Characteristics (p+-n diodes)
Figure 4.9 shows the measured I-V curves for two representative
p -n diodes; device No. 6 is a GBF diode; device No. 8 is a GB diode. A
summary of parameters for these two diodes and for diode No. 7 which
4-
contains only twins is in Tables 4.1 and 4.2. In contrast to the n -p
diodes, the effect of the GBs on diode No. 8 is very small. This is
evident both from Fig. 4.9 and Tables 4.1 and 4.2. The intragrain hole
diffusion length for the GBF p+-n diode No. 6, obtained from the dark
I-V curve [7], is 35 pm. Thus, for the GB diode No. 8, dG L ,
and the effect of the GB's on Iq-^q is negligible. At small bias levels
the SCR recombination currents are dominated by the recombination in
"f" GB
the SCR adjacent to the top p -n junction, IgCR and IgCR is negligible.
With several ideal assumptions (Appendix III), the Sah-Noyce-Shockley
theory [8] allows IgGR to be written as
FSCR ^AqWSCR.ni/(2TSCR> ]exp(qV/mkT),
(4.12)
where TgGR is the time constant controlling the recombination in the
SCR at small bias levels, and m 2.0. Using (4.12) we find
tscr ~ 0,2 psec for the p+-n GBF device No* 6 and tscr ~ 100 Psec for
the n+-p GBF device No. 1. This comparison of values for TcrtT, and also
oLK
a comparison of with explains the insensitivity of parameters in


7
Ln 100 pm. By the shifting approximation, the illuminated current of
the solar cell is
1 ISC IDARK
~ AG^JS(Pg JQNG0eXp(qV/,kT)-* + M(JS(Pp JQNPOeXp(qV/kT) ^
= A {Jsc [exp(qV/kT)][(AQF)JQNG0 + (1-AQF)JQNpQ]}. (2.1)
In (2.1), JqNGQ and are the dark saturation quasi-neutral current
densities of the good and poor areas of the cell, respectively. In the
good portion of the cell we are assuming that Jq^g is negligible compared
t0 JQSB- ThUS- JQNG0 JQNB0 ni VlnNAA 44 X A/C at C
where J.TT)^ is the dark saturation current density of the quasi-neutral
base as derived in [6], and is the electron diffusivity in the base.
In the poor portion of the cell we are assuming that Jq^g is negligible
compared to JQNE; thus JQNpo JqmQ. By defining JR JQNp0/JQNG0,
(2.1) may be rewritten as
I ~ A {Jsc -[exp(qV/kT)]JQNG()[AQF + (l-AQF)JR]}.
(2.2)
From (2.2), we calculate [Appendix I] and plot the open-circuit voltage
Vnp, the fill-factor FF, and the power conversion efficiency n as a
function of AQF with JR as a parameter in Figs. 2.3, 2.4, and 2.5,
respectively. These figures show that even a small poor-material area,
for example 5% (corresponding to AQF = 0.95) of the total solar cell
area, can drastically decrease the overall performance of the solar cell.
2 +
The parameter value JR = 10 corresponds to a silicon n -p thin-junction
solar cell with negligible recombination in the space-charge region,
Jscr <<: dqjyj* Tp,e surface of the good-quality subcell is covered by a


ACKNOWLEDGEMENTS
The author sincerely thanks the chairman of his supervisory
committee, Dr. Arnost Neugroschel, and the co-chairman,
Dr. Fredrik A. Lindholm, for their help and guidance during the course
of the research presented in this dissertation. The author also thanks
the other members of his supervisory committee, Dr. Jerry G. Fossum,
Dr. Paul H. Holloway, and Dr. Arun K. Varma for their friendly
assistance.
Appreciation is extended to the authors colleagues and friends for
stimulating discussions: Shing C. Pao, J. Ignacio Arreola,
Franklin N. Gonzalez, Dersun Lee, and Phillip E. Russell. Appreciation
is also extended to Raymond Wilfinger, William Axson, Dean Schoenfeld,
Bruce Chovnick, and William Wagner for technical assistance during the
fabrication of devices.
The author gratefully acknowledges the financial support and
technical assistance of the U.S. Department of Energy and the Solar
Energy Research Institute during the course of this research.
Last, but not least, the author thanks his parents for their
frequent support and encouragement throughout his graduate school
career.
n



o o o o o
APPENDIX II
FORTRAN PROGRAM FOR PROJECTING THE PERFORMANCE OF A SOLAR
CELL GIVEN THE EMPIRICAL PARAMETER VALUES OF THE SUBCELLS
C THE PROGRAM MODELS THE ENTIRE SOLAR CELL AS THE PARALLEL COMBINATION
C OF N SUBCELLS. THE SHIFTING APPROXIMATION IS ASSUMED TO BE VALID.
C THE USER SUPPLIES THE FOLLOWING EMPIRICAL PARAMETERS FOR EACH
C SUBCELL: THE PHOTOGENERATED CURRENT, THE SPACE-CHARGE REGION SATURA-
C TION CURRENT, THE QUASI-NEUTRAL REGION SATURATION CURRENT, THE
C SPACE-CHARGE REGION RECIPROCAL SLOPE FACTOR, THE SERIES RESISTANCE,
C AND THE SHUNT RESISTANCE. THE PROGRAM THEN SOLVES N+l NODE VOLTAGE
C EQUATIONS IN N+l UNKNOWNS. THIS IS ACCOMPLISHED THROUGH THE USE OF
C THREE SUBROUTINES IN THE HARWELL SUBROUTINE LIBRARY FOR SOLVING
C SYSTEMS OF NONLINEAR ALGEBRAIC EQUATIONS. IN THE HARWELL LIBRARY
C THE SUBROUTINES ARE IDENTIFIED AS: NS01A,MC03AS, AND MB01C. THE
C PROGRAM OUTPUT CONSISTS OF VOC, ISC, VMP, IMP, FF, AND EFF FOR THE
C ENTIRE SOLAR CELL.
C
C THE FOLLOWING LISTING IS AN EXAMPLE FOR THE CASE N-2.
C
DIMENSION P2(3),P3(3),P4(3,3),P10(33)
REAL IL(2),MX(2),1X0(2),IQN0(2),RS(2),RSH(2),ISC,ILOAD,IMP
COMMON IL,MX,IXO,IQNO,RS,RSH,RLOAD
IP1 = 3
JJ1 = IP1-1
WRITE(6,10)
10 FORMAT(25X,'SOLAR SUBCELL EMPIRICAL PARAMETER VALUES ARE:',//)
DO 40 LL = 1,JJ1
READ(5,20) RS(LL),RSH(LL),MX(LL),IL(LL),IXO(LL),IQNO(LL)
20 FORMAT(6E9.3)
WRITE(6.30) RS(LL),RSH(LL),MX(LL),IL(LL),IXO(LL),IQNO(LL)
30 FORMAT(5X,'RS=',E10.4,3X,'RSH=',E10.4,3X,'MX=',E10.4,3X,
F'IL=',E10.4,3X,'1X0=',E10.4,3X,'IQNO=',E10.4.//)
40 CONTINUE
THE FOLLOWING ARE THE NS01A SUBROUTINE PARAMETERS.
IP = 3
P2(l) = 1.0
P2(2) = 1.0
P2(3) = 1.0
P5 = 0.0001
P6 = 3.0
P7 = 1.0E-12
121


127
Table Al Average calculated values for the junction depth x
with the two solutions and the two sample wafers.
Solution
x. for p+-n wafer
J
(ym)
x. for
J
Copper solution
0.76
. obtained
3
n+-p wafer
(ym)
1.51
HF solution
0.74
1.34


92
5.4 Inversion along the GB in the p-Type Bulk
We now consider that part of the GB which is adjacent to the
p-type bulk. Equation (5.13) shows that, with the assumption of a
uniform distribution of surface states in the energy gap, the band
2
bending at the GB is proportional to N For sufficiently large
N E (0) > E.(0) where E. is the intrinsic Fermi level, and the
region next to the GB becomes inverted. It is of interest to deter
mine the value of N necessary for the formation of an inversion lay-
er along that part of the GB which is adjacent to the p-type bulk.
In Fig. 5.4, it is seen that the onset of inversion occurs when
Ep(0) Ey(0) = q'fgg = E (0)/2. By substituting these relationships
into (5.13) with N replaced by N and with (¡> E (0)/3q, we may
UU fin O o
solve for the value of N necessary for the onset of inversion:
s s
(N ). = (12/q)[k£ N /E (0)]1/2.
ss inv ^ o M g
(5.17)
Since N is, in fact, not uniformly distributed in the energy gap,
(5.17) provides only an estimate of the value of N necessary for the
ss
onset of inversion. In Section 4.2, an argument based on experimental
data was presented to show that there does not exist an inversion layer
about the GB in the bulk. Consequently, (N^) represents an esti
mate of the upper limit of N along that part of the GB which is ad-
s s
jacent to the p-type bulk.
5.5 Experimental Procedure and Results
To demonstrate the above method for determining N two runs
s s
+
(39P and 40P) of n -p mesa diodes were fabricated on 5 fi-cm Wacker
polysilicon p-type substrates (Appendix IX). The mesa diodes were
made by the method of wax-masking a small dot on a chip that had been


Figure 2.2 Two-diode modeling of areal inhomogeneity in a solar cell, assuming the validity of the
shifting approximation, and neglecting the series and shunt resistances.


CHAPTER 2
DEGRADATION OF SOLAR-CELL PERFORMANCE
BY AREAL INHOMOGENEITY
2.1 Introduction
Areal inhomogeneity refers to the spatial variation of material
properties across the area of a solar cell. Unavoidable statistical
fluctuations in doping concentration across the area always occur. In
addition to this, fabrication procedures can sometimes result in large
areal fluctuations in recombination rates. For polycrystalline cells,
preferential diffusion of impurities down the grain boundaries and the
non-uniform spatial distribution of these grain boundaries can result in
drastic changes in the recombination rates across the area of the
cell [1-3]. The intent here is to quantitatively indicate the limita
tions on silicon p-n junction solar-cell performance that can be caused
by areal inhomogeneity.
To deal with the areal inhomogeneity, a solar cell can be modeled
as the parallel combination of as many one-dimensional diodes [4] as are
needed to approximate the spatial distribution of the material proper
ties. Resistive coupling of the diodes is then used to represent
interdiode paths for the recombination and shunt currents (Fig. 2.1).
The use of one-dimensional diodes in this modeling scheme is a first
approximation for polycrystalline solar cells having columnar grains in
which the grain diameter greatly exceeds the minority carrier diffusion
length in the base. This equivalent circuit representation of an illumi
nated solar cell assumes the validity of the shifting approximation that
3


103
modification includes the frequency dispersion of the G due to the
ns
random spatial variation of the surface potential. This treatment
leads to N (E) and also to a determination of the capture cross-sec-
ss
tion 0^ for majority carriers. The majority carrier capture probabili
ty c^ is then determined from c^ = nVth* using the principle of
detailed balance for the zero-bias case (no current flowing across the
GB), the majority carrier emission probability e can also be obtained.
n
5.7 Discussion
The main source of error in the determination of the surface-state
density in the energy gap by the capacitance method is the great sen
sitivity of C to CT,. A 10% error in CTT will result in an error of a-
J ss W W
bout a factor of 2 in the calculated values of C (5.9) and N (5.10)
ss ss
and an even larger error in the calculated value of qcf) (5.15). The
capacitance C was calculated with the assumption of a one-sided step
w
junction with constant substrate doping N^. It was also assumed that
all of the GB's are preferentially diffused to the same depth, and
thus, that C is proportional to the total length of the GB's (Fig. 5.5).
w
Consequently, an accurate determination of the total length of the GB's
is crucial to the success of the capacitance method. The accuracy in
the determination of C can be improved by (i) using a chip that has
w
only one GB, and which has a very small mesa diode straddling that GB;
(ii) making much larger than the parallel combination of and C^.
Method (i) can be achieved by using standard photolithographic tech
niques; and method (ii) can be achieved by using a lower resistivity
substrate (0.1 1 £2-cm), or possibly by means of forward-biasing the
diode.


BIOGRAPHICAL SKETCH
Jeffrey Alan Mazer was born in Fall River, Massachusetts, on
April 23, 1948. He received the B.S. degree in mathematics from
Purdue University, Lafayette, Indiana, in 1970 and the M.S. degree
in electrical engineering from Duke University, Durham, North Carolina,
in 1976. Since 1976, he has been working toward the Ph.D. degree in
electrical engineering at the University of Florida, Gainesville,
Florida.
144


13
that flow in from the contacts to support recombination with minority
carriers. In the poor-region of the cell, the recombination rate is
very high. Consequently, it is in the poor-region of the solar cell
where majority carrier currents, and thus series resistance effects, will
be most important. The series resistance must be included in the
parallel-subcell model if it causes a voltage drop which is a signifi
cant fraction of the terminal voltage. A two-parallel subcell model
that includes the series resistance has been considered [4,13]. The
significant finding in [4,13] is that the inclusion of the series
resistance has the effect of decoupling the subcells. This is because
the series resistance tends to suppress the currents flowing between
subcells. The result of this is that the degradation of solar-cell
performance is not as severe as that predicted when the series resis
tances are neglected. Estimation of the series resistance is given
in [4].
The idealization of two single-connected regions can be removed by
extending the two-parallel subcell model into an n-subcell model, where
n is sufficiently large to accurately describe the variation of material
properties across the area. A computer program that predicts the overall
performance of the solar cell when provided with the empirical parameters
of the subcells is given in Appendix II. A discussion of fringing
effects on the two-parallel subcell model is given in [4].


94
diffused with phosphorus and metallized. The unmasked portion of the
top surface of the chip was then etched to a depth slightly in excess
of the top p-n junction depth x^. The wax was then removed and the
chip was bonded onto a TO-5 header (Fig. 5.5). During the masking
step, care was taken to position the dot over an area that was inter
sected by several GB's. Consequently, after the etching step, the
GB's on the chip were all electrically connected to the emitter of
the mesa by virtue of the fact that the GBs were preferentially dif
fused with phosphorus to a depth d^ considerably in excess of x^. .
The low and high-frequency values of the GB component of the
capacitance can be expressed as C = (C. ) C and C = (C. )
Lr in LF GBF HF in HF
respectively, where is frequency independent until f ~ 1 GHz
GBr Gi5r
The accuracy of the determination of C and C can be improved by
LF HF
maximizing the ratio of C. to Consequently, in the fabrication
xn Gab
of the diodes, we used diffusion schedules that included high-tempera
ture drive-ins so as to make d large compared to x., and we made the
n j
top areas of the mesas much smaller than the top areas of the chips on
which they were fabricated. The ratio of d to x. was about 4.5 and
n J
2.4 for Runs 39P and 40P, respectively. The ratio of the chip area to
the mesa area was about 32:1 for Run 39P and 12:1 for Run 40P.
Figures 5.6 and 5.7 show the measured terminal capacitance
as a function of frequency at several temperatures for a representative
diode from each of the two experimental runs. The measurements were
made on HP 4274A and 4275A LCR meters. The measured and calculated
parameters for the two runs are listed in Tables 5.1 and 5.2. In Figs.
5.6 and 5.7, the measured C. vs. f curves generally follow (5.4), and
in
the step in the curves due to the inability of the surface states to


METHODS FOR INVESTIGATING THE PROPERTIES OF
POLYCRYSTALLINE SILICON P-N JUNCTION SOLAR CELLS
BY
JEFFREY ALAN MAZER
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1981

ACKNOWLEDGEMENTS
The author sincerely thanks the chairman of his supervisory
committee, Dr. Arnost Neugroschel, and the co-chairman,
Dr. Fredrik A. Lindholm, for their help and guidance during the course
of the research presented in this dissertation. The author also thanks
the other members of his supervisory committee, Dr. Jerry G. Fossum,
Dr. Paul H. Holloway, and Dr. Arun K. Varma for their friendly
assistance.
Appreciation is extended to the authors colleagues and friends for
stimulating discussions: Shing C. Pao, J. Ignacio Arreola,
Franklin N. Gonzalez, Dersun Lee, and Phillip E. Russell. Appreciation
is also extended to Raymond Wilfinger, William Axson, Dean Schoenfeld,
Bruce Chovnick, and William Wagner for technical assistance during the
fabrication of devices.
The author gratefully acknowledges the financial support and
technical assistance of the U.S. Department of Energy and the Solar
Energy Research Institute during the course of this research.
Last, but not least, the author thanks his parents for their
frequent support and encouragement throughout his graduate school
career.
n


TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS . ii
ABSTRACT vi
CHAPTER
1 INTRODUCTION 1
2 DEGRADATION OF SOLAR-CELL PERFORMANCE
BY AREAL INHOMOGENEITY 3
2.1 Introduction 3
2.2 Type 1 Areal Inhomogeneity 5
2.3 Type 2 Areal Inhomogeneity 11
2.4 Discussion 12
3 A METHOD FOR EXPERIMENTAL ASSESSMENT OF THE SHIFTING
APPROXIMATION, WITH APPLICATION TO POLYSILICON SOLAR
CELLS 14
3.1 Introduction 14
3.2 Method for Analyzing the Measured I-V Curves ... 15
3.3 Experimental Procedure 21
3.4 Experimental Results 24
3.5 Discussion 24
4 EFFECTS OF GRAIN BOUNDARIES ON THE CURRENT-VOLTAGE
CHARACTERISTICS OF POLYSILICON SOLAR CELLS 33
4.1 Introduction 33
4.2 Fabrication of Devices and Evaluation of Prefer
ential Grain-Boundary Diffusion 36
4.3 Analysis of the I-V Curves 45
4.3.1
4.3.2
Space-Charge Region Current Components
(n+-p diodes) 48
Quasi-Neutral Region Current Components
(n+ -p diodes) 53
4.3.2.1
4.3.2.2
4.3.2.3
rGB
3NB
55
tGB and GB Passivation 55
QNE
lgb
B
57
iii

PAGE
4.3.3 Illuminated I-V Curves (n -p diodes). . 58
4.3.4 Grain-Boundary Passivation by
Hydrogenation Treatment 62
4.3.5 I-V Characteristics (p+-n diodes) .... 65
4.3.6 Grain-Boundary Shunt Resistance
4.4 Comparison of Mesa Diode and Planar Diffusd
Diode I-V Curves 70
4.5 Discussion 71
5 SMALL-SIGNAL ADMITTANCE METHOD FOR DETERMINING THE
SURFACE-STATE DISTRIBUTION AT THE PREFERENTIALLY
DIFFUSED PART OF THE GRAIN BOUNDARY 77
5.1 Introduction 77
5.2 Small-Signal Equivalent Circuit Model of
a Diode with a Preferentially Diffused
Grain Boundary 78
5.3 An Admittance Method for Determining N .... 87
s s
5.4 Inversion along the GB in the p-Type Bulk .... 92
5.5 Experimental Procedure and Results 92
5.6 Conductance Method for Determining N ..... 101
5.7 Discussion ?S 103
6. DESCRIPTION OF SEVERAL METHODS INTENDED TO SUPPRESS
THE GRAIN-BOUNDARY DARK RECOMBINATION CURRENT .... 108
6.1 Introduction 108
6.2 Low-Temperature-Enhanced Preferential Diffusion
of Phosphorus 108
6.3 Low-Temperature-Enhanced Preferential Diffusion
of Boron 110
6.4 Grain-Boundary Passivation by Hydrogen Plasma
Treatment Ill
6.5 Preferential Etching of Grain Boundaries to
Enhance Performance 112
6.6 Discussion ..... 113
7 DISCUSSION 114
APPENDIX
IFORTRAN PROGRAMS FOR SIMULATING THE EFFECT OF AREAL
INHOMOGENEITY IN AN n+-p SILICON SOLAR CELL 117
IIFORTRAN PROGRAM FOR PROJECTING THE PERFORMANCE OF
A SOLAR CELL GIVEN THE EMPIRICAL PARAMETER VALUES
OF THE SUBCELLS 121
IIIDERIVATION OF A SIMPLIFIED EXPRESSION FOR THE SPACE-
CHARGE REGION RECOMBINATION CURRENT 124
iv

IV
PAGE
GROOVE AND STAIN EXPERIMENT TO DETERMINE THE
EXTENT OF STAINING 126
VSTANDARD WAFER CLEANING AND POLISHING PROCEDURES . 128
VIFABRICATION SCHEDULES FOR RUNS 4P4, 6P1, 7P, 8P1,
13P3 and 13P4 129
VIIFABRICATION SCHEDULE FOR RUNS 22P and 25P 132
VIIIFABRICATION SCHEDULES FOR RUNS 34P, 36P, AND 37P . 133
IXFABRICATION SCHEDULES FOR RUNS 39P AND 4OP 135
XCOMMENTARY ON THE RELIABILITY OF GROOVE AND STAIN
RESULTS IN CHAPTERS 4 AND 5. . 137
REFERENCES 139
BIOGRAPHICAL SKETCH 144
v

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
METHODS FOR INVESTIGATING THE PROPERTIES OF
POLYCRYSTALLINE SILICON P-N JUNCTION SOLAR CELLS
By
Jeffrey Alan Mazer
August 1981
Chairman: Dr. Arnost Neugroschel
Co-Chairman: Dr. Fredrik A. Lindholm
Major Department: Electrical Engineering
Experimental and analytical methods are developed for investi
gating the properties and performance-degrading mechanisms of poly
crystalline silicon p-n junction solar cells.
The degrading effects of areal inhomogeneity are demonstrated by
means of a parallel-subcell equivalent circuit model. It is shown that
it is the area of the poor-quality material in a silicon p-n junction
solar cell that dominates in determining the overall cell performance.
An experimental method is developed for assessing the validity of the
shifting approximation for solar cells made from polysilicon and other
material. The experimental data suggest that the shifting approximation
is valid for a variety of polysilicon solar cells in which the intra
grain base minority carrier diffusion length is smaller than or equal to
the average grain diameter. The current components associated with the
grain boundaries of diffused p-n junction polysilicon solar cells made on
vi

Wacker substrates are analyzed and experimentally identified. The
analysis shows that the dominant current component at small bias
levels (0-300 mV) is the recombination current at the grain boundary
within the p-n junction space-charge region. At higher bias levels
(V c V ^ z 500-600 mV), both this current component and the current
component due to recombination at that part of the grain boundary
which is adjacent to the quasi-neutral base region are important.
New electrical methods for determining the presence or absence of
preferential diffusion along the grain boundaries and for determining
the average doping density of preferentially diffused regions along
the grain boundaries are described. A small-signal admittance method
is developed for the determination of the grain-boundary surface-state
distribution in the energy gap for that part of a grain boundary which
has been preferentially diffused with phosphorus. Various experimen
tal attempts at suppressing the grain-boundary dark recombination
current are described. It is shown that the large leakage currents
of small polysilicon p-n junction mesa diodes cause the measured I-V
characteristics of these diodes to be of questionable value in
analyzing the grain boundary component of the current.
vii

CHAPTER 1
INTRODUCTION
Recent attention has been focused on polycrystalline silicon solar
cells because of their potential low cost. The anticipated advantage
of low cost is offset by the fact that polycrystalline solar cells
have displayed efficiencies that are much less than those of the
corresponding single-crystal devices [1,2,3]. This lower efficiency
is caused, to varying degrees, by the presence of dark recombination
currents associated with the grain boundaries, by the degrading effects
of areal inhomogeneity, by a low short-circuit current density, and
by a low shunt resistance. In this dissertation, we develop methods
for investigating the properties and performance-degrading mechanisms
of polysilicon p-n junction solar cells.
In Chapter 2, we demonstrate the degrading effects of areal inhomo
geneity by means of a parallel-subcell equivalent-circuit model.
Chapter 3 describes an experimental method for assessing the validity
of the shifting approximation. These two chapters are applicable to
single-crystal as well as to polycrystalline solar cells.
Most of the experimental devices used in this research were
fabricated on Wacker polysilicon substrates. Wacker material (both p
and n-type) was chosen because it has large enough grain diameters
(~1 mm) to conveniently enable the fabrication of devices that contain
either zero, or at most a few, grain boundaries. By comparing the data
(e.g., capacitance, current-voltage characteristic) on a device
1

2
containing a few grain boundaries with the corresponding data on a
similarly fabricated grain-boundary-free (GBF) device, the grain
boundary (GB) component of the data could be isolated and accurately
analyzed provided that the surface and edge leakage currents were
adequately suppressed. The fabrication of GBF devices also enabled
the determination of some of the intragrain material parameters,
e.g., the intragrain base minority carrier diffusion length. This
fabrication and measurement strategy was used frequently in the
research described in chapters 4, 5, and 6.
In Chapter 4, the current components associated with the grain
boundaries are analyzed and experimentally identified. New electrical
methods for determining the presence or absence of preferential
diffusion along the grain boundaries and for determining the average
doping density of preferentially diffused regions along the grain
boundaries are described.
Chapter 5 describes a small-signal admittance method for the determina
tion of the grain-boundary surface-state distribution in the energy
gap for that part of a grain boundary which has been preferentially
diffused with phosphorus.
Chapter 6 describes various experimental attempts at suppressing
the grain-boundary dark recombination current. Many of these experi
ments were done on 50-mil n+-p mesa diodes. Such experiments were
inconclusive because of the presence of large surface and edge leakage
currents. The subsequent awareness of this fact motivated the fabrica
tion of the 30-mil n+-p and p+-n dark diodes and solar cells used for
the research described in Chapter 4.

CHAPTER 2
DEGRADATION OF SOLAR-CELL PERFORMANCE
BY AREAL INHOMOGENEITY
2.1 Introduction
Areal inhomogeneity refers to the spatial variation of material
properties across the area of a solar cell. Unavoidable statistical
fluctuations in doping concentration across the area always occur. In
addition to this, fabrication procedures can sometimes result in large
areal fluctuations in recombination rates. For polycrystalline cells,
preferential diffusion of impurities down the grain boundaries and the
non-uniform spatial distribution of these grain boundaries can result in
drastic changes in the recombination rates across the area of the
cell [1-3]. The intent here is to quantitatively indicate the limita
tions on silicon p-n junction solar-cell performance that can be caused
by areal inhomogeneity.
To deal with the areal inhomogeneity, a solar cell can be modeled
as the parallel combination of as many one-dimensional diodes [4] as are
needed to approximate the spatial distribution of the material proper
ties. Resistive coupling of the diodes is then used to represent
interdiode paths for the recombination and shunt currents (Fig. 2.1).
The use of one-dimensional diodes in this modeling scheme is a first
approximation for polycrystalline solar cells having columnar grains in
which the grain diameter greatly exceeds the minority carrier diffusion
length in the base. This equivalent circuit representation of an illumi
nated solar cell assumes the validity of the shifting approximation that
3

EMITTER
Parallel-subcell model of a p-n junction silicon solar cell with areal inhomogeneity.
Rgg is series resistance in the emitter, is series resistance in the base, R^ is
shunt resistance, I is photogenerated current; and, I and I are the dark recom-
L SCR ON
bination currents in the space-charge region and quasi-neutral region, respectively.
Figure 2.1

5
illuminated current is equal to the dark current shifted by the short-
circuit photocurrent [5].
We consider a simple ideal case in which only two subcells are used;
one subcell represents the good-quality material part of the cell, and
the other represents the poor-quality material part of the cell. The
series and shunt resistances are neglected, and the current in each
subcell is assumed to be one-dimensional (Fig. 2.2). For this simple
case, two types of areal inhomogeneity for an n+-p Si solar cell are
considered. We define and to be the areas of the good and poor
regions of the cell, respectively. Then the areal quality factor is
defined to be AQF = A^/A, where A = A^ + Ap is the total solar cell area.
2.2 Type 1 Areal Inhomogeneity
For this type of areal inhomogeneity, the non-illuminated (or dark)
quasi-neutral current densities of the good-quality and poor-quality
diodes, and Jq^p> respectively, are allowed to differ by several
orders of magnitude. For both diodes, the recombination currents are
dominated by recombination in the quasi-neutral regions rather than in
the space-charge regions. Both diodes have the same short-circuit
current density JgC. This type of areal inhomogeneity could occur if the
quasi-neutral emitter dark recombination current density experiences
QNii
drastic areal variations due, for example, to impurity clusters or
variations in the surface recombination velocity in the heavily doped
emitter. For these variations in J..T to be important, J-XTT, must be the
QNE r QNE
dominant component of JqNp. To increase the likelihood of this, we will
17 ^
assume a high base doping concentration: N.A = 10 cm We assume
AA
further a long base diode for which the short-circuit current density
2
JSC ~ ^ mA/cm and the base minority carrier diffusion length

Figure 2.2 Two-diode modeling of areal inhomogeneity in a solar cell, assuming the validity of the
shifting approximation, and neglecting the series and shunt resistances.

7
Ln 100 pm. By the shifting approximation, the illuminated current of
the solar cell is
1 ISC IDARK
~ AG^JS(Pg JQNG0eXp(qV/,kT)-* + M(JS(Pp JQNPOeXp(qV/kT) ^
= A {Jsc [exp(qV/kT)][(AQF)JQNG0 + (1-AQF)JQNpQ]}. (2.1)
In (2.1), JqNGQ and are the dark saturation quasi-neutral current
densities of the good and poor areas of the cell, respectively. In the
good portion of the cell we are assuming that Jq^g is negligible compared
t0 JQSB- ThUS- JQNG0 JQNB0 ni VlnNAA 44 X A/C at C
where J.TT)^ is the dark saturation current density of the quasi-neutral
base as derived in [6], and is the electron diffusivity in the base.
In the poor portion of the cell we are assuming that Jq^g is negligible
compared to JQNE; thus JQNpo JqmQ. By defining JR JQNp0/JQNG0,
(2.1) may be rewritten as
I ~ A {Jsc -[exp(qV/kT)]JQNG()[AQF + (l-AQF)JR]}.
(2.2)
From (2.2), we calculate [Appendix I] and plot the open-circuit voltage
Vnp, the fill-factor FF, and the power conversion efficiency n as a
function of AQF with JR as a parameter in Figs. 2.3, 2.4, and 2.5,
respectively. These figures show that even a small poor-material area,
for example 5% (corresponding to AQF = 0.95) of the total solar cell
area, can drastically decrease the overall performance of the solar cell.
2 +
The parameter value JR = 10 corresponds to a silicon n -p thin-junction
solar cell with negligible recombination in the space-charge region,
Jscr <<: dqjyj* Tp,e surface of the good-quality subcell is covered by a

Voc/Voc
Figure 2.3 Normalized open-circuit voltage vs. areal quality factor.

FF/FF
O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Aq o o D ^TO T A L = AQF
Figure 2.4 Normalized fill-factor vs. areal quality factor.

Figure 2.5 Normalized power conversion efficiency vs. areal quality factor.

11
passivating thermal SiC>2> which yields a low surface recombination
velocity; and the surface of the poor-quality subcell is covered by an
ohmic contact.
2.3 Type 2 Areal Inhomogeneity
In this type of areal inhomogeneity, the p-type base lifetime and
diffusion length vary across the area of the cell for either of two
reasons: (i) as a result of large variations in the bulk recombination-
center density; or (ii) as a result of the presence of grain boundaries,
in which case T is an effective lifetime. The dark current JL4T1T, comes
n DARK
mainly from the junction space-charge region (SCR) and from the quasi
neutral base (QNB), whereas the short-circuit current Jg^, comes mainly
from the QNB. The shifting approximation then gives the illuminated
current density in each of the two subcells as
J JSC JDARK
(2.3)
= Jsc JQNB0[exp(qV/kT) 1] JSCR0[exp(qV/mkT) 1] (l in which the expression for J is derived in [7]. A simplified form
DARK
of (2.3), which follows from the Sah-Noyce-Shockley treatment of the SCR
recombination current [8] is
J = Jsc JQNB()[exp(qV/kT) 1] JSCR0[exp(qV/2kT) 1], (2.4)
where
SCRO
(2.5)
The details are given in Appendix III. The total illuminated current of
the solar cell is then

12
I AQF {USC)G (JQNBO^eXp^qV/,kT^ ^ ^JSCRO^G^eXp^qV//2kT^
+ (1 AQF) {(Jsc)p (JQNB0)p[exp(qV/kT) 1]
- (JSCR0)p[exp(qV/2kT) 1]}. (2.6)
To demonstrate this type of areal inhomogeneity, we let
3
=10 cm and, for the good portion of the cell, let
2
(L ). s 100 pm and (J__)= 25 mA/cm We assume that at any point on
no be u
the cell area Jc logCL ), where the constant of proportionality is that
bu XI
found in both experimental [9,10] and numerical [11] studies for
1 pm ^ L ^ 100 pm. We define the diffusion length ratio to be
n
DLR = (Ln)p/(Ln)g. From (2.6), we plot V^, FF, and q as a function of
AQF with DLR as a parameter in Figs. 2.3, 2.4, and 2.5, respectively.
Again, we notice that it is the poor-quality area of the solar cell that
_2
dominates the overall cell performance. The case for DLR = 10 corre
sponds to empirical observations by Schwuttke [12] that the generation
lifetime of silicon ribbon material (and thus the related defect density)
varies in a random fashion across the area of the ribbon by between four
and five orders of magnitude.
2.4 Discussion
The above treatment assumes several idealities: resistance and
fringing effects are neglected; the good and poor-material is concen
trated into two single-connected regions; the current flow in each region
is assumed to be one-dimensional. We now consider the effect of series
resistance on the illuminated solar cell.
In a solar cell with an adequate grid geometry, the dominant
component of series resistance will be that contributed by the bulk
material. This bulk component resists the current of majority carriers

13
that flow in from the contacts to support recombination with minority
carriers. In the poor-region of the cell, the recombination rate is
very high. Consequently, it is in the poor-region of the solar cell
where majority carrier currents, and thus series resistance effects, will
be most important. The series resistance must be included in the
parallel-subcell model if it causes a voltage drop which is a signifi
cant fraction of the terminal voltage. A two-parallel subcell model
that includes the series resistance has been considered [4,13]. The
significant finding in [4,13] is that the inclusion of the series
resistance has the effect of decoupling the subcells. This is because
the series resistance tends to suppress the currents flowing between
subcells. The result of this is that the degradation of solar-cell
performance is not as severe as that predicted when the series resis
tances are neglected. Estimation of the series resistance is given
in [4].
The idealization of two single-connected regions can be removed by
extending the two-parallel subcell model into an n-subcell model, where
n is sufficiently large to accurately describe the variation of material
properties across the area. A computer program that predicts the overall
performance of the solar cell when provided with the empirical parameters
of the subcells is given in Appendix II. A discussion of fringing
effects on the two-parallel subcell model is given in [4].

CHAPTER 3
A METHOD FOR EXPERIMENTAL ASSESSMENT OF THE SHIFTING
APPROXIMATION, WITH APPLICATION TO POLYSILICON SOLAR CEILS
3.1 Introduction
The shifting approximation that the illuminated current of a solar
cell is equal to the dark current shifted by the short-circuit photocur
rent is discussed in detail in [5,14]. We report here the results of an
experimental investigation of the validity of the shifting approximation
for four types of polycrystalline Si solar cells.
A solar cell may be thought of as a system with two inputs and two
outputs. The inputs are the optical generation rate in the base and the
excess minority carrier concentration at the edge of the space-charge
region in the base (if the recombination current in the quasi-neutral
emitter is negligible); the corresponding outputs are the short-circuit
photocurrent and the dark recombination current, respectively. It is
shown in [5] that the shifting approximation is valid if this system is
linear; in [14] it is shown that the shifting approximation may remain
practically valid despite some nonlinearity in the system. In a poly-
silicon solar cell, if the shifting approximation is not valid, it is
most likely because the system has been rendered nonlinear by the depen
dence of the material properties (e.g., the effective minority carrier
lifetime) on the illumination level or by the existence of a large series
or small shunt resistance. Recent data on the majority-carrier Hall
mobility in polysilicon material [15] indicate that the grain-boundary
potential barrier under illumination vanishes almost completely. This
14

15
suggests one possible origin of a dependence on illumination of the
effective minority carrier lifetime. Such a dependence would tend to
invalidate the shifting approximation.
The equivalent circuit diagram of a solar cell is shown in
Fig. 3.1. The shunt resistance is assumed to be large enough so that
the shunt current may be neglected. The combination of the current
generator and the dark diode constitute the intrinsic system [5] of the
solar cell. Even though the series resistance Rg may be large enough so
as to invalidate the shifting approximation for the overall solar cell,
it may nevertheless be the case that the shifting approximation is valid
for the intrinsic system of the cell. The approach taken here is to
measure the dark and illuminated I-V curves and then to compare these
curves after separating out the influence of Rg. (Shunt resistance for
these cells was determined to be large.) If, after the correction for
R the dark and illuminated I-V curves are identical except for being
O
shifted or translated by the short-circuit current Ig^,, then the
shifting approximation is valid for the intrinsic system of the solar
cell. It is this sense of the shifting approximation that we are
concerned with in this chapter. The validity of the shifting approxima
tion for a given solar cell considerably simplifies the theoretical
understanding of the performance of the cell, because then the dark I-V
characteristic and Ig^ can be considered separately [5].
3.2 Method for Analyzing the Measured I-V Curves
In Fig. 3.1, the voltage V across the terminals differs from the
voltage across the intrinsic system V^.g by a voltage drop across the
series resistance Rg. In the dark V = V^g + I^Rg, whereas under illumi
nation V = V^-g I^Rg. In Fig. 3.2, we illustrate qualitatively the

I 1
Intrinsic System
Figure 3.1 Equivalent circuit diagram of a solar cell. The dashed lines denote the intrinsic
system of the solar cell.

CURRENT (Arbitrary Units)
17
Figure 3.2(a) Schematic representation of the current-voltage depen
dencies of a solar cell.

CURRENT (Arbitrary Units)
18
Figure 3.2(b) Schematic representation of the current-voltage depen
dencies of a solar cell with all curves shown in the
same quadrant.

19
dependencies Ip V, IT V, and ISf, Vnf, for a solar cell. (Isr,)
SC OC
SC max
and (V) are the short-circuit current and open-circuit voltage at
the maximum illumination level of the Ig V^ dependence. Note that
the ideal (reciprocal slope = 1) Ig^, dependence is the I-V depen
dence of the intrinsic cell system, since Ig^ = I,, [exp(qVnfl/kT) 1] =
OC'
I [exp(qVTC/kT) 1], where I is the dark saturation current of the
o Jld o
cell. This is valid if Rg is small enough so that the externally
measured I is equal to the short-circuit current of the current gener-
bu
ator in Fig. 3.1. In general, the current-voltage dependencies will have
the following two properties: (i) the Ig^ V^ dependence will be
negligibly influenced by Rgj and (ii) the series resistance will shift
the I-V and Ip V curves to the left and right of the Ig^ V^c
curve, respectively.
It follows from the above discussion that the shifting approximation
will be valid if the series resistance R is independent of the illumina-
b
tion level, and if the I-V and I-V curves are symmetrically shifted
Li JJ
with respect to the Ig^, V^ curve. By symmetrically shifted we mean
that at any given current I ^ (I ) t^ie distance AV., between the
ID V and IgC VQC curves when the IgC VQC curve is shifted into the
first quadrant is the same as the distance AV£ between the 1.^ V and
Ic V curves when these two curves are rotated about the V-axis into
the first quadrant. This test for symmetry is shown in Fig. 3.3. Note
that the Ic Vn curves cross at (Ic ) /2 and, if symmetry holds,
dLi ol> max
then AV- = AV = AV at (I_) /2. The series resistance of the solar
1 / SC max
cell can then be calculated [16] as
Rg ^/[^scPmax/2] 2AV/[ ^SC^ax^ *

CURRENT (Arbitrary Units)
20
Figure 3.3 Illustration of the test for symmetry in the measured
I-V curves. The In curves cross at (I__) /2.
SC OC SC max
If the I-V curves are symmetric, then Aat any
given current I < (Isc)max >
1 (IscW2- "
and AV,
AV
AV at
9

21
To determine whether R is independent of the illumination level, we must
D
perform a second test which involves an independent determination of Rg
in the dark. This is done by a method employing small-signal admittance
measurements [17] at a frequency of 4 MHz with zero dc-bias. We then
compare this measured value of Rg with the value of Rg obtained from the
displacement of the curves. If the calculated and measured values of Rg
agree, then this would indicate that (i) Rg is independent of the
illumination level, and (ii) Rg is the only reason for the voltage
displacement of the curves in Fig. 3.3.
3.3 Experimental Procedure
The ID V, Ip V, and IgC VQp dependencies at 25.0C were
measured for the seven solar cells listed in Table 3.1. The illuminated
curves were obtained as tracings on an X-Y recorder by continuously
varying (with a helipot) the external load across the solar cell while
the cell was being illuminated by an Oriel solar simulator equipped with
an AMO filter. The level of illumination was varied from exactly 1 sun
intensity, which produced (I ) to about 1/3 sun intensity. Calibra-
b O THcL2C
tion was accomplished by using a single-crystal standard solar cell
(device No. 7) calibrated at the NASA Lewis Research Center. The dark
I-V curves at 25.0C were obtained by varying the dark diode current with
a digital current source and measuring the corresponding voltage across
the diode terminals. The experimental setup, for both the dark and
illuminated measurements (Fig. 3.4) used a four-point probe technique
so as to eliminate the effects of the contact resistance between the cell
and the measuring probes on the top, and between the cell and the vacuum
chuck on the bottom.

Table 3.1 The seven experimental solar cells for which the I-V dependencies were measured.
Device No.
Description
Total Area
(cm2)
Grain Diameter
(mils)
Source
1
n+-p 50 ym thick epi-layer grown on Dow
Corning grade 2P polysilicon substrate.
4.45
10 150
RCA
2
SnO^, on n-type Wacker polysilicon
substrate.
4.0
20 70
Exxon
3
Indium-Tin-Oxide on 0.1 0.3 fi-cm p-type
polysilicon substrate.
2.0
20 50
Colorado
State Un:
4
(25P4)
Phosphorus diffused on 5 ii-cm Wacker
polysilicon p-type substrate.
1.4
20 70
UF
5
(36P#28-L2)
Phosphorus diffused on 5 Q-cm Wacker
silicon p-type substrate. One grain bound
ary goes through the cell. This solar cell
is 30 mils in diameter and has an MOS guard
ring.
4.6 x 10-3
"15
UF
6
(36P#3-L1)
Same as No. 5, but with five grain bound
aries .
4.6 x 10-3
~6
UF
Diffused n -p single-crystal control.
7
2.0
Sandia

23
hv from solar simulator
.. ,
r >'
> Y
Solar Cell J <
Chuck
y
y v
(a)
(b)
Figure 3.4 Four-point probe experimental setup for investigating the
validity of the shifting approximation.
(a) Setup for measuring I -V and I -V p.
J-i bC O'-*
(b) Setup for measuring I^-V.
In both setups, X and Y are the voltage and current axes on
an X-Y recorder. The chuck is connected to a circulating
water bath. The temperature of the chuck is controlled by
the water bath and is measured by a thermocouple inside of
the chuck.

24
The small-signal admittance measurement for determining the value of
R at zero dc-bias in the dark was accomplished with an HP 4275A LCR
b
meter. The ac-signal was 10 mV. The values of the series resistance
determined by the small-signal admittance method and by the method of
comparing the dark and illuminated I-V curves are shown in Table 3.2.
3.4 Experimental Results
The symmetries exhibited in the I-V curves, Figs. 3.5 3.9, along
with the corresponding data on the series resistance, suggest that the
shifting approximation is valid for all of the devices measured. From
Table 3.2, note that the values of Rg for devices No. 5 and 6 are much
higher than those for the other devices. This is primarily because
devices No. 5 and 6 are much smaller in area than the other devices. If
we approximate the current flow as one-dimensional, then the value of Rg
2
for these two devices normalized to an area of 2 cm would be about
0.07 .
3.5 Discussion
As mentioned in Section 3.1, it is possible in polysilicon material
that the effective minority carrier lifetime will depend on the illumina
tion level. The likelihood of this dependency is increased if (i) the
illumination-induced lowering of the grain-boundary potential barrier
significantly changes the effective surface recombination velocity at the
grain boundary, and (ii) the intragrain base minority carrier diffusion
length L is greater than or equal to the average grain diameter d .
Thus, it is particularly interesting to investigate the validity of the
shifting approximation in polysilicon solar cells where L d_. All six
of the polysilicon devices in Table 3.1 have relatively large grain

25
Table 3.2 Values of series resistance by the small-signal admittance
method and by the method of comparing the dark and illumi
nated I-V curves.
Device No. Rg by small-signal
admittance method
(fi)
Rg by comparison
of the I-V curves
1
2
3
4
5
6
7
0.43
0.42
0.56
27
30
0.05
0.51
0.29
0.30
0.55
30
~50
0.05

26
Figure 3.5 I-V curves for device No. 1.

27
Figure 3.6 I-V curves for device No. 2.

28
VOLTAGE (mV)
Figure 3.7 I-V curves for device No. 3.

CURRENT (mA)
29
Figure 3.8 I-V curves for device No. 4.

30
(b)
Figure 3.9 Curve tracer photographs of the dark and illuminated I-V
curves for device No. 6. The symmetry of these curves is
displayed in this fashion rather than in the fashion of
Fig. 3.3 because the voltage displacement of the curves
is very small. Ig^ = 60 yA, = 467 mV.
(a) Dark I-V curve.
(b) Illuminated I-V curve.

31
diameters except device No. 6 (see Fig. 3.10) for which L d L was
determined by applying the method of [7] to the dark I-V dependence of a
small grain-boundary-free device and was found to be about 130 lim. For
the small grain-boundary-free device, I = 62 yA and V^ = 497 mV;
whereas, for device No. 6, IQ = 60 yA and V = 467 mV. The 30 mV
decrease in VQC resulting from the presence of the grain boundaries
corresponds to approximately a threefold increase in the dark recombi
nation current. These data show the degrading effect that the grain
boundaries have on the performance of device No. 6. We note, however,
that the shifting approximation remains valid for device No. 6 in spite
of the very strong influence of the grain boundaries on V. .
ULi
Though no general conclusions can be drawn from these experimental
results, they suggest that the nonlinearities introduced by illumination
levels of one sun are insufficient to invalidate the shifting approxima
tion in polysilicon solar cells. If this is true, then the simplifica
tions afforded to solar cell theory by the shifting approximation remain
intact for polysilicon. We emphasize that the experimental method
described here provides a general technique for assessing the validity
of the shifting approximation for solar cells made from polysilicon and
other material, including single crystal, polycrystalline, and highly
disordered semiconductors.

32
Figure 3.10 Microphotograph showing a top view of device No. 6. The
device is 30 mils in diameter and has five grain bound
aries going through it. The five small white circles
are the top ohmic contacts, and the white annulus is an
MOS guard-ring gate that overlaps the p-n junction dif
fusion edge.

CHAPTER 4
EFFECTS OF GRAIN BOUNDARIES ON THE CURRENT-VOLTAGE
CHARACTERISTICS OF POLYSILICON SOLAR CELLS
4.1 Introduction
The performance of polycrystalline solar cells is limited by the
effects of the grain boundaries (GB's) on the current-voltage (I-V)
characteristics. The I-V characteristics determine the efficiency of a
solar cell. Several theoretical models of the GB's and their influence
on the recombination currents have been published [18-23]. The purpose
here is to experimentally investigate the effects of the GB's on the
dark and illuminated I-V characteristics of polysilicon p-n junction
solar cells. The analysis of the experimental I-V characteristics, with
the help of the theoretical models [18-23], will lead to a determination
of the parameters which govern the recombination at the GB's. It will
also lead to a determination of the dominant GB current components.
Most experimental studies on polycrystalline solar cells have been
2
done on large area (~ 1 cm ) devices which, in general, contain hundreds
of GB's. Due to nonuniform distribution of the GB's and nonuniform grain
geometries, it is difficult to obtain reproducible results on such cells;
thus, an evaluation of the effects of the GB's and different fabrication
procedures on the performance of the cells is difficult. Moreover, poly
crystalline solar cells usually exhibit large leakage currents which can
mask the contribution of the GB's.
33

34
To overcome these difficulties, most of the work reported here was
done on small-area (30 mil in diameter) diodes which contain at most a
few GB's. On such devices the total length and the area of the GB's can
be found, and comparison among the devices can be easily made. The
length and area of the GB's have to be exactly known in order to derive
quantitative results concerning their parameters from the data. Large
area devices containing many GB's can be used mostly for qualitative
studies only.
To assure that the surface and edge currents are suppressed, the
diodes were fabricated with a thermally-grown silicon dioxide on the top
surface and an MOS guard-ring gate overlapping the edge of the diffused
layer, as shown in Fig. 4.1. The surface recombination current compo
nents, including the surface inversion channel current and the recombina
tion current through the surface states at the periphery and at the GB's
intersecting the edge of the diode, are suppressed by applying a suit
able gate voltage to the MOS guard-ring. The remaining current compo
nents are then only the bulk intragrain and grain-boundary components.
An additional and very important advantage of using small-size diodes is
the possibility of placing diodes inside of grains. This grain-boundary-
free (GBF) diode will then allow us to measure the properties of the
bulk of the grain and will serve as a reference diode for comparison
with a nearby diode containing GB's.
Diffusion of impurities into the polycrystalline material is
expected to proceed preferentially down the GB's [24-26]. The width and
average doping density of this enhanced grain-boundary diffusion region
is determined for the case of phosphorus dopant. Also, the current
components associated with the enhanced grain-boundary diffusion will be
discussed and analyzed here for the first time.

35
Gate
c
> <
>
/
l
1
X M V n+
7
iary
P type
^,Grain Boun
(a)
Figure 4.1 (a) Cross section of the 30 mil in diameter n -p solar cell
with MOS guard ring showing one columnar grain boundary
crossing through the middle.
(b) Top view showing five metal contact circles (5 mil in
diameter) and one grain boundary crossing the cell. The
total metal coverage is 20%.

36
4.2 Fabrication of Devices and Evaluation of Preferential Grain-Boundary
Diffusion
+ + +
Both n -p and p -n diodes were studied. The n -p diodes were
fabricated on 5 fi-cm p-type Wacker polycrystalline silicon substrates.
The phosphorus emitter was predeposited at 900C for 30 minutes followed
by a drive-in diffusion at 1050C for 40 minutes. Wet oxide about
O
3000 A thick was grown on the top surface during the drive-in step. The
junction depth x^ was 1.8 ym and the sheet resistance was 8 ii/square.
The p+-n diodes used 0.3 i2-cm n-type Wacker substrates. The boron was
predeposited at 900C for 25 minutes. The drive-in was done at 1000C
for 120 minutes resulting in a junction depth of 0.8 ym and sheet
resistance of 800 i)/square. The top surface was passivated by an SO2
layer, about 3000 thick, grown during the drive-in step.
In Fig. 4.2(a), a grooved and stained section [27,28] of an n+-p
diode shows a preferential diffusion of phosphorus down the GB's [24-26],
A copper staining solution was used. The preferential diffusion spike is
about 6 ym deep and is uniformly about 2.3 ym wide. (We refer to a
longitudinal cross-section, of a preferentially diffused grain-boundary
region as a diffusion spike.) It was determined by an investigation of
the cross-sections of the 15 mil thick substrate wafers that the GB's go
all the way through the material at an angle between 20 and 45 to the
normal [29]. This angle is referred to as a in Fig. 4.2(b). The GB
also cuts the groove at another angle which is referred to as 3 in
Fig. 4.2(b). Both of these angles were considered in calculating the
depth of the n-spike. No phosphorus preferential diffusion spikes were
observed after the 30 minute 900C predeposition step; however, we
measured 5-10 ym spikes after 48 hours heating at 600C after the
predeposition. For the p+-n diodes, no preferential diffusion spikes of

LO
''J
Figure 4.2(a) Grooved and stained section of the n -p junction showing preferential
phosphorus diffusion along the grain boundary. A copper staining solu
tion was used. The junction depth is about 1.8 pm; the depth of the
preferential diffusion is about 6 ym. A commentary on the reliability
of groove and stain results appears in Appendix X.

38
(b)
Figure 4.2(b) Diagram of a groove and stain sample showing the two
angles, a and 3, that define the orientation of the
GB-plane with respect to the substrate wafer. The spike
depth dn = d/cos a, where d is the depth for the plane
with a = 0; the angle 3 does not influence d^.

39
boron were observed for various diffusion schedules employing 900-1000C
for 20-120 minutes. In order to remove the uncertainties in delineating
the very narrow diffusion spikes by the groove and stain method, we have
developed an electrical measurement procedure which can positively
identify the presence or absence of a preferential diffusion down the
GB*s. This electrical measurement will also yield an average doping
density within the preferentially diffused region.
A test structure for determining the presence of preferential GB
diffusion is demonstrated for the case of n+-p mesa diodes made from a
wafer that received a 30 minute 900C phosphorus predeposition followed
by a 40 minute 1050C drive-in. As stated previously, for this diffusion
GB
schedule x. 3x. in the bulk. The mesa structures are formed by
J J
masking small dots on the top of the diffused wafer with wax or photo
resist and then etching off about a 2 pm layer of silicon. The etch
depth is just slightly in excess of x ^ This leaves about a 4 pm depth
of preferentially diffused GBs around the mesa diodes. Figure 4.3 shows
four mesa diodes, the top two of which are GBF, and the bottom two of
which are connected by a GB.
Two tests can be made on these mesa diodes. The first test, alluded
to above, is the measurement of conductance between the top two diodes
and between the bottom two diodes. The top two diodes represent back-to-
back n+-p junctions, and very little current will flow between them when
a bias is applied. The bottom two diodes, which are connected by the
diffused GB, constitute a structure similar to a JFET and will show a
current which is dependent on the conductance of the diffused GB channel.
For the second test, reverse-biased capacitance is measured between the
n+-diffusion layer and the p-type substrate. The capacitance measured

40
P- type
GB Conducting Channel
Figure 4.3 Test structures for determining the presence of a prefer
ential diffusion in the GB. The top two mesa diodes are
GBF; the bottom two mesa diodes are connected by a prefer
entially diffused GB conducting channel.

41
between one of the top two diodes and the substrate is merely the
capacitance of the GBF diode. The capacitance measured between the small
diode in the bottom pair and the substrate will be equal to the sum of
the capacitances of the two diodes on the bottom plus the capacitance
contributed by the diffused GB channel. Figure 4.4 shows the capacitance
of a 10-mil GBF diode and the capacitance of a 10-mil GB diode which is
connected by a diffused GB channel to a much larger GB diode.
Two conclusions can be made based on Fig. 4.4. First, the capaci
tance of the 10-mil GB diode is much larger than the capacitance of a
10-mil GBF diode at V = 0 V. This indicates that the diffusion sched-
K
ule used in the fabrication of these devices (30 minute 900C predeposi
tion followed by a 40 minute 1050C drive-in) resulted in a preferential
diffusion of phosphorus down the GB's. Such devices that share a common
GB will be electrically connected by that diffused GB. The 6 ym deep
preferential diffusion will increase the p-n junction area of the 10-mil
GB diode by only a few percent. This slight increase in the area cannot
account for the large value of capacitance at VB = 0 V, which is due
mainly to the contribution from the larger GB diode. Secondly, at
V_, 3 V, the capacitance of the 10-mil GB diode drops to the level of
the 10-mil GBF diode, and the two curves are identical for ^ 3 V.
The reason for this capacitance dependence on reverse bias is a widening
of the depletion layer in the channel by the reverse bias until the
channel is completely depleted. The GB-connected diodes thus become
electrically disconnected due to a depleted nonconducting channel.
This capacitance experiment also was done on n+-p devices made by a
30 minute diffusion at 900C and on the p+-n diodes. No capacitance
difference comparable to that exhibited in Fig. 4.4 was observed. This

CAPACITANCE (PF)
42
Figure 4.4 Capacitance versus reverse bias measured on the test struc
tures of Fig. 4.3. The insert shows the measured conduc
tance of the JFET-like channel between the two bottom GB
diodes of Fig. 4.3 as a function of voltage between the
diodes.

43
indicates that no inversion layer was created at the intersection of
the GB's with the silicon surface or along the GB's in the p-type bulk;
such an inversion layer could also lead to results shown in Fig. 4.4.
The stained width of the diffusion spike, Fig. 4.2(a) is about
2.3 pm. Based on a series of experiments (see Appendix IV) on both
f* f
n -p and p -n junctions, we concluded that the stained region using the
copper stain solution includes the p-n junction space-charge-region
(SCR) from both sides of the diffusion spike. Inside the spike, a GB
potential barrier is created due to the GB surface states [18,19]. The
reverse bias, V required to deplete the channel of width W (Fig. 4.5)
will have to push the edge of the p-n junction SCR to the edge of the
grain-boundary SCR. By using a linearly-graded junction approximation
for the p-n junction, we estimated that the average channel doping den-
16 3
sity is approximately 1 x 10 cm and Wn 0.5 pm. We assume
as a first approximation, that the width of the grain-boundary SCR is
independent of the reverse bias V .
R
The conductance test described above using the simple structure
created by black wax masking, which results in large spacing between
the GB diodes (~ 10 mil), will yield rather small channel current. It
was difficult to separate this channel current from the reverse leakage
current of the mesa diodes for the device with N ~ 10 cm The
conductance method is demonstrated here for another, more heavily doped,
structure diffused at 1050C for one hour which resulted in a preferen
tially diffused region 11 pm deep; the stained width of the n-spike was
about 3.6 pm and W 1 pm. The insert of Fig. 4.4 shows the measured
channel current of this JFET-like structure versus the applied voltage.
The existence of a large conductance confirms the occurrence of a

44
W
SCR
Figure 4.5 Section of an n+-p diode with a columnar GB and a preferen
tially diffused n-spike with depth d^. The broken lines
indicate the edges of the p-n junction SCR and the edges of
the GB potential barrier within the n-spike. For the polar-
GB GB
ities indicated, IrtATT) I_ and I.A7_ are negative currents.
LJMd d IJJNd
The p-n junction along the preferentially diffused GB is
modeled, as a first approximation, as having a square-well
shape with a one-sided step junction at the bottom of the
square well. A more accurate model for the diffusion pro
file along the GB is one in which the p-n junction appears
wedge-shaped with phosphorus dopant extending below the a-
pex of the wedge. In such a model, the phosphorus concentra
tion below the apex gradually diminishes to zero.

45
preferential diffusion. In addition, we can calculate the value of DD
from the linear portion of the channel current-voltage dependence and
geometry [30]:
NDD = G£GB/qUA 2 X 1017 cm"3
-3
where G 1 x 10 mhos is the conductance of the linear portion of the
-4
channel I-V dependence, 23 x 10 cm is the length of the channel,
2
U 400 cm /V-sec is the estimated electron mobility in the channel, and
-7 2
A 2.2 x 10 cm is the cross-sectional area of the channel. The gate
voltage between the p-type substrate and one of the GB diodes (source)
can be used to modulate the channel conductance and thus to study the
diffusion profile within the preferentially diffused region. also
can be estimated from the reverse gate bias required to deplete the
channel and decrease the channel current to zero; this was not possible
in this device because of the large and the wide channel.
4.3 Analysis of the I-V Curves
A solar cell under illumination is forward biased; the external
current is given by the photogenerated short-circuit current Ig^, minus
the dark current 1^, providing that the superposition principle is
valid [5], In the following discussion we will concentrate on the open-
circuit voltage Vq£ of the cell, and also on the dark current 1^, since
for many cells, V^ is degraded much more by the GBs than is Ig^, [31,32].
The illuminated I-V characteristics will be considered in more detail in
Section 4.3.3.
In order to analyze the I-V characteristics of GB diodes, we first
define and describe all current components. Figure 4.5 shows a cross-
section of a portion of the n"*"-p diode showing one columnar grain

46
boundary with the n-diffusion spike. We assume that the GB is perpen
dicular to the top surface. The presence of the GB and the diffusion
spike will result in dark current components in addition to those present
in the GBF device. All these additional components, shown in Fig. 4.5,
are designated by a superscript "GB''. The total dark current is equal to
the sum of all current components:
TGB _ T tGB tGB 4- 4- 4- T 4- V /t>^ (L 1 'S
ID XQNB + XQNE + ISCR + ISCR + ISCR' + *B + XQNB + XQNE + V/RSh* (4,1)
The dark current of the GBF diode is given by
ID IQNB + IQNE + ISCR + V/,RSh*
(4.2)
The current components in (4.1) and (4.2) are defined as follows: IqNB
and are the recombination currents within the quasi-neutral base
QNE ^
and emitter, respectively, and orginate from the lateral n+-p junction.
GB
I and E are the recombination components due to the carrier
SCR SCR
recombination in the bulk space-charge region (SCR) adjacent to the
lateral n -p junction, and adjacent to the n-diffusion spike, respec-
GB
tively. E is the recombination current at the GB within the
SCR
GB
SCR [23]; 1^ is the recombination current at the grain boundary adjacent
GB
to the quasi-neutral base (QNB) region; is the current component
injected from the diffusion spike and recombining within the QNB region;
is the current injected from the substrate into the emitter diffu-
QNE J
sion spike and recombining within the spike and at the GB surface; and
GB
R, and R, are the shunt resistances of the GBF and GB diodes, respec-
Sh Sh
tively. The components I^g, '*'QNE an<^ ''"SCR an(^ (^.2) are
nearly equal in a special case. Their equality requires that the
fundamental kinetic parameters (recombination-center density, capture

47
cross-sections, etc.) describing recombination in the bulk of the GBF
diode are the same as those relating to the bulk (as opposed to the GB
surface) of the GB diode under study. Additionally, (a) for I_
bCK
equality, the volume of the SCR straddling the lateral n+-p metallurgical
junction must be nearly the same for the GB and the GBF diodes; (b) for
Iq^B equality, the electron diffusion length in the quasi-neutral base
of a GB diode containing one GB must be much smaller than the diode
diameter d; and (c) for I ^ equality, the effective hole diffusion
length (which includes the influence of drift) in the quasi-neutral
emitter of a diode containing one GB must be much smaller than the diode
diameter.
The presence of current components associated with the GB will
result in a complicated two-dimensional current flow inside the diode.
The problem can be greatly simplified using an empirical relationship for
the measured I-V curve [7] which expresses the measured I-V dependence of
the GB diode as a sum of three terms:
rGB
rGB
GB.
Ij" = lJo[exp(qV/mpcT) 1] + I[exp(qV/kT) 1] + V/Rg", (4.3)
GB
GB GB
where 1^ is the lumped SCR saturation current component and m^ is the
GB
reciprocal slope factor of that component. *s t*ie lumPe current of all quasi-neutral current components, which have a reciprocal
GB
slope factor m = 1.0. The Ig is generally a function of injection level
in low injection [23], and its reciprocal slope factor m can be different
from m = 1.0. Hcwever, for very large surface recombination velocity
Sgg at the GB, which is the case for our devices as will be shown later,
GB
m = 1.0, and the Ig can then be lumped together with the other QN

48
components. Equation (4.3) is strictly valid only if one of the SCR
components in (4.1) is dominant or if all SCR components in (4.1) have
the same reciprocal slope factor.
Similarly for the GBF diode:
XD = IxotexpqV/n^kT) 1] + IQNQ[exp(qV/kT) 1] + V/R^. (4.4)
All I-V curves of diodes investigated in this work are described by (4.3)
or (4.4).
4.3.1 Space-Charge Region Current Components (n+-p diodes)
Figure 4.6 shows the measured dark I-V characteristics for five
representative n+-p diodes chosen from over 100 devices containing
either zero or a few grain boundaries. A summary including the total
length of the GBs and the parameters defined in (4.3) and (4.4) for
each of these diodes is shown in Table 4.1. A comparison of the data
for the GB diodes with the data for the GBF diode No. 1 shows the strong
effect of the GB's on the I-V characteristics. This is true even for
device No. 3 which had only one GB. The ratio of currents at 160 mV for
diodes No. 3 and No. 1 is about 40.
We now analyze the current components in the n+-p GB diodes by
comparing the I-V curves of these diodes with the I-V curve of a GBF
GB
diode, Fig. 4.6. The GB component of IQ can be obtained by subtracting
the measured current of the GBF diode from the measured current of the
GB
GB diode, i.e., I "In* However, we observe that the GB components
D
dominate the current at small biases, below about 300 mV. In this range
GB
m^ m^ -1.8; therefore we can write:
t^UOO 300 mV) lR + 4Br, + Vrt
(4.5)

CURRENT (A)
49
Figure 4.6 Measured dark I-V curves for five n -p solar cells: a GBF
cell (No. 1), a cell containing twins only (No. 2), and
three GB cells (No. 3, 4, and 5).

Device No
1
(36P//13-L2)
2
(36P/M-L1)
3
(36P#28-L2)
4
(36P25-L1)
5
(36P#3-L1)
6
(34P#4-L2)
7
(34P#1-D1)
8
(34P#1-L1)
Table 4.1
Parameter values
for devices
No. 1-
-8. T =
25.0C, A =
4.6 x 10 ^ cm2.
Type
Description
£gb
(mils)
I i
xo xo
(A)
GB
V x
I I^B
QNO QNO
(A)
SGB
(cm/sec)
+
n -p
GBF
0
2.1 x
10 12
1.18
9.7 x 10-14
+
n -p
twins only
160
4.8 x
lo"12
1.29
-13
1.6 x 10
65
+
n -p
one GB
25
4.0 x
io"10
1.83
2.5 x IO-13
3.4 x 10
+
n -p
several GB's
85
9.9 x
10-10
1.84
2.4 x IO-13
2.5 x 10'
+
n -p
several GB's
150
5.7 x
io-10
1.76
-13
3.4 x 10
8.2 x 10
+
p -n
GBF
0
1.1 X
io-9
2.0
5.1 x IO-14
+
p -n
twins only
75
1.8 x
io"10
1.88
-14
2.0 x 10
+
p -n
several GB's
60
7 x
io-10
1.94
3 x IO-14

51
GB
The recombination in the SCR adjacent to the n-diffusion spike I was
bCR
analyzed by Sah-Noyce-Shockley [8] and is, in fact, just an extension of
the I._ of the GBF diode. The area of the n-spike is A = 2iL,TJd where
SCR r n GB n
is the total length of the GB's in a diode and d is the GB
preferential diffusion depth. For the GB diodes No. 2-5 in Table 4.1,
2 -3 2
An A, where A = ird /4 4.6 x 10 cm is the top area of a 30-mil
GB
diode, and thus I0 can be neglected. This component could be impor-
bGR
tant in solar or metallurgical grade material where the impurities can
be segregated at the GB's resulting in a very short lifetime in the SCR
GB
adjacent to the n-spike and a large Ig ,. The recombination current at
the GB within the SCR can be expressed as [20,23]
tGB ^ .GB / GB. v
XSCR ASCR (lniSGBeXp^qV/,II1X kT^
(4.6)
where S is the GB surface recombination velocity at that part of the
UD
GB
.GB
21 is the approxi-
GB adjacent to the bulk, m^. 2.0, and AgCR GB"SCR
mate area over which the GB recombination current is described by
(4.6) [23]. is the SCR width of the GB barrier [18,19]. This cur
rent component is proportional to n.. Such a current will have an acti-
GB
vation energy of one-half of the bandgap (E /2). l!f was measured for
(jr D
the GB devices in the temperature range from 222K to 286K. The slope
factor m^ was almost constant in this temperature range. Figure 4.7
GB
shows the IR versus 1/T plot yielding activation energy
GB
E 0.59 eV Ep/2. This result very strongly suggests that I is
a. bGR
the dominant GB recombination component at small biases below about
PT
300 mV. The theoretical analysis [23] of Icor>, based on idealizations,
bLK
GB PR
predicts m^. =2.0. Our data give m^. m^. = 1.76 1.84 at 25C with
GB
most of the devices having 1.8. By using (4.6) and an estimate of

CURRENT (A)
52
Figure 4.7 The dark current of a GB diode measured at 150 mV versus
1/T showing an activation energy E = 0.59 eV E /2.

53
GB
^SCR ~ we can calculate the approximate values of S^g. The
results in Table 4.1 indicate that electrically active GB's do not have
GB
a uniform S. By using the values for 1^ Ior,n, where
GB*
SCRO
rr GB
K = Ac qn.S T3, we can calculate the average current per unit
bGKU bGK 1 GB
GB *"13
length of GB, 4.6 x 10 A/ym, with the average slope factor
oGK
GB
m^ nigQ^ 1.81. These two average values can then be used to predict
the behavior of the I-V curves for different grain sizes. The average
GB recombination velocity for devices No. 3-5 is S,,,, 2.2 x 10 cm/sec.
GB
The device No. 2 which contains only twin boundaries is almost identical
to the GBF device.
4.3.2. Quasi-Neutral Region Current Components (n*~-p diodes)
GB
Each value of Iq^q> Table 4.1, which includes the QN components
GB
plus the Ig from (4.1), is an increasing function of £^g, as expected.
Iqnq fr the GBF diode is a function of only the doping density in the
p-type substrate and the minority electron diffusion length. The I^g
can be neglected because of the low doping density in the base
Naa 3 x 1015 cm ^ [7], The diffusion length Ln 130 ym in the GBF
diode was obtained from the QNB component of the dark current [7]. In
the small area devices, such as the 30 mil diodes used in this work, the
two-dimensional spreading effects will be important if the radius d/2 is
comparable to the diffusion length Ln [33]. For the GBF diode, the
radius of the diode is d/2 = 380 ym > L^, which will assure almost one
dimensional current flow; but for the 30 mil diodes with several GBs,
the grain size could be comparable to the electron diffusion length and
the injected electrons will combine within the grain and at the GBs.
The recombination current in the device can then be described by
Shockley's filament theory [34]:

54
ZQN ^piqV/kl)
(4.7)
where A_ is the grain area and T is the effective electron life-
time [34] which includes recombination within the grain and at the GB's.
The effective lifetime can be calculated exactly from (4.7) for columnar
grains with rectangular or cylindrical geometry [34]. This is not the
case for the Wacker polycrystalline silicon material. We can, however,
GB
estimate an average effective electron diffusion length in the poly
crystalline material by measuring the X-ray induced current [35] on a
large area polycrystalline cell and then comparing this current to the
response of a single-crystal cell with known diffusion length. The
2 +
experiment used a 2 cm polycrystalline n -p cell with average grain
GB
size of 500-1000 ym and yielded IT 70 ym which is smaller than
L 100-130 ym for the GBF diode. This result demonstrates that the
n
effect of the GB's on the electrons injected from the top n+-p junction
in diodes No. 2-5 cannot be neglected. In addition, the GB's will
contribute to the Iq^q because of the preferentially diffused n-region
which increases the total area of the p-n junction and contributes
additional current components, as was discussed in Section 4.3.1. The
GB
separation of I ^ as defined in (4.3) into components for the general
case requires solution of a two-dimensional boundary value problem which
is beyond the scope of this work. We can, however, approximately
accomplish this for our devices by considering the components separately
GB
and identifying the dominant one. Neglecting there are three quasi
neutral current components associated with the grain boundary: I
GB GB
'QNE an<^ *B nOW cons:^er each f these components.
GB
QNB*

55
4.3.2.1 I
GB
QNB
-GB
The IqjjB component is due to the electrons injected from the prefer
entially diffused vertical GB region with an area into the base.
This current component, coupled with the electron current injected from
the top lateral junction with an area A, will result in a two-dimensional
current flow in the base. An accurate solution of such a two-dimentional
PR
problem is not presently available. If, however, An A, then IqNB can
be neglected. Considering our n+-p devices from Fig. 4.6 and Table 4.1,
the ratio A^/A is largest for device No. 5 and is only about 0.1. Thus,
GB
as a first approximation, we will neglect in further analysis of
GB
our devices. *q^b will be important for devices with large depths of
preferential diffusion in the GB.
PR
4.3.2^2. Xand GB Passivation
QNE
GB
IqNE "^S ^Ue t0 t^ie k^-es injected from the p-type substrate into the
preferentially diffused region of the GB and recombining inside that
region. The current transferred through the narrow n-spike, Fig. 4.5,
can be treated in a way similar to the current transferred through a
narrow emitter region of a solar cell. A detailed investigation of this
problem was done by Shibib et al. [36]. The recombination current in
the n-spike will be a function of the hole lifetime T in the bulk of
P
the spike, the hole transit time t through the spike, and the surface
recombination velocity S^B at the GB inside the spike. The transit time
can be expressed as [36]
T (W2/2D ) + (W /SG
t n p n p(eff)
(4.8)

56
where is the average diffusion coefficient corresponding to the
average doping density DD in the preferentially diffused GB region, Wn
is the width of the QN region of the n-spike, and is the effec
tive recombination velocity for holes at the edge of the GB SCR in the
n-spike [18,23]. We will assume now that xt << and check later for
self-consistency. For xt x the n-spike will be transparent to the
injected minority holes and the saturation current of the holes
recombining at the GB surface is [36]
GB
QNEO
2
GB
WV^^^pCeff)) + W]1-
(4.9)
This current has to be separated from two other I components:
T A XGB
XQNB and XB
GB
We approach this problem by calculating from (4.9).
IjJNrjO
GB ti
This requires a knowledge of Bp(ef£)* Let us assume that inside of
the n-spike is equal to the surface recombination velocity at that part
of the GB adjacent to the bulk, S
Table (4.1). From [18,23]:
GB*
GB
is obtained from I_, in
vjJo A
Sp(eff) SGB exP(q^g/kT),
(4.10)
where (¡>B is the barrier height of the GB-SCR. By using the estimate
<}>B 0.12 V for a forward-biased diode at 25C, we obtain
GB 6
S (eff) 1 x 10 cm/sec. By using this value in (4.9), along with the
16 -3 2.
values __ 1 x 10 cm D 11 cm /sec, and W 0.4 ym, we obtain
DD p 7 n
GB -~13
IqNeq ~ 2 x 10 A for the device No. 5. This value is close to the
GB
measured value of I^NQ (see Table 4.1), which implies that I^NE can
dominate the dark current of the GB diodes if the preferentially
diffused GB regions are lightly doped and Sa is large.

57
GB GB
Note, however, that ^g^gg expC^V/kT) is a one-dimensional
current linearly dependent on the total length of the GB's in the diode,
GB GB
since A = 2JL,T)d Therefore, if I- dominates the Inxrn of the n -p
n GB n QNEO QNO
GB
devices in Fig. 4.6 and Table 4.1, then IqNQ should be a linear function
GB
of The measured IzL^ is, however, much less than linearly depen-
GB QNO
dent on compare, for example, diodes No. 3 and No. 4 in Table 4.1.
GB
GB GB
This implies that the 1^ is dominated by Ig^g and We can thus
-GB
rGB
make a reasonable estimate that ~ 0.1 I_.T_.
QNEO QNO
B *
Then for device
PR A
No. 5, (4.9) implies that Sp(eff) ~ 4 x 10 cm/sec, and (4.10) implies
that sJL 400 cm/sec. This suggests that the recombination velocity of
the GB was lowered by the diffusion of phosphorus into the GB. Similar
conclusions are also valid for other devices investigated.
GB
We now use the above calculated value for S in (4.8) and
p(eff)
obtain T. ~ 0.1 ]isec. Thus, our assumption that T T is reasonable
t t p
16 3
for a relatively low doped n-spike, such as NQD ~ 10X cm found in our
devices.
4.3.2.3.
I
GB
B
Ig is the electron current recombining at the GB adjacent to the
QN base. This component will not be linearly proportional to due to
GB
the two-dimensional nature of the electron current flow injected from
GB
the top junction. The importance of Ig will depend on the grain size
dp, the electron diffusion length L and the surface recombination
ij n
velocity Sgg. Its influence on the total quasi-neutral current, Iqjj>
as defined in (4.3) and (4.7) can best be demonstrated by the dependence
f Tn(eff) on these parameters. For our devices with large
4
S ~ 10 cm/sec, we can write [23,37]:
GB

58
1/T(eff) "V'1 +
(4.11)
For d L T ,-,-v T and Irt.TT, dominates; for small d_, T < T
G n n(eff) n QNB G n(eff) n
GB
and Ig becomes important. For device No. 5 with diameter d = 760 pm
and five GB's, the approximate grain size is d 150 pm and
G
Tn(eff) ~ 0*9 Psec. This value is to be compared to Tn 6 psec,
GB
corresponding to Ln 130 pm for the GBF diode No. 1. For 1^ to be
important, the intragrain base electron diffusion length, Ln> has to be
larger than the preferential diffusion depth d^ 4 pm. From our
GB
experiment we found 130 pm d^. The effect of 1^ will obviously
increase with decreasing d
n
4.3.3. Illuminated I-V Curves (n -p diodes)
Table 4.2 shows the summary of results of measurements on illumi
nated diodes. The short circuit current Ig^ is almost constant except
for device No. 5, but V_,_, decreases slightly with increasing nT¡. This
UG GB
is consistent with previous results [31,32] and also with a recently
proposed model [38] for devices with grain size d^ > Ln. The decrease
GB
in Vnr, is due to increased IG which is directly proportional to ,
UG oLK GB
GB
and also due to increased 1^ The slight decrease in Ig^ for device
No. 5 is because, in this device with five GB's within the 760 pm diode,
the average grain size is comparable to 130 pm; thus, some of the
light-generated electrons will recombine at the GB's and will not
contribute to the external measured I .
DG
The preferentially diffused n-regions can contribute to the I if
BG
d ~ L For the devices studied, d L and no increase in I__ is
n n n n SC
observed for the GB diodes. The fill factor decreases with as
GB
expected due to the increasing importance of 1^ with m^. > 1.0.

59
Table 4.2 Parameter values for devices No. 1-8 while under 1 Sun AMO
illumination. T 25C, A = 4.6 x 10-3 cm2.
Device No. IgC VQC FF
(yA) (mV)
62
497
0.81
62
497
0.80
63
489
0.78
63
485
0.75
59
467
0.77
75
494
0.78
73
480
0.78
75
496
0.78
8

60
Another important consideration for the preferentially diffused
n-regions is the possibility of pinching-off the narrow-n-channel due to
the current passing through it. The detailed description of current flow
through the n-region, both in the dark and under illumination, is very
complicated; but we can roughly estimate the current required for pinch-
off. As a first approximation we will assume that the current leaves or
enters the n-region at a distance d^/2 from the top n+-p junction, i.e.,
in the middle of the n-region. We can then treat this n-region as the
channel of a JFET with floating drain and calculate the saturation
current of the n-region channel for our geometry and parameters [30].
This approximation gives I 2mA. The available I for 1-sun AMO
SSL DL*
conditions for the 30 mil diameter device is only about 0.14 mA [31].
This indicates that the preferentially diffused n-region will not be
pinched-off at 1-sun, even if the entire photogenerated current is
collected by this region. The n-region, however, could be pinched-off
at high concentrations of illumination or in devices which have narrower
W or lower I also can be directly measured by using the
conductance method on suitable structures shown in Fig. 4.3. This
measurement is demonstrated in the insert of Fig. 4.4.
The device No. 2 which contains only twins has about the same
and Igc as the GBF diode.
The n+-p diodes in Tables 4.1 and 4.2 are representative illumi
nated diodes (solar cells) from Run 36P. Parameter values for additional
diodes in Run 36P are presented in Tables 4.3 and 4.6. The fabrication
schedule for Run 36P is presented in Appendix VIII.

Table 4.3
Parameter values for additional
^RO XX0- T = 25*C A 4
diodes in Run
-3 2
.6 x 10 cm .
36P
Diode
Description
£gb
(mils)
I IGB
xo xo
(A)
GB
V x
I IGB
QNO QNO
(A)
SGB
(cm/sec)
36P#10-D1
GBF
-13
8.2 x 10
1.17
6.1 x
lo"14
36P#4-D1
twins only
100
4.7 x 10-12
1.32
1.4 x
io-13
8.4 x 10'
36P#14-D2
one GB
45
1.9 x 10_1
1.64
4.1 x
10"13
1.0 x 10
36P//9-D1
several GB's
45
2.4 x 10-1
1.71
1.9 x
io-13
9.2 x 10
36P#1-D2
several GB's
65
2.6 x 10-1
1.70
2.4 x
10-13
8.8 x 10
36P#34-Dl
several GB's
65
7.4 x 10_1
1.80
1.9 x
io-13
2.4 x 10
36P#8-L1
one GB
30
3.8 x 10-1
1.73
1.4 x
io-13
2.6 x 10
36P#9-L2
several GB's
65
9.2 x 10_1
1.81
2.2 x
io-13
3.0 x 10
Averages for
the GB diodes
GB diodes including
in Table 4.1:
64
c o ,n-10
5.2 x 10
1.76
2.5 x
10-13
2.0 x 10

62
4.3.4 Grain-Boundary Passivation by Hydrogenation Treatment
Tables 4.4 and 4.6 present parameter values for the n+-p diodes in
Run 37P. The Run 37P diodes underwent the same fabrication schedule as
the Run 36P diodes, except for an additional processing step [39] that
was intended to tie up dangling bonds along the grain boundaries with
monoatomic hydrogen [39,40]. After the 37P wafer had undergone the
drive-in step, the oxide grown during the drive-in was covered with a
6000 layer of vacuum-evaporated aluminum. The wafer was then sintered
at 450C for 12 hours in dry N£. The aluminum was then removed by
chemical etchant and the processing of the wafer was continued as in
Run 36P. This additional processing step is known to tie up dangling
bonds at the S-SO2 interface in MOS devices by the generation of some
form of active hydrogen at the SO2-AI interface [41]. By following
this procedure, we were able to use the diodes of Run 36P as a control
group for determining the effect of the hydrogenation step on the diodes
of Run 37P. The 37P wafer was not sintered after the ohmic contacts were
formed so as to avoid out-diffusion of the hydrogen from the GB's [39],
A comparison of the values of for Run 37P in Table 4.4 with
the values of for Run 36P in Table 4.3 shows that the hydrogenation
step has a negligible effect on S^. By applying both the method of [7]
and the method of [35] to several GBF diodes in Run 37P, it was deter
mined that the hydrogenation step lowers the intragrain base minority
carrier diffusion length Ln from about 130 pm to about 90.yin. This
lowering of Ln is reflected in the I-V characteristics shown in Fig. 4.8.
In agreement with the data reported in [39], Table 4.6 indicates that
the hydrogenation treatment slightly increases V^. This conclusion is
not firm though, because the increase observed averaged only 11 mV and
the spread of values of VQC was large.

Table 4.4 Parameter
values
for diodes in Run
37P.
T = 25
.0C, A
= 4.6 x 10 3
2
cm .
Diode
Description
GB
Ixo1
GB
XO
GB
V x
]
.GB
SCRO
GB
mSCR
IQN0
GB
QNO
SGB
(mils)
(A)
(A)
(A)
(cm/ sec)
37P#11-D2
GBF
4.0
,n-12
x 10
1.19
1.3 x
io"13
37P#12-Dl
GBF
7.5
m12
x 10
1.30
8.1 x
io-14
37P#2-D2
several GB's
140
1.3
in10
x 10
1.63
1.3
X
lo"10
1.67
4.1 x
io-13
2.0 x
io3
37P#1-Dl
several GB's
75
2.4
ln-ll
x 10
1.69
2.5
X
lo"10
1.75
4.3 x
io13
7.2 x
io3
37P#5-D2
several GB's
35
5.4
in"10
x 10
1.94
5.8
X
lo"10
2.02
2.9 x
io-13
3.6 x
io4
37P#9-D2
several GB's
90
8.0
in-n
x 10
1.59
8.5
X
io-11
1.71
2.3 x
10-13
2.0 x
10 3
37P//10-D1
one GB
20
1.7
in"10
x 10
1.61
1.8
X
10-10
1.67
4.0 x
io-13
1.9 x
io4
37P//2-L1
one GB
80
6.7
x 10-11
1.57
6.9
X
io"11
1.69
4.8 x
io-13
1.8 x
io3
37P#6-L1
several GB's
68
1.8
x 10-9
2.03
1.9
X
10-9
2.08
3.1 x
10-13
6.0 x
10 4
37P#8-L1
several GB's
150
3.5
x 10-9
2.01
3.6
X
10-9
2.05
3.8 x
io-13
5.2 x
io4
37P#11-L1
several GB's
50
3.6
in"10
x 10
1.93
3.9
X
io-10
2.03
4.8 x
io-13
1.7 x
io4
Averages :
for GB diodes:
79
7.4
in"10
x 10
1.78
8.0
X
io-10
1.85
3.8 x
io-13
2.2 x
io4

CURRENT (A)
64
VOLTAGE (V)
Figure 4.8 Measured dark I-V curves of two GBF n -p solar cells
showing the effect of the hydrogenation treatment on the
intragrain base minority carrier diffusion length, L .
The solar cells had identical fabrication schedules ex
cept that the cell represented by the upper curve under
went the hydrogenation treatment. This treatment lowered
L^ from about 130 ym to about 90 ym.

65
Figure 4.8 also displays the effect that the absence of sintering
of the ohmic contacts had on the series resistance of the 37P diodes:
the extra series resistance of the 37P diode causes the I-V curve of
that diode to bend to the right and cross the I-V curve of the 36P
diode.
4.3.5 I-i-V Characteristics (p+-n diodes)
Figure 4.9 shows the measured I-V curves for two representative
p -n diodes; device No. 6 is a GBF diode; device No. 8 is a GB diode. A
summary of parameters for these two diodes and for diode No. 7 which
4-
contains only twins is in Tables 4.1 and 4.2. In contrast to the n -p
diodes, the effect of the GBs on diode No. 8 is very small. This is
evident both from Fig. 4.9 and Tables 4.1 and 4.2. The intragrain hole
diffusion length for the GBF p+-n diode No. 6, obtained from the dark
I-V curve [7], is 35 pm. Thus, for the GB diode No. 8, dG L ,
and the effect of the GB's on Iq-^q is negligible. At small bias levels
the SCR recombination currents are dominated by the recombination in
"f" GB
the SCR adjacent to the top p -n junction, IgCR and IgCR is negligible.
With several ideal assumptions (Appendix III), the Sah-Noyce-Shockley
theory [8] allows IgGR to be written as
FSCR ^AqWSCR.ni/(2TSCR> ]exp(qV/mkT),
(4.12)
where TgGR is the time constant controlling the recombination in the
SCR at small bias levels, and m 2.0. Using (4.12) we find
tscr ~ 0,2 psec for the p+-n GBF device No* 6 and tscr ~ 100 Psec for
the n+-p GBF device No. 1. This comparison of values for TcrtT, and also
oLK
a comparison of with explains the insensitivity of parameters in

CURRENT (A)
66
VOLTAGE (V)
Figure 4.9
Measured dark I-V curves for two p+-n solar cells: No
is a GBF cell, No. 8 is a GB cell.
6

67
GB j-
Tables 4.1 and 4.2 (including I and V ) to the GBs in the p -n
Xu oc*
diodes. The grain size of p+-n diodes would have to be comparable to
1.^ 35 ]im in order to observe the effects of the GBs on the I-V curves.
4 *4*
The other important difference between the n -p and p -n diodes is
that no preferential diffusion of dopant impurity (boron) was observed
in the p+-n diodes. The differences in the values for and I_. for
XO QNO
the p"*-n devices in Table 4.1 are due mainly to the measured variations
16 -.3 15 3
in the base doping density (N^ 1.3 x 10 cm 2.6 x 10 cm J).
Notice also that the device No. 7 containing only twins is very similar
to the other two p -n diodes. Values for Ig^ are slightly higher for
the p+-n diodes than for the n+-p diodes because of the shallower
p+-junction depth of 0.8 ym compared to 1.8 ym for the n+-junction depth.
The p+-n diodes in Tables 4.1 and 4.2 are representative diodes
from Run 34P. Parameter values for additional diodes in Run 34P are
presented in Tables 4.5 and 4.6. The relative scattering of values for
these diodes (as opposed to the Run 36P n -p diodes) is attributed mainly
to the measured variation in base doping density.
4.3.6 Grain-boundary Shunt Resistance R
GB
Sh
The shunt resistance effects on the I-V curve will be most effective
at very small biases. An analysis of the I-V curves in the voltage
+ +
range of about 0-300 mV for both the n -p and p -n GBF and GB diodes
shows that the measured curves can be described by Iaexp[(qV/m^kT) 1]
i.e., they follow exactly an exponential dependence for a certain
p-D
constant slope factor n^. This indicates that the V/Rgh term in (4.3)
GB GB
and (4.5) can be neglected and Ggh = l/R^ 0. This is an important
Sh
conclusion regarding the shunt resistance. The effects of R01 on I-V
bn
curves can be confused with the effects of I^L or the edge effects.
SCR

Table 4.5
Parameter values
for additional diodes
in Run 34P. T
= 25.0C, A = 4.6
x 10-3 cm2.
Diode
Description
GB
(mils)
T IGB
XO* XO
(A)
GB
V x
I IGB
QNO QNO
(A)
34P#4-Dl
GBF
5.3 x 10-11
1.58
3.0 x 10-15
34P#9-D1
GBF
5.5 x 10-10
1.93
-14
5.1 x 10
34P//1-D1
twins only
70
.10
1.3 x 10
1.88
-14
2.0 x 10
34P#11-D2
one GB
90
1.2 x 10-1
1.74
-14
7.0 x 10
34P//1-D2
several GB's
40
2.8 x 10_1
2.06
-14
2.8 x 10
34P//3-D1
several GBs
50
5.7 x 10-10
1.72
2.4 x 10-14
34P//3-D2
several GB's
55
3.0 x 10"10
1.90
-14
3.2 x 10
34P//5-D1
several GB's
30
3.0 x 10_1
1.79
-14
1.8 x 10
34P#6-D2
several GB's
40
7.3 x 10-1
2.19
-14
5.4 x 10
34P#1-L2
several GB's
35
2.9 x 10-1
1.97
-14
1.4 x 10
Averages for GB diodes including
the GB diode in Table 4.1:
50
4.1 x 10_1
1.91
-14
3.4 x 10

Table 4.6 Summary of Ic and V for all 30-mll diameter solar cells.
bu UU Q ry
T = 25.0C, A = 4.6 x 10 cm 1 Sun AMO.
Run
Type
Number of
Diodes
Measured
VQC spread
(mV)
VQC average
(mV)
Igc spread
(pA)
Igc average
(pA)
34P
GBF
p -n 4
471 -
522
494
73 -
76
75
Twins
1
480
73
GB
12
451 -
558
496
66 -
84
75
36P
GBF
n -p 7
478 -
504
495
61 -
75
67
Twins
1
496
65
GB
12
466 -
491
481
59 -
74
68
37P
GBF
+
n -p
0
Twins
0
GB
7
468 502
492
64 82
70

70
However, the use of a structure with an MOS guard ring and the careful
analysis described above shows that the GB's in diffused p-n junction
polycrystalline solar cells made on Wacker material do not cause notice
able leakage effects due to the GB shunt resistance. This conclusion
is also supported by measuring the I-V curve in the reverse direction
which shows negligible current between zero and about IV of reverse
bias.
4.4 Comparison of Mesa Diode and Planar Diffused Diode I-V Curves
Prior to the fabrication of the 30-mil n -p and p -n planar diffused
diodes described in this chapter, we fabricated (Appendix VI) 50-mil n+-p
GB
dark mesa diodes and attempted to isolate the GB-component of 1^ by
GB
the method of subtracting IQ from 1^ ., The I-V measurements on these
mesa diodes tended to be instable and unreliable because of the surface
and edge leakage currents described in Section 4.1. In particular,
the leakage currents caused the measured values for the current densi-
GB
ties Jp and in the low voltage range (0-300 mV) to be as much as
three orders of magnitude higher for the mesa diodes than for the planar
diffused diodes. The mesa diodes also tended to have higher measured
GB
values of m^. and m^ (often approximately 2.0) than did the planar
diffused diodes. Since, for the 50-mil mesa diodes, the measured current
in the low voltage range (0-300 mV) was predominately leakage current,
it was not possible to isolate and accurately analyze the GB-component
GB
of I for these diodes. As described in Section 4.1, the surface and
edge leakage currents are suppressed in the planar diffused diodes by
the use of an oxide on the top surface and an MOS guard-ring gate over
lapping the edge of the diffused layer.

71
Figures 4.10 and 4.11 show the effect of leakage current on the J-V
characteristics of 50-mil n"*"-p mesa diodes. The leakage current of the
GB
GB mesa diode in Fig. 4.11 causes the measured value of I and conse
quently, the calculated value for S^, to be erroneously high. By the
method of Section 4.3.1, S is calculated to be 1.5 x 10* cm/sec. This
value exceeds the corresponding values for all of the n+-p diodes in
Tables 4.1 and 4.3 by more than a factor of four. Though can vary
significantly from diode to diode (Tables 4.1 and 4.3), the above
comparison demonstrates the questionable value of I-V measurements on
GB
small mesa diodes in analyzing the GB-component of 1^ Some researchers
have failed to notice this point [42]. In Fig. 9 of [42], for example,
GB
the I-V curves of 50-mil mesa diodes display values of >2.0, which
indicates that the current at low bias levels is dominated by recombina
tion at the surface around the perifphery of the diode [43]; and,
consequently, these I-V data are of little analytical use.
Surface leakage current is proportional to the circumference, and
thus to the radius r of the diode; whereas, the current of a leakage-
2
free diode is proportional to the area of the diode, and thus to r .
Consequently, in a mesa diode, the relative contribution of the surface
leakage current to the total measured current will increase as r
decreases. As seen in Fig. 4.10, for a mesa diode with r 25 mils,
the leakage current can dominate the total measured current at low bias
levels (0-300 mV).
4.5 Discussion
This chapter has described and analyzed the effects of GB's on the
performance of polysilicon p-n junction solar cells.

CURRENT DENSITY (A/cm )
72
VOLTAGE (V)
Figure 4.10 Measured dark J-V characteristics of GBF mesa and planar
diffused diodes showing the effect of leakage current on
the low-voltage current density and on the reciprocal
slope m^. of the mesa diode. Diode 4P2~l,3,f is a mesa
diode; diode 36P//10-D1 is a planar diffused diode with
an MOS guard ring.

CURRENT DENSITY (A/cm )
73
Figure 4.11 Measured dark J-V characteristics of GB mesa and planar
diffused diodes showing the effect of leakage current
on the low-voltage current density and on the reciprocal
GB
slope m^ of the mesa diode. Diode 4P2-4,8,f is a mesa
diode with 300 mils of GBs; diode 36P//1-D2 is a planar
diffused diode with an MOS guard ring and has 65 mils of
GBs. The leakage current of the mesa diode causes the
GB
measured value of I and consequently, the calculated
xo
value for S to be erroneously high.
GB

74
In order to obtain quantitative results about the GB-recombination
currents in the bulk of the cell, care must be exercised to eliminate
surface and edge-leakage currents. In our devices (30-mils in diameter)
this was accomplished by fabricating the diodes with a thermally-grown
SO2 on the top surface and an MOS guard-ring gate overlapping the edge
of the diffused layer.
Diffusion of phosphorus into polysilicon material results in a
preferential diffusion along the GB's. The preferential diffusion can
be directly observed by using a groove and stain procedure. This proce
dure was found to be unreliable, though, because the time and conditions
required to clearly delineate the very narrow preferentially diffused GB
region (spike) varied with the stain solution used and the doping
concentration in the spike. In Section 4.2 we described two new
electrical methods which can positively identify the presence or absence
of a preferentially diffused region. Once the preferentially diffused
region is identified, we may use a suitable groove and stain procedure
to measure the depth of the preferential diffusion and use electrical
methods to determine the average doping concentration in the region.
Our results show that a phosphorus predeposition at 900C for 30 minutes
followed by a drive-in at 1050C for 40 minutes will preferentially
diffuse the GBs in p-type Wacker material to a depth dn of about 4 ym
and will yield an average doping concentration in the diffused GB
16 ~3
regions of 1 x 10 cm The substrate doping was
15 -3
- 3 x 10 cm A predeposition at 1050C for 30 minutes followed
by a drive-in at 1050C for 30 minutes yields dn = 3 ym, and
17 -3
Ndd 2 x 10 cm The quasi-neutral width Wn of the preferentially
diffused n-region is about 0.5 ym for the first case and about 1.0 ym

75
for the second case. On the other hand, a diffusion at 900C for
30 minutes did not result in the creation of a p-n junction along the
GB's.
No preferential diffusion of boron was observed either by the groove
and stain method or by the electrical methods for various diffusions at
900 1000C for 20 120 minutes in n-type Wacker substrate with
Ndd 2 x 1016 cm-3.
Both the GB and the preferentially diffused region along the GB
will have recombination-current components associated with them. These
current components were identified by comparing the I-V characteristics
of the GB devices with the I-V characteristics of devices that were
grain-boundary-free (GBF). A first order analysis of the I-V curves of
the GB diodes, and separation of the total measured current into compo
nents, was done in Section 4.3. This analysis has shown that the
dominant current component in the GB diodes at small bias levels
(0-300 mV) is the recombination current at the GB within the p-n junction
GB PTC
SCR, lgCR At higher bias levels (V = VQC 500-600 mV), both IgCR and
the recombination current at that part of the GB which is adjacent to
GB
the quasi-neutral base region, I^ are important. Both of these
D
GB
components cause degradation in VAO and I ; I^ also degrades FF. It
Ut> bL dCK
was also observed that twin GB*s have very little effect on the I-V
characteristics of solar cells.
The preferentially diffused region along the GB increases the area
of the p-n junction. This will result in additional carriers injected
GB
from this region into the base, Irt_TT), and also in additional carrier
Jt>
GB
injection from the base into the region, Iq^r. A first order analysis
of these currents was done here for the first time.

76
This analysis suggests some important conclusions regarding the
effects of the preferential GB diffusion on the solar cell I-V curves.
(i) The surface recombination velocity at the GB within the preferen
tially diffused n-region is about two orders of magnitude smaller than
outside this region. This suggests that a phosphorus diffusion into the
GBs does indeed passivate the GBs. (ii) The preferentially diffused
18 -3 GB
regions should be heavily doped with 10 cm to suppress Iq^j.
n GB
even for large S^g and large d^. (iii) If I^g can be suppressed, then
the depth of the preferential diffusion should be made comparable to the
base diffusion length, i.e., dn Ln> so as to minimize Ig (iv) The
preferentially diffused regions will aid in collection of the photogen
erated carriers, thus increasing Ig^,. (v) Increased area of the p-n
GB
junction will increase the I g dark current component. However, the
total dark current will not increase proportionally to the total junction
area because of a two-dimensional coupling between I^g injected from the
GB
top lateral area and I,.-T_ injected from the vertical area. These two
currents tend to oppose each other.
Another important conclusion of this chapter is that the GBs do not
cause any measurable shunt resistance effects in diffused p-n junction
cells made on Wacker polysilicon material.

CHAPTER 5
SMALL-SIGNAL ADMITTANCE METHOD FOR DETERMINING
THE SURFACE-STATE DISTRIBUTION AT THE PREFERENTIALLY
DIFFUSED PART OF THE GRAIN BOUNDARY
5.1 Introduction
Lattice mismatch at the grain boundaries (GB's) of polysilicon
solar cells causes the formation of energy levels (surface states) in
the energy gap that serve as recombination centers. Surface states
can be either donor-type or acceptor-type. Those surface states that
are near the center of the energy gap will afford the highest recombina
tion rates [44] and, thus, will be the most efficient recombination
centers.
For an n+ -p polysilicon diode, methods for calculating the sur
face recombination velocity S at that part of a GB which is adjacent
to the quasi-neutral p-type bulk and for estimating the surface recom
bination velocity s at that part of a GB which is in a preferential-
ly diffused n-region have been demonstrated in sections 4.3.1 and
4.3.2.2, respectively. With the assumption of a uniform distribution
of surface states in the energy gap, the GB surface-state density N
ss
can be calculated [45] for both the diffused and undiffused sections
of the GB:
N = S/O v ,
ss th
(5.1)
where, S, O, and v ^ are the surface recombination velocity, capture
cross-section, and thermal velocity for minority carriers at the GB,
77

78
respectively. The above assumption is generally invalid and, con
sequently, (5.1) at best gives an estimate of N In order to de-
s s
termine the feasibility of preferential diffusion as a means of GB
surface-state passivation and, subsequently, as a means of lowering
the dark recombination current and increasing V and n5 a more ac-
UL
curate method for determining N must be developed. In this chapter,
ss
we develop a small-signal admittance method that enables the determina
tion of N in the energy gap for that part of the GB which is in a
ss
preferentially diffused n region. The method, in principle, can
yield the determination of all of the fundamental kinetic parameters
in the energy gap at the GB surface: N (E), E c (E ), c (E ) e (E ),
ss ini pi n i
and e (Em). In addition, the method can yield the GB barrier height,
P T
and the doping and mobility in the preferentially diffused region.
5.2 Small-Signal Equivalent Circuit Model of a Diode with a Prefer
entially Diffused Grain Boundary
We consider again the n+ -p diode with a preferentially diffused
n-region along the GB shown in Fig. 4.5. (The preferentially diffused
n-region of the GB, seen from the perspective of Fig. 4.5, is sometimes
referred to as the n-spike.) The equilibrium band diagram for that
part of the diode that is in the proximity of the preferentially
diffused GB is shown in Fig. 5.1. We assume that the region immediate
ly next to the GB is depleted due to the presence of the surface
states at the GB [18,19]. The band bending due to those surface states
GB
is qcj>_,,. The narrow depletion region of width W on both sides of
the GB is similar to the surface channel of an MOS transistor in the
depletion regime; and the GB with its surface states is similar to the
Si-SiC^ interface of that surface channel. Consequently, the simplified

79
Figure 5.1 (a) Cross-section of an n -p polysilicon diode showing the
preferentially diffused n-region of a GB.
(b) The corresponding thermal equilibrium band diagram. The
GB is located at x = 0. The width of the GB space-charge
region is W^; the width of the quasi-neutral n-region
in the n-spike is W^; the band-bending at the GB is

80
equilibrium small-signal transmission-line equivalent circuit model
of the preferentially diffused n-region shown in Fig. 4.5 will be
similar to the circuit model of the surface channel of an MOS tran
sistor [46']. This simplified model is shown in Fig. 5.2. By consider
ing the two-dimensional current flowing through the preferentially
diffused n-region, this model can be derived from the general small-
signal transmission-line equivalent circuit model developed by Sah [47]
for any two-terminal one-dimensional semiconductor device.
The circuit parameters in Fig. 5.2 are defined as follows:
is the per-unit-length resistance of the quasi-neutral n-region
in fi/cm;
is the capacitance of the p-n junction space-charge region
2
along the n-spike in F/cm ;
is the capacitance of the GB space-charge region in the n-spike
in F/cm^;
G is the electron capture conductance of the GB surface states
ns
in mhos/cm^;
2
C is the storage capacitance of the GB surface states in F/cm ;
s s
C is the capacitance of the lateral p-n junction space-charge
(jr
2
region in F/cm ; and,
Z is the length (into the plane of the paper) of the preferen
tially diffused n-region.
In Fig. 5.2., we have neglected the electron and hole storage
capacitances in the quasi-neutral regions, and we have assumed the
simple case of a single level of surface states at the GB. The
capacitive coupling between the n-spike and the substrate at the bot
tom of the spike is neglected on the grounds that the volume of the

81
Figure 5.2 Simplified equilibrium small-signal transmission-line
+
equivalent circuit model of a polysilicon n -p diode with
a preferentially diffused GB.

82
space-charge region at the bottom of the spike is small compared to the
volume of other regions that contribute capacitance. The resistive
coupling between the n-spike and the substrate through the GB can also
GB GB
be neglected since it was determined in Section 4.3.6 that G^, = 1/Ri
Dll bn
- 0. The Shockley-Read-Hall recombination through the deep trap levels
in the quasi-neutral bulk is also neglected. The equivalent circuit
model obtained by lumping the circuit elements from both sides of the
GB is shown in Fig. 5.3(a). The transmission line is open-circuited be-
GB
cause Ggk 0. This model is also applicable to an n -p diode contain
ing more than one GB, because the GB's are all electrically connected
to each other by the lateral n+ layer on the top.
We now assume, for the circuit shown in Fig. 5.3(a), that small-
signal admittance measurements will be made at frequencies that are
much less than the transmission-line characteristic frequency f [46].
With this assumption, the circuit elements can be shorted. The re
sult is the circuit shown in Fig. 5.3(b). The corresponding simple one-
lump circuit model is shown in Fig. 5.3(c). This model is valid for the
depletion and weak inversion regimes, i.e., for Ep(0) ~ E^(0), where
the GB is located at x = 0.
The input admittance for the circuit of Fig. 5.3(c) is
(5.2)
where
G.
C.
m
in
(5.3)
(5.4)

83
Pn^y
Figure 5.3(a) The equivalent circuit model obtained from Fig. 5.2
by lumping the circuit elements from both sides of
the GB.

84
Figure 5.3(b) The equivalent circuit model obtained by shorting the
circuit elements in Fig. 5.3(a).

85
in
Figure 5.3(c) The one-lump equivalent circuit model obtained from
Fig. 5.3(b). Here C C C and C are in farads,
D W SS (jJ5r
and G is in mhos,
ns

86
T = 1/co = C /G .
ss ss ns
(5.5)
Both (5.3) and (5.4) are dependent on C ; therefore, we can use
s s
either G. or C. to obtain information about the surface states,
m m
Experimentally, it is found that the surface states at an Si-SiO^
interface [48], and also the surface states at silicon GBs [22], are
continuously distributed in the energy gap rather than existing at a
single energy level. These continuously distributed surface states
can be represented in the circuit model of Fig. 5.3(c) as a parallel
array of G C circuit elements, each element representing surface
IIS s s
states at a certain energy level. The capacitance of a G C cir-
ns ss
cuit element is proportional to N at the given energy level, and G
ss ns
reflects the time constant of the surface states at the given energy
level. The problem of calculating the surface-state capacitance C
s s
for an MOS capacitor with a continuous distribution of surface states
has been considered by Sah [49]. In [49] it is shown that, for the
case of an MOS capacitor with a small-signal current flow, the net C
ss
for distributed states can be obtained by summing the contribution to
C from all the energy levels between and E referenced to a single
SS V C
Fermi level. The net C is determined by those states within about
ss
kT of the Fermi level at the Si surface. Since the equivalent circuit
of a preferentially diffused GB at zero-bias is similar to that of an
MOS capacitor in the depletion regime, the results of [49] may be ex
tended to include the preferentially diffused GBs of our devices.
Consequently, the circuit model of Fig. 5.3(c) is applicable to the
realistic case of a preferentially diffused GB with a continuous dis
tribution of surface states.

87
5.3 An Admittance Method for Determining N
ss
We now describe a small-signal admittance method in which we
use C. to obtain information about the surface states at that part
in
of a GB which has been preferentially diffused with phosphorus.
Figure 5.3(c) shows that the zero-bias small-signal capacitance
associated with the preferentially diffused region of the GBs in a
GB diode, C, is equal to the measured terminal capacitance of the
GB diode minus the measured terminal capacitance of the corresponding
GBF diode:
C in ~ CGBF
(5.6)
The capacitance Gnr¡T, is frequency-independent until f ~ 1 GHz. For
OJjr
sufficiently low frequency, f f = G /27rC the G can be
ss ns ss ns
short-circuited, and the equivalent circuit will reduce to that shown
in Fig. 5.3(d). From (5.4) and (5.6), the low-frequency limit for C
is then
CLF-CW(CSa + S)/(Css + S + For sufficiently high frequencies, f f the surface states can-
ss
not follow the signal and the C can be short-circuited. With the
ss
provision that the frequency f is less than the characteristic fre
quency fQ, the equivalent circuit model shown in Fig. 5.3(c) then
reduces to that shown in Fig. 5.3(e); and (5.4) and (5.6) yield the
high-frequency limit for C:
cHr W(CH + V-
(5.8)
From (5.7) and (5.8), we obtain an expression for C in terms of CT_
SS Lr
and CHF [50]:
Css CW[<-CLF/CW^/(1 ~ LF^V ^HF^W^1 ^F^V-*'
(5.9)

88
Figure 5.3(d) The equivalent circuit model obtained from Fig. 5.3(c)
for the low-frequency case, i.e., for f f .
s s

89
Y
in
Figure 5.3(e) The equivalent circuit model obtained from Fig. 5.3(c)
for the high-frequency case, i.e., for f << f fQ.

90
The surface-state density along the preferentially diffused part of
the GB's is then given by
N => C /q A ,
ss ss GB
(5.10)
where dQ Z is the total area of the preferentially diffused part
of the GBs.
We assume as a first approximation that the preferentially dif
fused n-region is uniformly doped. In Fig. 5.1(b), it is seen that
the position of the Fermi level for the preferentially diffused part
of the GB's is given by
yo) E.(0) = E (0)/2 ql>n qcj^,
(5.11)
where the GB is located at x = 0. In order to determine the position
of the Fermi level for the preferentially diffused part of the GB's,
qcj) and qc(> must be calculated,
n GB
With the use of the Boltzmann relation [51] for a nondegenerate
semiconductor in thermal equilibrium, the band diagram in Fig. 5.1(b)
shows that
q(>n = E (0)/2 kT In (N^/n.). (5.12)
The values of E^(0) and n^ as a function of the temperature T are
found in [52].
The band bending qc|> which is due to the surface states at the
Gd
GB can be approximately determined by the method of [46]. In [18], it
is assumed that N is uniformly distributed in the energy gap and
s s
that there exists a "neutral level" qcf)^ at approximately E^(0)/3 such
that, for E (0) = qcj) the net charge in the GB surface states is
X1 O
zero. The assumption concerning the energy gap position of qcj)^ is
supported by [53], With these assumptions, the requirement of overall

91
charge-neutrality in the n-region of the GB, and the band diagram in
Fig. 5.1(b), yield the following system of equations:
q*GB A* 2 [EF(0) *o]2/8|CEoNDD (5-13)
VO) Eg(0) q*n q*GB (5.14)
where 4>Q = Ey(0)/q + E^(0)/3q, and E^(0) is arbitrarily taken to be
zero. This system of equations can be solved for qcft to yield:
GB
qGB = [(2ot0 + 1) + (4a0 + l)1/2]/2a, (5.15)
where a = q2N 2 /8ke N and 0 = 2E (0)/3 [kT ln(N /N )].
SS o DD g C DD
In establishing (5.15), it is assumed that N is uniformly dis-
SS
tributed in the energy gap. This generally invalid assumption can
lead to an error in the calculation of qcf> With the assumption of
a one-sided depletion region at the GB, a more accurate expression
for the band bending at the GB is given by
The determination of q GB
bution of N between qd> and E(0) and is only obtainable by means
of iterative calculations. To avoid the laborious nature of the cal
culations associated with (5.16) while at the same time improving
upon the accuracy that would be afforded by (5.15) if one value of
N were used in (5.15), we have chosen to calculate q^ by using an
SS GB
average value for N in (5.15).
ss
With the calculation of qcj> and q n GB F
for various temperatures from (5.11). Thus, by measuring the small-
signal admittance at various temperatures, we can use (5.10) and
(5.11) to determine N vs. [E (0) E.(0)].
ss F i

92
5.4 Inversion along the GB in the p-Type Bulk
We now consider that part of the GB which is adjacent to the
p-type bulk. Equation (5.13) shows that, with the assumption of a
uniform distribution of surface states in the energy gap, the band
2
bending at the GB is proportional to N For sufficiently large
N E (0) > E.(0) where E. is the intrinsic Fermi level, and the
region next to the GB becomes inverted. It is of interest to deter
mine the value of N necessary for the formation of an inversion lay-
er along that part of the GB which is adjacent to the p-type bulk.
In Fig. 5.4, it is seen that the onset of inversion occurs when
Ep(0) Ey(0) = q'fgg = E (0)/2. By substituting these relationships
into (5.13) with N replaced by N and with (¡> E (0)/3q, we may
UU fin O o
solve for the value of N necessary for the onset of inversion:
s s
(N ). = (12/q)[k£ N /E (0)]1/2.
ss inv ^ o M g
(5.17)
Since N is, in fact, not uniformly distributed in the energy gap,
(5.17) provides only an estimate of the value of N necessary for the
ss
onset of inversion. In Section 4.2, an argument based on experimental
data was presented to show that there does not exist an inversion layer
about the GB in the bulk. Consequently, (N^) represents an esti
mate of the upper limit of N along that part of the GB which is ad-
s s
jacent to the p-type bulk.
5.5 Experimental Procedure and Results
To demonstrate the above method for determining N two runs
s s
+
(39P and 40P) of n -p mesa diodes were fabricated on 5 fi-cm Wacker
polysilicon p-type substrates (Appendix IX). The mesa diodes were
made by the method of wax-masking a small dot on a chip that had been

93
p-type bulk
E
c
E
E
F
V
Figure 5.4 Thermal equilibrium band diagram for that part of a GB
J"
which is adjacent to the p-type bulk of an n -p poly
silicon diode.

94
diffused with phosphorus and metallized. The unmasked portion of the
top surface of the chip was then etched to a depth slightly in excess
of the top p-n junction depth x^. The wax was then removed and the
chip was bonded onto a TO-5 header (Fig. 5.5). During the masking
step, care was taken to position the dot over an area that was inter
sected by several GB's. Consequently, after the etching step, the
GB's on the chip were all electrically connected to the emitter of
the mesa by virtue of the fact that the GBs were preferentially dif
fused with phosphorus to a depth d^ considerably in excess of x^. .
The low and high-frequency values of the GB component of the
capacitance can be expressed as C = (C. ) C and C = (C. )
Lr in LF GBF HF in HF
respectively, where is frequency independent until f ~ 1 GHz
GBr Gi5r
The accuracy of the determination of C and C can be improved by
LF HF
maximizing the ratio of C. to Consequently, in the fabrication
xn Gab
of the diodes, we used diffusion schedules that included high-tempera
ture drive-ins so as to make d large compared to x., and we made the
n j
top areas of the mesas much smaller than the top areas of the chips on
which they were fabricated. The ratio of d to x. was about 4.5 and
n J
2.4 for Runs 39P and 40P, respectively. The ratio of the chip area to
the mesa area was about 32:1 for Run 39P and 12:1 for Run 40P.
Figures 5.6 and 5.7 show the measured terminal capacitance
as a function of frequency at several temperatures for a representative
diode from each of the two experimental runs. The measurements were
made on HP 4274A and 4275A LCR meters. The measured and calculated
parameters for the two runs are listed in Tables 5.1 and 5.2. In Figs.
5.6 and 5.7, the measured C. vs. f curves generally follow (5.4), and
in
the step in the curves due to the inability of the surface states to

95
Figure 5.5 Microphotograph showing the top view of the n -p mesa diode
39P#2. The mesa diode is on a chip which is bonded to a
TO-5 header. The mesa appears as the roughly circular struc
ture near the center of the chip. The area of the chip is
-2 2
approximately 5.2 x 10 cm ; the area of the mesa is
3 2
approximately 1.6 x 10 cm ; the total length of the GBs
is . 3.43 cm; and the depth of preferential diffusion
GB
is d 9 pm.
n

Terminal Capacitance C.
io2 io3 io4 io5 io6 io7
Frequency (Hz)
Figure 5.6 Measured terminal capacitance as a function of frequency for the n+-p mesa diode 39P#2.
The capacitance of a GBF diode in Run 39P, normalized to the top area of the GB diode, is
shown for the temperature 145 K.

40
35
a.
t
CJ
CD
O
C
cD
30
H
a
C
p-
aj
U
25
CD
ti
e
s-i
H
20
15
10
Frequency (Hz)
Figure 5.7
Measured terminal capacitance C. as a function of frequency for the n -p mesa diode 40P#3.
V£5

Table 5.1 Parameter values for representative mesa diodes of Runs 39P and 40P. The values of C
Lr
and C are the low and high frequency measured values corrected for the GBF capacitance.
HF
The area of the preferentially diffused section of the GB's is A = £d .
GB n
Diode
T
A
CLF
CHF
cw
C
ss
E (O)-E.(O)
r 1
N
ss
(K)
( 2\
(cm )
(pF)
(pF)
(pF)
(pF)
(eV)
(eV)
/ 2 -1N
(cm eV )
39P//2
93
3.1 x 10"3
66
58
94
66
1.3 x 1011
39 P# 2
145
It
72
63
97
96
11
2.0 x 10
39P//2
198
II
79
68
102
134
2.7 x 1011
40P#3
93
9.2 x 10-4
23
18
28
78
-0.289
-0.25
5.3 x 1011
40P#3
145
II
25
19
29
122
-0.268
-0.23
8.3 x 1011
40P//3
198
It
28
21
31
213
-0.243
-0.20
12
1.4 x 10

Table 5.2
Additional parameter values for the diodes listed in Table 5.1. The capacitance
is calculated from the expression for C^, equation (5.8). The doping density
Np^(O) is calculated from the depletion approximation expression for C^.
Diode
uu
T
(K)
CD
(pF)
, -3.
(cm )
D
5dd from
Chapter 4
(cm 3)
39P//2
93
151
2 x 1017
39P#2
145
180
It
39P#2
198
204
It
40P#3
93
50
15
9.4 x 10
1 x 1016
40P#3
145
55
1.0 x 1016
II
40P#3
198
65
1.3 x 1016
If

100
follow the signal at frequencies of f > f is clearly visible. It
s s
is also seen that the value of f (the first break-point) moves to the
s s
right with increasing temperature. This is in agreement with theor
etical prediction [48].
The characteristic frequency f can be used in estimating the
electron mobility and the doping density in the preferentially diffused
region of the GB's [46]. In Fig. 5.6, the frequency dependence of the
input capacitance of a GBF diode, normalized to the top area of the GB
diode, has been plotted. It is seen that at a given temperature, 145K
for example, the capacitance of the GBF diode is essentially frequency-
independent (as expected), and the capacitance of the GB diode asymp
totically approaches the capacitance of the GBF diode for frequencies
£
beyond the second break-point (- 10 Hz). This strongly suggests that
the second break-point in the C vs. f curve indicates the character
istic frequency f for the GB diode. This idea is strengthened by the
observation that, for frequencies beyond the second break-point, the
1/2
vs. f curve drops with a slope of about w in agreement with the
theoretical work of [46].
The purpose of Figs. 5.6 and 5.7 and Table 5.1 is to demonstrate
that the above method can be used to profile the GB surface-state dis
tribution in the energy gap for E (0) > E (0). We note in Table 5.1
r
that the values of E (0) corresponding to the temperatures at which
F
C. was measured are about midway between E. and E By making meas-
in x C
urements at higher temperatures (up to about 400K) we could, in
principle, scan the energy gap down to E E^(0). In Figs. 5.6 and
5.7, it is seen that we have not included measurements of C. vs. f
at these higher temperatures. This is mainly because, at higher

101
temperatures, f approaches f which makes determination of C (and
ss o ss
thus N ) difficult; and also, because the low frequency measurements
s s
on the admittance bridges that we used (HP LCR meters) tended to be
very noisy at the higher temperatures.
For Runs 39P and 40P, (N ). was calculated from (5.17) to be
ss xnv
about 2 x 10^2 cm ^eV
5.6 Conductance Method for Determining N
ss
An alternative to the above capacitance method for determining
the distribution of N in the energy gap is a conductance method
SS
[48,50], In the conductance method, the parallel branch of the lumped
equivalent circuit shown in Fig. 5.3(c) is converted into a capacitance
Cp in parallel with a conductance as shown in Fig. 5.8. In Fig.
5.8, we have assumed the simple case of a single level of surface
states at the GB. The values of C and G are given by
P P
C = Cn + C /(I + o)2x2),
p D ss
G = C w2t/ (1 + 0)2T2) .
p ss
(5.18)
(5.19)
By measuring the zero-bias small-signal admittance of the diode
= G^ + jcoC^ as a function of frequency, the dependence G^/co vs.
a) can be plotted. The plot of G^/co vs. co goes through a maximum at
a) = 1/t. The value of G /u at the maximum is G /2. Thus, from the
p ss
plot of Gp/w vs. co, we can directly determine the values of both T
and C Then, by using (5.10) and (5.11), we can determine the dis-
s s
tribution of N in the energy gap.
s s
For a continuous distribution of surface states in the energy gap,
the conductance expression (5.19) must be modified [48,50]. This

102
GBF
in
Figure 5.8
The one-lump equivalent circuit model used in the conduc
tance method for determining the surface state distribu
tion in the energy gap. This model is obtained by convert
ing the parallel branch of the circuit model in Fig. 5.3(c)
into a capacitance C in parallel with a conductance G .

103
modification includes the frequency dispersion of the G due to the
ns
random spatial variation of the surface potential. This treatment
leads to N (E) and also to a determination of the capture cross-sec-
ss
tion 0^ for majority carriers. The majority carrier capture probabili
ty c^ is then determined from c^ = nVth* using the principle of
detailed balance for the zero-bias case (no current flowing across the
GB), the majority carrier emission probability e can also be obtained.
n
5.7 Discussion
The main source of error in the determination of the surface-state
density in the energy gap by the capacitance method is the great sen
sitivity of C to CT,. A 10% error in CTT will result in an error of a-
J ss W W
bout a factor of 2 in the calculated values of C (5.9) and N (5.10)
ss ss
and an even larger error in the calculated value of qcf) (5.15). The
capacitance C was calculated with the assumption of a one-sided step
w
junction with constant substrate doping N^. It was also assumed that
all of the GB's are preferentially diffused to the same depth, and
thus, that C is proportional to the total length of the GB's (Fig. 5.5).
w
Consequently, an accurate determination of the total length of the GB's
is crucial to the success of the capacitance method. The accuracy in
the determination of C can be improved by (i) using a chip that has
w
only one GB, and which has a very small mesa diode straddling that GB;
(ii) making much larger than the parallel combination of and C^.
Method (i) can be achieved by using standard photolithographic tech
niques; and method (ii) can be achieved by using a lower resistivity
substrate (0.1 1 £2-cm), or possibly by means of forward-biasing the
diode.

104
Aside from the error introduced by the calculated value for C ,
w
the accuracy in the determination of N and q ,, will depend on the
ss GB
accuracy of the physical models that are used. In particular, it is
to be noted that the model of [ 183 used to calculate q (5.15) is
highly simplistic. The simplicity of this model, coupled with the
great sensitivity of ql,, to the calculated value of CTT, tends to make
GB W
the calculated value of q<[> less reliable than the calculated value
GB
for N
ss
The depletion approximation expression for CD affords an alternate
expression for q GB
q*GB q2KEo %(0)/[2(CD/An)2] (5.20)
where N^CO) and C^/A^ are the doping density and depletion capacitance
per unit area, respectively, at the preferentially diffused part of the
GB. The area A is given by A = 2 d and the capacitance C_ can
n n n GB D
be calculated from C and C (5.8). Consequently, if an independent
rir W
measurement of N^(0) is available, (5.20) provides an alternate method
for determining q(t This alternate method is sensitive to the error
in C^, but has the advantage of being independent of the highly re
strictive model of [18].
If the electron capture cross-section cr at the GB is known, the
surface-state position E^(0) E^(0) can be directly determined from
the measured C vs. f dependence by the relation [48]
ss = an Vth ni exp{CEF() Ei(0)]/kT} (5.21)
where v ^ is the thermal velocity for electrons. The accuracy of this
method for determining E (0) E,(0) is limited by the accuracy of the
F i
value for o .
n

105
In Table 5.1, the calculated values for q and E (0) E.(0)
GB F i.
have not been Included for Run 39P because these values were highly un
reliable. This is because the value of q much greater than the values obtained from (5.15). We attribute this
large difference in the calculated values for to inaccuracies in
the model of [18]. The uncertainty in the energy gap position of the
surface states does not affect the determination of N
ss
The values of N in Table 5.1 suggest that N does not vary
SS ss
rapidly with position in the energy gap.
In Table 5.2, is calculated (5.8) from the high-frequency
capacitance measurement. The doping density at the preferentially
diffused part of the GB, NDD(0)> is calculated using (5.20). Values
of for Run 39P are not listed because of the unreliability of
the calculated values of q4> for that run. Table 5.2 also shows the
values of the average doping density in the preferentially diffused
n-region, N^, as determined in Section 4.2. In general, N^(0) will
not be exactly the same as because the diffusion process creates
a doping profile in the preferentially diffused n-region.
The conductance method has two main advantages over the capaci
tance method. Firstly, unlike the capacitance method, the conductance
method does not depend on C^. Secondly, the relative change of G^/to
vs. w in the conductance method is much greater than the relative change
of C. vs. to in the capacitance method [48], These two advantages
xn
enable the conductance method to yield a more accurate value for C
ss
than the capacitance method.
In our measurements of the devices in Runs 39P and 40P, we did not
observe a peak in the plot of G /to vs. to; and, consequently, we were

106
not able to apply the conductance method to determine N (E) x, and a .
ss n
This problem is illustrated in Fig. 5.9 where we plot the measured
values for C. and G. vs. f for a diode in Run 39P. The C. curve
in m m
follows (5.4), while the G curve monotonically increases without
reaching a plateau for f > f (which would be equivalent to G /(0 vs.
ss p
CO going through a peak at co = 1/x) The exact reason for this behavior
in G^n was not determined, but it is suspected that the large series
resistance of the p-type bulk is involved. The influence of series
resistance can be suppressed by using a lower resistivity substrate.
One of the main conclusions of this chapter is that the detailed
knowledge of the surface channel of the MOS transistor which has been
accumulated over many years can be applied to an analysis of the GB
surface states.

Terminal Capacitance C. (pF)
Figure
Terminal Conductance G. ( x 10 mhos)
m

CHAPTER 6
DESCRIPTION OF SEVERAL METHODS INTENDED TO SUPPRESS
THE GRAIN-BOUNDARY DARK RECOMBINATION CURRENT
6.1 Introduction
Prior to the fabrication of the planar diffused diodes discussed in
Chapter 4, we investigated several fabrication procedures that were
intended to suppress the grain-boundary (GB) component of the dark
recombination current. The experimental devices were 10-, 20-, and
+ +
50-mil n -p mesa diodes; 10-, 20-, and 50-mil n -p planar diffused
2 +
diodes with MOS guard rings; and large area (~1 cm ) n -p solar cells.
The substrates for these devices came from the same lot of 5 fi-cm p-type
wafers as did the substrates for the n+-p devices discussed in
Chapter 4. Table 6.1 presents a summary of the experimental runs
incorporating the special fabrication procedures. For the mesa and
planar diffused diodes, we attempted to isolate the GB component of the
dark recombination current by the method of subtracting the I-V
characteristic of a grain-boundary-free (GBF) diode from the I-V charac
teristic of a similarly fabricated diode containing a few GB's. As
mentioned in Chapter 1 and Section 4.4, the experimental results for
the small mesa diodes were inconclusive due to the presence of large
leakage currents.
6.2 Low-Temperature-Enhanced Preferential Diffusion of Phosphorus
In Runs 4P4 and 6P1 (Appendix VI), n -p mesa diodes were fabricated
on wafers that had undergone a 900C predeposition and a 900C drive-in
108

Table 6.1 Summary of experimental runs incorporating fabrication procedures intended to suppress
the grain-boundary component of the dark recombination current.
Run
Device Description
Purpose or Special Fabrication Step
4P4
n+-p 10-, 20-, 50-mil dark mesa
diodes.
Used as control group for comparison with Run 6P1.
6P1
n+-p 10-, 20-, 50-mil dark mesa
diodes.
48 hour 600C drive-in to enhance the preferential diffu
sion of phosphorus along the grain boundaries.
7P
n+-p 1 crn^ solar cells.
Low-temperature-induced preferential transport of mono-
atomic hydrogen along the GB's.
8P1
n+-p 50-mil dark mesa diodes.
Predeposition of boron followed by a 48 hour 600C drive-
in. The boron-doped top silicon layer was then removed,
and phosphorus was diffused to form the top n+-p junction.
13P3
n+-p 10-, 20-, 50-mil planar
diffused dark diodes with MOS
guard rings.
48 hour 600C drive-in to enhance the preferential diffu
sion of phosphorus along the grain boundaries.
13P4
n+-p 10-, 20-, 50-mil planar
diffused dark diodes with MOS
guard rings.
Used as control group for comparison with Run 13P3.
22P
n+-p 1 cm^ solar cells.
Preferential etching of GB's with Sirtl Etch before the
formation of the p-n junction. Wafers not polished.
25P
n+-p 1 cm^ solar cells.
Same as Run 22P, but with all wafers initially polished
in 2 HF : 15 HN(>3 : 5 CI^COOH solution.
109

110
for a total time of 130 minutes. The 6P1 wafer received the additional
treatment of a 48 hour 600C drive-in, in dry N in between the 900C
predeposition and the final 900C drive-in steps. The purpose of the
low-temperature step was to enhance the preferential diffusion of
phosphorus along the GB's [54,55], and thereby tie up dangling bonds
along the GB's. It has been reported that the intragain diffusivity
decreases faster with decreasing temperature than does the GB diffus
ivity [54]; and, at 600C, the preferential diffusion of phosphorus
along the GB's was anticipated to dominate the diffusion of phosphorus
into the intragrain bulk [54,55]. Zero-bias capacitance measurements
confirmed that the 600C treatment enhanced the preferential diffusion
of phosphorus along the GB's.
When it became clear to us that the measured currents of these
mesa diodes were dominated by leakage currents, we fabricated (Appen
dix VI) two runs of planar diffused diodes with MOS guard rings (Runs
13P3 and 13P4), one of which underwent a 48 hour 600C drive-in, in dry
in between the predeposition and final high-temper ature drive-in.
By using the subtraction method described in Section 6.1, it was de
termined that the low-temperature treatment had a negligible effect
on the GB component of the dark recombination current.
6.3 Low-Temperature-Enhanced Preferential Diffusion of Boron
In Run 8P1 (Appendix VI), n+-p mesa diodes were fabricated with a
diffusion schedule that included a 1 hour predeposition of boron at
1050C followed by a 48 hour boron drive-in at 600C. The boron doped
top Si layer was then removed and phosphorus was diffused to form the
top n -p junction. The low-temperature step was intended to enhance

Ill
the preferential diffusion of boron along the GB's. It was hypothesized
that such a preferential diffusion could result in a lowering of the GB
component of the dark recombination current either by the formation of
a high-low (p+-p) junction along the GB's or by the compensation of
dangling bonds along the GB's. A high-low junction [56] would decrease
the effective surface recombination velocity of minority carrier elec
trons flowing into the GB's. Due to large leakage currents, I-V meas
urements were inconclusive. It is suggested that this GB passivation
technique, repeated with planar diffused diodes, might be the subject
of future research.
6.4 Grain-Boundary Passivation by Hydrogen Plasma Treatment
In Run 7P (Appendix VI), phosphorus diffused p-type wafers
2
(~1 cm ) were sent to Sandia National Laboratories to receive a hydrogen
plasma treatment similar to that described in [40,57], This treatment
was intended to cause the preferential transport of monoatomic hydrogen
along the GB's, and thereby passivate the GB's by tying up dangling
bonds. Several n+-p wafers were kept at the University of Florida as
controls. After the sample wafers were returned from Sandia, both sam
ples and controls were fabricated into solar cells. This fabrication
used only low-temperature techniques (~ 130C) to avoid any out-gassing
of the hydrogen from the GB's. Dark and illuminated measurements on
these solar cells showed that the hydrogen plasma treatment had a negli
gible effect on the measured dark recombination current, short-circuit
current, and open-circuit voltage.

112
6.5 Preferential Etching of Grain Boundaries to Enhance Performance
In Runs 22P and 25P (Appendix VII), the GB's of p-type wafers
2
(~1 cm ) were preferentially etched with Sirtl Etch (50 g CrO^, 100 ml
H^O, 100 ml HF) in an ultrasonic bath for 10 minutes. The wafers were
then diffused with phosphorus and fabricated into n+-p solar cells.
The Sirtl Etch removed 23 ym from the intragrain top and bottom surfaces,
while at the same time preferentially etching the GB's to an average
depth of 15 ym below the intragrain top and bottom surfaces. The pur
pose of the Sirtl Etch treatment was to preferentially remove part of
the GB's. In each run, some of the wafers were fabricated into solar
cells without receiving the Sirtl Etch treatment, and those cells were
used as controls. Unlike the wafers of Run 22P, the wafers of Run 25P
were polished with a solution of 2 HF : 15 HNO^ : 5 CH^COOH
(Appendix V) for 10 minutes at the beginning of the wafer processing.
This polishing removed 27 ym from the top and bottom intragrain surfaces
and was only slightly preferential to the GB's.
In Run 22P, the measured at 1 sun AMO was between 60 and 70 mV
higher for the cells that had received the Sirtl Etch treatment than
for the control cells; but, in Run 25P, the Sirtl Etch cells and the
control cells displayed a negligible difference in V^. Also, the dark
I-V curves for the Sirtl Etch cells and the control cells in Run 25P
were essentially identical. These data strongly suggest that the
improvement in V for the Sirtl Etch cells of Run 22P was due to the
removal of saw damage by the Sirtl Etch and not to the preferential
etching of the GB's. The data are consistent with an observation by
Schwuttke that the saw damage in Wacker wafers extends into the material
to a depth of about 25 ym [58].

113
The improvement of solar cell performance by fabrication techniques
involving the preferential etching of the GB's is a topic of on-going
research [59].
6.6 Discussion
The n+-p solar cells of Runs 7P, 22P, and 25P were large-area
2
devices (~1 cm ) that had their edges etched in a solution of
3HF : 5HN0g : 3CHgC00H for 10 minutes. Consequently, leakage currents
did not dominate the measured dark recombination currents of these
devices. This edge-etching technique has been used successfully in
our laboratory for both single-crystal and polycrystalline Si solar
cells.
As previously mentioned, the intragrain base minority carrier
diffusion length in the p-type Wacker substrates has been determined
-f.
to be about 130 ym. The average grain diameter for the n -p solar
cells in Runs 7P, 22P, and 25P was about 1000 ym. The large ratio of
average grain diameter to base diffusion length tended to minimize the
effects that the special fabrication procedures may have had on the
GB component of the dark recombination current.

CHAPTER 7
DISCUSSION
The main contributions of this dissertation are:
(A) the development and analysis of a parallel-subcell equivalent-
circuit model to quantitatively indicate the limitations on
silicon p-n junction solar-cell performance that can be caused
by areal inhomogeneity (Chapter 2);
(B) the development of an experimental method for assessing the
validity of the shifting approximation for solar cells made
from polysilicon and other material (Chapter 3);
(C) the analysis and experimental identification of the current
components associated with the grain boundaries in polysilicon
diodes (Chapter 4);
(D) the development of new electrical methods for determining the
presence or absence of preferential diffusion along the grain
boundaries and for determining the average doping density of
preferentially diffused regions along the grain boundaries
(Chapter 4); and,
(E) the development of a small-signal admittance method for determining
the grain-boundary surface-state distribution in the energy gap
for that part of a grain boundary which has been preferentially
diffused with phosphorus (Chapter 5).
Approximations used in the interpretation of measurements in
Chapters 4 and 5 do not, in all instances, yield highly accurate
numerical values for the parameters involved. We emphasize again that
the intent of this dissertation is the development of experimental and
analytical methods for investigating the properties and performance
degrading mechanisms of polycrystalline silicon p-n junction solar
cells. The detailed statistical evaluation of a large number of
empirical data was not investigated in this work. The methods we have
114

115
developed can be used by other researchers who need detailed statistical
evaluations of large quantities of empirical data.
Although Chapters 4 and 5 deal with polysilicon solar cells and
mesa diodes, the work of these chapters used concepts from JFET and
MOSFET theory to develop methods for determining N^, Ngg (E), c^ (E^),
e (E} etc., for phosphorus diffused polysilicon diodes. In light
n 1
of the growing importance of polysilicon in the integrated-circuit
technology, the methodology developed in Chapters 4 and 5 may find
application to the device physics of integrated circuits.
Most of the devices measured (and, in particular, all of the
devices in Chapters 4 and 5), were fabricated from Wacker Silso poly-
silicon material. For both p and n-type Wacker material, the average
grain diameter was significantly larger than the base minority carrier
diffusion length and only one substrate doping concentration was avail
able. Wacker material is cast polysilicon supplied as 15 mil thick
wafers. Polysilicon solar cells of the future may be made from small-
grain thin-film material.
Several topics associated with the concepts presented in this
dissertation which might be the subject of future research include the
following: (i) a detailed statistical study correlating grain-boundary
crystallographic orientation with the extent of GB preferential diffusion,
with the GB fundamental kinetic parameters, and with the various carrier
recombination velocities; (ii) a study of the effects of deep preferen
tial diffusions in small-grain thin-film polysilicon material on short-
circuit current and open-circuit voltage; (iii) the development of a
methodology for determining the GB surface-state distribution in the
energy gap for that part of the GB which is adjacent to the quasi-neutral

116
base; (iv) an investigation of the validity of the shifting approxi
mation for polysilicon solar cells under high-injection conditions and
for polysilicon solar cells in which the average grain size is smaller
than the base diffusion length; and (v) the demonstration of the con
ductance method discussed in Sections 5.6 and 5.7.

APPENDIX I
FORTRAN PROGRAMS FOR SIMULATING THE EFFECT OF AREAL
INHOMOGENEITY IN AN n+-p SILICON SOLAR CELL
Type 1 Areal Inhomogeneity
C VOC, FF, AND EFF ARE CALCULATED AS FUNCTIONS OF QF WITH JR AS A
C PARAMETER.
C QF = AGOOD/ATOTAL IS THE AREAL QUALITY FACTOR.
C JR = J01P/J01G IS THE DARK SATURATION CURRENT DENSITY RATIO.
C J01G = 4.42E-13 A/CM2 IS THE DARK SATURATION CURRENT DENSITY OF THE
C GOOD PORTION OF THE SOLAR CELL.
C JSC = 0.025 A/CM2 IS THE SHORT CIRCUIT CURRENT DENSITY.
C THE BASE DOPING DENSITY IS 1.0E17/CC. NI = 1.33E10/CC. THE ELEC-
C TRON DIFFUSIVITY IN THE BASE IS 15.6 CM2/SEC. THE ELECTRON
C DIFFUSION LENGTH IN THE BASE IS 100 UM. T = 300 DEGREES KELVIN.
C
C
C
REAL KTQ, KT, JSC, J01G, J01B, ISC, IMP, JR
COMMON M, N, VOC, KTQ, ISC
KT 4.14E-21
Q = 1.602E-19
KTQ = 0.02584
JSC = 0.025
ISC = 0.025
J01G = 4.42E-13
DO 10 N = 1,20
QF = N*0.05
WRITE(6,2)
2 FORMAT(1H1)
WRITE(6,3) QF
3 FORMAT(5X,'FOR QUALITY FACTOR:',F5.2)
DO 20 M = 1,9
J01B = (10**(M-1))*J01G
JR = J01B/J01G
VOC = KTQ*ALOG(JSC/((QF*J01G)+((1-QF)*J01B)))
K = 1
5 IMP = 0.0100 + K*0.0001
CALL FCTVAL(IMP,FILF)
FX = FILF
K = K+l
IMP = 0.0100 + K*0.0001
CALL FCTVAL(IMP,FILF)
GX = FILF
DIF = GX-FX
117

118
IF(DIF.LT.0.0) GO TO 40
GO TO 5
40 WRITE(6,45) M,N,K
45 FORMAT(5X,316,/)
FAC = KTQ*ALOG(1.0-(IMP/ISC))
FF = ((VOC + FAC)*IMP)/(VOC*ISC)
EFF = FF*VOC*ISC
WRITE(6,46) JR
46 FORMAT(23X,'THE SAT. CURRENT DENSITY RATIO IS:',F10.0,/)
WRITE(6,47) VOC,IMP,FF,EFF
47 FORMAT(23X,4F8.5,//)
20 CONTINUE
10 CONTINUE
STOP
END
SUBROUTINE FCTVAL(IMP,FILF)
REAL KTQ,KT,JSC,J01G,J01B,ISC,IMP,JR
COMMON M,N,VOC,KTQ,ISC
KTQ = 0.02584
FILF = (VOC+KTQ*(ALOG(1.0-IMP/ISC)))*IMP/(VOC*ISC)
RETURN
END

119
Type 2 Areal Inhomogeneity
C VOC, FF, AND EFF ARE CALCULATED AS FUNCTIONS OF QF WITH DLR AS A
C PARAMETER.
C QF = AGOOD/ATOTAL IS THE AREAL QUALITY FACTOR.
C DLR = BDL/GDL IS THE DIFFUSION LENGTH RATIO.
C GDL IS THE BASE DIFFUSION LENGTH IN THE GOOD PORTION OF THE CELL
C BDL IS THE BASE DIFFUSION LENGTH IN THE POOR PORTION OF THE CELL
C JSCG IS THE SHORT CIRCUIT CURRENT DENSITY IN THE GOOD PORTION OF
C CELL.
C JSCB IS THE SHORT CIRCUIT CURRENT DENSITY IN THE POOR PORTION OF
C CELL.
C USE NAA = 1.0E16/CC, WSCR = 3.37E-5 CM, NI = 1.33E10/CC,
C D = 25.6 CM2/SEC, T = 300 DEG KELVIN, GDL = 100 UM, JSCG = 0.025
C A/CM2.
C
C
C
REAL JSCG,JSCB,JO1G,J02G,J01B,J02B,J01,J02,JSC
REAL JR,JSCR,ISC,I01,I02,KT,IMP
COMMON M,N,EP1,EP2,I01,I02,ISC
KT = 4.14E-21
Q = 1.602E-19
GDL = 100.0E-4
JSCG = 0.025
DO 10 N = 1,20
QF = N*0.05
WRITE(6,2)
2 FORMAT(1H1)
WRITE(6,3) QF
3 FORMAT(5X,FOR QUALITY FACTOR:',F5.2)
4 DO 20 M = 1,10
DLR = 0.01*M
BDL = GDL*DLR
JSCB = ((ALOGIO(BDL*1.0E4))/ALOGIO(GDL*1.0E4)))*JSCG
J01G = (7.25E-14)/GDL
J02G = (9.19E-13)/(GDL**2)
J01B = (7.25E-14)/BDL
J02B = (9.19E-13)/(BDL**2)
J01 = J01G + J01B
J02 = J02G + J02B
JSC = JSCG + JSCB
JR = J02/J01
JSCR = JSCB/JSCG
ISC = (JSCG*QF) + ((1-QF)*JSCB)
101 = (J01G*QF) + ((1-QF)*J01B)
102 = (J02G*QF) + ((1-QF)*J02B)
K = 1
5 VMP = 0.0500 + K*0.0005
CALL FCTVAL(VMP,D7)
FX = D7
K = K + 1
VMP = 0.0500 + K*0.0005

120
CALL FCTVAL(VMP,D7)
GX = D7
IF((FX.LT.O.O).AND.(GX.GT.0.0)) GO TO 40
GO TO 5
40 WRITE(6,45) M,N,K
45 FORMAT(5X,316,/)
QKT = 38.70
Q2KT = 19.35
D9 = ISC-(I01*EP1)-(I02*EP2)
IMP = ABS (D9)
DIO = ((SQRT((I02**2)+(4*ISC*I01)))~I02)/(2*101)
VOC = (2*(KT/Q))*ALOG(DIO)
FF = (VMP*IMP)/(VOC*ISC)
EFF = VOC*ISC*FF
WRITE(6,47) DLR
47 FORMAT(23X,'DIFF LENGTH. RATIO:' ,E12.4,/)
51 WRITE(6,101) VOC,FF,EFF
101 FORMAT(22X,VOC=',F8.5,3X,,FF=,F8.5,3X,'EFF=',F8.5,//)
20 CONTINUE
10 CONTINUE
STOP
END
SUBROUTINE FCTVAL(VMP,D7)
REAL JSCG,JSCB,J01G,J02G,J01B,J02B,JOl,J02,JSC
REAL JR,JSCR,ISC,I01,I02,KT,IMP
COMMON M,N,EP1,EP2,I01,I02,ISC
KT = 4.14E-21
Q 1.602E-19
QKT = 38.70
Q2KT = 19.35
Dl = QKT*VMP
D2 = Q2KT*VMP
EP1 = EXP(Dl)
EP2 = EXP(D2)
D3 = 102/101
D4 = ((Q*VMP)+(2*KT))/(2*((Q*VMP)+KT))
D5 = D3*D4
D6 = (ISC*KT)/(((Q*VMP)+KT)*I01)
D7 = EP1+(D5*EP2)-D6
RETURN
END

o o o o o
APPENDIX II
FORTRAN PROGRAM FOR PROJECTING THE PERFORMANCE OF A SOLAR
CELL GIVEN THE EMPIRICAL PARAMETER VALUES OF THE SUBCELLS
C THE PROGRAM MODELS THE ENTIRE SOLAR CELL AS THE PARALLEL COMBINATION
C OF N SUBCELLS. THE SHIFTING APPROXIMATION IS ASSUMED TO BE VALID.
C THE USER SUPPLIES THE FOLLOWING EMPIRICAL PARAMETERS FOR EACH
C SUBCELL: THE PHOTOGENERATED CURRENT, THE SPACE-CHARGE REGION SATURA-
C TION CURRENT, THE QUASI-NEUTRAL REGION SATURATION CURRENT, THE
C SPACE-CHARGE REGION RECIPROCAL SLOPE FACTOR, THE SERIES RESISTANCE,
C AND THE SHUNT RESISTANCE. THE PROGRAM THEN SOLVES N+l NODE VOLTAGE
C EQUATIONS IN N+l UNKNOWNS. THIS IS ACCOMPLISHED THROUGH THE USE OF
C THREE SUBROUTINES IN THE HARWELL SUBROUTINE LIBRARY FOR SOLVING
C SYSTEMS OF NONLINEAR ALGEBRAIC EQUATIONS. IN THE HARWELL LIBRARY
C THE SUBROUTINES ARE IDENTIFIED AS: NS01A,MC03AS, AND MB01C. THE
C PROGRAM OUTPUT CONSISTS OF VOC, ISC, VMP, IMP, FF, AND EFF FOR THE
C ENTIRE SOLAR CELL.
C
C THE FOLLOWING LISTING IS AN EXAMPLE FOR THE CASE N-2.
C
DIMENSION P2(3),P3(3),P4(3,3),P10(33)
REAL IL(2),MX(2),1X0(2),IQN0(2),RS(2),RSH(2),ISC,ILOAD,IMP
COMMON IL,MX,IXO,IQNO,RS,RSH,RLOAD
IP1 = 3
JJ1 = IP1-1
WRITE(6,10)
10 FORMAT(25X,'SOLAR SUBCELL EMPIRICAL PARAMETER VALUES ARE:',//)
DO 40 LL = 1,JJ1
READ(5,20) RS(LL),RSH(LL),MX(LL),IL(LL),IXO(LL),IQNO(LL)
20 FORMAT(6E9.3)
WRITE(6.30) RS(LL),RSH(LL),MX(LL),IL(LL),IXO(LL),IQNO(LL)
30 FORMAT(5X,'RS=',E10.4,3X,'RSH=',E10.4,3X,'MX=',E10.4,3X,
F'IL=',E10.4,3X,'1X0=',E10.4,3X,'IQNO=',E10.4.//)
40 CONTINUE
THE FOLLOWING ARE THE NS01A SUBROUTINE PARAMETERS.
IP = 3
P2(l) = 1.0
P2(2) = 1.0
P2(3) = 1.0
P5 = 0.0001
P6 = 3.0
P7 = 1.0E-12
121

122
IP8 = 1000
IP9 = IP8
C
C
C WE NOW CALCULATE OPEN CIRCUIT VOLTAGE OF THE ENTIRE CELL, VOC.
C
C
RLOAD = 1.0E+12
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
WRITE(6,50)
50 FORMAT(1H0)
DO 70 KK = 1,IP1
WRITE(6,60) KK,P2(KK)
60 FORMAT(5X,'VOLTAGE AT NODE',13.IX,'DURING OPEN CRT IS:',E12.5.//)
70 CONTINUE
VOC = P2(1P1)
WRITE(6,80) VOC
80 FORMAT(5X,'THE OPEN CIRCUIT VOLTAGE OF ENTIRE CELL IS:',E12.5)
C
C
C WE NOW CALCULATE SHORT CIRCUIT CURRENT OF THE ENTIRE CELL, ISC.
C
C
RLOAD = 1.0E-12
ISC = 0.
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
WRITE(6,90)
90 FORMAT(1HO)
DO 110 KK = 1,JJ1
ISC = ISC + (P2(KK)-P2(IP1))/RS(KK)
YY2 = (P2(KK)-P2(IP1))/RS(KK)
WRITE(6,100) KK,YY2
100 FORMAT(5X,'THE SC CURRENT FROM SUBCELL',I3,1X,'IS:',5X,E12.5,//)
110 CONTINUE
WRITE(6,120) ISC
120 FORMAT(5X,'THE SC CURRENT OF THE ENTIRE CELL IS:',2X,E12.5,//)
C
C
C WE NOW CALCULATE FILL FACTOR FF AND EFFICIENCEY EFF.
C
c
RLOAD = 6.5
DO 130 KK = 1,10
KKDUMM = KK
C DDKUMM TELLS US HOW LONG IT TAKES TO GET TO RLOAD FOR MAX POWER.
C (NOTE: KKDUMM=1 IF RLOADMP INITIALLY OVERSHOT. TRY LARGER RLOAD.)
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
ILOAD = P2(IP1)/RLOAD
POWERl = ILOAD*P2(IP1)
RLOAD = RLOAD-0.1
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
ILOAD = P2(IP1)/RLOAD
POWER2 = ILOAD*P2(IP1)
IF((POWER2 POWERl).LT.0.0) GO TO 140

i2a
130 CONTINUE
GO TO 190
140 VMP = P2(1P1)
IMP = ILOAD
WRITE(6,150)
150 FORMAT(1HO)
WRITE(6,160) P2(IP1),IMP
160 FORMAT(5X,VMP IS:' ,F7.4,5X,'IMP IS:',E9.4.//)
FF = (VMP*IMP)/(VOC*ISC)
EFF = VOC*ISC*FF
WRITE(6,170)
170 FORMAT(1H1)
WRITE(6,180) VOC,ISC,VMP,IMP,FF,EFF
180 FORMAT(5X,'VOC=',E12.5,3X,'ISC=',E12.5,3X,VMP=,E12.5,3X,
FIMP=',E12.5,3X,'FF=E12.5,3X,EFF=,E12.5,//)
GO TO 210
190 WRITE(6,200)
200 FORMAT(5X,RLOAD FOR VMP, IMP HAS NOT BEEN FOUND',//)
210 CONTINUE
WRITE(6,220) KKDUMM
220 FORMAT(5X,KKDUMM=,13,//)
STOP
END
C
C
SUBROUTINE CALFUN(NP,XP,FP)
DIMENSION XP(1),FP(1)
REAL IL(2),MX(2), 1X0(2),IQNO(2),RS(2),RSH(2),ISC,ILOAD
COMMON IL,MX,IXO,IQNO,RS,RSH,RLOAD
QKT = 38.61
Al (XP(l)-XP(3))/RS(1)
A2 = (XP(2)-XP(3))/RS(2)
B1 = IXO(1)*(EXP(QKT*XP(1)/MX(1))-1.0)
B2 = IXO(2)*(EXP(QKT*XP(2)/MX(2))-1.0)
Cl = IQNO(1)*(EXP(QKT*XP(1))-1.0)
C2 = IQNO(2)*(EXP(QKT*XP(2))-1.0)
FP (1) = IL (1) -Bl-Cl- (XP (1) /RSH (1) ) -A1
FP(2) = IL(2)-B2-C2-(XP(2)/RSH(2))-A2
FP(3) = A1+A2-(XP(3)/RLOAD)
RETURN
END

APPENDIX III
DERIVATION OE A SIMPLIFIED EXPRESSION FOR
THE SPACE-CHARGE REGION RECOMBINATION CURRENT
For a forward-biased p-n junction, the steady-state net recombina
tion rate for electrons or holes in nondegenerate material is given by
Equation (6) in reference [8] as
U = (pn ni2)/Tno[P + niexp[(Ei Et)/kT]] (Al)
+ TpQ[n + nexp[(Et E)/kT]]},
where Tno and XpQ are the low-injection level minority-carrier lifetimes
for electrons and holes, respectively; E^ is the energy level of the
recombination-generation centers; and E^ is the intrinsic Fermi level.
If we assume that there is a spatially-uniform monoenergetic distribution
of recombination-generation centers located at the middle of the bandgap
and T = T = T then (Al) may be written as
no po o ^
U = (pn ni2)/[Xo(p + n + 2n)]. (A2)
2
Because of forward bias, pn m and p + n 2m. Thus,
U pn/[TQ(p + n)]. (A3)
We further assume that U = U throughout the SCR. This implies that
max r
p = n throughout the SCR, so that
U n/2TQ. (A4)
124

125
Since n = n + An, the net recombination rate of excess electrons and
o
holes is
U U = where Uq is the thermal equilibrium recombination rate of electrons and
holes. We also assume that the quasi-fermi levels for majority carriers
are nearly flat across the quasi-nertral regions and nearly flat across
the SCR. This implies that n = p = n^exp(qV/2kT) so that
U Uq (n/2To)[exp(qV/2kT) 1]. (A5)
Finally, we assume that Dn = = Dq throughout the SCR, so that
U U (n.D /2L 2)[exp(qV/2kT) 1]. (A6)
o in n
The SCR current is then Jcn q(U U )Wor, -
bLK O bLK
(qn.W^^D /2L 2)[exp(qV/2kT) -1], where Wc is the width of the SCR.
i oLK n n
Equation (2.3) may then be rewritten as
J JgC JQNBQ[exp(qV/kT) 1] JSCR()[exp(qV/2kT) -1], (A7)
where the SCR saturation current is
JSCRO <
APPENDIX IV
GROOVE AND STAIN EXPERIMENT TO DETERMINE THE EXTENT OF STAINING
To accurately measure the stained width of a preferential diffusion
spike in a grooved and stained sample, it is necessary to know which
parts of the p-n junction SCR are stained by the staining solution. To
determine the extent of staining by the copper solution referred to in
Section 4.2 and by the commonly used HF solution, we compared the values
of the p-n junction depth x^ obtained [28] by using these two solutions
on two sample wafers. The copper solution was Philtec Company Stain
No. 2. The HF solution consisted of HNO^ : HF : ^0 = 1 : 10 : 89,v/v.
The sample wafers were p+-n and n+-p single-crystal wafers. It is known
that the HF solution will stain only the quasi-neutral p-region in a
grooved sample [60]; the copper solution will stain n-type material.
Table A1 presents the average calculated values for x^ obtained
with the two solutions and the two sample wafers. For each wafer, the
Stain solutions yield approximately the same values for x^. This
suggests that the copper solution stains both the quasi-neutral n-region
and the entire p-n junction SCR in a grooved sample.
126

127
Table Al Average calculated values for the junction depth x
with the two solutions and the two sample wafers.
Solution
x. for p+-n wafer
J
(ym)
x. for
J
Copper solution
0.76
. obtained
3
n+-p wafer
(ym)
1.51
HF solution
0.74
1.34

APPENDIX V
STANDARD WAFER CLEANING AND POLISHING PROCEDURES
Standard Wafer Cleaning Procedure
1. Scrub with cotton swab soaked with trichloroethylene (TCE).
2. Boil in TCE for 5 minutes.
3. Boil in fresh TCE for 5 more minutes.
4. Boil in acetone for 5 minutes.
5. Boil in methanol for 5 minutes.
6. Rinse in deionized water (p ~ 10 Mfi-cm) for 5 minutes.
7. Dip in 1 ^SO^ : 1 ^02 solution, v/v, for 10 minutes.
8. Remove oxide by dipping in 1 HF : 9 ^0 solution, v/v, for
10 seconds.
9. Rinse in deionized water for 5 minutes.
10.Blow dry with ^ gas gun.
Standard Wafer Polishing Procedure
1. Clean and degrease by following steps 1-6 above.
2. Swirl wafers in a solution of 2 HF : 15 HN0 : 5 CH-C00H, v/v, for
10 minutes.
3. Rinse in deionized water for 5 minutes.
4. Blow dry with N2 gas gun.
128

APPENDIX VI
FABRICATION SCHEDULES FOR RUNS 4P4, 6P1, 7P, 8P1, 13P3, AND 13P4
All runs were fabricated on 5 fi-cm p-type Wacker polysilicon sub
strates.
Run 4P4
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Phosphorus predeposition. 30 minutes at 900C in an atmosphere of
90 cc/min N2 bubbling through P0C13 at 30C, 170 cc/min dry C>2,
1500 cc/min N2 carrier gas.
3. Drive-in: 100 minutes at 900C in 1500 cc/min N2<
4. Etch phosphosilicate glass in 10% HF solution for 10 seconds.
5. Rinse in deionized water.
6. Remove n+-layer on backside by lapping with SiC slurry.
7. Standard wafer cleaning.
8. Metallization. Front: Al. Back: Ti, Ag.
9. Anneal: 10 minutes at 400C in 400 cc/min N2
10. Photolithography to define mesa diode pattern.
11. Etch in Al and Si etches to form mesa diodes.
Run 6P1
Same as Run 4P4, but with the following diffusion schedule:
Predeposition: 60 minutes at 900C.
Drive-in: 30 minutes at 900C.
Drive-in: 48 hours at 600C.
Drive-in: 40 minutes at 900C.
129

130
Run 7P
Steps:
1. Same as step 1 in Run 4P4.
2. Same as step 2 in Run 4P4.
3. Drive-in: 100 minutes at 900C in 100 cc/min dry 0
4. Same as step 4 in Run 4P4.
5. Same as step 5 in Run 4P4.
6. The wafers sent to Sandia were exposed to H+-plasma at 350C and
2 Torr for 18 hours.
7. Remove n+-layer on backside by lapping with SiC slurry.
8. Standard wafer cleaning.
9. Metallization. Front: Ti, Ag. Back: Ti, Ag.
10. Photolithography and etching to form solar cell grid.
11. Etch wafer edges in a solution of 3 HF : 5 HNO^ : 3 CH^COOH for
10 minutes.
Run 8P1
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Boron predeposition (BN-1150 solid source): 60 minutes at 1050C
in 200 cc/min ^.
Drive-in: 48 hours at 600C in 1500 cc/min N2.
3. Remove boron doped top Si layer with 3 HF : 5 HNO^ : 3 CH^COOH
solution.
4. Phosphorus predeposition. 20 minutes at 900C in an atmosphere
of: 90 cc/min N2 bubbled through POCl^ at 30C, 170 cc/min dry
0^ 1500 cc/min ^ carrier gas.
5-10. Same as steps 6-11 in Run 4P4.

131
Runs 13P3 and 13P4
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Oxidation in 1700 cc/min O2 at 1050C: 5 minutes in dry O2,
35 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry O2. Oxide thickness = 4400 .
3. Photolithography to open holes for phosphorus diffusion.
4. Standard Cleaning.
5. Phosphorus predeposition: same as step 2 in Run 4P4.
6. Drive-in (13P3 only): 48 hours at 600C in dry N2.
7. Etch phosphosilicate glass in 10% HF solution for 10 seconds.
8. Drive-in at 1050C in 1700 cc/min 02^ 15 minutes in dry O2,
20 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry O2. Oxide thickness = 3000 .
9. Remove n+-layer on backside by lapping with SiC slurry.
10. Standard cleaning.
11. Photolithography to open holes for metallization.
12. Standard cleaning.
13. Metallization. A1 front and back.
14. Photolithography to define top contact and MOS guard ring.
15. Solvent cleaning.
16. Anneal: 10 minutes at 450C in 400 cc/min N2.

APPENDIX VII
FABRICATION SCHEDULE FOR RUNS 22P AND 25P
Both runs were fabricated on 5 fi-cm p-type Wacker polysilicon sub
strates .
Steps:
1., Standard wafer cleaning.
2. Standard wafer polishing (25P only).
3. Etch sample wafers in Sirtl Etch (50 g CrO^, 100 ml H^O, 100 ml HF)
in ultrasonic bath for 10 minutes. Do not etch control wafers.
4. Remove oxide by dipping in 10% HF solution.
5. Phosphorus predeposition. 15 minutes at 850C in an atmosphere of:
90 cc/min N^ bubbled through POCl^ at 30C, 170 cc/min dry 0^,
1500 cc/min ^ carrier.gas.
-j.
6. Remove n -layer on back side by lapping with SiC slurry.
7. Solvent cleaning.
8. Metallization. Use OCLI-supplied mask to form solar cell grid
pattern on front side.
9. Etch edges in 3 HF : 5 HNO^ : 3 CH^COOH solution for 10 minutes.
132

APPENDIX VIII
FABRICATION SCHEDULES FOR RUNS 34P, 36P, AND 37P
Run 34P
Substrate: 0.3 U-cm n-type Wacker polysilicon.
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Oxidation in 1700 cc/min 0^ at 1050C: 5 minutes in dry O2,
50 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry O2. Oxide thickness = 5200 .
3. Photolithography to open holes for boron diffusion.
4. Solvent cleaning.
5. Boron predepostion (BN-975 solid source): 20 minutes at 900C in
200 cc/min N2, 5 minutes at 900C in 170 cc/min O2.
6. Remove boron glass and thin oxide down to 2500 with B0E etchant.
p = 310 ft/o.
s
7. Drive-in at 1000C in 1700 cc/min O2: 90 minutes in dry O2,
25 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry 0. New oxide thickness = 2900 . p = 810 f2/o.
2- S
x. =0.77 ym.
3
8. Remove n+-layer from backside by lapping with SiC slurry.
9. Solvent cleaning.
10. Photolithography to open holes for metal contacts.
11. Solvent cleaning.
12. Metallization: Ti, Ag front and back.
13. Photolithography to define top contact and MOS guard ring.
14. Solvent cleaning.
15. Anneal: 10 minutes at 400C in 400 cc/min N^.
133

134
Runs 36P and 37P
Substrate: 5 Q-cm p-type Wacker polysilicon.
Steps:
1-4. Same as steps 1-4 in Run 34P.
5. Phosphorus predeposition. 30 minutes at 900C in an atmosphere of
90 cc/min N2 bubbled through POCl^ at 30C, 170 cc/min dry 02,
1500 cc/min N2 carrier gas.
6. Remove phosphosilicate glass and thin oxide down to 3200 with
BOE etchant, p =20 Q/O.
s
7. Drive-in at 1050C in 1700 cc/min 02: 15 minutes in dry 02,
20 minutes in wet 02 bubbled through deionized water at 95C,
O
5 minutes in dry 02> New oxide thickness = 3000 A. pg = 7.7 ti/o.
x. = 1.8 ym.
3
8. For Run 37P only: deposit 6000 A1 on front surface; anneal at
450C for 12 hours in 400 cc/min N2; remove A1 with A1 etchant.
9. Remove n+-layer from back side by lapping with SiC slurry.
10. Solvent cleaning.
11. Photolithography to open holes for metal contacts.
12. Solvent cleaning.
13. Metallization: A1 front and back.
14. Photolithography to define top contact and MOS guard ring.
15. Solvent cleaning.
16. Anneal (36P only): 10 minutes at 400C in 400 cc/min N2.

APPENDIX IX
FABRICATION SCHEDULES FOR RUNS 39P AND 40P
All runs were fabricated on 5 i2-cm p-type Wacker polysilicon sub
strates.
Run 39P
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Phosphorus predeposition. 30 minutes at 1050C in an atmosphere of
90 cc/min ^ bubbling through POCl^ at 30C, 170 cc/min dry O2
1500 cc/min N9 carrier gas; p = 3 fi/o.
z s
3. Etch phosphosilicate glass in 10% HF solution for 10 seconds.
4. Rinse in deionized water.
5. Drive-in: 30 minutes at 1050C in 1500 cc/min ^5 pg = 2 Q/o.
6. Remove n+-layer from backside by lapping with SiC slurry.
7. Standard wafer cleaning.
8. Metallization with Al.
9. Anneal: 10 minutes at 400C in 400 cc/min
10. Dice into 90 mil x 90 mil squares.
11. Wax dot masking to define a mesa diode on each square.
12. Etch in Al and Si etches to form mesa diodes. This step removes
the top (lateral) p-n junction around the mesa diode without
significantly etching the preferentially diffused grain boundaries.
The Si etching requires 70 seconds in 1 HF : 6 HNO^ : 1 CH^COOH
solution.
135

136
Run 4OP
Same as Run 39P but with the following changes:
Step 2. Predeposition: 30 minutes at 900C; pg = 288 tifu.
Step 5. Drive-in: 40 minutes at 1050C; p =63 ft/.
s
Step 12. The Si etching requires 60 seconds in 1 HF : 6 HNO^ : 1 CH^COOH
solution.

APPENDIX X
COMMENTARY ON THE RELIABILITY OF GROOVE AND
STAIN RESULTS IN CHAPTERS 4 AND 5.
In chapters 4 and 5, we report the average values for the prefer
ential diffusion depth d for several diffusion schedules. These
n
values were determined by the method of groove and stain. For the
diffusion schedule consisting only of a 30 minute 900C predeposition
of phosphorus into p-type material, and for the diffusion schedules
consisting of boron diffusion into n-type material at 900-1000C for
20-120 minutes, the groove and stain method did not detect any preferen
tial GB diffusion. Published theoretical and experimental results al
luded to in Sections 4.2 and 6.2 lead us to presume that the above
diffusion schedules did produce some degree of preferential GB diffusion,
and that, the groove and stain method did not have adequate sensitivity
to detect the preferential GB diffusion.
For each diffusion schedule for which the groove and stain method
did detect preferential GB diffusion (Sections 4.2 and 5.5), it was the

case that some GB's (as much as 50%) did not stain. We attribute this
phenomenon to some unknown property or parameter of the groove and stain
method. It was nevertheless the case that all GB diodes fabricated by
such diffusion schedules showed greater zero-bias capacitance than the
corresponding GBF diodes. For those diffusion schedules for which the
groove and stain method did detect preferential GB diffusion, the cal
culated values for d were scattered by as much as + 15%. Because it
n -
is reasonable to believe that GB's with different crystallographic
137

138
orientations will have different rates of preferential diffusion, the
variation in the calculated values for d is attributed to variations
n
in the individual GB diffusion rates. The reported value for d for a
n
given diffusion schedule was based on the observation of at least ten
GB's that showed preferential diffusion as a result of the given dif
fusion schedule.

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BIOGRAPHICAL SKETCH
Jeffrey Alan Mazer was born in Fall River, Massachusetts, on
April 23, 1948. He received the B.S. degree in mathematics from
Purdue University, Lafayette, Indiana, in 1970 and the M.S. degree
in electrical engineering from Duke University, Durham, North Carolina,
in 1976. Since 1976, he has been working toward the Ph.D. degree in
electrical engineering at the University of Florida, Gainesville,
Florida.
144

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Arnost Neugroschel, Chairman
Associate Professor of Electrical
Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
v
Fredrik A. Lindholm, Co-Chairman
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
' -
Fossum
cofessor of Electrical Engineering

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Paul H. Holloway
Associate Professor of Materials
Science and Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Arun K. Varma
Professor of Mathematics
This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
August 1981
'tdzl.
Dean, College of Engineering
Dean for Graduate Studies and Research

2?GLtH
Internet Distribution Consent Agreement
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AUTHOR: Mazer, Jeffrey
TITLE: Methods for Investigating the Properties of Polycrystalline
Silicon...
PUBLICATION 1981
DATE:
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hereby grant specific and limited archive and distribution rights to the Board of Trustees
of the University of Florida and its agents. I authorize the University of Florida to digitize
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This grant of permissions prohibits use of the digitizedtversions for commercial use or
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04/23/2008
Date of Signature



APPENDIX VIII
FABRICATION SCHEDULES FOR RUNS 34P, 36P, AND 37P
Run 34P
Substrate: 0.3 U-cm n-type Wacker polysilicon.
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Oxidation in 1700 cc/min 0^ at 1050C: 5 minutes in dry O2,
50 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry O2. Oxide thickness = 5200 .
3. Photolithography to open holes for boron diffusion.
4. Solvent cleaning.
5. Boron predepostion (BN-975 solid source): 20 minutes at 900C in
200 cc/min N2, 5 minutes at 900C in 170 cc/min O2.
6. Remove boron glass and thin oxide down to 2500 with B0E etchant.
p = 310 ft/o.
s
7. Drive-in at 1000C in 1700 cc/min O2: 90 minutes in dry O2,
25 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry 0. New oxide thickness = 2900 . p = 810 f2/o.
2- S
x. =0.77 ym.
3
8. Remove n+-layer from backside by lapping with SiC slurry.
9. Solvent cleaning.
10. Photolithography to open holes for metal contacts.
11. Solvent cleaning.
12. Metallization: Ti, Ag front and back.
13. Photolithography to define top contact and MOS guard ring.
14. Solvent cleaning.
15. Anneal: 10 minutes at 400C in 400 cc/min N^.
133


CURRENT (mA)
29
Figure 3.8 I-V curves for device No. 4.


Figure 2.5 Normalized power conversion efficiency vs. areal quality factor.


54
ZQN ^piqV/kl)
(4.7)
where A_ is the grain area and T is the effective electron life-
time [34] which includes recombination within the grain and at the GB's.
The effective lifetime can be calculated exactly from (4.7) for columnar
grains with rectangular or cylindrical geometry [34]. This is not the
case for the Wacker polycrystalline silicon material. We can, however,
GB
estimate an average effective electron diffusion length in the poly
crystalline material by measuring the X-ray induced current [35] on a
large area polycrystalline cell and then comparing this current to the
response of a single-crystal cell with known diffusion length. The
2 +
experiment used a 2 cm polycrystalline n -p cell with average grain
GB
size of 500-1000 ym and yielded IT 70 ym which is smaller than
L 100-130 ym for the GBF diode. This result demonstrates that the
n
effect of the GB's on the electrons injected from the top n+-p junction
in diodes No. 2-5 cannot be neglected. In addition, the GB's will
contribute to the Iq^q because of the preferentially diffused n-region
which increases the total area of the p-n junction and contributes
additional current components, as was discussed in Section 4.3.1. The
GB
separation of I ^ as defined in (4.3) into components for the general
case requires solution of a two-dimensional boundary value problem which
is beyond the scope of this work. We can, however, approximately
accomplish this for our devices by considering the components separately
GB
and identifying the dominant one. Neglecting there are three quasi
neutral current components associated with the grain boundary: I
GB GB
'QNE an<^ *B nOW cons:^er each f these components.
GB
QNB*


CURRENT (A)
66
VOLTAGE (V)
Figure 4.9
Measured dark I-V curves for two p+-n solar cells: No
is a GBF cell, No. 8 is a GB cell.
6


118
IF(DIF.LT.0.0) GO TO 40
GO TO 5
40 WRITE(6,45) M,N,K
45 FORMAT(5X,316,/)
FAC = KTQ*ALOG(1.0-(IMP/ISC))
FF = ((VOC + FAC)*IMP)/(VOC*ISC)
EFF = FF*VOC*ISC
WRITE(6,46) JR
46 FORMAT(23X,'THE SAT. CURRENT DENSITY RATIO IS:',F10.0,/)
WRITE(6,47) VOC,IMP,FF,EFF
47 FORMAT(23X,4F8.5,//)
20 CONTINUE
10 CONTINUE
STOP
END
SUBROUTINE FCTVAL(IMP,FILF)
REAL KTQ,KT,JSC,J01G,J01B,ISC,IMP,JR
COMMON M,N,VOC,KTQ,ISC
KTQ = 0.02584
FILF = (VOC+KTQ*(ALOG(1.0-IMP/ISC)))*IMP/(VOC*ISC)
RETURN
END


44
W
SCR
Figure 4.5 Section of an n+-p diode with a columnar GB and a preferen
tially diffused n-spike with depth d^. The broken lines
indicate the edges of the p-n junction SCR and the edges of
the GB potential barrier within the n-spike. For the polar-
GB GB
ities indicated, IrtATT) I_ and I.A7_ are negative currents.
LJMd d IJJNd
The p-n junction along the preferentially diffused GB is
modeled, as a first approximation, as having a square-well
shape with a one-sided step junction at the bottom of the
square well. A more accurate model for the diffusion pro
file along the GB is one in which the p-n junction appears
wedge-shaped with phosphorus dopant extending below the a-
pex of the wedge. In such a model, the phosphorus concentra
tion below the apex gradually diminishes to zero.


LO
''J
Figure 4.2(a) Grooved and stained section of the n -p junction showing preferential
phosphorus diffusion along the grain boundary. A copper staining solu
tion was used. The junction depth is about 1.8 pm; the depth of the
preferential diffusion is about 6 ym. A commentary on the reliability
of groove and stain results appears in Appendix X.


122
IP8 = 1000
IP9 = IP8
C
C
C WE NOW CALCULATE OPEN CIRCUIT VOLTAGE OF THE ENTIRE CELL, VOC.
C
C
RLOAD = 1.0E+12
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
WRITE(6,50)
50 FORMAT(1H0)
DO 70 KK = 1,IP1
WRITE(6,60) KK,P2(KK)
60 FORMAT(5X,'VOLTAGE AT NODE',13.IX,'DURING OPEN CRT IS:',E12.5.//)
70 CONTINUE
VOC = P2(1P1)
WRITE(6,80) VOC
80 FORMAT(5X,'THE OPEN CIRCUIT VOLTAGE OF ENTIRE CELL IS:',E12.5)
C
C
C WE NOW CALCULATE SHORT CIRCUIT CURRENT OF THE ENTIRE CELL, ISC.
C
C
RLOAD = 1.0E-12
ISC = 0.
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
WRITE(6,90)
90 FORMAT(1HO)
DO 110 KK = 1,JJ1
ISC = ISC + (P2(KK)-P2(IP1))/RS(KK)
YY2 = (P2(KK)-P2(IP1))/RS(KK)
WRITE(6,100) KK,YY2
100 FORMAT(5X,'THE SC CURRENT FROM SUBCELL',I3,1X,'IS:',5X,E12.5,//)
110 CONTINUE
WRITE(6,120) ISC
120 FORMAT(5X,'THE SC CURRENT OF THE ENTIRE CELL IS:',2X,E12.5,//)
C
C
C WE NOW CALCULATE FILL FACTOR FF AND EFFICIENCEY EFF.
C
c
RLOAD = 6.5
DO 130 KK = 1,10
KKDUMM = KK
C DDKUMM TELLS US HOW LONG IT TAKES TO GET TO RLOAD FOR MAX POWER.
C (NOTE: KKDUMM=1 IF RLOADMP INITIALLY OVERSHOT. TRY LARGER RLOAD.)
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
ILOAD = P2(IP1)/RLOAD
POWERl = ILOAD*P2(IP1)
RLOAD = RLOAD-0.1
CALL NS01A(IP1,P2,P3,P4,P5,P6,P7,IP8,IP9,P10)
ILOAD = P2(IP1)/RLOAD
POWER2 = ILOAD*P2(IP1)
IF((POWER2 POWERl).LT.0.0) GO TO 140


CHAPTER 3
A METHOD FOR EXPERIMENTAL ASSESSMENT OF THE SHIFTING
APPROXIMATION, WITH APPLICATION TO POLYSILICON SOLAR CEILS
3.1 Introduction
The shifting approximation that the illuminated current of a solar
cell is equal to the dark current shifted by the short-circuit photocur
rent is discussed in detail in [5,14]. We report here the results of an
experimental investigation of the validity of the shifting approximation
for four types of polycrystalline Si solar cells.
A solar cell may be thought of as a system with two inputs and two
outputs. The inputs are the optical generation rate in the base and the
excess minority carrier concentration at the edge of the space-charge
region in the base (if the recombination current in the quasi-neutral
emitter is negligible); the corresponding outputs are the short-circuit
photocurrent and the dark recombination current, respectively. It is
shown in [5] that the shifting approximation is valid if this system is
linear; in [14] it is shown that the shifting approximation may remain
practically valid despite some nonlinearity in the system. In a poly-
silicon solar cell, if the shifting approximation is not valid, it is
most likely because the system has been rendered nonlinear by the depen
dence of the material properties (e.g., the effective minority carrier
lifetime) on the illumination level or by the existence of a large series
or small shunt resistance. Recent data on the majority-carrier Hall
mobility in polysilicon material [15] indicate that the grain-boundary
potential barrier under illumination vanishes almost completely. This
14


93
p-type bulk
E
c
E
E
F
V
Figure 5.4 Thermal equilibrium band diagram for that part of a GB
J"
which is adjacent to the p-type bulk of an n -p poly
silicon diode.


CHAPTER 5
SMALL-SIGNAL ADMITTANCE METHOD FOR DETERMINING
THE SURFACE-STATE DISTRIBUTION AT THE PREFERENTIALLY
DIFFUSED PART OF THE GRAIN BOUNDARY
5.1 Introduction
Lattice mismatch at the grain boundaries (GB's) of polysilicon
solar cells causes the formation of energy levels (surface states) in
the energy gap that serve as recombination centers. Surface states
can be either donor-type or acceptor-type. Those surface states that
are near the center of the energy gap will afford the highest recombina
tion rates [44] and, thus, will be the most efficient recombination
centers.
For an n+ -p polysilicon diode, methods for calculating the sur
face recombination velocity S at that part of a GB which is adjacent
to the quasi-neutral p-type bulk and for estimating the surface recom
bination velocity s at that part of a GB which is in a preferential-
ly diffused n-region have been demonstrated in sections 4.3.1 and
4.3.2.2, respectively. With the assumption of a uniform distribution
of surface states in the energy gap, the GB surface-state density N
ss
can be calculated [45] for both the diffused and undiffused sections
of the GB:
N = S/O v ,
ss th
(5.1)
where, S, O, and v ^ are the surface recombination velocity, capture
cross-section, and thermal velocity for minority carriers at the GB,
77


83
Pn^y
Figure 5.3(a) The equivalent circuit model obtained from Fig. 5.2
by lumping the circuit elements from both sides of
the GB.


131
Runs 13P3 and 13P4
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Oxidation in 1700 cc/min O2 at 1050C: 5 minutes in dry O2,
35 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry O2. Oxide thickness = 4400 .
3. Photolithography to open holes for phosphorus diffusion.
4. Standard Cleaning.
5. Phosphorus predeposition: same as step 2 in Run 4P4.
6. Drive-in (13P3 only): 48 hours at 600C in dry N2.
7. Etch phosphosilicate glass in 10% HF solution for 10 seconds.
8. Drive-in at 1050C in 1700 cc/min 02^ 15 minutes in dry O2,
20 minutes in wet O2 bubbled through deionized water at 95C,
5 minutes in dry O2. Oxide thickness = 3000 .
9. Remove n+-layer on backside by lapping with SiC slurry.
10. Standard cleaning.
11. Photolithography to open holes for metallization.
12. Standard cleaning.
13. Metallization. A1 front and back.
14. Photolithography to define top contact and MOS guard ring.
15. Solvent cleaning.
16. Anneal: 10 minutes at 450C in 400 cc/min N2.


48
components. Equation (4.3) is strictly valid only if one of the SCR
components in (4.1) is dominant or if all SCR components in (4.1) have
the same reciprocal slope factor.
Similarly for the GBF diode:
XD = IxotexpqV/n^kT) 1] + IQNQ[exp(qV/kT) 1] + V/R^. (4.4)
All I-V curves of diodes investigated in this work are described by (4.3)
or (4.4).
4.3.1 Space-Charge Region Current Components (n+-p diodes)
Figure 4.6 shows the measured dark I-V characteristics for five
representative n+-p diodes chosen from over 100 devices containing
either zero or a few grain boundaries. A summary including the total
length of the GBs and the parameters defined in (4.3) and (4.4) for
each of these diodes is shown in Table 4.1. A comparison of the data
for the GB diodes with the data for the GBF diode No. 1 shows the strong
effect of the GB's on the I-V characteristics. This is true even for
device No. 3 which had only one GB. The ratio of currents at 160 mV for
diodes No. 3 and No. 1 is about 40.
We now analyze the current components in the n+-p GB diodes by
comparing the I-V curves of these diodes with the I-V curve of a GBF
GB
diode, Fig. 4.6. The GB component of IQ can be obtained by subtracting
the measured current of the GBF diode from the measured current of the
GB
GB diode, i.e., I "In* However, we observe that the GB components
D
dominate the current at small biases, below about 300 mV. In this range
GB
m^ m^ -1.8; therefore we can write:
t^UOO 300 mV) lR + 4Br, + Vrt
(4.5)


95
Figure 5.5 Microphotograph showing the top view of the n -p mesa diode
39P#2. The mesa diode is on a chip which is bonded to a
TO-5 header. The mesa appears as the roughly circular struc
ture near the center of the chip. The area of the chip is
-2 2
approximately 5.2 x 10 cm ; the area of the mesa is
3 2
approximately 1.6 x 10 cm ; the total length of the GBs
is . 3.43 cm; and the depth of preferential diffusion
GB
is d 9 pm.
n


106
not able to apply the conductance method to determine N (E) x, and a .
ss n
This problem is illustrated in Fig. 5.9 where we plot the measured
values for C. and G. vs. f for a diode in Run 39P. The C. curve
in m m
follows (5.4), while the G curve monotonically increases without
reaching a plateau for f > f (which would be equivalent to G /(0 vs.
ss p
CO going through a peak at co = 1/x) The exact reason for this behavior
in G^n was not determined, but it is suspected that the large series
resistance of the p-type bulk is involved. The influence of series
resistance can be suppressed by using a lower resistivity substrate.
One of the main conclusions of this chapter is that the detailed
knowledge of the surface channel of the MOS transistor which has been
accumulated over many years can be applied to an analysis of the GB
surface states.


142
41. P. L. Castro and B. E. Deal, "Low-temperature reduction of
fast surface states associated with thermally oxidized sili
con," J. Electrochem. Soc., vol. 118, pp. 280-286, Feb. 1971.
42. B. L. Sopori, Abstract of "Investigations on photovoltaic losses
due to grain boundaries in polycrystalline silicon," presented
at SERI topical polycrystalline silicon subcontractors review
meeting, Colorado Springs, CO., Nov. 1980.
43. C. T. Sah, "Effect of surface recombination and channel on p-n
junction and transistor characteristics," IRE Trans. Electron
Devices, vol. 9, pp. 94-108, Jan. 1962.
44. W. Shockley and W. T. Read, "Statistics of the recombinations
of holes and electrons," Phys. Rev., vol. 87, pp. 835-842,
Sept. 1952.
45. A. S. Grove, Physics and Technology of Semiconductor Devices,
p. 136, John Wiley and Sons, Inc., New York, 1967.
46. C. C. Shiue and C. T. Sah, "New mobility-measurement technique
on inverted semiconductor surfaces near the conduction thresh
old," Phys. Rev. B, vol. 19, pp. 2149-2162, Feb. 1979.
47. C. T. Sah, "The equivalent circuit model in solid state elec-
tronics-III," Solid State Electronics, vol. 13, pp. 1547-1575,
Dec. 1970.
48. E. H. Nicollian and A. Goetzberger, "The Si-SiO^ interface-elec
trical properties as determined by the metal-insulator-silicon
conductance technique," Bell Syst. Tech. J., vol. 46, pp. 1055-
1130, July-Aug., 1967.
49. C. T. Sah, Solid State Electronics Laboratory, Technical Report
No. 1, University of Illinois, 1964.
50. A. Goetzberger, E. Klausmann, and M. J. Schulz, "Interface
states on semiconductor/insulator surfaces," CRC Critical Re
views in Solid State Sciences, pp. 1-43, Jan. 1976.
51. S. M. Sze, Physics of Semiconductor Devices, p. 37, John Wiley
and Sons, Inc., New York, 1969.
52. C. T. Sah, P. C. H. Chan, C. K. Wang, R. L. Y. Sah, K. A.
Yamakawa, and R. Lutwack, "Effect of zinc impurity on silicon
solar-cell efficiency," IEEE Trans. Electron Devices, vol. ED-28,
pp. 304-313, March 1981.
53. C. A. Mead and W. G. Spitzer, "Fermi-level position at metal-
semiconductor interfaces," Phys. Rev., vol. 134, pp. A713-A716,
May 1964.


90
The surface-state density along the preferentially diffused part of
the GB's is then given by
N => C /q A ,
ss ss GB
(5.10)
where dQ Z is the total area of the preferentially diffused part
of the GBs.
We assume as a first approximation that the preferentially dif
fused n-region is uniformly doped. In Fig. 5.1(b), it is seen that
the position of the Fermi level for the preferentially diffused part
of the GB's is given by
yo) E.(0) = E (0)/2 ql>n qcj^,
(5.11)
where the GB is located at x = 0. In order to determine the position
of the Fermi level for the preferentially diffused part of the GB's,
qcj) and qc(> must be calculated,
n GB
With the use of the Boltzmann relation [51] for a nondegenerate
semiconductor in thermal equilibrium, the band diagram in Fig. 5.1(b)
shows that
q(>n = E (0)/2 kT In (N^/n.). (5.12)
The values of E^(0) and n^ as a function of the temperature T are
found in [52].
The band bending qc|> which is due to the surface states at the
Gd
GB can be approximately determined by the method of [46]. In [18], it
is assumed that N is uniformly distributed in the energy gap and
s s
that there exists a "neutral level" qcf)^ at approximately E^(0)/3 such
that, for E (0) = qcj) the net charge in the GB surface states is
X1 O
zero. The assumption concerning the energy gap position of qcj)^ is
supported by [53], With these assumptions, the requirement of overall


APPENDIX V
STANDARD WAFER CLEANING AND POLISHING PROCEDURES
Standard Wafer Cleaning Procedure
1. Scrub with cotton swab soaked with trichloroethylene (TCE).
2. Boil in TCE for 5 minutes.
3. Boil in fresh TCE for 5 more minutes.
4. Boil in acetone for 5 minutes.
5. Boil in methanol for 5 minutes.
6. Rinse in deionized water (p ~ 10 Mfi-cm) for 5 minutes.
7. Dip in 1 ^SO^ : 1 ^02 solution, v/v, for 10 minutes.
8. Remove oxide by dipping in 1 HF : 9 ^0 solution, v/v, for
10 seconds.
9. Rinse in deionized water for 5 minutes.
10.Blow dry with ^ gas gun.
Standard Wafer Polishing Procedure
1. Clean and degrease by following steps 1-6 above.
2. Swirl wafers in a solution of 2 HF : 15 HN0 : 5 CH-C00H, v/v, for
10 minutes.
3. Rinse in deionized water for 5 minutes.
4. Blow dry with N2 gas gun.
128


71
Figures 4.10 and 4.11 show the effect of leakage current on the J-V
characteristics of 50-mil n"*"-p mesa diodes. The leakage current of the
GB
GB mesa diode in Fig. 4.11 causes the measured value of I and conse
quently, the calculated value for S^, to be erroneously high. By the
method of Section 4.3.1, S is calculated to be 1.5 x 10* cm/sec. This
value exceeds the corresponding values for all of the n+-p diodes in
Tables 4.1 and 4.3 by more than a factor of four. Though can vary
significantly from diode to diode (Tables 4.1 and 4.3), the above
comparison demonstrates the questionable value of I-V measurements on
GB
small mesa diodes in analyzing the GB-component of 1^ Some researchers
have failed to notice this point [42]. In Fig. 9 of [42], for example,
GB
the I-V curves of 50-mil mesa diodes display values of >2.0, which
indicates that the current at low bias levels is dominated by recombina
tion at the surface around the perifphery of the diode [43]; and,
consequently, these I-V data are of little analytical use.
Surface leakage current is proportional to the circumference, and
thus to the radius r of the diode; whereas, the current of a leakage-
2
free diode is proportional to the area of the diode, and thus to r .
Consequently, in a mesa diode, the relative contribution of the surface
leakage current to the total measured current will increase as r
decreases. As seen in Fig. 4.10, for a mesa diode with r 25 mils,
the leakage current can dominate the total measured current at low bias
levels (0-300 mV).
4.5 Discussion
This chapter has described and analyzed the effects of GB's on the
performance of polysilicon p-n junction solar cells.


58
1/T(eff) "V'1 +
(4.11)
For d L T ,-,-v T and Irt.TT, dominates; for small d_, T < T
G n n(eff) n QNB G n(eff) n
GB
and Ig becomes important. For device No. 5 with diameter d = 760 pm
and five GB's, the approximate grain size is d 150 pm and
G
Tn(eff) ~ 0*9 Psec. This value is to be compared to Tn 6 psec,
GB
corresponding to Ln 130 pm for the GBF diode No. 1. For 1^ to be
important, the intragrain base electron diffusion length, Ln> has to be
larger than the preferential diffusion depth d^ 4 pm. From our
GB
experiment we found 130 pm d^. The effect of 1^ will obviously
increase with decreasing d
n
4.3.3. Illuminated I-V Curves (n -p diodes)
Table 4.2 shows the summary of results of measurements on illumi
nated diodes. The short circuit current Ig^ is almost constant except
for device No. 5, but V_,_, decreases slightly with increasing nT¡. This
UG GB
is consistent with previous results [31,32] and also with a recently
proposed model [38] for devices with grain size d^ > Ln. The decrease
GB
in Vnr, is due to increased IG which is directly proportional to ,
UG oLK GB
GB
and also due to increased 1^ The slight decrease in Ig^ for device
No. 5 is because, in this device with five GB's within the 760 pm diode,
the average grain size is comparable to 130 pm; thus, some of the
light-generated electrons will recombine at the GB's and will not
contribute to the external measured I .
DG
The preferentially diffused n-regions can contribute to the I if
BG
d ~ L For the devices studied, d L and no increase in I__ is
n n n n SC
observed for the GB diodes. The fill factor decreases with as
GB
expected due to the increasing importance of 1^ with m^. > 1.0.


APPENDIX VI
FABRICATION SCHEDULES FOR RUNS 4P4, 6P1, 7P, 8P1, 13P3, AND 13P4
All runs were fabricated on 5 fi-cm p-type Wacker polysilicon sub
strates.
Run 4P4
Steps:
1. Standard wafer cleaning and polishing (Appendix V).
2. Phosphorus predeposition. 30 minutes at 900C in an atmosphere of
90 cc/min N2 bubbling through P0C13 at 30C, 170 cc/min dry C>2,
1500 cc/min N2 carrier gas.
3. Drive-in: 100 minutes at 900C in 1500 cc/min N2<
4. Etch phosphosilicate glass in 10% HF solution for 10 seconds.
5. Rinse in deionized water.
6. Remove n+-layer on backside by lapping with SiC slurry.
7. Standard wafer cleaning.
8. Metallization. Front: Al. Back: Ti, Ag.
9. Anneal: 10 minutes at 400C in 400 cc/min N2
10. Photolithography to define mesa diode pattern.
11. Etch in Al and Si etches to form mesa diodes.
Run 6P1
Same as Run 4P4, but with the following diffusion schedule:
Predeposition: 60 minutes at 900C.
Drive-in: 30 minutes at 900C.
Drive-in: 48 hours at 600C.
Drive-in: 40 minutes at 900C.
129


35
Gate
c
> <
>
/
l
1
X M V n+
7
iary
P type
^,Grain Boun
(a)
Figure 4.1 (a) Cross section of the 30 mil in diameter n -p solar cell
with MOS guard ring showing one columnar grain boundary
crossing through the middle.
(b) Top view showing five metal contact circles (5 mil in
diameter) and one grain boundary crossing the cell. The
total metal coverage is 20%.


120
CALL FCTVAL(VMP,D7)
GX = D7
IF((FX.LT.O.O).AND.(GX.GT.0.0)) GO TO 40
GO TO 5
40 WRITE(6,45) M,N,K
45 FORMAT(5X,316,/)
QKT = 38.70
Q2KT = 19.35
D9 = ISC-(I01*EP1)-(I02*EP2)
IMP = ABS (D9)
DIO = ((SQRT((I02**2)+(4*ISC*I01)))~I02)/(2*101)
VOC = (2*(KT/Q))*ALOG(DIO)
FF = (VMP*IMP)/(VOC*ISC)
EFF = VOC*ISC*FF
WRITE(6,47) DLR
47 FORMAT(23X,'DIFF LENGTH. RATIO:' ,E12.4,/)
51 WRITE(6,101) VOC,FF,EFF
101 FORMAT(22X,VOC=',F8.5,3X,,FF=,F8.5,3X,'EFF=',F8.5,//)
20 CONTINUE
10 CONTINUE
STOP
END
SUBROUTINE FCTVAL(VMP,D7)
REAL JSCG,JSCB,J01G,J02G,J01B,J02B,JOl,J02,JSC
REAL JR,JSCR,ISC,I01,I02,KT,IMP
COMMON M,N,EP1,EP2,I01,I02,ISC
KT = 4.14E-21
Q 1.602E-19
QKT = 38.70
Q2KT = 19.35
Dl = QKT*VMP
D2 = Q2KT*VMP
EP1 = EXP(Dl)
EP2 = EXP(D2)
D3 = 102/101
D4 = ((Q*VMP)+(2*KT))/(2*((Q*VMP)+KT))
D5 = D3*D4
D6 = (ISC*KT)/(((Q*VMP)+KT)*I01)
D7 = EP1+(D5*EP2)-D6
RETURN
END


62
4.3.4 Grain-Boundary Passivation by Hydrogenation Treatment
Tables 4.4 and 4.6 present parameter values for the n+-p diodes in
Run 37P. The Run 37P diodes underwent the same fabrication schedule as
the Run 36P diodes, except for an additional processing step [39] that
was intended to tie up dangling bonds along the grain boundaries with
monoatomic hydrogen [39,40]. After the 37P wafer had undergone the
drive-in step, the oxide grown during the drive-in was covered with a
6000 layer of vacuum-evaporated aluminum. The wafer was then sintered
at 450C for 12 hours in dry N£. The aluminum was then removed by
chemical etchant and the processing of the wafer was continued as in
Run 36P. This additional processing step is known to tie up dangling
bonds at the S-SO2 interface in MOS devices by the generation of some
form of active hydrogen at the SO2-AI interface [41]. By following
this procedure, we were able to use the diodes of Run 36P as a control
group for determining the effect of the hydrogenation step on the diodes
of Run 37P. The 37P wafer was not sintered after the ohmic contacts were
formed so as to avoid out-diffusion of the hydrogen from the GB's [39],
A comparison of the values of for Run 37P in Table 4.4 with
the values of for Run 36P in Table 4.3 shows that the hydrogenation
step has a negligible effect on S^. By applying both the method of [7]
and the method of [35] to several GBF diodes in Run 37P, it was deter
mined that the hydrogenation step lowers the intragrain base minority
carrier diffusion length Ln from about 130 pm to about 90.yin. This
lowering of Ln is reflected in the I-V characteristics shown in Fig. 4.8.
In agreement with the data reported in [39], Table 4.6 indicates that
the hydrogenation treatment slightly increases V^. This conclusion is
not firm though, because the increase observed averaged only 11 mV and
the spread of values of VQC was large.


5
illuminated current is equal to the dark current shifted by the short-
circuit photocurrent [5].
We consider a simple ideal case in which only two subcells are used;
one subcell represents the good-quality material part of the cell, and
the other represents the poor-quality material part of the cell. The
series and shunt resistances are neglected, and the current in each
subcell is assumed to be one-dimensional (Fig. 2.2). For this simple
case, two types of areal inhomogeneity for an n+-p Si solar cell are
considered. We define and to be the areas of the good and poor
regions of the cell, respectively. Then the areal quality factor is
defined to be AQF = A^/A, where A = A^ + Ap is the total solar cell area.
2.2 Type 1 Areal Inhomogeneity
For this type of areal inhomogeneity, the non-illuminated (or dark)
quasi-neutral current densities of the good-quality and poor-quality
diodes, and Jq^p> respectively, are allowed to differ by several
orders of magnitude. For both diodes, the recombination currents are
dominated by recombination in the quasi-neutral regions rather than in
the space-charge regions. Both diodes have the same short-circuit
current density JgC. This type of areal inhomogeneity could occur if the
quasi-neutral emitter dark recombination current density experiences
QNii
drastic areal variations due, for example, to impurity clusters or
variations in the surface recombination velocity in the heavily doped
emitter. For these variations in J..T to be important, J-XTT, must be the
QNE r QNE
dominant component of JqNp. To increase the likelihood of this, we will
17 ^
assume a high base doping concentration: N.A = 10 cm We assume
AA
further a long base diode for which the short-circuit current density
2
JSC ~ ^ mA/cm and the base minority carrier diffusion length


CURRENT (A)
64
VOLTAGE (V)
Figure 4.8 Measured dark I-V curves of two GBF n -p solar cells
showing the effect of the hydrogenation treatment on the
intragrain base minority carrier diffusion length, L .
The solar cells had identical fabrication schedules ex
cept that the cell represented by the upper curve under
went the hydrogenation treatment. This treatment lowered
L^ from about 130 ym to about 90 ym.


Table 6.1 Summary of experimental runs incorporating fabrication procedures intended to suppress
the grain-boundary component of the dark recombination current.
Run
Device Description
Purpose or Special Fabrication Step
4P4
n+-p 10-, 20-, 50-mil dark mesa
diodes.
Used as control group for comparison with Run 6P1.
6P1
n+-p 10-, 20-, 50-mil dark mesa
diodes.
48 hour 600C drive-in to enhance the preferential diffu
sion of phosphorus along the grain boundaries.
7P
n+-p 1 crn^ solar cells.
Low-temperature-induced preferential transport of mono-
atomic hydrogen along the GB's.
8P1
n+-p 50-mil dark mesa diodes.
Predeposition of boron followed by a 48 hour 600C drive-
in. The boron-doped top silicon layer was then removed,
and phosphorus was diffused to form the top n+-p junction.
13P3
n+-p 10-, 20-, 50-mil planar
diffused dark diodes with MOS
guard rings.
48 hour 600C drive-in to enhance the preferential diffu
sion of phosphorus along the grain boundaries.
13P4
n+-p 10-, 20-, 50-mil planar
diffused dark diodes with MOS
guard rings.
Used as control group for comparison with Run 13P3.
22P
n+-p 1 cm^ solar cells.
Preferential etching of GB's with Sirtl Etch before the
formation of the p-n junction. Wafers not polished.
25P
n+-p 1 cm^ solar cells.
Same as Run 22P, but with all wafers initially polished
in 2 HF : 15 HN(>3 : 5 CI^COOH solution.
109


41
between one of the top two diodes and the substrate is merely the
capacitance of the GBF diode. The capacitance measured between the small
diode in the bottom pair and the substrate will be equal to the sum of
the capacitances of the two diodes on the bottom plus the capacitance
contributed by the diffused GB channel. Figure 4.4 shows the capacitance
of a 10-mil GBF diode and the capacitance of a 10-mil GB diode which is
connected by a diffused GB channel to a much larger GB diode.
Two conclusions can be made based on Fig. 4.4. First, the capaci
tance of the 10-mil GB diode is much larger than the capacitance of a
10-mil GBF diode at V = 0 V. This indicates that the diffusion sched-
K
ule used in the fabrication of these devices (30 minute 900C predeposi
tion followed by a 40 minute 1050C drive-in) resulted in a preferential
diffusion of phosphorus down the GB's. Such devices that share a common
GB will be electrically connected by that diffused GB. The 6 ym deep
preferential diffusion will increase the p-n junction area of the 10-mil
GB diode by only a few percent. This slight increase in the area cannot
account for the large value of capacitance at VB = 0 V, which is due
mainly to the contribution from the larger GB diode. Secondly, at
V_, 3 V, the capacitance of the 10-mil GB diode drops to the level of
the 10-mil GBF diode, and the two curves are identical for ^ 3 V.
The reason for this capacitance dependence on reverse bias is a widening
of the depletion layer in the channel by the reverse bias until the
channel is completely depleted. The GB-connected diodes thus become
electrically disconnected due to a depleted nonconducting channel.
This capacitance experiment also was done on n+-p devices made by a
30 minute diffusion at 900C and on the p+-n diodes. No capacitance
difference comparable to that exhibited in Fig. 4.4 was observed. This


APPENDIX VII
FABRICATION SCHEDULE FOR RUNS 22P AND 25P
Both runs were fabricated on 5 fi-cm p-type Wacker polysilicon sub
strates .
Steps:
1., Standard wafer cleaning.
2. Standard wafer polishing (25P only).
3. Etch sample wafers in Sirtl Etch (50 g CrO^, 100 ml H^O, 100 ml HF)
in ultrasonic bath for 10 minutes. Do not etch control wafers.
4. Remove oxide by dipping in 10% HF solution.
5. Phosphorus predeposition. 15 minutes at 850C in an atmosphere of:
90 cc/min N^ bubbled through POCl^ at 30C, 170 cc/min dry 0^,
1500 cc/min ^ carrier.gas.
-j.
6. Remove n -layer on back side by lapping with SiC slurry.
7. Solvent cleaning.
8. Metallization. Use OCLI-supplied mask to form solar cell grid
pattern on front side.
9. Etch edges in 3 HF : 5 HNO^ : 3 CH^COOH solution for 10 minutes.
132


Table 4.6 Summary of Ic and V for all 30-mll diameter solar cells.
bu UU Q ry
T = 25.0C, A = 4.6 x 10 cm 1 Sun AMO.
Run
Type
Number of
Diodes
Measured
VQC spread
(mV)
VQC average
(mV)
Igc spread
(pA)
Igc average
(pA)
34P
GBF
p -n 4
471 -
522
494
73 -
76
75
Twins
1
480
73
GB
12
451 -
558
496
66 -
84
75
36P
GBF
n -p 7
478 -
504
495
61 -
75
67
Twins
1
496
65
GB
12
466 -
491
481
59 -
74
68
37P
GBF
+
n -p
0
Twins
0
GB
7
468 502
492
64 82
70


CHAPTER 1
INTRODUCTION
Recent attention has been focused on polycrystalline silicon solar
cells because of their potential low cost. The anticipated advantage
of low cost is offset by the fact that polycrystalline solar cells
have displayed efficiencies that are much less than those of the
corresponding single-crystal devices [1,2,3]. This lower efficiency
is caused, to varying degrees, by the presence of dark recombination
currents associated with the grain boundaries, by the degrading effects
of areal inhomogeneity, by a low short-circuit current density, and
by a low shunt resistance. In this dissertation, we develop methods
for investigating the properties and performance-degrading mechanisms
of polysilicon p-n junction solar cells.
In Chapter 2, we demonstrate the degrading effects of areal inhomo
geneity by means of a parallel-subcell equivalent-circuit model.
Chapter 3 describes an experimental method for assessing the validity
of the shifting approximation. These two chapters are applicable to
single-crystal as well as to polycrystalline solar cells.
Most of the experimental devices used in this research were
fabricated on Wacker polysilicon substrates. Wacker material (both p
and n-type) was chosen because it has large enough grain diameters
(~1 mm) to conveniently enable the fabrication of devices that contain
either zero, or at most a few, grain boundaries. By comparing the data
(e.g., capacitance, current-voltage characteristic) on a device
1


59
Table 4.2 Parameter values for devices No. 1-8 while under 1 Sun AMO
illumination. T 25C, A = 4.6 x 10-3 cm2.
Device No. IgC VQC FF
(yA) (mV)
62
497
0.81
62
497
0.80
63
489
0.78
63
485
0.75
59
467
0.77
75
494
0.78
73
480
0.78
75
496
0.78
8