Title Page
 Table of Contents
 Physical-short channel model
 Model verification and applications...
 Model characterization
 Model extensions
 Summary and conclusions with...
 Biographical sketch

Title: Modeling small-geometry silicon-on-insulator transistors for device and circuit computer-aided design
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00082288/00001
 Material Information
Title: Modeling small-geometry silicon-on-insulator transistors for device and circuit computer-aided design
Physical Description: vi, 172 leaves : ill. ; 28 cm.
Language: English
Creator: Veeraraghavan, Surya, 1962-
Publication Date: 1988
Subject: Metal oxide semiconductor field-effect transistors   ( lcsh )
Thin film devices   ( lcsh )
Transistor circuits -- Data processing   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1988.
Bibliography: Includes bibliographical references.
Statement of Responsibility: by Surya Veeraraghavan.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00082288
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 001115792
oclc - 19956067
notis - AFL2515

Table of Contents
    Title Page
        Page i
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
    Physical-short channel model
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
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    Model verification and applications to device design
        Page 43
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    Model characterization
        Page 71
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        Page 110
    Model extensions
        Page 111
        Page 112
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    Summary and conclusions with recommendations
        Page 137
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    Biographical sketch
        Page 172
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        Page 174
Full Text









I wish to express a very deep sense of gratitude to my advisor,

Professor Jerry Fossum, who has been a constant source of support,

guidance, and friendship throughout the time that I have known him. I

would also like to thank the other members of my committee, Professors

Lindholm, Burk, Eisenstadt, and Holloway, for their interest in this

research and patience in reading through the manuscript.

I am grateful to Harris Semiconductor, Texas Instruments, the

Semiconductor Research Corporation, and the Naval Research Laboratory

for the financial and technical support that made this work possible,

and to the Hewlett-Packard Corporation for its generous donation of

the TECAP software package. In particular, I wish to acknowledge Mr.

Dan FitzPatrick for rewriting the SPICE2 code to implement the SOI

model, and Drs. Wade Krull, Rich Cherne, Ravi Sundaresan, and Jean-

Pierre Colinge for providing test devices.

These acknowledgements would be incomplete without a mention of at

least some of the many people I count as both colleagues and friends.

In particular, I would like to mention Drs. Robert McDonald, Adelmo

Ortiz, and Shuy-Young Yung, and Messrs. Hang-geun Jeong and Myung-suk

Jo for countless hours of stimulating discussions.

Finally, I wish to express my gratitude to my soccer team,

Entropy, my very good friends Ajit Lalwani and Marcos Rubinstein, and

last but far from the least, Anne Hynek and my sisters and parents,

whose love and encouragement have sustained me through the years.



ACKNOWLEDGEMENTS.................................................. ii

ABSTRACT.......................................................... v


1 INTRODUCTION.................................................... 1

2 PHYSICAL SHORT-CHANNEL MODEL .................................... 8

2.1 Introduction.. ........................... .................... 8
2.2 Physical Model................................................ 8
2.2.1 Charge Sharing............................................ 9
2.2.2 Drain-Induced Conductivity Enhancement.................... 13
2.2.3 Carrier Velocity-Field Model .............................. 17
2.3 Triode Region............................................... 20
2.4 Saturation Region............................................ 21
2.4.1 Saturated Drain Current................................... 21
2.4.2 Channel-Length Modulation ................................. 23
2.4.3 Impact-Ionization Current.................................. 25
2.5 Charge-Based Model ............................................ 27
2.5.1 Triode and Saturation Regions.............................. 27
2.5.2 Cutoff Region ..................... ............................. 31
2.6 SPICE2 Implementation........................................ 33
2.7 Summary.............. ............... .......................... 42


3.1 Introduction........................ ........................ 43
3.2 Threshold-Voltage Reduction.................................... 44
3.3 Drain-Induced Conductivity Enhancement (DICE)................ 50
3.4 Velocity Saturation and Channel-Length Modulation ............ 53
3.5 Hot-Carrier Effects.......................................... 60
3.6 Subthreshold Slope........................................... 60
3.7 Back-Surface Charge Modulation............................... 64
3.8 Summary/Conclusions.... ..................... .................. 69

4 MODEL CHARACTERIZATION........................................... 71

4.1 Introduction.............................. .................... 71
4.2 Model Selection Criteria..................................... 72
4.3 Parameter Extraction ......................................... 79
4.3.1 Threshold Voltage Measurements........................... 82
4.3.2 Linear-Region Conductance Measurements.................... 86
4.3.3 Determination of Empirical Charge-Sharing Parameters...... 94
4.3.4 Body-Current Measurements.................................. 96
4.4 Discussion ................................................... 102

5 MODEL EXTENSIONS................................................

5.1 Introduction................................
5.2 TFA-TFD Model Unification (TFAD)............
5.2.1 Physical Model...........................
5.2.2 Steady-State Currents ....................
5.2.3 Charge Calculations......................
5.3 Bulk and TFA-TFAD-TFD Model Unification.....
5.4 Subthreshold Conduction Model...............
5.5 Nonuniform Film Doping.....................
5.6 Surface-State Density........................
5.7 Bias-Dependent Parasitic Resistances........
5.7.1 Parasitic Drain and Source Resistances...
5.7.2 Parasitic Body Resistance................
5.8 Summary.....................................




B PISCES STUDY OF CHARGE SHARING..................................


D CALCULATION OF CHARGES..........................................


BIOGRAPHICAL SKETCH...............................................









. . . . . . . . ..
. . . . . . . . .

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




December 1988

Chairman: Dr. J.G. Fossum
Major Department: Electrical Engineering

This dissertation concerns the physical charge-based modeling of

small-geometry silicon-on-insulator (SOI) MOSFETs for large-signal

transient circuit simulation. A new model for the thin-film SOI MOSFET

(the basic device in a technology with the potential for becoming the

mainstream for submicron integrated circuits) that accounts for the

predominant thin-film and short-channel effects has been developed. The

thin-film effects include the coupling between the front and back

gates of the MOSFET, and associated floating-body effects. The short-

channel effects, which are physically linked to the thin-film effects,

include threshold-voltage reduction by charge sharing, drain-induced

conductivity enhancement, field-dependent mobility and velocity

saturation, channel-length modulation, and generation by impact

ionization. From the basic physical model, quasi-static charge

expressions are calculated for each of the five terminals of the

MOSFET. The new five-terminal charge-based model is then implemented in

the circuit simulation program SPICE2.

A systematic measurement-based parameter-extraction algorithm is

defined. The model parameters extracted using this technique, which

involves minimal optimization, are shown to be physically meaningful.

A preliminary demonstration of the model's predictive capability is

done for a contemporary SOI MOSFET technology.

Through measurements and from the theoretical predictions of the

model, short-channel effects in SOI MOSFETs are shown to be unique

because of dependence on film thickness and body and substrate (back-

gate) biases. The potential advantages of scaling the film thickness

with the channel length are demonstrated, and device design criteria

are discussed. A new short-channel effect, which we term "back-surface

charge modulation," is also presented, and is shown to be predictable

from the basic model analysis.


Thin-film silicon-on-insulator (SOI) technology is becoming

increasingly important and viable for very-large-scale-integrated

(VLSI) circuits [La87]. MOSFETs fabricated in these films (see Fig.

1.1) are well isolated from each other by the buried oxide layer (made,

for example, by oxygen implantation), thus completely eliminating the

problem of latch-up which exists in bulk technologies. The presence of

an insulating layer with lower permittivity than silicon enables a

lowering of the parasitic capacitance to the substrate. The reduced

volume occupied by each device also implies increased radiation

hardness. In addition, the structure of the device seems to indicate a

greater ability to scale the thin-film MOSFET than the bulk MOSFET

[Sa80, Th86], and holds out the possibility of three-dimensional

integration [Ak86].

While much effort has gone into technology and process development

[Ie86, Ie87], not as much work has been done on modeling the

electrical characteristics of thin films. Measurements and numerical

simulations of SOI MOSFETs have shown two major influences on the

current-voltage characteristics which are not accounted for in models

for bulk MOSFETs (without an underlying oxide). The first of these is

the effect of the back-gate (substrate) bias VGbS in determining the

conduction of the inversion region at the interface between the front

Silicon Film

Fig. 1.1 Cross-sectional view of a generic n-channel SOI MOSFET
showing the five terminals: the front gate (Gf), the back
gate (Gb), the source (S), the drain (D), and the body (B).


gate oxide and the silicon film (heretofore referred to as the "front

surface") [Li84b, Li84a, Co84]. For example, in n-channel MOSFETs, the

application of a large negative bias, VGbS, on the back gate creates an

accumulation layer at the interface between the buried oxide layer and

the silicon film (heretofore referred to as the "back surface"), thus

pinning the potential at that interface to the body voltage, VBS. This

causes the threshold voltage VTf to vary linearly with VBS, in

contrast to the nonlinear dependence in bulk MOSFETs [Sz81]. However,

for more positive VGbS, the back surface is depleted, and the threshold

voltage becomes independent of VBS, but starts to depend linearly on

VGbS. Another interesting fact brought out by the measurements and two-

dimensional simulations is the effect of leaving the film body

floating: in the saturation region, holes (in the n-channel device)

generated by impact ionization in the drain region [Ti75, E175, Ea78]

are injected into the floating body, causing a build-up of the

potential of the accumulation region at the back interface, if it

exists. This causes an enhancement in the conduction of the MOSFET, and

shows up as a "kink" in the ID(VD) characteristics of the device. A

similar phenomenon is seen when the MOSFET is turned on rapidly [Ea78,

Li84c]: here, the rapidly expanding depletion layer in the silicon

film forces holes to build up the body potential. In bulk CMOS

circuits, this phenomenon is usually insignificant because the body

voltage is kept fixed at the source voltage by an external contact

between the body and source terminals, and because the current due to

the generated holes is many orders of magnitude less than the channel

current. However, in SOI transistors with floating bodies (and even in


bulk CMOS devices with floating wells), it becomes essential to

properly model the effects of carriers generated by impact ionization.

Various authors [Sa80, Ka85, Ar86, Th86] have presented two-

dimensional numerical solutions of the semiconductor equations (i.e.,

Poisson's equation, the electron and hole continuity equations, and

the energy balance equations) for the potential 9, and the electron and

hole concentrations n and p, in SOI MOSFETs. Though this approach

provides insights into the important physical mechanisms involved in

the device operation, at present, it has limited use as a method to

study the performance of SOI MOSFETs in large circuits.

Another approach [Li84b, Li84a, Co84] has been to invoke the

gradual-channel approximation, coupled with simple physical models for

carrier transport, to get analytic solutions for the terminal current-

voltage characteristics. These models account for the coupling of the

front and back gates, and are a good basis for new model development.

In Appendix A it is shown that with simple extensions they can be used

to simulate, with the circuit simulator SPICE2 [Na75], the floating-

body effects described above. However these models do not incorporate

the effects of both small lateral dimensions (i.e. channel length and

width) and a thin, possibly floating, film that causes coupling between

the front and back gates of the device, and so they are not

comprehensive enough to be used in the detailed design of VLSI devices

and circuits.

This dissertation, then, is concerned with the development and

implementation of physically representative charge-based models for the

small-geometry enhancement-mode MOSFET fabricated in thin SOI films, as


well as the development of automated parameter-extraction techniques

for the model. This work will facilitate both the design of VLSI SOI

circuits using available devices, as well as an understanding of the

electrical behavior of the MOSFET and of ways to improve its

performance by innovative device designs. The main contributions made

in the work are as follows:

(1) development of a physically representative charge-based model for

the small-geometry SOI MOSFET;

(2) implementation of the developed model in the source code of the

circuit simulator SPICE2;

(3) demonstration of the unique scaling effects of SOI MOSFETs, and

use of the model to define device design criteria;

(4) definition of an algorithm to extract model parameters using TECAP


In Chapter 2 a novel physical model for the (five-terminal)

enhancement-mode SOI MOSFET is presented. This model accounts for some

of the obvious differences (between bulk and SOI MOSFETs) noted above

and in Appendix A, namely the floating body and coupling between the

gates, as well as the short-channel effects that have been modeled in

bulk MOSFETs [Sh85, Sz81]: the effect of the drain bias on channel

conductivity, field-dependent carrier mobility and velocity saturation,

channel-length modulation, and impact ionization. The physical model is

used to define a large-signal charge-based model for the SOI MOSFET,

which is then written directly into the source code of the circuit

simulator SPICE2 [Fi88].


In Chapter 3 short-channel effects in thin-film SOI MOSFETs are

examined, experimentally and theoretically, by means of the model

developed in Chapter 2, and are shown to be unique because of

dependence on film thickness and body and back-gate (substrate)

biases. The various predictions of the model, in particular the effects

of thinning the film, are shown to be consistent with measurements; and

the potential advantages of scaling the thickness of the film as well

as the lengths and widths of the transistors are demonstrated. The

dependence on film thickness and bias, which enable control of the

short-channel effects, are used to define design trade-offs.

Furthermore, a short-channel effect exclusive to SOI MOSFETs, "back-

surface charge modulation," is reported and its relevance to device

simulation is discussed.

Chapter 4 describes the practical use of the model developed in

Chapter 2. Criteria for selecting the appropriate model are defined,

and then an algorithm (using TECAP [He85]) to automatically extract the

physical parameters needed for device simulation is described. Because

of the physical nature of the model, the parameter extraction involves

minimal optimization and gives physically meaningful values. The

extraction scheme is applied to a contemporary SOI technology to verify

the model and to demonstrate its potential for both device and circuit


In Chapter 5, the limitations of the model, which include the

neglect of surface states, non-uniform film doping, etc., are

discussed. It is shown that, given the model framework developed

above, it is indeed possible to account for these effects in a


consistent manner. In the absence of unequivocal experimental data on

these process-dependent parameters, the completion of such models have

not been extensively pursued. The preliminary work done, however, opens

up the possibility of doing simple predictive modeling of device, and

in fact, circuit performance, when the technology becomes more stable.

In Chapter 6 the main accomplishments of this dissertation are

summarized and suggestions of areas for future work are made.

In Appendix A, a simple yet general technique using "user-defined

controlled sources" [Ha84] to incorporate arbitrary charge-based models

in the popular circuit simulator SPICE2 is described. This technique

is developed primarily as a tool to aid in the development of the

charge-based model. It is useful for checking new transient models in

an actual circuit environment, without investing excessive amounts of

time in implementation, prior to actually writing the models into the

source code of SPICE2. To demonstrate the utility of the technique,

various SOI test circuits are simulated, showing the effects of a

floating thin film on circuit performance.

In Appendix B, the two-dimensional numerical simulator PISCES-IIB

[Pi84] is used to study the charge-sharing effect that defines the

threshold voltage. The model in Chapter 2 for threshold-voltage

reduction in short-channel devices is based on this study.

Appendix C describes the algorithm used to determine the threshold

voltage for all bias conditions, which is a basis for the parameter

extraction described in Chapter 4.

Appendix D details some of the algebraic manipulations used in the

development of the quasi-static charge-based model.


2.1 Introduction

In this chapter a comprehensive, physically representative charge-

based large-signal model for the small-geometry enhancement-mode MOSFET

fabricated in thin SOI films is presented. The model is a major

revision of the strong-inversion model [Li85] used in Appendix A, and

includes the predominant short-channel effects. These effects, which

are unique in the thin-film SOI MOSFET, include threshold-voltage

reduction due to charge sharing, channel-conductivity enhancement due

to a drain bias, field-dependent carrier velocity including velocity

saturation, channel-length modulation, and generation current due to

impact ionization.

Section 2.2 details the new physical model, designed so that each

major short-channel effect is analyzed explicitly. This enables a

clearer understanding of the underlying physics and also allows for

model improvements where necessary. In Sections 2.3, 2.4, and 2.5, the

characterization of the drain current and quasi-static terminal

charges (based on the model in Section 2.2) is completed.

2.2 Physical Model

In contrast to conventional modeling [Sz81] of short-channel

effects (in bulk devices), in which long-channel current-voltage


characteristics are modified by introducing a drain-bias-dependent

threshold voltage, a more physical approach is taken. Based on

simplifying assumptions that preserve the physical essence, two-

dimensional characterizations of important mechanisms in the thin-film

SOI MOSFET structure are derived directly. Subsequent integration of

the defined channel charge from source to drain yields a representative

description of the short-channel effects on both the current-voltage

and stored charge-voltage characteristics. The model in this section is

presented for the n-channel enhancement-mode device; the corresponding

model for the p-channel MOSFET, which differs only in the algebraic

signs of some of the parameters, can be similarly derived.

2.2.1 Charge Sharing

The (front-channel) threshold voltage VTf, defined for low drain-

source voltage VDS, is reduced in short-channel MOSFETs because some of

the depletion charge under the gate is shared by the source and drain

[Ak82, Vi85]. In the SOI device, this sharing is influenced by the

coupling between the front and back gates.

For VDS 0, the solution of the two-dimensional Poisson equation,

which defines the charge sharing and hence VTf, is symmetric as

indicated in Fig. 2.1. In strong inversion, the thin film is assumed to

be completely depleted, except for sheets of surface charge, QcfO and

QcbO, at the front and back surfaces respectively. (The subscripts f

and b refer to the front and back surfaces, and the subscript 0 refers

to the solution for VDS 0.) The potential of the front surface Tsf0

is approximately constant between the source and drain and is given by



front oxide I

/ +
n film / n

d buried


Fig. 2.1 A simple charge-sharing model for the thin-film SOI MOSFET
showing the completely depleted film (doping density NA) and
the portions 1, 2, and 3, "controlled" by the gates, source
and drain respectively.




TI = 2EB. (OB is the Fermi potential of the neutral film, to which all

potentials are referenced.) At the back interface, the potential varies

from the junction built-in potential (Vbi) in the source and drain

contact regions ) a surface potential Tsb0 midway between the source

and drain.

The depletion charge may be regionally divided into three portions

as shown in Fig. 2.1, associated with the gates, source, and drain. The

portion 1, which is controlled by the front and back gates, is defined

approximately by a trapezoid, and hence the effective depletion charge

per unit area controlled by the gates is

Qb(eff) = -qNAtb(l-d/L) A Qb(l-d/L) ,(2.1)

where tb is the thickness of the silicon film and L is the channel

length of the MOSFET. The one-dimensional Poisson's equation is then

solved as in [Li84b], but with the doping density NA replaced by a

"smeared-out," constant NA(eff) NA(1 d/L). This gives

[ f Cb Cb b(eff)
Q f Vf (1+--- ) + c-- T +( (2.2a)
cf0 of GfS FB sf sbO
C C 2C
of of of


[VbS Cb Cb Qb(eff)

QcbO -Co V (1bO ) + f + (2.2b)
cb ob GbS FB sb0 sf0
ob ob ob

where Cb A Es/tb, Cof = cox/tof and Cob = cox/tob are the front and

back (buried) oxide capacitances per unit area, and VFB and Vb are the

front- and back-gate flatband voltages. (The quantities tof and tob are

the thicknesses of the front and back oxides.) Equations (2.2a) and


(2.2b) are equivalent to (1) and (2) of [Li85], with Qb replaced by


To characterize VTf, the distance d in (2.1) must be analytically

approximated. This is done by following [Fr69] to account for the two-

dimensional electric field near the back surface in portions 2 and 3.

The effective lateral component of the electric field, Eb(eff), at the

back interface is approximated as

b(eff) fE1 a- E2 + fE3
Sf0[qNA (Vbi- Isb0) / 2] 1/2 + (2.3)

e V e V-b +Vb
f ox GbS FB sb0 ox bi GbS FB
f + f
a t E t
s ob s ob

where the first term is due to the depletion charge and the second and

third terms are the fringing fields from portion 1 and the source to

the back gate. In (2.3), f0, fa, and fp are empirical factors between 0

and 1, and can be estimated by curve-fitting measured VTf data (see

Chapter 4 for details on parameter extraction, and Appendix B, where it

is demonstrated, through PISCES simulations, that this model is indeed

physically meaningful). Now

d = (Vbi 'sb0)/Eb(eff) (2.4)

When the back gate is biased to accumulate the back surface, QcbO >

0 and Tsb0 VBS, the body-source voltage. Then, in strong inversion,

with gsfO I, (2.1) through (2.4) yield

QcfO C Cof (VGfS VTf) (2.5)

where Vf ( V + (+C/C (C/C)V Qb(eff)/2Cof) depends
where VTf (V FB + (l+Cb/Cof)TI (Cb/Cof)VBS Qb(eff)/2Cof) depends


on L as well as VBS and VGbS. The back-surface accumulation charge QcbO

is also simultaneously defined by (2.1) through (2.4).

When VGbS is set to deplete the back surface, QcbO = 0, and TsbO >

VBS is unknown. In this case, (2.1) through (2.4) give a quartic

equation which must be solved to determine 'sbO, which, when inserted

into (2.2a), defines QcfO and VTf. In the model, TsbO is determined by

the following simple iterative scheme: (i) assuming no charge sharing,

calculate Tsb0 from (2.2b); (ii) use that value successively in (2.3),

(2.4), and (2.1) to determine Qb(eff); (iii) use (2.2b) to determine a

modified value for 9sb0 Steps (ii) and (iii) are repeated until the

solution converges, which in fact occurs in only a few iterations.

Note that distinct models have been defined for the two different

charge conditions at the back surface. In devices with very short

channels it is possible, for a given VGbS, that the charge condition

will depend on L. That is, the charge sharing tends to deplete the back

surface as L is decreased. This unique short-channel effect, which is

discussed through measurements in Chapter 3, can be modeled within the

above framework by defining the transition point between the two

distinct models, where bsb0 VBS and QcbO 0 simultaneously. The

details are in Appendix C.

2.2.2 Drain-Induced Conductivity Enhancement

When a drain voltage is applied to a short-channel MOSFET, the

channel current IDS cannot be adequately characterized by the gradual-

channel approximation [Sz81]. In this case, VDS modulates the channel

charge indirectly through the two-dimensional Poisson equation in the


film as well as directly through the induced gradient in gsf along the

channel. This drain-induced conductivity enhancement (DICE) in strong

inversion (which is analogous to drain-induced barrier lowering in weak

inversion [Sz81, Tr79]) is accounted for by modeling the VDS-induced

change, AQcf, in the channel charge.

On application of VDS > 0 the potentials T(x,y) in the film and

Tsf(y) and Tsb(y) are modified, as are Qcf(y) and Qcb(y), from their

values at VDS = 0 by the amounts AT(x,y), Aisf(y), A (sb(Y), AQcf(y),

and AQcb(y) (see Fig. 2.2). Since the depletion charge density in the

thin film cannot change (the film is completely depleted for VDS = 0),

Laplace's equation describes the incremental potential:

2 2
a 2(A) a2 (A)
+ =0 (2.6)
ax 8y

The boundary conditions for (2.6) are AQ(x,O) = 0, AT(x,L) VDS,

AT(O,y) Aisf(y), and Ag(tb,y) = AJsb(y). In addition, the incremental

boundary charges AQcf(y) and AQcb(y) are related to the incremental

transverse electric fields (AEx 6 -8(AW)/ax) at the respective surfaces

by Gauss's law.

To obtain a closed-form solution for (2.6), it is assumed that the

two partial derivatives are not strongly coupled. Extrapolation from

the long-channel case for which each term is zero (i.e., gradual

channel) gives

a2(A)/ax2 -2(A')/y2 (2.7)

where nj is a constant that must approach zero as L increases. The L

dependence of n is inferred by integrating (2.7) from y = 0 to y = L:


0 bi

VGf S 0
sf0 O cf0

flin depleted

V0 ^qNA e)
0 Go

0 bi

sbO cbO


SA*/ Y). AQ( y)



fA* r0


no charge

V2,A ) 0


A b( Y ).AQob( Y


Fig. 2.2 Illustration of the method of solution for the two-
dimensional Poisson equation in the SOI MOSFET. The super-
position of the solution for the VDS 0 boundary-value
problem (top) and the incremental solution for the VDS > 0
problem (bottom) gives the total solution for the general
case of arbitrary applied biases.

*_tjm_ -T_


7 (2/L2) [VDS + AEy(0)L] = (2/L2)VDS (2.8)

since the incremental longitudinal field AEy(O) at the source is

typically much less than the average field VDS/L.

Equation (2.7) is integrated once with respect to x to determine a

relationship between the incremental transverse fields AEsf(y) and

AEsb(y) at the front (x = 0) and back (x = tb) surfaces of the

silicon film, and then a second time to get a relationship between the

incremental surface potentials AJsf(y) and Agsb(Y):

AEsb(y) = AEsf(y) + ?tb (2.9)


A~sb(Y) Asf(Y) Esf(y)tb ntb2/2 (2.10)

In order to relate the fields and potentials derived above to the

incremental surface charges AQcf(y) and AQcb(y) the field in the oxide

is assumed to be approximately vertical. This is typically true for

modern transistors with thin gate oxides [Vi85]. Gauss's law applied to

the front and back interfaces, with (2.9) and (2.10), then yields

AQcf(y) (Cof+Cb)A sf(y) CbAsb(Y) estb/2 (2.11)

AQcb(y) = -CbAsf(y) + (Cob+Cb)Asb(Y) stbn/2 (2.12)

These equations are seen to be the incremental counterparts of Eqs. (1)

and (2) in [Li85], with the additional accounting for the two-

dimensionality in short-channel devices. By inserting the conditions

that A'sb 0 when the back surface is accumulated and AQcb 0 when

the back surface is depleted, a general expression for AQcf(y) as a

function of AMsf(y) is derived:

AQcf(y) Cof(l+a)A>,f(y) 3Cbtb/2 (2.13)


where a = Cb/Cof and P = 1 for accumulation at the back surface, and a

SCbCob/(Cb+Cob)Cof and 8 = 1 + Cb/(Cb+Cob) for depletion at the back


The expressions for the incremental surface potentials and charges

are now added to the solutions for VDS 0 to give the general

expressions for VDS > 0. Thus 'sf(Y) = sfO + Afsf(Y), Qcf(Y) = QcfO +

AQcf(y), etc.

2.2.3 Carrier Velocity-Field Model

Due to the possible high transverse electric field in the thin SOI

film, as well as the high longitudinal electric field in the short

channel, there can be considerable nonlinearity in the carrier

velocity-field characteristic. For increasing longitudinal field IEy

dPsf/dy in the channel, the velocity tends to saturate (at vsat = 107

cm/s in bulk silicon). In this work, the following piecewise-continuous

model [So84, Ga87] for the carrier velocity in the channel is used:

(y) for v(y) 5 v ,
1 + Ueff E y/2v sat'
eff y sat
Svsat otherwise. (2.14)

In (2.14), Aeff is the low-(longitudinal-)field mobility, which is

affected by the transverse electric field Ex in the channel as

illustrated in Fig. 2.3. This dependence, along the channel, is modeled

[Wh80, Su80, Ga87] in terms of the average Ex(y) in the channel:

neff (2.15)
S+ 0 E (y)




field Ex

field JEyl

Fig. 2.3 Sketch of the steady-state carrier velocity as a function of
applied electric field jEyI along the length of the channel,
for different applied vertical electric fields Ex. The slope
of each curve near the origin gives the value of Peff in


where 0 is an empirical constant. From the quasi-i-dimensional solution

to Poisson's equation at VDS 0 (with NA(eff) as in Section 2.2.1),

the maximum transverse electric field obtained at the front surface of

the fully-depleted silicon film can be expressed as

E (



sf+ it sb0

2 e


The average field in the inversion layer at VDS = 0 is then written as


E = E +
xO x0(max) 2
C (V -V ) -
of VGfS VTf) sf0 sb0
= +
2 Es tb

Similarly, from the DICE analysis (S

incremental transverse field at any positic

expressed as

AE (y)

Cof Apsf()
= +

2 e


section 2.2.2) the average

)n y along the channel can be

AQcf (y)

2 e

S(a-1) A sf(y)
2 e


a and p were defined earlier in the discussion of (2.13). (2.17) and

(2.18) are then added to yield the following expression for the average

transverse field in the channel for an arbitrary bias:

- -

Cof b(eff) Cb Cb tb
E (y) = iV V + 2-(9 r ) + F V
x) VGfS VTf- + 2 ( sb0 + P VDS
2e sC of C C L
2Es Cof of Gof L

(1 a) ATsf(y) (2.19)

With (2.19), (2.15) is rewritten as

eff 1 B (2.20)
1 B A'sf(y)

where the newly defined parameters p and B are bias-dependent but

spatially constant.

2.3 Triode Region

The steady-state channel current is

IDS = W Qcf(Y) v(y) (2.21)

Using the models in Section 2.2 for v[Tsf(y), d'sf/dy] in (2.21) yields

I p dW d-
IDSp sf dsf
-IDS(1-B A sf) + W Qcf (2.22)
2vsat dy dy

The voltage dependence of IDS is now derived by integrating (2.22) from

the source (y 0) to the drain (y L). To enable this integration, it

is noted from (2.13) that d(Qcf) E d(AQcf) = Cof(l+a)d(A'sf)

Cof(l+a)d(lsf), and so the second term on the right-hand side of (2.22)

can be rewritten as [W/Cof(l+a)].d[Qcf2/2]/dy. Further, since Agsf

varies from 0 to VDS from the source to the drain with an


approximately parabolic dependence on y, it is reasonable to define

JA1sfdy = fBVDSL, where fB is an empirical parameter of value between

0 and 0.5. The integration yields

2 2
W eff ( Q(0) Q (L))
IDS (2.23)
2 Co (1+a) L ( 1 + (eff/2v L) VDS)

with Peff defined as

eff A -(2.24)
1 fB B VDS

Interestingly, the direct use of the spatially independent mobility

model (2.24) in the integration for IDS results in the same final

expression (2.23) as derived more rigorously above. Therefore the

simpler expression (2.24) for the effective mobility in (2.14) will be

used in the subsequent analyses.

2.4 Saturation Region

In the saturation region of operation of the MOSFET, a high

longitudinal electric field occurs near the drain, causing the carrier

velocity in that region to saturate at vsat. The channel current in the

saturated-velocity portion (see Fig. 2.4) can be expressed as

IDS(sat) W Qcf(Le) vsat (2.25)
where Le 5 L due to channel length modulation. For long-channel

devices, (2.25) implies Qcf(L) = 0, which is the basis for the pinch-

off model for the saturation characteristics [Sz81]. Generally, (2.25)

must be used explicitly to model these characteristics, accounting for

Gaussian surface
_ // _

Y yiL i I
y= Le
e D

i l

-L. n

field-dependent saturated
velocity velocity

Fig. 2.4 Schematic cross-section along the length of the channel when
the SOI MOSFET is in saturation, showing the field-dependent-
and saturated-velocity portions.




channel-length modulation and impact ionization, both of which are

closely linked to the velocity saturation.

2 4.1 Saturated Drain Current

In the saturation region, the channel may be divided into a

portion (adjacent to the source), in which the carrier velocity is

field-dependent, and another (near the drain) in which the velocity is

saturated (see Fig. 2.4). At the boundary between the two portions, y =

Le, and we define VDS(eff) A A'sf(Le) (5 VDS). Note then that at the

onset of operation in the saturation region, Le = L and VDS(eff)

VDS(sat), where VDS(sat) is the actual drain saturation voltage.
In the region 0 s y : Le, (2.23) with L and VDS replaced by Le and

VDS(eff), expresses IDS(sat). This expression equated to (2.25) gives

VDS(eff) as a function of Le:

V (2.26)
1 -DS(eff) (Q(0)/C(l+a))(fBB +/2vsatLe)


1 r1 fB B Qcf(0)/Cof(l+a) 1/2

2 + L + [ B cf o ]
2 4 [1 (Qcf(0)/Cof(l+a))(fBB + /2vsatLe

Then IDS(sat) is fully characterized by (2.23) or (2.25), except for

the description of Le, which is derived in the next subsection.

2.4.2 Channel-Length Modulation

Channel-length modulation, which is reflected by finite output

conductance in the saturation region, is quantitatively defined by Ld A

L Le, the length of the portion of the channel in which the carrier

velocity is saturated. Following the analysis (for the bulk MOSFET) of

[E177a], we describe Ld by determining A'sf(y) and using the boundary

conditions at y Le and y L.

Since the carrier velocity in the high-field drain region is

saturated, the continuity of current in the steady state implies that

Qcf(y) is spatially constant in the region. To derive a differential
equation in Arsf(y), Gauss's law is applied to a narrow strip in the

region as shown (Fig. 2.4):

ds 2 [ As dx CofAsf + CobAsb AQcf Qcb (2.27)

Following the quasi-two-dimensional DICE analysis in Section 2.2, we

approximate the left-hand-side of (2.27) as

s -2 [ J s x s 2 [ A sf + A sb ] (2.28)
dy 0 2 dy

Using (2.28) in (2.27), and the conditions that AQcb = 0 when the back

is depleted or ALsb 0 when the back is accumulated, we obtain the

following second-order differential equation in Arsf(y):

2 2 C ( + ) (Asf VDS(eff) 2
2 (sf) b + (2.29)
dy Cb th b

where we have used AIsf(Le) = VDS(eff); a, 6, and j7 were defined

previously. The boundary conditions for (2.29) are A'sf(L) = VDS and

d(Adsf)/dy 2vsat//eff at y Le. The general solution of (2.29),

valid for Le : y : L, is

A sf- I 2 sat c sinh[ + cosh[ ]-1 (2.30)
sf- VDS(eff) [ 1 +1
eff 1 1

c 2 Cof (1+a) 3

For typical thin-film SOI MOSFETs, tb < L and the last term of

(2.30) can be neglected. Then, using A1sf(L) = VDS in (2.30), we get

-1 Aeff (VDS VDS(eff)
L L L 1 sinh DS(eff) (2.32)
sat c

The combination of (2.32) and the expression (2.26) for VDS(eff) gives

a transcendental equation for Le which can be solved numerically in a

few iterations.

2.4.3 Impact-Ionization Current

The flow of electrons through the high-field region near the drain

causes impact ionization, which generates holes that flow into the

MOSFET body and electrons that flow out the drain. To determine this

generation current, for weak impact ionization, we first express the

longitudinal electric field, Ey -d(Alsf)/dy, using the analysis of

the previous subsection:

E Ee 2 sf DS(eff))
Ey E cosh c EO 12 2 (2.33)
c 0 c


where EO A -2vsat/Peff. Since EO is relatively small in the high-field

region, (2.33) can be used to make the approximation that dEy/d5sf =


The generation current IGi due to impact ionization is now defined

in terms of an ionization integral in the drain region [E175, E177b].

Let M be defined as the multiplication factor of electron current (in

an n-channel device) due to impact ionization and IDS be the channel

current. Then

IGi (M-1) IDS (2.34)

It is noted that the bipolar current gain associated with the impact

ionization [E177b], which is typically quite small, has been neglected

in (2.34). The quantity (M-l) is approximated by the ionization

integral as follows (00 and P0 are assumed to be constant, and ED is

the lateral field at the drain, defined by (2.33)):

(M-1) 0 a e dy = 0 e/E (dy/d sf)(dcsf/dE)dE
E 0/E 0

S0 c e E 0 c E E e0
0 0

a ic -1 0/ED
0 ED e (2.35)

The last two steps need some justification. The former is seen to be

true, by expansion of the total differential, since 60 is typically

much larger than E; the latter is true if EO is small compared to ED.

With the further assumption that ED (VDS-VDS(eff))/lc, the following

expression for (M-l) is obtained:

I0 01c /(VDS- VDS(eff))
(M-l) (V V f)) e (2.36)
10 DS DS(eff) e2-

The impact-ionization current (2.34), when incorporated in the model,

accounts for the floating-body effects, e.g., the kink effect [E177b].

2.5 Charge-Based Model

In order to create a large-signal transient circuit model, the

charge dynamics as well as the steady-state currents in the device must

be described. To do this physically, the spatial dependence of the

charges within the MOSFET are integrated out, and then the quasi-static

approximation is used to express the charging current at each terminal

as the time derivative of a charge associated with that terminal [Ar77,

Wa78, Ya83]. For the SOI MOSFET model, the voltage dependence of the

integrated charges associated with the five terminals, QGf, QGb, QS,

QD, and QB are derived below, based on the analyses in the preceding

sections (with (2.24) for Peff in (2.14)). (See Appendix D for some of

the mathematical manipulations used in deriving the following charge


2.5.1 Triode and Saturation Regions

In the triode region, Gauss's law implies for the front-gate


Sw Cf ( sf)
QGf W Cof O (VGfS- MS Tsf) dy

V V DS (1 + s) (1 + a)
= WLC V + 1 (2.37)
2 12 [-Qcf(0)/Cof] [1 2u]

where 4MS is the front-gate work-function difference, and we define s

SPeffVDS/2VsatL and u A -Qcf(0)/Cof(l+a)VDS; Qcf(0) QcfO + AQcf(0)

given in Section 2.2.

The source and drain charges comprise, in part, partitioned

portions of the total channel charge QCH, which can be expressed as

QCH W Qcf(y) dy

2 z (z-1)3
WLCof(l+a)VDS + (u-z) (2.38)
3 (2z-l)

where z u (IDS/2vsatW)/Cof(l+a)VDS. Since the channel charge is

distributed, the drain and source portions, QD(CH) and QS(CH), cannot

be unambiguously defined. For the case of constant channel mobility, a

partition of QCH that, to first order, accounts for the finite carrier

transit time in the channel has been defined [Wa78, Li85, Fo86]. For

the general case however, in which the mobility is spatially dependent

(e.g., due to velocity saturation), Sevat [Se87] has proposed a

solution to the quasi-static charge-partitioning problem by assuming

that the MOSFET is analogous to a ladder network. At any point y along

the channel, he defines

aid 81
gD A and gS A s
a(Asf) a(sf)


which represent the differential conductances towards the drain and

source. Then, the drain and source partitions can be defined as

gD/(gD+gS) and gs/(gD+gS). In our case, the continuity equation can be

integrated from y 0 to arbitrary y to give

Iseff = sf
SY + Asf e0 Ae ffW Qcfd(Asf) (2.39)

(2.39) is differentiated with respect to AMsf and the quasi-static

approximation is applied to Is (i.e. Is = IDS) to yield

S effW Qcf + PeffIDS/2Vsat
gS = (2.40)
y + eff sf/2vsat

Similar manipulation yields

S effW Qcf + Ueff DS/2vsat
gD =- (2.41)
L y + eff(VD- Asf)/2vsat

Then, the source and drain partitioning ratios are

gs L y + eff(V- Asf)/2vsat
D + gs L + yeffVDS/2Vsat

gD Y + eff(VDS- Aifsf)/2vsat
gD + gs L + MeffVDS/2Vsat

These ratios are identical to those derived in a different manner by

[Ya87]. However, for short-channel MOSFETs the specific partition

assumed is not critical [Ya87], and for long-channel MOSFETs the

ratios defined above become the same as those defined in [Wa78]. In the


absence of a compelling reason to use the more complicated formulation

above, the simpler partition scheme [Wa78] is used in this work. Then,

in the triode region,

QD(CH) = W L Qcf(Y) dy

2 (z-1)3 4 [z5- (z-1)5] (u-z)
WLCf (l+a)V DS + + -- (2.44)
3 (2z-l) 15 (2z-l) 2


QS(CH) = QCH QD(CH) (2.45)
To ensure charge neutrality, the body depletion charge shared by

the source and drain (see Section 2.2.1), WL(Qb-Qb(eff))/2, must be

accounted for in QS and QD. Also, the excess charge in the drain

WLestbq associated with DICE (refer to (2.11) and (2.12)) must be

included in QD*

For the case of back-surface accumulation, Gauss's law implies for

the back-gate charge

QGb = W Cob 0 GbS MS sb) dy

SWLCob (VGbS- MS- VBS) (2.46)

where I@S is the back-gate work-function difference. The neutrality


QGf + QGb + QS + QD + QB + Qff + Qfb 0 (2.47)

where Qff and Qfb are the fixed charges at the front and back

interfaces, now defines QB*


For the case of back-surface depletion

QB WLQb ; (2.48)

then the neutrality condition (2.47) defines QGb-

In the saturation region, the above charge expressions are used

with L and VDS replaced by Le and VDS(eff) respectively, and are

supplemented with additional components corresponding to the high-field

region near the drain (Le : y 5 L). The previous analysis is used to

derive these supplementary components:

Q s c sat cosh e (2.49)
QGf= WCof [L-Le ]GfS- S I DS(eff) t cosh L (2.49)
"eff Ic

QCH W [L-Le Qcf(Le) (2.50)

(CH) = W Qcf(Le) [L2- Le/2L (2.51)

s s s
S(CH) C H (CH) (2.52)

2.5.2 Cutoff Region

In this subsection, a model for the cutoff region is derived, in a

manner consistent with the strong-inversion model presented above. (As

VGfS is made increasingly negative there is a possibility of incomplete

depletion of the film, or even accumulation at the front surface. The

analysis for these conditions follows bulk MOSFET theory [Sz81] and is

not included here.) This is done to ensure that there are no

convergence problems during transient circuit simulation due to dis-


continuities in the charge expressions at the (model) boundaries

between cutoff and strong inversion.

From the strong-inversion analysis above, the cutoff region is

defined by the conditions IDS = 0 and Tsf0 < TI, i.e.,

VGfS VTf (Cb/Cof )(tb/L)2DS (2.53)

In this region, with the film completely depleted,

V GfS Tf + p](Cb/Cof)(tb/L)2VDS
s- s 0 + Aso ) = ----- + (2.54)
sf sf0 sf(off) L[ Ij J+
Sl ff+ a 1 + a

where the terms due to the zero-VDS solution and the DICE solution have

been separated. The last term on the right-hand side of (2.54) can be

interpreted as a drain-induced barrier lowering [Tr79] in weak

inversion, and complements the conductivity enhancement (DICE) in

strong inversion.

When the back surface is accumulated, TsbO = VBS (as before). When

there is depletion at the back surface, the following expression for

Tsb in terms of TsbO and A'sb(off) can be derived:

SVbs, V FB + (Qbeff/2Cob) + (Cb/Cob)lsfO
1 + C b/Cob
sb sb sb(off + (t/L)2VD

S^sf(off) + Dtb/ VS(
+ (2.55)
1 + Cb/Cob

Following [Ta78, Fig.8], it is assumed that (2.54) and (2.55) are

valid from the source (y 0) to the effective end of the channel (y =

Le). To determine the channel-length modulation the (strong-inversion)

analysis of the high-field drain region is extended to the cutoff case.


This extension can be justified by arguing that even for weak inversion

carriers must flow by drift at the saturated velocity near the drain.

The following expression for Peff is used to get an expression for Le

that is consistent with (2.32), which was derived for the strong

inversion case:

= ff (2.56)
1 + (BCof/2Es) (2Cb(sfo0- sb )/Cof Qbeff)

The effective channel length Le is then given by (2.32) with Peff in

(2.56) and VDS(eff) = 0.

Finally, following the analysis of Sec. 2.5.1, QGf is expressed as

1 f 2v L cosh L-L 1] (2.57)
f c sat L
Q WLCf 4D f- T L cosh e -I (2.57)
Gf of GfS MS sf 2 -
'eff c

In the cutoff region, QCH = 0, and so are QD(CH) and QS(CH)- For

the case of back-surface accumulation, QGb is given by (2.46) and then

QB can be determined by the neutrality condition (2.47). For the case

of back-surface depletion, Qg and QGb are defined by (2.48) and (2.47)


2.6 SPICE2 Implementation

The complete network representation of the charge-based model

(neglecting parasitic capacitances) is shown in Fig. 2.5. The model is

quasi-static; the charging currents dQ/dt, as well as IDS and IGi are

defined by the steady-state analysis. The diodes IR and IGt simulate,

respectively, recombination associated with the source-body junction


R -








----*/V- D




Fig. 2.5 Network representation of the quasi-static large-signal
transient model for the SOI MOSFET.



(for VBS > 0) and thermal generation associated with the drain-body

junction (for VBD < 0).

The model was implemented in SPICE2, initially via user-defined

controlled sources (see Appendix A), and then by direct modification of

the source code [Fi88]. The new SPICE2 model allows a maximum of five

external terminals: if only four nodes are specified in the input deck,

the body terminal is automatically assumed to be floating. For

convenience, three separate models have been defined to account for SOI

devices fabricated on films of all thicknesses: the first two are the

thin-film models described above with the back surface accumulated

(TFA) and the back surface depleted (TFD), and the third is a semi-bulk

(SB) model derived by adding the back-oxide capacitance WLCob to the

bulk-MOSFET model BSIM [Sh85]. It is noted that in the TFD model, VB,

which is determined by Kirchoff's current law, is extrinsic in the

sense that it does not affect IDS or the charges. The parameters for

the model are listed in Table 2.1. In our implementation, we have

neglected the bipolar current gain associated with the impact

ionization because it is typically quite small. Within the model

subroutine, numerical differentiation has been used to calculate the

transconductance and transcapacitance matrices needed in the Newton-

Raphson iterative solution. The lack of analytic derivatives does not

seem to cause any significant degradation in convergence. At this

(preliminary) stage of the modeling, the advantages of such a numerical

approach seem to outweigh the disadvantages: it is very simple to make

an addition to the model without having to worry about time-consuming

re-calculation of the 24 independent derivatives.



Name Description Units Default


VFBF Front-gate flatband voltage V calc.
VFBB Back-gate flatband voltage V calc.
TOXF Front gate-oxide thickness cm 500e-8
TOXB Back gate-oxide thickness cm 0.5e-4
WKF Front-gate work function difference V calc.
WKB Back-gate work function difference V calc.
NQFF Fixed charge, front gate-oxide 1/cm2 0.0
NQFB Fixed charge, back gate-oxide 1/cm2 0.0

NSUB Substrate background doping density 1/cm3 l.Oe-14
NGATE Polysilicon-gate doping density 1/cm3 1.0e19
TPG Type of gate material -1.0
+1) opposite to body
-1) same as body
0) aluminum
TPS Type of substrate -1.0
+1) opposite to body
-1) same as body

NBODY Film (body) doping density 1/cm3 calc.
PHIB Twice Fermi potential of body V calc.
TB Film (body) thickness cm 0.le-4

UO Zero-field mobility cm2/Vs 550
THETA Mobility degradation coefficient cm/V l.Oe-6
BFACT VDS-averaging factor for p-degradation 0.0
VSAT Saturated carrier velocity cm/s 1.0e7

QSMO Charge-sharing parameter f 0.7
QSMA Charge-sharing parameter f 0.0
QSMB Charge-sharing parameter f 0.3

ALPHA Impact-ionization parameter 00 1/cm 1.6e6
BETA Impact-ionization parameter P0 V/cm 2.6e6

ETA On/off multiplier for DICE model 1.0 (ON)
LMOD On/off multiplier for channel-length
modulation model 1.0 (ON)


TABLE 2.1 -- continued

Name Description Units Default


CGFDO Gate-drain overlap capacitance F/cm 0.0
CGFSO Gate-source overlap capacitance F/cm 0.0
CGFBO Gate-body overlap capacitance F/cm 0.0

RHOSD Source and drain sheet resistivity 0/square 0.0
RHOB Body sheet resistivity 0/square 0.0
RD Drain parasitic resistance 0 0.0
RS Source parasitic resistance 0 0.0
RB Body parasitic resistance 0 0.0

IRO Parasitic diode current coefficient A/cm 1.0e-10
N Parasitic diode emission coefficient 2.0

DL Channel-length reduction cm 0.0
DW Channel-width reduction cm 0.0

CIITOL Avalanche current tolerance A 1.0e-12

Note: The DC/transient/AC characteristics of the model are defined by
TOXF, TOXB, TB, VFBF, VFBB, NBODY, and UO. If these values are not
specified, they are defaulted and/or computed (referred to in the
table as "calc.") by SPICE from the given values. If the kink
effect is negligible, consider making ALPHA and BETA zero to
improve execution time.


The charge dynamics are implicit in the model, and may be observed

in simulations of the various transcapacitive coefficients (Cil A

aQi/avl where i,l = Gf, D, B, Gb, or S). It is stressed that these

transcapacitances are not to be viewed as conventional capacitors (and

in fact cannot be properly represented by equivalent capacitors), but

are nonreciprocal coefficients that mathematically describe the charge

dynamics. To exemplify the physical nature of the model, simulations of

the gate transcapacitances CGfS, CGfD, CGfGf, and CGfB (neglecting

parasitic capacitances like overlap capacitances) for a short-channel

device are plotted in Fig. 2.6. These transcapacitances predominantly

control the charging of the front gate when the MOSFET is used as the

driving stage of a CMOS inverter. In contrast to long-channel devices,

where CGfGf in the saturation region does not depend on VGfS, for the

short-channel device velocity saturation and the concomitant Qcf(Le) <

0 cause CGfGf to increase with VGfS [Iw87]. Similarly, CGfD, which is

negligible for a long-channel device in saturation, is substantive in

the short-channel device. These results correspond to biases on the

back-gate that cause accumulation at the back surface and VBS 0, and

are, in fact, strongly influenced by those biases.

Simulation Example

To verify the implementation, various test circuits including CMOS

inverters, sense amplifiers, static memory cells, and ring oscillators

were simulated using the SPICE2 model. Fig. 2.7 shows a sample

simulation deck and output voltages of a five-stage CMOS ring

oscillator. For this simulation, all the body terminals of the MOSFETs

S. 1

D 2V 3V

0 VDS = 0 V

0.22 ,#/ 2V .-
'3 -----
U - -I_ -- -^ - - - -"

0 1 2 3 4 5


h VDS = OV


0. -

0 2V 3V
o, aV ? ---
0 ----- ~ --- -- -.__ -.- J ,^ ,
0 1 2 3 4 5

Fig. 2.6 Simulated gate transcapacitances for an L = 2.0 pm SOI MOSFET
with the back surface accumulated (CGfGb = 0) showing the
effects of velocity saturation. The solid lines correspond to
the normalized CGfS and CGfGf, and the dashed lines
correspond to the normalized CGfD and CGfB.

VON 1 0 PULSE 0.0 5.0 0 5N 5N 1 2
VCC 5 0 5.0
VGB1 6 0 -10.0

ZNO 2 1 0
ZPO 4 1 5
ZN1 4 3 2
ZP1 4 3 5
ZN2 7 4 0
ZP2 7 4 5
ZN3 8 7 0
ZP3 8 7 5
ZN4 9 8 0
ZP4 9 8 5
ZN3 3 9 0
ZP3 3 9 5

6 10
6 11





6 12 TFA ZNTFA L=2E-4 W=5E-4
6 TFD ZPTFD L=2E-4 W-5E-4

6 13


6 14 TFA
6 15 TFA

ZNTFA L-2E-4 W=5E-4
ZPTFD L-2E-4 W=5E-4










IBO 10 0 0.0
IB1 11 0 0.0
IB2 12 0 0.0
IB3 13 0 0.0
IB4 14 0 0.0
IB5 15 0 0.0
TPS=1 TPG-1 TOXF-2.5E-6 TOXB-4.5E-5 TB-0.25E-4 RD-10 RS-5 RB=5
DL=0 DW=0 UO=500 LMOD-1 ALPHA-1E6 BETA-2.6E6 WKF=0 WKB-0 THETA-3E-6
TPS--1 TPG=-1 TOXF=2.5E-6 TOXB=4.5E-5 TB-0.25E-4 RD=10 RS=10 RB=0
DL=0 DW-0 UO=300 LMOD=1 WKF=0 WKB-0 THETA=3E-6 VSAT-1E7 BFACT-0.4

Fig. 2.7 (a) Input deck for SOI CMOS ring-oscillator simulator. Note
that we use VGbS = -10 V for the simulation, implying that
the n-channel MOSFETs are TFA devices whereas the p-channel
MOSFETs are TFD devices.

10 15 20
Time (s)

25 x 10-i

Fig. 2.7--continued (b) SPICE2-simulated output voltage V9 (solid
line) of the 7-stage SOI CMOS ring-oscillator circuit. Shown
also is the body voltage V14 (dotted line) for the n-channel




-2 L


were left floating; the back-gate bias (VGbS = -10 V) was set to

accumulate the n-channel MOSFETs and deplete the p-channel MOSFETs.

Note that constant current sources of 0 A have been connected to the

body nodes of the n-channel MOSFETs to be able to monitor the body

voltages. As shown by the dotted lines in the simulation output (Fig.

2.7), the model predicts the correct transient VB(t) for the body

terminal of one of the n-channel MOSFETs in the circuit.

2.6 Summary

A comprehensive charge-based large-signal transient model for the

short-channel thin-film SOI MOSFET in strong inversion has been

presented. Although the model has been designed for use in circuit

simulators like SPICE2, it preserves a substantial amount of the

underlying device physics, and hence avoids large amounts of curve-

fitting, and can be used for predictive computer-aided device and

circuit design. Furthermore, the fact that each dominant effect has

been modeled separately enhances an understanding of the effects, and

makes it relatively easy to incorporate extensions as necessary,

without loss of self-consistency.


3.1 Introduction

In Chapter 2, a physical model for the short-channel SOI MOSFET

was derived. In this chapter it is verified, through measurements and

simulations, that the model indeed predicts in detail the unique short-

channel effects in thin-film silicon-on-insulator MOSFETs. In Sections

3.2-3.6 it is shown how these effects can be controlled by appropriate

biasing of the back-gate (i.e., the underlying substrate) and/or the

film body, or by changing the film thickness. In general, this study

reveals that the threshold-voltage reduction by charge sharing [Ak82],

drain-induced (channel) charge enhancement (drain-induced barrier

lowering [Tr79] in weak inversion), and channel-length modulation (and

consequently, the saturated drain conductance) are best controlled by

scaling the film thickness with the channel length and by biasing the

back gate (substrate) to accumulate the back surface. However, it is

shown that these improvements due to back-surface accumulation must be

traded-off for reduced saturated drain current, an increased inverse

subthreshold slope and possibly increased hot-electron degradation

problems. Finally, in Section 3.7, evidence is presented for a short-

channel effect unique to SOI MOSFETs whereby the back-surface charge

condition (i.e., accumulation or depletion) depends on the device

length as well as the applied drain bias.


3.2 Threshold-Voltage Reduction

In thin-film SOI MOSFETs, the back gate participates in the

depletion charge sharing [Ak82] with the front gate, source, and drain,

and thereby influences the threshold-voltage reduction. In this

section, previous studies [Se84, Co87b] of this effect are extended by

characterizing its voltage dependence.

Consider a p-channel MOSFET of channel length L and uniform body

doping ND fabricated on a thin SOI film of thickness tb (Fig. 3.1). As

long as TsbO stays constant as L is reduced, the reduction in threshold

voltage AVTf due to charge sharing can be written as

d qNDtb
AVTf(L,t IVTf(Qb) VTf(Qb(eff))l L (3.1)
L 2Cof

In Chapter 2, the distance d was related to the bias by defining it in

terms of an effective electric field Eb(eff) (see Fig. 3.1):

sb -bi
d A (3.2)

Eb(eff) comprises fringing fields from the back gate oxide, controlled

by the back-gate bias VGbS, as well as the component from the junction

depletion region. Note from (3.2) that for fixed 9sb0, an increase in

Eb(eff) by any means will reduce d and hence the charge-sharing. For

example, this may be done by increasing the film doping [De74].

When the back surface is accumulated by a large positive VGbS,

qsb0 is pinned at the body voltage VBS. In this case, AVTf is

proportional to tb/L as in (3.1). Then, if the film is made thinner as

its lateral dimensions are scaled, VTf will not decrease as much as if


I front oxide

\ depleted /
p film / t
E,:b() / sb, /



Fig. 3.1 P-channel SOI MOSFET showing the effective lateral field
Eb(eff) and distance d at the back surface that are used to
define the charge sharing.







tb were kept constant. This effect is demonstrated in Fig. 3.2 where

measured AVTf versus L and VGbS are plotted for two sets of SOI MOSFETs

fabricated identically on SOI films of different tb.

In addition to the dependence on thickness, the measured AVTf

plotted in Fig. 3.2 shows a dependence on VGbS. When VGbS is decreased

to deplete the back surface, AVTf is increased. Based on the preceding

discussion, this dependence is explained by noting that the fringing

fields in Eb(eff) decrease and hence d in (3.2) and the depletion

charge shared by the source and drain increases.

This effect of reducing the fringing fields on Eb(eff) is further

clarified by a PISCES [Pi84] simulation of an L 1.0 pm SOI MOSFET in

strong inversion. The equipotential contours plotted in Fig. 3.3 for

the cases of back-surface accumulation (VGbS 10 V) and back-surface

depletion (VGbS 0 V) show that indeed as VGbS decreases, Eb(eff)

decreases, causing d and AVTf to increase as mentioned above. (This

trend is also discussed in more detail in Appendix B.)

Note in Fig. 3.3 that as VGbS is decreased and the back surface is

depleted, bsb0 decreases, and ultimately would approach Vbi as the back

surface is inverted. Thus, it is noted from (3.2) that the AVTf(VGbS)

trend discussed above is reversed as (4sbO Vbi) approaches zero. This

reversal is illustrated in Fig. 3.4, where measured AVTf versus VGbS

are plotted for a MOSFET with a mask L = 1.0 pm, showing a maximum in

AVTf, for fixed VBS, as the back surface is swept from accumulation

(VGbS 20 V) to inversion (VGbS -5 V). (The dependence of AVTf on

VBS follows the trend in bulk MOSFETs: as the reverse bias on the

drain-body or source-body junction is increased, AVTf increases due to




iH 0.12
o. .


0 2 4 6 8 10

L (nm)

Fig. 3.2 Threshold-voltage reduction AVTf(L) for two sets of SOI p-
channel MOSFET's of film thicknesses tb 0.8 pm (solid
lines) and 1.3 pm (dotted lines) with identical processing
schedules, at two different back-gate (substrate) biases,
VGbS 20 V (D) and -5 V (A), corresponding to back-surface
accumulation and depletion respectively; VBS 2 V in all

Fig. 3.3 PISCES-simulated equipotential (T) contours in increments of
0.1 V for a tb 0.27 pm p-channel SOI MOSFET with (a) the
back surface accumulated (VGbS 10 V) and (b) the back
surface depleted (VGbS 0 V). Only the contours for Vbi < T
< Vbi+l are shown. In both cases, VDS 0 V (linear region),
VGfS -2.5 V (strong inversion), and the (minority-)
electron quasi-Fermi level is set at 0 V.


S3W.8 V 3 V

a p I a a a a I p p a a I . I a .
-5.8 8 5.8 19.8 15.8 28.8

VGbS (V)

Fig. 3.4 Measured threshold-voltage reduction AVTf(VBS, VGbS) for an L
1.0 pm p-channel MOSFET fabricated on an SOI film with tb
0.27 pm.


increased charge-sharing.) Other measurements reveal that the back-

gate bias at which the maximum in AVTf occurs depends on L.

With regard to scaled device design for minimum AVTf, it is noted

that MOSFET operation with the back surface close to inversion is

normally undesirable due to problems with leakage. Thus the only viable

design options for SOI MOSFETs are to scale tb with L, setting VGbS to

accumulate the back surface, and/or to thin the back gate oxide, all of

which tend to increase Eb(eff) and reduce the charge sharing. Of

course, other design considerations, some of which are discussed

herein, could imply necessary trade-offs as the device is scaled.

3.3 Drain-Induced Conductivity Enhancement (DICE)

When a large (negative) drain voltage VDS is applied to a short p-

channel MOSFET, the channel charge is modulated indirectly through the

two-dimensional Poisson equation in the film as well as directly

through the induced gradient in isf along the channel (the gradual-

channel approximation [Sz81] accounts for the latter effect). In this

section it is shown how the former modulation, i.e. DICE, is affected

by the back-surface charge condition in the thin-film SOI MOSFET.

From the DICE analysis of the previous chapter, the charge at the

source end of the channel can be expressed as

s tb
S(0)- Cf(VGf- VTf+ 2 VDS) (3.3)
S of(VfGfS- VTf(eff))

where f 1 or 1 + Cb/(Cb+Cob) depending on whether the back surface is

accumulated or depleted and VTf(eff) is defined, mathematically, as an


"effective" threshold voltage. For a given device and drain bias, the

difference between VTf and VTf(eff) is a measure of the modulation of

channel charge at the source due to the two-dimensional electric field

in the film, i.e., due to DICE. Therefore, (3.3) implies that the the

channel charge and hence the device conductance increasingly deviate

from the values predicted by the gradual-channel approximation as /

increases, or as the back surface goes from accumulation to depletion.

Also, (3.3) implies that the two-dimensional DICE effect is enhanced as

tb increases.

This control of the two-dimensionality of the potential

distribution in the film is demonstrated by a PISCES [Pi84] simulation

of the device in Fig. 3.3 with VDS -2.0 V. The equipotential contours

plotted in Fig. 3.5 clearly indicate that the distribution is more two-

dimensional when the back-surface is depleted (VGbS = 0 V) than when it

is accumulated (VGbS 10 V). This dependence on the back-surface

charge condition is explained qualitatively by noting that the VDS-

induced displacement in the depleted film (with fixed charge) must

terminate on excess surface charge. Thus the presence of an

accumulation layer at the back surface tends to limit the modulation of

the (front-) channel charge.

In the saturation region of operation for VGfS = VTf(eff) the p-

channel current can be written approximately as

W 2effCof 2 (3.4)
DS(sat) L (l+C) VGfS VTf(eff) ( )

where C/Cf r CCo/(C+Cb)Cf depending n whether the back

where a = Cb/Cof or CbCob/(Cb+Cob)Cof depending on whether the back

Fig. 3.5 PISCES-simulated equipotential contours in increments of 0.2
V for the SOI MOSFET of Fig. 3.3 with (a) the back surface
accumulated (VGbS 10 V) and (b) the back surface depleted
(VGbS 0 V). Only the contours for Vbi-2 V < 9 < Vbi+l V are
shown. In both cases, VDS -2 V, VGfS -2.5 V, and the
(minority-) electron quasi-Fermi level is set at 0 V.


surface is accumulated or depleted. For VGfS = VTf(eff), the effective

mobility Peff is virtually independent of VGfS, and the channel-length

modulation that determines the effective channel length Le is

controlled primarily by VDS. Thus, it is possible to estimate VTf(eff)

from a plot of JIDS versus VGfS in the saturation region near


Measured VTf(eff)(L) characteristics of the tb = 0.8 pm p-channel

device in Fig. 3.2, for different VGbS and VDS, are plotted in Fig.

3.6. These data confirm the conclusion derived above that the DICE

effect is minimized when the back surface is accumulated. The effect of

varying tb is shown by the data plotted in Fig. 3.7. Consistent with

(3.3), these data reveal that the DICE effect is increased as tb


With regard to scaled device design for minimizing the DICE then,

the same criteria mentioned for minimizing AVTf apply. In this case,

thinning the back gate oxide is effective in limiting the DICE effect

because it enables the back gate (substrate) to accommodate some of the

VDS-induced displacement.

3.4 Velocity Saturation and Channel-Length Modulation

In the saturation region of operation of a MOSFET, the drain

current IDS(sat) and the incremental drain conductance gDS(sat) depend

on the manner in which the carrier velocity in the channel saturates.

This velocity saturation and the channel-length modulation it produces

are important in short-channel devices because the channel charge that

remains near the drain in the saturation region is proportional to the



> 1 VGB = -3 V


VGB = -1 V


VGB = 3 V

0 2 4 6 8 10

L (pm)

Fig. 3.6 Effective threshold voltage VTf(eff)(L) for the tb 0.8 pm
MOSFET of Fig. 3.2, measured at VDS -2 V (+) and -5 V (x)
for VGbS ranging from 3 V (back-surface accumulation) to -3
V (back-surface depletion); VBS 2 V for all the









2 4

Fig. 3.7 Effective threshold voltage
devices of Fig. 3.2, measured
for tb 0.8 pm (solid lines)
VGbS 20 V and VBS 2 V.

6 8 10

L (pm)

VTf(eff)(L) for the p-channel
at VDS -2 V (+) and -5 V (x)
and 1.3 pm (dotted lines) with


current IDS(sat), which varies inversely with L. For SOI MOSFETs,

there are additional dependence on the back-surface charge condition

and on tb. In this section, it is shown that accumulating the back

surface and/or thinning the film result in a reduction of IDS(sat),

which is usually undesirable, as well as in a decrease of gDS(sat),

which is usually desirable. Thus, in conjunction with the previous

discussions, design trade-offs are implied.

For a long-channel thin-film SOI MOSFET, IDS(sat) c 1/(l+a) [Li84b]

as indicated in (3.4), and is accordingly decreased as the back

surface charge condition is changed from depletion to accumulation.

This decrease in IDS(sat) occurs because the transverse field in the

film increases and, via Gauss's Law, causes a decrease in the channel

charge for fixed (VGfS VTf), resulting in premature velocity

saturation. As discussed above, this effect is exacerbated as the

channel length is decreased. This is clearly seen in Fig. 3.8, where

the normalized quantity IDS(sat)L, derived from measurements on a tb =

0.8 pm device with (VGfS VTf) and VDS fixed, is plotted versus L. The

cases of back-surface accumulation (VGbS 20 V) and depletion (VGbS =

0 V) are shown in the figure. Additional measurements show the increase

in IDS(sat) with increasing tb.

In addition to the variation of IDS(sat) with L, the drain

conductance gDS(sat) associated with the channel-length modulation is

of interest. In Fig. 3.9, the measured normalized conductance gDS(sat)L

is plotted versus L for the SOI MOSFET of Fig. 3.8. The plot shows that

back-surface depletion results in an increase in gDS(sat) due to an



8 6000

5000 ** *
0 5 10 15 20 25

L (jm)

Fig. 3.8 Measured drain saturation current IDS(sat)(L), normalized by
1/L, for a tb 0.8 pm p-channel SOI MOSFET with (VGfS VTf)
-4 V and VDS -5 V for back-surface accumulation with VGbS
20 V (0) and back-surface depletion with VGbS 0 V (A);
VBS 2 V.





L (um)

Fig. 3.9 Incremental conductance gDS(sat)(L),
derived from IDS(sat) measurements for
Fig. 3.8 (VGbS 20 V (0) and 0 V (A))
lines) and 1.3 pm (dotted lines).

normalized by 1/L,
the bias conditions of
for tb 0.8 pm (solid


increase in channel-length modulation. This result is explained

qualitatively below based on the model developed in Chapter 2.

In Section 2.4.2, Gauss's law was applied to the (thin) high-field

region near the drain (where the carrier velocity is saturated) to

determine a solution for the potential in that region. This solution

was used to express the channel-length modulation Ld in terms of the

terminal voltages, including VGbS:

Ld- 1 sinh-1 eff DS DS(eff) (3.5)
Ld L Le 1 sinh (3.5)
de c 2 v 1 -
sat c

where 1ic (Ptb)1/2 was a characteristic length which depended on the

film thickness as well as the charge condition of the back surface (via

3, which we introduced previously). This dependence reflects the two-

dimensional effect of the back-surface accumulation layer in limiting

the potential variation in the film, and in confining all variations in

potential to a region very close to the front surface of the MOSFET. A

decrease in 1e has been related to an increase in the maximum

longitudinal electric field in the drain region (Em = (VDS-

VDS(eff))/lc), and a simultaneous reduction in the channel-length

modulation [E177b, Hu85a]. Thus, back-surface accumulation (which

reduces P) and/or reduction in tb must result in reduced channel-length

modulation, consistent with the measurements presented above.

To further clarify these effects on gDS(sat), PISCES-simulated

IDS(VDS) for the L 1.0 pm device of Figs. 3.3 and 3.5 (tb = 0.27 pm)

at VGbS = 0 V and VGbS = 10 V are compared with simulations of a

similar device with tb = 0.135 pm (Fig. 3.10). In order to cancel out


the effect of variable VTf, all the simulations were done with (VGfS-

VTf) constant. From the plots it is evident that reduction in tb as

well as back-surface accumulation tend to reduce the channel-length

modulation as well as IDS(sat)-

3.5 Hot-Carrier Effects

The above discussion is now related to previous studies on hot-

carrier generation in SOI MOSFETs. Through accelerated stress tests,

Colinge [Co87a] has shown that the lifetime of the MOSFET can be

improved by depleting the back surface or by allowing the body to float

with the back surface in accumulation. For a given VGfS, both these

conditions result in a lowered VTf, and hence increased VDS(sat), and

therefore a lowered electric field in the drain region. From the

discussion in the previous paragraphs, the reason for increased

channel-length modulation in thicker films or when the back is depleted

is similar: a decrease in the longitudinal electric field at the drain,

which we have modeled in terms of 1c. Thus, a large 1c correlates with

reduced hot-carrier generation. It therefore appears that the use of

ultra-thin SOI films and back-surface accumulation to improve short-

channel behavior would also result in increased device degradation

problems. However, further experimental studies are necessary to

conclusively prove this deduction.

3.6 Subthreshold Slope

In the subthreshold region of operation, the inverse slope S -

dVGfS/d(ln(IDS)) is a useful indicator of the switching speed of the

0 x 10-





Fig. 3.10 PISCES-simulated IDS(VDS) curves for the tb 0.27 pm (solid
lines) p-channel SOI MOSFET of Figs. 3.3 and 3.5 at VGbS 10
V (back-surface accumulation) and VGbS 0 V (back-surface
depletion) compared with simulations of a similar MOSFET with
tb 0.135 pm (dotted lines) at the same bias conditions. All
simulations were done with (VGfS VTf) = -5 V and the
electron (minority) quasi-Fermi level set to 0 V.


MOSFET. Most previous studies of the subthreshold behavior of thin-film

SOI MOSFETs [Ha85, Co87b, Yo87] have concentrated on the improvement

(i.e. reduction) in S gained by thinning the film while simultaneously

depleting the back surface. However, since this work indicates that

back-surface accumulation while thinning the film may be a desirable

design option for reducing short-channel effects, it is important to

investigate this option in the subthreshold region. From the model

given in Chapter 2 for the surface potential in the subthreshold

region, simple predictions can be made about the dependence of

subthreshold characteristics on the film thickness and back-gate bias.

From (2.54) one can write dIsf/dVGfS = l/(l+a). Since the subthreshold

(diffusion) current is proportional to the inversion charge density at

the source end of the channel which varies exponentially with Tsf, S is

proportional to (1+a). Therefore, since a is larger for accumulation

than for depletion and increases as tb is reduced, for thin films S is

expected to be larger when the back surface is accumulated than when

it is depleted. This prediction is confirmed in the PISCES simulations

shown in Fig. 3.11, where the inversion charge density QcfO/q (for VDS

0) is plotted against VGfS in the subthreshold region at different

back-gate biases for the tb 0.135 pm MOSFET of Fig. 3.10. In fact, as

the film is thinned further, our theory predicts that in the

accumulation case a steadily increases towards infinity (implying that

the device can never be turned on), whereas in the depletion case a

approaches unity. This large bias-dependent variability in subthreshold

slope is unique to thin-film SOI MOSFETs, and can be considered a

disadvantage of back-surface accumulation in a thin film.


1m 1017


> 1014 -

Iu\ VGBS = iV c
) o a VGBS = 10 V .

102 -

-2. 5 -2 -1.5 -1 -0.5 0

Fig. 3.11 PISCES-simulated inversion-charge density in the subthreshold
region of a tb 0.135 a&m p-channel SOI MOSFET showing the
increase of the inverse subthreshold slope as the back-
surface charge condition is changed from depletion (VGbS 0
V) to accumulation (VGbS 10 V).


3.7 Back Surface Charge Modulation

In the previous discussion, it has been implicitly assumed that the

back-surface charge condition depends only on the applied biases VBS

and VGbS. However, in this section it is shown that in general the

back-surface charge condition is also dependent on L.

It is possible, with fixed VBS and VGbS, for a back-surface

accumulation layer present in a long-channel SOI MOSFET to be partially

or completely depleted away by a sufficient reduction in L. This unique

depletion charge-sharing effect in SOI MOSFETs is reflected by

comparisons in Fig. 3.12 of the linear-region IDS(VGfS;VBS)

characteristics for a long and short device with VGbS fixed to

accumulate the back-surface of the long-L device. For the long-channel

device, the characteristics are seen to show a strong dependence on VBS

and, correspondingly, a weak dependence on VGbS (not shown), as

expected for back-surface accumulation. These dependence are reversed

for the short-channel device, as expected for back-surface depletion.

Similarly, any accumulation layer present at the back surface, for

a given device, can be partially or completely depleted away by a non-

zero VDS. This effect has been recognized previously even for long

MOSFETs [Li84a], but in fact is exacerbated as L is reduced due to the

two-dimensional potential distribution. The overall effect on the drain

current can be quite dramatic, as is evident from a comparison of

Figs. 3.13a and 3.13b, where we plot measured IDS(VDS, VBS)

characteristics for a long (L 5 pm) and a short (L 0.8 pm) SOI

MOSFET for fixed VGfS and VGbS. In the long device, the presence of an

accumulation layer at the back surface allows the applied VBS to

Measured linear-region IDS(VGfS, VBS) characteristics of (a)
a long (L 5 pm) and (b) a short (L = 0.8 pm) p-channel SOI
MOSFET with tb = 0.27 pm and VGbS = 10 V set to accumulate
the back-surface of the long-channel device.

Fig. 3.12


VGf E Volts 3

8 -1.8 -2.8
VGf [ Volts 3


Measured IDS(VDS, VBS) characteristics of (a) the long and
(b) the short SOI MOSFETs of Fig. 3.11, with VGbS = 10 V set
to accumulate the back-surface of the long-channel device. In
(b) note the disappearance of the effect of VBS as either VBS
or VDS is increased.

Fig. 3.13



o -48.8


-1.8 -2.8 -3.0 -4.0 -5.9
VD I Volts 3

-2.0 -3.0
VD C Volts I



modulate VTf, and therefore IDS. In the short-channel device, the back-

surface accumulation layer is modulated away at large VBS and/or large

VDS, and so IDS is much less dependent on VBS.

These back-surface charge modulations in short-channel SOI MOSFETs

can further cause a device designed (for long L) to operate as a semi-

bulk MOSFET to behave as a thin-film device when L is scaled down

sufficiently. With regard to SOI circuit simulation, it is noted that

most compact device models assume that the MOSFET operates with a

spatially-uniform back-surface charge condition. Thus the length

dependence of the back-surface charge condition must be incorporated

into any model selection or parameter extraction algorithm.

3.8 Summary/Conclusions

It has been shown that the presence of the additional (back-)gate

in SOI MOSFETs can significantly affect their short-channel behavior.

Through measurements and simulations, is has been shown that short-

channel effects like threshold-voltage reduction, drain-induced

conductivity enhancement, and channel-length modulation can be

controlled by thinning the SOI film and/or by accumulating the back

surface by an applied back-gate bias. However, these advantages of such

controls must be weighed against a reduced drive current, an increase

in the inverse subthreshold slope, and a possible increase in hot-

carrier degradation. A unique short-channel effect in SOI MOSFETs

whereby a reduction in the channel length can deplete away the whole

film, negating the control of device properties by the (film) body

voltage, has been reported. In essence, then, the short-channel model


developed in Chapter 2 has been shown to be a useful intuitive guide in

device design.


4.1 Introduction

This chapter addresses the practical use of the SOI MOSFET model

for simulation and design. As described in Chapter 2, the circuit-

simulation model for the thin-film MOSFET has been separated into two

models, one applicable when the back surface is depleted, and the other

applicable when the back surface is accumulated. This separation, which

was done to avoid undue model complexity, results in rather unique

characterization problems when applied to real devices. Since the

specialized models are not valid in all regions of operation, a

systematic measurement-based technique is required to evaluate the

physical parameters needed for device simulation. Such a technique is

presented below. First, in Section 4.2, the general applicability of

the model to SOI films of all thicknesses is discussed, and criteria

for model selection (i.e., the thin-film model versus an appropriately

modified bulk MOSFET model) are presented. Then, in Section 4.3, an

algorithm for extracting the parameters of the thin-film SOI model

developed in Chapter 2 is presented and is applied to a contemporary

SOI technology. The method described in Section 4.3 is to define

measurements that isolate groups of parameters and then use

simplifications of the model equations corresponding to those

measurements to evaluate the parameters individually. This enables the



examination of the inter-dependencies among the parameters, and the

identification of reasonable simplifications of the model. In general,

the extraction scheme uses local optimization rather than a global

optimization, and the parameters retain their physical values.

4.2 Model Selection Criteria

In the past years, the manufacturing trend for SOI MOSFETs has

been generally aimed towards the use of thin films. The scaling and

other advantages of such a trend have already been discussed in some

detail by many authors and in Chapter 3. Unfortunately, present-day SOI

technologies produce device structures that make it difficult to

ascertain in advance whether the SOI film is completely depleted or not

at a given bias condition. Depending on the film thickness, doping

density, and channel length, an SOI MOSFET can behave as a thin-film

transistor with a back gate that can influence the front-channel

conductivity, or as an effective bulk transistor with a neutral,

commonly floating body. For devices fabricated on a relatively thick

film it may, in some cases, be more appropriate to use a bulk MOSFET

model instead of the thin-film model derived in this work. Even for a

thin-film device one must be able to distinguish between the two major

modes of operation, namely, those with the back surface accumulated and

depleted, if one wishes to extract physically meaningful parameters and

simulate the transistor well. In this section, a preliminary method for

experimentally selecting SOI MOSFET models for circuit simulation

through measurements of threshold voltage is presented. The selection


criteria are based on the thin-film SOI MOSFET model, and on

comparisons between it and the bulk MOSFET model.

Three compact MOSFET models are defined for each device type, one

of which must be chosen as most representative. The three compact

models are (1) the thin-film accumulated (TFA) model, which assumes

back-surface accumulation, (2) the thin-film depleted (TFD) model,

which assumes back-surface depletion, and (3) the semi-bulk (SB)

model, which is simply a bulk-device model [Sh85], to which (floating-)

body effects (biasing) and an underlying body-back gate (substrate)

capacitance are added. It is of course possible that the actual charge

condition at the back surface may vary from accumulation to depletion

(inversion is generally avoided) between the source and drain. It is

shown in Chapter 5 that it is possible to model this condition, but the

resulting model is complex, and a strategic selection of the TFA or TFD

model would probably be sufficient in most cases. It must be noted here

that this approach of defining simplified models is strictly valid only

for SOI MOSFETs used more or less conventionally, where the body and/or

the back-gate biases are fixed. It will not in general apply to new

applications of SOI MOSFETs, for example in three-dimensional

circuits, where novel circuit configurations involving large variations

in VGbS may be used.

The threshold voltage VTf depends in general on both VBS and VGbS.

For the case of back-surface accumulation in a long-channel MOSFET


f Qb
VT VB + (+a)2 VBS (4.1)
Tf FB B 2Cof BS


with a Cb/Cof, and for back-surface depletion in a long-channel


f b b b (4.2)
Vf V + 2B -- V B + ---] (4.2)
2C 2C
of ob

with a CobCb/(Cob+Cb)Cof. It may be noted that for the accumulation

case, VTf of the thin-film MOSFET is linearly dependent on VBS, whereas

for the depletion case, VTf is not dependent on VBS. In contrast, VTf

of the semi-bulk MOSFET has a nonlinear dependence on VBS:

Tf = VB + 2B + [2sqNA(2 B- VBS)/2 (4.3)

which is applicable for VBS < 2DB, as are (4.1) and (4.2). With the

above insight regarding the VBS-dependence, the model selection

criteria can be defined in terms of the measured VTf(eff) (see Section

3.3) in the saturation region. This definition is done in the

saturation region, rather than the linear region, because the drain-

induced depletion under the gate tends to activate front gate-back gate

charge coupling. For digital CMOS circuits, in which the transistors

operate predominantly in the saturation region, this coupling is

significant even though the devices may behave as semi-bulk MOSFETs for

low VDS. Note that VBS will also influence the mode of operation since

it affects the depletion of the body.

The methodology for SOI MOSFET model selection for devices with

long L is detailed as follows. With VGbS biased for normal operation

and the drain set at the supply voltage (VDD) for the circuit, IDS(sat)

versus VGfS is measured for different values of VBS in the vicinity of


the normal operating body bias. (If the body is to float, then VBS 0

can be taken as the normal bias.) VTf(eff)(VBS, VGbS) is derived from

the measurement as described in Section 4.3, and this dependence

implies the proper model:

(a) if the dependence is negligibly weak [IdVTf(eff)/dVBSI << a in

(4.1)], then the TFD model is appropriate;

(b) if the dependence is linear [IdVTf(eff)/dVBSI a in (4.1)], then

the TFA model is appropriate;

(c) if the dependence is nonlinear and strong [IdVTf(eff)/dVBSI > a in

(4.1)], then the SB model is appropriate.

To demonstrate the above methodology, it is applied to p-channel

SOI MOSFETs fabricated at Harris Semiconductor. The measured current-

voltage characteristics plotted in Fig. 4.1 were taken from an

enhancement-mode p-channel device fabricated in a 0.8-pm-thick arsenic-

doped SIMOX film with a boron threshold-adjust implant that yields a

net doping density of 2-3 x 1015 cm3. The front-gate oxide thickness

is 325 A, and that of the back gate is approximately 3700 A. The (long)

channel length is 7.5 pm. The characteristics reflect, through the

VGbS-dependence, the front gate-back gate coupling. Note that when VGbS

is sufficiently positive, which implies accumulation at the back

surface, the VGbS dependence disappears, reflecting either TFA or SB

MOSFET behavior.

The proper selection is exemplified nicely by the measured

VTf(eff) plotted versus VBS for different values of VGbS in Fig. 4.2.
For the relatively thick SOI MOSFET the charge-coupling is controlled

by VBS. For VBS relatively small, the device is adequately represented

H /div

U) 5V

.0000 -3.000

Fig. 4.1 Measured (saturation-region) current-voltage characteristics
of a p-channel SIMOX/SOI MOSFET with W/L 50 pm/7.5 pm. The
square root of IDS(sat) is plotted against VGfS for VGbS
ranging from -5 V (depletion at back) to +5 V (accumulation
at back) in 2 V steps; VBS 2 V and VDS -5 V.


XVGBS = -2.5V


-1.0- 50V


-1.5 -- -,
0.0 1.0 2.0 3.0 4.0 5.0

Fig. 4.2 Measured threshold voltage versus VBS for different values of
VGbS. The slope (a) of the VTf(VBS) characteristic in the TFA
region is indicated.


by an SB model (criterion (c) applies), but for larger VBS, the device

is indeed a thin-film transistor. In this case, for VGbS 5 0 the TFD

model (criterion (a)) is appropriate, but for VGbS >> 0 the TFA model

(criterion (b)) is the proper one.

In general, more emphasis should be placed on the linearity

condition (4.1) in the model selection than on the actual value of a.

One reason is that the model assumes a negligible interfacial region

between the buried oxide and the silicon film, an assumption that

becomes worse as tb is reduced, and so there can be a fair amount of

error in calculating a from the process data. Besides, film thicknesses

for most processes are specified based on data gathered before

transistors are actually fabricated on the wafer. Thus, typically, the

effective film thicknesses are expected to be somewhat smaller than

those specified. Also, the device processing, which in some cases

involves a deep implant into the body to reduce leakage, can

effectively limit the maximum depletion layer thickness in the film,

and thus the effective tb. In such a case, where the bulk MOSFET model

is clearly inappropriate, the measured a can be used to define an

effective film thickness for use in the model.

For MOSFETs with shorter channel lengths, the back-surface charge

modulation effect discussed in the previous chapter can cause a device

designed (for long L) to operate with a neutral/accumulation layer near

the back surface to actually behave as a thin-film back-surface-

depleted device when L is scaled down sufficiently. This implies that

the length-dependence of the back-surface charge condition must, in

general, be incorporated into the model selection defined above. For a


well-scaled technology, this should not be a problem except for very

short devices. In this preliminary stage of the technology, however, it

is important to be constantly aware of this possibility, especially

while extracting parameters as described below. In fact, other

subjective criteria can also be used, e.g., in n-channel MOSFETs the

presence of a "kink" in the IDS(VDS) characteristics rules out the

possibility of operation in the TFD mode.

4.3 Parameter Extraction

In Chapter 2, the general short-channel model for the thin-film

SOI MOSFET was derived, with the physical and empirical parameters

listed in Table 2.1. In this section we present and demonstrate the use

of an algorithm to extract the parameters required to simulate device

characteristics. The general philosophy is to experimentally isolate as

many parameters as possible, thereby enabling their direct extraction

from the measurements. The advantages of such a scheme over a global

optimization method are, firstly, that it retains the physical meaning

of the parameters and hence the model, secondly, it enables one to

examine the inter-relations among the extracted parameters, and

lastly, that it is less time-consuming.

In principle, to characterize all the model parameters, only three

test devices are required: one with a large L and W, one with a short L

and long W, and one with a long W and short L. However, it is prudent

to use as many test devices as available to minimize errors in the

measurement and extraction process. Since narrow-width effects are

highly technology-dependent, it seems premature to quantify them; the


focus here is exclusively on the short-channel effects instead of a

more general treatment.

N-channel MOSFETs fabricated at Harris Semiconductor with nominal

SOI film thickness 0.25 pm, channel doping density approximately 1017

cm-3, and a nominal buried-oxide thickness of 0.45 pm are used as test

vehicles. The mask lengths of the test transistors are 25 pm, 5 pm,

2.5 pm, 1.7 pm, 1.3 pm, and 1 pm, with effective channel lengths down

to approximately 0.6 pm; the (wide) channel widths are all 50 pm. The

drain and source regions adjacent to the channel are lightly doped

using oxide-spacer (LDD) technology to reduce the maximum lateral

electric field.

The measurements and much of the subsequent data analysis are done

with the TECAP characterization system [He85] run from an HP-217 desk-

top computer. The TECAP system allows the user to make measurements

remotely using any instrument connected to an IEEE-488 standard

interface, store the measured data, and then compare and fit the

measurements to a user-specified model. The steady-state portion of

the short-channel model detailed in Chapter 2 is implemented as a

Pascal procedure in TECAP. The model contains 8 nodes (which can

collapse to as few as 5 nodes if the parasitic resistances are

neglected) and has the same topology as the SPICE2 model previously

described. This allows the user to check that the extracted parameters

adequately simulate the measured current-voltage characteristics. In

addition, various user-defined commands were added to enable the

automated extraction of quantities like threshold voltage and



The general extraction procedure comprises the following steps.

(Lm and Wm are used to denote the mask-lengths and widths, and L and W

to denote the corresponding electrically effective quantities, i.e.,

the values used in the model. Similarly, voltage differences, e.g.

VGfS, VDS, etc. are used to denote the biases applied to the intrinsic

device; for the terminal voltages, VGf, VD, etc., which are referenced

to VS,are used.)

(a) VTf is measured in the linear-region as a function of VGb and VB.

The measured VTf for the MOSFET with the longest Lm (where,

presumably, there are no short-channel effects) is used to

determine values for the parameters tb, tob, VFB, VFB, and possibly

NA. The VTf measurement is also used in the model selection and the

determination of channel-length reduction and parasitic


(b) The incremental channel resistance at VD = 0 V is measured as a

function of VGf and Lm (and Wm), and used to extract values for

channel-length reduction AL (and channel-width reduction AW) due to

processing, parasitic resistances RS and RD, mobility 0o, and

mobility degradation factor 0.

(c) The electrical channel lengths (and widths) extracted in (b) are

used with the short-channel VTf model to find the empirical

charge-sharing parameters that fit the short-channel VTf values

measured in (a).

(d) The body current IB and drain current ID are measured as a

function of VD and VGf in the saturation region with the body

reverse-biased. This information is used to extract the


coefficients a0 and P0 for the generation current due to impact

ionization, as well as to estimate the recombination current Iro

and body resistance RB.

In the following sub-sections, each of the above steps is described

in more detail, with discussions of the possible sources of measurement

error and how they can be avoided. The final extracted parameters are

listed in Table 4.1 at the end of the chapter.

4.3.1 Threshold-Voltage Measurements

The threshold voltage VTf in the linear region is controlled by

tof, tb, tob, VFB, VB, NA, and the empirical charge-sharing

parameters. Usually, tof can be determined independently (from C-V

measurements), or can be assumed to be given by the process data (in

our case 25 nm). To determine the rest of the parameters, their

relative importance in the various possible operating ranges must

first be considered. For long-channel devices, the model for the TFA

case depends on tb, VFB, and NA, and does not depend on tob and VFB.

The TFD model, however, is affected by all the parameters listed above.

For shorter channel lengths, the characterization of the charge-sharing

model in either the TFA or the TFD case depends on parameters common to

both models. There are the additional possibilities noted previously

that the SB model may be appropriate in certain bias ranges and that

the back-surface charge modulation (Chapter 3) is important in short-

channel devices at certain bias conditions, but not at others. In

summary, it is very difficult to completely decouple the parameter

extraction of the TFA and TFD (and SB) models while continuing to


retain an acceptable level of confidence in the physical nature of the

extracted parameters. Therefore the algorithm for the calculation of

VTf is extended to simultaneously account for the TFA, TFD, and SB

regions of operation so that VTf can be calculated as a continuous

function of both VBS and VGbS. The details are in Appendix C.

VTf is experimentally determined from the linear-region ID(VGf)

characteristic measured at a small value of VD (usually around 50 mV).

A common technique for extracting VTf is to find the tangent to the

ID(VGf) curve at the point of inflexion, and then subtract VD/2 from

the x-intercept of the tangent. This gives a value of VTf relatively

independent of the actual (small) value of VD used in the extraction.

It has been noted that the presence of a parasitic series resistance

(e.g., due to the LDD structure) comparable in magnitude to the channel

resistance in the linear region can cause an underestimate of VTf

[Hu87a]. With this potential problem, then, the measured VTf can be in

error by as much as 25 mV, a factor which is relatively unimportant in

the determination of the charge-sharing parameters, but can cause

errors in the determination of channel-length reduction. (If the

differences in measured VTf over a range of channel lengths were less

than 25 mV, it is probably good enough to assume that there are no

short-channel effects in that range!)

In Fig. 4.3 the measured VTf are plotted against VGb for different

reverse biases Vg for the Lm = 25 pm test device. From the plot, and

from other measurements similar to the ones in Fig. 4.2, it is deduced

that the MOSFET operates in the SB mode for VB 0 V. For the larger

values of VB shown, the thin-film models are applicable, with the


2.5 I I I

VB -2 V

vB -- -2v

S1 VB-0V


I ' I , I I I l I I' ' i
B -5.9 -1B.8 -15.8 -28.8
VGb (V)

Fig. 4.3 Measured VTf for a long (L 25 pm) n-channel SOI MOSFET
(solid lines connecting the '+' symbols) plotted against VGb
for VB ranging from 0 V (semi-bulk) to -2 V (thin-film). The
dashed lines are simulations using the parameters in Table
4.1 and the general VTf model in Appendix C.


distinction between the TFD (VGb = 0 V) and TFA (VGb = -20 V) modes of

operation becoming obvious for the Vg -2 V curve. More detailed

measurements of VTf(VB) at VGb = -20 V (which are not shown here)

indicate that the MOSFET is strictly an SB device at VB = 0 V in the

linear region, but is for all practical purposes a TFA device at small

body reverse biases (VB < -0.5 V), and should be modeled as a TFA

device for those biases.

The extraction procedure begins then with the measurements on the

Lm = 25 pm device at VGb -20 V. The slope of the VTf(VB) curve at Vg

0 V (SB) correlates well with the doping density of 1017 cm-3 given

from the process data, and hence it is reasonable to fix NA at that

value. For more negative Vg, the VTf(VB)-data is linear (TFA), and is

fitted to the model equation (4.1) to yield an approximate value for tb

and VFBf. Then, fitting the measured VTf-data at Vg = -2 V and VGb near

0 V (TFD) to (4.2) yields an approximate value for tob and VFB. With

these initial estimates then, the Levenberg-Marquardt nonlinear least-

squares-fitting algorithm in TECAP [Wa82, He85] is used to optimize
f b
tb, VFB, tob, and VFB to fit the measured VTf for the Lm 25 pm MOSFET

over the wider range of VB and VGb values for which measurements are

done. Fig. 4.3 also shows the simulated VTf using parameters optimized

after six iterations of the extraction algorithm. It may be noted that

the parameter values obtained (see Table 4.1) are physically

reasonable: the extracted tb was 0.18 pm, which is comparable to the
process specification of 0.25 pm; VFB correlates well with the work-

function difference due to an n+-polysilicon gate; the difference

between the extracted tob 0.39 pm and the process-specified 0.45 pm


can be explained by the fact that the capacitance due to surface-states

at the back interface (which has not been explicitly modeled here) adds

to Cob causing a reduction in the extracted tob. Due to the uncertain

nature of the interfaces between the buried oxide and the film and

substrate regions, no comments can be made regarding the physical
nature of the extracted VFB, except that it enables a good fit to the

measured data.

4.3.2 Linear-Region Conductance Measurements

The accuracy of the physical model is greatly dependent on the

accuracy of the channel length used in simulations. Usually, L and W

are less than the mask length and width Lm and Wm due to lateral

diffusion during the processing of the MOSFET. It can be usually

assumed that the reductions AL (- Lm L) and AW (- Wm W) are

constant for devices of all lateral dimensions on the same die. Since

the channel current in the linear region for a given gate bias is, to

first order, proportional to Wuo/L, measurements of the incremental

channel resistance in that region for various gate drives can be used

to extract AL, AW, and po. However, any measurement of the channel

resistance will necessarily include the parasitic RS and RD. If it is

assumed that for a given device width, RS and RD are constant for

devices of all channel lengths, AL, RS, and RD can be determined for a

given W as follows.

At VDS 0 V, (2.23) implies

[ dDS 1 1

dVD (VDs= 0) gDSO

0 L L [1 + 0[2Cb(l- Isb0)-Qb(eff)]/2Es]
RS+ RD+ + (4.4)
2csWDo 0 W Cof [VGfS- VTf]

Laux [La84] has shown that for LDD MOSFETs where the parasitic

resistances can be a function of the gate voltage, the assumption of

constant resistances is accurate enough for extraction of AL. In this

work, a slight modification of his method has been used. (Equation

(4.4) can also serve as a basis for extracting AW by exploitation of

the W-dependent terms in it.)

Equation (4.4) indicates that for constant (VGfS VTf), RON is

proportional to L, and therefore plots of RON versus the channel mask

length for various (VGfS VTf) define straight lines that intersect at

(AL, RS + RD). In practice, due to the variation of VTf with L, it is

inconvenient to measure resistance with fixed (VGfS VTf), so RON is

measured as a function of VGf instead, and the (VGfS VTf)-1

relationship in (4.4) is used to determine (intermediate) values for a

fixed set of (VGfS VTf) values by interpolation. (Note the implicit

assumption that VGfS VGf.) Figure 4.4 shows a typical set of measured

RON data plotted versus (VGfS VTf)-1 for four channel lengths and

with VGb -20 V and VB -1 V (TFA). For a fixed set of values of

(VGfS VTf), which will not in general correspond to measured values,
the values of RON are found by interpolating the data of Fig. 4.4. It

must be noted that the choice of (VGfS VTf)-l is critical to the

final parameters extracted. For VGfS values near VTf, errors in the


2000 I-



0 1000

500 -

0.5 1




Fig. 4.4 Measured incremental resistance RON at VD 0 V plotted
against 1/(VGfS VTf) for SOI MOSFET's of four different
channel lengths. In all cases, VGb -20 V and VB -1 V,
making the thin-film model applicable.



5 um

2. 5 um

1. 7 ur

1.3 um


measurement of VTf (as discussed in the previous subsection) can cause

large errors in the interpolated resistances. Furthermore (4.4),

which is based on the strong inversion model of Chapter 2, is itself

invalid for values of VGfS close to VTf. Based on this insight, then,

further extraction is limited to measurements made for the largest

values of VGfS. In the particular example chosen, (VGfS VTf) varies

from 2.0 V to 3.5 V. Plotting these (derived) resistances then versus

channel mask length (Fig. 4.5) for the various (VGfS VTf) defines a

family of straight lines which in principle should have a well-defined

intersection point (AL, (RS + RD)). In practice, due to measurement

errors, there is no well-defined intersection point, and another linear

regression is needed to determine the desired parameters [La84]. From

(4.4), it may be noted that the slopes A and y-intercepts B of the

fitted lines in Fig. 4.5 are linearly dependent as follows:

B (-AL)A + (RS + RD) .(4.5)

Thus a plot of B versus A (Fig. 4.6) defines a straight line, with the

slope equal to -AL and the y-intercept equal to (RS + RD). Since the

processing of the drain and source regions are identical, it can

further be assumed that RS = RD, resulting in an extracted value of

approximately 23 0 for these devices. This value can be compared to the

resistance of the LDD region which is expected to be the dominant

factor in RD. With an approximate LDD length of 0.2 pm, doping density

of 1018 cm-3 (implying PLDD = 250 cm2/V-s [Sz81]), and a conducting

area of 0.1 pm x 50 pm, a value of 10 0 is obtained, which is quite

close given the approximations made in the estimation. It must also be












Fig. 4.5 Interpolated values of RON for three values of 1/(VGfS VTf)
plotted against mask length.

5 10 15 20






-60 -


150 200



Fig. 4.6 Y-intercepts (B) of the linear fits to the data in Fig. 4.5
plotted against the corresponding slopes (A) for (VGfS VTf)
ranging from 1.5 V to 3 V in equidistant steps.


noted that the value AL extracted is not necessarily exact, and could

be in error for any given device by as much as the error in Lm [Sc87],

which can be 0.03 pm or so depending on the technology used.

Additional information can be extracted from the slopes of the

fitted straight lines in Fig. 4.5 [Mo82]. From (4.4), the slope A can

be expressed as:

[1 + 0[2Cb('I- sb)-Qb(eff)]/2Es] 0
A = + (4.6)
Ao W Cof (VGfS- VTf) 2esW

Thus, a plot of A versus (VGfS VTf)- (e.g., Fig. 4.7) is a straight

line, and its slope and y-intercept can, in principle, be used to

estimate both po and 0 simultaneously from (4.6). We extracted po = 537

cm2/Vsec, which was found to be adequate for simulating the I-V

characteristics. However, the intercept of the fitted straight line was

much smaller in magnitude than the values of A used in the fitting,

causing the extracted 0 to be very sensitive to the specific range of

VGf values used in the extraction. This sensitivity can be attributed

to the fact that at low VGf, mobility degradation is too insignificant

to be detected by RON measurements, and at high VGf, there can be

confusion in distinguishing between the effects of mobility degradation

and the parasitic resistances. In general, a statistical correlation

between the extracted values of (RS + RD) and 0 is expected. However,

the error in the extracted (RS + RD) is expected to be small, mainly

due to the fact that more devices with short L (where the voltage drop

in the series resistance was significant) were included in the

parameter extraction than devices with long L (where mobility






140 -



0. 4 0. 5 0. 6




Fig. 4.7 Slopes (A) of the linear fits to the data in Fig. 4.5 plotted
against l/(VGfS VTf) for (VGfS VTf) ranging from 1.5 V to
3 V in equidistant steps.


degradation is more important). In summary, it was found that the value

extracted for 0, 0.3 cm/MV, was an under-estimate, and had to be

adjusted to 0.5 cm/MV so that the TECAP model simulations fitted the

measured linear region ID(VGf) curves for the Lm = 25 pm MOSFET. This

value compares favorably with the value 0.7 cm/MV that can be derived

from the mobility model presented in [Ga87] (which differs only

formally from our model in Chapter 2). In retrospect, it appears that

instead of extracting 0 from conductance measurements, it is better to

estimate it as some representative value, e.g. 1 cm/MV, and then adjust

it to fit the measured ID(VGf) curves for the longest device as

indicated above.

4.3.3 Determination of Empirical Charge-Sharing Parameters

With the values of the effective channel length established for

each device by the procedure in Section 4.3.2, and the values for tb,
f b
VFB, tob, and VFB determined from the VTf-measurements on the Lm 25

pm MOSFET, the charge-sharing parameters f0, fc, and fP are optimized

as before (with the VTf(VBS, VGbS, L) model in Appendix C) to fit the

measured VTf-data for the rest of the MOSFETs. All the VTf-data

measured (i.e., from devices of all channel-lengths) were used to

reduce any possible errors in the parameters due to an error in

determination of L. However, it turned out that the parameters

extracted were fairly insensitive to such considerations. Fig. 4.8

shows the good fits obtained for the Lm 1.0 pm and L, 1.3 pm

devices. Similar or better fits were obtained for all the other devices

as well, with an overall maximum error of 5 percent, and a mean-square

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