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Low frequency conductance voltage (LFGV) characterization of Si/Gex/Si1-x/Si heterojunction bipolar transistors

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Title:
Low frequency conductance voltage (LFGV) characterization of Si/Gex/Si1-x/Si heterojunction bipolar transistors
Creator:
Li, Guoxin, 1964-
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English
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vi, 107 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Bipolar transistors ( jstor )
Doping ( jstor )
Electric current ( jstor )
Electric fields ( jstor )
Electrons ( jstor )
Energy gaps ( jstor )
Impurities ( jstor )
Minority carriers ( jstor )
Temperature dependence ( jstor )
Transistors ( jstor )
Bipolar transistors ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1998.
Bibliography:
Includes bibliographical references (leaves 100-106).
General Note:
Typescript.
General Note:
Vita.
General Note:
In title, x and 1-x are subscript.
Statement of Responsibility:
by Guoxin Li.

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LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) CHARACTERIZATION
OF Si/GexSilx/Si HETEROJUNCTION BIPOLAR TRANSISTORS









By

GUOXIN LI










A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1998














ACKNOWLEDGEMENTS



I would like to thank my supervising professors Dr. Arnost Neugroschel and Dr. Chih-Tang Sah for their guidance during my doctoral research. I would also like to thank Dr. Peter Zory, Dr. Vladimir Rakov and Dr. Mark Orazem for serving on my supervisory committee. I also thank Jin Cai, Wan-Peng Cao, Derek Martin, and Yi Wang for helpful discussions.































ii















TABLE OF CONTENTS

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

A B S T R A C T ..................................................................................................................... v

CHAPTERS

1. INTRODUCTION TO GeSi HETEROJUNCTION BIPOLAR TRANSISTOR....... 1

1.1 Introduction.................................................................................................... 1
1.2 GeSi HBT Fabrication...................................... ............................ 3
1.3 Pseudomorphic Growth, Critical Layer and Ge-induced Effects..................... 7
1.4 GeSi HBT Characteristics............................................................................ 8
1.5 Monte Carlo Simulation of Mobilities................................ .............. 16
1.6 Energy Band Diagram..................................................... 19
1.7 NcNv and ni Model for Linear Ge Distribution........................... ........ 24
1.8 S u m m ary ............................................................................................................. 2 6

2. LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) METHODOLOGY.. 28

2 .1 Introduction ......................................................................................................... 28
2.2 Base Thickness Modulation (BTM)..................................... ............. 30
2.3 LFGV M ethodology................................................................................... 33
2.4 Derivation of LFGV Methodology and Parameter Extraction......................... 41
2.5 Experiments and Results.......................................................................... 45
2.6 Sensitivity of tB and rl to T12 and XR/XB......................................................... 55
2.7 GeSi HBT Performance Enhancement....................................................... 61
2.8 Sum m ary............................................................................................................. 62

3. LFGV ANALYSIS OF GeSi HBT WITH NO REFERENCE Si BJT.................... 70

3.1 Introduction......................................................................................................... 70
3 .2 T h eory ................................................................................................................. 7 1
3.3 Experiments and Results.................................................... 74
3.4 LFGV Analysis with no Si Reference BJT.................................... ....... 84
3.5 Sum m ary ............................................................................................................. 86



111











4. SUMMARY AND CONCLUSIONS................................................................. 87

4 .1 S um m ary ............................................................................................................. 87
4.2 GeSi HBT Modeling and LFGV Methodology........................... ....... 88

APPENDIX A GENERAL EQUATIONS FOR BJT................................... ...... 89

APPENDIX B TRANSISTOR RELATION FOR A GAUSSIAN DOPANT IMPURITY
CONCENTRATION PROFILE IN THE BASE OF BJT.................... 92

APPENDIX C LIST OF SYMBOLS............................................... 98

R EFER E N C E S................................................................................................................. 100

BIOGRAPHICAL SKETCH.........................................................107

































iv














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

LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) CHARACTERISTICS
OF Si/GexSil_x/Si HETEROJUNCTION BIPOLAR TRANSISTORS By

Guoxin Li

December 1998


Chairman: Dr. Arnost Neugroschel Cochairman: Dr. Chih-Tang Sah
Major Department: Electrical and Computer Engineering

Low Frequency Conductance Voltage (LFGV) methodology for analysis of heterojunction bipolar transistors (HBTs) is presented. The LFGV methodology is based on a combined measurement of the dc collector and base currents and low frequency (-lkHz) small-signal conductance resulting from the base thickness modulation. It gives accurate and independent determination of the built-in electric field resulting from the spatially varying energy gap and dopant impurity concentration profile in the base layer. The LFGV methodology also gives accurate quantitative values for the minority-carrier transport parameters, including the minority carrier diffusion length and recombination lifetime, and a complete charge control analysis of the recombination losses in the emitter and base region of the HBT.



v









The LFGV methodology is used here to study the performance improvements of Si/GexSil_-/Si HBT over that of the Si BJT, including current gain, switch speed, and Early voltage which are primarily due to the aiding electric field.

Analytical models for the effective density-of-states NcNv and intrinsic carrier concentration ni as a function of Ge mole concentration for a linear Ge distribution in the base region are developed. Analytical solutions for the LFGV methodology are then derived for an arbitrary Ge and dopant impurity concentration profile. The analysis showed that the main effect of Ge in the base region with a linearly retrograded Ge concentration profile comes from the aiding electric field which reduces the base transit time and increases the collector current and the cutoff frequency fT. Accurate measurements of the base minority carrier diffusion length and recombination lifetime indicate large performance improvement of GeSi HBT over Si BJT. Design considerations for optimal performance of GeSi HBT are also investigated, such as the optimal Ge concentraction profile in the base region. The LFGV methodology is applicable to other bipolar junction transistors and HBTs, including those fabricated in EII-V materials.













vi















CHAPTER 1
INTRODUCTION TO GeSi HETEROJUNCTION BIPOLAR TRANSISTOR

1.1 Introduction

The concept of heterojunction bipolar junction transistor (HBT) was first proposed by Shockley in 1948 [1-2]. The purpose was to build bipolar junction transistors with larger energy gap in the emitter than in the base, which improves the emitter injection efficiency over that of the homogeneous bipolar junction transistors. The first detailed analysis of the HBT characteristics and performance was given by Kroemer [3].

Although the advantages of the heterostructures were known, practical applications were not realized until the 1970s when the epitaxial technology was developed. The first successful HBT was fabricated in 1972 by IBM [4] using AlGaAs/GaAs heterostructure to give the larger emitter energy gap. The anticipated superior performance of the HBT was demonstrated by these and other III-V compound HBTs. Until recently, the AlGaAs/GaAs HBTs have been the most successful. This is due to the excellent lattice matching between the two material which gives a nearly defect-free heterointerface. But GaAs or other HBTs based on III-V semiconductor materials are difficult to integrate with the existing Si integrated circuits due to the large lattice mismatch. Also III-V HBTs are difficult to fabricate and thus not cost efficient. GaAs HBT has been more successful in discrete devices, such as high frequency oscillators and amplifiers.


1







2

The breakthrough for an Si-compatible HBT was accomplished again by IBM in 1988 [5]. They used Germanium Silicon (GeSi) as the base material which has a smaller energy gap than that of the Si emitter and collector. A thin strained single crystal GexSilx film on Si substrate was grown pseudomorphically using ultra-high vacuum/chemical vapor deposition/low temperature epitaxy (UHV/CVD/LTE) process [6-8]. The energy gap of the base can be tailored by varying the Ge mole content in the base. Furthermore, the Ge distribution in the base region can be graded which will produce an aiding electric field for the minority carrier transport through the base. Ge incorporation in the base will also modify the effective mass and mobility of both majority and minority carriers. This results in a number of advantages of Si/GexSilx/Si HBT over Si BJT, such as higher collector current, higher current gain 3, superior high frequency performance (higher unit gain frequency fT and maximum oscillation frequency fmax), and excellent low noise behavior. The best high frequency performance was obtained at low voltages (VcE=1-3V), which is very useful for portable communication applications.

Since the introduction of the pseudomorphic growth mechanism in 1972 [1], the techniques of growing a thin base GeSi layer have been highly developed to accommodate the lattice mismatch between the GeSi layer and Si substrate. Technology has been developed for GeSi layer deposition in commercial epitaxial reactors. During the pseudomorphic growth, the lattice of the GeSi layer has to conform with that of the Si substrate; thus, the lattice of the GeSi layer is strained and distorted compared with that of the unstrained GeSi layer. This lattice strain is responsible for







3

the changes in the physical parameters that give the performance improvements of GeSi HBT over Si BJT. The performance of the GeSi HBT demonstrated so far is superior to, or comparable with, that of the GaAs HBTs [6-7]. The most important advantage of using thin GeSi layer is that its epitaxial deposition is fully compatible with Si integrated-circuit manufacturing technology; thus, monolithic integration of GeSi HBT with Si integrated circuit can be very easily accomplished. Also, the thermal conductivity of Si is three times higher than that of GaAs which is very important in power amplifiers and very large scale integrated circuit (VLSI). The GeSi HBT has very important applications in portable communication systems, such as mobile phones, pagers, DACs and others.

1.2 GeSi HBT Fabrication

Silicon and germanium are completely miscible in any mole fraction ratio. The GeSi material has a diamond lattice structure. The lattice constant can be calculated from the Vegard rule [5]:

a(GexSil-x) = a(Si) + x(a(Ge) a(Si)) (1.1) where x is the Ge mole fraction and a is the lattice constant. The lattice constant of Ge is 4.17 percent higher than that of Si. When Si and Ge atoms are mixed during the growth of the GeSi layer, the Si lattice is tetragonally distorted and strained. The lattice mismatch between the GeSi layer and the Si substrate can be accommodated by two ways. One is a generation of misfit dislocations at the GeSi/Si interface which may also propagate through the entire layer. This occurs when the GeSi layer is very thick and the strain is released by creation of misfit dislocations. The second possibility is







4

pseudomorphic growth. In pseudomorphic growth, if the GeSi layer thickness is below a critical thickness, the lattice mismatch is accommodated elastically with no dislocation created. The GeSi layer is under biaxial strain both in the x-y plane and in the z or growth direction.

Several epitaxial techniques for GeSi layer deposition were developed, such as the molecular beam epitaxy (MBE) [9-10] and limited reaction process (LRP-CVD) [11]. Figure 1.1 shows a HBT transistor structure used in this thesis which was fabricated by chemical vapor deposition (CVD) [11]. The single-crystal strained GeSi layer was grown over the n-Si collector to give the intrinsic base, and also on the LOCOS SiO2 layer which becomes poly-crystalline and is the extrinsic base regions. This results in an interface between the intrinsic and extrinsic base regions. Germane is the source of Ge during the growth and boron impurity doping was obtained with diborane. Boron was then implanted to give the extrinsic base. The oxide/nitride layer were deposited and etched to open the emitter region. The polysilicon layer was then deposited and implanted by a high concentration of arsenic and patterned to form the emitter. The impurity and GeSi concentrations were measured by SIMS (secondary ion mass spectroscopy) as shown in Fig. 1.2. The impurity and Ge concentration profiles can be precisely controlled during film growth to give specified Ge distribution in the base, such as a linearly retrograded Ge gradient. This Ge gradient produces an aiding electric field which accelerates the minority electrons in the base layer.





5



Emitter Boron n+poly p-type poly-Si base


/GeSi epi

n-Si Collecto n+ emitter
p-type intrinsic base



Fig. 1.1 Cross section view of GeSi HBT. Adapted from Neugroschel et al. [11-12].





6




10 22
E As -12 Ge:


B8 O__c- -8 E 1018
a

0
o 1016i I a
Emitter Base: Collector 0
1015 09
0 XR XB

Depth


Fig. 1.2 Secondary ion mass spectroscopy (SIMS) profile of GeSi HBT. The base doping level is about 3x1018 cm-3 and the Ge mole fraction in the base is about 10%. Adapted from Ron Tang et al. [13].







7

1.3 Pseudomorphic Growth, Critical Layer and Ge-induced Effects

During the pseudomorphic epitaxial growth of GeSi layer, the lattice mismatch between GeSi layer and Si substrate was accommodated by biaxial strain in the GeSi layer. A two-dimensional illustration of the pseudomorphic growth of GeSi layer is shown in Fig. 1.3. As is shown in Fig. 1.3b, under conditions that favor pseudomorphic growth, the GeSi layer is biaxially strained and its lattice assumes that of the substrate. On the other hand, lattice defects such as misfit dislocations occur at the GeSi/Si interface when the GeSi layer becomes relaxed (no strain) as shown in Fig. 1.3c. There is a critical layer thickness beyond which the layer will relax and create the misfit dislocations at the GeSi/Si interface. The dislocations may also penetrate the entire layer. This critical layer thickness can be calculated based on the strain of the GeSi layer and the thermal dynamics theory [5-7]. Figure 1.4 shows the theoretical and experimental critical layer thickness versus the Ge mole fraction [1]. As is shown in the figure, based on the model of People and Bean, for XGe=10% in the GexSilx layer, the critical layer thickness is almost 1 gm which is enough for high performance GeSi HBT whose base thickness is usually in the range of <1000A. The Ge-induced biaxial strain in the GeSi layer changes the physical and chemical properties of the layer, such as the energy band structure [14-16], electron and hole effective masses, and electron and hole mobility gn and g [17-18]. Figure 1.5 shows the constant energy surfaces in the GeSi layer under biaxial strain [17, 19]. As can be seen from the figure, the two surfaces in the z-direction (growth direction) are deformed which gives a smaller electron effective mass mn and also a higher electron concentration in the z direction, while the energy of







8

the four surfaces on the kx and ky axes is lowered. The resulting reduction in the energy gap and lowering of the effective mass are very beneficial for improved performance of GeSi HBT. The smaller energy gap increases the collector current and gain, while the smaller mn in the vertical minority-carrier electron flow direction (in npn HBT) increases the minority-carrier mobility which reduces the base transit time. Figure 1.6 illustrates the in-plane (x) of growth direction and normal to the growth plane or the growth (z) direction. Figure 1.7 shows the calculated values of energy gap reduction of strained GeSi layer and unstrained (bulk) material versus the Ge mole fraction. It shows that, for the strained GeSi layer, the energy gap reduction AEG-Ge is almost a linear function of the increasing Ge mole fraction XGe for XGe<-40%.

1.4 GeSi HBT Characteristics

Typical collector current and base current dependencies on VBE of GeSi HBT and Si BJT are shown in Fig. 1.8. The collector current of GeSi HBT, Ic(GeSi), shows large improvement over that in Si BJTs. The base current of GeSi HBT, IB(GeSi), is also slightly smaller than that in Si BJTs. This gives a much larger common emitter forward current gain 3F of GeSi HBT compared to that in Si BJT. Figure 1.9 shows a typical high frequency response versus collector current. Improvement by almost a factor of 2 in fT for GeSi HBT is shown. Recently, fT values as large as 116GHz or higher were reported [20]. This improvement of fT is very important for RF wireless communication applications. The improvement of fT is mainly due to the Ge-induced aiding electric field for the base minority carriers which reduces the minority carrier transit time through the base region which still is a limiting factor of fT. Other performance







9







Unstrained GexSi1-x Strained GexSil-x

- -











Si Si
(a) Relaxed GexSi1lx (b)














Si

(c)


Fig. 1.3 Two dimensional illustration of GeSi pseudomorphic growth. (a). Unstrained GeSi layer and Si substrate. (b). Strained GeSi layer. The lattice mismatch is accommodated by the strain in the GeSi layer. (c). Relaxed GeSi layer. There are misfit dislocations at the GeSi/Si interface. Adapted from Sah [1, Fig. 774.1, p. 947].





10





Wm Relaxed c 1 00nm
People and Bean

lOnm


O nm- Pseudomorphic

0 20 40 60 80 100 Ge fraction /(1%)


Fig. 1.4 Critical layer thickness of GeSi layer versus Ge fraction. The dashed line shows the theoretical results calculated from the thermal dynamics. The solid line gives the experimental results. Adapted from Sah [1, p. 949].















kZ
k



















Fig. 1.5 Constant energy surfaces in the conduction band in GexSil_-x under biaxial strain [17, 19]. The z direction corresponds to the growth direction. The two surfaces in the z-direction (growth direction) are raised in energy and deformed such that they give a smaller electron effective mass mn. The four x and y surfaces are lowered in energy. The overall energy gap is smaller and the electrons preferentially populate the two valleys in the z-direction in which mn is low. This is also the direction of the minority-carrier flow in HBT.







12








Emitter P-GeSi base Collector






Fig. 1.6 Direction illustration in vertical GexSil_-x HBT. The z direction corresponds to the growth direction and is also the direction of the minority electron flow in a vertical BJT. The in-plane direction is important and applicable for lateral MOS transistors.





13



1.2


Unstrained
1.0



0.8
Strained
LIU

0.6
0 0.2 0.4 0.6 0.8 1.0 Si Ge Atomic Fraction, XGe Ge

Fig. 1.7 Energy gap reduction for strained and unstrained GeSi layer versus Ge mole fraction in the layer. Adapted from Sah [1, p. 951].





14



10-1
GeSi HBT 10-3 ---- Si BJT -VCB=1V, T=296K IC,,,



107

10-9


10-11
0 0.2 0.4 0.6 0.8 1.0 VBE /(1 V)

Fig. 1.8 Typical I-V characteristics of GeSi HBT and Si BJT at VCB=1V. The GeSi HBT and Si BJT have the same dopant impurity concentration profile and geometry except the Ge in the base for GeSi HBT. The solid line is GeSi HBT and dashed line is Si BJT.





15




60
I
50

>' 40 GeSiHBT

30

u- 20

o 10 SiBJT

0 I I I I I I I II I
10-2 10-1 100 Collector Current Ic /(1 mA)

Fig. 1.9 Typical unit gain frequency fT versus Ic characteristics of GeSi HBT (full circles) and Si BJT (open circles). The GeSi HBT and Si BJT have the same dopant impurity concentration profile and geometry except the Ge in the base for GeSi HBT. Adapted from Merit Hong et al. [11].







16

improvements of GeSi HBT, such as higher Early voltage VA will be discussed in detail in later chapters.

1.5 Monte Carlo Simulation of Mobilities

The Ge-induced strain in the GeSi layer will change the E-k relationship in both the conduction and valence band, and thus change the effective masses of electrons and holes, mn and mp. The electron and hole mobilities, pn and gp, will be also affected by the change in the effective masses and become anisotropic. Monte Carlo simulations were used to calculate the electron and hole mobilities in strained and relaxed GeSi layers for different Ge mole fraction and dopant impurity concentrations [17-18]. Figure 1.10 and Fig. 1.11 show the calculated results for electron mobilities versus Ge mole fraction in p-type and n-type GeSi layer, respectively, for doping level of 1018 cm-3 close to that in a typical GeSi HBT [17]. The longitudinal mobility (upward triangles) is in the growth or z direction, the transverse mobility (downward triangles) is in the x-y plane. Figure 1.10 and Fig. 1.11 shows only a small (-2%) increase in the longitudinal mobility with Ge mole fraction at 300K. However, a much larger improvement (-50%) was calculated at 77K for xGe~-5-10%. The transverse mobility shows a large reduction with increasing XGe which is always smaller than that in Si (XGe=O) at any Ge concentration level. The results for the majority and minority hole mobilities are similar to those for the electron mobilities in Fig. 1.10 and Fig. 1.11. In summary, the expected minority electron mobility improvement for the doping level of about 1018 cm-3 is very small, gn(GeSi)/4tn(Si)=l.0. This agrees very well with our experimental results as will be shown in chapter 2.





17




co) 600
NAA=10 cm3, T=300K

E 500
longitudinal

400

E 300
C 0
200
., transverse

100
0
0.
0 0.05 0.10 0.15 0.20
Ge mole fraction /(1%)

Fig. 1.10 Minority electron mobility gn in p-type GexSil_- layer. The upward triangles are in the perpendicular z direction which is the growth direction and also the electron movement direction in vertical BJT. The downward triangles are in the x-y plane. Adapted from L.E. Kay and T.-W. Tang [17].





18




co 1.5
= 1 NDD=1018 cm3, T=300K
E
| longitudinal


0
E



0
a 0.5 transverse
a

0

0 0.05 0.10 0.15 0.20 Ge mole fraction 1/(1%)

Fig. 1.11 Majority electron mobility En in n-type GexSil-_ layer. The upward triangles are in the perpendicular z direction which is also the growth direction, and the downward triangles are in the x-y plane. Adapted from L.E. Kay and T.-W. Tang [17].







19




1.6 Energy Band Diagram

In Si/GexSil_-x/Si HBT, a GexSil_-x base layer with a smaller energy gap than that of pure Si is sandwiched between the Si emitter and collector. The energy band diagram is very important for analysis and design optimization of the GeSi HBT. Figure 1.12, Fig. 1.13, Fig. 1.14, and Fig. 1.15 show the energy band diagrams for triangular Ge distribution and trapezoidal Ge distribution in the base region at equilibrium (zero bias) and forward active mode (VBE>OV, VCB
XGe(X) = XGe(O) + [XGe(XR) XGe(O)].X/XR (O
Ebi = (1/q)(dEc/dx) = (1/q)(AEG-Ge/XR) = independent of x

= (kT/q)(r/xR) O




20




AEG-Ge(O) AEG-Ge(XB)


Ec Base E
n+Si /n-Si
Emitter Collector
Ev
Ge,
NAA .


0 XB

Fig. 1.12 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with a triangular Ge distribution in the base region at equilibrium (zero bias). EF is the Fermi level at equilibrium. AEG-Ge(O) is the Ge-induced energy gap reduction at x=O in the quasineutral base region. AEG-Ge(XB) is the Ge-induced energy gap reduction at x=XB in the quasineutral base region. AEG-Ge = AEG-Ge(XB) AEG-Ge(O) is the total Geinduced energy gap reduction through the base region.






21






AEG-Ge(O) AEG-Ge(XB)



Vb-B ----------------- F
Ec n "P-GeSi Base- FP
FN --- -- --- Vbi+VCB
n+Si qVBE
Ev Emitter


Ge n-Si F NAA --Collector


0 XB


Fig. 1.13 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with a triangular Ge distribution in the base region under forward active operation, VBE>OV, VCB>OV. FN is the quasi-Fermi level for electrons and Fp is the quasi-Fermi level for holes. Vbi is the built-in potential of the p/n junction. AEG-Ge(O) is the Ge-induced energy gap reduction at x=O in the quasineutral base region. AEG-Ge(XB) is the Geinduced energy gap reduction at X=XB in the quasineutral base region. AEG-Ge = AEG-Ge(XB) AEG.Ge(O) is the total Ge-induced energy gap reduction through the base region.







22







AEG-Ge(O) AEG-Ge(XB)




Ec Base
-EF


Ev Emitter Collector
v, Ge
----- ----I






0 XR XB



Fig. 1.14 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with a trapezoidal Ge distribution in the base region at equilibrium (zero bias). EF is the Fermi level at equilibrium. AEG-Ge(O) is the Ge-induced energy gap reduction at x=O in the quasineutral base region. AEG-Ge(XB) is the Ge-induced energy gap reduction at X=XB in the quasineutral base region. AEG-Ge = AG-Ge(XB) AEG-Ge(o) is the total Geinduced energy gap reduction through the base region.






23






AEG-Ge(O) AEG-Ge(XB)


Vbi-VBEL ---a-e
F _- ----- ----- FN Vbi+VCB
n+Si qVBE/\
E, Emitter //
Ge -------------Ev ",----- -- n~iFN

n-Si FN N ,,"" ",Collector


0 XR XB


Fig. 1.15 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with a trapezoidal Ge distribution in the base region under forward active operation, VBE>0V, VcB>0V. FN is the quasi-Fermi level for electrons and Fp is the quasi-Fermi level for holes. Vbi is the built-in potential of the p/n junction. AEGGe(O) is the Geinduced energy gap reduction at x=O in the quasineutral base region. AEG-Ge(XB) is the Ge-induced energy gap reduction at x=XB in the quasineutral base region. AEG-Ge = AEG-Ge(XB)-AEG-Ge(O) is the total Ge-induced energy gap reduction through the base region.







24



1.7 NcNv and n. Model for Linear Ge Distribution

The Ge in the base region changes not only the energy gap, but also other electronic material parameters. The effective density of states in the conduction band and valence band, Nc and Nv, will change because they are a function of the electron and hole effective masses me and mh, respectively which change with the Ge-induced strain and change of the E-k relationship in the epitaxial GeSi layer [17-18]. Nc and Nv are given by [1]

Nc = 2(27rmekT/h2)3/2 (1.6a) N, = 2(2rmhkT/h2)3/2. (1.6b) Figure 1.16 shows the theoretical calculations of the normalized density of states product NcNv versus Ge mole fraction [17-22]. In order to obtain analytical models for the GeSi HBT, we approximate the NcNv product by an exponential function leastsquares fitted to the theoretical data,

Nc(x)Nv(x) = Nc(O)Nv(O).exp(-C.x/XR) (1.7)

where the constant C is a nonlinear least squares fit (NLSF) parameter. The model fits the theory well for XGe < 10%, with C = 0.770.1, in particular to the theoretical models of Prinz et al. [20-21] and Jain et al. [22] which are also supported by the photoluminescence data and electrical measurements in Si/GexSil_-/Si HBTs. The Nc(x)Nv(x) model given by (1.7) enables the de-coupling of the diffusivity DB from the NcNv product, as will be shown later.

The Ge-induced energy gap reduction AEG-Ge in the base region will change the intrinsic carrier concentration ni which can be expressed as [1]






25




1.0
1 .0 1 I I I I I 1 1 k. Jain et al. [22] c 0.8 Prinz et al. [21]
Z C=0.66
o 0.6
Z- .. C=0.76

S 0.4
>- Theory
Z 0.2 NLSF
0 T=300K

0.0
0 2 4 6 8 10 12 14

Ge fraction XGe /(1%)


Fig. 1.16 The theoretical calculations of the normalized density of states product NcNv versus Ge mole fraction [17-22]. The solid lines are from calculations in [21-22]. The dashed lines are the NLSFs to (1.7) for C=0.66 and C=0.76.







26

nf(x) = Nc(x)Nv(x).exp(-EG(x)/kT). (1.8) For a linear Ge distribution using results from section (1.6), we have

EG(X) = EGO AEGHD AEG-Ge(O) AEG-Ge'X/XR (1.3) where AEG-Ge = AEG-Ge(XR) AEG-Ge() is the total energy gap reduction across the quasineutral base region. AEG-HD is the energy gap reduction due to heavy doping effect, and AEG-Ge(O) is the Ge-induced energy gap reduction at x=O in the quasineutral base region. Inserting equations (1.3) and (1.7) into equation (1.8), gives an analytical expression for the intrinsic carrier concentration ni for a linear Ge distribution,

n2(x) = ni0 2.exp(AEGGe(O)/kT). exp(AEG-HD/kT).exp(x/xl), (1.9) where nio is the intrinsic carrier concentration of Si

ni2 = Nc(O)Nv(O).exp(-EGo/kT) (1.10) The constant x1 is defined as 1/Xl=(1/XB)[(AEG-Ge/kT)-C]. For a simplicity, we define =AEGGe(O)/kT and y=AEG-HD/kT, then equation (1.9) becomes

n?(x) = nio 2*expa.exp y.exp(x/xl). (1.11)


1.8 Summary

In conclusion, the basic parameters governing the GeSi HBT performance were discussed in this chapter, including fabrication by pseudomorphic epitaxial growth, critical layer thickness, and electronic properties of the GeSi layer. The lattice mismatch between the GeSi layer and the Si substrate is accommodated by the biaxial strain in the GeSi layer. This Ge-induced strain in the GeSi layer is responsible for changes in electronic material parameters important for HBT performance, in particular, the energy gap, density of states, and mobility. For the Ge mole fraction XGe <~40%,







27

the energy gap in strained GeSi layer decreases linearly with XGe. Monte Carlo simulation results for minority and majority electron and hole mobilities were also discussed. Analytical approximations for the intrinsic carrier concentration n; and density of states dependence on the Ge mole fraction were developed here in this thesis for an idealized linearly-graded Ge concentration profile in the GeSi base layer.

Measured IB-VBE and Ic-VBE curves and high frequency responses of GeSi HBT and Si reference BJT have demonstrated the performance improvements in GeSi HBT compared to Si BJT.















CHAPTER 2
LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) METHODOLOGY

2.1 Introduction

In the last chapter, we presented a preliminary qualitative analysis of the GeSi HBT and its comparison with the Si BJT. In this chapter, we describe a low-frequencyconductance-voltage (LFGV) methodology developed in order to obtain accurate quantitative values for the dominant minority-carrier transport parameters that underlie the GeSi HBTs performance enhancement, such as the diffusion length, recombination lifetime, and diffusion coefficient in the base layer. The LFGV method also gives the analysis methodology of current gain and emitter injection efficiency based on a separation of the total base current into the recombination losses in the emitter and base. Thus, the LFGV method gives a complete charge-control analysis of the bipolar transistor performance. Analytical models are developed for the LFGV method for a trapezoidal and linearly graded Ge concentration profile in the base. However, the LFGV method is general and can be applied to any bipolar transistor with an arbitrary dopant impurity and material-composition profile, including those using the III-V compound semiconductors.

Comprehensive reviews of the Si/GexSilx/Si HBT technology, including fabrication, Ge-induced effects in the base layer, current-voltage characteristics, modeling, and performance comparison with Si BJT are discussed in chapter 1. Performance


28







29

improvements in collector current, transit time and output conductance in GeSi transistors over those in similar Si transistors were demonstrated qualitatively and graphically. In this chapter, we present detailed analysis based on an analytical model, to extract reliable and accurate values of the minority-carrier parameters in the GeSi material. These parameters are essential to assess the Ge-induced effects on transistor performance, design optimization and to verify theoretical predictions about the expected performance benefits due to Ge.

The key point in obtaining these quantitative values is a separation of the various Geinduced effects from the measured data. A lack of an experimental methodology for this analysis is the main reason why these values are still not available in the literature. For example, in GeSi transistors, the increase in the collector current Ic can arise from the aiding build-in electric field in the base due to the Ge retrograded profile, the base minority-carrier diffusivity enhancement, or both. An accurate separation of the performance improvement between the two parameters requires independent measurements of the built-in field and mobility. Yet another factor that affects the collector current is the reduction of the effective density of states, Nc and Nv, which are functions of the effective masses mn and mp, respectively. Theoretical calculations show that the density of states product, NcNv, in thin pseudomorphic GexSil_-x layers grown on (100) Si substrate is significantly decreased compared to that in Si due to Geinduced strain [17-18]. This gives (NcNv)GeSi/(NcNv)si 0.6 for GeSi layer with xGe = 5% [17-18]. The minority-carrier mobility was predicted to increase with Ge concentration for xGe,-<10% especially at higher base impurity concentration (1019







30

cm-3) and at low temperatures (-77K) [17]. But, the mobility enhancement has not yet been experimentally confirmed in fabricated GeSi HBTs. The built-in electric field and higher minority carrier mobility increases the collector current IC and current gain 1F, but this is compensated by the decrease in the density of states. Thus, a methodology to separate these Ge-induced effects is the key to a comprehensive quantitative analysis of the Si/GexSil-x/Si HBT.

In this work, we present the LFGV methodology for a complete charge-control analysis of HBTs, including a quantitative comparison with Si reference transistors, and an experimental demonstration giving the first quantitative measurements of the built-in electric field and minority-carrier recombination lifetime in the GeSi base.

2.2 Base Thickness Modulation (BTM)

Low-frequency-conductance-voltage (LFGV) methodology is based on the combination of the dc Ic-VBE and IB-VBE measurements with the low-frequency (-lkHz) small-signal conductance measurements resulting from the base thickness modulation [23-24]. The base thickness modulation (BTM) effect is illustrated in Fig. 2.1 for a Si BJT. The collector current IC is proportional to the gradient of the base minority carrier distribution in the base layer at a certain forward bias emitter-base voltage VBE and reverse bias collector-base voltage VCB. When a small-signal voltage Vcb is superimposed upon the dc base-collector junction voltage VCB, the quasineutral base thickness XB will be modulated by AXB, as shown in Fig. 2.1. The shadowed area in Fig. 2.1(b) shows the change in the minority carrier distribution in the quasineutral base due to the base thickness modulation, and the base minority carrier charge QB








31









AXB 4-H4


n+ p n



0 jib Xs

SII II II II
VBE vVc






N(0) AQB

B::






01 Xa


(b)







superimposed on dc value VCB.
(b) nority-carrier distribution in the base.
II II II II II





(b)







32

change by AQB with the small-signal Vcb. The minority carrier concentration at the emitter boundary of the quasineutral base at x=O, N(O), remains constant for a fixed VBE and is given by [n2/P(0)].exp(qVBE/kT), where P(O)=NAA(0) is the holeemitter boundary of the quasineutral base at x=O, N(O) remains constant for a fixed VBE and is given by [n2/P(0)].exp(qVBE/kT), where P(O)=NAA(O) is the hole concentration at x=O, k is the Boltzmann constant, and T is the temperature. The change in the slope of N(x) gives the small-signal collector current ic. The output conductance go is defined by

c10
go- (2.1)
Vcb VBE

The base current IB also changes due to a change in the base recombination current, QB/TB, with the base thickness modulation by the small-signal voltage Vcb. This produces the reverse transconductance gr which is defined by

Ib
gr-- (2.2)
Vcb VBE

where ib is the small-signal base current due to Vcb. Analytical expressions for go and gr can be derived (see appendix A),

ic Ic dXB
go90- (2.3)
Vcb VBE XB dVCB VBE

ib QB dXB
gr- = 0 (2.4)
Vcb VBE TB XB dVcB VBE

where XB is the quasineutral base thickness, QB is the base minority carrier charge corresponding to VBE and VCB, and B is the base minority carrier recombination lifetime. Since Ic and QB are exponential functions of the forward base-emitter voltage







33

VBE, go and gr are also exponential functions of VBE. Taking the ratio of equations (2.3) and (2.4), we obtain a very important relation for the analysis of the bipolar junction transistor [1, p. 822, 24-25]:

go Ic QB/tB TB
(2.5)
gr QB/TB QB/TB tB

where tB is the base minority carrier transit time.

In order to accurately measure the output conductance go and especially the reverse transconductance gr (gr<
2.3 LFGV Methodology

Two LFGV methodologies were developed. The first LFGV methodology described in this section is based on a comparison of the transistor characteristics measured in Si/GexSil_-/Si HBT and reference Si BJT where the difference between the measured characteristics is due to Ge only [26-27]. By analyzing this difference, we can then calculate the various Ge-induced material parameter changes. This approach has been commonly used by other investigators [28-34]. The basic assumption in this comparative approach is that the two transistors have nearly identical geometry and dopant impurity concentration profiles except the Ge incorporation in the GeSi HBT







34

base layer. The second method using only the GeSi HBT without the reference Si BJT will be discussed in chapter 3.

There are several performance enhancement gauges of GeSi HBT over Si BJT. The most important and also most commonly used by investigators is the dc collector current Ic enhancement [35-36]. For example, for a uniform base doping and uniform Ge concentration in the p-type base of npn transistor, the ratio of the collector currents can be written as

Ic(GeSi) (NcNV)GeSi Dn(GeSi)
exp(Ay).exp(AEG-Ge/kT) (2.6) Ic(Si) (NcNv)si Dn(Si )

where NC, Nv are the density of states of the conduction band and valence band, respectively, Dn is the minority-carrier electron diffusivity, AEG-Ge is the Ge-induced energy-gap reduction in the base, and Ay = AEGHD/kT=[AEG-HD(GeSi) AEG-HD(Si)]/kT is the normalized difference between the heavy doping-induced energy gap reduction in GeSi and Si base layers.

There are four unknowns in (2.6) all related to the Ge in the GeSi base layer. The key issue is how to separate these Ge-induced effects. Two approaches have been presented in the literature using the Ic ratio in (2.6) [29-32]. The first approach uses the measurement of the temperature dependence of Ic(GeSi)/Ic(Si), assuming that the density of states and mobility ratios are temperature independent. Then by plotting the Ic ratio versus 1/T, equation (2.6) yields an activation energy EA = AEG-Ge + AEG-HD = AEG-Ge. This AEG-Ge can then be used to calculate the improvements in the current gain, transit time, and other characteristics as a function of the Ge mole fraction and







35

temperature. But theoretical calculations show that the density of states and mobility have very complicated temperature dependence, so the assumption of the temperature independence of the two pre-exponential factors in (2.6) is unreliable and can lead to large errors in AEG-Ge, as also noted previously [32]. The second approach is to assume theoretically predicted values of (NcNv)GeSi and Dn(GeSi) and then calculate EA from (2.6). Apparently, there is another unknown, Ay, and also the theoretical results are strongly dependent on models and input parameters. Furthermore, both approaches give an estimate for the energy gap reduction term only and do not provide values or estimates for the mobility or recombination lifetime in the GeSi base.

The above discussion shows that an analysis based on the measurement of Ic(GeSi) only is not sufficient. The LFGV methodology, however, will use a combination of the dc IB-VBE and Ic-VBE characteristics with the small-signal output conductance go and reverse transconductance gr measurements. This novel methodology can overcome the limitations of the above and other approaches.

The LFGV methodology will be presented here for the idealized trapezoidal Ge concentration profile in the base which is shown in Fig. 2.2. In this model, the base dopant impurity concentration profile and the Ge distribution are divided into two regions. In the first region, O




36



16
1022
E NDD 12
C)
Ge
c 1020 N, (
,AA i E
o E
IZ 8

0 1018
4 4
Emitter Base: Collector 1016 0
0 XR XB
Depth


Fig. 2.2 Idealized model for the Ge and dopant impurity concentration profiles in GeSi HBT. The dopant impurity concentration profiles for Si BJT (no Ge in the base) are the same as those in GeSi HBT.







37

- AEG(O) is the total Ge-induced energy gap variation through O
Ebi = (1/q)(dEc/dx) = (1/q)(AEGGe)/XR = independent of x. (2.7a)

= (kT/q)(R/X,), (2.7b) where ir = AEGGe/kT is the normalized Ge-induced energy gap reduction through the base.

For XR
Ebi2 =(kT/q)[n2/(X,-XR)]. (2.8)

The LFGV methodology also uses the collector current ratio Ic(GeSi)/Ic(Si), but this ratio is modified. The Ge-induced NcNv reduction term NcNv(GeSi)/NcNv(Si) is lumped together with the Ge-induced energy gap reduction term AEG-Ge=(kT/q)r where the lumped parameter is described by a factor, rll. This modification gives several benefits. First, rlI can be measured directly and accurately, while the original two factors are not measurable. Secondly, all other GeSi HBTs parameters can be calculated in terms of rl. This modification also enables the de-coupling of the effects of NcNv from that of the mobility and heavy doping on Ic(GeSi).







38

The collector current density for nonuniform base can be expressed as [38]

Jc(GeSi)=[exp(qVBE/kT)-1]/fB [PB/qDn(x)ni(x)]dx (2.9) Using the analytical model for a trapezoidal Ge distribution in the base region as discussed in section 1.7, the intrinsic carrier density in the GeSi base is given by nm(x) = NcNv(x)exp(-EGo/kT).expa.expy.exp(r x/XR), (O
NBO (O P(x) = (2.11)
NBO.exp[-(x-xR)/x2] (XR
Ic(GeSi) NcNV(GeSi) DB(GeSi) a+Ay+q A + (l-A)(1-exp(-q2))/12
e (2.12) Ic(Si) NcN,(Si) D,(Si) expr-1 1-exp(-R2) A +(1-A)


where Ay = [AEGHD(GeSi)-AEG-HD(Si)]/kT and A=XR/XB. (2.12) can then be used to evaluate the effect of AEG-Ge from the temperature dependence measurement or calculation as discussed in section 2.1. But in LFGV method, we choose to use a simple model for the NcNv(x), as is discussed in section 1.7, and then lump this NcNv variation with the AEG-Ge.







39

Nc(x)Nv(x) = Nc(O)Nv(O)exp(-Cx/XR) (2.13)

where C is a LSF parameter. Then the intrinsic carrier concentration is given by

ni 2. expa. exp y. exp (x/x ) (O n =x (2.14)
n(x) ni expa.expy exp(xR/X1), (XR
where ni is the intrinsic carrier concentration in low doped Si given by

ni2 = Nc(O)Nv(O).exp(-EGO/kT), (2.14a) and XI=XB/[(AEG-Ge/kT)-C]=XB/ 1. Combining (2.9), (2.11) and (2.14) yields the ratio of the collector current in GeSi and Si Ic(GeSi) DB(GeSi) A+(1-A)[1-exp(-q2) /2]
exp(R1+a+Ay). (2.15) Ic(Si) D,(Si) A(expy1-1)/nI+(1-A)[1-exp(-q2) ]/2 where l = rl-C is the normalized effective energy gap variation through the base layer that includes the effects of variable Ge concentration and variation of density of states with XGe. In (2.15), DB(GeSi) = IB [P/n2(x)]dx / fB Pdx/Dn(x)n2(x) is the spatiallyaveraged electron diffusivity in the base. The weighting factor of DB(GeSi) is ni2(x) which increases with x or XGe. Thus, the value of DB(GeSi) is weighted toward the region close to X=XB. Since Dn(GeSi) is expected to be a very weak function of XGe for the average XGE<5% [28], defining DB(GeSi) in (2.7) causes only a negligible error. For a purely linearly-graded Ge concentration profile, XR = XB and A=1, which simplifies (2.15) to [27]

Ic(GeSi) Ri DB(GeSi)
.expa expAy (2.16) Ic(Si) 1-exp(-nj) D,(Si)

One reason for lumping the spatial variation of NcNv with the spatial variation of the energy gap AEG-Ge is that these two parameters always appear together as a product in







40

the calculation of other GeSi parameters, such as the transit time. Thus, the analysis of the GeSi HBT with a trapezoidal or linearly-graded Ge concentration profiles can be conveniently made in terms of a single parameter ll. It is important to note here that, as will be shown later, the value of the fitting parameter C = (r rl), which is model dependent, does not affect the determination of the base diffusion length, recombination lifetime, transit time, or diffusivity. It only affects the calculation of the built-in electric field Ebi and AEG-Ge, which may give a small error due to the uncertainty of the fitting parameter C. However, this analytical approach is much more accurate than using the spatially averaged value of NcNv in the integral equation (2.9), which allows taking NcNv outside the integral. Another very important feature of the new expression (2.15) is that it decouples the (NcNv) product from mobility in (2.12) and allows determination of the mobility ratio.

In order to analyze the Ge-induced Ic enhancement, we have to separate the measured ratio in (2.15) or (2.16) into five or four terms. A rough approximation for practical profiles with xGe(O)=0 is to assume that the enhancement in Ic is dominated by the built-in field which leaves only the first term in (2.16) and leads directly to the estimation of r 1. However, for an accurate analysis of the transistor and for purpose of acquiring a material database, more accurate approach is necessary. For example, an uncertainty in AEG-Ge(0) or AEG-HD of 10meV gives an error of -exp(10/25)= 1.5. Thus, an analysis of the performance of Si/GexSilx/Si HBT based on measurement of Ic only is clearly not sufficient.







41

The LFGV methodology described in the next section will give an accurate extraction of rl.

2.4 Derivation of LFGV Methodology and Parameter Extraction

Below we present detailed derivation and description of the LFGV methodology. As is discussed in section 2.2, the base thickness modulation gives rise to two small-signal conductances, an output conductance, go, and a reverse transconductance, g,. In the first step of the LFGV methodology, we need the go only. It can be derived from the Ic equations (2.9) and (2.15) and is given by (see appendix A)

Ic 1 aXB
go ... (2.17)
XB A(expr1-1)expl2/01 + (l-A)(expR2-l)/q2 aVcB VBE

From (2.17), we can see immediately that the expression (2.17) for go is simpler than (2.15) for Ic. The reason for this is that the unknown parameters, DB(GeSi)/DB(Si), a, and y are lumped into Ic which is a measurable quantity. This is one of the advantages of go compared with Ic and is one important aspect of the LFGV methodology. Useful relations (2.18a) and (2.18b) are derived by taking the ratios of the collector currents and the output conductances of the GeSi HBT and Si reference BJT, Ic(GeSi)/Ic(Si) A[(expn1-1)expR2]/R1 + (1-A)(expn2-1)/n2 (2.18a)
go(GeSi)/go(Si) Aexp2 + (1-A)(expR2-1)/ 2 Ic(GeSi)/Ic(Si) expRm-1
XR = XB (2.18b) go(GeSi )/go(Si) R

The only assumption in (2.18a) and (2.18b) is that aXB/aVCB is the same for GeSi HBT and Si reference BJT. This assumption is proven to be a very good approximation from measuring the junction capacitance CBC. These relations are used to calculate rl







42

uniquely and independently of diffusivity, density of states and heavy-doping effects which cancel out in the ratios of Ic and go.

Equivalent relations to those in (2.17), (2.18) can be derived for the reverse-active operation mode with the BC junction forward-biased and the EB junction reversebiased. For this case exp(rl) and exp(r2) are replaced by exp(-ll) and exp(-r2) and rl and rl2 are replaced by -T11 and -r12*

From (2.18b), we can see that for a triangular Ge distribution, we can calculate the rl directly from the measured collector current and output conductance. But for a trapezoidal Ge distribution in (2.18a), we need to know A=XR/XB and r2. In the later part of this section, we will show that r12 can be calculated from a combination of forward active measurement and reverse active measurement of Ic(Si), go(Si) and gr(Si) of the Si reference BJT. Also we will show that the Ic ratio is not sensitive to XR/XB and t12, since they are the same for GeSi HBT and Si BJT and nearly canceled out in the Ic ratio. After an independent determination of rll, the determination of other parameters is straightforward and will be discussed together with the experimental results in the next section.

The total base recombination current IB is composed of the recombination losses in the emitter and base regions,

QB QE
IB =- + (2.19)
TB TE

where QE and QB are the stored charges, and TE and TB are the charge-control minoritycarrier recombination lifetime or time constant in the emitter and base, respectively. In







43

(2.19) we neglected the space-charge region recombination components that can be easily separated out from the measured IgB In order to separate the recombination losses in (2.19), we need the gr measurement which results from the modulation of the base recombination loss. For the GeSi HBT, gr is derived as

QB X 1 aXB
gr (2.20)
TBXB Y A[(expql-1)/q1)]expq2 + (1-A)[(expq2-1)/q2] aVB "VBE In (2.20), the terms X and Y are given below

X = A2(exp1+i1-1)/012 +

A(1-A)[(expq1-1)/ 1].[(expn2-1)/02] +

(1 -A)2(exPq 2-1)02 / 022 (2.21a)

Y = A2[exp(-1)+1-1)]/q12 +

A(1-A)[1-exp(-q1)].[1-exp(-q2)]/R102 +

(1-A)2[exp(-q2)+02-]/022. (2.21b) When we take the ratio of gr and go, a useful expression is obtained:

gr tB
-B (2.22)
90 TB

where tB is the base minority carrier transit time, TB is the charge-control minority carrier base recombination lifetime, and B is a factor related to the built-in electric field in the base due to both Ge and doping nonuniformity (B=1.0 in field-free base). B is a function of rl, r12, ni(x), and hole concentration in the base P(x) and is given by (2.23) below [39]

1 XB ni 2(x) XB dx
B dx 1 (2.23)
tBDB 0O PB(x) 0 ni 2(x)/P(x)







44

= X/Y (2.24a)

expn1-1-1
X= = XB. (2.24b)
exp( -q)+Ri-1

A combination of the dc IB-VBE and small-signal measurements gives the expressions for the base diffusion length and ratio of the recombination losses in the emitter and base region:

QE/TE B(go/9r)
1 (2.25) QB/TB PF

L2 = X2(g0/gr){A2(expr--1)/R12 +

A(1-A)[(exprl-1)/om].[(exp2-1)/2] +

(1-A)2(expnr2- 2-1)/ 22} (2.26a)

0 +exp(-qi)-1
L2 = XB2( o/g ). XR = XB. (2.26b) r12

A combination of (2.19) and (2.25) gives (QB/TB)GeSi and (QB/TB)Si from the measured data. Using (2.26a) or (2.26b) we then calculate directly the diffusion length where the only unknown parameter is XB which can be measured by SIMS.

Expression (2.22) is also used to calculate the parameter r12 which determines the built-in field for XR
goF/goR BF tBF
(2.27)
9rF/9rR BR tBR







45

The ratio in (2.27) is a function of A=XR/XB and 12 only. If XR/XB is known from SIMS or fabrication conditions, r12 can be calculated from (2.27).

2.5 Experiments and Results

High performance GeSi HBT and reference Si BJT are used to demonstrate the LFGV methodology. SIMS profile of the completed GeSi HBT is shown in Fig. 1.2. The reference Si BJT is fabricated with the identical fabrication steps except it has no Ge in the base layer. Measurements of the EB junction capacitance (4.44fF/Lm2 for GeSi and 4.37fF/gm2 for Si), breakdown voltage (5.2V for GeSi and 5.1 for Si), and base sheet resistance under the emitter (6.2kG/square for GeSi and 6kKG/square for Si) confirm the similarity of the Si and GeSi base concentration and thickness, which is important for a quantitative performance analysis to delineate the effects of Ge. All the measurements are taken on large transistors with the EB junction area of 100.4x100.8gpm2 in order to eliminate the edge and sidewall effects.

Figure 2.3 shows typical IB-VBE and Ic-VBE characteristics of GeSi and Si transistors. Note the significant increase in Ic and slight decrease in IB for the GeSi transistor. The measured enhancement in the collector current Ic(GeSi)/Ic(Si) = 3.86. The insensitivity of Ic(GeSi) to the reverse base-collector voltage up to VBc=5V shows the absence of parasitic energy barrier at the BC junction that may reduce Ic [40-41]. Figure 2.4 gives the measured small-signal output conductance, go, reverse transconductance, gr, for both the forward active mode and reverse active mode, and the collector current Ic of GeSi HBT, as a function of VBE, showing the expected exp(qVBE/kT) dependence [42]. Figure 2.5 gives the measured small-signal output







46

conductance, go, reverse transconductance, gr, for both the forward active mode and reverse active mode and the collector current Ic of Si BJT. The measured dependencies in Figs. 3.4-3.6 are used for the LFGV analysis. The results for large square device (100.4x100.8lm2) are summarized in Table 2.1. A detailed discussion of the analysis and its implications follows.

The first step in the analysis is to find the parameter r12 using (2.27) which determines the built-in field for XR
With the known r12, we can then calculate the key parameter rl from the measured Ic and go for the GeSi and Si transistors using (2.18a). This gives rl1 = 1.98, and r = (r11 + C) = 2.7+0.1 using C = 0.70.1. The Ge-induced energy gap reduction at XGe=9.8% is AEG-Ge = (kT)r = 705meV. This corresponds to AEG-GE = 7XGE meV which is in very good agreement with the theoretical calculations and other experiments in GeSi as a function of XGe. This good agreement demonstrates the accuracy of our model that accounts for the dependence of the NcNv on Ge concentration. The value of the fitting parameter, C, causes only small uncertainty in the results. The Ge-induced aiding electric field within the linear Ge range, O
The mobility ratio DB(GeSi)/DB(Si) can be evaluated from (2.15). The remaining unknowns in (2.15) are a = AEG-Ge(O)/kT and Ay = AEE-HD/kT. SIMS profiles indicate a = 0 at VBE=0.52V. This gives [DB(GeSi)/DB(Si)].exp(Ay) = 1.6. This product cannot be separated without additional independent measurement of either the mobility ratio or






47





10'1

-GeSi HBT 10-3 ---- Si BJT ,, VCB=1 V, T=296K ,




S107/
109 / /


10 /11

0 0.2 0.4 0.6 0.8 1.0 VBE /(1 V)


Fig. 2.3 IC-VBE and IB-VBE characteristics of GeSi HBT and Si BJT. The measurements were taken on large transistors with the EB junction area of 100.4x100.8tm2 in order to eliminate the edge and sidewall effects. Note the significant increase in IC and slight decrease in IB for the GeSi transistor. The measured enhancement in the collector current Ic(GeSi)/Ic(Si) = 3.86.





48




10-4 Si/GexSil.x/Si HBT .oI 10.
T=296K ICF

10. go 90F 10grR <



S10-10 10-~9

10-12 I I I I 10-11
0.3 0.4 0.5 0.6 0.7 VBE /(1 V)


Fig. 2.4 The measured forward active mode and reverse active mode small-signal output conductances, go, reverse transconductance, gr, and the collector current, Ic, of GeSi HBT, as a function of VBE. All measured curves show the expected exp(qVBE/kT) dependence.





49


I I I
0-4 Si BJT 10T=296K goR

106 -_g 10-.5


0rF 10 2

0 10 10


10-12 I I I I 10-11
0.3 0.4 0.5 0.6 0.7 VBE /(1lV)


Fig. 2.5 The measured forward active mode and reverse active mode small-signal output conductances, go, reverse transconductance, gr, and the collector current, Ic, of Si BJT, as a function of VBE. All measured curves show the expected exp(qVBE/kT) dependence.







50

Table 2.1 Summary of experimental data and calculated parameters for Si/GexSilx/Si HBT and reference Si BJT. The top six lines give the measured dc and BTM ac data obtained at 23"C, VBE = 0.52V and VCB = 1V. The computed parameters using LFGV method are shown in the next eighteen lines. The first column is for Si/GexSil-x/Si HBT, the second for Si baseline BJT, and the third column gives the comparison ratio of the two previous columns. ABE=100.4x100.8pm2, XR=680A, X,=800A.


Parameter GeSi HBT Si BJT GeSi/Si


Ic (gA) 7.74 200.5 3.86 IB (nA) 59.4 69.9 0.85 OF 130.3 28.6 4.54 go (1/2) 2.125x10-8 1.67x10-8 1.27 gr (1/Q) 3.0x10-' 1.8x10-10 0.17 go/gr 708.3 92.78 7.63


102 2.7 2.7 I'l 1.98
AEG-Ge (meV) 68.6
Ebi (kV/cm) 10
B 12.6 2.6 4.8 LB (9m) 3.6 0.8 4.5 QB/TB (nA) 0.87 8.4 0.1 QE/'E (nA) 58.5 50.6 1.16 (QE/'E)/(QB/'B) 67 6 11.2 (QE/TE)/IB (%) 98.5 88 1.12 (QB/'B)/IB (%)) 1.5 12 0.13 QB (C) 21x10-8 10x10-18 2.1 DB (cm2/V.s) 5.5 5.5 1.0 tB (ps) 2.7 4.8 0.56 TB (ns) 24 1.1 22 Ay 0.47 AEG-HD (meV) 12 VA (V) 364 120 3.0







51

Ay. Figure 2.6 shows the measured temperature dependence of ln[exp(Ay).D B(GeSi)/DB(Si)] in the range of 200K-300K. The temperature dependence shows a small activation energy of EA-12meV. This is consistent with Ay = AEG-HD/kT = 0.47 or AEG-HD = 12meV which is calculated from the measured room temperature Ic ratio assuming a unity mobility ratio which is independent of temperature. A negligible improvement in the minority-carrier mobility for the average -5% Ge concentration and

-3x1018cm3 base doping at room temperature was also predicted theoretically as is discussed in section 1.5. The conclusion that DB(GeSi) = DB(Si) is also supported by the s-parameter measurements of the base transit time for HBTs. Using the measured data in Fig. 2.6, we can calculate the temperature dependence of the minority carrier diffusivity ratio assuming that AEG-HD= 12meV is constant with the temperature range of 200K-296K. The results are shown in Fig. 2.7 and are in good agreement with theoretical predictions [17].

The recombination components of IB are calculated from (2.19) and (2.25). The calculation shows that the recombination losses in the emitter and base constitute 98.5 and 1.5% of Ig, respectively in GeSi HBT and 88% and 12% in Si BJT. An important self-consistency result is that (QE/'E)GeSi = (QE/CE)Si, as anticipated since xGe=0 at the EB junction and, thus, the hole injection from the base into the emitter and the emitter recombination are expected to be the same in both transistors. The small differences can be explained by differences in the emitter profile and recombination properties at the n+polysilicon/n+Si emitter interface. The very significant reduction in the recombination losses in the base, (QB/tB)GeSi/(QB/TB)Si = 0.1 is due to a significantly





52




2 .0 1 1 1 1 1 1 1 1
2.0
m
1.5
a,
1.0


0.5 Experiment
AEG-HD=12meV C0 I I I
3 4 5 6 1000 /T /(1/1 K)


Fig. 2.6 The measured temperature dependence of ln[exp(Ay).D B(GeSi)/DB(Si)] in the
range of 200K-300K normalized to 296K in large 100.4x100.8gm2 transistor.





53



2.0
Co

1.5
0 1.5






0.5 I I
200 220 240 260 280 300 Temperature /(1 K)

Fig. 2.7 The measured temperature dependence of DB(GeSi)/DB(Si) in the range of
200K-300K normalized to 296K in large 100.4x100.8um2 transistor.







54

larger base minority recombination lifetime zB ratio 'B(GeSi)/TB(Si) = 24ns/1.lns = 21. The reasons for the significant improvement of the minority-carrier recombination lifetime in thin strained GeSi layers is not known and requires further study. The diffusion length ratio can be calculated from (2.26) and gives LB(GeSi)/LB(Si) = 3.6ptm/0.8 = 4.5 in the GeSi layer. This ratio is calculated directly from the small-signal BTM measurements without using the dc IB-VBE curve. This is an advantage for HBTs that have a large BE junction leakage or large space-charge layer recombination component. TB was calculated taking DB=5.5cm2/s [27] for both transistors. Although ZB is relatively short (=20ns), it has only a small effect on the gain since IB in the large 100.4x100.80m2 transistors is dominated by the emitter. Rough estimates of TB in GeSi HBTs were published previously [42-44], but our present measurements in large transistors are the first rigorous accurate data.

The minority carrier base charge QB is larger in GeSi transistor, QB(GeSi)/QB(Si) = 2.1 because of smaller energy gap in the base which increases ni2. This increase in the stored charge should be accounted for in speed calculations. The electron transit time across the quasineutral base layer is then calculated and gives 2.7ps/4.8ps=0.56, a factor of about two improvement for the GeSi HBT, as expected. This is due almost entirely to the built-in field from the graded Ge concentration profile rather than the mobility enhancement which is negligible. The Early voltage for GeSi HBT is significantly higher which is important for analog circuit application.

The results for a stripe transistor with narrow emitter fingers (0.8x26gm2 with 88 fingers) are summarized in Table 2.2. The major difference between large square







55

transistor and stripe transistor is due to the perimeter recombination at the edges of the stripe transistor. But, the narrow-emitter transistor is used in the circuit applications because the narrow-emitter geometry minimizes the base series resistance. So the measurements for stripe transistor are also important. Due to the edge effect, some measured parameters, especially those associated with the base current, such as IB, 3F, gr and go/gr, are different from those of the large square device. Two key parameters, rlI and tB, are however very similar for both transistors geometries. This is because rll and tB are calculated from Ic and go only which are essentially one-dimensional even for the narrow emitter transistor with a very thin base. Figure 2.8 shows the measured temperature dependence of ln[exp(Ay)DB(GeSi)/DB(Si)] in the range of 150K-300K. The temperature dependence shows a small activation energy of EA-8meV. For this transistor pair, the measured [DB(GeSi)/DB(Si)]exp(Ay) = 1.0 compared to 1.6 for the large transistor. This gives DB(GeSi)/DB(Si)=0.7. The disagreement with the DB(GeSi)/DB(Si)= 1.0 result obtained from the large transistor is due to the narrowfinger geometry.

2.6 Sensitivity of tB and il to n, and XR/XB

An idealized base dopant impurity concentration profile P(x) and Ge distribution in the base used for the analysis are shown in Fig. 2.2. The base region is divided into two regions, derived from the actual SIMS profile shown in Fig. 1.2. For O






56



Table 2.2 Summary of experimental data and calculated parameters for Si/GexSil-x/Si HBT and reference Si BJT. The top six lines give the measured dc and BTM ac data obtained at 23"C, VBE = 0.58V and VCB = 1V. The computed parameters using LFGV method are shown in the next eighteen lines. The first column is for Si/GexSil-x/Si HBT, the second for Si baseline BJT, and the third column gives the comparison ratio of the two previous columns. ABE=(0.8x26)x88pm2, XR=680A, XB=800A.

Parameter GeSi HBT Si BJT GeSi/Si


Ic (ptA) 14.42 5.16 2.79 IB (nA) 161.6 173.2 0.93 OF 89.2 29.8 3.0 go (1/92) 2.687x10-8 4.08x10-8 0.66 gr (1/Q2) 3.5x10-10 5.2x10-10 0.67 go/gr 76.77 78.46 0.98


T12 2.2 2.2 11 2.5
AEG-Ge (meV) 79
Ebi (kV/cm) 12
B 15 2 7.5 LB (pm) 1.2 0.7 1.7 QB/ZB (nA) 12 32 0.38 QE/'E (nA) 149 141 1.06 (QE/'E)/(QB/'B) 12 4.4 2.7 (QE/'E)/IB (%) 92 82 1.1 (QB/tB)/IB (%)) 8 18 0.4 QB (C) 35x10-8 25x10-18 1.4 DB (cm2/V-s) 4 5.5 0.7 tB (ps) 2.4 4.9 0.5 TB (ns) 2.8 0.8 3.5 Ay 0.3 AEG-HD (meV) 8 VA (V) 536 127 4.2






57





0.5 lI" "

C) Ex eriment
S0.4 LSF


co 0.3o 0.2O. 0.1



2 3 4 5 6 7 8

1 000/T /(1/1 K)


Fig. 2.8 The measured temperature dependence of ln[exp(Ay).D B(GeSi)/DB(Si)] in the range of 150K-300K normalized to 296K for stripe transistor. Least squares fit to the data is shown by the solid line and gives an activation energy of EA = AEG-HD = 8+0.2meV.







58

will certainly cause some errors since the SIMS profiles may not be very accurate for very thin base layers, especially near the collector junction. Note that the base dopant impurity concentration profile NAA(X) can be better approximated by a Gaussian distribution (see Appendix B for Gaussian distribution model). This results from the boron outdiffusion from the GeSi layer during subsequent fabrication. The increasing doping NAA(x) at x=0 shown in Fig. 1.2 will produce a retarding electric field which will decelerate the base minority carrier movement across this region. The decreasing doping density will produce an aiding electric field. Thus, an uncertainty in a precise location of XR can cause errors in calculation of the transit time and other parameters. In order to estimate the influence of this uncertainty on the GeSi HBT analysis, we investigate the dependence of r 1, tB on XR/XB and r12. Figure 2.9 shows the normalized Ge-induced electric field rl versus XR/XB with r12 as a parameter. r~l is the key parameter underlying the operation of GeSi HBT. Figure 2.10 shows the transit time ratio tB(GeSi)/tB(Si) versus XR/XB with '12 as a parameter for r11=2.0. As can be seen from Fig. 2.9 and Fig. 2.10, rl and tB(GeSi)/tB(Si) are rather insensitive to the location of the transition point XR. This is expected, since rl and tB(GeSi)/tB(Si) are calculated from the collector current ratio of the two transistors with nearly identical geometry and dopant impurity concentration profiles. The above sensitivity analysis shows that taking x=XR as the transition point where the Ge linear profile intersects the flat Ge concentration profile in the measured SIMS dependencies, Fig. 1.2, will result in a negligible error.





59



3.0 1 1 1


2.5

:. 2=1'6 1.8
2.03 2.7


1.5

1 .0 a .I I I I I I I I 1
0.6 0.7 0.8 0.9 1.0 XR/XB

Fig. 2.9 Sensitivity of TI, to XR/XB calculated from (2.18a) with r12 as a variable parameter.





60



1 .0 I I I
1=2.0
0.8

0.6
9 2=1.4 1.6 1.8
( 0.4
(.
m 0.2


0.5 0.6 0.7 0.8 0.9
XR/XB

Fig. 2.10 Sensitivity of tB(GeSi)/tB(Si) to XR/XB calculated from (A.12) with r12 as a variable parameter for 1=2.0.







61

2.7 GeSi HBT Performance Enhancement

In this section, we will plot the important GeSi HBT parameters as a function of rl normalized to that of Si BJT in order to show the performance enhancement of GeSi HBT over Si BJT. Since the triangular Ge distribution in the base region is a simple and also a very good approximation for the trapezoidal Ge distribution, we will use the triangular Ge distribution as a demonstration. The extension to the trapezoidal Ge concentration profile is straightforward. In fact, most of the important performance enhancements can be accomplished by the triangular Ge distribution in the base region.

The most important performance enhancement of GeSi HBT over Si BJT is the increase in the collector current Ic(GeSi), as is shown in Fig. 2.11. The collector current ratio Ic(GeSi)/Ic(Si) varies almost linearly with rl for r1>-3.0. For 1l>-3.0, the collector current ratio Ic(GeSi)/Ic(Si) can be modeled by a linear function, Ic(GeSi)/Ic(Si) o- r oc (AEG-GekT)-C.

The output conductance ratio go(GeSi)/go(Si) vs rl is shown in Fig. 2.12. As can be seen from the figure, the go ratio shows a rapid decrease for 1.0






62

The base minority electron distribution for 1q1=2.0 is shown in Fig. 2.13. As can be seen from the figure, n(x) throughout the base is larger for GeSi HBT. This is because the intrinsic carrier concentration n2 of GeSi HBT is larger than that of Si BJT.

The base minority carrier charge ratio QB(GeSi)/QB(Si)>1.0 vs rl is shown in Fig. 2.14. The increase of base minority carrier charge will not affect the performance of GeSi HBT significantly because the aiding electric field in the base region increases Ic. Thus, the minority-carrier transit time through the base, tB=QB/Ic is still smaller for the GeSi HBT. This is shown in Fig. 2.15 for the forward active mode.

The transit time improvement is very important for high frequency performance. As is shown in the figure, the base transit time can give a factor of two improvement for r11=2.0, which corresponds to about 10% Ge in the base. The improvement of tB(GeSi) is due to the Ge-induced aiding electric field Ebi, rather than the enhancement of diffusivity Dn, which is negligible according to our measurements and theoretical calculations.

The base transit time ratio tB(GeSi)/tB(Si) for the reverse active mode is shown in Fig. 2.16. As expected for the Ge concentration profile in Fig. 1.2, tBR(GeSi)/tBR(Si) >>

1.0.

2.8 Summary

In conclusion, a new LFGV methodology was developed and a complete analysis of the effects of Ge in the base of Si/GexSil_-/Si HBT was presented. The LFGV methodology is based on a one-dimensional BJT theory and accurate dc and lowfrequency measurements of similar GeSi and Si transistors. It is accurate, expedient and





63




10
T=300K
O

0

C)




0 .- i I, 1, I, I I, I, I, 1 ,
0 2 4 6 8 10


Fig. 2.11 Collector current ratio Ic(GeSi)/Ic(Si) vs r11 (normalized to [DB(GeSi)/DB(Si)].exp(a+Ay)). For r1>-3.0, the collector current ratio Ic(GeSi)/Ic(Si) can be modeled by a linear function, Ic(GeSi)/Ic(Si) o i11 o (AEG-Ge/kT)-C.






64





1.0
T=300K
0.8

0
0 0.6


a 0.4

o 0.2

0

0 2 4 6 8 10



Fig. 2.12 Output Conductance ratio go(GeSi)/go(Si) vs rll for the forward-active mode (normalized to [DB(GeSi)/DB(Si)].exp(a+Ay)). The go ratio shows a rapid decrease for 1.0




65



1.0
T=300K
0.8 ""

0.6 "0.4
-- n(x) GeSi HBT
0.2 --- n(x) Si BJT


0 0.2 0.4 0.6 0.8 1.0
x/XB

Fig. 2.13 Base minority carrier distribution of GeSi HBT and Si BJT vs x/XB for r1=2.0 in forward active mode (normalized to ni.[exp(qVBE)- 1]/NB).





66




2.0
0 1.8% T=300K
C 1.8
O
1.6

C)
a) 1.4

m 1.2

1.0
0 2 4 6 8 10 r1i

Fig. 2.14 Base minority carrier charge ratio QB(GeSi)/QB(Si) vs rl for the forward active mode (normalized to exp(a+Ay)).





67




1.0
T=300K
0.8
U)




(3
0.6

0.4

m 0.20 2 4 6 8 10



Fig. 2.15 Base minority carrier transit time ratio tB(GeSi)/tB(Si) in forward active mode vs rl (normalized to DB(GeSi)/DB(Si)). The base transit time can give a factor of two improvement for 111=2.0 which corresponds to about 10% Ge in the base.





68




100
-- T=300K
C/) 80

C 60 a 40

a20


0 2 4 6 8 10 rT

Fig. 2.16 Base minority carrier transit time ratio tB(GeSi)/tB(Si) in reverse active mode vs 1I (normalized to DB(GeSi)/DB(Si)). The reverse base transit time is much larger than in the forward active mode.







69

general. The analytical model for the Ge-concentration-dependence of the density of states product decouples it from the minority-carrier mobility and heavy-doping effects. A combination of Ic and go measurements gives a unique determination of the critical parameter rll. All the important minority-carrier transport parameters underlying the improved performance of GeSi HBT compared to similar Si BJT were determined and quantified.

The results show that the reduction in the base transit time is due to the Ge-induced aiding electric field in the region with linearly-variable Ge concentration. The minority carrier mobility or diffusivity enhancement was found to be negligible compared to Si BJT. The energy gap reduction due to the heavy doping (NBase=3x1018cm-3) is about 10meV larger in GeSi HBT than in Si BJT at room temperature. First accurate measurements of the minority carrier diffusion length and recombination lifetime in the base show greatly improved values in the GeSi base compared to Si. The base current was found to be dominated almost completely by the recombination within the emitter in the large 100.4x100.8gm2 transistors, while in circuit transistors with a narrow emitter stripe (<1m), the base recombination is more important due to increased importance of the sidewall and surface effects. Since the dc and low-frequency smallsignal measurements are independent of parasitics, accurate high-frequency and highspeed parameters can be readily obtained which are difficult to measure directly such as the -lps base transit time. The performance improvements of GeSi HBT over Si BJT were shown graphically as a function of rl1.















CHAPTER 3
LFGV ANALYSIS OF GeSi HBT WITH NO REFERENCE Si BJT

3.1 Introduction

In the previous chapters, the performance improvements of GeSi HBT over Si BJT are discussed and demonstrated. The LFGV methodology for accurate determination of parameters of GeSi HBT was also developed. This methodology is based on simultaneous measurement of GeSi HBT and Si BJT with nearly identical dopant impurity concentration profiles such that the difference in the performance is due to Ge only. The disadvantage of this approach is that a reference Si BJT is not always available. Furthermore, it is very difficult to fabricate GeSi and Si transistors with nearly identical dopant impurity concentration profiles. In this chapter, we describe another LFGV method for GeSi HBT analysis that does not use a reference Si BJT.

One of the key parameters in the LFGV methodology is the normalized Ge-induced energy gap reduction, i=AEGGe/kT, which is due to the compositional grading of Ge in the base. This energy gap variation produces an aiding electric field, Ebi which significantly decreases the electron transit time through the base layer that yields higher speed and fT [45-46]. Thus, accurate and independent measurement of the rl and the resulting Ebi is essential for the design, optimization and analysis of GeSi HBT, and for the verification of theoretical predictions about the expected performance benefits due to the compositional grading. The determination of rl is also a basis for a complete


70







71

charge-control analysis of the recombination components in the base current [47]. The new method is demonstrated for Si/GexSil_-/Si HBT with a linear or trapezoidal Ge concentration profile in the base. The Ge-induced energy-gap reduction parameter r is determined solely from the terminal measurement of GeSi HBT without any assumptions. The built-in electric field Ebi can be then calculated, independent of the minority carrier mobility and heavy-doping effects. The method also does not require a knowledge of the dopant impurity concentration profile in the base.

3.2 Theory

The SIMS profile for the analyzed GeSi HBT is shown in Fig. 1.2 [48]. The Ge is linearly graded within O
The collector current can be expressed for any base dopant impurity concentration profile and compositional variation in the GeSi base as [1, p. 760, 38]

q exp(qVBE/kT)
JC = (3.1)
XB P(x)
0 Dn(x) ni2( dx
0 D0(x).n12(x)







72

qDB exp(qVBE/kT)
(3.2)


X0 nP(x) dx

where DB = IP(x)/n2(x)/IP(x)/Dn(x)ni(x)dx is the average minority electron diffusivity in the base. If we superimpose a small sinusoidal signal on the dc reverse BC junction bias, with the BE junction forward-biased, the small-signal output conductance, goF, due to the base-thickness modulation can be obtained by taking the derivative of JC or IC with respect to VCB,

alC aXB Ic 1 P(XB) .aXB
g9oF = = (3.3)
aXB aVB IXB P(x) ni2(XB) aVcB dx
S ni2(x)

In (3.3), P(XB).a XB)/aVCB = (1/q)(aQB/aVcB) is the small-signal base-collector junction capacitance per unit area, CBC. Thus, (3.3) can be written as

ICF CBC
goF = (3.4)
0F XB P(x) n2(XB) dx
JO ni2(x)

Similarly, we can obtain goR for the reverse-active operation with the EB junction reverse-biased and the BC junction forward-biased,

ICR CBE
goR = (3.5)
90R XB P(x) ni2(0) (3.5)

0 ni2(x) dx

The integral in the denominator is the same both for the forward-active and reverseactive operation modes. Thus, the ratio of equations (3.4) and (3.5) gives







73


goR ICR n12(XB) CBE
=- (3.6)
90F ICF ni2(0) CBC
From (3.6) we obtain the ratio of the intrinsic carrier concentrations at the two edges of the quasineutral base layer which is given below in (3.7)


n2(XB) ICF g0R CBC
= (3.7a)
n (O0) ICR goF CBE

NC(XB)NV(XB)
= .exp(AEG-Ge/kT). (3.7b)
Nc(O)Nv(O)

The result in equation (3.7) is completely general and applies to any HBT or BJT with any compositional grading and dopant impurity concentration profile, including III-V HBTs.

Equation (3.7) uses no assumptions about the material composition or impurity doping in the base and gives the ratio of the intrinsic carrier concentrations at the two edges of the quasineutral base layer directly from the measured collector current, output conductance, and junction capacitances for any HBT or BJT. The approximation using the average base diffusivity in (3.2) does not affect the ratio in (3.7), since the integral relation for DB is the same for the forward-active and reverse-active operation modes.

One possible application of the result in (3.7) is measurement of the energy gap in GeSi as a function of Ge concentration using test structures with different Ge linearlygraded profiles as shown in Fig. 3.1. Equation (3.7) can be also used to measure the intrinsic carrier concentration ratio due to heavy-doping-induced energy gap reduction using structures with a high-low dopant impurity concentration profiles as shown in Fig.

3.2.







74

3.3 Experiments and Results

A high performance Si/GexSil-x/Si HBT is used to demonstrate the application of the result in equation (3.7). The Ge concentration profile is shown schematically in Fig. 1.2. The Ge gradient from SIMS showed a linearly-graded Ge concentration from about XGe=0% at the EB junction to a peak of about 10% at the BC junction. The base dopant density was nearly constant at =3x1018cm-3, and the quasi-neutral base thickness was about 800A. The experimental data is tabulated in Table 3.1. All the measurements were performed on large area 100.4x100.8 pm2 transistors to eliminate the perimeter edge and two-dimensional effects. The difference between ICF and ICR is due to slightly larger base thickness for the reverse mode, which is expected for very thin base. The output conductances goF and goR, and the junction capacitances CBC and CBE were measured at 1kHz using precise bridge WK B214.

With reference to the profile in Fig. 1.2 and the intrinsic carrier concentration model for linear Ge concentration profile in equations (2.10), and assuming that the difference in the intrinsic carrier density at x=0 and x=XB is due to Ge grading, we obtain from (3.7),

n? (XB)
n?() expq1 = exp(qr C) = exp [(AEGGe/kT) C], (3.8a)
n2(O)
ICF goR CBC
-(3.8b)
ICR goF CBE
where C is the least squares fitting parameter for the density of states product NCNv for linear Ge distribution discussed in detail in section 1.7. Using the data in Table 3.1 we obtain, n (XB)/n?(0) = 7.68 from (3.7). This gives T11=2.04 and AEG-Ge = 70meV where





75




G14
S 2Ge
E 1022
o 12

S102 E
83
CN C c 1018 NAA ( o0 4 E
O 1016 Emitter Base Collector 0
0 XR XB


Fig. 3.1 GeSi HBT with different Ge concentration profiles in the base region.






76





CO
1022
E ND
I


10, NAA(X)
C

10


S10 Emitter Base Collector

0 XR XB Depth


Fig. 3.2 Bipolar transistor with different high-low dopant impurity concentration profiles in the base region.







77

C=0.7 is used. The aiding electric field Ebi = (kT/q)(rj/XR) = (0.0255)(2.74/680x10-8) = 10.3kV/cm. This value compares very well to Ebi= 10kV/cm which is obtained by the comparative method discussed in chapter 2 (section 2.5) using the comparison LFGV methodology.

In conclusion, the above example demonstrates one application of the new measurement method, namely the measurement of the energy-gap variation due to the compositional grading across the GeSi base. Similar results can be obtained for III-V HBTs with graded base. The new non-reference methodology can be also used to measure the temperature dependence of the parameter ll. GeSi HBT shows a superior low temperature Ic enhancement compared to Si BJT. This is because the built-in electric field Ebi is inversely proportional to the temperature, Ebi" G-Ge/kT, where k is the Boltzmann constant and AEG-Ge is the Ge-induced energy gap reduction across the quasineutral base region. Thus, at lower temperature, the built-in electric field is greatly enhanced. All other parameters related to Ebi will be also enhanced. For example, the collector current Ic(GeSi) will increase, the output conductance go(GeSi) will decrease, and the base minority carrier transit time tB will decrease significantly which gives higher speed and fT. Theoretical calculations of the minority mobility as a function of temperature and doping were presented in the literature [17, 52-53]. In order to verify these theoretical predictions and analyze the GeSi HBT performance at lower temperature, the determination of the temperature dependence of 1 is very important. This was investigated by measuring the GeSi HBT characteristics at several different low temperatures. Using the models and equations given in the section 3.2, we can







78

calculate the important GeSi HBT parameters as a function of temperature. The results are shown in Table 3.2 and Table 3.3. From Table 3.2, we can see that the basecollector junction capacitance CBC remains constant as temperature decreases while the base-emitter junction capacitance CBE shows a slight decrease with decreasing temperature. This is because the thickness of the base-collector junction SCR, XBC, is much larger than XBE due to lower doping at the collector junction. This gives CBc<
From Fig. 3.3, we can see that rl obtained by a combination of (3.7) and (3.8), and thus the built-in electric field Ebi, increase almost linearly with 1/T. The dashed line is calculated using II=AEG-Ge/kT C, where AEG-Ge=70meV as measured at 297.15K, and C=0.7. The deviation of the theoretical curve from the experimental dependence may come from two sources: (1) decrease of the AEG-Ge with decreasing temperature, and (2) the increase of the fitting parameter C with decreasing T. The latter one is more reasonable since the NcNv product is a strong function of temperature as is shown in equations (1.6a) and (1.6b). The increase of C at low temperature means that the NcNv(GeSi)/NcNv(Si) is a decreasing function of temperature.

Figure 3.4 shows the measured diffusion length LB(GeSi) vs T. The diffusion length can be expressed as


LB(GeSi)= Dr = (kT/q)Pr (3.10)







79

Since the gt' product is not strongly temperature dependent [54-55], LB(GeSi)o4T, or increasing with increasing T, as shown in Fig. 3.4.

From Fig. 3.5, we can see that the base recombination component (QB/TB)GeSi/IB increases with decreasing temperature. Thus, the base recombination becomes more important as temperature decreases.







Table 3.1 Summary of measured parameters of GeSi HBT.



goF 2.125x10-8 (S) goR 6.549x10-6 (S) ICF 7.739 (gA) ICR 12.45 (A) CBC 1.446 (pF) CBE 39.676 (pF)







80



Table 3.2 Temperature dependence of measured parameters of GeSi HBT


T(K) goR/goF ICR/ICF CBC(pF) CBE(pF)

297.2 285.2 1.63 1.99 39.4 250 495.9 1.81 1.99 39.0 225 630.7 1.85 1.99 38.6 200 967.3 2.29 1.99 38.4 175 2792 3.94 1.99 38.2 150 4000 2.88 1.99 38.0 125 13,000 4.81 1.99 37.7



Note: AE=100.4x100.8jtm2, T=297.15K, VBE=0.52V, VBc=.0OV.
The junction capacitances CBC and CBE were measured at f=lkHz.






Table 3.3 Temperature dependence of GeSi HBT parameters
calculated from the measured data in Table 3.2

T(K) l1 LB [QB/TB] /B
(gm)

297.2 2.04 3.9 1.2% 250 2.60 4.3 0.9% 225 2.83 4.0 1.0% 200 3.05 3.2 1.5% 175 3.58 2.6 2.3% 150 4.25 1.8 4.4% 125 4.93 1.5 4.2%





81



8
Experiment
6 Theory
6



2

0 I i I I I I
2 4 6 8 10
1000/ /(1/1 K)

Fig. 3.3 Normalized energy gap reduction parameter rll vs 1000/T.





82




6

E
A *



() 2

0
-J
0 I I

100 150 200 250 300
Temperature /(1 K)


Fig. 3.4 Diffusion length LB(GeSi) T.





83



6
O




CO
0
0 I I
2 4 6 8 10 100ooo/T /(1/K)

Fig. 3.5 Base recombination component QB(GeSi)/IB(GeSi) vs 1000/T.







84

3.4 LFGV Analysis of GeSi HBT with no Si Reference

After the determination of rl described in the previous section, a complete chargecontrol analysis of the GeSi HBT can be made. The only other parameters needed for this analysis are 112 which determines the built-in electric field in the region of XR
goF/goR BF tBF
S- (3.10)
grF/grR BR tBR


The ratio in (3.10) is a function of rll, A=XR/XB and 112 only. Since 111 can be determined independently as described in section 3.2 and XR/XB is known from SIMS or estimated from fabrication conditions, r12 can be then calculated from (3.10). Using the data in Table 2.1 and r1=2.04, we obtained 112=2.6 which agrees very well with the comparative method in section 2.5 which gives 12=2.7. We assume that DB(GeSi)=DB(Si) as determined in chapter 2. The results of a complete charge control analysis for the GeSi HBT following the procedure described in chapter 2 are summarized in table 3.4. Since 11=2.04 and r12=2.6 obtained using the non-reference analysis are almost the same as those obtained using the comparative LFGV methodology in section 2.5 (r11=1.98 and r12=2.7), the results in table 3.4 are very similar to those in table 2.1.







85

Table 3.4 Summary of experimental data and calculated parameters for Si/GexSil-x/Si HBT by LFGV methodology with no Si reference BJT. The top six lines give the measured dc and BTM ac data obtained at 23C, VBE = 0.52V and VCB = 1V. The computed parameters are shown in the next sixteen lines. ABE=100.4x100.8pm2, XR=680A, X,=800A.

Parameter GeSi HBT


Ic (gA) 7.74 Ig (nA) 59.4 F 130.3 go (1/ 2) 2.125x10-8 gr (1/Q) 3.0x10-" go/gr 708.3

12 2.6 rll 2.0 AEG-Ge (meV) 69 Ebi (kV/cm) 10 B 12
LB (gm) 3.5 QB/'B (nA) 0.91 QE/TE (nA) 58.5 (QE/TE)/(QB/TB) 65 (QE/TE)/IB (%) 98.5 (QB/ZB)/IB (%)) 1.5 QB (C) 21x10-8 Dg (cm2/V-s) 5.5 tB (ps) 2.8 rB (ns) 23 VA (V) 364







86




3.5 Summary

In conclusion, a simple and unique methodology is presented for the direct measurement of the ratio of the intrinsic carrier densities at the two edges of the quasineutral base layer in HBT or BJT. The method is based on a combination of dc and small-signal low-frequency (-1kHz) measurement of the transistor characteristics. The normalized energy gap parameter il, the energy gap reduction AEG-Ge, and the built-in electric field Ebi are determined independently of the base dopant impurity concentration profile, minority carrier mobility and heavy-doping effects in GeSi HBT with a linear or trapezoidal Ge concentration profile. Then a complete charge control analysis of GeSi HBT is made without using a Si reference BJT. The temperature dependence of rl, diffusion length LB(GeSi), and base recombination component (QB/TB)GeSi were measured to investigate the performance of GeSi HBT as a function of temperature.















CHAPTER 4
SUMMARY AND CONCLUSIONS

4.1 Summary

In chapter one, we gave a general review of the GeSi HBT fabrication, including the discussion of pseudomorphic growth of GeSi layer and its critical layer thickness. A comparison of the Si/GexSilx/Si HBT characteristics with those for a Si reference BJT, Monte Carlo simulations of the mobility improvement and other Ge-induced changes in the material properties were also discussed. An exponential approximation model for the density of states NcNv dependence on the Ge concentration was given for a linear Ge distribution in the base. In chapter two, a low-frequency-conductance-voltage (LFGV) methodology was developed for detailed analysis of the Si/GexSilx/Si HBT. This methodology is based on a comparison of the GeSi HBT performance with that of a reference Si BJT. A brief review of the base thickness modulation method which underlies the LFGV method is also given. Experimental data were presented to demonstrate the LFGV methodology in high-performance Si/GelSil_x/Si HBTs. Important performance enhancements of GeSi HBT over Si BJT were measured and analyzed. In chapter three, we introduced a methodology for GeSi HBT analysis without using a reference Si BJT. In this non-reference analysis, the key parameter rl of GeSi HBT can be determined directly and a complete charge control analysis can be made. Experimental demonstration of the non-reference method was given.


87







88

4.2 GeSi HBT Modeling and LFGV Methodology

The LFGV methodology is applicable to an analysis of any heterojunction bipolar transistor (HBT), including those based on III-V materials. The LFGV methodology uses a combination of the dc and small-signal measurements of the transistor characteristics. The dc characteristics are the collector and base current as a function of the emitter-base junction bias. The small-signal characteristics are the output conductance and reverse transconductance resulting from the base thickness modulation. They are measured at low frequency (-lkHz) to avoid parasitic capacitance and inductance effects.

The LFGV methodology was applied for the analysis of Si/GexSil_-/Si HBT with a linearly-graded or trapezoidal Ge concentration profiles in the base. Analytical expressions for the dc and small-signal parameters were developed. Important minority carrier transport parameters, such as the base diffusion length, recombination lifetime, diffusivity, built-in electric field, and base transit time were determined. The LFGV methodology also allows a separation of the base current into the components recombining in the base and emitter region, respectively.














APPENDIX A
GENERAL EQUATIONS FOR BJT A. The general integral relations for calculation of important parameters in bipolar junction transistor are given below. Equations for a trapezoidal Ge distribution in the base and constant-exponential dopant impurity concentration profile in the base are given in section B.

1. Collector current Ic(GeSi) [1, p. 760, 38]

q exp(qVBE/kT)
IC = (A.1)
XB P ( x)

0 Dn(x).ni2(x)

2. Minority carrier distribution in the base [38]

Jc n (x) XB (Y)
n(x) dy (A.2)
q P(x) x Dn.ni2(y)

3. Minority carrier charge in the base

X,
QB= n(x)dx (A.3)


4. Minority carrier base transit time [38]

1 X, n?(x) XB P(y)
tB = -. dx (A.4)
Dn 0 P(x) x n2(y)

5. Correction factor B [27]
1 XB P(x) XB n (x)
B dx dx 1 (A.5)
DntB lo n2(x) P(x) 89







90

6. Output conductance go

alc aXB IC 1 P(XB) .aXB
go = = (A.6)
aXB aVcB [XB P(x) ni2(XB) aVCB
dx
0 ni2(x)

7. Reverse transconductance gr

a(QB/TB) aXB
gr = (A.7)
aXB aVcB


8. Current gain

IC q 1
p = (A.8)
IB IBO XB P(x)
dx
0 Dn(x) ni 2(x)

where IBO is the base saturation current.

9. Early voltage VA and OVA product

Ic qni2( ()Dn(X) XB P(x)
VA = dx (A.9)
go CBC 0 Dn(x). ni2(x)

q2
pVA n= ( (XB) .Dn(XB) (A.10)
IBO CBC

B. Equations for a trapezoidal Ge distribution and constant-exponential dopant

impurity concentration profile in the base of GeSi HBT (Fig. 2.2) obtained from the

general integral relation (A. 1)-(A. 10) are given below.







91

1. Collector current Ic

qDnnio2 .exp(a)exp(y)exp(01) .exp(qVBE/kT)
JC= (A.11)
NBoXB[(XR/XB)(expql-l)/l+(l-XR/XB)(1-exp(-2) )/R2]

2. Minority carrier base transit time tB

X 2
tB = Y (A.12)
Dn

3. Output conductance go

Ic 1 aXB
go (A.13)
XB A(expq1-1)/n)expn2 + (1-A)(expp2-1)/q2 aVCB VBE
4. Reverse transconductance gr

QB X 1 aX,
gr= *. (A.14)
TBXB Y A[(expnl-1)/q1)]expq2 + (1-A)[(expn2-1)/02] aVcB VBE In (A. 1.9) and (A.1.11), the terms X and Y are given below X = A2(expn1+n1-1)/012 + A(1-A)[(expno-1)/ll].[(expp2-1)/2I +

+ (1-A)2(expn2-n02-1)/q22 (A.15) Y = A2[exp(-n1)+n1-1)1]/12 + A(1-A)[1-exp(-0 )].[1-(exp-q2)]/ 192+

+ (1-A)2[exp(-02)+n2-11/n22. (A.16)

5. Correction factor B

B = X/Y (A.17)

6. PVA product
[ expl1-1 expn2-1
VA = XB A expn2 + (1-A) (A.18)
01 r2 aXB/aVcB
q2
PVA = ni02.Dn(XB) .expnl (A.19)
IBO CBC















APPENDIX B
TRANSISTOR RELATION FOR A GAUSSIAN
DOPANT IMPURITY CONCENTRATION PROFILE IN THE BASE OF BJT

I. Most bipolar junction transistors are fabricated using ion implantation to dope the base which gives a Gaussian dopant impurity concentration profile. For GeSi HBT, a Gaussian profile may result from the impurity doping outdiffusion from the epitaxially deposited base layer during subsequent fabrication. Thus, the relevant LFGV equations for the Gaussian distribution are important. Two different Gaussian distribution are considered and shown in Fig. B.1 and Fig. B.2. The Gaussian concentration profile P(x) shown in Fig. B.1 has a peak value at x=O. The profile shown in Fig. B.2 has a peak value inside the base layer. The dashed line shows the exponential approximation for P(x).

Following are the analytical derivations of the equations for the two Gaussian distributions P(x).

1. Base dopant impurity concentration profile P(x) shown in Fig. B. 1 P(x) = NAA.exp(-x2/r2) (B.1) where a is

U = XB/[In[NAA/P(XB)]'/2 (B.2) XB
f P(x)dx = 7/2 N.oAAN erf(XB/U) (B.3)





92





93




10'
Gaussian Distribution
--- Exponential Distribution c)






1016
0 400 800 1200 1600 2000

x/(1A)


Fig. B.1 Gaussian distribution and exponential approximation.







94



2. Collector current

qDnn2 [exp(qVBE/kT)-1]
I, = (B.4)
n/2 NAA erf(XB/o)

3. Minority carrier base transit time tB= [erf(XB/) fBexp(x2/U2)dx fBexp(x2/a2)erf(x/a)1dx (B.5)
2 Dn

4. Output conductance


21c exp(-XB2/g2) aXB
go = (B.6)
~ir. erf(XB/a) aVCB


5. Reverse transconductance


Ic exp(-XB2/a2) aXB
gr = [1Bexp(x2/U2)erf(x/a)dx]. (B.7)
DnTB erf(XB/) aVB

6. Correction factor

fBexp(x2/2) erf(x/)dx
B = (B.8)
erf(XB/o) fexp(x2/U2)dx fBexp(x2/g2)erf(x/u)dx


For the profile in Fig. B.1, the value for the correction factor is obtained numerically using (B.8) which gives B=7.0. The exponential approximation gives B=6.0 using much simpler analytical expression (A. 17). Thus, the exponential approximation of the Gaussian profile in the base of a bipolar junction transistor gives only a small error for the value of B. This allows a simple charge control analysis of bipolar junction transistor using the exponential profile approximation shown in sections 2.3 for




Full Text
86
3.5 Summary
In conclusion, a simple and unique methodology is presented for the direct
measurement of the ratio of the intrinsic carrier densities at the two edges of the
quasineutral base layer in HBT or BJT. The method is based on a combination of dc
and small-signal low-frequency (~lkHz) measurement of the transistor characteristics.
The normalized energy gap parameter r^, the energy gap reduction AEG_Ge, and the
built-in electric field Ebi are determined independently of the base dopant impurity
concentration profile, minority carrier mobility and heavy-doping effects in GeSi HBT
with a linear or trapezoidal Ge concentration profile. Then a complete charge control
analysis of GeSi HBT is made without using a Si reference BJT. The temperature
dependence of rj ¡, diffusion length LB(GeSi), and base recombination component
(QB^B^GeSi were measured to investigate the performance of GeSi HBT as a function of
temperature.


The LFGV methodology is used here to study the performance improvements of
Si/GexSij_x/Si HBT over that of the Si BJT, including current gain, switch speed, and
Early voltage which are primarily due to the aiding electric field.
Analytical models for the effective density-of-states NCNV and intrinsic carrier
concentration n as a function of Ge mole concentration for a linear Ge distribution in
the base region are developed. Analytical solutions for the LFGV methodology are then
derived for an arbitrary Ge and dopant impurity concentration profile. The analysis
showed that the main effect of Ge in the base region with a linearly retrograded Ge
concentration profile comes from the aiding electric field which reduces the base transit
time and increases the collector current and the cutoff frequency fT. Accurate
measurements of the base minority carrier diffusion length and recombination lifetime
indicate large performance improvement of GeSi HBT over Si BJT. Design
considerations for optimal performance of GeSi HBT are also investigated, such as the
optimal Ge concentraction profile in the base region. The LFGV methodology is
applicable to other bipolar junction transistors and HBTs, including those fabricated in
III-V materials.
vi


27
the energy gap in strained GeSi layer decreases linearly with xGe. Monte Carlo
simulation results for minority and majority electron and hole mobilities were also
discussed. Analytical approximations for the intrinsic carrier concentration n¡ and
density of states dependence on the Ge mole fraction were developed here in this thesis
for an idealized linearly-graded Ge concentration profile in the GeSi base layer.
Measured IB-VBE and IC-VBE curves and high frequency responses of GeSi HBT and
Si reference BJT have demonstrated the performance improvements in GeSi HBT
compared to Si BJT.


NcNv(GeS¡)/NcNv(Si)
25
Fig. 1.16 The theoretical calculations of the normalized density of states product NCNV
versus Ge mole fraction [17-22], The solid lines are from calculations in [21-22], The
dashed lines are the NLSFs to (1.7) for C=0.66 and C=0.76.


38
The collector current density for nonuniform base can be expressed as [38]
Jc (GeSi) = [exp (qVBE/kT)-1] / JB [PB/qDn (x) n? (x) ] dx (2.9)
Using the analytical model for a trapezoidal Ge distribution in the base region as
discussed in section 1.7, the intrinsic carrier density in the GeSi base is given by
nf(x) = NcNv(x)exp(-EGo/kT) .expa.expy.exp(rjx/XR), (0 nf(x) = NcNv(x)exp(-EGo/kT) expa.expy .exp(r?), (XR where a=AEG_Ge(0)/kT and y=AEG_HD(GeSi)/kT and have been defined in section 1.7.
The base doping in the GeSi base layer is given by
nbo
(0 P(x) =
(2.11)
lNB0.exp[-(x-xR)/x2] (xR where x2 is defined as x2=(XB-XR)/ln[NAA0/P(XB)].
If we use average values for the NCNV and the diffusivity Dn, then we can take these
two quantities out of the integral in (2.9) and obtain the following expression for the Ic
ratio
Ic(GeSi) NcNv(GeSi) DB(GeSi) a+Ay+q A+ (1-A)(l-exp(-i72))//?2
= e (2.12)
Ic(Si) NCNV(Si) Db(Si) exprj-l l-exp(-^2)
A +(1-A)
1 12
where Ay = [AEG_HD(GeSi)-AEG_HD(Si)]/kT and A=XR/XB. (2.12) can then be used to
evaluate the effect of AEG_Ge from the temperature dependence measurement or
calculation as discussed in section 2.1. But in LFGV method, we choose to use a simple
model for the NcNv(x), as is discussed in section 1.7, and then lump this NCNV
variation with the AEG.Ge.


42
uniquely and independently of diffusivity, density of states and heavy-doping effects
which cancel out in the ratios of Ic and g0.
Equivalent relations to those in (2.17), (2.18) can be derived for the reverse-active
operation mode with the BC junction forward-biased and the EB junction reverse-
biased. For this case exp(r|j) and exp(r|2) are replaced by expl-r^) and exp(-T]2) and rij
and r|2 are replaced by -iq x and -r|2.
From (2.18b), we can see that for a triangular Ge distribution, we can calculate the r|j
directly from the measured collector current and output conductance. But for a
trapezoidal Ge distribution in (2.18a), we need to know A=XR/XB and r|2. In the later
part of this section, we will show that r\2 can be calculated from a combination of
forward active measurement and reverse active measurement of Ic(Si), g0(Si) and gr(Si)
of the Si reference BJT. Also we will show that the Ic ratio is not sensitive to XR/XB
and r|2, since they are the same for GeSi HBT and Si BJT and nearly canceled out in the
Ic ratio. After an independent determination of iq x, the determination of other
parameters is straightforward and will be discussed together with the experimental
results in the next section.
The total base recombination current IB is composed of the recombination losses in
the emitter and base regions,
Qb Qe
IB = + (2.19)
tb te
where QE and QB are the stored charges, and xE and xB are the charge-control minority-
carrier recombination lifetime or time constant in the emitter and base, respectively. In



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45
The ratio in (2.27) is a function of A=XR/XB and r)2 only. If XR/XB is known from
SIMS or fabrication conditions, r|2 can be calculated from (2.27).
2,5 Experiments and Results
High performance GeSi HBT and reference Si BJT are used to demonstrate the
LFGV methodology. SIMS profile of the completed GeSi HBT is shown in Fig. 1.2.
The reference Si BJT is fabricated with the identical fabrication steps except it has no
Ge in the base layer. Measurements of the EB junction capacitance (4.44fF/pm2 for
GeSi and 4.37fF/pm2 for Si), breakdown voltage (5.2V for GeSi and 5.1 for Si), and
base sheet resistance under the emitter (6.2k£2/square for GeSi and 6k£2/square for Si)
confirm the similarity of the Si and GeSi base concentration and thickness, which is
important for a quantitative performance analysis to delineate the effects of Ge. All the
measurements are taken on large transistors with the EB junction area of
100.4x100.8pm2 in order to eliminate the edge and sidewall effects.
Figure 2.3 shows typical Ib_Vbe and Ic-VBE characteristics of GeSi and Si
transistors. Note the significant increase in Ic and slight decrease in IB for the GeSi
transistor. The measured enhancement in the collector current Ic(GeSi)/Ic(Si) = 3.86.
The insensitivity of Ic(GeSi) to the reverse base-collector voltage up to VBC=5V shows
the absence of parasitic energy barrier at the BC junction that may reduce Ic [40-41].
Figure 2.4 gives the measured small-signal output conductance, g0, reverse
transconductance, gr, for both the forward active mode and reverse active mode, and the
collector current Ic of GeSi HBT, as a function of VBE, showing the expected
exp(qVBE/kT) dependence [42]. Figure 2.5 gives the measured small-signal output


63
O 2 4 6 8 10
Til
Fig. 2.11 Collector current ratio Ic(GeSi)/Ic(Si) vs r| j (normalized to
PB(GeSi)/DB(Si)]exp(a+Ay)). For rj 1>~3.0, the collector current ratio Ic(GeSi)/Ic(Si)
can be modeled by a linear function, Ic(GeSi)/Ic(Si) oc (AEG.Ge/kT)-C.


14
VBE/(1V)
Fig. 1.8 Typical I-V characteristics of GeSi HBT and Si BJT at VCB=1V. The GeSi
HBT and Si BJT have the same dopant impurity concentration profile and geometry
except the Ge in the base for GeSi HBT. The solid line is GeSi HBT and dashed line is
Si BJT.


TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT v
CHAPTERS
1. INTRODUCTION TO GeSi HETEROJUNCTION BIPOLAR TRANSISTOR 1
1.1 Introduction 1
1.2 GeSi HBT Fabrication 3
1.3 Pseudomorphic Growth, Critical Layer and Ge-induced Effects 7
1.4 GeSi HBT Characteristics 8
1.5 Monte Carlo Simulation of Mobilities 16
1.6 Energy Band Diagram 19
1.7 NCNV and nf Model for Linear Ge Distribution 24
1.8 Summary 26
2. LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) METHODOLOGY.. 28
2.1 Introduction 28
2.2 Base Thickness Modulation (BTM) 30
2.3 LFGV Methodology 33
2.4 Derivation of LFGV Methodology and Parameter Extraction 41
2.5 Experiments and Results 45
2.6 Sensitivity of tB and rj x to r\2 and XR/XB 55
2.7 GeSi HBT Performance Enhancement 61
2.8 Summary 62
3. LFGV ANALYSIS OF GeSi HBT WITH NO REFERENCE Si BJT 70
3.1 Introduction 70
3.2 Theory 71
3.3 Experiments and Results 74
3.4 LFGV Analysis with no Si Reference BJT 84
3.5 Summary 86
iii


7
1.3 Pseudomorphic Growth, Critical Layer and Ge-induced Effects
During the pseudomorphic epitaxial growth of GeSi layer, the lattice mismatch
between GeSi layer and Si substrate was accommodated by biaxial strain in the GeSi
layer. A two-dimensional illustration of the pseudomorphic growth of GeSi layer is
shown in Fig. 1.3. As is shown in Fig. 1.3b, under conditions that favor pseudomorphic
growth, the GeSi layer is biaxially strained and its lattice assumes that of the substrate.
On the other hand, lattice defects such as misfit dislocations occur at the GeSi/Si
interface when the GeSi layer becomes relaxed (no strain) as shown in Fig. 1.3c. There
is a critical layer thickness beyond which the layer will relax and create the misfit
dislocations at the GeSi/Si interface. The dislocations may also penetrate the entire
layer. This critical layer thickness can be calculated based on the strain of the GeSi
layer and the thermal dynamics theory [5-7]. Figure 1.4 shows the theoretical and
experimental critical layer thickness versus the Ge mole fraction [1], As is shown in the
figure, based on the model of People and Bean, for xGe=10% in the Ge^i^ layer, the
critical layer thickness is almost 1 p.m which is enough for high performance GeSi HBT
whose base thickness is usually in the range of <1000A. The Ge-induced biaxial strain
in the GeSi layer changes the physical and chemical properties of the layer, such as the
energy band structure [14-16], electron and hole effective masses, and electron and hole
mobility pn and pp [17-18]. Figure 1.5 shows the constant energy surfaces in the GeSi
layer under biaxial strain [17, 19]. As can be seen from the figure, the two surfaces in
the z-direction (growth direction) are deformed which gives a smaller electron effective
mass mn and also a higher electron concentration in the z direction, while the energy of


Energy Gap /(1eV)
13
Fig. 1.7 Energy gap reduction for strained and unstrained GeSi layer versus Ge mole
fraction in the layer. Adapted from Sah [1, p. 951].


72
qDB exp(qVBE/k)
(3.2)
P(x)
dx
0 ni2(x)
where DB = JP(x)/n2(x)/JP(x)/Dn(x)n?(x)dx is the average minority electron diffusivity
in the base. If we superimpose a small sinusoidal signal on the dc reverse BC junction
bias, with the BE junction forward-biased, the small-signal output conductance, goF, due
to the base-thickness modulation can be obtained by taking the derivative of Jc or Ic
with respect to VCB,
air
aXR
Ir
1
P(XB) axB
9oF
(3.3)
axB avCB
dx
ni2(XB
av,
CB
0 n^Cx)
In (3.3), P(XB).dXB)/3VCB = (l/q)(0QB/3VCB) is the small-signal base-collector
junction capacitance per unit area, CBC. Thus, (3.3) can be written as
% CBC
9oF
P(X)
dx
ni (XB)
(3.4)
0 ni2(x)
Similarly, we can obtain goR for the reverse-active operation with the EB junction
reverse-biased and the BC junction forward-biased,
CR
-BE
9oR
P(x) ni2(0)
- dx
(3.5)
0 ni2(x)
The integral in the denominator is the same both for the forward-active and reverse-
active operation modes. Thus, the ratio of equations (3.4) and (3.5) gives


tB(GeSi)/tB(Si)
60
Fig. 2.10 Sensitivity of tB(GeSi)/tB(Si) to XR/XB calculated from (A. 12) with r\2 as a
variable parameter for ^^2.0.


APPENDIX B
TRANSISTOR RELATION FOR A GAUSSIAN
DOPANT IMPURITY CONCENTRATION PROFILE IN THE BASE OF BJT
I. Most bipolar junction transistors are fabricated using ion implantation to dope the
base which gives a Gaussian dopant impurity concentration profile. For GeSi HBT, a
Gaussian profile may result from the impurity doping outdiffusion from the epitaxially
deposited base layer during subsequent fabrication. Thus, the relevant LFGV equations
for the Gaussian distribution are important. Two different Gaussian distribution are
considered and shown in Fig. B.l and Fig. B.2. The Gaussian concentration profile P(x)
shown in Fig. B.l has a peak value at x=0. The profile shown in Fig. B.2 has a peak
value inside the base layer. The dashed line shows the exponential approximation for
P(x).
Following are the analytical derivations of the equations for the two Gaussian
distributions P(x).
1. Base dopant impurity concentration profile P(x) shown in Fig. B.l
P(x) = NM.exp(-x2/a2)
where a is
(B.l)
a = XB/[ln[NM/P(XB)]1/2
X.
(B.2)
(B.3)
92


82
100 150 200 250
Temperature /(1K)
Fig. 3.4 Diffusion length LB(GeSi) T.
300


106
[48] P.E. Cottrell, and Z.P. Yu, "Velocity saturation in the collector of Si/Ge^i^/Si
HBTs," EEEE Electron Device Lett., vol. 11, No. 10, pp. 431-433, Oct. 1990.
[49] Z.P. Yu, P.E. Cottrell, and R.W. Dutton, "Modeling and simulation of high-level
injection behavior in double heterojunction bipolar transistors," IEEE 1990
Bipolar Circuits and Technology Meetings, No. 8.5, pp. 192-194.
[50] C.T. Kirk, Jr., "A theory of transistor cutoff frequency (fT) falloff at high current
densities," IRE Trans. Electron Devices, pp. 164-174, Mar. 1962.
[51] E.J. Prinz, and J. C. Sturm, "Current gain-Early voltage products in heterojunction
bipolar transistors with nonuniform base bandgaps," IEEE Electron Device Lett.,
vol. 12, No. 12, pp. 661-663, 1991.
[52] E.J. Prinz, and J.C. Sturm, "Analytical modeling of current gain-Early voltage
products in Si/Si^Ge^Si Heterojunction Bipolar Transistors," IEDM, vol. 33,
No. 2, pp. 853-856, 1991.
[53]T. Manku and A. Nathan, "Effective mass for strained p-type Si^Ge^.," J. Appl.
Phys., vol. 69, pp. 8414-8416, June 1991.
[54]I.-Yun Leu and A. Neugroschel, "Minority-carrier transport parameters in heavily
doped p-type silicon at 296 and 77K," IEEE Trans. Electron Devices, vol. 40, pp.
1872-1875, Oct. 1993.
[55]Chih Hsin Wang, Konstantinos Misiakos, and A. Neugroschel, "Temperature
dependence of minority hole mobility in heavily doped silicon," Appl. Phys. Lett.,
vol. 57, No. 2, pp. 159-161, July. 1990.


Concentration /(cm 3)
36
Depth
Fig. 2.2 Idealized model for the Ge and dopant impurity concentration profiles in GeSi
HBT. The dopant impurity concentration profiles for Si BJT (no Ge in the base) are the
same as those in GeSi HBT.
Germanium /(1%)


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103
[25] A. Neugroschel, "Determination of recombination lifetimes and recombination
currents in p-n junction solar cells, diodes, and transistors," IEEE Trans. Electron
Devices, vol. 28, pp. 108-115, Jan. 1981.
[26] A. Neugroschel and Chih-Tang Sah,"Measurement of built-in electric field in
base of Si/Ge^i^/Si HBT with linearly-graded Ge concentration profile,"
Electronics Letters, vol. 32, No. 24, pp. 2280-2282, Nov. 1996.
[27]A. Neugroschel, C.-T. Sah, J.M. Ford, J. Steele, R. Tang, C. Stein, P. Welch, and
J. Watanabe, "Performance comparison analysis of GeSi and Si bipolar
transistors," Electronics Lett., pp. 1239-1241, June 20, 1996.
[28] D.M. Richey, J.D. Cressler, A.J. Joseph, "Scaling Issues and Ge concentration
profile Optimization in Advanced UHV/CVD SiGe HBTs," IEEE Electron
Device Letters, vol. 44, No. 3, pp. 431-440, Mar. 1997.
[29] J.D. Cressler, J.H. Comfort, E.F. Crabb, G.L. Patton, J.M.C. Stork, and J.Y.-C.
Sun, "On the profile design and optimization of epitaxial Si- and SiGe-base
bipolar technology for 77K applications-Part I: transistor dc design
considerations," IEEE Trans. Electron Devices, vol. 40, pp. 525-541.
[30] J.D. Cressler, E.F. Crabb, J.H. Comfort, J.M.C. Stork, and J.Y.-C. Sun, "On the
profile design and optimization of epitaxial Si- and SiGe-base bipolar technology
for 77K applications-Part II: circuit performance issues, IEEE Trans. Electron
Devices, vol. 40, pp. 542-555.
[31] C.A. King, J.L. Hoyt, and J.F. Gibbons, "Bandgap and transport properties of
Sij^Gex by analysis of nearly ideal Si/Si^Gex/Si heterojunction bipolar
transistor, IEEE Trans. Electron Devices, vol. 36, pp. 2093-2104, Oct. 1989.
[32] M. Schroter, M. Friedrich and H-M. Rein, "A Generalized Integral Charge-
Control Relation and its Application to Compact Models for Silicon-Based
HBTs," IEEE Trans. Electron Devices, vol. 40, No. 11, pp. 2036-2046, 1993.


39
nf (x)
Nc(x)Nv(x) Nc(0)Nv(0)exp(-Cx/XR) (2.13)
where C is a LSF parameter. Then the intrinsic carrier concentration is given by
ni o2. expa. exp y. exp (x/xx) (0 (2.14)
ni02. expa* exp y. exp^/x^. (xR where n¡Q is the intrinsic carrier concentration in low doped Si given by
ni02 = Nc(0)Nv(0).exp(-EGO/kT), (2.14a)
and x1=XB/[(AEG_Ge/kT)-C]=XB/ri1. Combining (2.9), (2.11) and (2.14) yields the
ratio of the collector current in GeSi and Si
Ic(GeSi) DB(GeSi) A+(l-A)[l-exp(-r?2)]//72]
= expt^+a+Ay).
(2.15)
Ic(Si) DB(Si) A(exp^1-l)/^1+(l-A)[l-exp(-^2)]/rj2
where r) x = r|-C is the normalized effective energy gap variation through the base layer
that includes the effects of variable Ge concentration and variation of density of states
with xGe. In (2.15), DB(GeSi) = /B [P/n2(x)]dx / JB Pdx/Dn(x)n2(x) is the spatially-
averaged electron diffusivity in the base. The weighting factor of DB(GeSi) is n¡2(x)
which increases with x or xGe. Thus, the value of DB(GeSi) is weighted toward the
region close to x=XB. Since Dn(GeSi) is expected to be a very weak function of xGe for
the average xGE<5% [28], defining DB(GeSi) in (2.7) causes only a negligible error. For
a purely linearly-graded Ge concentration profile, XR = XB and A=l, which simplifies
(2.15)to [27]
Ic(GeSi) 7]i DB(GeSi)
= .expa expAy (2.16)
Ic(Si) l-exp(-fn) Dg(Si)
One reason for lumping the spatial variation of NCNV with the spatial variation of the
energy gap AEG_Ge is that these two parameters always appear together as a product in


11
Fig. 1.5 Constant energy surfaces in the conduction band in GexS!_x under biaxial
strain [17, 19]. The z direction corresponds to the growth direction. The two surfaces
in the z-direction (growth direction) are raised in energy and deformed such that they
give a smaller electron effective mass mn. The four x and y surfaces are lowered in
energy. The overall energy gap is smaller and the electrons preferentially populate the
two valleys in the z-direction in which mn is low. This is also the direction of the
minority-carrier flow in FEBT.


24
1.7 NCNV and n? Model for Linear Ge Distribution
The Ge in the base region changes not only the energy gap, but also other electronic
material parameters. The effective density of states in the conduction band and valence
band, Nc and Nv, will change because they are a function of the electron and hole
effective masses me and mh, respectively which change with the Ge-induced strain and
change of the E-k relationship in the epitaxial GeSi layer [17-18]. Nc and Nv are given
by [1]
Nc = 2(2jrmekT/h2)3/2 (1.6a)
Nv = 2(27rmhkT/h2)3/2. (1.6b)
Figure 1.16 shows the theoretical calculations of the normalized density of states
product NCNV versus Ge mole fraction [17-22], In order to obtain analytical models for
the GeSi HBT, we approximate the NCNV product by an exponential function least-
squares fitted to the theoretical data,
Nc(x)Nv(x) = Nc(0)Nv(0).exp(-C.x/XR) (1.7)
where the constant C is a nonlinear least squares fit (NLSF) parameter. The model fits
the theory well for xGe < 10%, with C = 0.70.1, in particular to the theoretical models
of Prinz et al. [20-21] and Jain et al. [22] which are also supported by the
photoluminescence data and electrical measurements in Si/Ge^i^/Si HBTs. The
Nc(x)Nv(x) model given by (1.7) enables the de-coupling of the diffusivity DB from the
NCNV product, as will be shown later.
The Ge-induced energy gap reduction AEG_Ge in the base region will change the
intrinsic carrier concentration n¡ which can be expressed as [1]


CHAPTER 1
INTRODUCTION TO GeSi HETEROJUNCTION BIPOLAR TRANSISTOR
1.1 Introduction
The concept of heterojunction bipolar junction transistor (HBT) was first proposed
by Shockley in 1948 [1-2]. The purpose was to build bipolar junction transistors with
larger energy gap in the emitter than in the base, which improves the emitter injection
efficiency over that of the homogeneous bipolar junction transistors. The first detailed
analysis of the HBT characteristics and performance was given by Kroemer [3].
Although the advantages of the heterostructures were known, practical applications
were not realized until the 1970s when the epitaxial technology was developed. The
first successful HBT was fabricated in 1972 by IBM [4] using AlGaAs/GaAs
heterostructure to give the larger emitter energy gap. The anticipated superior
performance of the HBT was demonstrated by these and other III-V compound HBTs.
Until recently, the AlGaAs/GaAs HBTs have been the most successful. This is due to
the excellent lattice matching between the two material which gives a nearly defect-free
heterointerface. But GaAs or other HBTs based on III-V semiconductor materials are
difficult to integrate with the existing Si integrated circuits due to the large lattice
mismatch. Also III-V HBTs are difficult to fabricate and thus not cost efficient. GaAs
HBT has been more successful in discrete devices, such as high frequency oscillators
and amplifiers.
1


A
B
C
BJT
CP
-BC
"BE
Di
D
Ebi
Ebi2
AE(
AE,
G-Ge
G-HD
N
iT
§0
Sr
Ge
h
HBT
ib
!b
Ic
k
lb
APPENDIX C
LIST OF SYMBOLS
=XR/XB
Correction factor
Least squares fitting parameter for NCNV product
Bipolar junction transistor
Base collector junction capacitance
Base emitter junction capacitance
Averaged base minority carrier diffusion coefficient
Base minority earner diffusion coefficient
Built-in electric field in the base region due to Ge
Built-in electric field in the base region due to P(x)
Conduction band
Valence band
Energy gap
Energy gap reduction in the base region due to Ge
Energy gap reduction in the base region due to heavy doping
Electron quasi-Fermi level
Hole quasi-Fermi level
Cutoff frequency
Output conductance
Reverse transconductance
Germanium
Planck constant
Heterojunction bipolar transistor
Small-signal base current due to vcb
Small-signal collector current due to vcb
Base current
Collector current
Boltzmann constant
Diffusion length
98


105
[41]E.J. Prinz, P.M. Garone, P.V. Schwartz, X. Xiao, and J. C. Sturm, "The effect of
base dopant outdiffusion and undoped Si[.xGex junction spacer layers in
Si/Sij.xGex/Si heterojunction bipolar transistors," IEEE Electron Device Lett.,
vol. 12, No. 2, pp. 42-44, Feb, 1991.
[42] E.L. Heasell, "The derivation of a relationship for the charge-control base
recombination lifetime in Terms of the base and collector small-signal
conductances," IEEE Trans. Electron Devices, vol. Ed-28,No. 5, pp. 595-596,
May. 1981.
[43] A.J. Joseph, J.D. Cressler, R.C. Jaeger, D.M. Richey, and D.L. Harame, "Neutral
base recombination in advanced SiGe HBTs and its impact on the temperature
characteristics of precision analog circuits," IEDM Tech. Digest, pp. 755-758,
1995.
[44]Z.A. Shafi, C.J. Gibbings, P. Ashburn, I.R.C. Post, C.G. Tuppen, and D.J.
Godfrey, "The importance of neutral base recombination in compromising the
gain of Si/SiGe heterojunction bipolar transistors," IEEE Trans. Electron Devices,
vol. 38, pp. 1973-1976, Aug. 1991.
[45] C.H. Gan, J.A. del Alamo, B.R. Bennett, B.S. Meyerson, E.F. Crabb, C.G.
Sodini, and R. Reif, "Si/Sij.xGex valence band discontinuity measurements using
a semiconductor-insulator-semiconductor (SIS) heterostructure," IEEE Trans.
Electron Devices, vol. 41, pp. 2430-2439, Dec. 1994.
[46] S. Takagi, J.L. Hoyt, K. Rim, J.J. Welser, and J.F. Gibbons, "Evaluation of the
valence band discontinuity of Si/Si j_xGex/Si heterostructures by application of
admittance spectroscopy to MOS capacitors," IEEE Trans. Electron Devices, vol.
45, pp. 494-501, Feb. 1998.
[47] Z. Matutinovic-Krstelj, V. Venkataraman, E. J. Prinz, J.C. Sturm, and C.H.
Magee, "Base resistance and effective bandgap reduction in n-p-n Si/Sij.xGex/Si
HBTs with heavy base doping," IEEE Trans. Electron Devices, vol. 43, pp. 457-
466, Mar. 1966.


58
will certainly cause some errors since the SIMS profiles may not be very accurate for
very thin base layers, especially near the collector junction. Note that the base dopant
impurity concentration profile NAA(X) can be better approximated by a Gaussian
distribution (see Appendix B for Gaussian distribution model). This results from the
boron outdiffusion from the GeSi layer during subsequent fabrication. The increasing
doping Naa(x) at x=0 shown in Fig. 1.2 will produce a retarding electric field which
will decelerate the base minority carrier movement across this region. The decreasing
doping density will produce an aiding electric field. Thus, an uncertainty in a precise
location of XR can cause errors in calculation of the transit time and other parameters.
In order to estimate the influence of this uncertainty on the GeSi HBT analysis, we
investigate the dependence of T) j, tB on XR/XB and r|2. Figure 2.9 shows the normalized
Ge-induced electric field r| j versus XR/XB with r|2 as a parameter. r| j is the key
parameter underlying the operation of GeSi HBT. Figure 2.10 shows the transit time
ratio tB(GeSi)/tB(Si) versus XR/XB with r|2 as a parameter for ^=2.0. As can be seen
from Fig. 2.9 and Fig. 2.10, and tB(GeSi)/tB(Si) are rather insensitive to the location
of the transition point XR. This is expected, since ti, and tB(GeSi)/tB(Si) are calculated
from the collector current ratio of the two transistors with nearly identical geometry and
dopant impurity concentration profiles. The above sensitivity analysis shows that taking
x=XR as the transition point where the Ge linear profile intersects the flat Ge
concentration profile in the measured SIMS dependencies, Fig. 1.2, will result in a
negligible error.


16
improvements of GeSi HBT, such as higher Early voltage VA will be discussed in detail
in later chapters.
1.5 Monte Carlo Simulation of Mobilities
The Ge-induced strain in the GeSi layer will change the E-k relationship in both the
conduction and valence band, and thus change the effective masses of electrons and
holes, mn and mp. The electron and hole mobilities, p,n and ju.p, will be also affected by
the change in the effective masses and become anisotropic. Monte Carlo simulations
were used to calculate the electron and hole mobilities in strained and relaxed GeSi
layers for different Ge mole fraction and dopant impurity concentrations [17-18].
Figure 1.10 and Fig. 1.11 show the calculated results for electron mobilities versus Ge
mole fraction in p-type and n-type GeSi layer, respectively, for doping level of 1018
cm"3 close to that in a typical GeSi HBT [17]. The longitudinal mobility (upward
triangles) is in the growth or z direction, the transverse mobility (downward triangles) is
in the x-y plane. Figure 1.10 and Fig. 1.11 shows only a small (~2%) increase in the
longitudinal mobility with Ge mole fraction at 300K. However, a much larger
improvement (-50%) was calculated at 77K for xGe~5-10%. The transverse mobility
shows a large reduction with increasing xGe which is always smaller than that in Si
(xGe=0) at any Ge concentration level. The results for the majority and minority hole
mobilities are similar to those for the electron mobilities in Fig. 1.10 and Fig. 1.11. In
summary, the expected minority electron mobility improvement for the doping level of
about 1018 cm'3 is very small, |xn(GeSi)/p,n(Si)=1.0. This agrees very well with our
experimental results as will be shown in chapter 2.


62
The base minority electron distribution for r|,=2.0 is shown in Fig. 2.13. As can be
seen from the figure, n(x) throughout the base is larger for GeSi HBT. This is because
the intrinsic carrier concentration r^ of GeSi HBT is larger than that of Si B JT.
The base minority carrier charge ratio QB(GeSi)/QB(Si)>1.0 vs r|j is shown in Fig.
2.14. The increase of base minority carrier charge will not affect the performance of
GeSi HBT significantly because the aiding electric field in the base region increases Ic.
Thus, the minority-carrier transit time through the base, tB=QB/Ic is still smaller for the
GeSi HBT. This is shown in Fig. 2.15 for the forward active mode.
The transit time improvement is very important for high frequency performance. As
is shown in the figure, the base transit time can give a factor of two improvement for
r| j=2.0, which corresponds to about 10% Ge in the base. The improvement of tB(GeSi)
is due to the Ge-induced aiding electric field Ebi, rather than the enhancement of
diffusivity Dn, which is negligible according to our measurements and theoretical
calculations.
The base transit time ratio tB(GeSi)/tB(Si) for the reverse active mode is shown in
Fig. 2.16. As expected for the Ge concentration profile in Fig. 1.2, tBR(GeSi)/tBR(Si)
1.0.
2.8 Summary
In conclusion, a new LFGV methodology was developed and a complete analysis of
the effects of Ge in the base of Si/Ge^i^/Si HBT was presented. The LFGV
methodology is based on a one-dimensional BJT theory and accurate dc and low-
frequency measurements of similar GeSi and Si transistors. It is accurate, expedient and


I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Amost Neugroschel, Chairman
Professor of Electrical and Computer Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Chih-Tang Sah, CocMirman
Eminent Scholar and Graduate Research
Professor of Electrical and Computer Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Peter S. Zory
Professor of Electrical
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Professor of Electrical and Computer Engineering


78
calculate the important GeSi HBT parameters as a function of temperature. The results
are shown in Table 3.2 and Table 3.3. From Table 3.2, we can see that the base-
collector junction capacitance CBC remains constant as temperature decreases while the
base-emitter junction capacitance CBE shows a slight decrease with decreasing
temperature. This is because the thickness of the base-collector junction SCR, xBC, is
much larger than xBE due to lower doping at the collector junction. This gives
Cbc< fraction of xBC. Figure 3.3-Fig. 3.5 show the measured temperature dependence of r\{,
the diffusion length LB(GeSi), and the base recombination component QB/xB(GeSi)/IB
vs temperature, respectively.
From Fig. 3.3, we can see that r| j obtained by a combination of (3.7) and (3.8), and
thus the built-in electric field Ebi, increase almost linearly with 1/T. The dashed line is
calculated using qpAE^Qg/kT C, where AEG_Ge=70meV as measured at 297.15K,
and C=0.7. The deviation of the theoretical curve from the experimental dependence
may come from two sources: (1) decrease of the AEG_Ge with decreasing temperature,
and (2) the increase of the fitting parameter C with decreasing T. The latter one is more
reasonable since the NCNV product is a strong function of temperature as is shown in
equations (1.6a) and (1.6b). The increase of C at low temperature means that the
NcNv(GeSi)/NcNv(Si) is a decreasing function of temperature.
Figure 3.4 shows the measured diffusion length LB(GeSi) vs T. The diffusion length
can be expressed as
LB(GeSi )=1l Dr
\(kT/q)^r
(3.10)


Concentration /(cm 3)
75
Fig. 3.1 GeSi HBT with different Ge concentration profiles in the base region.
Germanium /(1%)


41
The LFGV methodology described in the next section will give an accurate
extraction of rij.
2.4 Derivation of LFGV Methodology and Parameter Extraction
Below we present detailed derivation and description of the LFGV methodology. As
is discussed in section 2.2, the base thickness modulation gives rise to two small-signal
conductances, an output conductance, g0, and a reverse transconductance, gr. In the first
step of the LFGV methodology, we need the g0 only. It can be derived from the Ic
equations (2.9) and (2.15) and is given by (see appendix A)
d XR
9o =
XB A(expp1-l)expp2/hi + (l-A)(expp2-l)/n2
3V
CB
(2.17)
'BE
From (2.17), we can see immediately that the expression (2.17) for g0 is simpler than
(2.15) for Ic. The reason for this is that the unknown parameters, DB(GeSi)/DB(Si), a,
and y are lumped into Ic which is a measurable quantity. This is one of the advantages
of g0 compared with Ic and is one important aspect of the LFGV methodology. Useful
relations (2.18a) and (2.18b) are derived by taking the ratios of the collector currents
and the output conductances of the GeSi HBT and Si reference BJT,
Ic(GeSi)/Ic(Si) A[(expp1-l)expp2]/p1 + (l-A)(expp2-l)/p2
= (2.18a)
g0(GeSi)/g0(Si)
Ic(GeSi)/Ic(Si)
g0(GeSi)/g0(Si)
Aexpp2 + (l-A)(expp2-l)/p2
expr^-l
(2.18b)
hi
The only assumption in (2.18a) and (2.18b) is that 3XB/3VCB is the same for GeSi HBT
and Si reference BJT. This assumption is proven to be a very good approximation from
measuring the junction capacitance CBC. These relations are used to calculate r) t


97
Fig. B.2 Gaussian distribution and its exponential approximation.


69
general. The analytical model for the Ge-concentration-dependence of the density of
states product decouples it from the minority-carrier mobility and heavy-doping effects.
A combination of Ic and g0 measurements gives a unique determination of the critical
parameter r|j. All the important minority-carrier transport parameters underlying the
improved performance of GeSi HBT compared to similar Si BJT were determined and
quantified.
The results show that the reduction in the base transit time is due to the Ge-induced
aiding electric field in the region with linearly-variable Ge concentration. The minority
carrier mobility or diffusivity enhancement was found to be negligible compared to Si
BJT. The energy gap reduction due to the heavy doping (NBase=3xl018cm"3) is about
lOmeV larger in GeSi HBT than in Si BJT at room temperature. First accurate
measurements of the minority carrier diffusion length and recombination lifetime in the
base show greatly improved values in the GeSi base compared to Si. The base current
was found to be dominated almost completely by the recombination within the emitter
in the large 100.4x100.8pm2 transistors, while in circuit transistors with a narrow
emitter stripe ( importance of the sidewall and surface effects. Since the dc and low-frequency small-
signal measurements are independent of parasitics, accurate high-frequency and high
speed parameters can be readily obtained which are difficult to measure directly such as
the ~lps base transit time. The performance improvements of GeSi HBT over Si BJT
were shown graphically as a function of r|j.


Critical Layer Thickness
10
Fig. 1.4 Critical layer thickness of GeSi layer versus Ge fraction. The dashed line
shows the theoretical results calculated from the thermal dynamics. The solid line gives
the experimental results. Adapted from Sah [1, p. 949].


20
AEQ-Ge(O) AEG_Ge(XB)
P-GeSi
Base
n+Si
Emitter
-v
N
Ge
AA
0
X
B
n-Si
Collector
Fig. 1.12 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with
a triangular Ge distribution in the base region at equilibrium (zero bias). EF is the Fermi
level at equilibrium. AEG_Ge(0) is the Ge-induced energy gap reduction at x=0 in the
quasineutral base region. AEG.Ge(XB) is the Ge-induced energy gap reduction at x=XB
in the quasineutral base region. AEG.Ge = AEG_Ge(XB) AEG.Ge(0) is the total Ge-
induced energy gap reduction through the base region.


68
i i ItrTTl i I i I i I i I i I i I i
0 2 4 6 8 10
Til
Fig. 2.16 Base minority carrier transit time ratio tB(GeSi)/tB(Si) in reverse active mode
vs r| j (normalized to DB(GeSi)/DB(Si)). The reverse base transit time is much larger
than in the forward active mode.


61
2.1 GeSi HBT Performance Enhancement
In this section, we will plot the important GeSi HBT parameters as a function of r| j
normalized to that of Si BJT in order to show the performance enhancement of GeSi
HBT over Si BJT. Since the triangular Ge distribution in the base region is a simple and
also a very good approximation for the trapezoidal Ge distribution, we will use the
triangular Ge distribution as a demonstration. The extension to the trapezoidal Ge
concentration profile is straightforward. In fact, most of the important performance
enhancements can be accomplished by the triangular Ge distribution in the base region.
The most important performance enhancement of GeSi HBT over Si BJT is the
increase in the collector current Ic(GeSi), as is shown in Fig. 2.11. The collector current
ratio Ic(GeSi)/Ic(Si) varies almost linearly with r|j for r|j>~3.0. For ^^-3.0, the
collector current ratio Ic(GeSi)/Ic(Si) can be modeled by a linear function,
Ic(GeSi)/Ic(Si) c r)j c (AEG_Ge/kT)-C.
The output conductance ratio g0(GeSi)/g0(Si) vs is shown in Fig. 2.12. As can be
seen from the figure, the g0 ratio shows a rapid decrease for l.Odj^.O and tends to
zero for very large rj j. This means that the output resistance of GeSi HBT is much
larger than that of Si BJT for large pj and the Early voltage VA also increases rapidly
with r|!. So the figure-of-merit of (3VA improves greatly for large r) j. For example, for
r)1=2.0, g0(GeSi)/g0(Si) = 0.73, Ic(GeSi)/Ic(Si) = 2.3, and VA(GeSi)/VA(Si) = 2.3/0.72
= 3.0. The current gain (3 will also increase roughly 2.3 times for the same base current.
So the total (3VA improvement is ~ (3.0)(2.3)=7.0.


99
me Electron effective mass
mh Hole effective mass
n(x) Base minority carrier distribution
n Intrinsic carrier concentration
Nc Effective density of state in conduction band
Nv Effective density of state in valence band
P(x) Base dopant impurity concentration profile
QB Base minority carrier electric charge
Qe Emitter minority carrier electric charge
Si Silicon
tB Base minority carrier transit time
vcb Small-signal voltage superimposed upon VCB (~lkHz)
VA Early voltage
xGe Germanium concentration in the base region
XR Transition position of the Ge distribution in the base
XB Base thickness
Vbi Built-in potential of the p-n junction
VBE Base emitter junction bias
VCB Base collector junction bias
a AEG_Ge(0)/kT (normalized energy gap reduction at x=0 in the base region)
(3, PF Common emitter current gain
Y AEG_HD/kT (normalized energy gap reduction in the base region
due to heavy doping)
Ay [AEG_HD(GeSi)-AEG_HD(GeSi)]/kT
r) Normalized (to thermal voltage kT/q) energy gap reduction due
to Ge in the base region
r\2 Field factor due to nonuniform base doping
r]j Normalized energy gap reduction in the base region
Tg Base minority recombination lifetime
xE Recombination time constant in the emitter
pn Base minority carrier mobility


APPENDIX A
GENERAL EQUATIONS FOR BJT
A. The general integral relations for calculation of important parameters in bipolar
junction transistor are given below. Equations for a trapezoidal Ge distribution in the
base and constant-exponential dopant impurity concentration profile in the base are
given in section B.
1. Collector current Ic(GeSi) [1, p. 760, 38]
q.exp(qVBE/kT)
Ir
Xr
P(x)
dx
0 Dn(x). ni2(x)
2. Minority carrier distribution in the base [38]
Jc nf(x)
n(x) =
q P(x)
XB P(y)
x Dn.ni2(y)
-dy
3. Minority carrier charge in the base
(A. 1)
(A.2)
'B
n(x)dx
4. Minority carrier base transit time [38]
tB ~
XB nf(x)
P(x)
P(y)
5. Correction factor B [27]
dx
1
B =
Dn,t;B
XB P(X)
n2(x)
-dx
x n?(y)
XB n?(x)
dx 1
P(x)
(A.3)
(A.4)
(A.5)
89


35
temperature. But theoretical calculations show that the density of states and mobility
have very complicated temperature dependence, so the assumption of the temperature
independence of the two pre-exponential factors in (2.6) is unreliable and can lead to
large errors in AEG.Ge, as also noted previously [32], The second approach is to assume
theoretically predicted values of (NcNv)GeSi and Dn(GeSi) and then calculate EA from
(2.6). Apparently, there is another unknown, Ay, and also the theoretical results are
strongly dependent on models and input parameters. Furthermore, both approaches give
an estimate for the energy gap reduction term only and do not provide values or
estimates for the mobility or recombination lifetime in the GeSi base.
The above discussion shows that an analysis based on the measurement of Ic(GeSi)
only is not sufficient. The LFGV methodology, however, will use a combination of the
dc IB-VBE and IG-VBE characteristics with the small-signal output conductance g0 and
reverse transconductance gr measurements. This novel methodology can overcome the
limitations of the above and other approaches.
The LFGV methodology will be presented here for the idealized trapezoidal Ge
concentration profile in the base which is shown in Fig. 2.2. In this model, the base
dopant impurity concentration profile and the Ge distribution are divided into two
regions. In the first region, 0 Ge distribution is assumed to be retrograded linear. In the second region, XR base doping is approximated by an exponential function and the Ge distribution is
assumed to be constant. In the region with the linear Ge distribution (0 Eg(0) AEG_Ge(x/XR) [1], where EG(0) is the energy gap at x=0, and AEG.Ge = AEG(XR)


49
Fig. 2.5 The measured forward active mode and reverse active mode small-signal
output conductances, g0, reverse transconductance, gr, and the collector current, Ic, of Si
BJT, as a function of VBE. All measured curves show the expected exp(qVBE/kT)
dependence.
IC/(1A)


Concentration /(cm 3)
76
Depth
Fig. 3.2 Bipolar transistor with different high-low dopant impurity concentration
profiles in the base region.


CHAPTER 4
SUMMARY AND CONCLUSIONS
4.1 Summary
In chapter one, we gave a general review of the GeSi HBT fabrication, including the
discussion of pseudomorphic growth of GeSi layer and its critical layer thickness. A
comparison of the Si/GexSi,_x/Si HBT characteristics with those for a Si reference BJT,
Monte Carlo simulations of the mobility improvement and other Ge-induced changes in
the material properties were also discussed. An exponential approximation model for
the density of states NCNV dependence on the Ge concentration was given for a linear
Ge distribution in the base. In chapter two, a low-frequency-conductance-voltage
(LFGV) methodology was developed for detailed analysis of the Si/GexSij.x/Si HBT.
This methodology is based on a comparison of the GeSi HBT performance with that of
a reference Si BJT. A brief review of the base thickness modulation method which
underlies the LFGV method is also given. Experimental data were presented to
demonstrate the LFGV methodology in high-performance Si/GejSi^/Si HBTs.
Important performance enhancements of GeSi HBT over Si BJT were measured and
analyzed. In chapter three, we introduced a methodology for GeSi HBT analysis
without using a reference Si BJT. In this non-reference analysis, the key parameter r| j
of GeSi HBT can be determined directly and a complete charge control analysis can be
made. Experimental demonstration of the non-reference method was given.
87


101
[8]B.S. Meyerson, "UHV/CVD growth of Si and Si:Ge alloys: Chemistry, physics,
and device applications," Proceedings of the IEEE, vol. 80, No. 10, pp. 1592-
1608, Oct. 1992.
[9]A. Gruhle, H. Kibbel, U. Erben, and E. Kasper, "MBE-grown Si/SiGe HBTs with
high P, fT, and fmax," IEEE Electron Device Letters, vol. 13, No. 4, pp. 206-208,
Apr. 1992.
[10]A. Pruijmboom, J.W. Slotboom, D.L. Gravesteijn, C.W. Fredriksz, A.A. van
Gorkum, R.A. van de Heuvel, J.M.L.van Rooij-Mulder, G. Streutker, and G.F.A.
van de Walle, "Heterojunction bipolar transistors with SiGe base grown by
molecular beam epitaxy," IEEE electron Device Lett., vol. 12, pp. 357-359, July
1991.
[11]M. Hong, E. de Frsart, J. Steele, A. Zlotnicka, C. Stein, G. Tam, M. Racanelli, L.
Knoch, Y.-C. See, and K. Evans, "High-performance SiGe epitaxial base bipolar
transistors produced by a reduced-pressure CVD reactor," IEEE Electron Device
Letters, vol. 14, pp. 450-452, Sep. 1993.
[12] A. Neugroschel, C.-T. Sah, J.M. Ford, J. Steele, R. Tang, and C. Stein,
"Comparison of time-to-failure of GeSi and Si bipolar transistors," IEEE Electron
Device Lett., vol. 17, pp. 211-213, May 1996.
[13] R. Tang, J. Ford, B. Pryor, S. Ansndakugan, P. Welch and C. Burt, "Extrinsic
base optimization for high-performance RF SiGe heterojunction bipolar
transistors," IEEE Electron Device Lett., vol. 18, pp. 426-428, Sep. 1997.
[14] R. People and J.C. Bean, "Band alignments of coherently stained Ge^i^/Si
heterostructures on <001> GeySij_y substrates," Appl. Phys. Lett., vol. 48, pp.
538-540, Feb. 1986.
[15]J.C. Bean, "Silicon-based semiconductor heterostructures: Column IV bandgap
engineering," Proceedings of the IEEE, vol. 80, No. 4, pp. 571-587, Apr. 1992.


21
AEo-Ge(O) AEG_Ge(XB)
Fig. 1.13 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with
a triangular Ge distribution in the base region under forward active operation, VBE>0V,
VCb>0V. Fn is the quasi-Fermi level for electrons and Fp is the quasi-Fermi level for
holes. Vbi is the built-in potential of the p/n junction. AEG_Ge(0) is the Ge-induced
energy gap reduction at x=0 in the quasineutral base region. AEG_Ge(XB) is the Ge-
induced energy gap reduction at x=XB in the quasineutral base region. AEG_Ge =
AEG-Ge(XB) AEG-Ge(O) is total Ge-induced energy gap reduction through the base
region.


DB(GeSi)/DB(Si)
53
Temperature /(1K)
Fig. 2.7 The measured temperature dependence of DB(GeSi)/DB(Si) in the range of
200K-300K normalized to 296K in large 100.4x100.8pm2 transistor.


3
the changes in the physical parameters that give the performance improvements of GeSi
HBT over Si BJT. The performance of the GeSi HBT demonstrated so far is superior
to, or comparable with, that of the GaAs HBTs [6-7]. The most important advantage of
using thin GeSi layer is that its epitaxial deposition is fully compatible with Si
integrated-circuit manufacturing technology; thus, monolithic integration of GeSi HBT
with Si integrated circuit can be very easily accomplished. Also, the thermal
conductivity of Si is three times higher than that of GaAs which is very important in
power amplifiers and very large scale integrated circuit (VLSI). The GeSi HBT has
very important applications in portable communication systems, such as mobile phones,
pagers, DACs and others.
1.2 GeSi HBT Fabrication
Silicon and germanium are completely miscible in any mole fraction ratio. The GeSi
material has a diamond lattice structure. The lattice constant can be calculated from the
Vegard rule [5]:
a(GexS!.x) = a(Si) + x(a(Ge) a(Si)) (1.1)
where x is the Ge mole fraction and a is the lattice constant. The lattice constant of Ge
is 4.17 percent higher than that of Si. When Si and Ge atoms are mixed during the
growth of the GeSi layer, the Si lattice is tetragonally distorted and strained. The lattice
mismatch between the GeSi layer and the Si substrate can be accommodated by two
ways. One is a generation of misfit dislocations at the GeSi/Si interface which may also
propagate through the entire layer. This occurs when the GeSi layer is very thick and
the strain is released by creation of misfit dislocations. The second possibility is


I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
ical Engineering
1/
This dissertation was submitted to the Graduate Faculty of the College of
Engineering and to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December 1998
Winfred M. Phillips
Dean, College of Engineering
M. J. Ohanian
Dean, Graduate School


32
change by AQB with the small-signal vcb. The minority carrier concentration at the
emitter boundary of the quasineutral base at x=0, N(0), remains constant for a fixed VBE
and is given by [n^/P(0)]exp(qVBE/kT), where P(0)=NAA(0) is the holeemitter
boundary of the quasineutral base at x=0, N(0) remains constant for a fixed VBE and is
given by [n?/P(0)]exp(qVBE/kT), where P(0)=NAA(0) is the hole concentration at x=0,
k is the Boltzmann constant, and T is the temperature. The change in the slope of N(x)
gives the small-signal collector current ic. The output conductance g0 is defined by
9o=
'cb
(2.1)
BE
The base current IB also changes due to a change in the base recombination current,
Qb/tb, the base thickness modulation by the small-signal voltage vcb. This
produces the reverse transconductance gr which is defined by
9r=
'cb
(2.2)
BE
where ib is the small-signal base current due to vcb. Analytical expressions for g0 and gr
can be derived (see appendix A),
IC dXB
^be
9o=
'cb
^BE XB
dV
9r=-
'cb
CB
dXR
(2.3)
^BE tB*XB d^CB
(2.4)
'BE
where XB is the quasineutral base thickness, QB is the base minority carrier charge
corresponding to VBE and VCB, and xB is the base minority carrier recombination
lifetime. Since Ic and QB are exponential functions of the forward base-emitter voltage


67
0 2 4 6 8 10
Hi
Fig. 2.15 Base minority carrier transit time ratio tB(GeSi)/tB(Si) in forward active mode
vs rj j (normalized to DB(GeSi)/DB(Si)). The base transit time can give a factor of two
improvement for 1^=2.0 which corresponds to about 10% Ge in the base.


55
transistor and stripe transistor is due to the perimeter recombination at the edges of the
stripe transistor. But, the narrow-emitter transistor is used in the circuit applications
because the narrow-emitter geometry minimizes the base series resistance. So the
measurements for stripe transistor are also important. Due to the edge effect, some
measured parameters, especially those associated with the base current, such as IB, PF,
gr and g0/gr, are different from those of the large square device. Two key parameters, r|j
and tB, are however very similar for both transistors geometries. This is because r|j and
tB are calculated from Ic and g0 only which are essentially one-dimensional even for the
narrow emitter transistor with a very thin base. Figure 2.8 shows the measured
temperature dependence of ln[exp(Ay)DB(GeSi)/DB(Si)] in the range of 150K-300K.
The temperature dependence shows a small activation energy of EA~8meV. For this
transistor pair, the measured [DB(GeSi)/DB(Si)]exp(Ay) = 1.0 compared to 1.6 for the
large transistor. This gives DB(GeSi)/DB(Si)=0.7. The disagreement with the
DB(GeSi)/DB(Si) = 1.0 result obtained from the large transistor is due to the narrow-
finger geometry.
2.6 Sensitivity of tB and r|1 to r|2 and XR/XB
An idealized base dopant impurity concentration profile P(x) and Ge distribution in
the base used for the analysis are shown in Fig. 2.2. The base region is divided into two
regions, derived from the actual SIMS profile shown in Fig. 1.2. For 0 doping P(x) is flat and the Ge distribution is retrograded linear, and for XR base doping decreases exponentially and the Ge distribution is flat. The transition point
is defined as XR. Although XR can be obtained from the measured SIMS profiles, this


2
The breakthrough for an Si-compatible HBT was accomplished again by IBM in
1988 [5], They used Germanium Silicon (GeSi) as the base material which has a
smaller energy gap than that of the Si emitter and collector. A thin strained single
crystal GexSij.x film on Si substrate was grown pseudomorphically using ultra-high
vacuum/chemical vapor deposition/low temperature epitaxy (UHV/CVD/LTE) process
[6-8], The energy gap of the base can be tailored by varying the Ge mole content in the
base. Furthermore, the Ge distribution in the base region can be graded which will
produce an aiding electric field for the minority carrier transport through the base. Ge
incorporation in the base will also modify the effective mass and mobility of both
majority and minority carriers. This results in a number of advantages of Si/GexSij.x/Si
HBT over Si B JT, such as higher collector current, higher current gain (3, superior high
frequency performance (higher unit gain frequency fT and maximum oscillation
frequency fmax), and excellent low noise behavior. The best high frequency
performance was obtained at low voltages (VCE=1-3V), which is very useful for
portable communication applications.
Since the introduction of the pseudomorphic growth mechanism in 1972 [1], the
techniques of growing a thin base GeSi layer have been highly developed to
accommodate the lattice mismatch between the GeSi layer and Si substrate.
Technology has been developed for GeSi layer deposition in commercial epitaxial
reactors. During the pseudomorphic growth, the lattice of the GeSi layer has to conform
with that of the Si substrate; thus, the lattice of the GeSi layer is strained and distorted
compared with that of the unstrained GeSi layer. This lattice strain is responsible for


8
the four surfaces on the kx and ky axes is lowered. The resulting reduction in the energy
gap and lowering of the effective mass are very beneficial for improved performance of
GeSi HBT. The smaller energy gap increases the collector current and gain, while the
smaller mn in the vertical minority-carrier electron flow direction (in npn HBT)
increases the minority-carrier mobility which reduces the base transit time. Figure 1.6
illustrates the in-plane (x) of growth direction and normal to the growth plane or the
growth (z) direction. Figure 1.7 shows the calculated values of energy gap reduction of
strained GeSi layer and unstrained (bulk) material versus the Ge mole fraction. It shows
that, for the strained GeSi layer, the energy gap reduction AEG_Ge is almost a linear
function of the increasing Ge mole fraction xGe for xGe<~40%.
1.4 GeSi HBT Characteristics
Typical collector current and base current dependencies on VBE of GeSi HBT and Si
BJT are shown in Fig. 1.8. The collector current of GeSi HBT, Ic(GeSi), shows large
improvement over that in Si BJTs. The base current of GeSi HBT, IB(GeSi), is also
slightly smaller than that in Si BJTs. This gives a much larger common emitter forward
current gain $F of GeSi HBT compared to that in Si BJT. Figure 1.9 shows a typical
high frequency response versus collector current. Improvement by almost a factor of 2
in fT for GeSi HBT is shown. Recently, fT values as large as 116GHz or higher were
reported [20]. This improvement of fT is very important for RF wireless communication
applications. The improvement of fT is mainly due to the Ge-induced aiding electric
field for the base minority carriers which reduces the minority carrier transit time
through the base region which still is a limiting factor of fT. Other performance


37
- AEg(0) is the total Ge-induced energy gap variation through 0 aiding electric field, Ebi, for the electrons in the p-type GeSi base with a uniform boron
doping and position dependent energy gap EG(x) from the graded Ge concentration
profile is given by [37]
Ebi = (1/q)CdEc/dx) = (1/q)(AEG_Ge)/XR = independent of x. (2.7a)
= (kT/q)(p/XR), (2.7b)
where r| = AEG.Ge/kT is the normalized Ge-induced energy gap reduction through the
base.
For XR can be approximated assuming an exponential profile, NAA(x) = NAA(0)exp[-r|2(x-
Xr)/(Xb-Xr)], where r|2 = In [NAA(XR)/NAA(XB)]. The constant built-in aiding field
for XR Ebi2 =(kT/q)[t?2/(XB-XR)]. (2.8)
The LFGV methodology also uses the collector current ratio Ic(GeSi)/Ic(Si), but this
ratio is modified. The Ge-induced NCNV reduction term NcNv(GeSi)/NcNv(Si) is
lumped together with the Ge-induced energy gap reduction term AEG_Ge=(kT/q)r| where
the lumped parameter is described by a factor, rip This modification gives several
benefits. First, rij can be measured directly and accurately, while the original two
factors are not measurable. Secondly, all other GeSi HBTs parameters can be calculated
in terms of rij. This modification also enables the de-coupling of the effects of NCNV
from that of the mobility and heavy doping on Ic(GeSi).


CHAPTER 2
LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) METHODOLOGY
2.1 Introduction
In the last chapter, we presented a preliminary qualitative analysis of the GeSi HBT
and its comparison with the Si BJT. In this chapter, we describe a low-frequency-
conductance-voltage (LFGV) methodology developed in order to obtain accurate
quantitative values for the dominant minority-carrier transport parameters that underlie
the GeSi HBTs performance enhancement, such as the diffusion length, recombination
lifetime, and diffusion coefficient in the base layer. The LFGV method also gives the
analysis methodology of current gain and emitter injection efficiency based on a
separation of the total base current into the recombination losses in the emitter and base.
Thus, the LFGV method gives a complete charge-control analysis of the bipolar
transistor performance. Analytical models are developed for the LFGV method for a
trapezoidal and linearly graded Ge concentration profile in the base. However, the
LFGV method is general and can be applied to any bipolar transistor with an arbitrary
dopant impurity and material-composition profile, including those using the III-V
compound semiconductors.
Comprehensive reviews of the Si/GexSij_x/Si HBT technology, including fabrication,
Ge-induced effects in the base layer, current-voltage characteristics, modeling, and
performance comparison with Si BJT are discussed in chapter 1. Performance
28


56
Table 2.2 Summary of experimental data and calculated parameters for Si/GexSij.x/Si HBT
and reference Si BJT. The top six lines give the measured dc and BTM ac data obtained at
23C, VBE = 0.58V and VCB = IV. The computed parameters using LFGV method are
shown in the next eighteen lines. The first column is for Si/GexSi1_x/Si HBT, the second
for Si baseline BJT, and the third column gives the comparison ratio of the two previous
columns. ABE=(0.8x26)x88pm2, XR=680, XB=800.
Parameter
GeSi HBT
Si BJT
GeSi/Si
Ic (PA)
14.42
5.16
2.79
IB (nA)
161.6
173.2
0.93
Pf
89.2
29.8
3.0
g0 (i/a)
2.687xl08
4.08xl08
0.66
gr (l/Q)
3.5xlO~10
5.2xlO"10
0.67
go^gr
76.77
78.46
0.98
*12
2.2
2.2
2.5
AEG_Ge (meV)
79
Ebi (kV/cm)
12
B
15
2
7.5
Lb (pm)
1.2
0.7
1.7
Qb/tb (nA)
12
32
0.38
Qe/te (nA)
149
141
1.06
(Qe^eVCQiAb)
12
4.4
2.7
(Qe/te)/Ib (%)
92
82
1.1
(Qb/tb)/Ib (%))
8
18
0.4
Qb (C)
35xl0~18
25xl018
1.4
Db (cm2/V-s)
4
5.5
0.7
tB (Ps)
2.4
4.9
0.5
tb (ns)
2.8
0.8
3.5
Ay
0.3
AEg.hd (meV)
8
VA (V)
536
127
4.2


96
6. Reverse transconductance
Ic exp(-(XB-X0)2/ 9r =
DnTB erf ((XBX0)/er) + erf(X0/cr)
{erf (Xg/cr) jBexp[(x-X0)2/cr2]dx + jBexp[(x-X0)2/o-2)]erf[(x-X0/cj)]dx}
(B.16)


80
Table 3.2 Temperature dependence of measured parameters of GeSi HBT
T(K)
SoR^SoF
^CR^CF
Cbc(pF)
CBE(PF)
297.2
285.2
1.63
1.99
39.4
250
495.9
1.81
1.99
39.0
225
630.7
1.85
1.99
38.6
200
967.3
2.29
1.99
38.4
175
2792
3.94
1.99
38.2
150
4000
2.88
1.99
38.0
125
13,000
4.81
1.99
37.7
Note: AE= 100.4x100.8¡am2, T=297.15K, VBE=0.52V, VBC=1.0V.
The junction capacitances CBC and CBE were measured at f=lkHz.
Table 3.3 Temperature dependence of GeSi HBT parameters
calculated from the measured data in Table 3.2
T(K)
hi
(pm)
[Qb^bI^b
297.2
2.04
3.9
1.2%
250
2.60
4.3
0.9%
225
2.83
4.0
1.0%
200
3.05
3.2
1.5%
175
3.58
2.6
2.3%
150
4.25
1.8
4.4%
125
4.93
1.5
4.2%


26
n-f (x) = Nc(x)Nv(x).exp(-EG(x)/kT). (1.8)
For a linear Ge distribution using results from section (1.6), we have
Eg(x) = EG0 AEG_HD AEG_Ge(0) AEG_Ge.x/XR (1.3)
where AEG.Ge = AEG_Ge(XR) AEG.Ge(0) is the total energy gap reduction across the
quasineutral base region. AEG.HD is the energy gap reduction due to heavy doping
effect, and AEG_Ge(0) is the Ge-induced energy gap reduction at x=0 in the quasineutral
base region. Inserting equations (1.3) and (1.7) into equation (1.8), gives an analytical
expression for the intrinsic carrier concentration n¡ for a linear Ge distribution,
nf(x) = niQ 2 exp(AEG_Ge(0)/kT).exp(AEG_HD/kT) exp(x/x^, (1.9)
where ni0 is the intrinsic carrier concentration of Si
nio2 = Nc(0)Nv(0).exp(-EGO/kT) (1.10)
The constant Xj is defined as l/x1=(l/XB)[(AEG.Ge/kT)-C]. For a simplicity, we define
a=AEG_Ge(0)/kT and y=AEG.HD/kT, then equation (1.9) becomes
n2(x) = ni0 2 .expa.expy.explx/x^. (1.11)
1.8 Summary
In conclusion, the basic parameters governing the GeSi HBT performance were
discussed in this chapter, including fabrication by pseudomorphic epitaxial growth,
critical layer thickness, and electronic properties of the GeSi layer. The lattice
mismatch between the GeSi layer and the Si substrate is accommodated by the biaxial
strain in the GeSi layer. This Ge-induced strain in the GeSi layer is responsible for
changes in electronic material parameters important for HBT performance, in particular,
the energy gap, density of states, and mobility. For the Ge mole fraction xGe <~40%,


88
4.2 GeSi HBT Modeling and LFGV Methodology
The LFGV methodology is applicable to an analysis of any heterojunction bipolar
transistor (HBT), including those based on III-V materials. The LFGV methodology
uses a combination of the dc and small-signal measurements of the transistor
characteristics. The dc characteristics are the collector and base current as a function of
the emitter-base junction bias. The small-signal characteristics are the output
conductance and reverse transconductance resulting from the base thickness modulation.
They are measured at low frequency (~lkHz) to avoid parasitic capacitance and
inductance effects.
The LFGV methodology was applied for the analysis of Si/GexSi1_x/Si HBT with a
linearly-graded or trapezoidal Ge concentration profiles in the base. Analytical
expressions for the dc and small-signal parameters were developed. Important minority
carrier transport parameters, such as the base diffusion length, recombination lifetime,
diffusivity, built-in electric field, and base transit time were determined. The LFGV
methodology also allows a separation of the base current into the components
recombining in the base and emitter region, respectively.


Concentration /(cm'3)
6
Depth
Fig. 1.2 Secondary ion mass spectroscopy (SIMS) profile of GeSi HBT. The base
doping level is about 3xl018 cm'3 and the Ge mole fraction in the base is about 10%.
Adapted from Ron Tang et al. [13].
Germanium /(1%)


9
Unstrained GexSUx Strained GexSi^
Si Si
(a) Relaxed GexSUx
1
t
J
n
/
\
(
Si
Fig. 1.3 Two dimensional illustration of GeSi pseudomorphic growth, (a). Unstrained
GeSi layer and Si substrate, (b). Strained GeSi layer. The lattice mismatch is
accommodated by the strain in the GeSi layer, (c). Relaxed GeSi layer. There are
misfit dislocations at the GeSi/Si interface. Adapted from Sah [1, Fig. 774.1, p. 947],


104
[33] B. Le Tron, M.D.R. Hashim, P. Ashbum, M. Mouis, A. Chantre, and G. Vincent,
"Determination of bandgap narrowing and parasitic energy barriers in SiGe HBTs
integrated in a bipolar technology," IEEE Trans. Electron Devices, vol. 44, pp.
715-722, May 1997.
[34] P. Ashburn, H. Boussetta, M.D.R. Hashim, A. Chantre, M. Mouis, G.J. Parker,
and G. Vincent, "Electrical determination of bandgap narrowing in bipolar
transistors with epitaxial Si, Sij.xGex, and ion implanted bases," IEEE Trans.
Electron Devices, vol. 43, pp. 774-783, May 1996.
[35] J.D. Cressler, E.F. Crabbe, J.H. Comfort, J. Wamock, K.A. Jenkins, J.M.C. Stork,
and J.Y.C. Sun, "Profile Scaling constraints for ion-implanted and epitaxial
bipolar technology designed for 77k operation," IEDM, vol. 33, No.4, pp. 861-
864, 1991.
[36]D. Vook, T.I. Kamins, G. Burton. P.J. Vande Voorde, H.-H. Wang, R. Coen, J.
Lin, D.F. Pettengill, P.-K. Yu, S.J. Rosner, J.E. Turner, S.S. Laderman, H.-Su Fu,
and A.S. Wang, "Double-diffused graded SiGe-base bipolar transistor," IEEE
Trans. Electron Devices, vol. 41, pp. 1013-1018, June 1994.
[37]D.J. Roulston, and J.M. McGregor, "Effect of bandgap gradient in the base region
of SiGe heterojunction bipolar transistors," Solid-State Electronics, vol. 35, No. 7,
pp. 1019-1020, 1992.
[38]H.Kroemer, "Two integral relations pertaining to the electron transport through a
bipolar transistor with a nonuniform energy gap in the base region," Solid-State
Electron., vol. 28, No. 11, pp. 1101-1103, Nov. 1985.
[39]A. Neugroschel, "Emitter injection efficiency in heterojunction bipolar transistor,"
Solid-State Electron., vol. 30, No. 11, pp. 1171-1173, 1987.
[40]J.W. Slotboom, G. Streutker, A. Pruijmboom, D.J. Gravesteijn, "Parasitic energy
barriers in SiGe HBTs," IEEE Electron Device Lett., vol. 12, No. 9, pp. 486-488,
Sep. 1991.


81
8
6
= 4
2
O
2 4 6 8 10
1000/T /(1/1K)
Fig. 3.3 Normalized energy gap reduction parameter rj2 vs 1000/T.


43
(2.19) we neglected the space-charge region recombination components that can be
easily separated out from the measured IB. In order to separate the recombination losses
in (2.19), we need the gr measurement which results from the modulation of the base
recombination loss. For the GeSi HBT, gr is derived as
Qg X 1 dXg
gr = (2.20)
igXg Y A[(expfj^-l)//7^)]sxprj2 + (l-A)[(sxpf72-l)/fj2] ^cb ^be
In (2.20), the terms X and Y are given below
X = A2(exp^1+^1-l)//j12 +
Ad-AlCiexp^-D/rji]. [(exp^2-l)/p2] +
(l-A)2(expp2-p2-l)/n22 (2.21a)
Y = A2[exp(-r?1)+p1-l)]/p12 +
A( 1-A) [l-exp( -/7X)2. [l-exp(-rj2)]/p1p2 +
(l-A)2[exp(-p2)+n2-l]/p22. (2.21b)
When we take the ratio of gr and g0, a useful expression is obtained:
9r tB
= B (2.22)
9o tb
where tB is the base minority carrier transit time, xB is the charge-control minority
carrier base recombination lifetime, and Bisa factor related to the built-in electric field
in the base due to both Ge and doping nonuniformity (B=1.0 in field-free base). B is a
function of rij, r|2, nf(x), and hole concentration in the base P(x) and is given by (2.23)
below [39]
1
B =
iV(x)
-dx
dx
0 PB(x)
0 ni2(x)/P(x)
1
(2.23)


93
X/(1)
Fig. B.l Gaussian distribution and exponential approximation.


LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) CHARACTERIZATION
OF Si/Ge^i^/Si HETEROJUNCTION BIPOLAR TRANSISTORS
By
GUOXIN LI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1998


50
Table 2.1 Summary of experimental data and calculated parameters for Si/GexSi1_x/Si HBT
and reference Si BJT. The top six lines give the measured dc and BTM ac data obtained at
23C, VBE = 0.52V and VCB = IV. The computed parameters using LFGV method are
shown in the next eighteen lines. The first column is for Si/GexSij.x/Si HBT, the second
for Si baseline BJT, and the third column gives the comparison ratio of the two previous
columns. ABE=100.4xl00.8pm2, XR=680, XB=800.
Parameter
GeSi HBT
Si BJT
GeSi/Si
Ic (PA)
7.74
200.5
3.86
IB (nA)
59.4
69.9
0.85
Pf
130.3
28.6
4.54
go (I/O)
2.125x1o-8
1.67xl0-8
1.27
gr (1/G)
3.0xl0-11
1.8xl0-10
0.17
go^gr
708.3
92.78
7.63
^2
2.7
2.7
Bi
1.98
AEG_Ge (meV)
68.6
Ebi (kV/cm)
10
B
12.6
2.6
4.8
Lb (!im)
3.6
0.8
4.5
Qb^b (A)
0.87
8.4
0.1
Qe/te (nA)
58.5
50.6
1.16
(Qe^Wb)
67
6
11.2
(Qe/te)/Ib (%)
98.5
88
1.12
(Qb/tb)/Ib (%))
1.5
12
0.13
Qb (C)
21xl0-18
10xl0-18
2.1
Db (cm2/V*s)
5.5
5.5
1.0
tB (Ps)
2.7
4.8
0.56
tb (ns)
24
1.1
22
Ay
0.47
AEg.hd (meV)
12
VA (V)
364
120
3.0


102
[16] R. People, "Indirect band gap of coherently strained Ge^i^ bulk alloys on
<001> silicon substrates," The American Physical Society, vol. 32, No. 2, pp.
1405-1408,July. 1985.
[17] L.E. Kay and T.W. Tang, "Monte Carlo calculation of strained and unstrained
electron mobilities in GexSi(1_x) using an improved ionized-impurity model," J.
Appl. Phys., vol. 70, No. 3, pp. 1483-1488, Aug. 1991.
[18] S.K. Chun and K.L. Wang, "Effective mass and mobility of holes in strained
Sij_xGex layers on (001) Sij.yGey substrate," IEEE Trans. Electron Devices, vol
39, pp. 2153-2164, Sep. 1992.
[19]B. Pejcinovic, L.E. Kay, T.W. Tang and D.H. Navon, "Numerical Simulation and
Comparison of Si BJTS and Sij.xGex HBTs," IEEE Trans, electron Devices, vol
36, pp. 2129-2137, Oct. 1989.
[20] A. Schiippen, U. Erben, A. Gruhle, H. Kibbel, H. Schumacher and U. Kdnig,
"Enhanced SiGe heterojunction bipolar transistors with 160GHz-fmax," IEDM
1995, p. 743-746.
[21] E.J. Prinz, P.M. Garone, P.V. Schwartz, X. Xiao, and J. C. Sturm, "The effect of
base-emitter spacers and strain-dependent density of states in Si/Sij.xGex/Si
heterojunction bipolar transistors," IEDM Tech. Digest, pp. 639-642, 1989.
[22] S.C. Jain, J. Poortmans, S.S. Iyer, J.J. Loferski, J. Nijs, R. Mertens, and R. van
Overstraeten, "Electrical and optical bandgaps of GexSij_x strained layers, IEEE
Trans. Electron Devices, vol. 40, pp. 2338-2343, Dec. 1993.
[23] J.M. Early, "Effects of space-charge layer widening in junction transistors,"
Proceedings of the IRE, pp. 1401-1406, Nov. 1952.
[24] M.S. Birrittella, A. Neugroschel, and F.A. Lindholm, "Determination of the
minority-carrier base recombination lifetime of junction transistors by
measurements of basewidth-modulation conductances, IEEE Electron Device
Lett., vol. 26, pp. 1361-1363, Sep. 1979.


46
conductance, g0, reverse transconductance, gr, for both the forward active mode and
reverse active mode and the collector current Ic of Si BJT. The measured dependencies
in Figs. 3.4-3.6 are used for the LFGV analysis. The results for large square device
(100.4x100.8p,m2) are summarized in Table 2.1. A detailed discussion of the analysis
and its implications follows.
The first step in the analysis is to find the parameter r|2 using (2.27) which
determines the built-in field for XR ln[NAA(XR)/NAA(XB)] = 2.7 for both Si BJT and GeSi HBT. This corresponds to
NAa(Xr)/Naa(Xb) = 15, which agrees well with the SIMS profiles in Fig. 1.2.
With the known r|2, we can then calculate the key parameter r| j from the measured Ic
and g0 for the GeSi and Si transistors using (2.18a). This gives = 1.98, and r\ = (r^ +
C) = 2.70.1 using C = 0.70.1. The Ge-induced energy gap reduction at xGe=9.8% is
^G-Ge = (kT)r) = 705meV. This corresponds to AEg_ge = 7xGE meV which is in very
good agreement with the theoretical calculations and other experiments in GeSi as a
function of xGe. This good agreement demonstrates the accuracy of our model that
accounts for the dependence of the NCNV on Ge concentration. The value of the fitting
parameter, C, causes only small uncertainty in the results. The Ge-induced aiding
electric field within the linear Ge range, 0 The mobility ratio DB(GeSi)/DB(Si) can be evaluated from (2.15). The remaining
unknowns in (2.15) are a = AEG_Ge(0)/kT and Ay = AEE_HD/kT. SIMS profiles indicate
a = 0 at Vbe=0.52V. This gives [DB(GeSi)/DB(Si)]exp(Ay) = 1.6. This product cannot
be separated without additional independent measurement of either the mobility ratio or


85
Table 3.4 Summary of experimental data and calculated parameters for Si/GexSij_x/Si HBT
by LFGV methodology with no Si reference BJT. The top six lines give the measured dc
and BTM ac data obtained at 23C, VBE = 0.52V and VCB = IV. The computed parameters
are shown in the next sixteen lines. ABE=100.4xl00.8pm2, XR=680, XB=800.
Parameter
GeSi HBT
Ic (PA)
7.74
IB (nA)
59.4
3f
130.3
g0 (m
2.125xl0-8
gr (l/Q)
3.0xl0~n
go^gr
708.3
112
2.6
Til
2.0
AEQ_Ge (meV)
69
Ebi (kV/cm)
10
B
12
Lb (pm)
3.5
Qb^b (ttA)
0.91
Qe/te (nA)
58.5
(Qe/xe)/(Qb/t;b)
65
(Qe/te)/Ib (%)
98.5
(Qb^b)Ab (%))
1.5
Qb (C)
21xl018
Db (cm2/V-s)
5.5
tB (PS)
2.8
tb (ns)
23
VA (V)
364


77
C=0.7 is used. The aiding electric field Ebi = (kT/q)(r|/XR) = (0.0255)(2.74/680xl(T8) =
10.3kV/cm. This value compares very well to Ebi=10kV/cm which is obtained by the
comparative method discussed in chapter 2 (section 2.5) using the comparison LFGV
methodology.
In conclusion, the above example demonstrates one application of the new
measurement method, namely the measurement of the energy-gap variation due to the
compositional grading across the GeSi base. Similar results can be obtained for III-V
HBTs with graded base. The new non-reference methodology can be also used to
measure the temperature dependence of the parameter r\,. GeSi HBT shows a superior
low temperature Ic enhancement compared to Si BJT. This is because the built-in
electric field Ebi is inversely proportional to the temperature, Ebi=AEG_Ge/kT, where k is
the Boltzmann constant and AEG_Ge is the Ge-induced energy gap reduction across the
quasineutral base region. Thus, at lower temperature, the built-in electric field is greatly
enhanced. All other parameters related to Ebi will be also enhanced. For example, the
collector current Ic(GeSi) will increase, the output conductance g0(GeSi) will decrease,
and the base minority carrier transit time tB will decrease significantly which gives
higher speed and fT. Theoretical calculations of the minority mobility as a function of
temperature and doping were presented in the literature [17, 52-53]. In order to verify
these theoretical predictions and analyze the GeSi HBT performance at lower
temperature, the determination of the temperature dependence of r) j is very important.
This was investigated by measuring the GeSi HBT characteristics at several different
low temperatures. Using the models and equations given in the section 3.2, we can


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
LOW FREQUENCY CONDUCTANCE VOLTAGE (LFGV) CHARACTERISTICS
OF Si/GexSi1.x/Si HETEROJUNCTION BIPOLAR TRANSISTORS
By
Guoxin Li
December 1998
Chairman: Dr. Amost Neugroschel
Cochairman: Dr. Chih-Tang Sah
Major Department: Electrical and Computer Engineering
Low Frequency Conductance Voltage (LFGV) methodology for analysis of
heterojunction bipolar transistors (HBTs) is presented. The LFGV methodology is
based on a combined measurement of the dc collector and base currents and low
frequency (~lkHz) small-signal conductance resulting from the base thickness
modulation. It gives accurate and independent determination of the built-in electric
field resulting from the spatially varying energy gap and dopant impurity concentration
profile in the base layer. The LFGV methodology also gives accurate quantitative
values for the minority-carrier transport parameters, including the minority carrier
diffusion length and recombination lifetime, and a complete charge control analysis of
the recombination losses in the emitter and base region of the HBT.
v


ln[exp(Ay)DB(GeSi)/DB(Si)]
52
1000/T /(1/1K)
Fig. 2.6 The measured temperature dependence of ln[exp(Ay)D B(GeSi)/DB(Si)] in the
range of 200K-300K normalized to 296K in large 100.4x100.8pm2 transistor.


66
Til
Fig. 2.14 Base minority carrier charge ratio QB(GeSi)/QB(Si) vs r) j for the forward
active mode (normalized to exp(a+Ay)).


19
1.6 Energy Band Diagram
In Si/Ge^i^/Si HBT, a Ge^i^ base layer with a smaller energy gap than that of
pure Si is sandwiched between the Si emitter and collector. The energy band diagram is
very important for analysis and design optimization of the GeSi HBT. Figure 1.12, Fig.
1.13, Fig. 1.14, and Fig. 1.15 show the energy band diagrams for triangular Ge
distribution and trapezoidal Ge distribution in the base region at equilibrium (zero bias)
and forward active mode (VBE>0V, VCB<0V). Also from Fig. 1.7, we can see that for
Ge mole fraction xGe<~35%, the energy gap reduction AEG_Ge is almost a linear
function of xGe. For trapezoidal Ge distribution, we have
xGe(x) = xGe(0) + [xGe(XR) xGe(0)]x/XR (0 Eg(x) = Ego AEg_hd AEG_Ge(0) AEG_Gex/XR (0 where AEG_Ge = AEG_Ge(xR) AEG_Ge(0) (1.4)
is the total Ge-induced energy gap reduction through the base region. AEG_HD is the
energy gap reduction due to heavy doping and AEG.Ge(0) is the energy gap reduction
due to Ge at x=0 in the quasineutral base region. The Ge gradient will produce an
aiding electric field Ebi:
Ebi = (l/q)(dEc/dx) = (l/q)(AEG_Ge/XR) = independent of x
= (kT/q)(tj/xR) 0 where r) = AEG. -Ge^kT'


4. SUMMARY AND CONCLUSIONS
87
4.1 Summary 87
4.2 GeSi HBT Modeling and LFGV Methodology 88
APPENDIX A GENERAL EQUATIONS FOR B JT 89
APPENDIX B TRANSISTOR RELATION FOR A GAUSSIAN DOPANT IMPURITY
CONCENTRATION PROFILE IN THE BASE OF BJT 92
APPENDIX C LIST OF SYMBOLS 98
REFERENCES 100
BIOGRAPHICAL SKETCH 107
IV


64
Til
Fig. 2.12 Output Conductance ratio g0(GeSi)/g0(Si) vs r( j for the forward-active mode
(normalized to [DB(GeSi)/DB(Si)]exp(a+Ay)). The g0 ratio shows a rapid decrease for
1.0 GeSi HBT is much higher than that of Si B JT for large r\ t and the Early voltage VA also
increases rapidly with r) j. Thus the figure-of-merit, (3VA, improves significantly for
large r| j for the GeSi HBT.


47
Vbe/(1V)
Fig. 2.3 Ic-VBE and IB-VBE characteristics of GeSi HBT and Si BJT. The
measurements were taken on large transistors with the EB junction area of
100.4x100.8|um2 in order to eliminate the edge and sidewall effects. Note the
significant increase in Ic and slight decrease in IB for the GeSi transistor. The measured
enhancement in the collector current Ic(GeSi)/Ic(Si) = 3.86.


31
AXB
(b)
Fig. 2.1 (a) Cross-sectional view of an n+/p/n BJT. Small-signal voltage vcb is
superimposed on dc value VCB.
(b) Minority-carrier distribution in the base.


34
base layer. The second method using only the GeSi HBT without the reference Si BJT
will be discussed in chapter 3.
There are several performance enhancement gauges of GeSi HBT over Si BJT. The
most important and also most commonly used by investigators is the dc collector
current Ic enhancement [35-36], For example, for a uniform base doping and uniform
Ge concentration in the p-type base of npn transistor, the ratio of the collector currents
can be written as
Ic(GeSi) (NcNv)GeSi Dn(GeSi)
= exp(Ay) exp(AEG_Ge/kT) (2.6)
IC(Si) (NCNV)S1 Dn(Si)
where Nc, Nv are the density of states of the conduction band and valence band,
respectively, Dn is the minority-carrier electron diffusivity, AEG_Ge is the Ge-induced
energy-gap reduction in the base, and Ay = AEG_HD/kT=[AEG_HD(GeSi) -
AEG-Ho(Si)]/kT is the normalized difference between the heavy doping-induced energy
gap reduction in GeSi and Si base layers.
There are four unknowns in (2.6) all related to the Ge in the GeSi base layer. The
key issue is how to separate these Ge-induced effects. Two approaches have been
presented in the literature using the Ic ratio in (2.6) [29-32], The first approach uses the
measurement of the temperature dependence of Ic(GeSi)/Ic(Si), assuming that the
density of states and mobility ratios are temperature independent. Then by plotting the
Ic ratio versus 1/T, equation (2.6) yields an activation energy EA = AEG_Ge + AEG_HD =
AEG-Ge- This AEC,C can then be used to calculate the improvements in the current
gain, transit time, and other characteristics as a function of the Ge mole fraction and


12
z*
>
X
Emitter
f f^zz
P-GeSi base
^M-xx
Collector
Fig. 1.6 Direction illustration in vertical GexSij_x HBT. The z direction corresponds to
the growth direction and is also the direction of the minority electron flow in a vertical
BJT. The in-plane direction is important and applicable for lateral MOS transistors.


84
3.4 LFGV Analysis of GeSi HBT with no Si Reference
After the determination of r), described in the previous section, a complete charge-
control analysis of the GeSi HBT can be made. The only other parameters needed for
this analysis are r\2 which determines the built-in electric field in the region of
XR equation (2.22) is used to calculate the parameter r\2. From the measurement of the
output conductance, g0, and reverse transconductances, gr, for the forward (subscript F)
and reverse (subscript R) modes of operations and taking the ratio of equation (2.22) for
these two modes:
90f/90r tBF
. (3.10)
9rF/,9rR Br tBR
The ratio in (3.10) is a function of rj j, A=XR/XB and r\2 only. Since rjj can be
determined independently as described in section 3.2 and XR/XB is known from SIMS
or estimated from fabrication conditions, r\2 can be then calculated from (3.10). Using
the data in Table 2.1 and ^¡=2.04, we obtained r)2=2.6 which agrees very well with the
comparative method in section 2.5 which gives r\2=2.7. We assume that
DB(GeSi)=DB(Si) as determined in chapter 2. The results of a complete charge control
analysis for the GeSi HBT following the procedure described in chapter 2 are
summarized in table 3.4. Since r)j=2.04 and ri2=2.6 obtained using the non-reference
analysis are almost the same as those obtained using the comparative LFGV
methodology in section 2.5 (r)j=1.98 and r)2=2.7), the results in table 3.4 are very
similar to those in table 2.1.


33
VBE, g0 and gr are also exponential functions of VBE. Taking the ratio of equations (2.3)
and (2.4), we obtain a very important relation for the analysis of the bipolar junction
transistor [1, p. 822, 24-25]:
90 Ic Qb^b tb
= = = (2.5)
9r Qb^ t b Qb^ tb tB
where tB is the base minority carrier transit time.
In order to accurately measure the output conductance g0 and especially the reverse
transconductance gr (grg0), a precise equipment is needed. Two instruments were
used to measure g0 and gr, a manual Wayne Kerr bridge B214 and an automated IEEE
bus controlled HP7245A LCR meter. Most of the data were obtained using WK B214
because of its high conductance sensitivity (~10"12 l/£2) required for gr measurement in
bipolar transistors with high base doping where the BTM is very small.
2.3 LFGV Methodology
Two LFGV methodologies were developed. The first LFGV methodology described
in this section is based on a comparison of the transistor characteristics measured in
Si/GexSij_x/Si HBT and reference Si BJT where the difference between the measured
characteristics is due to Ge only [26-27]. By analyzing this difference, we can then
calculate the various Ge-induced material parameter changes. This approach has been
commonly used by other investigators [28-34], The basic assumption in this
comparative approach is that the two transistors have nearly identical geometry and
dopant impurity concentration profiles except the Ge incorporation in the GeSi HBT


Majority electron mobility /(cm2/V*S)
18
Fig. 1.11 Majority electron mobility pn in n-type Ge^i^ layer. The upward triangles
are in the perpendicular z direction which is also the growth direction, and the
downward triangles are in the x-y plane. Adapted from L.E. Kay and T.-W. Tang [17].


Minority electron mobility /(cm2/V*S)
17
0 0.05 0.10 0.15 0.20
Ge mole fraction /(1%)
Fig. 1.10 Minority electron mobility p,n in p-type GexSii_x layer. The upward triangles
are in the perpendicular z direction which is the growth direction and also the electron
movement direction in vertical BJT. The downward triangles are in the x-y plane.
Adapted from L.E. Kay and T.-W. Tang [17].


44
= X/Y (2.24a)
exprji-in-1
= XR = XB. (2.24b)
exp(-r?i)+/ji-l
A combination of the dc IB-VBE and small-signal measurements gives the expressions
for the base diffusion length and ratio of the recombination losses in the emitter and
base region:
Qe/te B(g0/gr)
= 1 (2.25)
Qb^ t b £f
L| = XB2(g0/gr){A2(exptj1-tj1-l)/f]12 +
A(l-A)[(exp^1-l)/ni] [(exprj2-l)/n2] +
(l-A)2(expr72-n2-l)/h22} (2.26a)
r/1+exp(-r7x)-1
Lb2 = XB2(g0/gr). XR = XB. (2.26b)
ni2
A combination of (2.19) and (2.25) gives (Qs/^oeSi ar*d (Qb/tb)s from measured
data. Using (2.26a) or (2.26b) we then calculate directly the diffusion length where the
only unknown parameter is XB which can be measured by SIMS.
Expression (2.22) is also used to calculate the parameter r|9 which determines the
built-in field for XR Measuring the output and reverse conductances for the forward (subscript F) and reverse
(subscript R) mode of operations we obtain the following ratio:
Sof/QoR Bp tgp

Br tBR
StF^OpR
(2.27)


65
Fig. 2.13 Base minority carrier distribution of GeSi F1BT and Si BJT vs x/XB for
r|1=2.0 in forward active mode (normalized to n-[exp(qVBE)-l]/NB0).


Cutoff Frequency fT /(1GHz)
15
Collector Current lc /(1mA)
Fig. 1.9 Typical unit gain frequency fT versus Ic characteristics of GeSi HBT (full
circles) and Si BJT (open circles). The GeSi HBT and Si BJT have the same dopant
impurity concentration profile and geometry except the Ge in the base for GeSi HBT.
Adapted from Merit Hong et al. [11].


4
pseudomorphic growth. In pseudomorphic growth, if the GeSi layer thickness is below
a critical thickness, the lattice mismatch is accommodated elastically with no dislocation
created. The GeSi layer is under biaxial strain both in the x-y plane and in the z or
growth direction.
Several epitaxial techniques for GeSi layer deposition were developed, such as the
molecular beam epitaxy (MBE) [9-10] and limited reaction process (LRP-CVD) [11].
Figure 1.1 shows a HBT transistor structure used in this thesis which was fabricated by
chemical vapor deposition (CVD) [11]. The single-crystal strained GeSi layer was
grown over the n-Si collector to give the intrinsic base, and also on the LOCOS Si02
layer which becomes poly-crystalline and is the extrinsic base regions. This results in
an interface between the intrinsic and extrinsic base regions. Germane is the source of
Ge during the growth and boron impurity doping was obtained with diborane. Boron
was then implanted to give the extrinsic base. The oxide/nitride layer were deposited
and etched to open the emitter region. The polysilicon layer was then deposited and
implanted by a high concentration of arsenic and patterned to form the emitter. The
impurity and GeSi concentrations were measured by SIMS (secondary ion mass
spectroscopy) as shown in Fig. 1.2. The impurity and Ge concentration profiles can be
precisely controlled during film growth to give specified Ge distribution in the base,
such as a linearly retrograded Ge gradient. This Ge gradient produces an aiding electric
field which accelerates the minority electrons in the base layer.


95
transistors with a Gaussian or Gaussian-like profile in the base with a small error
compared with accurate numerical solution.
II. Following are the equations for the Gaussian distribution P(x) shown in Fig. B.2.
1.Base dopant impurity concentration profile P(x)
P(x) = NM.exp[-(x-X0)2/cr2]
where x0 is the peak value position of the P(x) and cr is equal to
(X-Xn)2
CT2 =
ln[NM/P(XB)]
XB
r P(x)dx =
Jo
^ tt/2-ctNaa-{erf[(XB-X0)/o-] + erf(X0/cr)}
(B.9)
(B.10)
(B.11)
2. Collector current
qD^2 [exp(qVBE/kT) -1 ]
Ic = ttz (B. 12)
l^/2.(rNAA.{erf[(XB-X0)/c7] + erf(X0/cr)}
3. Minority base transit time
i ncr
tB= {erf[(XB-X0)/(j]JB exp[(x-X0)2/cj2]dx -
2Db
JB exp[(x-X0)2/CT2]erf[(x-X0)/cr]dx} (B.13)
4. Correction factor
erf(X0/cj) jBexp[(x-X0)2/cr2]dx + JBexp[(x-X0)2/cr2]erf[(x-X0)/o-]dx
B = (B. 14)
erf[(XB-X0)/cr]jBexp[(x-X0)2/(T2]dx jBexp[(x-X0)2/o-2]erf[(x-X0)/cr]dx
5. Output conductance
2IC exp[-(XB-X0)2/cr2] 0XB
g0 =
7Tcr erf[(XB-X0)/cr] + erf(X0/ (B.15)


79
Since the px product is not strongly temperature dependent [54-55], LB(GeSi)WT, or
increasing with increasing T, as shown in Fig. 3.4.
From Fig. 3.5, we can see that the base recombination component (QB/xB)GeSi/IB
increases with decreasing temperature. Thus, the base recombination becomes more
important as temperature decreases.
Table 3.1 Summary of measured parameters of GeSi HBT.
§oF
2.125xl0-8(S)
§oR
6.549xl0-6(S)
IcF
7.739 (pA)
!cr
12.45 (pA)
Cbc
1.446 (pF)
Cbe
39.676 (pF)


51
Ay. Figure 2.6 shows the measured temperature dependence of
ln[exp(Ay)D B(GeSi)/DB(Si)] in the range of 200K-300K. The temperature dependence
shows a small activation energy of EA~12meV. This is consistent with Ay = AEG.HD/kT
= 0.47 or AEg.hd = 12meV which is calculated from the measured room temperature Ic
ratio assuming a unity mobility ratio which is independent of temperature. A negligible
improvement in the minority-carrier mobility for the average ~5% Ge concentration and
~3xl018cm"3 base doping at room temperature was also predicted theoretically as is
discussed in section 1.5. The conclusion that DB(GeSi) = DB(Si) is also supported by
the s-parameter measurements of the base transit time for HBTs. Using the measured
data in Fig. 2.6, we can calculate the temperature dependence of the minority carrier
diffusivity ratio assuming that AEG_HD=12meV is constant with the temperature range
of 200K-296K. The results are shown in Fig. 2.7 and are in good agreement with
theoretical predictions [17].
The recombination components of IB are calculated from (2.19) and (2.25). The
calculation shows that the recombination losses in the emitter and base constitute 98.5
and 1.5% of IB, respectively in GeSi HBT and 88% and 12% in Si BJT. An important
self-consistency result is that (QE/TE)Gesi = (Qe/te)sp as anticipated since xGe=0 at the
EB junction and, thus, the hole injection from the base into the emitter and the emitter
recombination are expected to be the same in both transistors. The small differences
can be explained by differences in the emitter profile and recombination properties at
the n+polysilicon/n+Si emitter interface. The very significant reduction in the
recombination losses in the base, (Qb/^GcS^Qb^b^ 0.1 is due to a significantly


90
6. Output conductance g0
3IC dXg
9o
axB av,
CB
XB P(x)
dx
0 ni2(x)
7. Reverse transconductance gr
a (Qb/ tg) 8XB
8 Xr
av,
CB
l P(XB). axB

ni2(XB) avCB
(A.6)
(A.7)
8. Current gain
q
I BO
P(X)
0 Dn(x).ni2(x)
dx
where IB0 is the base saturation current.
9. Early voltage VA and (3VA product
Va =
qni2(XB)Dn(XB)
9o
JBC
P(x)
0 Dn(x) ni2(x)
dx
!bo*cbc
.n?(XB).Dn(Xg)
(A.8)
(A.9)
(A.10)
B. Equations for a trapezoidal Ge distribution and constant-exponential dopant
impurity concentration profile in the base of GeSi HBT (Fig. 2.2) obtained from the
general integral relation (A.l)-(A.IO) are given below.


83
Fig. 3.5 Base recombination component QB(GeSi)/tB(GeSi) vs 1000/T.


71
charge-control analysis of the recombination components in the base current [47]. The
new method is demonstrated for Si/Ge^i^/Si HBT with a linear or trapezoidal Ge
concentration profile in the base. The Ge-induced energy-gap reduction parameter r\ is
determined solely from the terminal measurement of GeSi HBT without any
assumptions. The built-in electric field Ebi can be then calculated, independent of the
minority carrier mobility and heavy-doping effects. The method also does not require a
knowledge of the dopant impurity concentration profile in the base.
3.2 Theory
The SIMS profile for the analyzed GeSi HBT is shown in Fig. 1.2 [48]. The Ge is
linearly graded within 0 varies as EG_Ge(x)=EG .Ge(0)-AEG.Ge(x/XR) [49-51], where EG(0) is the energy gap
magnitude at the EB junction edge of the quasineutral base, x=0, XB is the base
thickness, and AEG_Ge=AEG.Ge(XB)-AEG_Ge(0) is the total variation of the energy gap
due to the Ge gradient. This gives a spatially-constant aiding electric field for the
electrons in the p-type base in the linearly-graded region, Ebi(x) = (l/q)(AEG/XR) =
(kT/q)(ri/XR) = independent of x, where r\ is the normalized energy gap drop through
the base, r|=AEG_Ge/kT.
The collector current can be expressed for any base dopant impurity concentration
profile and compositional variation in the GeSi base as [1, p. 760, 38]
q*exp(qVBE/kT)
Jc = (3.1)
XB P(x)
dx
.0 Dn(x) -n12(x)


91
1. Collector current Ic
qDnnl02 exp(a)exp( v)exp(/71) exp(qVBE/kT)
jc=
NBoXB[(XR/XB) (exprji-1)///!+( 1-Xr/Xb) (l-exp(-^2) )//j2]
2. Minority carrier base transit time tB
Xb2
tB = Y
Dn
3. Output conductance g0
XB A(expr?1-l)/i?1)exp^2 + (l-AKexp^-l)/^
4. Reverse transconductance gr
Qb X 1
0Xr
av,
CB
axB
9r *
tbXb Y A[(exp^1-l)/^1)]expn2 + (l-A)[(exp/j2-l)/ff2] aVCB
In (A. 1.9) and (A. 1.11), the terms X and Y are given below
X = A2(exp^1+/71-l)/n12 + A(l-A)[(expHi-l)//?!.] [(exp/?2-l)/r?2] +
+ (l-A)2(expri2-ri2-l)/ri22
Y = A2[exp(-/71)+/71-l)]/r712 + A( 1-A)[1-expC-^j_)] [l-(exp-r}2)l/r¡inz+
+ (l-A)2[exp(-ri2)+ri2-l]/ii22.
5. Correction factor B
%
B = X/Y
6. PVA product
Va = XB
exp^-l expn2-l
A exprjg + (1-A)
'll
12
BO CBC
ni^ Dn(XB) expr?i
1
axB/avCB
(A.11)
(A.12)
(A.13)
(A.14)
(A.15)
(A.16)
(A.17)
(A.18)
(A.19)


54
larger base minority recombination lifetime tb ratio TB(GeSi)/TB(Si) = 24ns/l.lns = 21.
The reasons for the significant improvement of the minority-carrier recombination
lifetime in thin strained GeSi layers is not known and requires further study. The
diffusion length ratio can be calculated from (2.26) and gives LB(GeSi)/LB(Si) =
3.6pm/0.8 = 4.5 in the GeSi layer. This ratio is calculated directly from the small-signal
BTM measurements without using the dc Ib"Vbe curve. This is an advantage for HBTs
that have a large BE junction leakage or large space-charge layer recombination
component. xB was calculated taking DB=5.5cm2/s [27] for both transistors. Although
tb is relatively short (=20ns), it has only a small effect on the gain since IB in the large
100.4x100.8p,m2 transistors is dominated by the emitter. Rough estimates of tb in GeSi
HBTs were published previously [42-44], but our present measurements in large
transistors are the first rigorous accurate data.
The minority carrier base charge QB is larger in GeSi transistor, QB(GeSi)/QB(Si) =
2.1 because of smaller energy gap in the base which increases n¡2. This increase in the
stored charge should be accounted for in speed calculations. The electron transit time
across the quasineutral base layer is then calculated and gives 2.7ps/4.8ps=0.56, a factor
of about two improvement for the GeSi HBT, as expected. This is due almost entirely
to the built-in field from the graded Ge concentration profile rather than the mobility
enhancement which is negligible. The Early voltage for GeSi HBT is significantly
higher which is important for analog circuit application.
The results for a stripe transistor with narrow emitter fingers (0.8x26|im2 with 88
fingers) are summarized in Table 2.2. The major difference between large square


40
the calculation of other GeSi parameters, such as the transit time. Thus, the analysis of
the GeSi HBT with a trapezoidal or linearly-graded Ge concentration profiles can be
conveniently made in terms of a single parameter r^. It is important to note here that, as
will be shown later, the value of the fitting parameter C = (rj rjx), which is model
dependent, does not affect the determination of the base diffusion length, recombination
lifetime, transit time, or diffusivity. It only affects the calculation of the built-in electric
field Ebi and AEG_Ge, which may give a small error due to the uncertainty of the fitting
parameter C. However, this analytical approach is much more accurate than using the
spatially averaged value of NCNV in the integral equation (2.9), which allows taking
NCNV outside the integral. Another very important feature of the new expression (2.15)
is that it decouples the (NCNV) product from mobility in (2.12) and allows
determination of the mobility ratio.
In order to analyze the Ge-induced Ic enhancement, we have to separate the
measured ratio in (2.15) or (2.16) into five or four terms. A rough approximation for
practical profiles with xGe(0)=0 is to assume that the enhancement in Ic is dominated by
the built-in field which leaves only the first term in (2.16) and leads directly to the
estimation of r^. However, for an accurate analysis of the transistor and for purpose of
acquiring a material database, more accurate approach is necessary. For example, an
uncertainty in AEG_Ge(0) or AEG.HD of lOmeV gives an error of ~exp(10/25)= 1.5. Thus,
an analysis of the performance of Si/GexSi1.x/Si HBT based on measurement of Ic only
is clearly not sufficient.


29
improvements in collector current, transit time and output conductance in GeSi
transistors over those in similar Si transistors were demonstrated qualitatively and
graphically. In this chapter, we present detailed analysis based on an analytical model,
to extract reliable and accurate values of the minority-carrier parameters in the GeSi
material. These parameters are essential to assess the Ge-induced effects on transistor
performance, design optimization and to verify theoretical predictions about the
expected performance benefits due to Ge.
The key point in obtaining these quantitative values is a separation of the various Ge-
induced effects from the measured data. A lack of an experimental methodology for
this analysis is the main reason why these values are still not available in the literature.
For example, in GeSi transistors, the increase in the collector current Ic can arise from
the aiding build-in electric field in the base due to the Ge retrograded profile, the base
minority-carrier diffusivity enhancement, or both. An accurate separation of the
performance improvement between the two parameters requires independent
measurements of the built-in field and mobility. Yet another factor that affects the
collector current is the reduction of the effective density of states, Nc and Nv, which are
functions of the effective masses mn and mp, respectively. Theoretical calculations
show that the density of states product, NCNV, in thin pseudomorphic Ge^i^ layers
grown on (100) Si substrate is significantly decreased compared to that in Si due to Ge-
induced strain [17-18]. This gives (NcNv)GeSi/(NcNv)Si ~ 0.6 for GeSi layer with xGe =
5% [17-18]. The minority-carrier mobility was predicted to increase with Ge
concentration for xGe~<10% especially at higher base impurity concentration (1019


94
2. Collector current
qDnn.¡2. [exp(qVBE/kT)-l]
Ic = 7= (B.4)
^/2.crNAA.erf(XB/cr)
3. Minority carrier base transit time
\ na
tB= [erf(XB/cr) JBexp(x2/ 2.Dn
4. Output conductance
2IC exp(-Xb2/ct2) aXB
90 = -p (B.6)
i;:.<7 erf(XB/cr) aVCB
5. Reverse transconductance
Ic exp(-Xg2/cr2) aXB
gr = [JBexp(x2/cr2)erf(x/cr)dx]. (B.7)
DntB erf(XB/cr) aVCB
6. Correction factor
JBexp(x2/a2)erf(x/cr)dx
B = (B.8)
erf(XB/cr) jBexp(x2/<72)dx jBexp(x2/<72)erf(x/o-)dx
For the profile in Fig. B.l, the value for the correction factor is obtained numerically
using (B.8) which gives B=7.0. The exponential approximation gives B=6.0 using
much simpler analytical expression (A. 17). Thus, the exponential approximation of the
Gaussian profile in the base of a bipolar junction transistor gives only a small error for
the value of B. This allows a simple charge control analysis of bipolar junction
transistor using the exponential profile approximation shown in sections 2.3 for


48
Vbe /< 1V)
Fig. 2.4 The measured forward active mode and reverse active mode small-signal
output conductances, g0, reverse transconductance, gr, and the collector current, Ic, of
GeSi HBT, as a function of VBE. All measured curves show the expected exp(qVBE/kT)
dependence.
(VU)/ l


74
3.3 Experiments and Results
A high performance Si/Ge^i^/Si HBT is used to demonstrate the application of the
result in equation (3.7). The Ge concentration profile is shown schematically in Fig.
1.2. The Ge gradient from SIMS showed a linearly-graded Ge concentration from about
xGe=0% at the EB junction to a peak of about 10% at the BC junction. The base dopant
density was nearly constant at =3xl0iscm3, and the quasi-neutral base thickness was
about 800. The experimental data is tabulated in Table 3.1. All the measurements
were performed on large area 100.4x100.8ptm2 transistors to eliminate the perimeter
edge and two-dimensional effects. The difference between ICF and ICR is due to slightly
larger base thickness for the reverse mode, which is expected for very thin base. The
output conductances goF and goR, and the junction capacitances CBC and CBE were
measured at 1kHz using precise bridge WK B214.
With reference to the profile in Fig. 1.2 and the intrinsic carrier concentration model
for linear Ge concentration profile in equations (2.10), and assuming that the difference
in the intrinsic carrier density at x=0 and x=XB is due to Ge grading, we obtain from
(3.7),
n?(XB)
n?(0)
= exp?^ = exp(r? C) = exp [(AEG_Ge/kT) C],
% 90r cbc

*CR 9oF CBE
(3.8a)
(3.8b)
where C is the least squares fitting parameter for the density of states product NCNV for
linear Ge distribution discussed in detail in section 1.7. Using the data in Table 3.1 we
obtain, nf(XB)/nf(0) = 7.68 from (3.7). This gives ^=2.04 and AEG.Ge = 70meV where


Emitter
Fig. 1.1 Cross section view of GeSi HBT. Adapted from Neugroschel et al. [11-12].


REFERENCES
[1] C.-T. Sah, Fundamentals of Solid-State Electronics, River Edge, NJ and
Singapore: World Scientific, Nov. 1991. See sections 770-774 on pp. 931-954,
on history and operation principle of GeSi bipolar junction transistors.
[2] W.B.Shockley, "Circuit element utilizing semiconductive materials," U.S. Patent
2569347. Filed Jun. 26, 1948, granted Sep. 25, 1951, expired Sep. 24, 1968. (17-
year statue of limitation.)
[3] Herbert Kroemer, "Heterostructure bipolar transistors and integrated circuits, "
Proc. IEEE, vol. 70, No. 1, pp. 13-25, Jan. 1982.
[4] W.P. Dumke, J.M. Woodal, and V.L. Rideout (IBM), "GaAs-GaAsAl
heterojunction transistor for high frequency operation, Solid-State Electronics
15(12), 1339-1345, Dec. 1972.
[5] S.S. Iyer, G.L. Patton, J.M.C. Stork, B.S. Meyerson, and D.L. Harame,
"Heterojunction bipolar transistors using Si-Ge alloys, "IEEE Trans. Electron
Devices, vol. 36, pp. 2043-2064, Oct. 1989.
[6] D.L.Harame, J.H. Comfort, J.D. Cressler, E.F. Crabb, J.Y.-C. Sun, B.S.
Meyerson, and T. Tice, "Si/SiGe epitaxial-base transistors-Part I: Materials,
physics, and circuits," IEEE Trans. Electron Devices, vol. 42, pp. 455-408, Mar.
1995.
[7]D.L.Harame, J.H. Comfort, J.D. Cressler, E.F. Crabb, J.Y.-C. Sun, B.S.
Meyerson, and T. Tice, "Si/SiGe epitaxial-base transistors-Part II: Process
integration and analog applications," IEEE Trans. Electron Devices, vol. 42, pp.
469-481, Mar. 1995.
100


BIOGRAPHICAL SKETCH
Guoxin Li was born in Beijing, P.R. China, in 1964. He received the Bachelor of
Science degree in electrical engineering with high honors from the TsingHua
University, Beijing, P.R. China, in 1987 and was recommended to enter the Graduate
School of TsingHua University without any examination. He received the Master of
Science degree in electrical engineering in 1989 with high honors and was also awarded
the XinHua Prize for the outstanding graduate electrical engineering student. He will
receive the Doctor of Philosophy degree in electrical and computer engineering at the
University of Florida, Gainesville, in December 1998 under the supervision of Dr.
Amost Neugroschel and Dr. Chih-Tang Sah. His doctoral research involved advanced
GeSi HBT modeling, MOS transistor modeling and reliability. His interests are in
submicron transistor technology development and modeling.
107


23
AEG_Qe(0) AEG_Ge(XB)
Fig. 1.15 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with
a trapezoidal Ge distribution in the base region under forward active operation,
vBE>ov, VCB>0V. Fn is the quasi-Fermi level for electrons and FP is the quasi-Fermi
level for holes. Vbi is the built-in potential of the p/n junction. AEG_Ge(0) is the Ge-
induced energy gap reduction at x=0 in the quasineutral base region. AEG.Ge(XB) is the
Ge-induced energy gap reduction at x=XB in the quasineutral base region. AEG_Ge =
AEG_Ge(XB)-AEG_Ge(0) is the total Ge-induced energy gap reduction through the base
region.


CHAPTER 3
LFGV ANALYSIS OF GeSi HBT WITH NO REFERENCE Si BJT
3.1 Introduction
In the previous chapters, the performance improvements of GeSi HBT over Si BJT
are discussed and demonstrated. The LFGV methodology for accurate determination of
parameters of GeSi HBT was also developed. This methodology is based on
simultaneous measurement of GeSi HBT and Si BJT with nearly identical dopant
impurity concentration profiles such that the difference in the performance is due to Ge
only. The disadvantage of this approach is that a reference Si BJT is not always
available. Furthermore, it is very difficult to fabricate GeSi and Si transistors with
nearly identical dopant impurity concentration profiles. In this chapter, we describe
another LFGV method for GeSi HBT analysis that does not use a reference Si BJT.
One of the key parameters in the LFGV methodology is the normalized Ge-induced
energy gap reduction, r|=AEG_Ge/kT, which is due to the compositional grading of Ge in
the base. This energy gap variation produces an aiding electric field, Ebi which
significantly decreases the electron transit time through the base layer that yields higher
speed and fT [45-46], Thus, accurate and independent measurement of the r\ and the
resulting Ebi is essential for the design, optimization and analysis of GeSi HBT, and for
the verification of theoretical predictions about the expected performance benefits due
to the compositional grading. The determination of r\ is also a basis for a complete
70


57
2
3
4
5
6
7
8
1000/T /(1/1K)
Fig. 2.8 The measured temperature dependence of ln[exp(Ay).DB(GeSi)/DB(Si)] in the
range of 150K-300K normalized to 296K for stripe transistor. Least squares fit to the
data is shown by the solid line and gives an activation energy of
Ea = AEg.hd = 80.2meV.


30
cm"3) and at low temperatures (~77K) [17]. But, the mobility enhancement has not yet
been experimentally confirmed in fabricated GeSi HBTs. The built-in electric field and
higher minority carrier mobility increases the collector current Ic and current gain |3F,
but this is compensated by the decrease in the density of states. Thus, a methodology to
separate these Ge-induced effects is the key to a comprehensive quantitative analysis of
the Si/GexSij.x/Si HBT.
In this work, we present the LFGV methodology for a complete charge-control
analysis of HBTs, including a quantitative comparison with Si reference transistors, and
an experimental demonstration giving the first quantitative measurements of the built-in
electric field and minority-carrier recombination lifetime in the GeSi base.
2.2 Base Thickness Modulation (BTM)
Low-frequency-conductance-voltage (LFGV) methodology is based on the
combination of the dc Ic_VBE and ^b'^be measurements with the low-frequency
(~lkHz) small-signal conductance measurements resulting from the base thickness
modulation [23-24], The base thickness modulation (BTM) effect is illustrated in Fig.
2.1 for a Si BJT. The collector current Ic is proportional to the gradient of the base
minority carrier distribution in the base layer at a certain forward bias emitter-base
voltage VBE and reverse bias collector-base voltage VCB. When a small-signal voltage
vcb is superimposed upon the dc base-collector junction voltage VCB, the quasineutral
base thickness XB will be modulated by AXB, as shown in Fig. 2.1. The shadowed area
in Fig. 2.1(b) shows the change in the minority carrier distribution in the quasineutral
base due to the base thickness modulation, and the base minority carrier charge QB


59
Fig. 2.9 Sensitivity of r), to XR/XB calculated from (2.18a) with r\2 as a variable
parameter.


ACKNOWLEDGEMENTS
I would like to thank my supervising professors Dr. Arnost Neugroschel and Dr.
Chih-Tang Sah for their guidance during my doctoral research. I would also like to
thank Dr. Peter Zory, Dr. Vladimir Rakov and Dr. Mark Orazem for serving on my
supervisory committee. I also thank Jin Cai, Wan-Peng Cao, Derek Martin, and Yi
Wang for helpful discussions.
11


22
Ec
Ev
AEG_Ge(0) AEG_Ge(XB)
P-GeSi
Base
0 XR XB
E
F
Fig. 1.14 Energy band diagram of GeSi HBT (dashed line) and Si BJT (solid line) with
a trapezoidal Ge distribution in the base region at equilibrium (zero bias). EF is the
Fermi level at equilibrium. AEG.Ge(0) is the Ge-induced energy gap reduction at x=0 in
the quasineutral base region. AEG_Ge(XB) is the Ge-induced energy gap reduction at
x=XB in the quasineutral base region. AEG_Ge = AEG_Ge(XB) AEG_Ge(0) is the total Ge-
induced energy gap reduction through the base region.


73
9oR !cR ni2^XB) CBE
= . (3.6)
90F JCF ni2(0) CBC
From (3.6) we obtain the ratio of the intrinsic carrier concentrations at the two edges
of the quasineutral base layer which is given below in (3.7)
ni2(XB^ % 90R CBC
= (3.7a)
n?(0) JCR 90f cbe
Nc(Xb)Nv(Xb)
= exp(AEG_ge/kT). (3.7b)
Nc(0)Nv(0)
The result in equation (3.7) is completely general and applies to any HBT or BJT
with any compositional grading and dopant impurity concentration profile, including
m-V HBTs.
Equation (3.7) uses no assumptions about the material composition or impurity
doping in the base and gives the ratio of the intrinsic carrier concentrations at the two
edges of the quasineutral base layer directly from the measured collector current, output
conductance, and junction capacitances for any HBT or BJT. The approximation using
the average base diffusivity in (3.2) does not affect the ratio in (3.7), since the integral
relation for DB is the same for the forward-active and reverse-active operation modes.
One possible application of the result in (3.7) is measurement of the energy gap in
GeSi as a function of Ge concentration using test structures with different Ge linearly-
graded profiles as shown in Fig. 3.1. Equation (3.7) can be also used to measure the
intrinsic carrier concentration ratio due to heavy-doping-induced energy gap reduction
using structures with a high-low dopant impurity concentration profiles as shown in Fig.
3.2.