Large-signal modeling results of SiGe HBTs with HICUM (High Current Transistor Model)are presented.Moreover,a new and robust method to determine the substrate network elements of bipolar transistors from S-parameter measurements is proposed in this work.The investigated substrate network is compatible with HICUM and includes the substrate- collector depletion capacitance,substrate resistance and capacitance

Basaran, U.

Berroth, M.

English

AMS Acta

   Abstract—Large-signal modeling results of SiGe HBTs with HICUM (High Current Transistor Model) are presented. Moreover, a new and robust method to determine the substrate network elements of bipolar transistors from S-parameter measurements is proposed in this work. The investigated substrate network is compatible with HICUM and includes the substrate-collector depletion capacitance, substrate resistance and capacitance. I. INTRODUCTION ITH the introduction of SiGe into the base, bipolar                            transistors have achieved a tremendous improvement in their operating frequencies and current gain. As a consequence of this improvement and reduced transistor dimensions, the demands for more accurate and broadband transistor models can only be met with more complicated and up-to-date transistor models which cover a wide frequency and bias range. The parasitic effects associated with the isolation layers, the substrate and the distributed characteristics of the base-emitter and base-collector junctions are taken into account in HICUM (High Current Transistor Model) improving the modeling of the RF transistor operation up to our upper measurement frequency limit, 40 GHz. A detailed description of the outstanding features of HICUM can be found in [1].  This paper is organized as follows. In the second section DC and RF modeling and measurement results of a SiGe HBT (Heterojunction Bipolar Transistor) will be presented. The modeling accuracy will be discussed by means of the high frequency linear and nonlinear measurements besides the conventional DC measurements. In the third section, a new substrate network extraction method will be introduced and its compatibility with HICUM will be investigated. The substrate network consists of the substrate-collector depletion capacitance, the substrate resistance due to the resistivity, and the substrate capacitance due to the permittivity of the substrate. The analytically derived equations enable a fast and accurate extraction of the substrate network elements from simple S-parameter measurements. The parameter extraction of the substrate network takes place in different frequency regions, since each substrate network element governs the high frequency output admittance of the transistor in a certain frequency range. )1222 Y+Re(Y  falls off with increasing frequency owing to the existence of the substrate capacitance subC  connected parallel to the substrate resistance subR . From this fall-off subC  can be analytically obtained. This phenomenon will be explained in detail in Section III.     II. DC AND RF MODELING AND MEASUREMENT RESULTS The device under test is a SiGe HBT from AMI Semiconductor with an emitter length of 9.4 mP  in common-emitter configuration. All the devices have a single emitter finger and a grounded substrate contact. DC characteristics of the transistor were measured using an Agilent 4155 Semiconductor Parameter Analyzer and the S-parameters were measured using an HP 8510 Network Analyzer. The high frequency nonlinear and noise characteristics of the transistor were measured using an HP 70820 Microwave Transition Analyzer and an HP 8970 in conjunction with a mechanical tuner  to adjust the source reflection coefficient seen by the transistor, respectively. The DC measurement and modeling results can be viewed in Fig. 1. The weighting factors available as model parameters have been optimized to model the base-width modulation  accurately. Large-Signal Modeling of SiGe HBTs Including a New Substrate Network Extraction Method  Umut Basaran, Manfred Berroth                                                   Institute of Electrical and Optical Communication Engineering, University of Stuttgart,  Pfaffenwaldring 47, 70327, Stuttgart, Germany                                        Tel : 49 711 685 7918 / Fax : 49 711 685 7900 / E-mail : basaran@int.uni-stuttgart.de W Fig. 1.  Measured and simulated DC characteristics of the SiGe HBT9.4eL  mP11th GAAS Symposium - Munich 2003 437  Fig. 2. Simulated (with pads) and measured large-signal characteristics of the SiGe HBT The large-signal measurement and simulation results performed for a fundamental tone of 2 GHz are illustrated in Fig. 2. inP  denotes the RF power at the transistor input.  The fundamental tone can be accurately predicted whereas the measured third harmonic tends to deviate from the simulated curve for small input powers which is attributed to the limited dynamic range of the transition analyzer.  To take into account the parasitics associated with the contact pads, the transistor model has been extended by the equivalent circuit of the contact pads as can be seen Fig. 3. The base-collector coupling capacitance pbcC  has a negligible effect on the large-signal simulation results of the investigated transistor.      The measured and simulated S-parameters for a typical operating point ( 1.5CV  V  and 0.18CJ  2/mA mP ), where the collector current density has been optimized for a low minimum noise figure, are shown in Fig. 4. The measured S-parameters have been de-embedded using the two-step de-embedding method with open and short test structures [2]. This de-embedding procedure shifts the measurement reference planes from the GSG on-wafer probe tips to the actual transistor reference planes. Noise parameters of our reference transistor with an emitter length of 9.4 mP  have been measured at 5 GHz with a mechanical tuner using the Cold-Source Technique [3]. Fig. 5 shows the associated gain and the measured and simulated minimum noise figure at different biases. The model predicts the minimum noise figure of the transistor at low current densities in Fig. 5  accurately whereas the agreement between the measurement and the simulation has been found to be slightly degraded at higher current densities. This is attributed for the time being to the interaction of the second stage noise contribution of the noise parameter measurement setup due to a lower transistor gain and a slight deviation of the extracted parameter values  describing the high current operation [4] of the transistor from their physically correct values. Fig. 4. Measured and simulated S-parameters of the SiGe HBT with an emitter length of 4.9 mP  ( 40-1=freq GHz ).  define bjtnpn (C B E S )  ;input parasitics  C:Cox1 B o1 C=112E-015 R:Rsub1 o1 E  R=93  C:Csub1 o1 E  C=30E-015 ;output parasitics  C:Cox2 C o1 C=116E-015 R:Rsub2 o2 E  R=90  C:Csub2 o2 E  C=43E-015 ;base-collector coupling  C:Cpbc B C C=2.2E-015  MAIN:HICUM C B E S 0   model MAIN HICUM  \  ………  end bjtnpn CpbcCox1 Cox2Rsub1 Rsub2 Csub2Csub1Fig. 3. Equivalent circuit of the contact pads used for large-signal simulations. This circuit has been implemented using the hpeesof simulator in ICCAP of Agilent.   o2 o1 11th GAAS Symposium - Munich 2003438  The thermal noise contribution and the power loss due to the contact pads add to the measured minimum noise figure of the transistor and therefore have been subtracted from the noise correlation matrix of the transistor using the noise and electrical transformation matrices [5], [6]   *min2min1221 | |2n n optAn opt n optFR R YC kTF R Y R Y                 (1)  where AC  is the noise correlation matrix and minF , optY  and nR  are the measured noise parameters.  III. SUBSTRATENETWORK    In Fig. 6, the equivalent circuit of the transistor under the cutoff operation is illustrated. With the substrate node being connected to the ground, the substrate-collector depletion capacitance becomes a function of only the applied collector voltage and can be generally expressed as                                01scscsc mscscCCVV I     .                           (2)    scC  and subR  can be calculated by                      22 12Im( ) /scC Y Y Z                                  (3)                     222 12 22 12Re( ) / Im( )subR Y Y Y Y               (4)  provided that 2 2 2( )sub sc subG C CZ!!  .    Having determined scC  and subR , subC  can be calculated by                   2 2222 122( )Re( ) ( )sub sc scsubsub sc scG C V GY YC C VZZ             (5)  where 1/sub subG R . The substrate-collector capacitance scC  has been written in (5) as a function of scV  to emphasize the bias-dependence of scC . B CECbc(Vbc)RbRsub CsubCbe(Vbe)Csc(Vsc)Fig. 6. Equivalent circuit of the npn-transistor under the cutoff operation with the substrate connected to the ground 17.0 Fig. 5. Measured and simulated minimum noise figure and associated gain at 5 GHz 9.4eL  mP  Fig. 7. Calculated (solid line) and measured (shapes) scC  versus collector voltage for three transistor lengths ( 0.5bV   V , 1.9freq  GHz  9.4eL  2mP    19eL  2mP 38.2eL  2mPFig. 8. Extracted substrate resistance subR  for three transistor emitter dimensions ( bV   0.5 V , cV  varied between 2  and 1.5 V ). 11th GAAS Symposium - Munich 2003 439     As a result, subC  is extracted in the highest frequency range where (5) has somewhat a flat frequency response.  This lies in the fact that the influence of subC  on                2 222 12 2 2 2Re( ) ( )sc subsub sc subC GY YG C CZZ                (6)  becomes critical due to an increase in the denominator of (6) with increasing frequency from which (5) is derived. The accuracy of the method can be verified by comparing the simulated and measured 22Y  of the transistor in the forward-active mode. The HICUM model     yields good results up to 40 GHz  as shown in Figures 10a and 10b.  TABLE I EXTRACTED SUBSTRATE RESISTANCE AND CAPACITANCE VALUES FOR THREE TRANSISTOR GEOMETRIES Emitter Length    9.4 mP            19 mP           38.2 mP         subR                   83 :               52 :               30 :         subC                   17 fF             32 fF              56 fF  IV. CONCLUSIONS DC and RF modeling results of SiGe HBTs with HICUM (High Current Transistor Model) have been presented. The model accuracy has been verified by DC, S-parameter and noise parameter measurements. Moreover, a new analytical direct extraction method to determine the substrate network parameters has been presented. The suggested extraction procedure has been successfully applied to the HICUM model. The investigated substrate network can accurately model the substrate effects up to 40 GHz and takes into account both resistive and dielectric behavior of the substrate.  ACKNOWLEDGMENTS The authors wish to thank the modeling group of Alcatel HCAD Department Stuttgart and AMIS (AMI Semiconductor) Belgium for their support in this work. REFERENCES [1] Michael Schröter, “Staying Current with HICUM”, IEEE Circuits and Devices Magazine, May 2002 [2] Koolen, M.C.A.M., Geelen J.A.M., Versleijen, M.P.J.G., “ An improved de-embedding technique for on-wafer high-frequency characterization”, Bipolar Circuits and Technology Meeting, 1991, Sept. 1991, pp. 188 -191 [3] V. Adamian and A. Uhlir, “A Novel Procedure for Receiver Noise Characterization”, IEEE Trans. Instrum. Meas., Vol. IM-22, pp. 181-182, June 1973. [4] Michael Schröter, “HICUM, A Scalable Physics-Based Compact Bipolar Transistor Model”, Description of Model Version 2.1, December, 2000  [5] Hillbrand, H.; Russer, P., “An efficient method for computer aided noise analysis of linear amplifier networks”, IEEE Transactions on Circuits and Systems, Volume: 23 Issue: 4 , Apr. 1976, pp. 235 -238 [6] G. D. Vendelin, A. M. Pavio, “Microwave Circuit Design Using Linear and Nonlinear Techniques”, John-Wiley & Sons Inc., 1990     Figure 9. Extracted substrate capacitance subC  for three transistor dimensions (  bV 0.5 V , cV  varied between 2  and 1.5 V ). 9.4eL  2mP  19eL  2mP  38.2eL  2mP                                            (a)                                       (b)  Figure 10.  Measured and modeled (a) real and (b) imaginary part of 22Y  for collector voltages between 0.5  and 1.5 V   up to 40 GHz. 9.4eL  mP  9.4eL  mP  11th GAAS Symposium - Munich 2003440

Large-Signal Modeling of SiGe HBTs Including a New Substrate Network Extraction Method W

 
 
 
Abstract—Large-signal modeling results of SiGe HBTs 
with HICUM (High Current Transistor Model) are 
presented. Moreover, a new and robust method to 
determine the substrate network elements of bipolar 
transistors from S-parameter measurements is proposed 
in this work. The investigated substrate network is 
compatible with HICUM and includes the substrate-
collector depletion capacitance, substrate resistance and 
capacitance. 
I. INTRODUCTION 
ITH the introduction of SiGe into the base, bipolar                            
transistors have achieved a tremendous 
improvement in their operating frequencies and current 
gain. As a consequence of this improvement and 
reduced transistor dimensions, the demands for more 
accurate and broadband transistor models can only be 
met with more complicated and up-to-date transistor 
models which cover a wide frequency and bias range. 
The parasitic effects associated with the isolation layers, 
the substrate and the distributed characteristics of the 
base-emitter and base-collector junctions are taken into 
account in HICUM (High Current Transistor Model) 
improving the modeling of the RF transistor operation up 
to our upper measurement frequency limit, 40 GHz. A 
detailed description of the outstanding features of 
HICUM can be found in [1].  
This paper is organized as follows. In the second 
section DC and RF modeling and measurement results 
of a SiGe HBT (Heterojunction Bipolar Transistor) will be 
presented. The modeling accuracy will be discussed by 
means of the high frequency linear and nonlinear 
measurements besides the conventional DC 
measurements. In the third section, a new substrate 
network extraction method will be introduced and its 
compatibility with HICUM will be investigated. The 
substrate network consists of the substrate-collector 
depletion capacitance, the substrate resistance due to 
the resistivity, and the substrate capacitance due to the 
permittivity of the substrate. The analytically derived 
equations enable a fast and accurate extraction of the 
substrate network elements from simple S-parameter 
measurements. The parameter extraction of the 
substrate network takes place in different frequency 
regions, since each substrate network element governs 
the high frequency output admittance of the transistor in 
a certain frequency range. )1222 Y+Re(Y  falls off with 
increasing frequency owing to the existence of the 
substrate capacitance subC  connected parallel to the 
substrate resistance 
subR . From this fall-off subC  can be 
analytically obtained. This phenomenon will be explained 
in detail in Section III.    
 
II. DC AND RF MODELING AND MEASUREMENT RESULTS 
The device under test is a SiGe HBT from AMI 
Semiconductor with an emitter length of 9.4 m  in 
common-emitter configuration. All the devices have a 
single emitter finger and a grounded substrate contact. 
DC characteristics of the transistor were measured using 
an Agilent 4155 Semiconductor Parameter Analyzer and 
the S-parameters were measured using an HP 8510 
Network Analyzer. The high frequency nonlinear and 
noise characteristics of the transistor were measured 
using an HP 70820 Microwave Transition Analyzer and 
an HP 8970 in conjunction with a mechanical tuner  to 
adjust the source reflection coefficient seen by the 
transistor, respectively. The DC measurement and 
modeling results can be viewed in Fig. 1. The weighting 
factors available as model parameters have been 
optimized to model the base-width modulation  
accurately. 
Large-Signal Modeling of SiGe HBTs Including a 
New Substrate Network Extraction Method 
 Umut Basaran, Manfred Berroth                                                   
Institute of Electrical and Optical Communication Engineering, University of Stuttgart,  
Pfaffenwaldring 47, 70327, Stuttgart, Germany                                        
Tel : 49 711 685 7918 / Fax : 49 711 685 7900 / E-mail : basaran@int.uni-stuttgart.de 
W 
Fig. 1.  Measured and simulated DC characteristics of the SiGe HBT
9.4eL m
11th GAAS Symposium - Munich 2003 437
 
 
Fig. 2. Simulated (with pads) and measured large-signal 
characteristics of the SiGe HBT 
The large-signal measurement and simulation results 
performed for a fundamental tone of 2 GHz are 
illustrated in Fig. 2. inP  denotes the RF power at the 
transistor input.  The fundamental tone can be accurately 
predicted whereas the measured third harmonic tends to 
deviate from the simulated curve for small input powers 
which is attributed to the limited dynamic range of the 
transition analyzer.  
To take into account the parasitics associated with the 
contact pads, the transistor model has been extended by 
the equivalent circuit of the contact pads as can be seen 
Fig. 3. The base-collector coupling capacitance pbcC  has 
a negligible effect on the large-signal simulation results 
of the investigated transistor.  
 
 
 
 
The measured and simulated S-parameters for a 
typical operating point ( 1.5CV V  and 
0.18CJ
2/mA m ), where the collector current density 
has been optimized for a low minimum noise figure, are 
shown in Fig. 4. The measured S-parameters have been 
de-embedded using the two-step de-embedding method 
with open and short test structures [2]. This de-
embedding procedure shifts the measurement reference 
planes from the GSG on-wafer probe tips to the actual 
transistor reference planes. 
Noise parameters of our reference transistor with an 
emitter length of 9.4 m  have been measured at 5 GHz 
with a mechanical tuner using the Cold-Source 
Technique [3]. Fig. 5 shows the associated gain and the 
measured and simulated minimum noise figure at 
different biases. The model predicts the minimum noise 
figure of the transistor at low current densities in Fig. 5  
accurately whereas the agreement between the 
measurement and the simulation has been found to be 
slightly degraded at higher current densities. This is 
attributed for the time being to the interaction of the 
second stage noise contribution of the noise parameter 
measurement setup due to a lower transistor gain and a 
slight deviation of the extracted parameter values  
describing the high current operation [4] of the transistor 
from their physically correct values. 
Fig. 4. Measured and simulated S-parameters of the SiGe HBT 
with an emitter length of 4.9 m  ( 40-1=freq GHz ). 
 define bjtnpn (C B E S ) 
 ;input parasitics 
 C:Cox1 B o1 C=112E-015
 R:Rsub1 o1 E  R=93 
 C:Csub1 o1 E  C=30E-015
 ;output parasitics 
 C:Cox2 C o1 C=116E-015
 R:Rsub2 o2 E  R=90 
 C:Csub2 o2 E  C=43E-015
 ;base-collector coupling 
 C:Cpbc B C C=2.2E-015 
 MAIN:HICUM C B E S 0  
 model MAIN HICUM  \ 
 ……… 
 end bjtnpn 
Cpbc
Cox1 Cox2
Rsub1 Rsub2 Csub2Csub1
Fig. 3. Equivalent circuit of the contact pads used for large-signal 
simulations. This circuit has been implemented using the hpeesof 
simulator in ICCAP of Agilent.  
 
o2 o1 
11th GAAS Symposium - Munich 2003438
 
 
The thermal noise contribution and the power loss due 
to the contact pads add to the measured minimum noise 
figure of the transistor and therefore have been 
subtracted from the noise correlation matrix of the 
transistor using the noise and electrical transformation 
matrices [5], [6]  
 
*min
2min
1
2
2
1
| |
2
n n opt
A
n opt n opt
F
R R Y
C kT
F
R Y R Y
 
 
 
 
 
 
          (1) 
 
where AC  is the noise correlation matrix and minF , optY  
and nR  are the measured noise parameters. 
 
III. SUBSTRATENETWORK 
 
 
 
In Fig. 6, the equivalent circuit of the transistor under 
the cutoff operation is illustrated. With the substrate node 
being connected to the ground, the substrate-collector 
depletion capacitance becomes a function of only the 
applied collector voltage and can be generally expressed 
as 
 
                              0
1
sc
sc
sc m
sc
sc
C
C
V
V
 
 
 
 
.                           (2) 
 
 
 
scC  and subR  can be calculated by 
 
                    22 12Im( ) /scC Y Y                                 (3) 
                   
2
22 12 22 12
Re( ) / Im( )
sub
R Y Y Y Y             (4) 
 
provided that 2 2 2( )
sub sc sub
G C C . 
 
 
 
Having determined scC  and subR , subC  can be 
calculated by 
 
                 
2 2
2
22 12
2
( )
Re( )
( )
sub sc sc
sub
sub sc sc
G C V
G
Y Y
C C V            (5) 
 
where 1/sub subG R . The substrate-collector capacitance 
scC  has been written in (5) as a function of scV  to 
emphasize the bias-dependence of scC . 
B C
E
Cbc(Vbc)Rb
Rsub Csub
Cbe(Vbe)
Csc(Vsc)
Fig. 6. Equivalent circuit of the npn-transistor under the cutoff 
operation with the substrate connected to the ground 
17.0 
Fig. 5. Measured and simulated minimum noise figure and 
associated gain at 5 GHz 
9.4
e
L m  
Fig. 7. Calculated (solid line) and measured (shapes) 
sc
C  versus 
collector voltage for three transistor lengths ( 0.5bV V , 
1.9freq GHz  
9.4eL
2m  
 
 
19eL
2m 
38.2eL
2m
Fig. 8. Extracted substrate resistance 
subR  for three transistor 
emitter dimensions (
bV 0.5 V , cV  varied between 2  and 
1.5 V ). 
11th GAAS Symposium - Munich 2003 439
 
 
 
 
 
As a result, subC  is extracted in the highest frequency 
range where (5) has somewhat a flat frequency 
response.  This lies in the fact that the influence of subC  
on  
 
             
2 2
22 12 2 2 2
Re( )
( )
sc sub
sub sc sub
C G
Y Y
G C C
             (6) 
 
becomes critical due to an increase in the denominator 
of (6) with increasing frequency from which (5) is 
derived. The accuracy of the method can be verified by 
comparing the simulated and measured 
22Y  of the 
transistor in the forward-active mode. The HICUM model  
 
 
 
yields good results up to 40 GHz  as shown in Figures 
10a and 10b. 
 
TABLE I 
EXTRACTED SUBSTRATE RESISTANCE AND CAPACITANCE VALUES FOR 
THREE TRANSISTOR GEOMETRIES 
Emitter Length 
   9.4 m            19 m           38.2 m  
 
      
subR                   83               52               30  
 
      
subC                   17 fF             32 fF              56 fF  
IV. CONCLUSIONS 
DC and RF modeling results of SiGe HBTs with 
HICUM (High Current Transistor Model) have been 
presented. The model accuracy has been verified by DC, 
S-parameter and noise parameter measurements. 
Moreover, a new analytical direct extraction method to 
determine the substrate network parameters has been 
presented. The suggested extraction procedure has 
been successfully applied to the HICUM model. The 
investigated substrate network can accurately model the 
substrate effects up to 40 GHz and takes into account 
both resistive and dielectric behavior of the substrate.  
ACKNOWLEDGMENTS 
The authors wish to thank the modeling group of 
Alcatel HCAD Department Stuttgart and AMIS (AMI 
Semiconductor) Belgium for their support in this work. 
REFERENCES 
[1] Michael Schröter, “Staying Current with HICUM”, 
IEEE Circuits and Devices Magazine, May 2002 
[2] Koolen, M.C.A.M., Geelen J.A.M., Versleijen, 
M.P.J.G., “ An improved de-embedding technique for 
on-wafer high-frequency characterization”, Bipolar 
Circuits and Technology Meeting, 1991, Sept. 1991, 
pp. 188 -191 
[3] V. Adamian and A. Uhlir, “A Novel Procedure for 
Receiver Noise Characterization”, IEEE Trans. 
Instrum. Meas., Vol. IM-22, pp. 181-182, June 1973. 
[4] Michael Schröter, “HICUM, A Scalable Physics-
Based Compact Bipolar Transistor Model”, 
Description of Model Version 2.1, December, 2000  
[5] Hillbrand, H.; Russer, P., “An efficient method for 
computer aided noise analysis of linear amplifier 
networks”, IEEE Transactions on Circuits and 
Systems, Volume: 23 Issue: 4 , Apr. 1976, pp. 235 -
238 
[6] G. D. Vendelin, A. M. Pavio, “Microwave Circuit 
Design Using Linear and Nonlinear Techniques”, 
John-Wiley & Sons Inc., 1990   
 
 
Figure 9. Extracted substrate capacitance 
subC  for three transistor 
dimensions ( bV 0.5 V , cV  varied between 2  and 1.5 V ). 
9.4eL
2m  
19eL
2m  
38.2eL
2m   
 
 
                                       (a) 
                                      (b) 
 Figure 10.  Measured and modeled (a) real and (b) imaginary part of 
22Y  for collector voltages between 0.5  and 1.5 V   up to 40 GHz. 
9.4
e
L m  
9.4eL m  
11th GAAS Symposium - Munich 2003440


AMS Acta - Alm@DL - Università di Bologna

 
 
 
Abstract—Large-signal modeling results of SiGe HBTs 
with HICUM (High Current Transistor Model) are 
presented. Moreover, a new and robust method to 
determine the substrate network elements of bipolar 
transistors from S-parameter measurements is proposed 
in this work. The investigated substrate network is 
compatible with HICUM and includes the substrate-
collector depletion capacitance, substrate resistance and 
capacitance. 
I. INTRODUCTION 
ITH the introduction of SiGe into the base, bipolar                            
transistors have achieved a tremendous 
improvement in their operating frequencies and current 
gain. As a consequence of this improvement and 
reduced transistor dimensions, the demands for more 
accurate and broadband transistor models can only be 
met with more complicated and up-to-date transistor 
models which cover a wide frequency and bias range. 
The parasitic effects associated with the isolation layers, 
the substrate and the distributed characteristics of the 
base-emitter and base-collector junctions are taken into 
account in HICUM (High Current Transistor Model) 
improving the modeling of the RF transistor operation up 
to our upper measurement frequency limit, 40 GHz. A 
detailed description of the outstanding features of 
HICUM can be found in [1].  
This paper is organized as follows. In the second 
section DC and RF modeling and measurement results 
of a SiGe HBT (Heterojunction Bipolar Transistor) will be 
presented. The modeling accuracy will be discussed by 
means of the high frequency linear and nonlinear 
measurements besides the conventional DC 
measurements. In the third section, a new substrate 
network extraction method will be introduced and its 
compatibility with HICUM will be investigated. The 
substrate network consists of the substrate-collector 
depletion capacitance, the substrate resistance due to 
the resistivity, and the substrate capacitance due to the 
permittivity of the substrate. The analytically derived 
equations enable a fast and accurate extraction of the 
substrate network elements from simple S-parameter 
measurements. The parameter extraction of the 
substrate network takes place in different frequency 
regions, since each substrate network element governs 
the high frequency output admittance of the transistor in 
a certain frequency range. )1222 Y+Re(Y  falls off with 
increasing frequency owing to the existence of the 
substrate capacitance subC  connected parallel to the 
substrate resistance subR . From this fall-off subC  can be 
analytically obtained. This phenomenon will be explained 
in detail in Section III.    
 
II. DC AND RF MODELING AND MEASUREMENT RESULTS 
The device under test is a SiGe HBT from AMI 
Semiconductor with an emitter length of 9.4 m?  in 
common-emitter configuration. All the devices have a 
single emitter finger and a grounded substrate contact. 
DC characteristics of the transistor were measured using 
an Agilent 4155 Semiconductor Parameter Analyzer and 
the S-parameters were measured using an HP 8510 
Network Analyzer. The high frequency nonlinear and 
noise characteristics of the transistor were measured 
using an HP 70820 Microwave Transition Analyzer and 
an HP 8970 in conjunction with a mechanical tuner  to 
adjust the source reflection coefficient seen by the 
transistor, respectively. The DC measurement and 
modeling results can be viewed in Fig. 1. The weighting 
factors available as model parameters have been 
optimized to model the base-width modulation  
accurately. 
Large-Signal Modeling of SiGe HBTs Including a 
New Substrate Network Extraction Method 
 Umut Basaran, Manfred Berroth                                                   
Institute of Electrical and Optical Communication Engineering, University of Stuttgart,  
Pfaffenwaldring 47, 70327, Stuttgart, Germany                                        
Tel : 49 711 685 7918 / Fax : 49 711 685 7900 / E-mail : basaran@int.uni-stuttgart.de 
W 
Fig. 1.  Measured and simulated DC characteristics of the SiGe HBT
9.4eL ? m?
11th GAAS Symposium - Munich 2003 437
 
 
Fig. 2. Simulated (with pads) and measured large-signal 
characteristics of the SiGe HBT 
The large-signal measurement and simulation results 
performed for a fundamental tone of 2 GHz are 
illustrated in Fig. 2. inP  denotes the RF power at the 
transistor input.  The fundamental tone can be accurately 
predicted whereas the measured third harmonic tends to 
deviate from the simulated curve for small input powers 
which is attributed to the limited dynamic range of the 
transition analyzer.  
To take into account the parasitics associated with the 
contact pads, the transistor model has been extended by 
the equivalent circuit of the contact pads as can be seen 
Fig. 3. The base-collector coupling capacitance pbcC  has 
a negligible effect on the large-signal simulation results 
of the investigated transistor.  
 
 
 
 
The measured and simulated S-parameters for a 
typical operating point ( 1.5CV ? V  and 
0.18CJ ? 2/mA m? ), where the collector current density 
has been optimized for a low minimum noise figure, are 
shown in Fig. 4. The measured S-parameters have been 
de-embedded using the two-step de-embedding method 
with open and short test structures [2]. This de-
embedding procedure shifts the measurement reference 
planes from the GSG on-wafer probe tips to the actual 
transistor reference planes. 
Noise parameters of our reference transistor with an 
emitter length of 9.4 m?  have been measured at 5 GHz 
with a mechanical tuner using the Cold-Source 
Technique [3]. Fig. 5 shows the associated gain and the 
measured and simulated minimum noise figure at 
different biases. The model predicts the minimum noise 
figure of the transistor at low current densities in Fig. 5  
accurately whereas the agreement between the 
measurement and the simulation has been found to be 
slightly degraded at higher current densities. This is 
attributed for the time being to the interaction of the 
second stage noise contribution of the noise parameter 
measurement setup due to a lower transistor gain and a 
slight deviation of the extracted parameter values  
describing the high current operation [4] of the transistor 
from their physically correct values. 
Fig. 4. Measured and simulated S-parameters of the SiGe HBT 
with an emitter length of 4.9 m?  ( 40-1=freq GHz ). 
 define bjtnpn (C B E S ) 
 ;input parasitics 
 C:Cox1 B o1 C=112E-015
 R:Rsub1 o1 E  R=93 
 C:Csub1 o1 E  C=30E-015
 ;output parasitics 
 C:Cox2 C o1 C=116E-015
 R:Rsub2 o2 E  R=90 
 C:Csub2 o2 E  C=43E-015
 ;base-collector coupling 
 C:Cpbc B C C=2.2E-015 
 MAIN:HICUM C B E S 0  
 model MAIN HICUM  \ 
 ……… 
 end bjtnpn 
Cpbc
Cox1 Cox2
Rsub1 Rsub2 Csub2Csub1
Fig. 3. Equivalent circuit of the contact pads used for large-signal 
simulations. This circuit has been implemented using the hpeesof 
simulator in ICCAP of Agilent.  
 
o2 o1 
11th GAAS Symposium - Munich 2003438
 
 
The thermal noise contribution and the power loss due 
to the contact pads add to the measured minimum noise 
figure of the transistor and therefore have been 
subtracted from the noise correlation matrix of the 
transistor using the noise and electrical transformation 
matrices [5], [6]  
 
*min
2min
1
22
1 | |
2
n n opt
A
n opt n opt
FR R Y
C kT
F R Y R Y
? ?
 
?  
? ?
 
 
          (1) 
 
where AC  is the noise correlation matrix and minF , optY  
and nR  are the measured noise parameters. 
 
III. SUBSTRATENETWORK 
 
 
 
In Fig. 6, the equivalent circuit of the transistor under 
the cutoff operation is illustrated. With the substrate node 
being connected to the ground, the substrate-collector 
depletion capacitance becomes a function of only the 
applied collector voltage and can be generally expressed 
as 
 
                              0
1
sc
sc
sc m
sc
sc
CC
V
V ?
?
 
? 
 
 
.                           (2) 
 
 
 
scC  and subR  can be calculated by 
 
                    22 12Im( ) /scC Y Y ?? ?                                 (3) 
                   ? ?222 12 22 12Re( ) / Im( )subR Y Y Y Y? ? ?             (4) 
 
provided that 2 2 2( )sub sc subG C C??? ? . 
 
 
 
Having determined scC  and subR , subC  can be 
calculated by 
 
                 
2 2
2
22 12
2
( )
Re( ) ( )
sub sc sc
sub
sub sc sc
G C V G
Y YC C V
?
?
?
?
? ?            (5) 
 
where 1/sub subG R? . The substrate-collector capacitance 
scC  has been written in (5) as a function of scV  to 
emphasize the bias-dependence of scC . 
B C
E
Cbc(Vbc)Rb
Rsub Csub
Cbe(Vbe)
Csc(Vsc)
Fig. 6. Equivalent circuit of the npn-transistor under the cutoff 
operation with the substrate connected to the ground 
17.0 
Fig. 5. Measured and simulated minimum noise figure and 
associated gain at 5 GHz 
9.4eL ? m?  
Fig. 7. Calculated (solid line) and measured (shapes) scC  versus 
collector voltage for three transistor lengths ( 0.5bV ? ? V , 
1.9freq ? GHz  
9.4eL ?
2m?  
 
 
19eL ?
2m? 
38.2eL ?
2m?
Fig. 8. Extracted substrate resistance subR  for three transistor 
emitter dimensions ( bV ? ? 0.5 V , cV  varied between 2  and 
1.5 V ). 
11th GAAS Symposium - Munich 2003 439
 
 
 
 
 
As a result, subC  is extracted in the highest frequency 
range where (5) has somewhat a flat frequency 
response.  This lies in the fact that the influence of subC  
on  
 
             
2 2
22 12 2 2 2Re( ) ( )
sc sub
sub sc sub
C GY Y
G C C
?
?
? ?
? ?
             (6) 
 
becomes critical due to an increase in the denominator 
of (6) with increasing frequency from which (5) is 
derived. The accuracy of the method can be verified by 
comparing the simulated and measured 22Y  of the 
transistor in the forward-active mode. The HICUM model  
 
 
 
yields good results up to 40 GHz  as shown in Figures 
10a and 10b. 
 
TABLE I 
EXTRACTED SUBSTRATE RESISTANCE AND CAPACITANCE VALUES FOR 
THREE TRANSISTOR GEOMETRIES 
Emitter Length 
   9.4 m?            19 m?           38.2 m?  
 
      subR                   83 ?               52 ?               30 ?  
 
      subC                   17 fF             32 fF              56 fF  
IV. CONCLUSIONS 
DC and RF modeling results of SiGe HBTs with 
HICUM (High Current Transistor Model) have been 
presented. The model accuracy has been verified by DC, 
S-parameter and noise parameter measurements. 
Moreover, a new analytical direct extraction method to 
determine the substrate network parameters has been 
presented. The suggested extraction procedure has 
been successfully applied to the HICUM model. The 
investigated substrate network can accurately model the 
substrate effects up to 40 GHz and takes into account 
both resistive and dielectric behavior of the substrate.  
ACKNOWLEDGMENTS 
The authors wish to thank the modeling group of 
Alcatel HCAD Department Stuttgart and AMIS (AMI 
Semiconductor) Belgium for their support in this work. 
REFERENCES 
[1] Michael Schröter, “Staying Current with HICUM”, 
IEEE Circuits and Devices Magazine, May 2002 
[2] Koolen, M.C.A.M., Geelen J.A.M., Versleijen, 
M.P.J.G., “ An improved de-embedding technique for 
on-wafer high-frequency characterization”, Bipolar 
Circuits and Technology Meeting, 1991, Sept. 1991, 
pp. 188 -191 
[3] V. Adamian and A. Uhlir, “A Novel Procedure for 
Receiver Noise Characterization”, IEEE Trans. 
Instrum. Meas., Vol. IM-22, pp. 181-182, June 1973. 
[4] Michael Schröter, “HICUM, A Scalable Physics-
Based Compact Bipolar Transistor Model”, 
Description of Model Version 2.1, December, 2000  
[5] Hillbrand, H.; Russer, P., “An efficient method for 
computer aided noise analysis of linear amplifier 
networks”, IEEE Transactions on Circuits and 
Systems, Volume: 23 Issue: 4 , Apr. 1976, pp. 235 -
238 
[6] G. D. Vendelin, A. M. Pavio, “Microwave Circuit 
Design Using Linear and Nonlinear Techniques”, 
John-Wiley & Sons Inc., 1990   
 
 
Figure 9. Extracted substrate capacitance subC  for three transistor 
dimensions ( ??bV 0.5 V , cV  varied between 2  and 1.5 V ). 
9.4eL ?
2m?  
19eL ?
2m?  
38.2eL ?
2m?   
 
 
                                       (a) 
                                      (b) 
 Figure 10.  Measured and modeled (a) real and (b) imaginary part of 
22Y  for collector voltages between 0.5  and 1.5 V   up to 40 GHz. 
9.4eL ? m?  
9.4eL ? m?  
11th GAAS Symposium - Munich 2003440


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Large-Signal Modeling of SiGe HBTs Including a New Substrate Network Extraction Method W

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