Electrical parameter extraction & modeling of SiGe HBT for HFapplications

Journal of Electrical and Control Engineering JECE

Electrical Parameter Extraction & Modeling of
Si1-xGex HBT for HF Applications
Pradeep Kumar#1, R. K. Chauhan*2
#1
Department of ECE, Ideal Institute of Management & Technology, Ghaziabad, INDIA
*2
Department of ECE, M.M.M. Engineering College, Gorakhpur, INDIA
1
pradeep.hitesh@gmail.com; 2rkchauhan27@gmail.com

Abstract-SiGe technology is sincerely challenging III/V and II/VI submillimeter wave transceiver designs, where progressive
technologies in the realm of high frequency electronics improvements in transistor bandwidth enable the evolution of
applications, for example optical fibre and mobile communications and radars ICs operating to higher frequencies.
communications. In this paper a model of SiGe HBT with uniform In addition, faster transistors enable the wider band mixed-
impurity doping in the base for high frequency application is signal ICs (e.g., analog-to-digital converters, digital-to-analog
studied. The high frequency parameters are extracted with the converters, etc.) that improve the resolution of radars and
help of simulated Z- and Y- parameters of two port equivalent
communications systems [2]. Meanwhile, several hundred GHz
circuits of the proposed SiGe HBT device and electrical
applications are starting to expand from the initial niche
parameters are calculated with the help of small-signal analysis of
projected device. Later, the topics are also involved in
markets of Earth, planetary, and space science to the larger
instantaneous investigation of effect of Ge concentration on commercial markets in biomedical imaging, non-metallic
various electrical as well as HF parameters of this SiGe HBT. This object detection, quality control, and secure communications.
method is validated by the examination of certain linear relations For the meantime, application fields related to THz
of device frequency behaviour as forecasted by the analogous frequency range are expanded from the initial markets of
theoretical analysis. Further, the precision of our method is planetary, earth and space science [3]–[6] to a bigger
validated by simulated S–parameter plots. The device
commercial markets in biomedical imaging, quality control,
characteristics of the proposed model are found much advanced
secure communications, and non-metallic object detection [7].
to those of III-V semiconductor devices. These results have been
also validated using a viable numerical device simulator ATLAS
In present time, THz sensors are prepared from heterodyne
from Silvaco International. semiconductors and novel direct detectors such as quantum-dot
single-photon detectors and schottky diodes. THz sources are
Keywords-Silicon; SiGe；HBT; Ge Concentration; Small-signal usually achieved through several optical techniques [8]. But,
Analysis; Intrinsic Parameters deficient existing oscillators and amplifiers made of active
semiconductor transistors become a bottleneck. Furthermore,
I. INTRODUCTION improved bandwidth in a transistor normally associates well
During the past several years, SiGe HBT technology has with improved RF performance e.g. higher gain and lower
entered the global semiconductor electronics market. Now noise. Thus THz transistors can significantly widen the design
SiGe HBT technologies are being increasingly deployed in limitations of existing performance-constrained lower
North America, Europe (such as dot5 project) for a wide frequency (RF through millimeter-wave) circuits and systems
variety of communications circuit applications such as cellular [9][10]. An ample range of space electronics platforms (for
phones, in the microwave region and the semiconductor instance analog, digital, and RF) are designed to operate at
industry investing heavily to improve the performance of space and planetary ambient conditions which can be enabled
silicon devices for high frequency applications. The by high-bandwidth bandgap-engineered transistors without
multibillion semiconductor industry is rapidly using bulky and power-hungry heating units [11].
devices/transistors working in several GHz regions and is
pushing to demonstrate useful solid-state transistors, and The purpose of this work is to search physical issues of the
resultant circuits built from them, capable of operating near the device modelling of small-signal equivalent circuits for SiGe
THz regime. There are two major driving forces for SiGe solid- HBTs with uniform impurity doping in the base. During the
state devices: 1) high frequency communications and radars last few years, various methods for parameter extraction and
and 2) various niche THz applications. Recent research has HBT high frequency small-signal modelling have been
focused on expanding THz options from two-terminal devices published and developed [12] – [16]. In 2002, Basaran and
(e.g., Schottky diodes) to three-terminal devices (transistors) Berroth presented their model to extract the device parameters
for both application areas. In high-frequency communications but it is not a simple and complete extraction method [17]. For
and radars, higher bandwidth transistors are desirable in a ease of extraction process, a simple and accurate method is
number of applications. Optical fiber communications require depicted in this proposed model. This device is simulated in
active amplifiers in decision circuits, multiplexers, and phase- ATLAS device simulator. In this process Y-, Z- and S-
lock loops operating at 100-GHz clock frequency and above parameters are extracted directly by ATLAS. Then the
[1]. electrical parameters are calculated with the help of above
parameters and small-signal equivalent circuit analysis. In this
High current-gain and power-gain frequencies (fT and fmax) work, a numerical simulation results are preferred instead of
are also demanded in microwave, millimeter-wave, and

JECE Vol. 2 No. 2, 2012 PP. 27-34 ○2011-2012 World Academic Publishing
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real measurement results for avoiding the interference from
extrinsic parts in the calculation of small-signal parameters.
In this paper, we model the electrical as well as HF
parameters and calculate the unity current-gain frequency and
unity power-gain frequency for high speed applications of n-p-
n SiGe HBT with uniform impurity doping in the base with the
help of directly extracted Z-, Y-, and S-parameters. At the
same time the effect of Ge concentration is investigated for
above device parameters. With this impulse, we address small-
signal HF modelling in the second section. In the third section,
the simulation and calculated results are discussed. At last, we
concluded with general protrusions and remarks in section-IV.

II. SMALL-SIGNAL HF MODELING
In this section, a simple, accurate, and novel extraction
method is presented for discussing the transistor HF
performance along with procedures to find out the parameters Fig. 1 A small-signal Π equivalent circuit of an HBT device (a) contains
of SiGe HBT by means of small-signal π-topology equivalent intrinsic and extrinsic circuit elements. The intrinsic elements (b) can be
circuits of this HBT with uniform impurity doping in the base. determined from the admittance parameters of the device at a number of
different bias points
The algorithm is useful for extracting both intrinsic as well as
extrinsic elements. The conventional methods derived from The maximum stable gain is calculated by y21 and y12 as
simple bias measurements work very sound when we [18],
determine formerly the extrinsic elements of the HBT. Through
different procedures for example DC or optimization can be y 21 (1)
used for this strategy [18]. MSG 
y 12
It is often very hard to accurately determine the values of And the maximum available gain is extracted as [18],
parasitic elements of the HBT because the typical DC and cut-
off techniques present poor performance for Silicon y 21 (2)
MAG  (k  k 2  1)
Germanium HBT devices. So an innovative procedure has been y12
developed to circumvent this problem. In this technique only Where k is ‘Rollett stability factor’ and extracted by this
scattering (S)-parameters at different biases are measured. For equation as [18],
fitting the measured S-parameters appropriately, linear models
by way of π-topology have been experienced. For simplicity, 2 Re( y 11) Re( y 22 )  Re( y 12 y 21)
k
(3)
we ignored emitter resistance, the collector resistance, together
with the output resistance due to early effect [19]. y 12 y 21
Mansion’s gain is obtained by the following equation as
Using ATLAS, the S-parameters which are obtained from
[18],
AC analysis are simply converted into Y-, Z- or H-parameters.
Various Power Gains for example MAG, MSG, as well as 2

MAUG (are used for such analysis. Furthermore, a figure-of- y 12  y 21 (4)
U 
merit that has been used extensively such characterization is 4[Re( y 11) Re( y 22 )  Re( y 12 ) Re( y 21)]
maximum stable gain. At high frequencies these quantities are The maximum available unilateral gain is calculated by this
calculated from the measured small-signal scattering equation as [18],
parameters due to simplicity of measurement [18].
2
y 21 (5)
MAUG 
4 Re( y11) Re( y 22)

We get the MAG when both input and output are
concurrently conjugate matched. When k > 1, the device is
unconditionally stable and MAG exists. It is obvious from
Equations (4) and (5), if the device is unilateral (y12 = 0) then
U equals to MAUG. The MAG equals to MSG and vice-versa
when the device is unconditionally stable. Maximum frequency
at which MSG becomes unity is frequently termed as fmax. As
power gain with no impedance transformation is achieved by
common-emitter microwave transistors. This is the reason why
these transistors may comprise useful gain when inserted into a
system with 50 Ω [18]. For this model, MSG is called a figure
of merit. This device is unconditionally stable here.

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A. Frequency Response The collector-emitter junction resistance is obtained by the
In most HF and millimeter wave circuit applications, it is equation as follows [21],
the frequency response of transistor that confines system 1
performance. One of the imperative figures of merit in this R CE  Re    Re  
context is the unity–gain cutoff frequency (fT), which is given Y 12  Y 22  (12)
as [20]
1
1 The collector-emitter junction resistance is expressed by the
f T  [ (C eb  C Cb)  b  c  e] equation as follows [21],
gm (6) 1
R BE  Re    Re  
Y 11 Y 12  (13)
Where and are the EB and CB capacitances, gm is In this method CBE are intrinsic junction capacitances and
the transconductance and , , are the base, emitter, and RBC, RCE and RBE are intrinsic junction resistances.
collector transit times, respectively. The transistor cut-off C. Calculation of Extrinsic Parameters
frequency is thus a valuable metric for evaluating different As the device dimension shrinks, the parameters RB and
technologies. usually limits the maximum transistor in the parasitic capacitances start to measure the high frequency
usual Si BJT’s,. behaviour of the device and have to be taken into account in
the equivalent circuit to improve the transistor model accuracy
In the context of HF and millimetre-wave applications, the in the broad frequency range from Y parameters under the
unity power-gain frequency ( ), or maximum oscillation reverse-bias condition.
frequency is a more relevant figure of merit because The extrinsic resistance is obtained by the equation as
depends not only on the intrinsic transistor performance ( ) follows [18],
but also the parasitics of the device, as [20]
R B  Z 11  Z 12 (14)
The base-collector junction capacitance can be measured as
fT [17],
f max 
8 C Cb R B  I m Y 12 
(7)  
C BC   (15)
Where RB is the base resistance and CBC is the base- And the base-emitter junction capacitances can be
collector junction capacitance. Thus from Equation (7) it is measured as [17],
clear that for the higher value of fmax, the value of base-
collector junction capacitance and base resistance should be  I m Y 12  Y 11
 
lower. So the cut-off frequency fT increases as transit time C BE   (16)
decreases which in turn affect the fmax.
B. Calculation of Intrinsic Parameters III. RESULTS & DISCUSSION
The intrinsic and extrinsic parameters in Fig. 1 can be On the basis of above model and method the values of
extracted by the following method: the base-emitter junction many performance parameters such as electrical parameters
capacitance is calculated by the equation as follows [21], and device high frequency parameters which include various
intrinsic as well as extrinsic elements, current-gain (β),
I m Y 11  I m Y 12 
    collector current, base resistance, junction capacitance,
C BE  maximum oscillation frequency fmax, unity current-gain
i (8) frequency (i.e. cut-off frequency) fT, are calculated for n-p-n
The base-collector junction capacitance is expressed by the SiGe HBT with uniform impurity doping in the base. Along
equation as follows [21], with this effort, an investigation is also performed regarding
the effect of Ge concentration on these parameters. For this
 I m Y 12 
 
C BC  purpose we find out the value of above parameters at different
i (9) Ge concentrations. The HBT considered in this paper has the
The base-collector junction capacitance is expressed by the base width of 0.1µm. Average Ge concentration in this base
equation as follows [21], region considered in our calculations is varied from 10%-28%
as higher than this are not supported by present epitaxial
I m Y 22   I m Y 12 
    technologies and beyond it the improvement associated with
C CE  Ge seizes may be due to lattice constant mismatch [18].
i (10) ATLAS simulation of SiGe HBT is performed to prove
The base-collector junction capacitance is calculated by the precision. All important physical effects, such as impact
equation as follows [21], ionization (II) is appropriately modeled and accounted for the
1 simulation for obtaining admirable pact with characteristics.
R BC  Re   The impact ionization results in a strong improvement of
Y 12  (11) collector-current. AC simulation needs apposite DC calibration

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which is an important prerequisite for it [18]. For this shows the intrinsic as well as extrinsic element of HBT while
simulation, it is compulsory to take the complete device the part (b) intrinsic part only. The intrinsic elements (b) can be
composition into account with the aim of considering the determined from extracted Y- parameters of the device at a
capacitance between substrate and collector (CCS) as well as number of different bias points.
capacitance between base and collector (CBC).
A. Determination Of Collector Current, Base Current And
Gain Enhancement
A very important consequence of adding Ge into the base
of a transistor is its effect on the collector current density (Jc).
With Ge in the base, electron injection at the emitter base
junction is made easier, and thus more charge can flow from
the emitter to the collector with a resultant increase in Jc. Also,
because of the Ge-induced band offset, there is a decrease in
intrinsic carrier density in the base which also increases Jc [3].
As the emitter regions of both a Si BJT and a SiGe, HBT are
essentially the same, implying an identical base current density
(JB). The net result is that adding Ge increases the current gain
of the transistor (β = JC/ JB) as in Figure 4. In testing, the
maximum current-gain is found about 912 at 28% Ge content.
Fig. 3 Effect of germanium content on collector current

Fig. 4 Effect of Ge concentration over current-gain

Fig. 2 Collector & Base currents of SiGe HBT

This plot indicates that the important DC consequence of
adding Ge into the base, however, lies with the collector
current density. Figure 2 shows the variation of IC & IB of
SiGe HBT at various bias points. Figure 3 shows that effect of
Germanium content on collector current and it is found that the
IC increases as the concentration of Ge increases. We also
investigated that the collector current is maximum at 28% Ge
concentration and after this Ge concentration it does not follow
the rule due to lattice constant mismatch.
The simulated SiGe HBT is shown in Figure 5.
B. Determination Of Intrinsic & Extrinsic Parameters
The intrinsic and extrinsic parameters are determined by
Figure 1 and using Equations (8) to (16). Figure 1 is a small
signal equivalent circuit of SiGe HBT device. The part (a) of it Fig. 5 Simulated SiGe HBT Device with 0.1 µm Base width

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(1) Collector-Base junction Capacitance (CBC) (2) Base Resistance (RB)
The collector–base capacitance is a junction capacitance. From Equation (7) it is clear that the base resistance should
From Equation (6) and Equation (7) it is clear that the value of be low for higher fmax. It can be calculated by Z-parameters as
parasitic capacitance should be low for HF response. The in Equation (14). 】
collector-base junction capacitance can be calculated by
imaginary part of Y12 as in Equation (9). The plot of CBC at is
presented in Figure 6. The effect of germanium on the
capacitance CBC can be visualized in Figure 7.

Fig. 8 Effect of Ge concentration on base resistance RB

The Z-parameters are calculated from device simulator
ATLAS. Figure 8 represents the effect of Ge concentration on
base resistance. It is found that RB decreases as the
concentration of Ge increases. 30.12 Ω RB has been obtained
at 0.28 Ge concentration.
C. Determination of S- Parameters Plots
Figure 9 to Figure 12 show the simulated S-parameters
plots for this device. Because of the intuitive relationship
between coefficients S11 and S22 are conveniently on a smith
chart, while S21 and S12 are representing the gain response
and that’s why they are typically displayed on a polar plot. The
S11 for a bipolar transistor always moves clockwise as
Fig. 6 Base-collector junction capacitance CBC frequency increases on the smith chart. The Figures 9 to 12 are
simulated S11, S12, S21, and S22.
From this Figure it can be interpreted that on increasing the
Ge concentrations the corresponding collector–base D. Determination of Maximum Oscillation Frequency (fmax)
capacitance decreases which in turn increases the maximum and Cut-Off Frequency (fT) for Proposed Device
oscillation frequency fmax [22]. The value of CBC is 2.76 ×10-
15
.F at 0.28 Ge concentration. The maximum oscillation frequency fmax is calculated by
the method of extrapolation. This method requires the
calculation of power-gain i.e. MSG. The power gain is
calculated with the help of S- and Y-parameters of Si-Ge HBT
device that are extracted from ATLAS. In this work MSG is
calculated by Equation (1). The frequency vs. MSG plot is
shown in Figure 13. As it is described above, the fmax is
extracted at the point where MSG becomes 0 dB from MSG (in
dB) versus log (frequency) plot. The extrapolated fmax is
calculated 438 GHz at 0.28 Ge concentration from Figure 13. it
is investigated that the maximum oscillation frequency fmax
increases on increasing the Ge contents till 0.28 concentration
beyond 28% it decreases due to lattice constant mismatch. At
0.28 Ge concentration a record 398 GHz corresponding fT is
calculated. It is also investigated that the fT increases on
increasing Ge concentration till 28% value of Ge contents.
Figure 14 dipicts the variation of extrapolted fmax w.r.t.
collector current. The Table 1 describes the overall summary of
HF operation of SiGe HBT. It is found that this Si-Ge HBT
device is operated at fmax and fT near half terahertz. This HBT
in half Tera-Hertz frequencies encompass definite water
Fig. 7 Effect of germanium on collector-base junction capacitance (CBC)
absorption rates and imitate off metal. Apart from these areas,

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this device can infiltrate fog and fabrics [23]. Chemical will be helped by these THz devices. This HBT in THz Radar
detection, medicine, chemical spectroscopy, transportation, and will accommodate in investigating hidden universe and planet
national security in addition with weapon fields will also be as well as space applications [18]. This data can be valuable for
enriched with this HBT. The study of dust & gas chemistry, Dot 5 project.
stellar and galactic constituents as well as evolution cosmology

Fig. 9 Simulated S11 Fig. 11 Simulated S21

Fig. 10 Simulated S12 Fig. 12 Simulated S22

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IV. CONCLUSIONS
In this paper, a simple and accurate method of electrical
parameter calculation and HF parameter extraction is presented
for SiGe HBT with uniform impurity doping in the base. This
is performed by simulated Z- and Y- parameters of proposed
device and small signal equivalent circuit method. With the
help of these parameters we calculated the intrinsic as well as
extrinsic device parameters with higher precision. We found
the fine value of base resistance and base-collector junction
capacitance which are 30.12 Ω and 2.76 fF respectively. These
two values are very helpful for figuring out the high frequency
response of proposed device. The extrapolated unity power-
gain frequency is calculated 438 GHz. The corresponding unity
current-gain frequency is calculated 398 GHz. In our
investigation we found that the device current-gain and
collector current increases with increasing concentration of
germanium. The β is calculated 912 at 28% Ge. While the base
resistance and base-collector junction decreases with increasing
values of Ge. The high frequency response of proposed model
depicted near half tera hertz unity power-gain as well as unity
current-gain frequencies. After 28% Ge concentration, these
are not supported by present epitaxial technologies and beyond
it the improvement associated with Ge seizes may be due to
Fig. 13 Plot of frequency (HZ) vs. MSG (dB) lattice constant mismatch. The proposed device with such
frequency may be helpful in the realm of medicine, chemical
spectroscopy and other space applications, and dot 5 project.

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[14] L Degachi and F M Ghannouchi, “Systematic and rigorous extraction R. K. Chauhan was born in Dehradoon, India in
method of HBT small-signal model parameters”, IEEE Trans Microw 1967. He received the B.Tech. degree in
Theory Tech, 54(2): 682, 2006. Electronics & Communication Engineering, from
[15] K Lee, K Choi and S H Kook, “Direct parameter extraction of SiGe G.B.P.U.A.T - Pantnagar, in 1989 and M.E. in
HBTs for the VBIC bipolar compact model”, IEEE Trans Electron Control & Instrumentation, from MNNIT-
Devices, 52(3): 375, 2005. Allahabad in 1993 and Ph.D in Electronics
[16] T R Yang, J M L Tsai and C L Ho, “SiGe HBT’s small-signal pi Engineering, from IT-BHU, Varanasi, INDIA in
modeling”, IEEE Trans Microw Theory Tech, 55(7): 1417, 2007. 2002. He joined the department of ECE, Madan
Mohan Malviya Engineering College, Gorakhpur,
[17] Umut Basaran, and Manfred Berroth, “High frequency noise modeling of India as a lecturer, in 1993, as an Assistant
SiGe HBTs using a direct-parameter extraction method”, in Proceedings Professor since 2002 and thereafter as an
of IEEE, 2002. Associate Professor since Jan, 2006 to till date in
[18] Pradeep Kumar and R. K. Chauhan, “Device parameter optimization the same institute. He also worked as a Professor in Department of ECE,
osilicon germanium HBT for THz applications”, International Journal on Faculty of Technology, Addis Ababa University, Ethiopia between 2003 to
Electrical Engineering and Informatics, Vol, 2, No. 4, 2010. 2005. He is reviewer of Microelectronics Journal, CSP etc. His research
[19] “Device Simulation Software”, ATLAS User’s manual, SILVACO interests include device modeling and simulation of MOS, CMOS and HBT
International, 2004. based circuits. He was selected as one of top 100 Engineers of 2010 by
[20] J. D. Cressler, “SiGe HBT technology: a new contender for Si-based RF International Biographical Centre, Cambridge, England.
and microwave circuit applications”, IEEE Trans. Microw Theory Tech., E-mail: rkchauhan27@gmail.com
vol. 46, issue 5, pp. 572–589, 1998. Ph: +91-9235500556
Department of ECE, Madan Mohan Malviya Engineering College, Gorakhpur-
[21] J.M. Zamanillo, A. Tazon, A. Mediavilla and C. Navarro, “Simple
273010, India.
Algorithm Extracts SiGe HBT Parameters”, Microwaves & RF, pp. 48-57,
1999.
[22] Ankit Kashyap and R. K. Chauhan. “Effect of the Ge profile design on
the performance of an n-p-n SiGe HBT-based analog circuit”,
Microelectronics journal, MEJ: 2554, 2008.
[23] Frank Chang. “Terahertz CMOS SoC for Imaging/Communication
Systems” tech. ppt, UCLA, High-Speed Electronics Laboratory.

Pradeep Kumar was born in Allahabad, India
in 1985. He received his B.Tech. degree in
Electronics & Communication Engineering
from KCNIT Banda in 2006 and M. Tech
degree in Digital Systems from Madan Mohan
Malviya Engineering College, Gorakhpur, India.
He initially joined VINCENTIT Hyderabad in
2006 and thereafter worked as a lecturer in Dr.
K.N.M.I.E.T. Modinagar, Ghaziabad between
2007 and 2008. He is currently working as
Assistant Professor in the Deptt. Of Electronics
& Communication Engineering at Ideal
Institute of Management and Technology
Ghaziabad India. His research interests include characterization & modeling of
SiGe HBT based circuits, THz & millimeter-wave circuit application and
mixed signal processing.
E-mail: pradeep.hitesh@gmail.com
Ph: +91-9540642891
Department of ECE, Ideal Institute of Management and Technology Ghaziabad,
INDIA.

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