Progress in Electromagnetic Research Symposium 2004, Pisa, Italy, March 28 - 31
A New Optimisation-Based Methodology for Determination of
Small-Signal Equivalent Circuit Model Parameters for a Si/SiGe HBT
Process
H. Taher
K.U.Leuven, div. ESAT-TELEMIC,
Kasteelpark Arenberg 10, B-3001
Leuven-Heverlee, Belgium
e-mail:
hany.taher@esat.kuleuven.ac.be;
B. Nauwelaers
K.U.Leuven, div. ESAT-TELEMIC,
Kasteelpark Arenberg 10, B-3001
Leuven-Heverlee, Belgium
e-mail:
Bart.Nauwelaers@esat.kuleuven.a
c.be
D. Schreurs
K.U.Leuven, div. ESATTELEMIC,
Kasteelpark Arenberg 10, B3001
Leuven-Heverlee, Belgium
e-mail:
Dominique.Schreurs@esat.kul
euven.ac.be;
R.Gillon
Technology R&D Dept. AMI
Semiconductor, Westerring 15,
B-9700 Oudenaarde, Belgium
e-mail
RENAUD.GILLON@MIE.AL
CATEL.BE
A. Alabadelah
K.U.Leuven, div. ESATTELEMIC,
Kasteelpark Arenberg 10, B-3001
Leuven-Heverlee, Belgium
e-mail:
ahmed.alabadelah@esat.kuleuve
n.ac.be;
E.Vestiel
Technology R&D Dept. AMI
Semiconductor, Westerring 15, B9700 Oudenaarde, Belgium
e-mail
eric_vestiel@amis.com
Abstract
An accurate and simple method for determining the small-signal equivalent circuit model
parameters of Si/SiGe heterojunction bipolar transistors is presented. This method differs from the
previous ones in that it overcomes the often less accurate parasitic elements’ extraction by finding out
the proper equivalent circuits for the dummy structures, used to assess the access interconnects’
contribution, and incorporate those in the complete circuit of the model. The method is based on
optimization and requires the S-parameter measurements of the dummy structure and the active
device. It is shown that it can be easily implemented in commercial software. To validate our
methodology, we determined the model elements of a Si/SiGe HBT in the active region. Excellent
results were obtained up to 20 GHz.
I.
Introduction
A small-signal equivalent circuit model is a physics based model. This means that it reflects the
important physical characteristics of the device. There are two main methods to extract the model
parameters. The first way is a direct parameter extraction method [1-3]. These methods suffer from the
problem that the extracted element values may be frequency dependent [4], and therefore often need
an additional optimization step. Also, the intrinsic part is virtually limited to eight elements, as we
have to determine all values from four complex S-parameters. This implies for example that the
distributed effect of the base can not be represented. The second method to determine equivalent
scheme model elements is optimization, meaning that numerical search algorithms are used to
minimize the error between the measured and some simulated error function. The drawback of this
technique is that it can yield non-physical element values. In this work, we developed an optimizationbased methodology. Separating the optimisation of the extrinsic element values from the intrinsic part
reduces the potential problem of non-physical values. Note that in case of HBT’s, the majority of the
modelling papers are focused on GaAs or InP based HBT’s. Due to the semi-insulating substrate, the
determination of their parasitic element values is simple and straightforward. As this paper
concentrates on Si/SiGe HBTs, special attention to the extrinsic network is required.
This paper is organized as follows: firstly, we determine the extrinsic parasitic network using the Sparameter measurements of dummy structures Next, we optimize the intrinsic elements while fixing
the extrinsic element values, obtained in the previous step. Experimental results are presented in
Section III. Finally, conclusions are drawn in section IV.
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Progress in Electromagnetic Research Symposium 2004, Pisa, Italy, March 28 - 31
II.
Modeling procedure
II.1 Modeling of the pad and access transmission line parasitics
The complete small-signal equivalent circuit for a Si/SiGe HBT as seen from the probe tips is
shown in fig. 1. We distinguish two parts: the intrinsic core of the device and the external parasitics. In
this subsection we concentrate on the parasitics, while the extraction of the intrinsic elements is
discussed in the next Subsection. Concerning the parasitics, we can deduce three types from fig. 1: pad
parasitics, impedance or series parasitics of the access transmission lines, and admittance or parallel
parasitics of the access transmission lines. In case of the direct extraction technique, the first step
would be to subtract the effect of these parasitics. Their values can be obtained from measuring
dummy structures, as shown in fig. 2, and then applying any one from the methods described in Refs.
[1-3]. This approach however has two disadvantages: firstly, the subtracting process increases
sensitivity of the model parameters w.r.t. measurement error propagation [5], and secondly, some
residual access transmission lines pad contributions may appear in the intrinsic core equivalent circuit
As a consequence, one might get frequency-dependent intrinsic elements, which is not physical.
A possible alternative solution is to first find an equivalent circuit for the access transmission lines.
The proposed equivalent circuits for each of the dummy structures are shown in figure 3. They are
built on the same concept as in Ref. [6]. Note that we are supposing that S12=S21=0 for all dummy
structures. This can be justified as follows:
In case of the pad and open-circuit dummy structures, there is a negligible physical path between
base and collector through the substrate. Also, as the transmission through is very small, we decided to
neglect it. Finally, in case of the short-circuit dummy structure, it is clear that there is no transmission
between the input and output. As a result, as the topologies of the base-emitter and collector-emitter
networks are identical, only the former is shown. The complexity of the circuits comes from the
dispersive nature of the Si substrate. The element values of these parasitic networks, as well as the
element values of the intrinsic device (see II.2) have been obtained by a random search optimization
method. This optimizer-based parameter extraction method involves that numerical search algorithms
are used to minimize the error between the measured and simulated S-parameters.
Yo.cBC
B
C
Intrinsic part
Zs.cB
YpB
Yo.cB
Zs.cC
Yo.cC
YpC
E
Figure 1. Representation of the SiGe HBT in the measurement configuration. The actual transistor is represented by the
rectangle called ‘intrinsic transistor’. The series impedances and parallel admittances model the probe pads and access
transmission lines.
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Progress in Electromagnetic Research Symposium 2004, Pisa, Italy, March 28 - 31
Figure 2. Pad, short-circuit, and open-circuit dummy structures.
B
RpadB1
RpadB2
C padB1
Ls.c. B
Rs.c. B
B
B
C padB2 CpadB1
CpadB1
C padB2
(a)
RpadB2
RpadB1
RpadB2
RpadB1
(b)
CpadB2
Ro.c B
C o.c B
(c)
Figure 3. Equivalent circuits of a) pad, b) short-circuit, and c) open-circuit dummy structures.
II.2 Modeling of the intrinsic core
In the previous step, we have built a model for pad and access transmission lines. The present step
concerns the modeling of the intrinsic core of the HBT as shown in fig. 4 [7]. This equivalent circuit
contains more than 8 elements and thus permits us to model the base distributed effect through Cf and
Cbc. Firstly, we measure the S-parameters of an on-wafer Si/SiGe HBT using a VNA. The instrument
calibration is such that the reference plane is at the probe tips. Next, we fix the values of the parasitic
elements as obtained in the previous step. By using a random search algorithm, we consequently try to
find the best set of intrinsic element values that minimizes the difference between simulated and
measured S-parameters.
Cf
B/
Cbc
Rb
C/
Gm e-j
Csub
Cbe
Rbe
Rei
E
Figure 4. Equivalent circuit model for intrinsic part of HBT.
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Progress in Electromagnetic Research Symposium 2004, Pisa, Italy, March 28 - 31
III.
Experimental results
Smodel(1,2)
Smeas(1,2)
freq (40.00MHz to 20.02GHz)
4
6
Smeas(2,2)
Smodel(2,2)
Smodel(2,1)
Smeas(2,1)
0.05
0.04
0.03
0.02
0.01
2
0.00
0
-0.01
-2
-0.02
-4
-0.03
-6
-0.04
freq (40.00M Hz to 20.02GHz)
-0.05
Smodel(1,1)
Smeas(1,1)
We characterized a 0.8 µm x 9.6 µm Si/SiGe HBT in the frequency range from 40 MHz to 20GHz
and biased at several Vbe [0.8 V-0.95 V] and Vce [1 V-1.5V]. In all cases, we obtain an excellent
agreement between the simulated and measured S–parameters. Due to limited page space, we show
results Vbe= 0.94 V and Vce = 1.5 V in fig. 5. The maximal deviation between measurements and
simulations is 9%, and this occurs for the S12 parameter in the low frequency range (below 1 GHz). As
the absolute value of the S12 is very small, this deviation can be largely contributed to the limited
dynamic range of the measurement system.
freq (40.00M Hz to 20.02GHz)
freq (40.00M Hz to 20.02GHz)
Figure 5. Comparison between measured S-parameters (solid line) and simulations (dotted line) using the element values as
extracted by proposed methodology.
IV. Conclusions
A new methodology for optimizing the HBT small-signal equivalent circuit model has been
presented. The basic principle is that it first determines the extrinsic element values using S-parameter
measurements on dummy structures. Next, these values are fixed while the intrinsic element values are
being optimized. The excellent agreement between the measured and simulated S-parameters proves
the accuracy of the proposed methodology.
Acknowledgement
This work has been supported with AMI Semiconductors, the FWO and the IWT.
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