RF CMOS Device Modeling: BSIMBased Physical Model with RootLike Construction Approach  Small Signal Modeling
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology
Abstract
A novel extraction method of high frequency smallsignal model parameters for MOSFET is proposed. From Sparameter measurement, this technique accurately extracts the MOSFET model parameters including the charge conservation capacitance parameters. To consider charge conservation, nonreciprocal capacitance is considered. The modeled Sparameters fit the measured ones well without any optimization after parameter extraction.
I. Introduction
As the gatelength of MOSFET reduces, its high frequency characteristics
improve [1][2]. MOSFET is good candidate for RF IC application because
of low cost, high integration and onechip solution possibility for analog
and digital circuits. The extraction of smallsignal equivalent circuit
parameters is important for the development of accurate large signal model.
Recently, many suggestions have been made to improve the prediction of
AC properties at high frequencies. Simple modifications to the conventional
MOSFET equivalent circuit and a few methods of extracting smallsignal
equivalent circuit parameters have been reported [3][5]. However these
are based on the MESFET model and require complex curve fitting and optimization.
They also do not consider charge conservation capacitance parameters which
are important in intrinsic capacitance modeling. Previous smallsignal
equivalent circuit models that do not consider charge conservation cannot
accurately model the intrinsic capacitance.
BSIM3v3 model has been recognized as an accurate and scalable Si MOSFET model at the low frequency range, however the parameter extraction procedure for high frequencies has not been established yet. In particular, submicron MOSFET capacitances are difficult to extract in the MHz frequency rangne and the numerical optimization process may fail to obtain the physical parameter. The determination of the model capacitances, based on large area CV test structure measurement proved to be inaccurate in the high frequency range [8].
In this paper, we have developed a systematic parameter extraction method for MOSFET which includes charge conservation capacitance parameters, from measured Sparameters, and verified the results match well with measured data.
II. New Extraction Method of
SmallSignal Parameters
The proposed commonsource equivalent circuit of a MOSFET after deembedding
parasitics of onwafer pads and interconnection lines is shown in Figure
1. The circuit elements between the substrate and source are excluded
because the substrate is shortcircuited to the source as in most highfrequency
application. In this case, the substrate resistance that exists between
the source and substrate is negligible. The proposed equivalent circuit
is basically scalable since all its element are physically meaningful.
The gate resistance Rg represents the effective channel resistance which
consists of the distributed channel resistance seen from the gate and
the distributed gate electrode resistance [9], which affect the input
admittance Y11 at RF. The drain junction capacitance and the bulk spreading
resistance are represented by Cjd and Rsubd. Substrate coupling effects
through the drain junction and the substrate resistance play an important
role for the output admittance Y22 [6].
Figure 1. The proposed commonsource equivalent circuit of a MOSFET after deembedding parasitics of onwafer pads and interconnection lines. Four independent intrinsic capacitances Cgs, Cgd, Cdg, and Cds are needed for charge conservation. The definitions of each capacitance are also shown. 
In the sourcebody tied three terminal structure, four
independent intrinsic capacitances Cgs, Cgd, Cdg, and Cds
are needed for charge conservation. The definitions of each capacitance
are shown in Figure 1. The gate current Ig and the drain current
Id and their associated charges Qg and Qd are related
by the following equations.
We have written Cdg and Cgd separately in the above equations, and Cdg is not equal to Cgd because of the difference in the signal excitation direction. These nonreciprocal capacitances are necessary for charge conservation of small signal model [10]. In equivalent circuit of MOSFET shown in Figure 1, overlap capacitances are included in Cgs, Cgd, Cdg and intrinsic capacitances are obtained by deembedding overlap capacitances. The new extraction procedure uses linear regression approach for the Yparameters which are converted from measured Sparameters. The smallsignal equivalent circuit shown in Figure 1 can be analyzed in terms of Yparameters as follows,
For operation frequencies up to 10GHz, (Cgs+Cgd)Rg<< 1, (Cgs+Cgd)Rg<< 1, and << 1. By using these assumptions, Yparameters can be expressed as following.
Parameter extraction is performed from real and imaginary parts of the above Yparameters. Cgd, Rg, Cgs, gm, Cdg, and gds can be obtained by Eq. (11)(16). gm and gds are obtained from yintercept of Re[Y21] versus and from intercept of Re[Y21] versus , respectively.
Rsubd and Cjdjd are obtained from linear regression of / [Re[Y22]  gds  CdgRg] vs. using the following relation.
Rsubd is determined from slope of /[Re[Y22]  gds  CdgRg] as a function of and Cjd is extracted from (18).
Finally, Cds is obtained from (19) as
III. Parameter Extraction Results
The test devices are multifingered nMOSFET's of AMS
0.35 ?m CMOS technologies having unit gate width of 5 ?m. The parameter
extraction has been performed for an nMOSFET with 100 mm width having
twentyunit gate fingers. To remove pad parasitics, deembedding technique
was carried out by subtracting parasitics of open pad structure from measured
device Sparameters.
The small signal parameters including charge conservation capacitance
parameters were extracted at Vgs = 1 V and Vds = 2 V using Eq. (11)(19).
Transconductance gm of 16.6 mS was obtained from yintercept of Re[Y21]
versus w2 as shown in Figure 2(a) and conductance gds of 0.31 mS was obtained
from intercept of Re[Y22] versus ,
as shown in Figure 2(b). Rsubd of 200
was determined from slope of
/[Re[Y22]  gds  CdgRg]
as a function of
as shown in Figure 3.


Figure 2. Extraction of conductance
gm and gds.
(a) gm was obtained from yintercept of Re[Y21] versus w2 . Extracted value of gm was 16.6 mS. (b) gds was obtained from yintercept of Re[Y22] versus w2 . Extracted value of gds was 0.31 mS. 
Figure 3. Rsubd was determined from the slope of w2 / [Re[Y22]  gds  w2Cdg2Rg] as a function of w2. Extracted value of Rsubd was 200 W. 
The frequency dependence of extracted
smallsignal capacitance parameters for the nMOSFET biased to Vgs =
1 V and Vds = 2 V are shown in Figure 4. Also, extracted gate resistance
Rg as a function of frequency for the nMOSFET biased to Vgs = 1 V and
Vds = 2V is shown in Figure 5. The frequency range is from 0.5 GHz to
10.5 GHz. The results shows that extracted parameters remains almost
constant with frequency. Figure 4 and Figure 5 verified that this extraction
method is accurate and reliable.
Figure 4. The frequency dependence of extracted capacitance parameters for an nMOSFET having 100 mm width and biased to Vgs = 1 V and Vds = 2 V. Extracted parameters remain almost constant with frequency.  Figure 5. The frequency dependence of gate resistance Rg for an nMOSFET having 100 mm width and biased to Vgs = 1 V and Vds = 2 V. Gate resistance Rg remains almost constant with frequency. 
For the extracted parameter values,
(Cgs + Cgd)2 Rg2 is calculated to be 0.06 at 10 GHz, which is much smaller
than one. This verifies the validity of using the assumption in simplifying
Eq. (3)  Eq. (6) to Eq. (7)  Eq. (10).
Figure 6 shows measured and modeled Yparameters using extracted model
parameters and the small signal equivalent circuit shown in Figure 1.
It shows that the modeled Sparameter fit the measured ones well without
any optimization after parameter extraction.
Figure 6. The measured and modeled Yparameters using extracted model parameters for the nMOSFET biased to Vgs = 1 V and Vds = 2 V. The frequency range is from 0.5 GHz to 10.5 GHz. (a)Y11 (b)Y12 (c)Y21 (d)Y22. It shows that the modeled Sparameters fit the measured ones well 
Figure 6 shows measured and modeled Yparameters
using extracted model parameters and the small signal equivalent circuit
shown in Figure 1. It shows that the modeled Sparameter fit the measured
ones well without any optimization after parameter extraction. The admittance
Y11 fits the measured data well with gate resistance model and Y22 fits
well with substrate resistance model. The nonreciprocal capacitance
Cgd and Cdgcontribute to match imaginary part of Y12 and Y21.
In Figure 7, gatebias dependence of the extracted smallsignal parameters
for the nMOSFET biased to Vds = 2 V is shown. In Figure 7(a), Cgs increases
gradually as gate bias increases in the saturation region and drops
in the linear region. Since the intrinsic gatedrain capacitance is
small compared to overlap capacitance in the saturation region, Cgd
and Cdg are almost constant in the saturation region and increase gradually
in the linear region. The smooth behaviors for Cgs, Cgd and Cdg are
because the regiontoregion transition is very gradual due to shortchannel
effects. Figure 7(b) shows that transconductance gm increases as gate
bias increases for small Vgs and gm decreases for high gate bias due
to mobility degradation. Drain conductance gds increases almost proportional
to gate bias in the saturation region due to short channel effects and
gds rapidly increases with Vgs in the linear region because for higher
gate bias drain current increases more rapidly with drain bias in the
linear region.
Figure 7. The gatebias dependence of extracted parameters for an nMOSFET having 100 mm width and biased to Vds = 2 V. (a) Capacitances (b) Conductances and resistances. 
IV. Conclusions
A novel extraction method of obtaining an accurate high frequency smallsignal
parameters for MOSFET has been demonstrated. The nonreciprocal capacitance
was introduced and this technique accurately extracted the charge conservation
capacitance parameters. The proposed model from parameter extraction
has been evaluated with measured Sparameter and good agreement has
been observed. Developed extraction method is an effective parameter
extraction technique for the largesignal BSIM3v3 model.
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