RF CMOS Device Modeling: BSIM-Based Physical Model with Root-Like Construction Approach - Small Signal Modeling

Ickjin Kwon, Minkyu Je, Kwyro Lee, and Hyungcheol Shin
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology


Abstract

A novel extraction method of high frequency small-signal model parameters for MOSFET is proposed. From S-parameter 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 S-parameters fit the measured ones well without any optimization after parameter extraction.

 

I. Introduction

As the gate-length 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 one-chip solution possibility for analog and digital circuits. The extraction of small-signal 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 small-signal 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 small-signal 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 C-V 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 S-parameters, and verified the results match well with measured data.

 

II. New Extraction Method of Small-Signal Parameters

The proposed common-source equivalent circuit of a MOSFET after de-embedding parasitics of on-wafer pads and interconnection lines is shown in Figure 1. The circuit elements between the substrate and source are excluded because the substrate is short-circuited to the source as in most high-frequency 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 common-source equivalent circuit of a MOSFET after de-embedding parasitics of on-wafer 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 source-body 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 de-embedding overlap capacitances. The new extraction procedure uses linear regression approach for the Y-parameters which are converted from measured S-parameters. The small-signal equivalent circuit shown in Figure 1 can be analyzed in terms of Y-parameters as follows,



For operation frequencies up to 10GHz, (Cgs+Cgd)Rg<< 1, (Cgs+Cgd)Rg<< 1, and << 1. By using these assumptions, Y-parameters can be expressed as following.



Parameter extraction is performed from real and imaginary parts of the above Y-parameters. Cgd, Rg, Cgs, gm, Cdg, and gds can be obtained by Eq. (11)-(16). gm and gds are obtained from y-intercept 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 multi-fingered n-MOSFET's of AMS 0.35 ?m CMOS technologies having unit gate width of 5 ?m. The parameter extraction has been performed for an n-MOSFET with 100 mm width having twenty-unit gate fingers. To remove pad parasitics, de-embedding technique was carried out by subtracting parasitics of open pad structure from measured device S-parameters.

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 y-intercept 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 y-intercept of Re[Y21] versus w2 . Extracted value of gm was 16.6 mS. (b) gds was obtained from y-intercept 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 small-signal capacitance parameters for the n-MOSFET 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 n-MOSFET 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 n-MOSFET 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 n-MOSFET 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 Y-parameters using extracted model parameters and the small signal equivalent circuit shown in Figure 1. It shows that the modeled S-parameter fit the measured ones well without any optimization after parameter extraction.

Figure 6. The measured and modeled Y-parameters using extracted model parameters for the n-MOSFET 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 S-parameters fit the measured ones well

Figure 6 shows measured and modeled Y-parameters using extracted model parameters and the small signal equivalent circuit shown in Figure 1. It shows that the modeled S-parameter 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 non-reciprocal capacitance Cgd and Cdgcontribute to match imaginary part of Y12 and Y21.

In Figure 7, gate-bias dependence of the extracted small-signal parameters for the n-MOSFET 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 gate-drain 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 region-to-region transition is very gradual due to short-channel 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 gate-bias dependence of extracted parameters for an n-MOSFET 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 small-signal 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 S-parameter and good agreement has been observed. Developed extraction method is an effective parameter extraction technique for the large-signal BSIM3v3 model.


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