Indirect fitting procedure to separate the effects of mobility degradation and source-and-drain resistance in MOSFET parameter extraction

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Abstract

A new procedure is presented to separate the effects of source-and-drain series resistance and mobility degradation factor in the extraction of MOSFET model parameters. It requires only a single test device and it is based on fitting the ID(VGS, VDS) equation to the measured characteristics. Two types of bidimensional fitting are explored: direct fitting to the drain current and indirect fitting to the measured source-to-drain resistance. The indirect fitting is shown to be advantageous in terms of fewer number of iterations needed and wider extent of initial guess values range.

Introduction

Accurate model parameter extraction is crucial for modeling modern MOSFET devices. Extensive work abounds in the literature dedicated to this subject. Free-carrier mobility degradation and source-and-drain series resistance are two parameters of special importance for MOSFET characterization that are particularly cumbersome to extract independently from each other. Both of these parameters produce similar effects on the device’s transfer characteristics, ID(VGS), a fact that complicates their accurate extraction. Several ingenious procedures have been proposed to circumvent this difficulty [1], [2], [3], [4], [5]. Another method was proposed to extract these parameters from the drain current versus gate voltage characteristics in the saturation region using several devices of different mask channel lengths [6]. An alternative procedure was recently proposed to extract the source-and-drain series resistance independently of mobility degradation by using bias conditions under which the channel carrier mobility is kept constant [7].

In what follows we present a new procedure based on the above-threshold and below-saturation I–V characteristics of a single transistor. It is based on bidimensional fitting of the ID(VGS, VDS) model equation to measured data. This permits to separate the effects of mobility degradation and source-and-drain series resistance. The procedure is validated using synthetic data, and then applied to experimental data from a single MOSFET. The computational efficiency is finally analyzed in terms of number of iterations and the extent of initial values range tolerance.

The above-threshold drain current of a MOSFET in the triode region may be modeled by an equation of the form [8]:ID=K1+θ(Vgs-VT)Vgs-VT-αVds2Vds,whereVgs=VGS-IDR2,Vds=VDS-IDR,K=WLCoxμo.VGS is the externally applied gate voltage, VDS is the externally applied drain voltage, R is the total source-and-drain series resistance, μo is the low-field mobility, θ is the mobility degradation factor due to the gate field [9], α is the bulk-charge factor which accounts for threshold voltage dependence on channel potential due to depletion thickness nonuniformity along the channel [10], and the rest of the parameters have their usual meaning.

Although, for the sake of simplicity, we are using here the simple model represented by (1), which does not account for carrier velocity saturation and other short channel effects, such higher order effects could be included in the model equation without loss of generality.

Section snippets

Direct fitting

The extraction of the model’s parameters is commonly performed using direct optimization [11], by fitting the measured current–voltage characteristics to the model’s implicit Eq. (1). Such traditional methods are usually not computationally efficient because of the implicit nature of (1), (2), (3). The extraction of R and θ usually turns out to be difficult, considering, as already mentioned, the similar effect that the total source-and-drain series resistance and the mobility degradation have

Indirect fitting

To improve the numerical fitting efficiency, we propose to do an indirect bidimensional (VGS, VDS) fit to the measured source-to-drain resistance, instead of directly fitting the current (1), (5). The measured source-to-drain resistance is:RmVDSID.Substituting the variable ID by VDS/Rm in (1), (2), (3) and after some algebraic manipulations yields:aVDVDS+aVG(VGS-VT)-2Rm=0,where the two coefficients are given by:aVD=RmRK(2α-1)-Rm2Kα+R2K(1-α)+RθandaVG=2Rm2K-2Rmθ-2RmRK.

The proposed parameter

Results

Fig. 1a presents three below-saturation output characteristics of an experimental 0.15 μm channel length 4 nm oxide thickness test DRAM MOSFET, measured at three above-threshold gate voltages. This is the set of data points used in this demonstration of the extraction procedure. The figure also contains the resultant three model playbacks obtained using the parameters extracted by applying the indirect procedure of bidimensionally fitting Rm, as expressed by (9), to the values of the measured

Discussion

Fig. 3 portrays the convergence of the parameters as they are being extracted using each of the two bidimensional fitting procedures studied: “Direct fit” to (5), (6), (7) and “Indirect fit” to (9). The figure presents their evolution from the initial guess values, converging towards their final values, as the number of iterations progresses. For convenience of discussion, we define here a general factor “f” which represents the quotient between the initial guess and the correct parameter

Conclusions

We have presented a new procedure to separately extract the mobility degradation factor and the source-and-drain series resistance parameters of MOSFET models. Additionally, bulk-charge factor, and K are extracted. The procedure is based on the bidimensional fitting of their current–voltage characteristics model equations to the measured ID(VGS, VDS) data. The proposed procedure is applicable to a single device and it is able to surmount the usual difficulty of separating the effects of

References (17)

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