Temperature Dependence of the Channel and Drift Resistance of SiC Power MOSFETs Extracted from I-V and C-V Measurements

SiC power MOSFETs show very promising electrical performance for efficient and reliable high temperature operation. This work presents a novel approach for the determination of the temperature dependence of SiC power MOSFET’s channel and drift resistance components in the on-state, which are extracted based on current-voltage (I-V) and capacitance-voltage (C-V) measurements without the need of data extrapolation. The results show that the channel resistance has weak, whereas the drift resistance has strong temperature dependence.


Introduction
Characterization of SiC power MOSFETs at different temperatures is highly important for both device and system engineers to fully benefit from SiC material properties, and to better understand and model the device characteristics at elevated operation temperatures [1,2]. The resistance between the drain-source terminals (Rds) of a MOSFET is a strongly temperature dependent parameter. Rds (of planar gate or trench power MOSFETs) can be divided into the channel resistance (Rch) of the inversion layer at the oxide/SiC interface, and the sum of the JFET, epi-layer, and n + substrate resistances, which is denoted as Rdrift, Rds=Rch+Rdrift, see equivalent circuit 3c). The (small) contact resistances of the source and drain terminals are included in Rch and Rdrift, respectively, and are negligible in power MOSFETs. The value of Rch is controlled by Vgs and significantly reduces when the device is turned on by increasing Vgs above the threshold voltage (Vth). By contrast, Rdrift has only a small dependence on Vgs in the JFET region for Vgs > 0V. Both Rch and Rdrift depend on the applied drain-source bias (Vds).
Several methods have been proposed to extract the source (Rs) and the drain (Rd) residual resistance components, Rs+Rd=Rres (Rs and Rd do not depend on Vgs), of lateral MOSFETs e.g., in [3][4][5][6]. In [3,4] Rres is extrapolated at the intercept of Rds versus (Vgs−Vth) -1 . In addition, it was assumed that Rdrift(Vds, Vgs) ≈ Rdrift(Vds) ≈ Rres(const) for Vgs ~ 20 ≫ Vth. This extrapolation method was applied to SiC power MOSFETs in [7,8]. A similar method was developed for GaN FinFETs and validated by Technology Computer-Aided Design (TCAD) simulations in [9]. In [10] the components of the drainsource resistance were evaluated by means of TCAD simulations for SiC power MOSFETs of different nominal Vds.
In this paper we show a fast and simple technique for reliably extracting the components of the onstate resistance at different temperatures. The new method proposed in this work for estimating/extracting Rch, Rdrift is based on the measurement of the inter-terminal capacitances between gate-source (Cgs/Csg) and gate-drain (Cgd/Cdg) in the on-state, the estimation of the overlap capacitance (Cov) between the gate-source terminals, and the measurement of the drain-source resistance Rds [11]. In the following the extrapolation and the new C-V based method are explained and compared by the extraction of Rch and Rdrift for three different types of SiC power MOSFETs.

Extrapolation Method
The current-voltage characteristic of a power MOSFET can be expressed in the linear mode of operation for low Vds using the gradual channel approximation as where k=WeffµeffCox/Leff (Weff the effective channel width, µeff the effective channel mobility (assumed independent of Vgs), Cox the gate oxide capacitance per unit area, and Leff the effective channel length) [12]. Assuming Vgs−Vth >> 0.5(Vds−IdRdrift) and using the relation Rds= Vds/Id, (1) can be transformed into From (2) Rdrift can be determined at the vertical intercept of extrapolated Rds versus (Vgs−Vth) -1 (at maximum bias Vgs = 20V), see Fig. 2b). Rds is derived from the Id-Vgs characteristic shown in Fig. 1a) and 1b). The values of Vth are obtained from the Id-Vgs characteristic by linear extrapolation of Id at the Vgs values of maximum transconductance gm,max, as depicted in Fig. 2a).

New C-V based Extraction Method
The new extraction methodology for Rch and Rdrift is based on their dependence with the MOSFETs inter-terminal capacitances Cgs/Csg and Cgd/Cdg in the on-state [11,13]. The capacitances Cij = -∂qi/∂vi are defined based on the change of the small-signal charge q and voltage v at the device terminals i,j ∈ {g, d, s} [11]. These capacitance characteristics must be measured at lower frequency i.e., some ten kHz (~ 30kHz) as shown in Figs. 3a) and 3b), to limit the influence of the terminal series impedances Zg, Zd, and Zs [11]. By solving the power MOSFET simplified lumped electrical equivalent circuit in the on-state, see Fig. 3c) [13], [14], using the conditions |Zd|, |Zs| << Rch, Rdrift and the relation Cgg=Cg'+Cov, where Cgg is the total terminal gate capacitance, Cov the overlap capacitance between the gate and source metallization in parallel to the capacitance between the gate and the n + source, and Cg'=Cg1+Cg2 is the oxide capacitance over the channel and JFET region, Cdg and Csg can be extracted as The value of Cov is approximated at the maximum depletion of the channel region when the value of Csg becomes minimal, which leads to C ov ≈ min(C sg ).
By defining Csg' = Csg−min(Csg) ≈ Csg−Cov the ratio of Cdg/Csg' yields Finally, based on (5) and (6) the relation between Rds, Rch, and Rdrift can be derived as

Results
The new C-V and the extrapolation method were applied to extract Rch and Rdrift of three SiC power MOSFETs M1-M3 listed in Tab. 1 The Id-Vgs characteristics of M1-M3, as depicted for M1 in Fig 1 a)  The C-V characteristics of Csg and Cdg depicted for M1 in Figs. 3a) and 3b) were measured with the impedance analyzer Keysight E4990A and the test fixture Keithley 16047E. The MOSFET's terminals were connected to the high, low, and guard terminals [11], respectively. The values of Cov were obtained from the Csg characteristic according to (5). Cov(T) of M1-M3 vary less than 1% in the measured temperature range. The ratios of Cdg/Csg'(T) at Vgs=20 V, which were derived based on (7), are plotted in Fig. 4 and listed in Tab. 3.     1%. Yet, a larger discrepancy of Rdrift is observed for M2 and M3 with relative difference up to 27.1%. These differences might be introduced by the linear extrapolation, the approximation of Rdrift ≈ Rres, and/or the simplified equivalent circuit in Fig. 3c) of the MOSFETs distributed behavior.

Conclusion
This work demonstrates a new and simple approximation technique to determine Rch(T) and Rdrift(T) from the MOSFET's Id-Vgs, Csg and Cdg characteristics. The separation of Rds(T) into Rch(T) and Rdrift(T) allows a more accurate modeling of the heat generation within SiC power MOSFETs during hightemperature operation [16]. In addition, the new method serves as quality control of the MOSFET's gate structure and can be applied to extract other MOSFET parameters e.g., µeff, when comparing devices with different channel length L, and suchlike.