4.5.4.2 MESFET Simulation

The 4H-SiC MESFET shown in Fig. 4.36 is simulated. For the calibration the specifications obtained from Cree's CRF-24010 4H-SiC MESFET are used to define the simulated device. The charge carrier transport characteristics (charge carrier mobility and saturated velocity), the device dimensions and the doping details are adjusted until good agreement between the simulated and measured IV characteristics is obtained.

The optimized transistor parameters are listed in Table 4.7. The simulated and measured DC IV characteristics are compared in Fig. 4.37. Excellent agreement between the simulated and measured data were obtained. This MESFET produces a maximum channel current of about 250 mA/mm.

Figure 4.37: DC IV characteristics (left), and transfer characteristics (right) of 4H-SiC MESFET.

The ability of the gate bias to turn the device off and on is good, as indicated by the channel current with zero and high reverse gate bias applied.

Figure 4.38: Current density (left), and reverse bias characteristics (right) in 4H-SiC MESFET.

Very good turn-off characteristics are observed for a reverse bias of -10V.

The ability of the device to modulate current is given by the device transconductance, which for this device is about $g_\mathrm{m}$=160 mS/mm. The zero gate voltage drain current at V $_\mathrm{DS}=10$ V is 1.5 A/mm. The current density profile at the gate quiescent voltage of V $_\mathrm{GS}=-9$ V and V $_\mathrm{DS}=40$ V is displayed in Fig. 4.38 (left). This device has a drain source breakdown voltage of 110 V with a leakage current of 1 $\mu$A/mm as depicted in Fig. 4.38 (right).

Once a good agreement is obtained between both the measured and simulated DC performance, the simulator can be used for a variety of purposes. AC simulation is conducted for the frequency range from 100 MHz to 4 GHz to determine the desired small signal RF characteristics of 4H-SiC MESFET. The S-parameters obtained from the simulation are modeled using the small-signal equivalent circuit shown in Fig. 4.39 [187]. This equivalent circuit which consists of capacitance $C$, inductance $L$, resistance $R$, and a current source involving transconductance $g_\mathrm{m}$ and delay time $\tau_\mathrm{t}$, can be divided into two parts.

i) Extrinsic elements: $L_\mathrm{g}$, $R_\mathrm{g}$, $C_\mathrm{pg}$, $L_\mathrm{s}$, $R_\mathrm{s}$, $R_\mathrm{d}$ $C_\mathrm{pd}$, and $L_\mathrm{d}$ are independent of the bias.
ii) Intrinsic elements: $g_\mathrm{m0}$, $R_\mathrm{i}$, $C_\mathrm{gs}$, $R_\mathrm{gd}$, $C_\mathrm{gd}$, $R_\mathrm{ds}$, $C_\mathrm{ds}$, and $\tau_\mathrm{t}$ are function of the bias.

In order to determine the small-signal RF characteristics of this device the extrinsic elements are first set according to the measured data at cold-MESFET conditions obtained from [187]. Then, de-embedding the obtained extrinsic elements yields the values of the intrinsic elements as listed in Table 4.8.

Figure 4.39: Small-signal equivalent circuit (left), and comparison of measured and simulated S-parameters (right) of 4H-SiC MESFET.

Table 4.8: Optimized small-signal circuit elements for 4H-SiC MESFET.

extrinsic	$L_\mathrm{g}=40.7$pH	$R_\mathrm{g}=15.5\Omega$	$L_\mathrm{s}=0.97$pH	$R_\mathrm{s}=11.4\Omega$
	$R_\mathrm{d}=0.1\Omega$	$L_\mathrm{d}=1.0$mH	$C_\mathrm{pg}=0$	$C_\mathrm{pd}=0$
intrinsic	$g_\mathrm{m0}=7.9$mS	$R_\mathrm{i}=0.1\Omega$	$C_\mathrm{gs}=82$fF	$R_\mathrm{gd}=10\mathrm{M}\Omega$
	$C_\mathrm{gd}=10.8$fF	$R_\mathrm{ds}=1.1\mathrm{k}\Omega$	$C_\mathrm{ds}=19.6$fF	$\tau _\mathrm{t}=4.7$psec

The measured and simulated S-parameters for this device are depicted in the right side of Fig. 4.39. Very good agreement between the simulated and measured data was obtained. It is important to note that the RF results presented here were obtained at a high drain-to-source bias voltage of 40 V and gain-to-source voltage of -9 V.

Once the S-parameter values are determined, a simulation is performed at frequency of up to 40 GHz in order to extract other important performance FOM for RF devices: the cutoff frequency $f_\mathrm{t}$, the maximum frequency $f_\mathrm{max}$, the unilateral power gain (Masson's gain, U), the maximum available gain (MAG), and the maximum stable gain (MSG).

The cutoff frequency (unity current gain frequency) $f_\mathrm{t}$ can be calculated by extrapolation of the short circuit current gain parameter $H_\mathrm{21}$, given by

$$H_\mathrm{21}=\displaystyle\frac{-2S_{21}}{(1-S_{11})(1+S_{22})+S_{12}\cdot S_{21}}.$$ (4.11)

$H_\mathrm{21}$ drops with a slope of -20 dB/dec, and has a magnitude of unity at $f=f_\mathrm{t}$

$$\left\vert H_\mathrm{21}\right\vert _{f=f_\mathrm{t}}=1.$$ (4.12)

The value of $f_\mathrm{max}$ can be determined in two ways depending on the invariants used for its definition [188]. The first is from the unilateral power gain (U), reads

$$U(f)=\displaystyle\frac{\left\vert\displaystyle\frac{S_{21}}{S_{1... ...12}}\right\vert-2\,\mathrm{Re}\left(\displaystyle\frac{S_{21}}{S_{12}}\right)},$$ (4.13)

where $k$ is Kurokawa's stability factor, defined as [188]

$$k(f)=\displaystyle\frac{1-\left\vert S_{11}\right\vert^2-\left\ve... ...\right\vert^2}{2\left\vert S_{12}\right\vert\cdot\left\vert S_{21}\right\vert}.$$ (4.14)

The second way to determine $f_\mathrm{max}$ is to use the maximum available gain (MAG) and the maximum stable gain (MSG)

$$MAG(f)=\left\vert\displaystyle\frac{S_{21}}{S_{12}}\right\vert\cdot(k\pm\sqrt{k^2-1}),$$ (4.15)

for $k\geq 1$, $f_\mathrm{max}$ is then determined from

$$\left\vert MAG \right\vert _{f=f_\mathrm{max}}=1$$ (4.16)

otherwise, the maximum stable gain (MSG) is used to determine $f_\mathrm{max}$ for $k\leq 1$

$$MSG=\left\vert\displaystyle\frac{S_{21}}{S_{12}}\right\vert.$$ (4.17)

The MAG drops with a slope of -20 dB/dec as a function of the frequency near to $\left\vert MAG\right\vert=1$, and the MSG drops with -10 dB/dec as a function of the frequency.

Figure 4.40: Small signal current and power gain for 4H-SiC MESFET.

The transition between MAG and MSG ($k=1$) is defined as the stability point where the value of $f_\mathrm{max}$ can eventually be extrapolated with a slope of -20 dB/dec for a given gate width $W_\mathrm{g}$.

The small-signal current and power gain depicted in Fig. 4.40 yields an $f_\mathrm{t}=5.62$ GHz and $f_\mathrm{max}=37.18$ GHz at 0 dB H $_\mathrm{21}$ and MAG/MSG, respectively. This device produced 15dB at 1 GHz. These results clearly demonstrate the advantages of 4H-SiC for high-power microwave application where its high-thermal conductivity, high-voltage and high-power density capability are very attractive.

T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation