For high temperature, high power applications Silicon Carbide (SiC) continues to be a useful material for device fabrication because of its wide band gap, high breakdown field, and high thermal conductivity [1]. Some common power devices utilizing SiC include the following: Schottky and p-n junction diodes, thyristors, and UMOSFETs. Recent research has further contributed to the characterization of the electrical transport properties of 6H-SiC and 4H-SiC [2].

Model parameters reported in [2] are used in the standard field-dependent mobility model in ATLAS, and the velocity-field characteristics for 6H-SiC and 4H-SiC are simulated for several temperatures. A UMOSFET device simulation example is created with ATLAS, and the reported model parameters for 4H-SiC at 23 C are used to simulate the drain characteristics for several gate voltages.

Model Description

As the electric field in a semiconductor is increased, the carriers gain energy and accelerate in the electric field until no further energy can be imparted to the carriers. Ultimately, near high electric fields the carrier velocity reaches an upper limit at which it can travel no faster, the carrier saturation velocity. Carrier saturation velocity effects are incorporated in the standard field-dependent mobility model for electrons in ATLAS. This model is described by an analytical expression given by [3]

where ?n0 is the low field electron mobility, E is the electric field parallel to the current flow, VSATN is the electron saturation velocity, and BETAN is a unitless experimentally determined parameter.

This model is activated in ATLAS using the FLDMOB parameter on the MODEL statement. A plot of equation (1) for several values of BETAN is shown in Figure 1 where ?n0=450 cm/Vs and VSATN=2.2x10 cm/s have been used. As expected the electron mobility monotonically decreases as a function of increasing electric field, and the magnitude of the slope of the mobility increases with increasing BETAN.

Figure 1: Mobility Versus Electric Field Generated Using Equation (1)
for Several Values of BETAN (?n0=450 cm/Vs, VSATN=2.2x10 cm/s)

Simulation Results

Electron drift velocity as a function of electric field has recently been measured for conduction in the (0001) plane of 6H-SiC and 4H-SiC [2]. From the velocity-field measurements equivalent parameters for ?n0,VSATN, and BETAN were determined at room temperature and elevated temperatures.

The extracted model parameters from [2] are specified in the FLDMOB model in ATLAS, and are summarized in Table 1 and Table 2 for 6H-SiC and 4H-SiC, respectively. A uniformly doped substrate ( Nd=1x10 cm) is created in ATLAS and the voltage across the sample is ramped such that the electric field varies between 10 and 10 V/cm. Using the PROBE statement the electron mobility and electric field are saved as a function of bias voltage in an ATLAS log file. The statements used for this operation are shown below

LOG OUTF=VEL_FIELD.LOG
PROBE X=0.5 Y=0.05 DIR=90 / FIELD NAME=E_FIELD
PROBE X=0.5 Y=0.05 DIR=90 / N.MOB NAME=N_MOB

	23C	135C	320C
?n0 (cm2/Vs)	215	120	56
VSTN (cm2 /s)	1.9x10	1.4x10	1x10
BETAN (unitless)	1.7	2.5	4

Table 1. Model Parameters [2] Used in Velocity-Field Simulations for 6H-SiC

	23C	320C
?n0 (cm2/Vs)	450	130
VSTN (cm2 /s)	2.2x10	1.6x10
BETAN (unitless)	1.2	2.2

Table 2: Model Parameters [2] Used in Velocity-Field Simulations for 4H-SiC

The electron velocity is calculated from the product of the electron mobility and electric field. The simulated velocity field characteristics for 6H-SiC and 4H-SiC are shown in Figure 2 and Figure 3, respectively with the experimental data [2] overlaid. As expected the simulated curves show very good agreement with the experimental results.


Figure 2: Velocity-Field Characteristics for (0001) 6H-SiC for 23 C, 135 C, and 320 C, Simulated (solid lines), Experimental (symbols).	Figure 3: Velocity-Field Characteristics for (0001) 4H-SiC for Room Temperature and 320 C, Simulated (solid lines), Experimental (symbols)

The next simulation results are generated using a UMOSFET device. As previously reported in [4, 5], Id-Vd characteristics for UMOSFETs can be simulated without anisotropic mobility models because the majority of the current flows in the (0001) plane. A UMOSFET device similar to the one described in [6, 7] is created using ATLAS. The resulting structure is shown in Figure 4, where the doping levels in the structure and electrode locations have been indicated. Using the field-dependent mobility parameters for 4H-SiC at 23 C, the drain characteristics are generated with ATLAS and are shown in Figure 5.


Figure 4: 4H-SiC UMOSFET Structure Generated with ATLAS (n=5x10 cm, n-=2x10 cm, p-=2x10 cm)	Figure 5: Drain Characteristics for UMOSFET Structure for Vg=12V, Vg=16V, and Vg=20V (?n0=450 cm/Vs, VSATN=2.2x10 cm/s, BETAN=1.2)

Conclusion

The standard field-dependent mobility model (FLDMOB) has been reviewed with emphasis on its application to 6H-SiC and 4H-SiC materials. Model coefficients extracted from recent experimental results have been used in the mobility model, and the velocity-field characteristics for 6H-SiC and 4H-SiC were generated using the PROBE feature in ATLAS. The extracted mobility coefficients were used to simulate the drain characteristics of a 4H-SiC UMOSFET at room temperature. Using the updated coefficients obtained from [2] in ATLAS will allow more accurate simulation results for devices based on 6H-SiC and 4H-SiC materials.

References

Jayarama N. Shenoy et al, "High-Voltage Double-Implanted Power MOSFETs in 6H-SiC," IEEE Trans. Electron Devices, Vol. 18, No. 3, pp. 93-95, March 1997.

Imran A. Khan and James A. Cooper, "Measurement of High-Field Electron Transport in Silicon Carbide," IEEE Trans. Electron Devices, Vol. 47, No. 2, pp. 269-273, February 2000.

ATLAS User's Manual.

"ATLAS Simulation of SiC Devices Using Anisotropic Mobility Models," Simulation Standard, Vol. 8, No. 11, November 1997.

Lades M. and Wachutka G., " Extended Anisotropic Mobility Model Applied to 4H/6H-SiC Devices", Proc. IEEE SISPAD, pp.169-171, 1997.

Charles E. Weitzel et al., "Silicon Carbide High-Power Devices," IEEE Trans. Electron Devices, Vol. 43, No. 10, pp. 1732-1741, October 1996.

B. Jayant Baliga, "Trends in Power Semiconductor Devices," IEEE Trans. Electron Devices, Vol. 43, No. 10, October 1996.