Simplified scattering rate calculation in nonparabolic hydrodynamic equations

A method is presented to simplify the calculation of the scattering rates in a hydrodynamic model based on the nonparabolic balance equations. A four-dimensional integral to calculate the scattering rates is reduced to a two-dimensional integral. This method has been applied to calculate the linear and nonlinear electron transport in a SiC system. The results obtained using the simplified method and the regular method differ only slightly up to an electric field strength of 200 kV/cm, both being in good agreement with Monte Carlo simulation, but the computation time is reduced by two orders of magnitude. Since the momentum and energy relaxation times are functions of these scattering rates, this method will be very useful in device simulations for nonparabolic semiconductors.