High field density-functional-theory based Monte Carlo: 4 H -SiC impact ionization and velocity saturationA full-band ensemble Monte Carlo simulation has been used to study the high-field carrier transport properties of 4H-SiC. The complicated band structure of 4H-SiC requires the consideration of band-to-band tunneling at high electric fields. We have used two models for the band-to-band tunneling; one is based on the overlap test and the other on the solution of the multiband Schrödinger equations. The latter simulations have only been performed for holes in the c-axis direction, since the computer capacity requirement are exceedingly high. Impact-ionization transition rates and phonon scattering rates have been calculated numerically directly from the full band structure. Coupling constants for the phonon interaction have been deduced by fitting of the simulated low-field mobility as a function of lattice temperature to experimental data. Secondary hot electrons generated as a consequence of hole-initiated impact ionization are considered in the study for both models of band-to-band tunneling. When the multiband Schrödinger equation model is used for holes in the c-axis direction, a significant change in the electron energy distribution is found, since the hole impact-ionization rate is very much increased with this model. The secondary electrons increase the average energy of the electron distribution leading to a significant increase in the electron-initiated impact-ionization coefficients. Our simulation results clearly show that both electrons and holes have to be considered in order to understand electron-initiated impact ionization in 4H-SiC.

A set of equations for calculating the probability for electric-field-induced interband transitions in periodic crystals (Krieger and Iafrate 1986 Phys. Rev. B 33 5494) can be used in combination with the full band Monte Carlo method to study high-field electronic transport properties in semiconductors. However, when the equations are applied to realistic cases in which the underlying band structure is obtained from numerical band structure programmes, the equations are not directly solvable because of the indeterminacy of the phases of the band structure Bloch wavefunctions. Here we discuss this problem and present a method for choosing the phases of the Bloch functions in such a way that the equations yield physically correct interband transition probabilities.

Monte Carlo simulation of electron transport in 2H-SiC using a three valley analytical conduction band modelA full band Monte Carlo study of the electron transport in 3C-SiC is presented based on an ab initio band structure calculation using the local density approximation to the density functional theory. The scattering rates and impact ionization transition rates have been calculated numerically from the ab initio band structure using both energy dispersion and numerical wave functions. This approach reduces the number of empirical parameters needed to a minimum. The two empirical coupling constants used have been deduced by fitting the simulated mobility as a function of lattice temperature to experimental data. The peak velocity was found to be approximately 2.2 ϫ10 7 cm/s with a clear negative differential mobility above 600 kV/cm. The electron initiated impact ionization coefficients were found to be 2-10 times stronger than the reported values for the hole initiated impact ionization.