Development of Full Band Monte Carlo Methods for the Simulation of High Energy Electron Transport in Ultra-Wide Band Gap Semiconductors

Abstract

Silicon is approaching the physical limits of its capabilities in power electronics and so interest turns instead to ultra-wide bandgap semiconductors. This thesis is primarily concerned with understanding charge transport in two ultra-wide bandgap materials, diamond and cubic boron nitride (cBN). The wider band gaps of these materials mean that devices with smaller form fac tors and higher operating efficiencies can be fabricated, while their high thermal conductivities and radiation hardness makes them ideal for harsh environment applications. Due to the nascent stage of research into ultra-wide bandgap semiconductors, theoretical methods are employed to make up for the dearth of experimental results. To this end, density functional theory was used to calculate the ideal crystal structure from which the band structure was calculated and stored on a non-uniform tetrahedral grid that refines itself to minimise error. This was then used to calculate the numerical density of states (DOS) which compared well with what was given in the literature on diamond and cBN. Density functional perturbation theory was also utilised in the calculation of scattering parameters that are generally calculated empirically. A pre-existing Monte Carlo code was modified to enable the simulation of indirect band gap semiconductors with scattering rates determined by the numerically calculated DOS and scattering parameters. These methods were initially applied to silicon to benchmark the process, and the simulation results showed excellent agreement with analytic simulation and experimental results. These methods were then applied to diamond and cBN. The results for diamond compared well with analytic simulation and experimental results given by the literature. Similarly, the results for cBN compared well with analytic simulations from literature. The use of these methods then allows for the simulation of semiconductors at higher energies and for new and emerging materials where experimental results are sparse and empirical methods cannot be employed.