Monte Carlo Simulation of Electron-Electron Interactions in Bulk Silicon

Abstract

We have developed a novel Monte Carlo (MC) algorithm to study carrier transport in semiconductors in the presence of electron-electron scattering (EES). It is well known that the Boltzmann scattering operator for EES is nonlinear in the single-particle distribution function. Numerical solution methods of the resulting nonlinear Boltzmann equation are usually based on more or less severe approximations. In terms of the pair distribution function, however, the scattering operator is linear. We formulate a kinetic equation for the pair distribution function and related MC algorithms for its numerical solution. Assuming a spatially homogeneous system we derived a two-particle MC algorithm for the stationary problem and an ensemble MC algorithm for the transient problem. Both algorithms were implemented and tested for bulk silicon. As a transient problem we analyzed the mixing of a hot and a cold carrier ensemble. The energy of the hot ensemble relaxes faster with EES switched on. The cold ensemble is temporarily heated by the energy transferred from the hot ensemble. Switching on the electric field rapidly is known to result in an velocity overshoot. We observe that EES enhances the overshoot. The stationary algorithm was used to calculate the energy distribution functions at different field strengths.