Advantages of collocation methods over finite differences in one-dimensional Monte Carlo simulations of submicron devices

Collocation methods are very useful when one-dimensional Monte Carlo simulations of semiconductor submicron devices require a very accurate solution of Poisson's equation. Potential and electric field may be solved simultaneously with better accuracy than using finite differences. The extension to two dimensions is also outlined. We present the results obtained for Monte Carlo simulation of submicron W/Si and AuGaAs Schottky barrier diodes under forward bias conditions. The accurate solution for the electric field at the ohmic contact boundary allows us to model the injected current and to account for depletion of carriers. Tunnelling effects across the barrier are also included in the simulation.