Comparison of Monte Carlo and Deterministic Simulations of a Silicon Diode

Electron transport models in Si transistors with channel length of 0.4 microns and 50 nanometers are examined and compared between classical Direct Monte Carlo Simulations and deterministic WENO solvers for a self-consistent kinetic field-relaxation Poisson model. This model is a well accepted low density reduction of the full non-equilibrium transport phenomena. In this comparison we control the calibration of the field dependent, saturated mobility. Our computations show that, at channel length of order 0.4 microns, the relaxation model captures the the first two moments of the particle distribution function inside the channel. In particular a domain decomposition technique that implements classical drift diffusion in the high density regions and augmented drift diffusion inside the channel region gives a correction to the classical drift diffusion simulations, and produces similar qualitative results to the Monte Carlo simulations with a 0.002 CPU time reduction factor. However, we show that in the case of a 50 nanometer channel, the kinetic field-relaxation model fails to approximate well even the first moment, and in particular it does not approximate weil the current voltage curve output from Monte Carlo simulations, making it necessary to incorporate high energy effects into the collision operator.