Approximation of the BTE by a Relaxation-time Operator: Simulations for a 50 nm-channel Si Diode

In this work we present comparisons between DSMC simulations of the full BTE and deterministic simulations of a relaxation‐time approximation for a nowadays size Si diode. We assume a field dependent relaxation time fitted to give the same drift speed (mean velocity) as DSMC simulations for bulk Si. We compute the density, mean velocity, force field, potential drop, energy and I‐V curves of both models and plot the pdf of the deterministic relaxation‐time model. We also compare the results to augmented drift‐diffusion models proposed in the literature to approximate the relaxation time system in the quasi‐ballistic regime. The quasi‐ballistic and ballistic regimes are distinguished by using local dimensionless parameters.