Spherical Harmonic Modeling of a 0.05 μmBase BJT: A Comparison with Monte Carloand Asymptotic Analysis

We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm base BJT. We find the SH and the MC methods give very similar results for the energy distribution function, using an analytical band-structure, at all points within the tested devices. However, the SH method can be as much as seven thousand times faster than the MC approach for solving an identical problem. We explain the agreement by asymptotic analysis of the system of equations generated by the SH expansion of the BTE.