Spherical Harmonic Modeling of a 0.05 μm Base BJT: A Comparison with Monte Carlo and Asymptotic Analysis

Abstract

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.

Advances in the Spherical Harmonic–Boltzmann–Wigner approach to device simulation

“…To make the BTE tractable we apply a spherical harmonic expansion method which, for 2D steady state device simulation, transforms it into a three-dimensional partial differential/difference equation. In previous work we have shown that the Spherical Harmonic Boltzmann method can provide the distribution function for an entire 2D MOSFET, and obtain agreement for current-voltage characteristics, as well as substrate current for a single device [4,10]. We have also shown that the method agrees with Monte Carlo simulations while being very efficient from a computational point of view.…”

“…Comparisons with Monte Carlo simulations have been performed on various devices including a bipolar junction transistor that has a base width of 0.075 µm [10], and N+NN+ structures of various widths. (We choose the N+NN+ structure because it is one-dimensional and has characteristics similar to that of a MOSFET inversion layer in the semiclassical approximation.)…”

“…The Spherical Harmonic Boltzmann method achieves device simulation by efficient direct solution of the Boltzmann transport equation (BTE) [1][2][3][4][5][6][7][8][9][10]. When coupled to the Poisson equation, the BTE-Poisson system will provide the self-consistent distribution function for an entire device.…”