Modeling impact ionization in a BJT by means of spherical harmonics expansion of the Boltzmann transport equation

A spherical-harmonics expansion method is used to find an approximate numerical solution of the Boltzmann transport equation (BTE) in a 1-D semiconductor device including acoustic and optical phonon, ionized impurity, and impact ionization scattering as well as a system of nonparabolic bands fitting the experimental density of states up to 2.6 eV. The method is applied to the simulation of a 1-D BJT and to the computation of the collector current multiplication factor. A comparison with experimental data is presented.>