Two dimensional submicron MOSFET simulation using generalized expansion method and fixed point iteration technique to the Boltzmann transport equation

2D MOSFET simulation is performed by direct solution of the Boltzmann equation. This method is based on a new generalized formulation of the Boltzmann equation which uses a spherical harmonic expansion to arbitrarily high order. The new formulation takes advantage of special properties of spherical harmonics to reduce the dimensionality of the problem, as well as facilitates analytical evaluation of the collision integral. This form is then solved using a fixed point SOR iterative technique, which avoids direct solution of large matrix equations. 2D MOSFET simulations provide the distribution function for the entire device, as well as average quantities including electron temperature, average velocity, and carrier concentration.