2-D MOSFET Simulation by Self-Consistent Solution of the Boltzmann and Poisson Equations Using a Generalized Spherical Harmonic Expansion

MOSFET simulation is performed by direct self-consistent solution of the Boltzmann, Poisson and Hole Continuity equations. To formulate the Boltzmann equation, a spherical harmonic approach has been developed which allows for expansion to arbitrarily high order. The self-consistent 2-dimensional MOSFET simulations incorporated four spherical harmonics. Simulation results provide the distribution function for the entire device, as well as substrate current, and average quantities including electron temperature, average velocity, and carrier concentration.