2-D MOSFET modeling including surface effects and impact ionization by self-consistent solution of the Boltzmann, Poisson, and hole-continuity equations

We present a new two-dimensional (2-D) MOSFET simulation method achieved by directly solving the Boltzmann transport equation for electrons, the hole-current continuity equation, and the Poisson equation self-consistently. The spherical harmonic method is used for the solution of the Boltzmann equation. The solution directly gives the electron distribution function, electrostatic potential, and the hole concentration for the entire 2-D MOSFET. Average quantities such as electron concentration and electron temperature are obtained directly from the integration of the distribution function. The collision integral is formulated to arbitrarily high spherical harmonic order, and new collision terms are included that incorporate effects of surface scattering and electron-hole pair recombination/generation. I-V characteristics, which agree with experiment, are calculated directly from the distribution function for an LDD submicron MOSFET. Electron-hole pair generation due to impact ionization is also included by direct application of the collision integral. The calculations are efficient enough for day-to-day engineering design on workstation-type computers.