LDD MOSFET simulation is performed by directly solving the Boltzmann Transport Equation for electrons, the Hole-Current Continuity Equation and the Poisson Equation self-consistently. The spherical harmonic expansion method is employed along with a new Scharfetter-Gummel like discretization of the Boltzmann equation. The solution efficiently provides the distribution function, electrostatic potential, and the hole concentration for the entire 2-D MOSFET.