Book excerpt: Numerical modeling of nonstationary transport effects using partial differential equations derived from the Boltzmann Transport Equation (BTE) is investigated. Augmented drift-diffusion (ADD) models and improved energy transport (ET) models for submicron device simulation are constructed and numerically implemented. Analytical derivation of the length coefficient for the ADD models is presented for both single- and multi-valley approximations. Results of typical $nsp+ - n - nsp+$ ballistic diodes for Si and GaAs are presented. The extension of the ADD model to two dimensions is then formulated, and the implementation problems with the standard box integration method, as used in conventional drift-diffusion (DD) models, are examined. Improved ET models are derived from the zeroth and second moments of the Boltzmann transport equation and from the presumed function form of the even part of the distribution function. Energy band nonparabolicity and non-Maxwellian distribution effects are included to first order. The ET models are amenable to an efficient self-consistent discretization, with standard techniques, taking advantage of the similarity between current and energy flow equations. Numerical results for ballistic diodes and MOSFETs are presented. Typical spurious velocity overshoot spikes, obtained in conventional hydrodynamics simulations of ballistic diodes, are virtually eliminated. By comparing the formulation of the ET and HD models, we find that the spurious spike is caused by the momentum relaxation time approximation and the resulting form of the thermal diffusion terms. Calculations based on a two-carrier-population model, at the anode junction, further confirm our analysis of the spurious spike.