Two-dimensional (2-D) effects are becoming increasingly important in the diffusion of impurities in submicrometer silicon devices. The authors describe a 2-D process simulator, PREDICT2, that handles implant damage effects, annealing, and lateral diffusion. PREDICT2 simulates the diffusion of impurities in silicon by using phenomenological diffusion coefficients. The phenomenological models are verified by comparing simulated and experimental results. This approach is compared with that of point-defect-based simulators. The experimental technique for measuring impurity profiles in two dimensions is outlined. The method for generating diffusion models is illustrated by examining 2-D phosphorous diffusion. Numerical simulations and experimental measurements are compared. The numerical methods used in the simulator are described, and directions for future work are suggested.>

Block iterative methods are applied to hydrodynamic simulations of a one-dimensional submicrometer semiconductor device. It is shown that block successive underrelaxation (SUR) converges with a fixed relaxation factor omega =0.13 for simulations at 300 K and omega =0.04 at 77 K. To demonstrate the robustness of the block iterative method, numerical simulations of a steady-state electron shock wave in Si at 300 K for a 0.1- mu m channel and at 77 K for a 1.0- mu m channel are presented. The block SUR method is parallelizable if each diagonal block solve can be done efficiently in parallel. Using chaotic relaxation and the preconditioned conjugate gradient method for the parallel diagonal block solves, a parallel speed up of approximately 2.5 is obtained on 10 processors of a Butterfly GP-1000.>

An introduction to the hydrodynamic model for semiconductor devices is presented. Special attention is paid to classifying the hydrodynamic PDEs (partial differential equations) and analyzing their nonlinear wave structure. Numerical simulations of the ballistic diode using the hydrodynamical device model are presented, as an illustrative elliptic problem. The importance of nonlinear block iterative methods is emphasized. Arguments for existence of solutions and convergence of numerical methods are given for the case of subsonic electron flow.>