Semiconductor nonlinear device modeling using multiwavelets

Modeling and simulation of semiconductor devices requires solution of highly nonlinear equations, such as the Boltzmann transport, hydrodynamic, and drift-diffusion equations. The conventional finite-element method (FEM) and finite difference (FD) schemes always result in oscillatory results, and are ineffective when the cell Reynolds number of the system is large. Several ad hoc schemes have been employed to address the instability issue, including the Scharfetter-Gummel transformation, Petrov-Galerkin method, and upwind algorithms; but each suffers from its shortcomings. We propose a new approach of the multiwavelet-based finite-element method (MWFEM) to solve the semiconductor drift-diffusion system. In this approach, multiscalets are employed as the basis functions. Due to its ability of tracking the tendency, namely, the first derivative of the unknown function, the MWFEM shares the versatility of the conventional FEM while remaining stable in a highly nonlinear system. Comparison with the Scharfetter-Gummel method, upwind FEM, and conventional FEM shows that the MWFEM performs excellently under circumstances of both small- and large-cell Reynolds numbers. A complete 1D drift-diffusion solver base on the MWFEM is implemented. Numerical results demonstrate the high efficiency and accuracy of the new method.