A new grid-generation method for 2-D simulation of devices with nonplanar semiconductor surface

A general analytical method is proposed to transform a 2-D multilayer physical domain with the nonplanar semiconductor surface into a 2-D rectangular mathematical domain with the planar surface, in which a set of Fourier series are used to describe a general conformal mapping for each layer. Based on the proposed method, a simple iteration algorithm, which incorporates a nonlinear Jacobian-iteration method with the fast-Fourier transformation (FFT), is developed to solve a system of nonlinear equations due to the mutually coupled boundary conditions. As a result of the analytical conformal mapping, a regular, deformable grid-structure can be applied to simulate the device structure with the nonplanar semiconductor surface, and the device simulator using the conventional rectangle-based grid can be easily modified to simulate the device with the nonplanar semiconductor surface.