A general analytical method is proposed for transforming a 2-D multilayer physical domain with the nonplanar semiconductor surface into a 2-D rectangular mathematical domain with a planar surface, with a set of Fourier series being used to describe a general conformal mapping for each layer. Based on the method, a simple iteration algorithm, which incorporates a nonlinear Jacobian-iteration method with the fast Fourier transform (FFT), is developed to solve the 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.>

A methodology for obtaining the self-consistent solution of semiconductor device equations discretized in the finite-difference scheme is proposed, in which a new discretized Green's function solution method is used to solve the two-dimensional discretized Poisson equation and a surface mapping technique is developed to treat arbitrary surface boundary conditions. The two-dimensional potential distribution can then be expressed in terms of charge density distribution and bias conditions. Using the derived potential distribution, the SLOR-nonlinear iteration for the current continuity equations of both carriers can be performed by incorporating a new algorithm to obtain the self-consistent solution of a full set of semiconductor device equations without any outer iteration. An Si MESFET simulation demonstrates that the convergent rate of the proposed method can be speeded up to 4-8 times that of Gummel's method. The new method can be incorporated with the conventional solution methods to get a stable and efficient computation scheme.>