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In this thesis, a monotone iterative method for solving two-dimensional semiconductor device equations is presented. We solve the semiconductor device equations by using decoupled approach to decouple three nonlinear PDE's, i.e., nonlinear Poisson equation, electron current continuity and hole current continuity equations. Then, finite difference approximation is applied to discretize the decoupled PDE's from which a system of nonlinear algebraic equations is obtained. Finally, monotone iterative method is applied to solve each system of nonlinear algebraic equations. The main concept of this method is that it takes some special nonlinear property of each equation, and analyzes each decoupled equation by using finite difference approximation and monotone iterative method.
Based on the fact of a high nonlinear property of each semiconductor equation, the proposed monotone iterative method has several advantages. First, it is global convergence. In other words, it converges monotonically for arbitrary initial guess. Secondly, by comparing with a standard Newton's method, this method is easy for implementation, relatively faster with much less computation time, and its algorithm is inherently parallel in scientific computation.
A two-dimensional N-MOSFET semiconductor device model problem under various bias conditions has been successfully implemented and several typical numerical results of this model problem, such as potential distribution and dc current characteristics of a device, are demonstrated. By comparing with a standard Newton's method, a speed-up factor of 30X can be achieved.
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