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A characteristic finite element algorithm based on domain decomposition is structured in this paper to approximate numerically multi-dimensional semiconductor transient problems of heat conduction. Finite element approximation is presented for the electric field potential equation, and a domain decomposition discretization with characteristic finite element is put forward for the electron concentration equation, hole concentration equation and heat conductor equation. An optimal order error estimate in L2 norm is derived for the coupled system by using some techniques such as variation, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, prior estimates theory and other techniques of partial differential equations. Finally, experimental data consistent with theoretical convergence rate are shown. This type of numerical method is of high computational efficiency and can successfully solve this international problem.

Domain Decomposition Modified with Characteristic Finite Element Method for Numerical Simulation of Semiconductor Transient Problem of Heat Conduction