Numerical Simulation of Thermal Oxidation Process in Semiconductor Devices Using Mixed—Hybrid Finite Elements
In this lecture, we present the basic mathematical and numerical tools for the simulation of the thermal oxidation process in semiconductor device technology. The mathematical model is first reviewed, emphasizing that it requires at each time level the solution of a diffusion-reaction problem and a fluid-structure interaction problem. Then, mixed-hybrid finite elements are introduced for the numerical approximation of each differential subproblem, with a detailed discussion of the static condensation procedure to eliminate the mixed variables in favor of the hybrid Lagrange multipliers. Several numerical examples are included to validate the accuracy and stability of the proposed computational procedure.
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