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A Block-Centered Upwind Approximation of the Semiconductor Device Problem on a Dynamically Changing Mesh

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Abstract

The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initial-boundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously. The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan, 250100, China

    Yirang Yuan

  2. Shandong Applied Financial Theory and Policy Research Base, Jinan, 250100, China

    Changfeng Li

  3. School of Economics, Shandong University, Jinan, 250100, China

    Changfeng Li

  4. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Huailing Song

Authors
  1. Yirang Yuan
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  2. Changfeng Li
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  3. Huailing Song
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Corresponding author

Correspondence to Changfeng Li.

Additional information

This research was supported the Natural Science Foundation of Shandong Province (ZR2016AM08), Natural Science Foundation of Hunan Province (2018JJ2028), National Natural Science Foundation of China (11871312).

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Yuan, Y., Li, C. & Song, H. A Block-Centered Upwind Approximation of the Semiconductor Device Problem on a Dynamically Changing Mesh. Acta Math Sci 40, 1405–1428 (2020). https://doi.org/10.1007/s10473-020-0514-x

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  • DOI: https://doi.org/10.1007/s10473-020-0514-x

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