The bipolar quantum drift-diffusion model |
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Authors: | Xiu Qing Chen Li Chen |
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Institution: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China;(2) School of Sciences, Beijing University of Posts and Telecommunications, Beijing, 100876, P. R. China |
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Abstract: | A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated
Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the
global existence and semiclassical limit are obtained, in which semiclassical limit describes the relation between quantum
and classical drift-diffusion models. Furthermore, in the case of constant doping, we prove the weak solution exponentially
approaches its constant steady state as time increases to infinity.
Supported by the Natural Science Foundation of China (No. 10571101, No. 10626030 and No. 10871112) |
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Keywords: | quantum drift-diffusion fourth order parabolic system weak solution semiclassical limit exponential decay |
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