Electron. J. Differential Equations, Vol. 2018 (2018), No. 200, pp. 1-19.

Solution to a multi-dimensional isentropic quantum drift-diffusion model for bipolar semiconductors

Jinmyong Ri, Sungjin Ra

Abstract:
We study the existence of weak solution and semiclassical limit for mixed Dirichlet-Neumann boundary value problem of 1,2,3-dimensional isentropic transient quantum drift-diffusion models for bipolar semiconductors. A time-discrete approximate scheme for the model constructed employing the quantum quasi-Fermi potential is composed of non-degenerate elliptic systems, and the system in each time step has a solution in which the components of carrier's densities are strictly positive. Some stability estimates guarantee convergence of the approximate solutions and performance of the semiclassical limit.

Submitted January 12, 2016. Published December 21, 2018.
Math Subject Classifications: 35A01, 35D30, 35J25, 35K35.
Key Words: Quantum drift-diffusion; bipolar semiconductor; time-discretization; mixed boundary value problem; semiclassical limit.

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Jinmyong Ri
Institute of Mathematics
State Academy of Sciences
Pyongyang, Korea
email: jmri2015@163.com
Sungjin Ra
Department of Mathematics
University of Science
Pyongyang, Korea
email: math.inst@star-co.net.kp

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