Time-periodic flows of electrons and holes in semiconductor devices

On a drift-diffusion system for semiconductor devices

In this note we study a fractional Poisson-Nernst-Planck equation modeling a semiconductor device. We prove several decay estimates for the Lebesgue and Sobolev norms in one, two and three dimensions. We also provide the first term of the asymptotic expansion as $t\rightarrow\infty$.

非线性半导体 Boltzmann 方程的亚矫顽性

Hypocoercivity for the non-linear semiconductor Boltzmann equation

本文研究了平坦环面上的半导体器件非线性动力学模型，通过亚矫顽性估计证明其在无小性假设下向平衡态呈指数衰减，并指出这是首个此类结果。

Classical solutions of drift-diffusion equations for semiconductor devices: the 2d case

We regard drift-diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes. This evolution equation falls into a class of quasi-linear parabolic systems which allow unique, local in time solution in certain Lebesgue spaces. In particular, it turns out that the divergence of the electron and hole current is an integrable function. Hence, Gauss' theorem applies, and gives the foundation for space discretization of the e…

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

We are concerned with the global existence and large time behavior of entropy solutions to the one dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy …