@Article{IJNAM-13-6,
author = {},
title = {Stationary Solutions to Hybrid Quantum Hydrodynamical Model of Semiconductors in Bounded Domain},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {6},
pages = {898--925},
abstract = {<p style="text-align: justify;">In this paper we study the behaviour of a micro-sized semiconductor device by means
of a hybrid model of hydrodynamic equations. First of all, taking into account the quantum effects
in the semiconductor device, we derive a new model called the hybrid quantum hydrodynamic
model (H-QHD) coupled with the Poisson equation for electric potential. In particular, we write
the Bohm potential in a revised form. This new potential is derived heuristically by assuming that
the energy of the electrons depends on the charge density $n$ and on $\bigtriangledown n$ just in a restricted part
of the device domain, whereas the remaining parts are modeled classically. Namely, the device is
designed with some parts that feel the quantum effects and some parts do not. The main target
is to investigate the existence of the stationary solutions for the hybrid quantum hydrodynamic
model. Since the quantum effect is regionally degenerate, this will also makes the working equation
regionally degenerate regarding its ellipticity, and the corresponding solutions are weak only. This
paper seems the first framework to treat the equation with regionally degenerate ellipticity. In
order to prove the existence of such weak solutions, we first construct a sequence of smooth QHD
solutions, then prove that such a sequence weakly converges and its limit is just our desired weak
solution for the hybrid QHD problem. The Debye length limit is also studied. Indeed, we prove
that the weak solutions of the hybrid QHD weakly converge to their targets as the spacial Debye
length vanishes. Finally, we carry out some numerical simulations for a simple device, which also
confirm our theoretical results.</p>},
issn = {2617-8710},
doi = {https://doi.org/2016-IJNAM-471},
url = {https://global-sci.com/article/83270/stationary-solutions-to-hybrid-quantum-hydrodynamical-model-of-semiconductors-in-bounded-domain}
}