Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time

Abstract

In this paper we propose a generalization of the hybrid model for semiconductors already discussed by Chiarelli et al.and Di Michele et al., including a non-constant pressure functional and relaxation time. Roughly speaking, we assume that the normalized electron temperature and the relaxation time in the classical and quantum domains are different from each other. We derive the model heuristically, introducing a generalization of the stress tensor, which accounts for an interface contribute, and afterwards we prove the existence and uniqueness of weak solutions for such a new hybrid model. We apply the approach proposed by Di Michele et al. to obtain the stationary solutions to our problem, namely we prove the existence of the solution for a regularized problem, then we achieve the existence of a weak solution for the hybrid problem as a proper limit of the regular solution previously obtained.

Existence of solutions for a viscous hybrid quantum system for arbitrary large current density

“…This approach is named hybrid. Many hybrid models have been proposed in the past, see previous works [1][2][3][4][5][6][7][8][9][10][11], and references therein. See also previous works [12][13][14] for other applications of the hybrid approach.…”

“…To introduce proper transmission conditions at the interface is the critical part of this approach since the choice is somehow arbitrary because it cannot be based on experimental data. In the works by Chiarelli et al [20] and Di Michele et al [8], a new approach, based on an intrinsically hybrid equation, has been proposed (see also previous works [9–11]). The idea is to describe the behaviour of the current density J , of the charge density n , and of the electrical potential V assuming the domain ideally split into a classical and a quantum part.…”

Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case

“…Particularly, the comprehensive reviews can be found in the recent interesting papers [3, 14, 25-28, 34, 54-56]. For the other topic on Euler-Poisson equations with quantum effect, we refer to [6][7][8][9][10].…”