加拿大Champlain学院和McGill大学梅茗学术报告预告

报告题目：Hydrodynamic System of Semiconductors with Quantum Effect

报告摘要：In this talk, 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 its derivative  just in a restricted part of the device domain, whereas the remaining parts are modeled classically. Namely, the device is designed where some parts 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. It is the first frame work 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 different devices, which also confirm our theoretical results.

This is a joint work with Federica Di Michelle, Bruno Robino and Rosella Samperlieri.

报告时间：2016年6月13日（周一）上午10：00-11：00

报告地点：教学二楼2126

欢迎教师和同学参加！