【作者】 陈晨；

【导师】 张凯军；

【作者基本信息】 东北师范大学 ， 运筹学与控制论， 2019， 硕士

【摘要】 在半导体物理中,经典的HD模型被用于描述半导体器件中带电粒子流的输运现象.从数学观点看,它是由带阻尼的Euler方程组和电场位势所满足的Poisson方程耦合而成的.本文旨在将Peng[19]对一维等熵的单极稳态HD模型的拟中性极限问题的研究结果推广到双极情形.因此我们考虑等熵的双极稳态HD模型的拟中性极限问题,并获得了以下主要结果:第一,基于渐近展开的思想,我们首先在给定区域的内部和边界附近对上述问题的无旋流做关于Debye长度λ的形式展开.然后利用标准的匹配技巧,推导出内函数和边界层函数所满足的方程组.第二,对于一维情形,我们分别应用了动力系统理论中的中心流形定理和著名的Schauder不动点定理,成功地建立了具有指数衰减性质的零阶边界层函数以及零阶误差函数的存在唯一性.在此基础上,经细致演算我们证明:当 λ → 0时,亚音速无旋流在L∞模意义下强收敛到零阶近似解,同时给出了相应的误差估计.更多还原

【Abstract】 In semiconductor physics,the classical HD model is used to describe the transport of charged particle flow in semiconductor devices.From a mathematical point of view,it is coupled by the damped Euler equation system and the Poisson equation satisfied by the electric potential.The purpose of this paper is to extend Peng[19]research results on quasi-neutral limit problem of one-dimensional isentropic unipolar steady-state HD model to bipolar case.So we consider the quasi-neutral limit problem of the isentropic bipolar steady-state HD model and obtain the following main results.First,based on the idea of asymptotic expansion,we first expand the irrotational flow of the above problem in the form of Debye length lambda in the interior and near the boundary of a given region.Then,using the standard matching technique,the equations satisfying the internal function and the boundary layer function are derived.Secondly,For one-dimensional case,we have successfully established the existence and uniqueness of zero-order boundary layer function with exponential decay property and zero-order error function by applying the central manifold theorem and the famous Schauder fixed point theorem in dynamic system theory,respectively.On this basis,it is proved by detailed calculus that when lambda→ 0 the subsonic non-swirling flow converges strongly to the zero-order approximate solution in the sense of L∞ module and the corresponding error estimates are given.更多还原