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Analysis of quantum-dot-induced strain and electric fields in piezoelectric semiconductors of general anisotropy

机译：各向异性压电半导体中量子点诱发的应变和电场分析

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摘要

Characteristics of the self-organized quantum dots (QDs) such as electron and hole energy levels and wave functions are dependent to the state of strain and electric field produced during the growing process of QDs in a semiconductor substrate. The calculation of the strain and electric field is one of the most challenging components in the QDs simulation process. It involves material anisotropy induced coupling between the elastic and electric fields and it must include the full three-dimensional and usually intricate shapes of the QDs. Numerical simulations are often performed by finite difference, finite element, or atomistic techniques, all require substantial computational time and memory. In this paper, we present a new Green's function approach which takes into account QDs of arbitrary shape and semiconductor substrates with the most general class of anisotropy and piezoelectricity. Following the literature of micromechanics, the problem is formulated as an Eshelby inclusion problem of which the solution can be expressed by a volume-integral equation that involves the Green's functions and the equivalent body-force of eiegenstrain. The volume integral is subsequently reduced to a line integral based on exploiting a unique structure of the Green's functions. The final equations are cast in a form that most of the computational results can be repeatedly used for QDs at different locations-a very attractive feature for simulating large systems of QD arrays. The proposed algorithm has been implemented and validated by comparison with analytical solutions. Numerical simulations are presented for pyramidal QDs in the substrates of gallium arsenide (GaAs) (0 0 1). (c) 2006 Elsevier Ltd. All rights reserved.
机译：自组织量子点（QD）的特性（例如电子和空穴能级以及波函数）取决于在半导体衬底中QD生长过程中产生的应变和电场状态。应变和电场的计算是量子点模拟过程中最具挑战性的组成部分之一。它涉及材料各向异性引起的弹性场和电场之间的耦合，并且必须包括完整的三维形状，通常是复杂的量子点形状。数值模拟通常通过有限差分，有限元或原子技术进行，所有这些都需要大量的计算时间和内存。在本文中，我们提出了一种新的格林函数方法，该方法考虑了任意形状的QD和具有最一般各向异性和压电性的半导体衬底。根据微力学的文献，该问题被表述为埃舍尔比包含问题，该问题的解决方案可以通过涉及格林函数和等效应变本征力的体积积分方程来表示。随后，基于利用格林函数的独特结构，将体积积分减小为线积分。最终方程式以大多数计算结果可以在不同位置重复用于QD的形式转换，这是模拟大型QD阵列系统的一个非常吸引人的功能。通过与解析解进行比较，已实现并验证了所提出的算法。提出了砷化镓（GaAs）（0 0 1）衬底中金字塔形QD的数值模拟。 （c）2006 Elsevier Ltd.保留所有权利。

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