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arXiv 0704.0067cond-mat.mtrl-sci
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外延自组装量子点有序度的线性分析

Order of Epitaxial Self-Assembled Quantum Dots: Linear Analysis

Lawrence H. Friedman

摘要:

外延自组装量子点(SAQD)在纳米结构光电和电子器件如激光器、光电探测器和纳米级逻辑中具有重要意义。SAQD的空间有序性和尺寸有序性对于可用器件的开发是重要的。很可能这两种类型的秩序是紧密联系在一起的;因此,对空间秩序的研究也将对大小秩序产生强烈的影响。在这里,空间秩序的研究进行了一个常用的模型SAQD形成的表面扩散的基础上使用的线性分析。给出了表征量子点空间有序度的薄膜高度关联函数的解析表达式和表征有序度的关联长度。初始原子尺度的随机波动导致相对较小的相关长度(约两个点)时,润湿电位的影响可以忽略不计,然而,相关长度发散时,SAQD被允许形成在近临界膜高度。目前的工作加强了以前的研究结果的各向异性和SAQD秩序,并提出了明确的和透明的机制与相应的解析方程。此外,SAQD形成的性质是一个随机过程,和各种数学方面的统计分析SAQD的形成和秩序。

英文摘要:

Epitaxial self-assembled quantum dots (SAQDs) are of interest for nanostructured optoelectronic and electronic devices such as lasers, photodetectors and nanoscale logic. Spatial order and size order of SAQDs are important to the development of usable devices. It is likely that these two types of order are strongly linked; thus, a study of spatial order will also have strong implications for size order. Here a study of spatial order is undertaken using a linear analysis of a commonly used model of SAQD formation based on surface diffusion. Analytic formulas for film-height correlation functions are found that characterize quantum dot spatial order and corresponding correlation lengths that quantify order. Initial atomic-scale random fluctuations result in relatively small correlation lengths (about two dots) when the effect of a wetting potential is negligible; however, the correlation lengths diverge when SAQDs are allowed to form at a near-critical film height. The present work reinforces previous findings about anisotropy and SAQD order and presents as explicit and transparent mechanism for ordering with corresponding analytic equations. In addition, SAQD formation is by its nature a stochastic process, and various mathematical aspects regarding statistical analysis of SAQD formation and order are presented.

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