Elektronische Zustände in Halbleiter-Nanostrukturen und Upscaling auf semiklassische Modelle

半导体纳米结构中的电子态和升级到半经典模型

• 批准号: 5276152
• 负责人: Dr. Jürgen Fuhrmann
• 金额: --
• 依托单位: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5276152?language=en
• 关键词: Elektronische; Zust; nde; Halbleiter; Nanostrukturen

Already at present time, the design of state of the art optoelectronic devices like semiconductor lasers is based on semiconductor nanostructures. The role of semiconductor nanostructures will increase in the future due to the advent of quantum electronic devices which is assisted by the increasing sophistication of fabrication technology. To unterstand and to predict the physical properties of such devices, new theoretical techniques for the computation of their electronic states are required. The ab initio solution of the many electron Schrödinger equations on the microscopic scale fails due to its computational effort. To overcome the computational burden, it appears to be natural to utilize the presence of two scales inherent to the problem - the mesoscopic scale of the variation of the materials in the nanostructure and the microscopic scale of the atoms of each material. The most promising approach in this direction has been proposed by Burt, who introduces envelope functions, which describe the slowly varying mesoscopic part of the locally highly oscillating microscopic wave functions. Burt points out a way to derive equations for the envelope functions in terms of the microscopic potential. In the result, one arrives at pseudodifferential equations for the envelope functions in real space or integral equations for Fourier transformed envelope functions. The aim of this project is a mathematically well understood presentation of Burt's approach, its precise formulation together with an investigation of the involved operators and the development of efficient numerical methods for solving the arising equations. On success, an efficient modeling and simulation tool for nanostructures will be available for physicists and engineers.

目前，像半导体激光器这样的现有技术光电器件的设计已经基于半导体纳米结构。由于量子电子器件的出现，半导体纳米结构的作用将在未来增加，这是由制造技术的日益复杂化所辅助的。为了理解和预测这些器件的物理性质，需要新的理论技术来计算它们的电子态。微观尺度上的许多电子薛定谔方程的从头算解由于其计算工作量而失败。为了克服计算负担，利用问题固有的两个尺度的存在似乎是自然的-纳米结构中材料变化的介观尺度和每种材料原子的微观尺度。在这个方向上最有前途的方法已经由伯特提出，他引入了包络函数，它描述了局部高度振荡的微观波函数的缓慢变化的介观部分。伯特指出了一种方法来推导方程的包络函数的微观潜力。结果得到真实的空间中包络函数的伪微分方程或傅立叶变换包络函数的积分方程。该项目的目的是一个数学上很好地理解介绍伯特的方法，其精确的制定连同调查所涉及的运营商和发展有效的数值方法来解决所产生的方程。一旦成功，物理学家和工程师就可以使用一种有效的纳米结构建模和模拟工具。