Finite difference method for calculation of electronic structure of semiconductor quantum dots

• Main Authors: Ku, Chih-Hao, 古智豪
• Other Authors: Cheng, Shun-Jen
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/17673579864087793544

碩士 === 國立交通大學 === 電子物理系所 === 99 === We present finite difference method simulation for the electronic structures of semiconductor quantum dots in the framework of multi-band k?況 theory and envelope function approximation (EFA). By using the numerical techniques, the electronic structures of three kinds of quantum dots, i.e. hierarchical quantum dots[17], droplet epitaxy quantum dots[18] and InAs/GaAs self-assembled quantum dots[19] are computed. In the three-dimensional finite difference method with uniform grids, it is found that more than 70 grids in a dimension is necessary to get satisfactory convergence consequences. With the grid number, the numerical time more than 15 hours and 15GB RAM size are needed to execute a code on a machine of CPU 2.27GHz and linux O.S.. Among the three types of quantum dots under consideration, the hierarchical quantum dots have greater sizes than others with height ~7nm and length ~ 70nm. As a result, the lateral quantization of hierarchical quantum dots is about 5meV for an electron and about 1.5meV for a valence hole. For droplet epitaxy quantum dots, whose heights are close to the hierarchical quantum dots but lengths are smaller, the quantization energy are about 10meV for a conduction electron and about 3meV for a valance hole. Self-assembled quantum dots usually have the smallest sizes than others. It turns out that the quantization is about 70meV for a conduction electron and about 25meV for a valance hole confined in a self-assembled dot.