自聚式量子點應變效應之研究
Date Issued
2004
Date
2004
Author(s)
廖柏亭
DOI
zh-TW
Abstract
Abstract
This research investigates the strain effects and the optical properties of In(Ga)As/GaAs self-assembled quantum dots. There are three different models in the literatures using thermal stress theories to investigate the strain fields of heterojunction problems. In this work, it is shown analytically that these three different models lead to the identical result, at least for unburied quantum dots.
A Model based on linear elasticity and thermal stress theory is then developed to analyze the strain field induced by lattice-mismatch between quantum dot and substrate. Some obtained numerical results are then compared against to the experimental data reported by others using high resolution image processing. The misinterpretation of strain in above-mentioned data is pointed out and the experimental data are then re-interpreted. It is found that the numerical results and the re-interpreted data have excellent agreement as long as the concentration of In is taken into account.
Finally, the induced strain field in the quantum dot is incorporated, with the aid of the Pikus-Bir Hamiltonian and Luttinger-Kohn formalism, into the three-dimensional steady state effective mass Schrödinger equation. The solutions of the steady state Schrödinger equations are solved numerically again by using of a commercial finite element package. The energy levels as well as the wave functions of both conduction and valence bands of quantum dot are calculated. Energies and wavelengths of interband optical transitions are then obtained numerically.
Subjects
有限元素法
薛丁格方程式
自聚式量子點
應變
strain
finite element method
Schrodinger equation
self-assembled quantum dot
Type
thesis