Theoretical Study Of Strain Distribution And Electronic Structure Of InAs/GaAs Self-Assembled Quantum Dots

The continuous progress in all kinds of growth techniques for semiconductor materials, particularly epitaxial growth and patterning technology offers today essentially possibilities to fabricate nanosize semiconductor heterostructures. We can fabricate quantum dot nanostructures, which exhibit quantum confinement of charge carriers in three spatial dimensions and show many unexpected fancy properties. Especially that it can be applied to semiconductor laser successfully can explain this issue well. In this dissertation, the strain distribution and the electronic strucsture are studied to a certainty in the InAs/GaAs self-assembled quantum dots.The main focus of this dissertation consists two parts. First, we establish a simple and effective method to calculate the strain distribution in InAs/GaAs self-assembled quantum dots structure. Second, we calculate energy band structure of quantum dots under considering the influence of different shapes, strain distribution and spin-orbit interactions. Furthermore, we calculate Stark effect in self-assembled quantum dots based on former part.The specific heterostructures treated in this dissertation are InAs/GaAs self-assembled quantum dots embedded in GaAs matrix, grown by molecular beam epitaxy, in Stranski-Krastanow growth mode. The electronic and optical properties of these lattice-mismatched heterostructures are strongly influenced by strain distribution. In order to calculate the strain fields in quantum dots, we adopt Hooke rule method based on continuum elastical mechanics. By this method we obtain analytical solutions for quantum dots with several familiar shapes. The advantage of the analytical function method is that it can obtain the interrelation between every physical quantities associated with strain distribution straightforwardly. At the same time, the speed of calculation is much faster than that of other numerical methods. Compared with the results calculated by other method, it demonstrates that our analytical model is quite validity.The electronic structure will be calculated in five familiar quantum dots with geometrical symmetry by derivating Schroedinger's equation of single electron. It is greatly beneficial to the physical understanding how the shape influences its quantum confinement energy. We also provide the full process of derivation and necessary mathematics tricks in the special coordinate system for two given shapes, which the expressions for energy and wave function have been obtained.In addition to the influence of variable shapes, it must take account of the influence of strain distribution in quantum dots on the conduction band and valence band because of the growth mechanism of self-assembled quantum dots. Pyramidal quantum dot is accepted by most of researchers, and therefore the parameters and the information of the shape and size etc. could be conveniently obtained from many experimental data for this kind of quantum dots. In this dissertation, k ? p perturbation model usually used in the calculations of semiconductor energy band is introduced into calculating the electronic structure of InAs/GaAs self-assembled quantum dots with the hydrostatic strain and the biaxial strain obtained from the first part. The results illuminate that the strain distribution has greatly changed the electronic structure of quantum dots, especially valence band structure.In the end of the dissertation, we carry out the calculation for the Stark effect in InAs/GaAs self-assembled quantum dots. We adopt the method of efficient plane envelope function to determine correlation between the electronic structure of ground state and the size of quantum dots with three different shapes. Our theoretical model based on one-band k ? p perturbation theory is used to derivate the Hamiltonian equation of envelope function for electron and hole. In our model, it takes account of not only the influence of strain distribution, piezoelectric effect and spin-orbit interaction on the Hamiltonian quantities but also the influence of multiband and strain distribution on the electron effective mass. At last, the Stark effect in a pyramidal quantum dot is calculated and compared with the recent experimental results. Our calculated results can offer the sound theoretical explain for this experiment.