Excitonic structure of absorption edge in quantum dots

Mgr. Vlastimil Křápek, Ph.D.

Doctoral thesis

Abstract:

The goal of the thesis is twofold: (i) to develop a theoretical model describing electronic structure and optical properties of quantum dots, and (ii) to apply it to some interesting topics of the quantum dot physics. Effective mass theory was chosen as the appropriate theoretical method for a description of quantum dots, which represents a reasonable trade-off between accuracy and completeness on the one hand, and simplicity, easy interpretation of results and short calculation time on the other hand. In the framework of this approach I have developed a method of approximate variable separation, which enables a numerically simple retrieval of wave functions and energies of bound states in flat quantum dots of arbitrary shape. For a set of important characteristic quantum dot shapes (cone, lens, cylinder), I further implemented a variational method of solution of the Schr\"{o}dinger equation, which gives more accurate results at the price of slower calculations and lower generality. Both methods provide qualitatively correct results and, regarding limited knowledge of quantum dot structure, are suitable for the interpretation of experimental data. An implementation of eight band k.p theory developed at Technische Universitaet Berlin was used for comparison. An important goal of quantum dot technology is to achieve long wavelength luminescence from InAs/GaAs quantum dots, namely communication wavelengths of 1.3 micro-m and 1.55 micro-m. Multilayer quantum dot systems may be used for this purpose. The red shift is caused by the wave function extension over the dots in the stack, and by the influence of the lower layer to the upper dot layer growth - the dots in upper layers are usually larger. Comparing experimental data with our model, we determine the proportion of these factors in contributing to the red shift (differentiating further between the increased lateral or vertical dimensions for the case of increased volume) for various values of the spacer layer thickness and number of layers in the system. Long luminescence wavelengths can also be achieved by using ternary InGaAs strain-reducing capping layers. The red shift is due to a lower strain influencing the band energies, lower potential barrier on the capping layer side, and increased dot volume due to modified strain and chemical composition during the growth of the capping layer. Comparing experimental data with the model results, we again determine the importance of the factors mentioned above. The last part of the thesis is dedicated to magneto-optical properties of quantum dots. We discuss the effect of structural properties on the magnetooptical properties and a possibility to determine the shape of the dots from measured magnetooptical spectra. We demonstrate a fair sensitivity of the spectra to the lateral elongation of the wave functions, which may be connected with lateral elongation of the quantum dots or with piezoelectric fields.

Keywords

quantum dots, InAs/GaAs, photoluminescence, magnetoluminescence, III-V semiconductors

Language used: English

Date on which the thesis was submitted / produced: 18. 3. 2008

Thesis defence

• Date of defence: 28. 3. 2008
• Supervisor: prof. RNDr. Josef Humlíček, CSc.
• Reader: doc. RNDr. Roman Grill, CSc., Mgr. Jan Soubusta, Ph.D.

Masaryk University

Faculty of Science

Doctoral programme / field:
Physics (4-years) / Solid Matter Physics