Empirische Tight-Binding-Modellierung geordneter und ungeordneter Halbleiterstrukturen

Abstract

In this thesis, we investigate the electronic and optical properties of pure as well as of substitutionally alloyed II-VI and III-V bulk semiconductors and corresponding semiconductor quantum dots by means of an empirical tight-binding (TB) model. In the case of the alloyed systems of the type AB, where A and B are the pure compound semiconductor materials, we study the influence of the disorder by means of several extensions of the TB model with different levels of sophistication. Our methods range from rather simple mean-field approaches (virtual crystal approximation, VCA) over a dynamical mean-field approach (coherent potential approximation, CPA) up to calculations where substitutional disorder is incorporated on a finite ensemble of microscopically distinct configurations. In the first part of this thesis, we cover the necessary fundamentals in order to properly introduce the TB model of our choice, the effective bond-orbital model (EBOM). In this model, one s- and three p-orbitals per spin direction are localized on the sites of the underlying Bravais lattice. The matrix elements between these orbitals are treated as free parameters in order to reproduce the properties of one conduction and three valence bands per spin direction and can then be used in supercell calculations in order to model mixed bulk materials or pure as well as mixed quantum dots. Part II of this thesis deals with unalloyed systems. Here, we use the EBOM in combination with configuraton interaction calculations for the investigation of the electronic and optical properties of truncated pyramidal GaN quantum dots embedded in AlN with an underlying zincblende structure. Furthermore, we develop a parametrization of the EBOM for materials with a wurtzite structure, which allows for a fit of one conduction and three valence bands per spin direction throughout the whole Brillouin zone of the hexagonal system. In Part III, we focus on the influence of alloying on the electronic and optical properties. Therefore, we introduce the combination of the EBOM with the VCA, the CPA and the simulation of exact substitutional disorder on finite ensembles and systematically compare the results. We then use the TB model to calculate the nonlinear dependence of the band gap of bulk CdZnSe on the concentration x and draw the comparison to experimental results. As an application to mixed quantum dots, we calculate the optical spectra of alloyed CdZnSe nanocrystals and again compare our results to experimental data from the literature. Special attention is paid to the proper choice of material parameters and the elimination of spurious results. For the CdZnSe bulk system, as well as for the nanocrystals of the same material, the combination of the EBOM with disorder on a finite ensemble yields results in very good agreement with the experiments. We close this work with results for the concentration-dependent band gap of cubic bulk GaAlN as an outlook to future applications.