In this thesis a new method based on the Tight-Binding Linear Muffin Tin Orbital (TB-LMTO) formalism and the Quasiparticle Self-consistent GW (QSGW) approximation is proposed. The method is capable of generating accurate electronic bands structure of large supercells necessary to model alloys structures. The strategy consist in building simple and small hamiltonian from linear Muffin-tin-orbitals (LMTO). Parameters in this hamiltonian are then used to fit the difference in QSGW self-energies and LDA exchange-correlation potentials. The parameter are assumed to transfer to new environments --- a procedure we check carefully by comparing our predicted band to QSGW bands for small supercells. The method possess both the accuracy of the QSGW approximation, (which is the most reliable way to determine energy bands accurately, and yet too expensive for the large supercells required here), and the efficiency of the TB-LMTO method. The accurate and highly efficient hamiltonian is used to predict the electronic and optical transitions of Si1-xGex alloys and SnxSiyGe1-x-y alloys. The goal is to engineer direct band gap material compatible with the silicon technology. The results obtained are compared to available experimental data.

This thesis focuses on the theoretical work done to determine thermodynamic properties of a chalcopyrite thin-film material for use as a photovoltaic material in a tandem device. The material of main focus here is ZnGeAs2, which was chosen for the relative abundance of constituents, favorable photovoltaic properties, and good lattice matching with ZnSnP2, the other component in this tandem device. This work is divided into two main chapters, which will cover: calculations and method to determine the formation energy and abundance of native point defects, and a model to calculate the vapor pressure over a ternary material from first-principles. The purpose of this work is to guide experimental work being done in tandem to synthesize ZnGeAs2 in thin-film form with high enough quality such that it can be used as a photovoltaic. Since properties of photovoltaic depend greatly on defect concentrations and film quality, a theoretical understanding of how laboratory conditions affect these properties is very valuable. The work done here is from first-principles and utilizes density functional theory using the local density approximation. Results from the native point defect study show that the zinc vacancy (VZn) and the germanium antisite (GeZn) are the more prominent defects; which most likely produce non-stoichiometric films. The vapor pressure model for a ternary system is validated using known vapor pressure for monatomic and binary test systems. With a valid ternary system vapor pressure model, results show there is a kinetic barrier to decomposition for ZnGeAs2.