Application of the tight-binding electronic structure method to study defect formation and optical absorption in covalently bonded materials

Tight-binding or linear combination of atomic orbitals is a method for computing the electronic structure of materials. Like Density Functional Theory (DFT), it depends on the single electron approximation, but is significantly less expensive because it includes parameters from DFT, other ab-initio methods, and experiments. In terms of the system sizes usually studied in materials behavior computation, tight-binding bridges the distance and time domains between those typically covered by density functional theory (DFT) and classical molecular dynamics (MD) where the interactions between atoms are given by a pre-determined function, and the quantum mechanical nature of electrons is not accounted for. In order to account for the quantum mechanical nature of electrons, the Schrodinger equation has to be solved for the electron wavefunction. The Schrodinger equation is a second order differential equation;one can think of it as a laplacian (∇2) with inhomogeneities of the type 1|r| and other potentials, which themselves depend on the wavefunction (or charge density) and whose functional form is determined by several approximations. This is the problem solved by DFT, where in the ideal case, a complete continuous orthogonal basis set is used to solve the Schrodinger equation self-consistently. However, the basis set necessarily has to be discrete and finite, and convergence suffers because of the type and spatial extent of the inhomogeneity (1r type potentials).For many materials, specially insulators and semiconductors, it is often more convenient to assume a basis set centered around atoms - i.e. by assuming that a bond is a perturbation of an atom[52], we can write the electronic wavefunction of real crystals in terms of atomic orbitals. We may then solve the DFT problem on a small system of atoms with this type of basis set, and obtain values of various interactions between orbitals of atoms. These values become parameters that can be used with tight-binding, and have the potential to scale the quantum mechanical treatment of electrons to computations involving hundreds of thousands of atoms. Traditionally, experimental results have also been used to determine parameters for tight-binding. In this thesis, we present several applications of and extensions to the tight-binding method. After a brief description of the tight-binding method in chapter 1, we apply tight-binding to smaller, heterogeneous unit cells in chapters 2 and 3. In particular, we use tight-binding calculations as a part of total energy computation, and use it to get an insight into the kinetics of defect formation in chapter 2. Then in chapter 3, we compute the rates of optical absorption and individual atomic contributions to total absorption. Then in chapter 4, we present past work and our own developments that allow us to scale the applications in chapters 2 and 3 to larger system sizes, where tight-binding as a method is most promising