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The ability to model ground-state properties in density function theory (DFT) is a ected by the theoretical treatment of the electrons and the numerical approach to the theory. The electron-electron interaction energy is approximated by exchange- correlation (XC) functionals which are functions of the electron density. Popular functionals include the localized density approximation (LDA) or one of many gen- eralized gradient approximations (GGA). The numerical approaches used are the core-electron approximating pseudopotential (PsP) or the more accurate all-electron (AE) method. We test whether PsP calculations for some new GGA's can accurately reproduce AE values for cohesive energy, lattice constant, and bulk modulus for six- teen solids. We compare our PsP results to AE results for several XC functionals and gauge the quality of functionals by comparison to experiment. This allows us to determine which errors are caused by functionals and which are caused by PsP's.

Semiconductor superlattices and alloys based on III-V semiconductors have important applications in the design of optoelectronic devices in particular photodetectors. Understanding the electronic properties of such system is critical to be able to properly design and optimize the performance of such devices. Atomistic modelling is the most suitable approach to understand the microscopic properties of these systems. While density functional theory (DFT) is the approach of choice for many studies, it cannot be applied to systems comprised of a large number of atoms. The goal of this thesis is to explore the possibility of applying the empirical pseudopotential method associate with hybrid pseudopotential method to compute the electronic structure and optical properties of Ga_xAl_1-xAs alloy. The proposed work will address first the derivation of portable continuous screened atomic pseudopotentials for the constituent atoms. These will be validated using calculation on small systems. Subsequently, the atomic pseudopotential will be used to study Ga_xAl_1-xAs alloy with different microstructure.

We study the effects of vibrations in the Pd₃ system using first-principles pseudopotential calculations. We find that upon disordering from the DO₂₂ phase, the decreases by 0.07kB. We explain our results in terms of atomic relaxations and size effects. / Singapore-MIT Alliance (SMA)

Nanostructures often possess unique properties, which may lead to the development of new microelectronic and optoelectronic devices. They also provide an opportunity to test fundamental quantum mechanical concepts such as the role of quantum confinement. Considerable effort has been made to understand the electronic and structural properties of nanostructures, but many fundamental issues remain. In this work, the electronic and structural properties of nanostructures are examined using several new computational methods. The effect of dimensional confinement on quantum levels is investigated for hydrogenated Ge <110> using the plane-wave density-functional-theory pseudopotential method. We present a real-space pseudopotential method for calculating the electronic structure of one-dimensional periodic systems such as nanowires. As an application of this method, we examine H-passivated Si nanowires. The band structure and heat of formation of the Si nanowires are presented and compared to plane wave methods. Our method is able to offer the same accuracy as the traditional plane wave methods, but offers a number of computational advantages such as the ability to handle large systems and a better ease of implementation for highly parallel platforms. Doping is important to many potential applications of nano-regime semiconductors. A series of first-principles studies are conducted on the P-doped Si <110> nanowires by the real-space pseudopotential methods. Nanowires of varied sizes and different doping positions are investigated. We calculate the binding energies of P atoms, band gaps of the wires, energetics of P atoms in different doping positions and core-level shift of P atoms. Defect wave functions of P atoms are also analyzed. In addition, we study the electronic properties of phosphorus-doped silicon <111> nanofilms using the real-space pseudopotential method. Nanofilms with varied sizes and different doping positions are investigated. We calculate the binding energies of P atoms, band gaps of the films, and energetics of P atoms in different doping positions. Quantum confinement effects are compared with P-doped Si nanocrystals and as well as nanowires. We simulate the nanofilm STM images with P defects in varied film depths, and make a comparison with the experimental measurement. / text

A method of generating and testing pseudopotentials will be presented. This required the development of PPTester, a custom software program to analyze and quantify various parameters. These methods were first used to study bulk Si and verify the installation and performance of SIESTA. Plots, which agreed with published results, for band gap and charge density were generated.Next, pseudopotentials for Cd and Se were constructed and tested. Two separate Cd potentials were evaluated. Electronic structure calculations for two, four and six atom small cadmium selenide (CdSe) colloidal quantum dots were performed. The changes in geometry of initial versus relaxed atomic positions of these systems were evaluated. Output values of the electronic structure calculation, for example Fermi energy, were analyzed. / Department of Physics and Astronomy

Thesis (Ph.D.)--Wake Forest University. Dept. of Physics, 2006. / Vita. Includes bibliographical references (leaves 90-95)

<p> The energy bands and Fermi surface of mercury have been calculated using local and non-local pseudopotentials. The non-local pseudopotentials were an approximation in which the repulsive potentials of the outer atomic core states were explicitly represented by non-local projection operators. </p> <p> A search was made for the regions of parameter space where the pseudopotential generated a Fermi surface having a good fit to the experimental magneto-acoustic calipers and de Haas-van Alphen extremal cross sectional areas. </p> <p> De Haas-van Alphen frequencies and cyclotron masses were calculated for symmetry planes using a local pseudopotential. </p> <p> General questions of pseudopotential theory, the symmetry of the energy bands, the occurrence of degeneracies, and the influence of spin-orbit coupling are also considered. </p> / Thesis / Doctor of Philosophy (PhD)

The electronic band structure of a semiconductor is an essential property to determine most of its optical characteristics. The complexity of the energy band structure calculations makes analytical calculations impossible. Any calculation leading to electronic band structures has to utilize numerical methods. In this thesis, two solvers were developed to calculate the energy band structure of 1D Kronig-Penney lattice, 30 diamond lattice-structure and silicon lattice. In this thesis, many of the important methods of calculating the energy band structures were discussed. Through comparisons among different methods, we have determined that Self-Consistent Pseudopotential Method, SCPM, is the most suitable method for calculating the energy band structures when self-sufficiency and accuracy are of special importance. The SCPM is an iterative method which was utilized in this thesis by using efficient numerical methods. Instead of using conventional numerical methods such as Finite Difference Method or Finite Element Method which cause inefficiency, this thesis calculates the energy band structure by utilizing Orthogonal Plane-Wave expansion of the potentials. The 1D electronic band structure solver was developed as a foundation for the implementation of the 30 electronic band structure solver. It uses a minimal number of Fourier coefficients to calculate the energy band structure of the 1D Lattices without compromising accuracy. The 30 electronic band structure solver development needs multiple changes and modifications to the 1D solver. As the 30 solver is essentially made using the 10 solver platform, it is also efficient and needs a minimal number of Fourier coefficients for accurate results. The 30 solver can be used for either Nearly Free Electron Method, NFEM, or SCPM calculations. The NFEM calculations were done on the diamond lattice structure. The results were shown to be the same as the benchmarks of [28, 80]. The silicon lattice energy band structure was also calculated with the 30 solver using SCPM with LOA. The results were in the same range as the four sets of data gathered from three benchmarks [58, 81, 82], showing good agreement. Based on the two comparisons made for the 30 solver, it was shown that it is a reliable and efficient program to calculate energy band structures of the 30 lattices. / Thesis / Master of Applied Science (MASc)

We present a self-consistent calculation of the mono vacancy formation energy for seven simple metals Li, Na, K, Rb, Cs (all bcc), Al (fcc) and Mg (hcp) using both model and ab initio pseudopotential used in earlier unified studies. The local model pseudopotential calculations show small variations with respect to different exchange-correlation functions and the results are in fair agreement with other similar calculations and the available experimental data. The comparisons show that reliable model (pseudo) potential for simple metals can indeed be obtained for explaining a host of properties. Also, considering the importance of third order term in ab initio calculations, the results of our second order calculation appear fairly reasonable and are comparable with other first principle calculations. The perturbation series being an oscillating one, we hope to improve the calculational results using suitable series convergence acceleration method in the next part of our study.