First principles calculation of material properties of group IV elements and III-V compounds.

摘要

This thesis presents first principles calculations on the properties of group IV elements and group III-V compounds. It includes investigations into what structure a material is likely to form in, and given that structure, what are its electronic, optical, and lattice dynamical properties as well as what are the properties of defects that might be introduced into the sample. The thesis is divided as follows:;• Chapter 1 contains some of the conceptual foundations used in the present work. These involve the major approximations which allow us to approach the problem of systems with huge numbers of interacting electrons and atomic cores.;• Then, in Chapter 2, we discuss one of the major limitations to the DFT formalism introduced in Chapter 1, namely its inability to predict the quasiparticle spectra of materials and in particular the band gap of a semiconductor. We introduce a Green's function approach to the electron self-energy Σ known as the GW approximation and use it to compute the quasiparticle band structures of a number of group IV and III-V semiconductors.;• In Chapter 3 we present a first-principles study of a number of high-pressure metastable phases of Si with tetrahedral bonding. The phases studied include all experimentally determined phases that result from decompression from the metallic β-Sn phase, specifically the BC8 (Si-III), hexagonal diamond (Si-IV), and R8 (Si-XII). In addition to these, we also study the hypothetical ST12 structure found upon decompression from β-Sn in germanium.;• Our attention is then turned to the first principles calculations of optical properties in Chapter 4. The Bethe-Salpeter equation is then solved to obtain the optical spectrum of this material including electron-hole interactions. The calculated optical spectrum is compared with experimental data for other forms of silicon commonly used in photovoltaic devices, namely the cubic, polycrystalline, and amorphous forms.;• In Chapter 5 we present first principles calculations of the quasiparticle and optical excitation spectra of recently predicted silicon and germanium polytypes in the body-centered-tetragonal (bct) structure. The quasiparticle spectra calculated within the GW approximation predict that both silicon and germanium in the bct structure are small band gap materials. The optical spectra are then evaluated by solving the Bethe-Salpeter equation taking into account.;• We examine the low-pressure phases of Ge in Chapter 6 by performing first principles calculations of the electronic structure and lattice dynamics of the R8, BC8, ST12, and hexagonal diamond structures of Ge. To aid future experimental investigation, we include predictions of the Raman-active frequencies of these phases as well as present the full phonon dispersion throughout the zone.;• In Chapter 7 we demonstrate how first principles calculations can be used to predict new structures. In a study aimed at finding new useful forms of silicon, we use an ab initio random structure searching (AIRSS) method to identify a new phase of silicon in the Ibamstructure. The Ibam phase is found to be semimetallic within density functional theory with a small band overlap, and it is expected that quasiparticle corrections using the GW approximation would yield a semiconducting state with a small band gap.;• We present a first-principles study of boron and phosphorus substitutional defects in Si-XII in Chapter 8. Recent result from nanoindentation experiments reveal that the Si-XII phase is semiconducting and has the interesting property that it can be doped n- and p-type at room temperature without an annealing step. Using the hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE), we examine the formation energies of the B and P defects at the two distinct atomic sites in Si-XII to find on which site the substitutional defects are more easily accommodated. We also estimate the thermodynamic transition levels of each defect in its relevant charge states. (Abstract shortened by UMI.).