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

- Author(s): Malone, Brad Dean
- Advisor(s): Cohen, Marvin L
- et al.

## Abstract

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. This involves a discussion of the Born-Oppenheimer approximation, Bloch's Theorem, the concept of the pseudopotential, and the empirical pseudopotential method (EPM). We end with a discussion of density functional theory (DFT), which is methodology by which the majority of solid state work is carried out today.

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 $Sigma$ known as the $GW$ approximation and use it to compute the quasiparticle band structures of a number of group IV and III-V semiconductors. Our fully first principles calculations, which include spin-orbit effects, are in very good agreement with experimental values and illustrate the power of this approach to calculate quasiparticle energies.

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 $beta$-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 $beta$-Sn in germanium. We find that the DFT incorrectly predicts the Si-XII phase to be semimetallic and that the true quasiparticle spectrum exhibits a band gap.

Our attention is then turned to the first principles calculations of optical properties in Chapter 4. The optical spectrum of the Si-XII is studied, which was shown in Chapter 3 to exhibit a small, indirect band gap. 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. The calculated values of the optical functions relevant to photovoltaic absorption are found to exhibit show greater overlap with the incident solar spectrum in Si-XII than those found in these other silicon phases.

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. Calculated equation of states within the LDA reveal a small pressure region where the R8 phase is energetically favored over the other metastable BC8 and ST12 structures, although the energy differences involved are relatively small and affected by the approximations used in the choice of pseudopotential. The calculated zone-center Raman-active frequencies are then used to further support experimental evidence which suggests the R8 phase of Ge to have been formed in indented samples of amorphous Ge. We also show that from an analysis of th

e pressure dependence of the zone-center Raman-active phonon frequencies that previous experimental results claiming to have the ST12 phase of Ge in their experimental sample were actually likely seeing the signature of the R8 phase, a phase which in Ge had until then remained unobserved.

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 *Ibam*structure. 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. Calculation of the lattice dynamics reveals that the structure is locally stable. Enthalpy-pressure relations are calculated for the *Ibam* structure as well as all other known Si structures, including the previously predicted st12 and bct phases. These results indicate that *Ibam* silicon is metastable over the pressure range considered. Calculated coexistence pressures of the other known phase transitions are in good agreement with experimental observation. We end this section with a discussion on evolutionary algorithms and their application to the problem of structure prediction. We then use this method to determine some interesting low-energy candidate structures for the unknown phase Si-VIII.

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. The hybrid calculations also give an independent prediction that Si-XII is semiconducting, in agreement with recent experimental data.