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Title: A ï¬ rst-principles study of structural, electronic and optical properties of GaN, ZnO and (GaN)1−x(ZnO)x
Authors: Allen, Philip B
Fernandez-Serra, Maria V
Liu, Jian
Department of Physics
Dawber, Matthew
Hybertsen, Mark S
Issue Date: 1-Dec-2015
Publisher: The Graduate School, Stony Brook University: Stony Brook, NY.
Abstract: The pseudobinary (GaN)$_{1-x}$(ZnO)$_{x}$ alloy is attractive for its high efficiency in photocatalytic water splitting. Its reduced band gap is a main advantage for harvesting solar energy. Short-range order (SRO) dramatically affect the atomic and electronic structures due to the non-isovalent nature of the alloy. In this thesis, I perform Monte-Carlo simulations on a first-principles-based cluster-expansion model to show the existence of SRO in (GaN)$_{1-x}$(ZnO)$_{x}$ alloy. I also construct the “special quasi-ordered structures†to faithfully include SRO in a computationally affordable supercell. Subsequent density-functional theory (DFT) calculations reveal significant influence of SRO on the structural, electronic and optical properties of (GaN)$_{1-x}$(ZnO)$_{x}$ alloy. The short-range ordered alloys experience smaller lattice bowing as well as band gap bowing than the disordered alloys. The role of SRO in the band-gap reduction is dominated by the Zn3$d$-N2$p$ repulsion. SRO inhibits the nearest-neighbor Zn-N pairs, which affects the strength of the Zn3d-N2p repulsion and consequently the top of the valence band. Electronic structure method can now handle fairly large supercells (e.g., over 100 atoms). For the study of non-isovalent semiconductor alloys, a large supercell is generally favored in order to average out the fluctuation error due to the ï¬ nite size of the supercell. As large structural relaxations are expected, DFT total energy and force calculations have the merit of rigor, but are computationally expensive. Therefore it is desirable to pre-relax the internal atomic positions in an economical way. In this thesis, the bond valence method (BVM) and its application in (GaN)$_{1-x}$(ZnO)$_{x}$ alloy is studied. Particular attention is paid to the role of SRO. A physical interpretation based on atomic orbital interaction is proposed and examined by DFT calculations. Bond-length distribution and bond-angle variation are predicted by parameter-fitting BVM empirical correlations to reliable DFT-calculated structural data. The correlation between bond valence and bond stiffness is revealed. The concept of bond valence is extended into the modelling of an atomistic potential. The pure end-member semiconductors of (GaN)$_{1-x}$(ZnO)$_{x}$ alloy, GaN and ZnO, have spontaneous polarizations comparable with those of ferroelectric materials. Nowadays spontaneous polarization can be predicted at the first-principles level. However, pyroelectricity, namely the temperature dependence of the spontaneous polarization, has not been investigated at the first-principles level. In this thesis, I discuss the pyroelectric theory of Born in detail. Through first-principles calculations, the primary pyroelectricity is calculated according to the anharmonic internal displacements of the Born effective charges on the cations and anions. While the primary (anharmonic internal displacement) pyroelectricity contributes the major part of the total pyroelectricity at low temperatures, the secondary (thermal expansion) pyroelectricity becomes comparable with the primary pyroelectricity at high temperatures. An efficient way of calculating third-order force constants at zone-center using the dynamical matrix is proposed. In this thesis, I also include a chapter on a preliminary study of combining Allen-Heine-Cardona (AHC) theory with the Virtual Crystal Approximation (VCA) in order to obtain the temperature dependence of the band gap of isovalent semiconductor alloy Ga$_{1-x}$In$_x$N. I report on the structural, electronic and vibrational properties of the Ga$_{1-x}$In$_x$N alloy from first-principles. I show that VCA ignores disorder effect and is therefore unable to describe the broadening of the phonon spectra upon alloying. The role of electron-phonon interaction in the temperature dependence of the band gap is also studied for GaN, InN and their alloy Ga$_{1-x}$In$_x$N. The calculated zero-point motion renormalization and the fitted Varshni parameter over the entire composition range are discussed.
Description: 92 pg.
Appears in Collections:Stony Brook Theses and Dissertations Collection

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