Theoretical Studies Of GaN Nanotubes And Development Of GaN Tight-binding Model

As a kind of wide band gap semiconductors, GaN materials have attracted great attention. Up to now, GaN bulk structures and GaN films have been studied extensively. However, the investigation of the one-dimensional GaN nanomaterials, i.e. single-crystal GaN nanotubes, is at the initial stage. Though some researches have been focused on the preparation of single-crystal GaN nanotubes, the physical properties of the nanotubes are studied rarely. This dissertation is devoted to the theoretical study of the mechanical, electronic, optical adsorption and vibrational properties of single-crystal GaN nanotubes. On the theoretical side, both of the methods (empirical potentials and density functional theory (DFT)) exhibit the limitation in studying the GaN nanotubes. Although a DFT method can provide an accurate description of the materials, the computational cost is huge for studying large complex systems. In contrast, an empirical potential can be used to simulate the systems consisting of a large number of atoms, but the most properties of the system are not described correctly. The tight-binding method bridges the gap between the DFT method and the empirical potential scheme: A tight-binding potential model is more accurate than the empirical potential in the description of the physical properties of a condensed matter system, as well as the tight-binding potential model can be much faster than DFT methods in calculations because the Hamiltonian matrix elements in a tight-binding potential model are expressed by a set of parameterized functions. In order to study the physical properties of the single-crystal GaN nanotubes in the further, we develop a tight-binding potential model for GaN, which is presented in this dissertation in detail.There are two parts in the dissertation: The first part including chapter 1 to chapter 3, and the second part including chapter 4 to chapter 5. In the first chapter, we introduce the features of single-walled carbon nanotubes, multi-walled carbon nanotubes, and single-crystal nanotubes, together with review of some relevant reports of GaN nanotubes. In chapter 2, we briefly introduce the methods used in my calculations, including empirical potential models, molecular dynamics, and density functional theory. In chapter 3, we describe the structural, mechanical, electronic, optical adsorption and vibrational properties of GaN nanotubes, and the effects of the hydrogen on the electronic structures of the nanotubes. In chapter 4, we introduce the theory of the tight-binding potential method and review some relevant previous work. A tight-binding potential model for GaN is developed and tested in the last chapter. In this dissertation, we obtain the main results as below.1. Through the classical molecular dynamics calculations, we find the GaN nanotubes that are constructed by conventional method are not thermally stable. So, we develop a new scheme to generate atomic structure of a single-crystal GaN nanotube, where the single-crystal GaN nanotube is isolated from the bulk GaN. The created structure of a GaN nanotube is not only thermally stable, but also matches the structural features available from experiment.2. For the single-crystal GaN nanotubes with different lateral facets and different inner/outer diameters, we calculate their energies and Young's modulus respectively, and find the calculated energies and the Young's modulus decrease with increasing the ration P (the ratio of the number of bulk atoms to the number of surface atoms). If a single-crystal GaN nanotube contains vacancy defects, the Young's modulus will decrease slightly as the concentration of defects increases with a linear trend. However, the effect of the grain boundaries on the Young's modulus of the GaN nanotube is somewhat complicated: The grain boundaries parallel to the axis of the nanotubes (IDB and IDB*) slightly decrease the Young's modulus of the tubes, whereas the grain boundaries normal to the axis of the nanotube may significantly decrease the Young's modulus.3. For wurtzite GaN nanotubes, the threefold-coordinated Ga atoms and. N atoms contribute to the states at the edge of conduction band and valance band respectively, causing a peak (peak D) in the calculated imaginary parts of the dielectric functions (ε₂). As the wall thickness of the GaN nanotube increases, thepeak D decreases and the peak related with the states arising from fourfold-coordinated atoms (peak B) increases. For zinc-blende GaN nanotubes, the electronic structures are more complicated. Besides the threefold-coordinated atoms attribute their atomic orbitals to the states at the band edges, the twofold-coordinated Ga atoms in the surface can generate defect states. The presence of the defect states result in the metallicity of the nanotube. In addition, the adsorption of hydrogen in the tube can affect the electronic and optical properties of the nanotubes. From the calculated density of states (DOS), we find that H adsorption can weaken the states at band edge and the defect states. Additionally, the surface atoms with H can generate new electronic states, which are reflected in the relatedε₂ curve.4. We find a characteristic vibrational mode for single-wall GaN nanotbues. The relationship between the frequencies of this kind of vibrational modes and the diameters of the tubes can be expressed as a decay function, which is different from the inversely proportional relation between the frequencies of the radial breathing modes and the diameters of carbon nanotubes.5. We develop a GaN tight-binding model. The parameters in the model (including Ga-GaN N-N and Ga-N) are determined by fitting to the electronic band structures and the cohesive energy versus volume curves for crystal gallium, N₂ and crystal GaN, respectively. The optimal lattice constants, bulk modulus, melting point and the surface energies of wurtzite GaN obtained by using this model agree well with those from experiments or DFT calculations. In addition, the electronic structure calculations of GaN nanotubes exhibit the advantages of this model. However, disadvantages also exist in this model, e.g. the calculated optical branches with high frequencies of the phonon dispersion curves can not match the results from DFT calculations very well. In the future, therefore, we need to improve this GaN tight-binding model.