| Electronic band structure of crystal can be used to interpret electrical and optical properties of solid materials. First-principle calculation without free parameters investigates material properties based only on basic physical laws. Though it is generally more computationally intensive comparing to empirical and semi-empirical formulations, first-principle method has greater prediction power since atomic species is the only necessary input information to start a calculation. Hartree-Fock theory and density functional theory (DFT) are widely used in quantum chemistry and solid state science. By using electronic density as degree of freedom, DFT can significantly reduce the amount of degrees of freedom comparing to the formulation based on wave function. Since exact exchange-correlation functional is unknown, a local density approximation (LDA) is often adopted in DFT. Pseudopotential can be constructed to further reduce the computational burden with a requirement that it keeps the same scattering properties as real potential for valence electrons outside a core region. DFT-LDA has been applied successfully in the calculation of structural and ground electronic properties of molecule and crystal. However, DFT-LDA often underestimates the value of band gap. To obtain an accurate band structure, a quasiparticle calculation is required. Though accurate sclf-energy of quasiparticle can be calculated by solving the Hedin equations self-consistently in principle, it's very difficult to calculate the vertical function practically due to the existence of derivative functional in the calculation of vertical function. A first order approximation for vertical function is often employed. GW approximation of self-energy has shown good agreement with experimental results and is accepted as an accurate method for quasiparticle band structure calculation.In this work, ABINIT package was used to calculate the band structures of diamond, Si, Ge, BN, and six polymorphs of Ge3N4. Overall band structure diagram is obtained by DFT-LDA, and then GW approximation is used to correct band energies for some high symmetric k points to get accurate prediction. Convergence of calculation parameters such as cut-off energy is thoroughly tested. Good agreement with available experiments has been obtained for diamond, Si, Ge, and BN. Geometry optimization and band structure calculation were carried out for six phase of Ge3N4. Ge3N4 are less studied in literature and our theoretical prediction can be helpful for their future research and industry application. Band structure diagrams show thatα,β, pseudocubic and cubic phases of Ge3N4 have indirect band gap while the y and Graphitic phases have direct band gap. As our calculation predicts that it has a direct bandgap of about 3.0 eV, y-Ge3N4 can be a promising photocatalyst. Though minimum band gap of pseudocubic Ge3N4 is indirect, it also has a direct band gap of 2.68 eV that is just 0.17 eV larger than the indirect bandgap.2.68 eV is corresponding to photon energy of blue light, so pseudocubic Ge3N4 can be a candidate semiconductor material for phtotocatalyst or optoelectronics.This thesis is organized as follows. Chapter 1 gives an introduction to the theory background and studied materials. Calculation methods (DFT and GW method) and a brief description of software package are present in Chapter 2. In Chapter 3, we describe band structures of threeⅣgroup materials of the FCC structure (diamond, Si and Ge). Selection of plane wave cut-off energy has been discussed. Energy levels for special highly symmetric k points are corrected by GW method, and a comparison with experimental data validates the reliability of our calculation. Chapter 4 presents crystal structures and band structures of six polymorphs of Ge3N4. Chapter 5 is the conclusion of the thesis. |
