GW Method And Quasiparticle Band Structures Of Semiconductors

The electronic band structure gives important information about the electrical and optical properties of a solid. So, calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. Like in Hartree-Fock theory, the excitation energies can be determined by solving a single-particle Schr?dinger-like equation. Exchange and correlation effects are rigorously contained in the so-called self-energy operator, which has a clear interpretation in the picture of quasiparticles that closely mirrors the experimental situation. In this article the Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. We describe the GW approximation which has turned out to be a fruitful approximation to the self-energy.The thesis is divided into six chapters. In the first chapter, we review the history of ab initio calculations and GW approximation, and point out the merit of GW approximation. In chapter two, we elaborate the theories of GW approximation. The Hedin equations have been educed from the theory of Green function. Then simplified the equations and adopted the appropriate models, we got the GW approximation. In chapter three, we introduce two codes—Abinit and Paratec, which were used to calculation in our work. In chapter four, we have studied the effect of Si's and Ge's core electrons in quasiparticle bands. The results show that the effect of semicore electrons can be ignored. Because all electron calculations didn't deal with the constringency, the results were not ideal. In chapter five, we have studied the compounds of Ba-VIb. We found that the 4d electrons of Ba strongly impact the electric characters of the compounds. So, 4d electrons of Ba are not as core electrons in pesupotential. In chapter six, we design the direct gap Si-based material-- Si0.875Sn0.125/Si by the rules which were advanced by Prof. Meichun Huang. The minimum gap of the material at Gamma point, and quasiparticle gap is 0.96eV.The main progresses of this work are lists as follows:1. We point out that the effect of action between semicore electrons and valence electrons can be neglected in self-energy correct. Now, GW approximation is based on all electron calculation (LMTO+GW) and plane wave pseudopotential method (PP+GW). Some calculation results show that there is obvious difference between LMTO+GW and experimentation, but results of PP+GW agree well with experiments. To explain this inconsistency, it was proposed that the pseudopotential approach does not correctly describe the effect of core orbits in the self energy corrections to the energy gaps, resulting in overestimated corrections. And it is fortunate to get the good results for PP+GW. We renew to construct the pseudopotentails of Si and Ge, which valence electrons include the semicore electrons. And we perform the convergent tests. The results show that the valence only pseudopotential method does not suffer from large error from the neglect of core states. And the lack of the conductor bands induce the bad results of LMTO+GW.2. After calculations, we get the results that BaO is direct gap semiconductor, which minimum gap at X, but BaS, BaSe and BaTe are indirect gap semiconductors. The 4d electrons of Ba strongly influence the electric properties of barium compounds. G.Q.Lin and coworkers took for that compounds of Ba-VIb were direct gap semiconductors. We found that they adopted super cell in calculations, which bring on folding Brillouin zone(BZ). X point in rocksalt structure fold toΓpoint in cubic structure. This leads the error results. We found that the energy levels had obviously changed when 4d electrons of Ba were as valence electrons, and gaps of quasiparticle agreed well with the experimentations. It shows that the effect of 4d electrons of Ba could not be neglected in barium compounds.3. We design a Si based direct gap material--Si0.875Sn0.125/Si, and forecast its gap is 0.96eV. It has important significance for the materials of Si based direct gap. But there is no theory to judge the gap character of semiconductors. After studying a lot of materials, Prof. Meichun Huang advance three rules: core states effect, electronegativity difference effect, symmetry effect. Following the rules, we design a superlattice Si0.875Sn0.125/Si. The results of PP+GW calculation show that the superlattice energy gap is about 0.96eV. This can guide experiments.