First-Principles Calculations for Electronic Structures of Nitrides

• Main Authors: Rong-Quan Lee, 李榮銓
• Other Authors: Jiann Lin
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/67256659855248681173

碩士 === 國立彰化師範大學 === 物理學系 === 92 === Nitrogen-based Ⅲ-Ⅴ semiconductors have attracted considerable interest in the last few years due to their applications in optic devices, for high-density optical data storage, including LED (Light Emitting Diode), semiconductor lasers, and else. Extensive experimental and theoretical researchers have devoted themselves to investigate the physic properties of Ⅲ-nitrides. However, there are still many issues such as bowing parameter of energy gap and deviation from Vegard’s law for lattice constant. When Ⅲ-nitrides are grown on substrates, compressive or tensile stress will be caused in the junction by the lattice mismatch. However, if the stress is in the acceptable range, it may improve electronic and optic properties of materials. In 1982, S. Yoshido et al. has discovered that the lattice constant c of wurtzite AlxGa1-xN alloys does not follow Vegard’s law; and M. Ferhat and F. Bechstedt have found that the lattice constant of zinc-blende InxGa1-xN and InxAl1-xN alloys deviate Vegard’s law with theoretical calculations in 2002. Some professors state that First-principles pseudopotential plane-wave calculations are useful to investigate the electronic, structural, and thermodynamic properties of nitride alloys. The first-principles means that the calculation for properties of solids are solved in the Schrödinger equation directly, without experimental parameters. In addition, if the physic theories are correct, the calculated results in theories and experiments should be coincident. Else, the theory itself is incomplete, and then it has to be modified. In this paper, I have performed the first-principles density-functional theory (DFT) in the local density approximation (LDA) with norm-conserving pseudopotentials to examine some fundamental properties of Ⅲ-nitrides (including lattice constant, cell volume, band-gap, and else) under stress, deviations from Vegard’s law for the lattice constant variation in AlxGa1-xN, InxAl1-xN, and InxGa1-xN alloys, and the bowing parameter of wurtzite AlxGa1-xN alloys. For the underestimation of band-gaps in LDA, I corrected it in ccGDFT/LDA developed by Professor Ming-Hsien Lee and his student Shyong K. Chen in the department of physics, Tamkang University. In chapter 1 and chapter 2, I simply described the crystal and band structure in solid state physic, and the basic theorems of calculations respectively. In chapter 3 (Calculations of Nitride Electronic Structures under Stress), I calculated variation of the lattice constants c, cell volumes, stress and band-gap with the lattice constant a of GaN, AlN and InN under stress. In chapter 4 (Calculations of the Lattice Constant in InxAl1-xN, GaxAl1-xN, InxGa1-xN alloys: Deviation from Vegard’s law), I found the lattice constants of InxAl1-xN, GaxAl1-xN, InxGa1-xN alloys all a little deviate from the Vegard’s law. In chapter 5 (First-Principles Calculations of the Bowing Parameter in AlxGa1-xN alloys), I derived the band-gap bowing parameter of wurtzite AlxGa1-xN alloys is equal to 0.351eV. In the final, I review the last three chapters, and make a conclusion for my calculated results