System-size convergence of point defect properties: The case of the silicon vacancy

Abstract

We present a comprehensive study of the vacancy in bulk silicon in all its charge states from 2+ to 2-, using a supercell approach within plane-wave density-functional theory, and systematically quantify the various contributions to the well-known finite size errors associated with calculating formation energies and stable charge state transition levels of isolated defects with periodic boundary conditions. Furthermore, we find that transition levels converge faster with respect to supercell size when only the Gamma-point is sampled in the Brillouin zone, as opposed to a dense k-point sampling. This arises from the fact that defect level at the Gamma-point quickly converges to a fixed value which correctly describes the bonding at the defect centre. Our calculated transition levels with 1000-atom supercells and Gamma-point only sampling are in good agreement with available experimental results. We also demonstrate two simple and accurate approaches for calculating the valence band offsets that are required for computing formation energies of charged defects, one based on a potential averaging scheme and the other using maximally-localized Wannier functions (MLWFs). Finally, we show that MLWFs provide a clear description of the nature of the electronic bonding at the defect centre that verifies the canonical Watkins model.

10 pages, 6 figures

References in corpus (1)

• Defect Energy Levels in Density Functional Calculations: Alignment and Band Gap Problem

Cited by in corpus (17)

• Maximally localized Wannier functions: Theory and applications
• Electrostatics-based finite-size correction for first-principles point defect calculations
• A Computational Framework for Automation of Point Defect Calculations
• Point defect modeling in materials: coupling ab initio and elasticity approaches
• PyCDT: A Python toolkit for modeling point defects in semiconductors and insulators
• Anisotropic charge screening and supercell size convergence of defect formation energies
• Electrostatics of solvated systems in periodic boundary conditions
• Giant Anomalous Hall Effect due to Double-Degenerate Quasi Flat Bands
• Lithiation of silicon via lithium Zintl-defect complexes
• First-principles study of the dynamic Jahn-Teller distortion of the neutral vacancy in diamond
• Combining the $\Delta$-Self-Consistent-Field and GW Methods for Predicting Core Electron Binding Energies in Periodic Solids
• Reliable methods for seamless stitching of tight-binding models based on maximally localized Wannier functions
• Ab initio electron-defect interactions using Wannier functions
• Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study
• Inert gas as electronic impurity in semiconductors: The case for active infrared absorption in silicon
• A first principles study of As doping at a disordered Si--SiO${}_2$ interface
• Negative-U properties for substitutional Au in Si