Finite-size correction for slab supercell calculations of materials with spontaneous polarization

Su-Hyun Yoo,Mira Todorova,Jörg Neugebauer,Leigh Weston,Chris G Van De Walle,Darshana Wickramaratne

doi:10.1038/s41524-021-00529-1

Abstract

The repeated slab approach has become a de facto standard to accurately describe surface properties of materials by density functional theory calculations with periodic boundary conditions. For materials exhibiting spontaneous polarization, we show that the conventional scheme of passivation with pseudo hydrogen is unable to realize a charge-neutral surface. The presence of a net surface charge induces via Gauss’s law a macroscopic electric field through the slab and results in poor size convergence with respect to the thickness of the slab. We propose a modified passivation method that accounts for the effect of spontaneous polarization, describes the correct bulk limits and boosts convergence with respect to slab thickness. The robustness, reliability, and superior convergence of energetics and electronic structure achieved by the proposed method are demonstrated using the example of polar ZnO surfaces.

Highlights

Density functional theory (DFT) has evolved into the work-horse approach for electronic structure calculations allowing to study of almost all aspects of materials and their properties
The translational symmetry along the direction perpendicular to the surface is broken by the introduction of a vacuum region within the supercell
If the thickness of the substrate or epitaxial film to which the surface is attached is thicker than the DFT slab, which is the case for typical technological applications and devices, convergence with respect to the slab thickness needs to be carefully controlled

Summary

INTRODUCTION

Density functional theory (DFT) has evolved into the work-horse approach for electronic structure calculations allowing to study of almost all aspects of materials and their properties. The second strategy is to employ boundary conditions such that the correct asymptotic limit is already reproduced in the finite-size supercells This strategy has been successfully applied to remove long-range electric fields that arise when studying unpassivated polar surfaces[9,18,19]. We will follow the second strategy and derive a concept that efficiently overcomes the extremely slow 1/d convergence (with d the slab thickness) when computing surface properties, such as surface states or surface energies, for systems exhibiting spontaneous polarization. This type of polarization is present in many technologically relevant semiconductors and insulators. The energy difference between the two EC structures of interest is defined as

RESULTS AND DISCUSSION

METHODS

CODE AVAILABILITY