Linear scaling calculation of band edge states and doped semiconductors

TL;DR

This paper introduces an efficient linear scaling (O(N)) method for calculating band edge states and doped semiconductors, enabling accurate analysis of optical properties and chemical reactions in large systems.

Contribution

It develops a novel O(N) algorithm for band edge states and doped semiconductors based on density matrix purification, extending linear scaling methods to energy levels and wavefunctions.

Findings

Successfully applied to BN nanotubes with consistent results.

Demonstrated linear scaling behavior in large systems.

Computed band gaps and acceptor levels accurately.

Abstract

Linear scaling methods provide total energy, but no energy levels and canonical wavefuctions. From the density matrix computed through the density matrix purification methods, we propose an order-N (O(N)) method for calculating both the energies and wavefuctions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematicly and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory.