Calculating the Energy Band Structure Using Sampling and Greens Function Techniques

TL;DR

This paper introduces a novel method combining Greens function theory and Fourier analysis to efficiently compute the energy band structure of various nanostructures with high accuracy.

Contribution

It proposes a new approach that samples potential energy with delta functions and transforms the lattice equations into reciprocal space, reducing computational complexity.

Findings

Accurately approximates atomic potential energy in crystals.

Reduces calculation time for band structure analysis.

Applicable to 1D, 2D, and 3D crystalline structures.

Abstract

In this paper, a new method based on Greens function theory and Fourier transform analysis has been proposed for calculating band structure with high accuracy and low processing time. This method utilizes sampling of potential energy in some points of crystals unit cell with Dirac delta functions, then through lattice Fourier transform gives us a simple and applicable formula for most of nanostructures. Sampling of potential in a crystal lattice of any kind contains accurate approximation of actual potential energy of atoms in the crystal. The step forward regarding the method concentrated on two novel ideas, Firstly, the potential was sampled and approximated by delta functions spread over the unit cell. Secondly, the principal equation of lattice is translated into reciprocal lattice and resulted in a huge reduction of calculations. By this method, it is possible to extract the band structure of any one, two or three dimensional crystalline structure.