Influence of single vacancy defect at varying length on electronic properties of zigzag graphene nanoribbons

Kien Liong Wong,Afiq Hamzah,Michael Tan,Mu Wen Chuan,Cheng Siong Lim,Mohd Shahrizal Bin Rusli,Wee Khang Chong,Nurul Ezaila Binti Alias

doi:10.11591/ijeei.v7i2.1138

Abstract

Graphene, identified in 2004, is now an established two-dimensional (2D) material due to its outstanding physical and electronic characteristics namely its superior electrical conductivity. Graphene is a zero-gap material that has linear dispersion with electron-hole symmetry. As pristine sheet, it cannot be utilized in digital logic application without the induction of a band gap inside the band structure. In our work, the modeling and simulation of graphene nanoribbons (GNRs) are carried out to determine its electronics properties that are benchmarked with other published simulation data. A 4-Zigzag GNRs (4-ZGNRs) under different length are utilized. A single vacancy defects is introduced at various positions inside the atomic structure. The theoretical model is implemented based on single-neighbour tight binding technique coupled with a non-equilibrium Green’s function formalism. The single vacancy defects are represented by the elimination of tight binding energies in the Hamiltonian matrix. Subsequently, these matrix elements are utilized to compute dispersion relation and density of states (DOS) through Green’s function. It is found that single vacancy defects at different positions in 4-ZGNRs’ atomic structure under varying length has no significant impacts on the sub-band structure but these vacancies impact the DOS that are computed throught Green’s function approach.

Highlights

Graphene Nanoribbons (GNRs) or strips of graphene are theoretically introduced by Mitsutaka Fujita in 1997 [1]
The α matrix of each unit cell is located at the diagonal of Hamiltonian matrix whereas the β matrix is located at the top of the diagonal matrix
Tight binding is sufficient for a simple system and less computationally expensive than Density Functional Theory (DFT) approaches

Summary

Introduction

Graphene Nanoribbons (GNRs) or strips of graphene are theoretically introduced by Mitsutaka Fujita in 1997 [1]. Because of its remarkable electronic properties that can be engineered by controlling its width, length and edge orientation as well as defects [3, 4]. Hamiltonian matrix that is a solution of Schrödinger’s equation is obtained to compute electronic properties of. 4-ZGNRs with single vacancy defects at different locations inside the band structure [6,7,8]. The nanoribbon system can be described by Hamiltonian matrix the elements [9, 10]. A tight binding 4-ZGNR model is produced by disintegrating 4-ZGNRs’ quasi-2D structure into an equivalent one-dimensional (1D) matrix system with alpha and beta matrices [11, 12].

Methods

Results

Conclusion