An Analytical Approach to Investigate the Band Structure of Strained Graphene Using Tight-Binding Model

Abstract— In this study, using tight binding model a simple analytical approach has been proposed to investigate the energy dispersion of graphene under the conditions of different planner strain distribution. Here the change in the angle between the primitive unit vectors due to application of external strain has been taken into consideration to propose the approach. From our proposed model it is found that graphene under relaxed or symmetrical strain distribution is a zero bandgap semiconductor. However a band gap is opened as the asymmetrical strain is applied to it. It is seen that upto a certain level of strain (i.e. 12.2 % parallel to carbon-carbon bond and 7.3% perpendicular to carbon-carbon bond) the band gap of graphene increases and then begin to fall . So, four different assumptions have been made for angular change of primitive unit vectors for four different regions of applied strain (i.e. before and after the strain of 12.2 % parallel to carbon-carbon bond & before and after the strain of 7.3% perpendicular to carbon-carbon bond). The result obtained in the present study are compared and found an excellent agreement, with more or less 96% accuracy with that of determined from first principle technique.

Keywords—Graphene, planner strain, tight binding model, energy dispersion, band-gap.
I. INTRODUCTION

Graphene, a strictly two-dimensional material having unusual and interesting properties [1] is a rapidly rising star on the horizon of material science and condensed matter physics. It is a material of interest in semiconductor industry because of its exceptionally high crystal and electronic quality, excellent transport properties (i.e. high electron mobility [2] and high thermal conductivity), and as it is planner, it is capable of extreme device scaling comparing with silicon technology. However these excellent properties are associated with a major drawback; graphene is a zero bandgap semiconductor or semimetal [3]-[4]. For large scale

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