Modeling SWCNT Bandgap and Effective Mass Variation Using a Monte Carlo Approach

Abstract

Abstract-SynthesizingSingle-Walled Carbon-Nanotubes (SWCNTs) with accurate structural control has been widely acknowledged as an exceedingly complex task culminating in the realization of CNT devices with uncertain electronic behavior. In this paper we apply a statistical approach in predicting the SWCNT band-gap and effective mass variation for typical uncertainties associated with the geometrical structure. This is firstly carried out by proposing a simulation-efficient analytical model that evaluates the band-gap (Eg) of an isolated SWCNT with a specified diameter (d) and chirality (θ). Similarly, we develop a SWCNT effective mass model, which is applicable to CNTs of any chirality and diameters > 1nm. A Monte Carlo method is later adopted to simulate the band-gap and effective mass variation for a selection of structural parameter distributions. As a result, we establish analytical expressions that separately specify the band-gap and effective mass variability (Eg σ , m* σ ) with respect to the CNT mean diameter (d µ ) and standard deviation (d σ ). These expressions offer insight from a theoretical perspective on the optimization of diameter-related process parameters with the aim of suppressing band-gap and effective mass variation.Index Terms-Single Walled Carbon Nanotube (SWCNT), Third-Nearest-Neighbor Tight-Binding (TB) model, Band-gap variation, Effective mass variation, CNT device models.I. INTRODUCTION ARBON NANOTUBES (CNTs) possess distinctive electronic properties that make them ideal candidates for next generation on-chip devices and interconnects [1][2][3][4]. Unlike other nanoscale materials, they can remarkably exhibit semiconducting (Eg > 0) or metallic (Eg = 0) behavior depending on their geometrical structure, which consists of the diameter (d) and chirality (θ) [5]. At present, the fabrication of CNTs with accurate diameter and chirality control is a serious challenge and as a result a large band-gap (Eg) variability is

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