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

Abstract

Synthesizing single-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 bandgap and effective mass variation for typical uncertainties associated with the geometrical structure. This is first carried out by proposing a simulation-efficient analytical model that evaluates the bandgap (Eg) of an isolated SWCNT with a specified diameter (d) and chirality (¿). Similarly, we develop an SWCNT effective mass model, which is applicable to CNTs of any chirality and diameters >1 nm. A Monte Carlo method is later adopted to simulate the bandgap and effective mass variation for a selection of structural parameter distributions. As a result, we establish analytical expressions that separately specify the bandgap and effective mass variability (Eg <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> , m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> ) with respect to the CNT mean diameter (d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> ) and standard deviation (d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> ). These expressions offer insight from a theoretical perspective on the optimization of diameter-related process parameters with the aim of suppressing bandgap and effective mass variation.