An Ab Initio Investigation of Energy Bandgap of Monolayer and Bilayer Graphene Nanoribbon Based on Different Basis Sets

Abstract

We investigated the electronic structure of monolayer and bilayer graphene nanoribbon with armchair edges (AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> and AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> respectively) based on density functional theory using single-zeta (SZ) and double -zeta (polarized) (DZP) basis sets. We first optimize the atomic structure of an AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> and found that DZP is better suited to account for the interlayer interaction. Next we calculate the energy band diagram of the AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> and AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> of different width, and study dependence of the band gap (E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> ) on the widths. Like AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> , AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> also shows three different groups in terms of energy bandgap vs. width. In general, AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> is found to have a lower E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> than AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> . Especially for N=3p+2 family, while it is semiconducting for AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> , the E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> of AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> is very small and can be considered as metallic at room temperature. Furthermore, we investigate the relationship between E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> and the interlayer distance (D) of AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> . From our calculation, E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> is found to be strongly influenced by D and E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> increases as D increases. Finally, comparing solely on E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> , we can see that both SZ and DZP calculations provide information on the three trends of the AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> and AGNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , with small differences in the absolute values and hence it may be possible to use SZ for rapid preliminary investigation of the electronic properties of AGNR systems.