Band gap engineering in finite elongated graphene nanoribbon heterojunctions: Tight-binding model

Abstract

A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width WL, the middle part is a GNR of width WM , and the right part is a GNR of width WR. We assume that the left and right parts of the GNR heterojunction interact with the middle part only. Under this approximation, the Hamiltonian of the system can be expressed as a block tridiagonal matrix. The matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal TB approximation. The electronic structure of the GNR heterojunction is analyzed by computing the density of states. We demonstrate that for heterojunctions for which WL = WR, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in GNRs. Our TB results were compared with calculations employing divide and conquer rule in combination with density functional theory (DFT) and were found to agree nicely. I. INTRODUCTIONGraphene is a two-dimensional (2D) allotrope of carbon with excellent electronic and mechanical properties, making it suitable for multiple applications in nanoscale electronics and nanophotonics. 1,2 A major deficiency in graphene's properties is the absence of a band gap rendering it impossible for use in switching circuits. 3 Several approaches have been used to induce a band gap in graphene such as electrically gated bilayer graphene, 4-6 substrate induced band gap, 7,8 or isoelectronic codoping with boron and nitrogen. 9 Recently, it has become possible to engineer the band gap of graphene by etching or patterning along a given direction to produce ultra narrow quasi one-dimensional (1D) nano sheets referred to as graphene nanoribbons (GNRs) [10][11][12] with remarkable properties such as width-dependent tunable band gaps, exciton-dominated optical spectra, and room temperature ballistic transport. [13][14][15] As quasi 1D materials, GNRs are extremely sensitive to their surrounding conditions, which provides a route for manipulating their electronic properties. Additionally, other factors such as finite size effect, 16,17 edge effect, 18-23 and the presence of strain 24-27 could be used to effectively tune the electronic properties GNRs.