Effects of the edge shape and the width on the structural and electronic properties of silicene nanoribbons

Under the generalized gradient approximation (GGA), the structural and electronic properties are studied for H-terminated silicene nanoribbons (SiNRs) with either zigzag edge (ZSiNRs) or armchair edge (ASiNRs) by using the first-principles projector-augmented wave potential within the density function theory (DFT) framework. The results show that the length of the Si-H bond is always 1.50 Å, but the edge Si-Si bonds are shorter than the inner ones with identical orientation, implying a contraction relaxation of edge Si atoms. An edge state appears at the Fermi level E_F in broader ZSiNRs, but does not appear in all ASiNRs due to their dimer Si-Si bond at edge. With increasing width of ASiNRs, the direct band gaps exhibit not only an oscillation behavior, but also a periodic feature of Δ_3n > Δ_3n+1 > Δ_3n+2 for a certain integer n. The charge density contours analysis shows that the Si-H bond is an ionic bond due to a relative larger electronegativity of H atom. However, all kinds of the Si-Si bonds display a typical covalent bonding feature, although their strength depends on not only the bond orientation but also the bond position. That is, the larger deviation of the Si-Si bond orientation from the nanoribbon axis as well as the closer of the Si-Si bond to the nanoribbon edge, the stronger strength of the Si-Si bond. Besides the contraction of the nanoribbon is mainly in its width direction especially near edge, the addition contribution from the terminated H atoms may be the other reason.