Strain modulated band gap of edge passivated armchair graphene nanoribbons

Strain modulated band gap of edge passivated armchair graphene nanoribbons

Xihong Peng, 1,* Selina Velasquez2 1 Department of Applied Sciences and Mathematics, Arizona State University, Mesa, AZ 85212 2 College of Technology and Innovation, Arizona State University, Mesa, AZ 85212

ABSTRACT First principles calculations were performed to study strain effects on band gap of armchair graphene nanoribbons (AGNRs) with different edge passivation, including hydrogen, oxygen, and hydroxyl group. The band gap of the H-passivated AGNRs shows a nearly periodic zigzag variation under strain. For O and OH passivation, the zigzag patterns are significantly shifted by a modified quantum confinement due to the edges. In addition, the band gap of the O- passivated AGNRs experiences a direct-to-indirect transition with sufficient tensile strain (~ 5%). The indirect band gap reduces to zero with further increased strain, which may indicate a formation of metallic nanoribbons.

Keywords: armchair graphene nanoribbons, uniaxial strain, band structure, band gap, quantum confinement, edge passivation

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Recently graphene, a two-dimensional (2D) sheet of sp2-bonded carbon honeycomb lattice, has been considered as a promising material for many advanced applications in future electronics, such as ballistic single-electron transistors and interconnects.1-3 The 2D graphene sheet demonstrates a zero band gap. For practical applications in semiconductor technology, the band gap of graphene has to be tuned to a finite value. A series of strategies were explored to engineer the band gap of graphene, for example, by applying an external electric field4-7 or utilizing multilayer graphene structures.7, 8 Tailoring the 2D graphene sheet into nanoribbons has been one of the promising approaches to create a finite value band gap. Individual factors, such as size9-14, edge effect,9, 15-17 and external strain,18-23 can be employed to effectively tune the band gap of the graphene nanoribbons. However, it is still not clear what the combined effects of these factors are, especially strain and edge passivation, on the band gap of AGNRs In present work, a theoretical study was conducted to investigate strain modulation of the band gap of the AGNRs with various edge passivation, including hydrogen, bridged oxygen and hydroxyl group. It was found that the zigzag pattern of strain-dependence of the band gap is significantly shifted by different passivation. In addition, a transition from direct to indirect band gap in the O-passivated AGNRs is observed by applying tensile strain around 5%. The ribbons could become metallic with further increased tensile strain.
Density-functional theory (DFT)24 calculations were performed using VASP code.25, 26 Local density approximation (LDA) was applied. In detail, a pseudo-potential plane wave approach was employed with a kinetic energy cutoff of 400.0 eV. Core electrons were described using Vanderbilt ultra-soft pseudo-potentials (US-PP).27 Projector augmented wave (PAW) potentials28, 29 were also used to check the calculations and no significant difference in the results was found between US-PP and PAW. Reciprocal space was sampled at 4 × 1× 1 using Monkhorst Pack meshes centered at  point. 21 K-points were included in band structure calculations. Dangling bonds on the edge of AGNRs were saturated in three scenarios: (1) by hydrogen atoms; (2) by oxygen atoms; and (3) by hydroxyl group (see Fig. 1). The initial lattice constant in a ribbon was set to be 4.22 Å, taken from the 2D graphene sheet. The lateral size of the simulation cell in the ribbon plane was chosen so that the vacuum distance between the ribbon and its replica (due to periodic boundary conditions) is more than 12 Å, and an 8 Å of vacuum separation was used to eliminate the interaction between ribbon layers. The total energy was converged to within 0.01 meV. Atoms were fully relaxed until forces are less than 0.02

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eV/Å. The lattice constant along the armchair direction (i.e. x-axis) of all AGNRs was optimized through the technique of energy minimization.
The width L and the lattice constant a of a ribbon are defined as in Fig. 1(a). Based on the relaxed structure of a ribbon with an optimized lattice constant, uniaxial strain within the range of ±16% was applied by scaling the lattice constant (see Fig. 1(b)). The positive values of strain refer to uniaxial expansion, while negative corresponds to compression (note that the y and z coordinates of the ribbon are further relaxed at a given strain). It is known that, due to quantum confinement effects, AGNRs can be classified into three families according to the width L falling in the categories of 3n, 3n+1, and 3n+2, where n is a positive integer.21, 23 In present work, AGNRs with a width of 12, 13, and 14 were chosen to represent those three families. In Table I, the studied AGNRs are listed wi