Effect of hydrogenation on the band gap of graphene nano-flakes
Introduction
During the last decade, the graphene-based molecular devices were widely used as energy-related material, sensor, field-effect transistor, and biomedical application, due to their excellent electrical, mechanical, and thermal properties [1], [2]. As well as pure graphene, functionalized graphenes were synthesized and characterized by several groups [3], [4], [5], [6]. The tuning of graphene-based molecular devices to obtain the higher performance molecular devices is now an important field.
Recently, Elias et al. have investigated hydrogenated graphene by exposing to hydrogen plasma [7]. They found that a highly conductive graphene is converted from semimetal to insulator after the hydrogenation. Raman spectroscopy revealed that the hydrogenation breaks the π-bonding system of graphene surface after the formation of sp3 carbon–hydrogen bonds. Transmission electron microscopy study indicates that the original hexagonal bonding arrangement is retained, whereas the lattice constant is significantly reduced. The hydrogenation is reversible through annealing, thereby restoring the conductivity and structure of graphene. This reversibility also creates the possibility of using such materials for hydrogen storage. Thus, the addition of hydrogen atom can be used to tune the electronic properties of graphene-based molecular devices [8].
From a theoretical point of view, density functional theory (DFT) calculations of hydrogenated graphene have been carried out by several groups [9], [10], [11], [12], [13], [14]. Sofo et al. proposed that full hydrogenation of graphene forms a stable two dimensional (2D) hydrocarbon named graphane [10]. By means of the DFT computations, they also predicted that graphane has a wide band gap. Gao et al. calculated the band gap as a function of coverage in the range of 66–100% [11]. They found that the band gap increases gradually up to 8 eV.
Casolo et al. investigated the adsorption of hydrogen atom to a 5 × 5 surface unit cell of graphene using DFT method [14]. The binding energy per hydrogen atom was calculated to be 0.8–1.9 eV. It suggested that the change of hybrid orbital from sp2 to sp3 is important due to the hydrogen atom adsorption to graphene.
Thus, the binding energy of hydrogen atom on the surface of graphene is quite well understood. However, the coverage dependence of band gap was only investigated in the range of 0.7–1.0 coverage (i.e., higher coverage regions). Therefore, the relation between the band gap and coverage in a wider coverage range remains unclear.
In the present study, the DFT method was applied to the hydrogen atom interacting with a graphene flake. The dependence of band gap on hydrogen coverage was investigated in detail in order to elucidate the effects of hydrogen addition on the electronic structures of graphene nano-flakes. In a previous paper [15], we conducted a preliminary investigation on the effects of hydrogen addition on the electronic states of graphene surface. We found that hydrogen addition causes a lowering of band gap of graphene flake in case of low coverage regions. However, the calculation was carried out at the semi-empirical PM3 molecular orbital level. In the present study, accurate DFT calculation was performed for the hydrogen added graphene to elucidate the origin of specific band gap property.
The paper is organized as follows: in Section 2, we present the method of calculations. In Section 3, the structures and electronic states of hydrogenated graphene with 19 benzene rings are reported. Subsequently, we give the results of larger graphene with 37 benzene rings to elucidate the size-dependence of the band gap. In Section 4, we discuss the specific band gap properties of hydrogenations.
Section snippets
Method of calculation
Graphene nano-flakes composed of 19 and 37 benzene rings (n = 19 and 37) were used as models (denoted by GR(19) and GR(37), respectively). The edge carbon of graphene was terminated by a hydrogen atom. In case of hydrogenation of GR(19), even hydrogen atoms (from m = 2 to 54) were bonded to the surface carbon atoms, where m means the number of hydrogen atoms added to the surface. This addition causes a change of coverage from zero to 1.0.
The hydrogen atoms were first added to the carbon atoms at
Results
- A.
Structures of hydrogenated graphene flakes
The structure of GR(19) optimized at the B3LYP/6-31G(d) level is illustrated in Fig. 1 (m = 0). The optimized structure of GR(19) (m = 0) showed a purely planar form. The C–C bond distance was calculated to be 1.420 Å around the center of graphene.
Next, two hydrogen atoms were added to the carbon atoms around the central region of GR(19), and then the structure was fully optimized. The optimized structure is illustrated in Fig. 1 (m = 2). The C1–H bond
Discussion
In general, it is considered that the band gap increases with increasing coverage of hydrogen atom on the surface of graphene. However, the present calculations showed that the band gap of graphene behaves as a specific feature.
On the basis of the present calculations, a model of coverage dependence of band gap in the graphene nano-flakes is proposed. A schematic illustration of the model is given in Fig. 9. Upper figure indicates the relationship between band gap and coverage. The curve of
Acknowledgments
This work is partially supported by a Grant-in-Aid for Scientific Research on Innovation Areas “Evolution of Molecules in Space”. H.T also acknowledges a partial support from a Grant-in-Aid for Scientific Research (C) [JSPS KAKENHI Grant Number 2455000102].
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