Study on Electronic and Optical Properties of Graphene Oxide Under an External Electric Field From First-principles

Electronic and optical properties of graphene oxide (GO), under an external electric field ( 𝐸 𝑒𝑥𝑡 ) applied in three directions of space (x, y, z), are investigated using the density functional theory (DFT). The application of the 𝐸 𝑒𝑥𝑡 , causes a significant modifications to the electronic and optical properties of GO material. It has change the band gap, total density of states (TDOS), partial density of states (PDOS), absorption coefficient (α) , dielectric function, optical conductivity, refractive index and loss function. The band gap of GO layer increases under the effects of the 𝐸 𝑒𝑥𝑡 , applied in x and y directions. On the other hand, for z direction, the band gap decreases by the effects of the 𝐸 𝑒𝑥𝑡 . The peaks of the TDOS around the Fermi level, change by the 𝐸 𝑒𝑥𝑡 applied in (x, y, z) directions . The α peaks of the GO sheet, decreases by the 𝐸 𝑒𝑥𝑡 applied in x direction, and increases if 𝐸 𝑒𝑥𝑡 applied in y and z directions. It is found that, the electronic and optical properties of GO layer, could be affected by the effects of the 𝐸 𝑒𝑥𝑡 and by its direction of application.


Introduction
Electronic states of graphene derived from π electrons of the carbon atoms, can be calculated using the DFT calculation. In two-dimensional graphene, the carbon atoms form a triangular lattice with the lattice constant = √3 − , and the carbon bond length in graphene sheet is dc-c= 0.142 nm [1]. A single layer of graphene, the band structure shows zero gap at the K point of the Brillouin zone. This points is also termed Dirac points, which can be opened by the external perturbations such as the application of the or by the strain [2]. Hofmann and Holst proposed a structural model of GO layer, with the epoxy groups (C2O) only. They supposed that the oxygen functional groups, are bound to the carbon atoms of the hexagon sheet planes [3]. Yan et al. [4,5] studied the arrangement of the epoxy groups on graphene layer, using the first-principles calculations. The epoxy groups are orderly arranged in a chained on the basal plane of graphene, forming specific oxygen-containing groups put on the both sides of graphene sheet.
In several cases, the effects of the can modify the electric current in a semiconductor device [6].
The electric field is simply modifiable in directions. The effects of the adjust the optical response of the 2D graphene. The external dc gates control the Fermi energy and help the photocurrents in graphene material, which are essential for optical modulators and photodetectors, respectively [7]. Therefore, it is very necessary to study the effects of the , on optical and electronic properties of GO. The effects of the has the advantage of being easy to attain and control the physical properties of 2D materials. The applied on electronic and optical properties of GO, have received great attract for fundamental and applied research.
Applying an electric field on materials can cause an electro-optical effects, and change their optical and electronic properties [8,9]. In this paper, the effects of an on electronic structure and optical properties of GO layer, are studied using the first-principles calculations [10]. Including the band gap, density of states and optical properties of GO structure. In the case of applying the on GO layer, a perturbation of electrostatic potential to the Hamiltonian of π-electrons is expected. The effects of an applied in the three directions (x, y, z) of space, modifies the Hamiltonian H of the system as: Where 0 is the Hamiltonian of the system without the effects of the .
Our paper is outlined as follows: In section 2, we briefly present the Computational Methods. Section 3 is devoted to discuss the numerical results and give our interpretations. Finally, the conclusions of our study is included in Section 4.

Computational methods
The electronic structure simulations and optical properties of the GO model, are calculated based on the DFT calculations. All calculations are performed using the CASTEP code, by the OTFG ultrasoft pseudopotentials [11,12]. Only the valence electrons (C 2s 2 2p 2 and O 2s 2 2p 4 ) are considered using ultrasoft pseudopotentials. The exchange-correlation energy was treated within the generalized gradient approximation (GGA) in the form of Perdew, Burke and Ernzerhof (PBE) functional [13]. A plane-wave energy cut-off was set to 600 eV for all the calculations.
The K-point of the Brillouin zone was sampled using 6×6×1 gamma-centered Monkhorst-Pack grid during the geometry optimizations of GO [14]. However, during all structural relaxations, the convergence tolerance criteria for the geometry optimization was set to 2x10 -6 eV/atom for the energy. During the atomic relaxations, the positions of atoms are optimized until the convergence of the force on each atom, was less than 0.003 eV/Å and 0.005 Å for the displacement. The self-consistent field (SCF) convergence tolerance, was set to 2x10 -6 eV/atom. The internal stress components are less than 0.1 GPa.
In the present simulation, the GO structure is shown in Fig.1

Optical gap
To Applying an is a method to control the energy band gap of 2D-materials. It is very important to

Density of stats
The density of states (DOS) is a quantum property, that is used in solid-state physics. It refers to the number

Absorption
In the present study, we have presented the variation of absorption coefficient α as a function of photon energy (ℎ ), under an from 0 V/A˚ to 0.50 V/A˚, applied in (x, y, z) directions of GO layer in 0 -8 eV range, as shown in Fig.6. For the absence of an , the absorption spectrum consists of two peaks with different intensities. The first peak with low intensity appear at 3.01 eV, and the second peak identified at 5.69 eV [16]. The source of peaks arises from two essential transitions between electronic states of GO.
The first peak corresponds to the transition from occupied n to unoccupied n* state in the conduction bands.
The large second peak corresponds to the transition of π-π* states for C-C bond in sp 2 hybrid regions.
According to these two peaks,

Dielectric function
The complex frequency-dependent dielectric function, ɛ( ) can be used to descript the optical properties of 2D-material, and describes how light interacts when propagating through matter. It determines the dispersion effects by its real part, ɛ 1 ( ) and the absorption effects by the imaginary part, ɛ 2 ( ). We measured the energy dependence of GO dielectric function, under the applied in (x, y, z) directions.
The complex dielectric function ɛ( ) is the sum of real and imaginary parts: In the present study, the real and imaginary parts of the GO dielectric function, are calculated in absence and presence of the effects of the , applied in (x, y, z) directions in 0 -8 eV range, as presented in Fig.7.
At low energies, ɛ( ) is associated with electronic intraband transitions inside the conduction band. In this spectral range, the optical response is dominated by the free electron behavior. At higher energies, ɛ( )  Table.3.
The difference between ɛ 1 ( ) values in (x, y, z) directions, suggests that an anisotropic behavior of the optical properties of GO material, under the . For an applied in both x and z directions of GO structure, ɛ 2 ( ) has two peaks in 2-8 eV range, are always related to the electron excitation. The ɛ 2 ( ) part, has a low value for the incident photons has the energy ( = ℎ ) less than 2 eV Fig.7. In addition, it is noteworthy to say that the value of ɛ 1 ( ) > 0 and ɛ 2 ( ) = 0 in 0-1 eV range, means that this region transparent. It means that there is no absorption at low energy, because in this case the valence electrons of GO layer, cannot react fast with the , and the transition between the valance band maximum and the conduction band minimum or between the orbitals is forbidden. Then, under an , GO material is an absorbent material for a wide range of energy, which indicates that this material can be used as an important element in several optoelectronic devices, such as the transparent conducting films and photovoltaic devices.

Refractive index
Propagation in absorbing materials, can be described by the complex-valued of the refractive index * ( ).
The variation of ( ) and ( ) of GO layer, under the effects of the from 0 V/Å to 0.50 V/Å, applied in (x, y, z) directions in terms of frequency, are found using the CASTEP code and depicted in  Table.5 and Fig.8. When we analyse the graphs of 2( ) and ( ) parts, a similar physical behavior is observed in Fig.7 and Fig.8. These results give the information's of the absorption light by GO material.

Conductivity
It is interesting to know the complex optical conductivity ( ) of GO material, because we can derive valuable physic information's from it. The parts of ( ) are given by the following relation [18]: Optical conductivity was calculated of GO layer under the effects of the , applied in (x, y, z) directions. The 1 ( ) and 2 ( ) parts as a function of frequency are plotted in Fig.9. In the case of the  Table.6. In (x, z) directions, 2 ( ) has a negative value in 0-8 eV range, which indicates that the charge is well-distributed in GO layer Fig.9. Additionally, in (x, z) directions, its noteworthy to say 1 ( ) = 0 1 in 0-1 eV range, by reason of no absorption at low frequency, because the cannot react with the valence electrons inside the GO structure. The Fermi level can be identified by the local minimum of 2 ( ) part. The application of the on GO layer therefore pushes the Fermi level, relative to the Dirac point of the Brillouin zone.
Although, it has been reported that the effects of the on GO structure, can modify the position and the shape of the van Hove singularity peaks in the visible range.

Loss function
The electron loss function ( ) describes the energy loss of a fast electron traversing a material, with the change of frequency. From the real and imaginary parts of ɛ( ), the energy loss function can easily be obtained by [19]: The ( ) of GO layer under the applied in (x, y, z) directions, shown in Fig.10. The origin of ( ) peaks in 0-8 eV range, due to the collective excitations at various photon energies. The ( ) exhibits two peaks approximately at 3 and 6 eV, which are associated with the plasma frequency. These two peaks indicate the maximum energy lost in GO sheet, under the effects of the . The application of the on GO layer in x direction, lead to decrease the peaks of ( ) in both visible and UV ranges. On the other hand, the effect of an = 0.25 V/Å applied on GO sheet in y direction, lead to decrease the peaks of ( ) in both visible and UV ranges. But, the effect of an = 0.50 V/Å lead to increase the peaks of ( ) in both visible and UV ranges. Additionally, the application of the on GO in z direction, lead to increase the first peaks of ( ) in visible range, by reason of the increase the scattering between the incident visible light and the different particles inside GO structure Table.7. The peaks at 6 eV, due to the energy lost for π electrons and the peaks at 3 eV are due to the energy lost for π and σ electrons in GO layer, under an effects. A peak in the ( ) corresponds to a dip in the ɛ 1 ( ) part, as shown in Fig.7 and Fig.10.

Conclusions
To conclude, we have studied the electronic and optical properties of GO layer, under the effects of the by using the DFT calculations. The application of the on GO sheet in (x, y, z) directions, produces different modifications in the band structures and optical properties. We have shown that the GO is a semiconductor material, and its band gap can be significantly modulate by applying an in the three direction of space (x, y, z). We observed the changes of the dielectric function and the absorption peaks, by reason of the modification of the band gap energy under the . These insights provide a basis for the applications of GO material under the effects of the in optoelectronic devices.