Bandgap Engineering in Iron Doped Graphene Nanosheets: Electrical Performance Boosting for Application in Nano-electronics

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Introduction Nanotechnology [1] is a standout amongst the most delicate research territories that cover various orders including biomedical building and development materials. Generally, nanotechnology has been ascribed to the advancements in the field of material science [2], microelectronics [3] and medicines [4]. Nanotechnology is a field that is influenced by the progress in basic chemistry and physics research, where occurrence on molecular and atomic level are used to give structures and materials that execute tasks that are highly impossible for the materials in their typical microscopic form. The enhancement of instrumentation and technology as well as its co related scientific field as Chemistry and Physics are fabricating the research on nanotechnology competitive and progressive. Before the discovery of graphene in 2004, it was assumed that the two-dimensional crystals were not existed as thermodynamic fluctuation does not allow it. Graphene was discovered by a scientist named Andre Geim by the mechanical exfoliation method from graphite [5].
Because of the exceptional property of Graphene, it has been explored for various applications. Graphene is also used to make conductive plates of ultra-capacitors due to its large surface area to mass ratio. Upon doping with different hetero material impurities in bare graphene nanosheets, changes appear in terms of physical and chemical properties [6,7]. Previously the effects of metal atom doping in carbon nanomaterials is already studied [8][9][10][11][12]. Doping of extrinsic impurities to the pristine graphene nanosheets can increase the extent of chemisorptions in a large extent as when compared to physisorption cases. Impurities like N, Al, S and B have been investigated earlier either onto Graphene or Single walled carbon nanotubes by experimentally [13][14][15] as well as theoretically [16][17][18]. Chemical potential, bandstructure, density of states, total energy, transmission spectrum, optical spectrum, Eigen value, Eigen vector, all these parameters of a pristine graphene nanosheet are expected to get altered when extrinsic impure materials are doped selectively in that sheet. This has led the authors to study the role of iron (Fe) impurity in electrical performance boosting of bare graphene nanosheets for futuristic applications in nano-electronics and photonics.
To study the underlying interaction mechanism of iron dopant and bare graphene nanosheets semi empirical DFT based ATK-VLN QuantumWise software is used. Iron atoms are introduced by ab-initio approach and by Van der Waals force at different interstitial position of bare graphene nanosheets for estimating various electrical, chemical and electronic properties. In comparison to the earlier study by Wang et al. (2009) [19], the present study will throw light on defect free graphene for Fe doping to study its influence over the DOS analysis, band structure modulation and transmission spectrum. Through the controlled doping of iron, it is expected to observe band gap morphology modulation from metallic to semi-metal and semi-metal to semi-conductor like behavior. This possibility has been explored comprehensively through this analytical study.

Simulation Methodology
In this work, the authors have utilized a nano-simulation software, Atomistix Tool Kit-Virtual Nano Lab (ATK-VNL) [19]. (Density Functional Theory (DFT) can be used to correct the self-interaction error by defining an atomic self-energy potential, which is calculated for atomic sites in the system, that cancels the electron-hole self-interaction energy [20]. This potential can be calculated as the difference between the potential atom and that of a charged ion which is formed by the removal of a fraction of its charge of the range between 0 and 1 electrons. Self-energy potential is can be defined as the sum of these atomic potentials.
ATK-DFT generally uses the energy level of conduction band and it eliminates the selfinteraction energy effect and as a result an accurate study of electronic properties can be obtained. Numerical Linear Combination of Atomic Orbitals (LCAO) is utilized for all the analyses at fixed algorithm parameters of ATK-DFT. The LCAO Calculator [21] uses DFT and norm-conserving pseudo potentials to give a brief description of electronic structures. In the DFT method, the exchange-correlation term is used to approximate the quantum mechanical part of the electron-electron interactions. A large number of different approximate exchange-correlation density functions exists in DFT.

Defect creation in Graphene upon doping Iron atoms
The doped Iron defects could be observed at different excited charge conditions shown by 'q' in Graphene systems. The energy formation denoted by 'EF' of distorted defect comprising of KFe Iron atoms in varied proportion of KFe1 to KFe3 inserted to replace K(C)n atoms of Graphene, viz. KFe1 + KFe2 + KFe3 = K(C)n could be represented by the expression as shown in Equation (1). where, and ( ) are the analysed total energies containing distorted and defect pristine Graphene architecture, respectively. 'q' represents the charge condition of the defect architecture; Energy position of the valence band is denoted by ; and µ represents the electronic chemical potential, defined under the bandgap in relation to [22]. 6 µ( ) and (µ ) (1−3) denotes the net chemical potentials of the prevalent elemental components in the systems. When equilibrium condition is reached, the expression of the doped system could be shown as in Equation (2), where, µ( ) is defined as the net cumulative energy per hexagonal ring of carbon in the Graphene architecture. Selection of µ( ) is described by the net growth conditions of Graphene, and it is very helpful to aid in maintaining the stoichiometry between the Iron atoms in the Graphene network.
Electron temperature is taken as 300 K, the grid mesh-cut value is considered as 20 Hartree, charge is zero, spin is unpolarized, k-points (a, b, c) are (9, 9, 1) and the Carbon energy is 0.0 eV.

Results and Discussions Band Structure Analysis
Graphene is generally a zero-band gap material because the valence band and conduction band of graphene are overlapped in nature. Figure 1 shows the device configurations of all the variants. Figure

Density of States Analysis
The specific value of DOS at a characteristic energy level in eV explains the number of states available for occupation by the electrons in a system. Figure 3 show that undoped graphene nanosheet exhibits a DOS value of ~330 eV-1 at energy value ~12 eV. But in case of doped graphene nanosheets, the DOS values are ~290 eV -1 , ~270 eV -1 , ~250 eV -1 respectively for one, two and three atoms doped graphene nanosheets at a same energy value of ~12 eV. It implies that the peak value is decreasing with the increasing number of doped atoms. The doping concentration in the basic and stable 9 construction of graphene conveys a charge transfer reaction at the electronic sites of the graphene between carbon and iron atom, which is ascribed to the ensuing retort in the plot. So, with increase in the doping atom concentration in graphene the band structure behavior also changes.

Chemical Potential Analysis
The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are integrated to the system. In present study, in   It is also observed that, for bare graphene, there is lack of development of peaks at the conduction band. When one Iron atom is doped, there is an incidence of development of narrow peaks around the Fermi level. The concentrations of peaks are getting more distinct due to the charge transfer mechanism happened at graphene-iron inter-phase.
This result due to a partial formation of forbidden gap around defined Fermi level. Graphene is a well-known Bio compatible nano-material, with the help of which highly accurate and precise sensors can be designed. We want to design a bio-compatible photo sensor with Graphene, through ab-initio study, which sensors can be implemented in non-invasive diagnostics.