Investigation of the Stability and Electronic Structures for Exohedral Aln Doped (Mono and Double)-Layer MgO Nanosheet s: A DFT Approach

In present work, a detailed analysis of density functional theory (DFT) study performed on pure and doped MgO nanosheet(MgONs). The aim of this work is to explore the stability skeleton, and electronic properties of mono layer of the MgO nanosheets and analogous double-layers with various positions of exohedral Aln dopant atoms. Our results for pure and doped MgO nanosheet corroborate with previous theoretical and experimental data. Optimized structures of monolayer and analogous double-layers of MgO nanosheet (MgONs) result in stable 2-D configuration, especially on doping with large concentrations. It has been observed that the band gap decreases with the increase in concentration of doping while the electronegativity increases.


Introduction
Nanomaterials have attracted a great interest for theoretical and experimental research due to their unique physical and chemical characteristics which depend on the shape and size of nanomaterials, like hardness with high conductivit, [1,2].
One of the important nanomaterial is Magnesium oxide, which is a famous simple oxide with rock salt structure in bulk phase. The 2D-MgO with both polar (111) and nonpolar (001) orientations have been successfully grown on various substrates experimentally [3][4][5][6][7][8][9][10]. This leads to the possibility of changing the electronic structure through doping which has recognized as a favorable alleyway to tune the properties of oxide materials toward the demands of different physics and chemistry applications. Dopants are supposed to disturb the lattice structure locally by breaking bonds to nearby atoms. As a consequence, interatomic coupling gets [11]. Density functional theory (DFT) study for electronic calculations of MgO mono-layer have also shown to display a more fascinating feature than its bulk phase for instance shrinking the band gap from 7.8 eV to 3.1 eV (for GGA) and 4.2 eV (for GGA-mBJ) [12]. The DFT calculations of Cr doped Rocksalt MgO reveal that CrMg3O4 is a promising spintronic material due to its half-metallic ferromagnet property as well as its resistivity to deform due to the large bulk modulus and shear modulus [13]. Fascinated by the interesting properties of doped MGO NSs, we perform density functional theory (DFT) to examine the stable structure, and electronic properties (binding energy, ionization potential, electron affinity, electronegativity and hardness) of hexagonal MgO NSs (111) after exohedral doping by Aln. Three geometries i.e mono layer of MgO NSs in first and second case, and two layers of MgONs in the third case have been considered for investigation.

Computational Approach
Ab initio calculations in this study have been performed using the Spanish initiative for electronic simulations with thousands of atoms (SIESTA) program package [14,15] which implements density functional theory (DFT) using exchange correlation functional of generalized gradient approximation (GGA) [16,17] and utilizing the double zeta basis (DZ) to exhibit spin polarization [18]. The pseudo-potential standards are built by using Trouiller-Martins schemes which are described as the interaction of valence electrons with atomic central. Pseudopotentials with 2s 2 2p 6 3s 2 and 3s 2 3p 1 valence electron configurations were used for Mg, O, and Al ISSN: 00333077 3633 www.psychologyandeducation.net atoms, respectively. Conjugate gradient (CG) algorithm is used to get optimized structures of MgO NSs. The positions of all atoms are allowed to fully relax until the force on each atom is less than 0.008 eV/Å during relaxation. The energy cut-off of 200Ry has been used to define the finite real space grid for numerical integrals.

Doping of Aln(n=1-7) on single layered MgO NS:
We start by investigating a pure MgO NSs by optimizing it with the atomic structure focused along either the (100) or (111) direction.The lattice constant for the optimized MgO NSs(100) and the MgO NSs (111) obtained were 3.85 and 3.18 Å respectively which are in good agreement with the previous results (4.01 and 3.26 Å) [19][20][21][22]. Also, the resulting Mg−O bond length of optimized pure MgO (111) NSs comes out to be 1.99 Å with bond angles between Mg-O-Mg bonds equal to 120 o which is comparable to formerly obtained results [7,21] as shown in Fig.1. Further on comparing the binding energies of both structures, it was found that, the binding energy of the optimized MgONs(111) system decreases by about 0.28 eV per Mg−O pair, which indicates that this MgONs(111) is more stable than the MgONs(100).
Where, , and are total energies of the Al doped MgONs and the pristine MgO NS, respectively, while n represent the number of dopant, total energy of the Al dopant and N is the total number of atoms in a supercell (n=82). A negative value of binding energy corresponds to a metastable or stable bound dopant when both are present in the system [22]. The variation of binding energy per atom for doped MgO NS is ISSN: 00333077 3634 www.psychologyandeducation.net shown in Fig.3. It is clear from Fig. 3 that with the increase in the number of Al dopants, the binding energy of the MgO NS attains its maximum value at -17.4 eV for Al7. The binding energy oscillates for Al4 for Al6 dopants. From the structural analysis, it is found that the stability of MgO NS strongly depends upon the number of dopant atoms in the sheet. The energy gaps of Aln@MgO NS are lesser than that of the related MgO NS and they depend on the type of dopant, number of dopants as shown in Fig.4. The band gaps for Aln@MgO NS were calculated from highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) play a very important role [24]. The gap between HOMO and LUMO energy levels can be used to measure the kinetic stability of system under consideration. Larger the HOMO-LUMO gap, Larger will be the kinetic stability as it is energetically not favorable to add electrons to a high lying LUMO or to remove electrons from a low-lying HOMO. Further, we notice that the doping with Al4, Al5, and Al7 are found to decrease the bandgaps of the MgO NS with increase the number of dopant. It is observed that the increase of the bandgap of the MgO with the decrease of the number of dopant [25]. This indicates that as the number of dopant increases, calculations show that all cases of Aln@MgO NS display semiconducting behavior and the Aln@MgO NS becomes energetically favorable. We have calculated the ionization potential (IP) by making nanosheet of Aln@MgO one electron deficient. Total energy for Aln@MgO NS complex is computed and then the total energy of neutral Aln@MgO NS is subtracted from it [26].
In the similar manner, electron affinity (EA) is calculated by putting one extra electron in neutral Aln@MgO NS and computing the total energy for the same and then subtracting the total energy of neutral Aln@MgO NS (n=1-7) [26,27]. It is clear that, exohedral doping of MgO NS effects EA more than that of IP. IP is independent on the postion of the atom, but in case of n=7 the structure has higher IP, as illustrated in Fig.5.
While the calculated EA of the studied structures is of the order of n=1-7. At the same time, this structure has the higher value of electron affinity EA. It is clear from the graphs shown in figure 5 that   Next, we obtain the electronegativity (EN) which is a linear combination of two known physical quantities i.e. ionization energy and electron affinity and is expressed as [20]: (2) As discussed, the hardness (H) is defined in terms of ionization energies and electron affinities, the hardness is half of the energy gap between two frontier orbitals [27]:  According to Fig. 6(a), the behavior of the electronegativity (EN) is shown for Al exohedral doped in MgONS. One can see that the addition of Al dopant atoms in MgONS leads to increase in the EN of the MgONS, this may come from the variation in the electronegativity of Mg atoms (1.3eV) and O atoms (3.5eV). The influence of the hardness H is illustrated in Fig. 6  Also, variation of binding energy for Al-doped configurations for each doping concentration is represented in Fig.8. It is observed that the binding energy decreases with increase in concentration of dopants, indicating the decreasing structural stability as compared to the Al7@MgONs (Eb = -17.40 eV per atom). This is due to the surface area to MgO NS as well as the nearly similar size of the atomic radius of Aldoped which means there is lesser structural distortion.  On the other hand in Fig. 10(a), the ionization potential is less sensitive and increases exponentially with the increase in the concentration of Al doping to MgO NS structure. This indicates that the ionization potential does not show much dependence on the crystal structure of MgO NS. Also, it is independent of the width of the MgO NS. The structure Al35@MgO NS has higher ionization potential. This means that Al28@MgO NS need large energy to become cation as compared to the other two. Fig. 10(b) shows the calculated electron affinity of the structures Aln@MgO NS (n=14, 28, and 35) increasing, That means these structures have a high ability to acceptance electrons and become anions, and in comparison with structure Al7@MgO NS they are cannot easily to donate an electron to the surrounding species. In order to study the influence of dopants on the electronic structures, the electronagtivity indices of Aln@MgO NS (n=14, 28, and 35) are evaluated and shown in Fig.11(a). It is obvious from the graph that electronagtivity increases as the Al content increases and can be related to the band gap narrowing with increase of the Al concentration. Fig.11

Doping of Al7 and Al35 on double layered MgO NS:
In this step, the GGA calculations have been used to obtain optimized structures of two sheets of MgO. As shown in Fig. 12, two layers of MgO contain sixty hexagons with the symmetry having the angles in hexagons between 3º to 122.9º [28]. The distance between the two layers are 2.98 Å while two individual Mg-O bonds are distinguished within the layers and another between a hexagon with average bond lengths of 1.88 and 1.95 Å, respectively. This indicates that the structure possesses a real fixed point on surface potential from 120. After that the two layers were doped by exohedral method. In the first case, the two layers were doped with seven Al atoms and the bond length between Al-Mg was kept at about 2.68 Å. In the same manner, two layers were doped with thirty-five atoms of Al. We notice that as compared to the binding energy