The effect of pressure on structural, stability, electronic, and optical properties of hydrogenated silicene: A first-principle study

The structural, electronic, and optical properties of hydrogenated silicene have been studied under different pressures using first-principle calculations. The binding energy and band structure have been calculated for two stable structures: Chair (C-) and Boat (B-) in the range of 0-21 GPa external pressure. The behavior of stability and energy bandgap have been analyzed under different external pressures. The stability has been verified using binding energy and phonon data. The C- and B- structures have zero bandgaps at 21 GPa and become unstable. The optical properties of B-configuration have been studied in the energy range of 0-20 eV. Five optical parameters such as conductivity threshold (σ th ), dielectric constant ε(0), refractive index n(0), birefringence Δn(0) and plasmon energy (ħω p ) have been calculated for the first time under different pressures. The calculated values are in good agreement with the reported values at 0 GPa. ______________________________________________________________________________


Introduction
In the last decade, increasing interest has been given to the study of two-dimensional graphene due to its exceptional properties such as high carrier mobility, current carrying capacity, non-zero berry's phase, unusual quantum Hall effect, linear dispersion energy bands, etc [1][2][3]. However, graphene may not be compatible with the present silicon technology and integrated circuits. Accordingly, researchers investigated the other IVA group elements, such as silicene and germanene. Silicene and Germanene are the graphene analogy of silicon and germanium. Silicon is the more abundant element compared to germanium, and also silicene has exceptional properties such as linear dispersing energy bands, massless Dirac distribution, and quantum Hall effect [4][5][6] ferromagnetic [7], half metallicity [8], giant magneto resistance [9], and superconductivity properties [10]. It exhibits good spin-orbit coupling, a spin-orbit gap at Dirac points [11], the emergence of valley polarized metal phase for spintronic applications [12,13]. Silicene has zero energy bandgap like graphene and also has less thermal conductivity [14,15]. To introduce the energy band gap many procedures have been used such as chemical functionality [16,17], application of electric field [18], doping [19], substrate effect [20], nanoribbon [21,22], and introducing nanoholes [23,24]. Hydrogenation is a well-known technique to creates a bandgap and increases the thermal conductivity of silicene [25,26]. The hydrogenated silicene is normally referred to as silicane, which is experimentally observed on Ag (111) [27][28]. The silicane is stable up to 450 K temperature, and after that, dehydration occurs, and the surface restores initial silicene [29].
Several researchers have performed first-principle calculations to study the structural, electronic, magnetic, and thermal properties of hydrogenated silicene [30][31][32][33][34][35]. Lui et al. [36] have calculated the thermal properties of silicane and predicted that hydrogenation leads to a large increment of thermal conductivity from 22.5 Wm -1 K -1 to 78.0 Wm -1 K -1 . The effect of hydrogen in the silicene sheet has been studied in which half-silicane shows ferromagnetic behavior [37]. Nguyen et al. [38] have studied the hydrogenated silicene and graphene that confirms silicene has a strong binding with hydrogen compared to graphene. Some researchers calculated the carrier mobility and electron transport properties of silicene and hydrogenated silicene [39][40][41]. Molecular dynamics simulation reveals the stability of adsorption configurations of hydrogenated silicene [42].
Some researchers have reported the hydrogenation of silicene for different structures [25,26] out of which chair (C-), boat (B-) structures are most stable. Recently, the authors [43][44][45] have studied the several properties of hydrogenated graphene, hydrogenated silicene, and hydrogenated germanene using first-principle calculations. The authors have also have studied the pressure effect on the various properties of functionalized graphene and germanene [46][47][48].
Till now, no work has been carried out on the properties of C-and B-structures of hydrogenated silicene under different pressures. Therefore, we thought it would be of interest to study the structural, electronic, and optical properties of C-and B-conformers of hydrogenated silicene under external pressures.
In this paper, first-principle calculations have used to calculate the lattice constants (a, b, and c), bond lengths (dSi-Si and dSi-H), bond angles (θSi-Si-Si and θSi-Si-H), energy bandgap (Eg), and binding energy (Eb) in the pressure range of 0 GPa -21 GPa. The stability has been analyzed using the binding energy and phonon calculations. The behavior of the energy bandgap has been studied for every 3 GPa rise in external pressures. The optical parameters of B-configuration such as (σth), ε(0), n(0), Δn(0) and ћωp have been calculated in in-plane (E⊥c) and out of plane (E||c) polarization for the first time.

Methodology
The calculations have been performed using the Cambridge Sequential Total Energy Package (CASTEP) code [49]. The generalized gradient approximation (GGA) has been used with the Perdew-Burke-Ernzerhof scheme (PBE) [50][51][52]. A plane-wave basis set kinetic energy cut-off of 272 eV has been used in an ultra-soft Pseudopotential representation in reciprocal crystal lattice [53]. The optimized structure has been obtained by applying the Broyden, Fletcher, Goldfarb, and Shanno BFGS scheme [54]. Throughout the optimization of geometry, maximum tolerance of total energy convergence of 0.2 × 10 −4 eV/atom, Fermi energy convergence of 0 .27 × 10 −13 eV, Hellmann-Feynman ionic force of 0.05 eV/Å, maximum stress component 0.1 GPa, and ionic displacement of 0 .2 × 10 −2 Å have been used.

Structural and Electronic properties
The hydrogenation of silicene leads to disrupt the π-bonding of adjacent pz orbitals of silicon atoms. The hexagonal sp 2 hybridized silicene lattice changes to tetrahedral sp 3 hybridized silicane (hydrogenated silicene) with strong σ-bonding. It results in an increase in perpendicular distance between A-type and B-type silicon sub-lattices, which increases the lattice constant and bond lengths. The hydrogenation of silicene forms many structures out of which chair (C-) and boat (B-) structures are the most stable structures [25,26]. The perspective view of C-silicane is shown in Fig. 1(a). The C-silicane belongs to a space group of P-3M1, which is a trigonal structure having lattice constants of 3.857 Å, 3.857 Å, and 4.59 Å for a, b and c, respectively.
The B-silicane belongs to the orthorhombic structure having a space group of PMMN. The perspective view of B-silicane is shown in Fig. 1(b). The optimized lattice parameters are 6.271 Å, 3.714 Å, and 6.015 Å. The calculated bond lengths (dSi-Si and dSi-H) and bond angles (θSi-Si-Si and θSi-Si-H) are listed in Table 1 for C-configuration and in Table 2 for B-configuration. There are two pairs of Si-Si bond lengths in B-configuration, one is parallel to the plane, and the other is perpendicular to the plane, which is bonded with hydrogen. The first bond length has a high value compared to the second due to H-H repulsion [55]. The bond length (dSi-Si) of two configurations of hydrogenated silicene shows a higher value compared to pristine silicene due to the depopulation of bonding orbitals of silicon atoms. This depopulation is due to the electronegativity difference between hydrogen and silicon atoms.  Table 1 and Table 2

Pressure effect on structural and electronic properties
The behavior of structural and electronic properties under different pressures has been studied for C-and B-configurations. The calculated values of lattice constants, bond lengths, bond angles, total energy, unit cell volume, energy bandgap, and binding energy have been listed in Table 1 for C-structure under different pressures from 0 to 21 GPa, and in Table 2 for Bconformer from 0 GPa to 21 GPa. The value of binding energy shows that the stability decreases with the increase of external pressures. The negative value of Eb shows that C-and B-configurations are unstable at 21 GPa external pressure. The above statement is verified by the phonon calculation in which imaginary frequencies (ω 2 (k, j<0)), shown as negative values below the zero level. These negative values are called soft modes. The soft modes that occur at K-point confirm instability. Table 1 shows the indirect bandgap of C-conformer decreases for every 3 GPa rise in pressure and becomes zero at 21 GPa, whereas for B-configuration, the bandgap becomes zero at 21 GPa.

Optical properties
The shows high Plasmon energies compared to pristine silicene due to the Π to σ bond translation, which causes transitions from the lowest occupied valence band to the highest unoccupied conduction band (σ- * plasmons).

Conclusions
The behavior of lattice constants, bond lengths, bond angles, energy band gap, total energy, unit cell volume, binding energy has been successfully studied using first-principles from 0 GPa to 21 GPa external pressures. The density of states has been calculated for Bconfiguration in which H-1s and Si-3p states play a major role in the creation of the energy bandgap. The C-configuration shows an indirect bandgap, and B-the structure has a direct bandgap. Table 1 and Table 2 shows the energy bandgap for two structures decreases with an increase in external pressure and becomes metallic at 21 GPa external pressure. The stability also decreases with the increase of pressure and becomes unstable at 21 GPa. The stability has been verified using binding energy and phonon calculations. Table 3