The electronic and optical properties of 3d transition metals doped silicene sheet: A DFT study

Based on density functional theory calculations, we study the structural, electronic and optical properties of doped Silicene with 3d-transition metals Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn. Optical properties such as dielectric function, refractive index, reflectivity, absorption, electron loss function, and optical conductivity are investigated in both cases of in-plane (⊥) and out of the plane (∣∣) light polarization. Due to the doping of pristine silicene, the intensity of absorption peaks decreases and the maximum absorption peaks become visible in pristine silicene for out of the plane light polarization (∣∣). As light is polarized in-plane (⊥), the maximum absorption peak observed in Cu-doped silicene structure. Our computational results; indicate that the refractive index is anisotropic in both directions for all structures. In order to doping of silicene by transition metals structural, electronic and optical properties of pristine silicene modified. We believe that our results provide a useful strategy for applications in the optoelectronic industries.

region for ten transition metals doped SnO 2 nanosheets and the absorption shows red shift for Ni, Fe, Mn and Cr doped silicene [51].
In this paper, we investigate the structural and electronic properties of pristine silicene and doped silicene with nine transition metals Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn. With this type of doping, we calculate the values of the dielectric function and refractive index in both cases of in-plane (⊥) and out of the plane (||) light polarization to calculate some optical items like reflectivity, electron loss function, absorption, optical conductivity, and reflection.

Computational method
The calculations were performed within the framework of density functional theory (DFT) as accomplished by the VASP Package [52]. The generalized gradient approximation (GGA) [53] and GGA+U [54] performed with the parameterization scheme of Perdew-Burke-Ernzerhof (PBE) [53] for the applied exchange-correlation functional. Calculations done with different values of U (U Ti =3 [55], U V =3.2, U Cr =3.6, U Mn =3.9, U Fe =4, U Co =3. 35, U Ni =6, U Cu =4 [56], U Zn =5 [57]). The energy of the self-consistent field (SCF) converged to 10 -6 eV. The density functional theory calculations carried out with the plane wave cutoff energy of 400 eV on a 5×5×1 K-point mesh Monkhorst-pack scheme [58]. We studied silicene with a size of 3×3 supercell that includes 18 silicon atoms. As usual for avoiding interactions of the silicene sheet with its periodic images, a vacuum gap of 25 Å in the z-direction used.

Structural and electronic properties of doped silicene
At first, the optimization process is done in each system to reach the minimum energy for determining the most stable state. According to our calculation, the optimized Si-Si bond length, Si-Si-Si bond angle, lattice constant and buckling height for pristine silicene obtained 2.26 Å, 115.71°, 3.83 Å, and 0.47 Å, respectively. Our calculation for pristine silicene is in good agreement with previous findings based on DFT calculations [59]. The optimized structures of pristine and doped silicene are shown in figure 1.
Structural and electronic properties of doped silicene including binding energies (E B ), Si-X bond lengths, bond angle (Si-X-Si), lattice constant (a), local bulking (h z ), Fermi level energy (E f ), total magnetic moment per supercell (total (μ B )), magnetic moment contributed from 3d-transition metals (3d (μ B )) and magnetic moment contributed from sum of all Si atoms (Si (μ B )) are reported in table 1. Atomic radius reduces [60] from Ti to Zn but the bond length (Si-X) does not follow this downward trend. The largest bond length (Si-X) revealed in Ti (2.53 Å) and lowest amount of 2.23 Å revealed in the case of Fe, Ni-doped silicene. The bond length has a decreasing trend except for Co, Cu and Zn-doped silicene. For bond angle (Si-X-Si), the largest and lowest value of 92.64 Å and 118.82 Å are belonged to the Ti and Zn-doped silicene, respectively. On the base of our findings in table 1, local buckling increased in Ti, V, and Cr-doped silicene because of their angle nears to tetrahedral (sp 3 hybridization) bond angle. In contrary to Cu and Zn, other atoms projected out of the silicene plane. The largest value of lattice constant (a) is for Zn-doped silicene 4 Å and the lowest value is 3.47 Å for Fedoped silicene. According to the Fermi level energy (E f ) analysis, Cu-doped silicene (−3.58 eV) has a maximum amount in comparison with that other systems.
The density of states (DOS) and band structure plots for pristine and doped silicene with nine transition metals are shown in figure 2. The minimum of the conduction band (MCB) and the maximum of the valence band (MVB) touch at a single point known as the Dirac point. Although pristine silicene shows a semimetallic behavior, the doped silicene shows a metallic behavior with crossing bands at the Fermi level. According to the band structure plots, the Fermi level of doped silicene shifted up toward the conduction band. In DOS plots of V, Cr, Mn, Fe, Co, Ni and Cu-doped silicene, an asymmetry observed near the Fermi level, resulted from the difference value of spin up and down. The largest value of difference observed in Mn-doped silicene 5μ B . The major contribution of the magnetic moment comes from the difference between the majority and minority spin bands of coupled TM with Si atoms. Based on DOS results shown in the left-hand side of figure 2, observing an asymmetry in the spin up and spin down states near the Fermi level, gives rise to a net magnetic moment of values. An enhancement in the density of states implies that doping may lead to the formation of extended magnetic moments and enhance the tendency of the system towards ferro or anti ferromagnetism. The prediction of total magnetic moment for TM d orbitals by keeping together the ferromagnetic ordering between Si and TM atoms presented in table 1.
The TM atoms and three nearest-neighbor Si atoms are magnetically ordered in the cases of V, Cr, Mn, Fe, Co, Ni, and Cu. The results demonstrate that as the atomic number increases from Ti to Mn, the 3d orbitals become increasingly half-filled and total magnetic moment increased from zero to 5μ B . After that from Mn to Zn, spins are aligned antiparallel at the smallest volumes, owing to the Pauli's exclusion principle equal spins prevent from occupying in the same spot. This reduces the magnetic moment of TM doped silicene from 5 μ B to zero. In the other hands, when the atoms are incorporated into a silicene, some of the electrons are forced into common spatial wave functions which forces their spins antiparallel and reduces the overall magnetic moment. This interaction changes its sign as soon as the wave functions cease to overlap strongly between TM and silicene surface in the case of V, and Cr doped. This produces antiferromagnetic coupling between V, Cr atoms and silicene surface. In the Zn atom, 3d orbitals are completely filled and no induced magnetism is expected, hence we also realize the nonmagnetic state in the case of Zn doped silicene, which agrees well with Zn-adsorbed graphene and germanene results [61]. As can see in table 1, total magnetic moment for Zn is zero and there is no charge redistribution between Zn atom and silicene surface. In the DOS structure of Zn-doped silicene, there is no difference between up and down electron spin, therefore Zn doped silicene is nonmagnetic. Additionally, we have calculated the binding energies of TM atoms onto silicene surface as defined in previous literature [61]: where E TM+silicene and E silicene are the energies of silicene containing the vacancy with and without an additional TM atom, respectively. E TM is the total energy of the isolated atom in its ground state. The calculated values for    The PDOS analysis of all structures is shown in figure 3. The highest peak for 3d orbitals (V, Cr, Mn, Fe, Co, Ni and Cu-doped silicene) doesn't locate around the Fermi level. According to our results, all structures showed the highest peak of d orbital in valence part in contrast to the d orbital of Ti-doped silicene which is located in the conduction part. The density of states and band structure plots for pristine silicene and Al, B, N, and P-doped silicene had been investigated by Mousavi-Khoshdel et al [37]. They reported an asymmetric for N-doped silicene with 0.75 μ B as a net magnetic moment and asymmetric for Al, B and P atoms. Compared to N-doped silicene, V, Cr, Mn, Fe, Co, Ni, and Cu-doped silicene have more values in the present work.

Optical properties of doped silicene
In this work, the optical properties of pristine and doped silicene with nine transition metals Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn have calculated. The optical properties give us information about the dielectric function, refractive index, reflectivity, electron loss function, absorption, optical conductivity, and reflection. There is no doubt the main part of optical properties is dielectric function; it is calculated from ε (ω)=ε 1 (ω)+iε 2 (ω) [62]. The real part of the dielectric function ε 1 (ω) calculated from the imaginary part by using Kramers-Krong [63] transformation with this equation [64]: The imaginary part of the dielectric function ε 2 (ω) is calculated from [65]: where ω is the photon frequency, i and j are the first and final states, M is dipole matrix, f i is Fermi distribution function, E i and E f are electron energy for first and final states, respectively. Other optical constants like refractive index, reflectivity, electron loss function, absorption, optical conductivity and reflection calculated from the imaginary part and real part of the dielectric function. The real part of refractive index with dielectric function given by [66] The imaginary part of refractive index with dielectric function is given by The electron loss function can be calculated using the relations [67] w e w e e = + w w The absorption coefficient which is given by [68] w w e w e e = -+ + w w The reflectivity was estimated as [69] w e w e w = -+

Dielectric function
Dielectric Function is a complex function that describes the optical properties. It has two parts; the real part means radiation photon scattered by materials and the imaginary part is related to the absorbed energy by the materials [45]. Real and imaginary curves of the dielectric function for pristine silicene and doped silicene with nine transition metals Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn are shown in figure 4. The real part of dielectric function starts almost from zero energy when light is in-plane (⊥) polarization. Results of the real part of dielectric function in both cases of in-plane (⊥) and out of the plane (||) light polarization reported in table 2.
It needs to understand that an oscillatory behavior of all the materials exists only up to 0.85 eV for out of the plane (||) light polarization. The roots of the ε 1 (ω) have a physical idea and therefore, it is an essential condition for the massive plasmon in materials but enough condition is considering the loss energy of them. Also, in the negative ε 1 (ω) area, the waves are not released and the processes of absorption and loss occur [65]. As shown in figure 4(b), ε 1 (ω) is negative for pristine silicene from 0.46 to 9.90 eV for out of the plane (||) light polarization and the plasma frequency for pristine silicene is 9.90 eV. The calculated negative part of ε 1 (ω) for pristine silicene is about 4.18 eV to 5 eV for out of the plane (E||C) light polarization which is in agreement with 4.86 eV the previous work [45]. The results of imaginary parts of dielectric function in both cases of in-plane (⊥) and out of the plane (||) light polarization is presented in figures 4(c)-(d) and table 3. The imaginary part of dielectric function starts almost at zero energy when light is in-plane (⊥) polarization and is zero after 13 eV.

Refractive index
The refractive index of a material is a dimensionless number that describes how fast light propagates through the material [67]. It consists of real and imaginary parts; the real part is the phase velocity and the imaginary part is the extinction coefficient. The extinction coefficient for a material refers to measures the light electromagnetic of material in the absorption event [66]. Real and imaginary parts of the refractive index curves of pristine and doped silicene are shown in figure 5. Because of decreasing the velocity of light when it polarizes along the direction of electrons in the lattice, the refractive index values are larger in (||) than (⊥) light polarization. According to our results, the refractive index is anisotropic in both directions for all structures (as shown in figure 5) and the real part has isotropic behavior for pristine silicene above 13 eV and other doped silicene structures above 9 eV in both polarization directions. One can see, all structures were red-shifted. The refractive index of pristine silicene is in agreement with the previous reports in both polarization direction directions [45]. Real and imaginary parts of the refractive index were greater in both cases of in-plane (⊥) and out of the plane (||) light polarization for pristine silicene, it was greater than nine transition metals in both parts. The real part of the refractive index for out of the plane (||) light polarization had been reported for silicene 3.25 that our result was greater than it [45].

Reflectivity
Reflectivity defined as the amplitude or intensity of the reflected wave relative to the wave of the event. It is an important idea in the fields of optics, solar thermal energy, physics, and electrical engineering. Reflectivity curves of pristine and doped silicene in both cases of in-plane (⊥) and out of the plane (||) light polarization is shown in figure 6.
In-plane (⊥) light polarization reflection occurs in the UV region (0-10 eV) whiles in out of the plane (||) polarization of light, reflectivity is in the IR and visible regions (low frequency region, up 10 eV). Reflectivity curves start almost at zero energy when light is in both polarization directions. The maximum reflectivity peaks  are shown in table 4 for pristine silicene and other doped systems in both cases of in-plane (⊥) and out of the plane (||) light polarization. These results indicate that Cu-doped silicene has more value in comparison with other doped systems. According to our results, peaks formed to be red-shifted in both polarization directions. For pristine silicene, the value of reflectivity was higher than the doped silicene with nine transition metals for out of plane (||) light  polarization and Cr-doped silicene has the highest peak for in-plane (⊥) light polarization. The peak position of pristine silicene reported by Rita john et al [45] exhibited between 0-12 eV using DFT calculations. The Reflectivity of Al and P-doped silicene was limited in low energy (less than 4 eV) and high energy (more than 8 eV) in both cases of in-plane (⊥) and out of the plane (||) light polarization, respectively [49]. 3d-transition metals reflectivity doped SnO 2 nanosheets increased in the visible light region (0-3 eV [45]). According to our findings, the peak position of pristine silicene and doped silicene are between 0-15 eV in both light polarization directions.

Electron loss function
The electron energy loss function (L (ω)) is a probability of passing electrons through the material loss of their energy. The observed peaks in the loss function diagram are descriptive of the parameters related to the plasma response. The most prominent peaks in loss function known as plasmon peak that describes collective excitation of the electron charge density. The electron energy loss function plots of pristine and doped silicene in both cases of in-plane (⊥) and out of the plane (||) light polarization is shown in figure 7. According to our calculation, obvious peaks in both polarization directions are found to be red-shifted. The most significant peaks in the energy loss function are seen at 0-10 eV for in-plane polarization of light (⊥) and 5-7 eV and 9-11 eV for out of the plane (||) light polarization, respectively.   polarization reported by Rita John et al [45] for graphene, silicene, germanene, and stanine, respectively. The electron energy loss spectra of pristine silicene and Al and P-doped silicene examined by Das et al with the expand of doping concentration, the peaks were red-shifted [49].

Absorption
As we know, another major optical property is absorption and its calculations closely depend on the light of polarization direction and the imaginary part of the dielectric function. In this paper, we studied the absorption of the pristine and doped silicene with nine transition metals in both cases of in-plane (⊥) and out of the plane (||) light polarization (in figure 8). The energy interval was presented from 0 to 15 eV. When light polarized, the peaks appear from 0-13 eV in both directions. The value of first and the second maximum absorption peaks that occurred for in-plane (⊥) light polarization are shown in table 6. The highest intensity of the first maximum absorption peak revealed in Cu-doped silicene (7.95 eV) and the second one seen in the pristine silicene curve (5.60 eV).
As light is polarized out of the plane (||), the maximum absorption peaks become visible: 1.18, 4.05, 4.12, 4.13, 4.15, 4.16, 4.17 and 4.19 eV in pristine silicene, Ti, Cr and Ni, Fe, Mn and Co, V, Zn and Cu-doped silicene, respectively. Another peak appears at 4.41, 2.12, 2.07, 1.98 and 1.94 eV in pristine silicene, Cr and Fe, V, Mn and Cu, and Zn-doped silicene, respectively. All nine transition metals doped silicene sheets have red-shifted to lower energies in both cases of in-plane (⊥) and out of the plane (||) light polarization. The intensity of peaks was less than pristine silicene for out of the plane (||) light polarization. The highest peaks 14.5, 8.34, 8.31 and 6.7 eV in graphene, silicene, germanene and stanine that peaks were due to the existence of saddle points along M to K    [70]. Yong Feng et al [51] studied ten transition metals doped SnO 2 nano sheets and all TM doped SnO 2 nano sheets have shifted to the low energies (red-shift). The absorption peaks of Cr, Fe, and Ni were below 1.5 eV but Mn located around 2.20 eV. Zakerian et al [47] determined absorption spectrum of pristine silicene and mono-vacancy defected and reported main peaks around 1.2 and 4 eV for pristine silicene and 0.9 and 3.7 eV for mono-vacancy defected silicene within a manybody green function and Bethe-Salpeter equation formal. Absorption coefficients for pristine silicene and Al and P-doped silicene were done by Das et al [49] with DFT calculation (GGA/PBE). Their results showed an absorption coefficient of 4.07 eV for pristine silicene for E ║ and 9.11 eV for E ⊥ which are in the ultraviolet range. In the case of doped silicene, the value of absorption coefficient was higher than the pristine silicene through the ultraviolet range. Optical absorption spectra had been reported for silicene by Wei et al and the π→π * resonant excitation in silicene appeared at 1.23 eV [71].

Conductivity
Optical conductivity is conductivity in the presence of an alternating electric field. In order to study the optical conductivity for pristine silicene and doped silicene, we performed optical conductivity calculations in both cases of in-plane (⊥) and out of the plane (||) light polarization that are shown in figure 9. According to the computational results, we can find a real part of optical conductivity starts at 1.5 eV for in-plane (⊥) but optical  conductivity starts at 0 eV for out of the plane (||). Compared to the real part, more attractively the energy at which the imaginary part of optical conductivity is zero in both polarization directions. As light polarized (⊥), the optical conductivity plot is in agreement with the loss function plot in the same direction. The real and imaginary parts of the optical conductivity of pristine silicene reported by Rita John et al were in good agreement with the present work in (⊥) direction [45].

Conclusion
The electronic and optical properties for pristine silicene and Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn-doped silicene were studied using DFT calculations. The imaginary part of dielectric function decreases from 441.42 until 0.76 for out of the plane (||) light polarization and the oscillatory behavior of all the materials exists only up to 0.85 eV along the (||) polarization direction. The maximum intensity absorption peak occurs for Cu-doped silicene when light is in-plane (⊥) and the maximum absorption highest peaks become visible in pristine silicene in polarizing (||) direction. The optical conductivity plot when light is polarized (⊥) is in good agreement with the loss function plot in the same direction and according to our information, obvious peaks are in both polarization directions that they are found to be red-shifted. The most significant peaks in the energy loss function are seen at 0-10 eV in (⊥) polarization direction and 5-7 and 9-11 eV, respectively in (||) polarization direction. Reflectivity curves start almost at zero energy when light is in both polarization directions and the highest peak of reflectivity occurs in Cr-doped silicene and pristine silicene in both cases of in-plane (⊥) and out of the plane (||) polarization of light, respectively. Real and imaginary parts of the refractive index were greater in (||) than (⊥) polarization direction for pristine silicene and corresponding to our findings, the refractive index is anisotropic in both directions for all structures. The present paper will help for further understanding that nine transition metals doped silicene can be change electronic and optical properties of pristine silicene and more importantly, they may be useful for interesting application such as designing optoelectronic industries.