- Email: [email protected]
Pressure induced electronic and optical properties of rutile SnO2 by first principle calculations
Superlattices and Microstructures 90 (2016) 236e241
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Pressure induced electronic and optical properties of rutile SnO2 by first principle calculations Khush Bakht a, Tariq Mahmood b, *, Maqsood Ahmed a, Kamran Abid c a
Centre for High Energy Physics, University of the Punjab, Lahore, 54590, Pakistan Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan c Punjab University College of Information Technology, University of the Punjab, Lahore, Pakistan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2015 Received in revised form 14 December 2015 Accepted 18 December 2015 Available online 23 December 2015
Tin dioxide (SnO2) is the most important semiconductor material due to its large number of technological applications. In this work we carried out the electronic and optical properties under pressure of rutile SnO2. The ultra-soft pseudopotential method is used by employing the local density approximation functional proposed by Ceperley-Alder and Perdew-Zunger to calculate the exchange correlation potential within the framework of density functional theory. Firstly we optimized the structure to obtain the ground state energy of the system with the increase of cutoff energy (Fig. 1 (b)). The investigated band structure and density of states show that energy bandgap is increasing with the increase of pressure due to the movement of valence bands from higher to low energy levels and the conduction bands from lower to higher energy levels respectively (Fig. 1 (a)). The effect of pressure on lattice constants demonstrates the increase in lattice constants. Optical properties, comprising refractive index, dielectric function, absorption and energy loss spectrum are investigated. The obtained results are in good agreement with the previous reported theoretical and experimental results. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Local density approximation Band structure Pressure Dielectric constant Refractive index
1. Introduction In current era, technologically most important metal oxides are SnO2 and TiO2. Mostly electrical conductors are dense and most of optical transparent materials are insulator but in the case of SnO2 both the optical transparency and electrical conductivity are present together [1]. In Li-ion batteries, dye-sensitized solar cells and choosy gas sensors, SnO2 is one of the metal oxides those are used to enhance the performance of these applications [2e4]. The performances of bulk SnO2 for example, lattice dynamics, electronic properties, phase transitions and optical properties continued to pay attention for both experimental and theoretical studies. For anti-microbial system, self-cleaning and organic oxidation, the material should have photo-catalytic and electro-catalytic characteristics [5,6]. Experimentally by x-ray diffraction Shieh et al., Haines and Leger and Huang et al. calculated structural parameters of tin dioxide [7e9]. The two photon spectroscopy technique was use to measure the electronic bandgap energy of SnO2 by Frohlich et al., in 1978 [10] and Schweitzer et al., in 1999 [11]. 1n 1972, Jacquemin et al. first time investigated the electronic and optical properties by employing the Hohn-Korringa-Rostoker
* Corresponding author. E-mail address: [email protected] (T. Mahmood). http://dx.doi.org/10.1016/j.spmi.2015.12.021 0749-6036/© 2015 Elsevier Ltd. All rights reserved.
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
237
method [12]. Although, many research groups have studied similar properties one after another, such as of SnO2 such as Chun-Mei Liu et al. [13], Mayer et al. [14], Errico [15], Rehman et al. [16], Li et al. [17] and Liu et al. [18]. SnO2 have seven polymorphs among which rutile-type is the most stable and occur in large number naturally at ambient temperature and pressure. It has tetragonal structure and it belongs to P42/mnm space group [1]. Inspite of that large numbers of theoretical and experimental studies have been done; tin dioxide still needed more studies to explain its electronic and optical properties. So, in this study we have considered the theoretical approach based on Density Functional Theory (DFT) to investigate the pressure induced electronic and optical properties of rutile-SnO2, including band structure, density of states and dielectric constant. In this paper we have organized our work as follows: Section 2 explains the computational methods. Results and discussion are presented in section 3 and section 4 describes the conclusion. 2. Computational method In computational materials science DFT is the most popular tool to investigate theoretically the electronic, mechanical, magnetic and optical properties of different materials [19]. Although DFT based methods are very popular in theoretical studies but it also has inherent limitations and defects. Theorists already have been improved and trying to improve the quality of theoretical models by considering missing terms [20e23]. We have employed Cambridge Serial Total Energy Package (CASTEP) code [24] to investigate the pressure induced electronic and optical properties of SnO2. The effects of electroneelectron exchange correlation are depicted by CA-PZ functional in Local Density Approximation (LDA) [25,26] within DFT. The well efficient basis sets the ultrasoft pseudo-potentials are accomplished for electroneion interactions. In the irreducible Brillion zone the Monkhorst-Pack grid 5 5 8 K points were considered. The cutoff energy 500 eV is used after finding the minimum ground state energy of the system (as shown in Fig. 1 (b)) to expand the electronic wave function which corresponds to a condition of convergence of energy 0.1 105 eV/atom. 3. Results and discussion Firstly, we optimized the geometry by choosing cutoff energies with the difference of 20eV to find out the minimum ground state energy of the 2 2 2 supper cell of rutile SnO2. From Fig. 1 (b) one can see that the total energy and energy bandgap of the system remains unchanged or change is in very small fraction around 500 eV at pressure 0 GPa. The third Birch-Murnaghan equation of state is used to calculate the energy-volume data [27].
Fig. 1. (a) bandgap vs pressure and (b) bandgap and total energy w. r. t. cutoff energy.
Table 1 The calculated equilibrium Lattice parameters (a and c) (Å), Energy gap Eg (eV), Volume V, Bulk modulus B0 (GPa) of rutile-type SnO2.
a
Methods
A (Å)
C (Å)
B0 (GPa)
References
LDA (CA-PZ) LDA GGA-PBE GGA-PBE Others Experiments
4.6807 4.695 4.928 4.830 4.776a, 4.826b 4.737c, 4.746d
3.1534 3.160 3.288 3.236 3.212a, 3.237b 3.186c, 3.189d
236.6 242.4 204.5 173 179a 205c
Present [13] [13] [28] a [29], b [30] c [7], d [8]
Ref. [29];
b
Ref. [30]; c Ref. [7];
d
Ref. [8].
238
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
io i3 0 h i2 h 2 2 2 9B0 V0 n h ðV0 =VÞ 3 1 B0 þ ðV0 =VÞ 3 1 6 4ðV0 =VÞ 3 16 =
=
=
EðVÞ ¼ E0 þ
0
(1)
Where E(V), E0 , V0 , B0 and B0 are the total energy of the system, ground state energy, equilibrium volume, bulk modulus at the pressure 0 GPa and first derivative of B0 with respect to pressure.
Fig. 2. (a) Lattice parameters and volume versus pressure (b) a/a0, c/c0, V/V0, and c/a ratios vs pressure.
Fig. 3. Pressure induced band structures of the rutile-SnO2.
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
239
Table 1 describes the investigated equilibrium lattice parameters and bulk modulus of ReSnO2 at 0 GPa pressure with the comparison of previous theoretical and experimental results. The calculated values of lattice parameters a, c and the bulk modulus B0 are observed as 4.6807 Å, 3.1534 Å and 236.6 GPa respectively. Our calculated values of equilibrium lattice parameters and bulk modulus at zero GPa pressure are in good agreement with C. M. Liu et al. from LDA method [13] and seems to be comparable with the experimental values [7,8]. From Table 1, one can observe that the previously calculated results from GGA are higher than LDA based calculations. For pressure induced studies we continued the calculation by using LDA-CA-PZ method. Fig. 2 (a) shows that lattice parameters and volume are inversely proportional to pressure; the decrease in lattice parameters with the increase in pressure is negligible. The variation in the values of lattice parameters and volume is occurred as a ¼ 4.6807 Å to 4.2588 Å and c ¼ 3.1534 Å to 3.0231 Å and 69.0864 Å3 to 54.8302 Å3 respectively. Fig. 2 (b), illustrates the effect of pressure on the ratios a/a0, c/c0, c/a (axial ratio) and V/V0 which shows that the ratios a/a0, c/c0 and V/V0 are inversely proportional and c/a is directly proportional to pressure. Where, c/a is called the axial ratio and V/ V0 is the normalized primitive cell volume of rutile-type SnO2. We notice that as the pressure increases, the ratio a/a0 drops quite rapidly than the ratio c/c0 which shows that there is greater compression along a-axis. Hence we can say that the lattice constant “a” has greater effectiveness towards pressure as compared to the lattice constant “c”. The Band gap energies Eg are calculated at different pressures. The dotted line at 0 eV indicates the Fermi energy level. The occupied states lying below the Fermi energy correspond to valence bands, whereas the unoccupied states just above the Fermi energy are the conduction bands. The energy bandgap occurs between the maximum of the valence bands and the minimum of the conduction bands. Fig. 3 indicates that rutile-type SnO2 has direct band gap. The band structures for rutileSnO2 are comparable to each other with the variation in pressure but energy gap seems to increase with the increase in pressure from 0 to 100 GPa. In Fig. 1 (a), one can see a linear increment in the bandgap with the increase in pressure which occurs when the conduction bands transfer to higher energy levels and the lower valence bands move towards the lower energy levels. The minimum bandgap is at symmetry point G-G than others in the entire pressure range which infer the nature of bandgap that is direct. The calculated energy bandgap in this work at 0 GPa is 1.31 eV which is very small as compare to experimental values 3.6 eV [31] and 2.9 eV [32]. However, our calculated bandgap energy is in good agreement with the theoretical results, 1.38 eV (LDA) by Li et al. [17] but better than C. M. Liu et al. (1.211 eV by LDA) [13], Liu et al. (0.134 eV) [18] and F. El et al. (0.832 eV by GGA) [33]. As usual underestimation problem with DFT is faced here to calculate the energy bandgap.
Fig. 4. Total density of states and partial density of states rutile-SnO2 at different pressures.
240
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
Fig. 5. (a) Pressure induced Dielectric Constant, (b) Refractive index, (c) Absorption and (d) Energy loss function of rutile-SnO2.
Fig. 4 is the graphical representations of the total density of states (TDOS) and partial density of states (PDOS) of s-orbitals (O 2s and Sn 5s) and p-orbitals (O 2p and Sn 5p) of rutile SnO2 at different pressures. Fig. 4(b) and (c) infer that the lowest energy bands in the energy range from 21 eV to 15 eV are dominated by O 2s electrons with minor contribution of Sn 5p and Sn 5s electrons. The valence bands near to fermi level consist majorly of O 2p electrons with small contribution of 5s and 5p electrons. While the conduction bands constructed by the major contribution of Sn 5s and Sn 5p orbitals and with minor contribution of O 2p electrons. Further we become aware of hybridizations in between O 2s, O2p, Sn 5s and Sn 5p orbitals which the evidence of covalent interaction between them. Fig. 5 elucidates the pressure induced optical properties including dielectric function, refractive index, absorption spectrum and energy loss function. From Fig. 5 (a) and 5 (b) one can observe that the values of dielectric constant (from 4.02 to 3.15) and refractive index (from 2.01 to 1.77) are decreasing with the increase in pressure from 0 to 100 GPa. The decreases of dielectric constant infer us that the electric flux density is decreasing of rutile SnO2 and decreases of refractive index shows that the hardness to travel light from rutile SnO2 is decreasing with the increase of pressure. The real part of dielectric function, it resembles the refractive index graph but the real part values are equal to n2 (n is refractive index). The imaginary part of dielectric function somewhat resembles the absorption spectrum, the first peak occurs due to excitation from valence band to conduction band and the other two peaks occur due to the energy state transitions. Furthermore, the Fig. 5(c) exposes the absorption spectrum which agrees with the imaginary part of the dielectric function. One can notice the absorption peaks are positioned at 4.6, 7.73, 10.48, 15.1 and 29.3 eV under an ambient condition. Additionally, Fig. 5 (d) infers that with the increase of pressure from 0 to 30 GPa, the Energy loss peaks are slightly increasing while as we increased the pressure further, energy loss peaks start to decrease. The sharp peaks represent the interaction between the energy and plasma resonance. The energy loss function (L(⍵)) attains its maximum value when the real dielectric function reaches zero as shown in Fig. 5 (d). 4. Conclusion In this work we have selected LDA-CAPZ method to explore the structural, electronic and optical properties of rutile SnO2 at zero plus high pressure within the limit of density functional theory. Our calculated equilibrium lattice parameters and bulk modulus are well consistent with experimental (with the underestimation of about 1%) and other LDA based theoretical results. The pressure induced structural parameters (lattice parameters, volume and their ratios (a/a0, c/c0, c/a (axial ratio) and V/V0)), band structures, total and partial densities of states are also investigated. We observe that the band gap rutile SnO2 is
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
241
direct at G-G under high pressure as well as zero pressure. The calculated energy bandgap at zero pressure is 1.31 eV. Moreover, we comprehensively concluded the hybridization of O 2s, O 2p, Sn 5s and Sn 5p electrons Additionally we have investigated the optical properties together with dielectric function, refractive index, absorption spectrum and energy loss function at equilibrium as well as elevated pressure of rutile SnO2 like Dielectric constant, refractive index for the first time. Acknowledgement One of the authors (Dr Tariq Mahmood) would like to thank for the supervision and fruitful guidance to complete this work. Also, we would like to thank the Government of Pakistan for providing Laptops to graduate students, which is used to complete this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]
Çetin Kılıç, Alex Zunger, Phys. Rev. Lett. 88 (2002) 095501. D. Zhang, M. Wang, A.G. Brolo, J. Shen, X. Li, S. Huang, J. Phys. D Appl. Phys. 46 (2013) 024005. X. Song, J. Pan, L. Xiao, S. Mathur, Nanotechnology 24 (2013) 205401. V.V. Krivetskiy, M.N. Rumyantseva, A.M. Gaskov, Russ. Chem. Rev. 82 (10) (2013) 917. Y. Feng, Y. Cui, J. Liu, B.E. Logan, J. Hazard. Mater. 178 (2010) 29e34. S.H. Hwang, C. Kim, J. Jang, Catal. Commun. 12 (2011) 1037e1041. S.R. Shieh, A. Kubo, T.S. Duffy, V.B. Prakapenka, G. Shen, Phys. Rev. B 73 (2006) 014105. J. Haines, J.M. Leger, Phys. Rev. B 55 (17) (1997) 11144. E. Huang, A.S. Li, S. Yu, T.A.O. 3 (2) (1992) 111e127. D. Frohlich, R. Kenklies, R. Helbig, Phys. Rev. Lett. 42 (25) (1978) 1750. C. Schweitzer, K. Reimann, M. Steube, Solid State Commun. 110 (1999) 697e700. J.L. Jacquemin, C. Alibert, G. Bordure, Solid State Commun. 12 (1972) 1295. Chun-Mei Liu, Xiang-Rong Chen, Guang-Fu Ji, Comp. Mater. Sci. 50 (2011) 1571e1577. M. Meyer, G. Onida, A. Ponchel, L. Reining, Comput. Mater. Sci. 10 (1998) 319e324. L.A. Errico, Phys. B 389 (2007) 140. G. Rahman, V.M. Garcia-Suarez, S.C. Hong, Phys. Rev. B 78 (2008) 184404. Y. Li, W. Fan, H. Sun, X. Cheng, P. Li, X. Zhao, J. Hao, M. Jiang, J. Phys. Chem. A 114 (2010) 1052. Q.J. Liu, Z.T. Liu, L.P. Feng, Comput. Mater. Sci. 47 (2010) 1016. C.J. Cramer, D.G. Truhlar, Phys. Chem. Chem. Phys. 11 (2009) 10757. A.J. Cohen, P. Mori-Sanchez, W. Yang, Phys. Rev. B 77 (2008) 115123. A.J. Cohen, P. Mori-Sanchez, W. Yang, Science 321 (2008) 792. P. Mori-Sanchez, A.J. Cohen, W. Yang, Phys. Rev. Lett. 102 (2009) 066403. R.M. Nieminen, Model. Simul. Mater. Sci. Eng. 17 (2009) 084001. M.D. Segall, P.L.D. Lindan, M.J. Probert, C. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens Matter 14 (2002) 2717. D.M. Ceperley, B.J. Alder, Ground State of the Electron Gas by a Stochastic Method, Phys. Rev. Lett. 45 (1980) 566e569. J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23 (1981) 5048e5079. F. Birch, Phys. Rev. 74 (11) (1947) 809. I. Erdem, H.H. Kart, Mater. Sci. Semicond. Process. 28 (2014) 59e65. F.E.H. Hassan, S. Moussawi, W. Noun, C. Salameh, A.V. Postnikov, Comput. Mater. Sci. 72 (2013) 86e92. Y. Duan, Phys. Rev. B 77 (2008) 045332. V.T. Agekyan, Phys. Status Solidi A 43 (1977) 11. A. Ferreira da Silva, I. Pepe, C. Person, J. Souza de Almeida, C. Moyses Araujo, B. Johansson, C.Y. An, J.H. Guo, Phys. Scr. T 109 (2004) 180. El Haj Hassan, S. Moussawi, W. Noun, C. Salameh, A.V. Postnikov, Comput. Mater. Sci. 72 (2013) 86e92.
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Pressure induced electronic and optical properties of rutile SnO2 by first principle calculations Khush Bakht a, Tariq Mahmood b, *, Maqsood Ahmed a, Kamran Abid c a
Centre for High Energy Physics, University of the Punjab, Lahore, 54590, Pakistan Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan c Punjab University College of Information Technology, University of the Punjab, Lahore, Pakistan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2015 Received in revised form 14 December 2015 Accepted 18 December 2015 Available online 23 December 2015
Tin dioxide (SnO2) is the most important semiconductor material due to its large number of technological applications. In this work we carried out the electronic and optical properties under pressure of rutile SnO2. The ultra-soft pseudopotential method is used by employing the local density approximation functional proposed by Ceperley-Alder and Perdew-Zunger to calculate the exchange correlation potential within the framework of density functional theory. Firstly we optimized the structure to obtain the ground state energy of the system with the increase of cutoff energy (Fig. 1 (b)). The investigated band structure and density of states show that energy bandgap is increasing with the increase of pressure due to the movement of valence bands from higher to low energy levels and the conduction bands from lower to higher energy levels respectively (Fig. 1 (a)). The effect of pressure on lattice constants demonstrates the increase in lattice constants. Optical properties, comprising refractive index, dielectric function, absorption and energy loss spectrum are investigated. The obtained results are in good agreement with the previous reported theoretical and experimental results. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Local density approximation Band structure Pressure Dielectric constant Refractive index
1. Introduction In current era, technologically most important metal oxides are SnO2 and TiO2. Mostly electrical conductors are dense and most of optical transparent materials are insulator but in the case of SnO2 both the optical transparency and electrical conductivity are present together [1]. In Li-ion batteries, dye-sensitized solar cells and choosy gas sensors, SnO2 is one of the metal oxides those are used to enhance the performance of these applications [2e4]. The performances of bulk SnO2 for example, lattice dynamics, electronic properties, phase transitions and optical properties continued to pay attention for both experimental and theoretical studies. For anti-microbial system, self-cleaning and organic oxidation, the material should have photo-catalytic and electro-catalytic characteristics [5,6]. Experimentally by x-ray diffraction Shieh et al., Haines and Leger and Huang et al. calculated structural parameters of tin dioxide [7e9]. The two photon spectroscopy technique was use to measure the electronic bandgap energy of SnO2 by Frohlich et al., in 1978 [10] and Schweitzer et al., in 1999 [11]. 1n 1972, Jacquemin et al. first time investigated the electronic and optical properties by employing the Hohn-Korringa-Rostoker
* Corresponding author. E-mail address: [email protected] (T. Mahmood). http://dx.doi.org/10.1016/j.spmi.2015.12.021 0749-6036/© 2015 Elsevier Ltd. All rights reserved.
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
237
method [12]. Although, many research groups have studied similar properties one after another, such as of SnO2 such as Chun-Mei Liu et al. [13], Mayer et al. [14], Errico [15], Rehman et al. [16], Li et al. [17] and Liu et al. [18]. SnO2 have seven polymorphs among which rutile-type is the most stable and occur in large number naturally at ambient temperature and pressure. It has tetragonal structure and it belongs to P42/mnm space group [1]. Inspite of that large numbers of theoretical and experimental studies have been done; tin dioxide still needed more studies to explain its electronic and optical properties. So, in this study we have considered the theoretical approach based on Density Functional Theory (DFT) to investigate the pressure induced electronic and optical properties of rutile-SnO2, including band structure, density of states and dielectric constant. In this paper we have organized our work as follows: Section 2 explains the computational methods. Results and discussion are presented in section 3 and section 4 describes the conclusion. 2. Computational method In computational materials science DFT is the most popular tool to investigate theoretically the electronic, mechanical, magnetic and optical properties of different materials [19]. Although DFT based methods are very popular in theoretical studies but it also has inherent limitations and defects. Theorists already have been improved and trying to improve the quality of theoretical models by considering missing terms [20e23]. We have employed Cambridge Serial Total Energy Package (CASTEP) code [24] to investigate the pressure induced electronic and optical properties of SnO2. The effects of electroneelectron exchange correlation are depicted by CA-PZ functional in Local Density Approximation (LDA) [25,26] within DFT. The well efficient basis sets the ultrasoft pseudo-potentials are accomplished for electroneion interactions. In the irreducible Brillion zone the Monkhorst-Pack grid 5 5 8 K points were considered. The cutoff energy 500 eV is used after finding the minimum ground state energy of the system (as shown in Fig. 1 (b)) to expand the electronic wave function which corresponds to a condition of convergence of energy 0.1 105 eV/atom. 3. Results and discussion Firstly, we optimized the geometry by choosing cutoff energies with the difference of 20eV to find out the minimum ground state energy of the 2 2 2 supper cell of rutile SnO2. From Fig. 1 (b) one can see that the total energy and energy bandgap of the system remains unchanged or change is in very small fraction around 500 eV at pressure 0 GPa. The third Birch-Murnaghan equation of state is used to calculate the energy-volume data [27].
Fig. 1. (a) bandgap vs pressure and (b) bandgap and total energy w. r. t. cutoff energy.
Table 1 The calculated equilibrium Lattice parameters (a and c) (Å), Energy gap Eg (eV), Volume V, Bulk modulus B0 (GPa) of rutile-type SnO2.
a
Methods
A (Å)
C (Å)
B0 (GPa)
References
LDA (CA-PZ) LDA GGA-PBE GGA-PBE Others Experiments
4.6807 4.695 4.928 4.830 4.776a, 4.826b 4.737c, 4.746d
3.1534 3.160 3.288 3.236 3.212a, 3.237b 3.186c, 3.189d
236.6 242.4 204.5 173 179a 205c
Present [13] [13] [28] a [29], b [30] c [7], d [8]
Ref. [29];
b
Ref. [30]; c Ref. [7];
d
Ref. [8].
238
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
io i3 0 h i2 h 2 2 2 9B0 V0 n h ðV0 =VÞ 3 1 B0 þ ðV0 =VÞ 3 1 6 4ðV0 =VÞ 3 16 =
=
=
EðVÞ ¼ E0 þ
0
(1)
Where E(V), E0 , V0 , B0 and B0 are the total energy of the system, ground state energy, equilibrium volume, bulk modulus at the pressure 0 GPa and first derivative of B0 with respect to pressure.
Fig. 2. (a) Lattice parameters and volume versus pressure (b) a/a0, c/c0, V/V0, and c/a ratios vs pressure.
Fig. 3. Pressure induced band structures of the rutile-SnO2.
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
239
Table 1 describes the investigated equilibrium lattice parameters and bulk modulus of ReSnO2 at 0 GPa pressure with the comparison of previous theoretical and experimental results. The calculated values of lattice parameters a, c and the bulk modulus B0 are observed as 4.6807 Å, 3.1534 Å and 236.6 GPa respectively. Our calculated values of equilibrium lattice parameters and bulk modulus at zero GPa pressure are in good agreement with C. M. Liu et al. from LDA method [13] and seems to be comparable with the experimental values [7,8]. From Table 1, one can observe that the previously calculated results from GGA are higher than LDA based calculations. For pressure induced studies we continued the calculation by using LDA-CA-PZ method. Fig. 2 (a) shows that lattice parameters and volume are inversely proportional to pressure; the decrease in lattice parameters with the increase in pressure is negligible. The variation in the values of lattice parameters and volume is occurred as a ¼ 4.6807 Å to 4.2588 Å and c ¼ 3.1534 Å to 3.0231 Å and 69.0864 Å3 to 54.8302 Å3 respectively. Fig. 2 (b), illustrates the effect of pressure on the ratios a/a0, c/c0, c/a (axial ratio) and V/V0 which shows that the ratios a/a0, c/c0 and V/V0 are inversely proportional and c/a is directly proportional to pressure. Where, c/a is called the axial ratio and V/ V0 is the normalized primitive cell volume of rutile-type SnO2. We notice that as the pressure increases, the ratio a/a0 drops quite rapidly than the ratio c/c0 which shows that there is greater compression along a-axis. Hence we can say that the lattice constant “a” has greater effectiveness towards pressure as compared to the lattice constant “c”. The Band gap energies Eg are calculated at different pressures. The dotted line at 0 eV indicates the Fermi energy level. The occupied states lying below the Fermi energy correspond to valence bands, whereas the unoccupied states just above the Fermi energy are the conduction bands. The energy bandgap occurs between the maximum of the valence bands and the minimum of the conduction bands. Fig. 3 indicates that rutile-type SnO2 has direct band gap. The band structures for rutileSnO2 are comparable to each other with the variation in pressure but energy gap seems to increase with the increase in pressure from 0 to 100 GPa. In Fig. 1 (a), one can see a linear increment in the bandgap with the increase in pressure which occurs when the conduction bands transfer to higher energy levels and the lower valence bands move towards the lower energy levels. The minimum bandgap is at symmetry point G-G than others in the entire pressure range which infer the nature of bandgap that is direct. The calculated energy bandgap in this work at 0 GPa is 1.31 eV which is very small as compare to experimental values 3.6 eV [31] and 2.9 eV [32]. However, our calculated bandgap energy is in good agreement with the theoretical results, 1.38 eV (LDA) by Li et al. [17] but better than C. M. Liu et al. (1.211 eV by LDA) [13], Liu et al. (0.134 eV) [18] and F. El et al. (0.832 eV by GGA) [33]. As usual underestimation problem with DFT is faced here to calculate the energy bandgap.
Fig. 4. Total density of states and partial density of states rutile-SnO2 at different pressures.
240
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
Fig. 5. (a) Pressure induced Dielectric Constant, (b) Refractive index, (c) Absorption and (d) Energy loss function of rutile-SnO2.
Fig. 4 is the graphical representations of the total density of states (TDOS) and partial density of states (PDOS) of s-orbitals (O 2s and Sn 5s) and p-orbitals (O 2p and Sn 5p) of rutile SnO2 at different pressures. Fig. 4(b) and (c) infer that the lowest energy bands in the energy range from 21 eV to 15 eV are dominated by O 2s electrons with minor contribution of Sn 5p and Sn 5s electrons. The valence bands near to fermi level consist majorly of O 2p electrons with small contribution of 5s and 5p electrons. While the conduction bands constructed by the major contribution of Sn 5s and Sn 5p orbitals and with minor contribution of O 2p electrons. Further we become aware of hybridizations in between O 2s, O2p, Sn 5s and Sn 5p orbitals which the evidence of covalent interaction between them. Fig. 5 elucidates the pressure induced optical properties including dielectric function, refractive index, absorption spectrum and energy loss function. From Fig. 5 (a) and 5 (b) one can observe that the values of dielectric constant (from 4.02 to 3.15) and refractive index (from 2.01 to 1.77) are decreasing with the increase in pressure from 0 to 100 GPa. The decreases of dielectric constant infer us that the electric flux density is decreasing of rutile SnO2 and decreases of refractive index shows that the hardness to travel light from rutile SnO2 is decreasing with the increase of pressure. The real part of dielectric function, it resembles the refractive index graph but the real part values are equal to n2 (n is refractive index). The imaginary part of dielectric function somewhat resembles the absorption spectrum, the first peak occurs due to excitation from valence band to conduction band and the other two peaks occur due to the energy state transitions. Furthermore, the Fig. 5(c) exposes the absorption spectrum which agrees with the imaginary part of the dielectric function. One can notice the absorption peaks are positioned at 4.6, 7.73, 10.48, 15.1 and 29.3 eV under an ambient condition. Additionally, Fig. 5 (d) infers that with the increase of pressure from 0 to 30 GPa, the Energy loss peaks are slightly increasing while as we increased the pressure further, energy loss peaks start to decrease. The sharp peaks represent the interaction between the energy and plasma resonance. The energy loss function (L(⍵)) attains its maximum value when the real dielectric function reaches zero as shown in Fig. 5 (d). 4. Conclusion In this work we have selected LDA-CAPZ method to explore the structural, electronic and optical properties of rutile SnO2 at zero plus high pressure within the limit of density functional theory. Our calculated equilibrium lattice parameters and bulk modulus are well consistent with experimental (with the underestimation of about 1%) and other LDA based theoretical results. The pressure induced structural parameters (lattice parameters, volume and their ratios (a/a0, c/c0, c/a (axial ratio) and V/V0)), band structures, total and partial densities of states are also investigated. We observe that the band gap rutile SnO2 is
K. Bakht et al. / Superlattices and Microstructures 90 (2016) 236e241
241
direct at G-G under high pressure as well as zero pressure. The calculated energy bandgap at zero pressure is 1.31 eV. Moreover, we comprehensively concluded the hybridization of O 2s, O 2p, Sn 5s and Sn 5p electrons Additionally we have investigated the optical properties together with dielectric function, refractive index, absorption spectrum and energy loss function at equilibrium as well as elevated pressure of rutile SnO2 like Dielectric constant, refractive index for the first time. Acknowledgement One of the authors (Dr Tariq Mahmood) would like to thank for the supervision and fruitful guidance to complete this work. Also, we would like to thank the Government of Pakistan for providing Laptops to graduate students, which is used to complete this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]
Çetin Kılıç, Alex Zunger, Phys. Rev. Lett. 88 (2002) 095501. D. Zhang, M. Wang, A.G. Brolo, J. Shen, X. Li, S. Huang, J. Phys. D Appl. Phys. 46 (2013) 024005. X. Song, J. Pan, L. Xiao, S. Mathur, Nanotechnology 24 (2013) 205401. V.V. Krivetskiy, M.N. Rumyantseva, A.M. Gaskov, Russ. Chem. Rev. 82 (10) (2013) 917. Y. Feng, Y. Cui, J. Liu, B.E. Logan, J. Hazard. Mater. 178 (2010) 29e34. S.H. Hwang, C. Kim, J. Jang, Catal. Commun. 12 (2011) 1037e1041. S.R. Shieh, A. Kubo, T.S. Duffy, V.B. Prakapenka, G. Shen, Phys. Rev. B 73 (2006) 014105. J. Haines, J.M. Leger, Phys. Rev. B 55 (17) (1997) 11144. E. Huang, A.S. Li, S. Yu, T.A.O. 3 (2) (1992) 111e127. D. Frohlich, R. Kenklies, R. Helbig, Phys. Rev. Lett. 42 (25) (1978) 1750. C. Schweitzer, K. Reimann, M. Steube, Solid State Commun. 110 (1999) 697e700. J.L. Jacquemin, C. Alibert, G. Bordure, Solid State Commun. 12 (1972) 1295. Chun-Mei Liu, Xiang-Rong Chen, Guang-Fu Ji, Comp. Mater. Sci. 50 (2011) 1571e1577. M. Meyer, G. Onida, A. Ponchel, L. Reining, Comput. Mater. Sci. 10 (1998) 319e324. L.A. Errico, Phys. B 389 (2007) 140. G. Rahman, V.M. Garcia-Suarez, S.C. Hong, Phys. Rev. B 78 (2008) 184404. Y. Li, W. Fan, H. Sun, X. Cheng, P. Li, X. Zhao, J. Hao, M. Jiang, J. Phys. Chem. A 114 (2010) 1052. Q.J. Liu, Z.T. Liu, L.P. Feng, Comput. Mater. Sci. 47 (2010) 1016. C.J. Cramer, D.G. Truhlar, Phys. Chem. Chem. Phys. 11 (2009) 10757. A.J. Cohen, P. Mori-Sanchez, W. Yang, Phys. Rev. B 77 (2008) 115123. A.J. Cohen, P. Mori-Sanchez, W. Yang, Science 321 (2008) 792. P. Mori-Sanchez, A.J. Cohen, W. Yang, Phys. Rev. Lett. 102 (2009) 066403. R.M. Nieminen, Model. Simul. Mater. Sci. Eng. 17 (2009) 084001. M.D. Segall, P.L.D. Lindan, M.J. Probert, C. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens Matter 14 (2002) 2717. D.M. Ceperley, B.J. Alder, Ground State of the Electron Gas by a Stochastic Method, Phys. Rev. Lett. 45 (1980) 566e569. J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23 (1981) 5048e5079. F. Birch, Phys. Rev. 74 (11) (1947) 809. I. Erdem, H.H. Kart, Mater. Sci. Semicond. Process. 28 (2014) 59e65. F.E.H. Hassan, S. Moussawi, W. Noun, C. Salameh, A.V. Postnikov, Comput. Mater. Sci. 72 (2013) 86e92. Y. Duan, Phys. Rev. B 77 (2008) 045332. V.T. Agekyan, Phys. Status Solidi A 43 (1977) 11. A. Ferreira da Silva, I. Pepe, C. Person, J. Souza de Almeida, C. Moyses Araujo, B. Johansson, C.Y. An, J.H. Guo, Phys. Scr. T 109 (2004) 180. El Haj Hassan, S. Moussawi, W. Noun, C. Salameh, A.V. Postnikov, Comput. Mater. Sci. 72 (2013) 86e92.