- Email: [email protected]
bulk iodine defects of CsSnBr3 perovskite
SCT-21217; No of Pages 5 Surface & Coatings Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat
Electronic properties of surface/bulk iodine defects of CsSnBr3 perovskite S. Pramchu, Y. Laosiritaworn, A.P. Jaroenjittichai ⁎ Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
a r t i c l e
i n f o
Article history: Received 15 January 2016 Revised 19 May 2016 Accepted in revised form 21 May 2016 Available online xxxx Keywords: Perovskite DFT defect solar cell
a b s t r a c t Perovskites are one of a few semiconducting materials that have been shaping the progress of the third generation photovoltaic cells. The power conversion efficiency of the perovskite solar cell has been certified as 20.1% in 2015. In this work, CsSnBr3 perovskite has been considered as an alternative material for solar cell applications because of its appropriate band gap. The study has focused on the influence of iodine impurity on the electronic properties of CsSnBr3 perovskite modeled on the (001) surface structures. The crystal structures and the electronic properties have been calculated using density functional theory (DFT) within a plane wave pseudopotential framework. The GW method has been also employed to obtain more accurate band gaps. The results show that the iodine defect improves the efficiency of photo absorbance in perovskite solar cell by lowering its energy gap. In particular, the iodine bulk defect in the SnBr2-terminated surface structure was found to exhibit the narrowest band gap. This result suggests that iodine impurity deep into the structure, e.g. iodine-dopant created from high-energy implantation, plays an important role to improve the efficiency of light absorption in CsSnBr3 perovskite. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Perovskites have been recently introduced as promising materials for the photovoltaic applications because of their extremely suitable properties such as electric, ferroelectric, optical properties, which lead to long carrier diffusion length and wide wavelength-range absorption [1,2]. The use of perovskite as light absorber allows a rapid increase in power conversion efficiency of perovskites-based solar cell, certified as 20.1% in 2015 [3]. In order to continuously develop this type of solar cell, both theoretical and experimental studies of the physical and chemical properties of perovskites have gained very much intense investigations [4]. CsMX3 (M = Sn, Pb; X = Cl, Br, I) perovskite compounds are of interest because of their tunable optical properties [5]. At present, studies of CsMX3 perovskite with defects, especially theoretical investigation of surface defect, are somewhat limited. Most reports are based on perfect crystal calculated using either local density approximation (LDA) or generalized gradient approximation (GGA) [6–8]. However, both LDA and GGA cannot represent the quasiparticle properties due to an incomplete cancellation of a self-interaction and discontinuity of the exchange-correlation potential. More advanced methods are necessary to take into account such as GW approximation [9]. In this work we focus on CsSnBr3 because its band gap [10] is suitable for solar cell applications and also to avoid using of the toxic Pb. ⁎ Corresponding author at: Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, 239 Huay Kaew Rd. Suthep, Muang, Chiang Mai 50200, Thailand. E-mail address: [email protected] (A.P. Jaroenjittichai).
In addition, perovskite-based solar cell fabricated as a planar heterojunction structure has been proposed to achieve the cheap and high efficiency device [11]. In this type of structure, it requires the fabrication of perovskite materials as a thin film (surface structure with a specified substrate). Thus, it is more applicable to study CsSnBr3 modeled as surface structures or supercells (with not yet identified substrate). As a prototype study, we selected (001) texture of cubic CsSnBr3 (α-phase) because their (100), (010), and (001) surface textures are symmetrically equivalent. In this work, we aim to investigate the influence of iodine (I) impurity incorporated into the α-CsSnBr3. The doping was divided into two types, i.e. bulk doping and surface doping, where I foreign atom substitutes for Br in the bulk and on the surface of CsSnBr3, respectively. The reason for choosing these two defects is that they can represent high and low dopant energies when the ion implantation induces defects. We expect that the I-doped α-CsSnBr3 will lower the energy gap and then improve the efficiency of photo absorption. The details of each defective supercell and computational method will be described in the next section. 2. Methodology In this work, cubic CsSnBr3 (α-phase) has been introduced as a supercell, which is about ten times the size of its unit cell. For this prototype study, we focused on (001) growth direction. In this direction, the surface structure consists of the neutral CsBr and SnBr2 alternating sublayers. Therefore, there are two possible surface terminations for this (001) texture: namely, the surface structures terminated by CsBr and by SnBr2 layers. The top and bottom layers of these slab models
http://dx.doi.org/10.1016/j.surfcoat.2016.05.062 0257-8972/© 2016 Elsevier B.V. All rights reserved.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
2
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx
have been constructed with the same surface termination in order to avoid the undesirable electrostatic interaction between different surfaces. The CsBr- and SnBr2-terminated structures, as presented in Fig. 1 (a) and (b) consist of 52 and 53 atoms respectively while the unit cell of CsSnBr3 are formed with 5 atoms. Then, an iodine impurity was introduced to α-CsSnBr3 by substituting Br located on the surface or Br situated at the middle of bulk structures. Surface and bulk doping in this context could be related to ion implantation with low and high kinetic energies, respectively. Note that the surface roughness and other structural complexities due to scattering effect can be considered using mesoscopic simulation beyond the scope of this DFT work, e.g. molecular dynamics [12]. In this work, all supercell structures (with and without I impurity) has been studied by means of density functional theory. The calculations were performed under the framework of a plane wave method implemented in Quantum-Espresso package [13]. Ultrasoft pseudopotentials from the GBRV pseudopotential library [14] constructed under the
generalized gradient approximation (GGA) within Perdew-BurkeErnzerhoff approach (PBE) [15] were used to optimize the lattice constants and atomic positions inside the unit cell of CsSnBr3. The electrons from Cs {5s, 5p, 6s}, Sn {4d, 5s, 5p}, I {4d, 5s, 5p} and Br {4s, 4p} were employed in this calculation. The energy cutoff of 35 and 280 Rydberg were found sufficiently large for wavefunctions and charge density expansion considered in this work. The k-point meshes of 8 × 8 × 8 and 8 × 8 × 1 (based on Morshost-Pack approach [16]) were used for bulk α-CsSnBr3 unit cell and surface structure calculations. The (001) surface structures were spaced by 20 Å vacuum along the nonperiodic direction orthogonal to the surface plane. To ignore the contribution from finite thickness of surface structure, we constructed all surface structures with 10 unit cells thickness (about 58 Å), where we found that the systems did not display significant changes in their properties, such as the band gap, with increasing thicknesses. Apart from the structural calculation, an electronic band structure was obtained using the local density approximation (LDA) [17] and then it was corrected using a more advance technique called GW approximation, as implemented in Yambo package [18]. In this approach, a self-energy approximated by Hedin [9] was used in solving KohnSham equation instead of the LDA exchange correlation potential (Vxc). However, the calculation within GW approximation requires large computational resource, especially when applied to the system with several hundred electronic states (bands) as in our supercell. Therefore, we calculated how much each band edge (valence band maximum or conduction band minimum) being shifted from LDA to GW value in the bulk structure and called this shift as the GW correction. Then this correction was employed to estimate the band gap of surface structures. 3. Results and discussion
Fig. 1. Surface structures of (001) CsSbBr3 perovskite, (a) CsBr and (b) SnBr2 terminated structures; Cs = light blue, Br = red, and Sn = gray. The supercells represent the CsBr and SnBr2 – terminated structures containing of 52 and 53 atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Before performing I doped CsSnBr3 computation, the calculation of pristine CsSnBr3 should be firstly considered. In this work, the structure of bulk CsSnBr3 was relaxed using PBE approach. It gave a calculated lattice constant of 5.802 Å which was in good agreement with the experimental results (5.804 Å) [19]. This guarantees that our pseudopotential technique and relaxation method are reliable. Apart from the structural calculation, the band gaps were calculated using LDA and yielded a value of 0.35 eV comparable with 0.35 eV from LMTO-LDA calculation [5]. However, it is well known that LDA underestimates band gaps. The more advance technique called GW approximation was applied in order to correct the band gap calculation. Our GW correction provided the band gap of 1.56 eV, which is consistent with 1.69 eV from Huang et al. [5]. The discrepancy of about 0.13 eV may be due to the shift between the Sn s- and the Br p-levels, which are slightly different between using pseudopotentials and LMTO [20]. As described in Methodology, the calculation within GW approximation applied in large systems requires very large computational resource. Thus, we used the difference between LDA and GW band gaps of bulk CsSnBr3, which is 1.2 eV, as a GW correction to LDA band gap of surface structures. The structural properties and band gap with GW correction of a pristine α-CsSnBr3 are represented in Table 1. The electronic band structure and partial density of states (PDOS) of the pristine α-CsSnBr3 can be virtually represented in Fig. 2. α-CsSnBr3 has a direct band gap (1.55 eV) at R symmetry point as shown in Fig. 2(a). As seen from Fig. 2(b), the PDOS analysis indicates that Br p- and Sn p-orbitals are the main contribution to valence band maximum (VBM) and conduction band minimum (CBM) respectively. These results and the calculated band structure reported with PDOS from Huang et al. [5] are in good agreement. For surface structures, there were two clean surfaces (undoped) for CsBr and SnBr2 termination. For each kind of termination, we defined two impurity structures, i.e. surface and bulk defective structures. This gives a total of six structures, i.e. clean surface with CsBr termination, bulk doping of CsBr termination, surface doping of CsBr termination, clean surface with SnBr2 termination, bulk doping of SnBr2 termination,
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx Table 1 The lattice constants and band gap (Eg) with GW correction of pristine CsSnBr3, and all supercell structures. The lattice constant, c of supercell structures were defined by the averaged thickness (10 unit cells) along z-direction from bottom to top of the structures. %Sx, %Sy, and %Sz are the calculated strains in x, y, and z directions. %S = 100 × (surface lattice constant−bulk lattice constant) / bulk lattice constant. The lattice constants (strain) a (%Sx) and b (%Sy) are equal to each other for all structures. Lattice parameters (Å) calculated using PBE
Ref. CsSnBr3 Our CsSnBr3c Model 1c Model 2c Model 3c Model 4c Model 5c Model 6c
a (%Sx)
c (%Sz)
5.804a 5.802 5.788 (−0.24) 5.786 (−0.28) 5.783 (−0.33) 5.786 (−0.28) 5.780 (−0.38) 5.781 (−0.36)
5.804a 5.802 5.836 (0.59) 5.819 (0.29) 5.821 (0.33) 5.874 (1.24) 5.872 (1.21) 5.899 (1.67)
Eg (eV) with GW
1.69b 1.56c 1.74 1.67 1.71 1.76 1.55 1.68
a
Ref [19] experimental value. Ref [5], DFT calculation using FP-LMTO with LDA and QSGW. Our calculation using pseudopotential with PBE for structural relaxation and GW for band gap correction. b c
and surface doping of SnBr2 termination, which were defined as model 1–6 respectively. Their structural and electronic properties are also presented in Table 1. The calculated lattice constants reported in Table 1 indicate that both CsBr and SnBr2 terminated (001) surfaces do not only cause a strain in z direction but also in x and y directions. Although it has been expected that the lattice constants of the clean surface structures (model 1 and 4) in x and y directions (a and b lattice constants) should not differ from their unit cell values because of the complete periodic boundary condition, the coupling between the out-of-plane strain (Sz) and in-plane strain (Sx, Sy) results in the change of in-plane lattice constants. The largest strain was found in model 6 since the dopant (I atom) moved away from the surface after a structural relaxation. The results from Table 1 also reveal that all surface structures experience crystal symmetry change from cubic to tetragonal lattice. In addition, the difference in the net force applied on each atom, based on the distance from the surface, leads the atoms to different environment after relaxation (e.g. different bond lengths). Thus, the reasons mentioned above are the main causes for energy band splitting from its degeneracy states in bulk CsSnBr3 band structure, which can be visually illustrated in Fig. 3 compared with that in Fig. 2 (a). Although the symmetry in reciprocal space of the electronic band structure is reduced from three to two dimensions when the surface structure is created, i.e. points R (0.5, 0.5, 0.5) and M (0.5, 0.5, 0.0) reduce to M (0.5, 0.5), the features of the band structures of surface and bulk structures are quite similar, except for the energy band splitting. This implies that the surface structures
3
with sufficiently large thickness preserve almost all bulk properties. Therefore, CsSnBr3 has the potentials to be fabricated as planar heterojunction solar cell, which requires thin film (surface structure) growth. The incorporation of I atom introduces a slight modification in band structures of bulk defective structures (Fig. 3 (a, b)) and surface defective structures (Fig. 3 (c, f)), which are quite similar to those from the clean surface structures (Fig. 3 (a, d)). To further analyse of the change in band gap, we considered the contribution from each atomic orbital. PDOS of all surface structures are presented as shown in Fig. 4. We found that Br-4p and Sn-5p orbitals were still the main contribution for VBM and CBM, respectively. This behavior does not change from that of the bulk CsSnBr3. In Fig. 4, the contributions from I-5s and I-5p orbitals in doped systems were combined with those from Br-4s and Br-4p orbitals, respectively. Considering the PDOS of I-5p and the average PDOS of Br-4p orbitals independently, the Br-4p, which is dominant at the top of valence bands, lies deeper in the valence bands than that of the I-5p as can be seen in Fig. 1 (c), which is an example of model 6. This suggests that I-dopant in surface and bulk structures of α-CsSnBr3 can reduce Eg and improve the optical properties. Furthermore, the spin-orbit coupling (SO) is also found to reduce Eg [5,21], thus it should be included in the calculation in order to get more accurate results, which can be taken into account in future work. It has been quite clear how the induction of I impurity atom into αCsSnBr3 structures leads to the improvement of optical properties. In addition, we found that bulk doping displayed larger change in Eg than surface doping does in both CsBr and SnBr2-terminated structures. The narrowest Eg is found in the case of bulk doping of SnBr2 termination (model 5), where Eg is about 1.55 eV; 0.21 eV less than 1.76 eV of the clean surface with SnBr2 termination. Note that, both clean surface structures yields higher Eg compared with 1.56 eV of pristine CsSnBr3 because of the surface supercell effect. Therefore, our results suggest that I impurity lying deep in the structure (bulk doping) most reduces band gap of CsSnBr3 and allows the material to absorb light in a wider range of wavelength. 4. Conclusion The creation of α-CsSnBr3 (001) surfaces introduces modification on structural and electronic properties. Both CsBr- and SnBr2-terminated surface structures yield the symmetry change from cubic to tetragonal lattice. This structural modification corresponds to the change in electronic properties, in particular the band gap. We found the increasing of band gap for clean surface structures (for both CsBr- and SnBr2 terminations). The incorporation of I foreign atom into α-CsSnBr3 (001) surfaces structures by substituting Br atom lowers band gap. Especially, the bulk doping of I atom into SnBr2-terminated surface structures exhibits
Fig. 2. (a) Electronic band structure and (b) total density of states (TDOS) and partial density of states (PDOS) of pristine α-CsSnBr3. (c) The shift of PDOS of I p-orbital with respected to the averaged PDOS of Br p-orbital which are the main contribution of states to the valence bands.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
4
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx
Fig. 3. Electronic band structures of (a) the clean surface with CsBr termination, (b) bulk doping of CsBr termination, (c) surface doping of CsBr termination, (d) clean surface with SnBr2 termination, (e) bulk doping of SnBr2 termination, and (f) surface doping of SnBr2 termination.
Fig. 4. Total density of states (TDOS) and partial density of states (PDOS) of (a) the clean surface with CsBr termination, (b) bulk doping of CsBr termination, (c) surface doping of CsBr termination, (d) clean surface with SnBr2 termination, (e) bulk doping of SnBr2 termination, and (f) surface doping of SnBr2 termination.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx
the narrowest Eg. Although the creation of α-CsSnBr3 (001) surfaces tends to increase Eg, the induction of I impurity can be used to adjust its optical property. According to our calculation, effective enhancement of Eg can be achieved by bulk doping. The acquirement of variable band gap will allow the material to absorb light in a wider range of wavelength. Acknowledgements This work was supported by the Development and Promotion of Science and Technology Talents Project (DPST) and the Institute for the Promotion of Teaching Science and Technology, (IPST, Thailand) under Grant No. 30/2557. References [1] K. Heidrich, W. Schafer, M. Schreiber, J. Sochtig, T. Grandke, H.J. Stolz, Electronic structure, photoemission spectra, and vacuum-ultraviolet optical spectra of CsPbCl3 and CsPbBr3, Phys. Rev. B 24 (1981) 5642–5649. [2] I. Chung, B. Lee, J.Q. He, R.P.H. Chang, M.G. Kanatzidis, All-solid-state dye-sensitized solar cells with high efficiency, Nature 485 (2012) 486–489. [3] S. Collavini, S.F. Völker, J.L. Delgado, Understanding the outstanding power conversion efficiency of perovskite-based solar cells, Angew. Chem. Int. Ed. 54 (2015) 9757–9759. [4] M.A. Green, A. Ho-Baillie, H.J. Snaith, The emergence of perovskite solar cells, Nat. Photonics 8 (2014) 506–514. [5] L. Huang, W.R.L. Lambrecht, Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl3, CsSnBr3, and CsSnI3, Phys. Rev. B 88 (2013) 165203. [6] G. Murtaza, I. Ahmad, First principle study of the structural and optoelectronic properties of cubic perovskites CsPbM3 (M = Cl, Br, I), Physica B 406 (2011) 3222–3229.
5
[7] M.A. Ghebouli, B. Ghebouli, M. Fatmi, First-principles calculations on structural, elastic, electronic, optical and thermal properties of CsPbCl3 perovskite, Physica B 406 (2011) 1837–1843. [8] Y.H. Chang, C.H. Park, K. Matsuishi, First-principles study of the structural and the electronic properties of the lead-halide-based inorganic-organic perovskites (CH3NH3)PbX3 and CsPbX3 (X = Cl, Br, I), J. Korean Phys. Soc. 44 (2004) 889–893. [9] L. Hedin, New method for calculating the one-particle green's function with application to the electron-gas problem, Phys. Rev. 139 (1965) A796–A823. [10] S.J. Clark, J.D. Donaldson, J.A. Harvey, Evidence for the direct population of solidstate bands by non-bonding electron pairs in compounds of the type CsMIIX3(MII = Ge, Sn, Pb; X = Cl, Br, I), J. Mater. Chem. 5 (1995) 1813–1818. [11] M. Liu, M.B. Johnston, H.J. Snaith, Efficient planar heterojunction perovskite solar cells by vapour deposition, Nature 501 (2013) 395–398. [12] K.M. Beardmore, N. Grønbech-Jensen, Efficient molecular dynamics scheme for the calculation of dopant profiles due to ion implantation, Phys. Rev. B 57 (1997) 7278–7287. [13] H.J. Limbach, A. Arnold, B.A. Mann, C. Holm, ESPResSo-an extensible simulation package for research on soft matter systems, Comput. Phys. Commun. 174 (2006) 704–727. [14] K.F. Garrity, J.W. Bennett, K.M. Rabe, D. Vanderbilt, Pseudopotentials for highthroughput DFT calculations, Comput. Mater. Sci. 81 (2014) 446–452. [15] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. [16] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188–5192. [17] J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23 (1981) 5048–5079. [18] A. Marini, C. Hogan, M. Gruning, D. Varsano, Yambo: an ab initio tool for excited state calculations, Comput. Phys. Comm. 180 (2009) 1392–1403. [19] J. Barrett, S.R.A. Bird, J.D. Donaldson, J. Silver, The Mössbauer effect in tin(II) compounds. Part XI. The spectra of cubic trihalogenostannates (II), J. Chem. Soc. A1971 (1971) 3105–3108. [20] S.K. Bose, S. Satpathy, O. Jepsen, Semiconducting CsSnBr3, Phys. Rev. B 47 (1993) 4276–4280. [21] L. Huang, W.R.L. Lambrecht, Lattice dynamics in perovskite halides CsSnX3 with X = I, Br, Cl, Phys. Rev. B 90 (2014) 195201.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
Contents lists available at ScienceDirect
Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat
Electronic properties of surface/bulk iodine defects of CsSnBr3 perovskite S. Pramchu, Y. Laosiritaworn, A.P. Jaroenjittichai ⁎ Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
a r t i c l e
i n f o
Article history: Received 15 January 2016 Revised 19 May 2016 Accepted in revised form 21 May 2016 Available online xxxx Keywords: Perovskite DFT defect solar cell
a b s t r a c t Perovskites are one of a few semiconducting materials that have been shaping the progress of the third generation photovoltaic cells. The power conversion efficiency of the perovskite solar cell has been certified as 20.1% in 2015. In this work, CsSnBr3 perovskite has been considered as an alternative material for solar cell applications because of its appropriate band gap. The study has focused on the influence of iodine impurity on the electronic properties of CsSnBr3 perovskite modeled on the (001) surface structures. The crystal structures and the electronic properties have been calculated using density functional theory (DFT) within a plane wave pseudopotential framework. The GW method has been also employed to obtain more accurate band gaps. The results show that the iodine defect improves the efficiency of photo absorbance in perovskite solar cell by lowering its energy gap. In particular, the iodine bulk defect in the SnBr2-terminated surface structure was found to exhibit the narrowest band gap. This result suggests that iodine impurity deep into the structure, e.g. iodine-dopant created from high-energy implantation, plays an important role to improve the efficiency of light absorption in CsSnBr3 perovskite. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Perovskites have been recently introduced as promising materials for the photovoltaic applications because of their extremely suitable properties such as electric, ferroelectric, optical properties, which lead to long carrier diffusion length and wide wavelength-range absorption [1,2]. The use of perovskite as light absorber allows a rapid increase in power conversion efficiency of perovskites-based solar cell, certified as 20.1% in 2015 [3]. In order to continuously develop this type of solar cell, both theoretical and experimental studies of the physical and chemical properties of perovskites have gained very much intense investigations [4]. CsMX3 (M = Sn, Pb; X = Cl, Br, I) perovskite compounds are of interest because of their tunable optical properties [5]. At present, studies of CsMX3 perovskite with defects, especially theoretical investigation of surface defect, are somewhat limited. Most reports are based on perfect crystal calculated using either local density approximation (LDA) or generalized gradient approximation (GGA) [6–8]. However, both LDA and GGA cannot represent the quasiparticle properties due to an incomplete cancellation of a self-interaction and discontinuity of the exchange-correlation potential. More advanced methods are necessary to take into account such as GW approximation [9]. In this work we focus on CsSnBr3 because its band gap [10] is suitable for solar cell applications and also to avoid using of the toxic Pb. ⁎ Corresponding author at: Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, 239 Huay Kaew Rd. Suthep, Muang, Chiang Mai 50200, Thailand. E-mail address: [email protected] (A.P. Jaroenjittichai).
In addition, perovskite-based solar cell fabricated as a planar heterojunction structure has been proposed to achieve the cheap and high efficiency device [11]. In this type of structure, it requires the fabrication of perovskite materials as a thin film (surface structure with a specified substrate). Thus, it is more applicable to study CsSnBr3 modeled as surface structures or supercells (with not yet identified substrate). As a prototype study, we selected (001) texture of cubic CsSnBr3 (α-phase) because their (100), (010), and (001) surface textures are symmetrically equivalent. In this work, we aim to investigate the influence of iodine (I) impurity incorporated into the α-CsSnBr3. The doping was divided into two types, i.e. bulk doping and surface doping, where I foreign atom substitutes for Br in the bulk and on the surface of CsSnBr3, respectively. The reason for choosing these two defects is that they can represent high and low dopant energies when the ion implantation induces defects. We expect that the I-doped α-CsSnBr3 will lower the energy gap and then improve the efficiency of photo absorption. The details of each defective supercell and computational method will be described in the next section. 2. Methodology In this work, cubic CsSnBr3 (α-phase) has been introduced as a supercell, which is about ten times the size of its unit cell. For this prototype study, we focused on (001) growth direction. In this direction, the surface structure consists of the neutral CsBr and SnBr2 alternating sublayers. Therefore, there are two possible surface terminations for this (001) texture: namely, the surface structures terminated by CsBr and by SnBr2 layers. The top and bottom layers of these slab models
http://dx.doi.org/10.1016/j.surfcoat.2016.05.062 0257-8972/© 2016 Elsevier B.V. All rights reserved.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
2
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx
have been constructed with the same surface termination in order to avoid the undesirable electrostatic interaction between different surfaces. The CsBr- and SnBr2-terminated structures, as presented in Fig. 1 (a) and (b) consist of 52 and 53 atoms respectively while the unit cell of CsSnBr3 are formed with 5 atoms. Then, an iodine impurity was introduced to α-CsSnBr3 by substituting Br located on the surface or Br situated at the middle of bulk structures. Surface and bulk doping in this context could be related to ion implantation with low and high kinetic energies, respectively. Note that the surface roughness and other structural complexities due to scattering effect can be considered using mesoscopic simulation beyond the scope of this DFT work, e.g. molecular dynamics [12]. In this work, all supercell structures (with and without I impurity) has been studied by means of density functional theory. The calculations were performed under the framework of a plane wave method implemented in Quantum-Espresso package [13]. Ultrasoft pseudopotentials from the GBRV pseudopotential library [14] constructed under the
generalized gradient approximation (GGA) within Perdew-BurkeErnzerhoff approach (PBE) [15] were used to optimize the lattice constants and atomic positions inside the unit cell of CsSnBr3. The electrons from Cs {5s, 5p, 6s}, Sn {4d, 5s, 5p}, I {4d, 5s, 5p} and Br {4s, 4p} were employed in this calculation. The energy cutoff of 35 and 280 Rydberg were found sufficiently large for wavefunctions and charge density expansion considered in this work. The k-point meshes of 8 × 8 × 8 and 8 × 8 × 1 (based on Morshost-Pack approach [16]) were used for bulk α-CsSnBr3 unit cell and surface structure calculations. The (001) surface structures were spaced by 20 Å vacuum along the nonperiodic direction orthogonal to the surface plane. To ignore the contribution from finite thickness of surface structure, we constructed all surface structures with 10 unit cells thickness (about 58 Å), where we found that the systems did not display significant changes in their properties, such as the band gap, with increasing thicknesses. Apart from the structural calculation, an electronic band structure was obtained using the local density approximation (LDA) [17] and then it was corrected using a more advance technique called GW approximation, as implemented in Yambo package [18]. In this approach, a self-energy approximated by Hedin [9] was used in solving KohnSham equation instead of the LDA exchange correlation potential (Vxc). However, the calculation within GW approximation requires large computational resource, especially when applied to the system with several hundred electronic states (bands) as in our supercell. Therefore, we calculated how much each band edge (valence band maximum or conduction band minimum) being shifted from LDA to GW value in the bulk structure and called this shift as the GW correction. Then this correction was employed to estimate the band gap of surface structures. 3. Results and discussion
Fig. 1. Surface structures of (001) CsSbBr3 perovskite, (a) CsBr and (b) SnBr2 terminated structures; Cs = light blue, Br = red, and Sn = gray. The supercells represent the CsBr and SnBr2 – terminated structures containing of 52 and 53 atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Before performing I doped CsSnBr3 computation, the calculation of pristine CsSnBr3 should be firstly considered. In this work, the structure of bulk CsSnBr3 was relaxed using PBE approach. It gave a calculated lattice constant of 5.802 Å which was in good agreement with the experimental results (5.804 Å) [19]. This guarantees that our pseudopotential technique and relaxation method are reliable. Apart from the structural calculation, the band gaps were calculated using LDA and yielded a value of 0.35 eV comparable with 0.35 eV from LMTO-LDA calculation [5]. However, it is well known that LDA underestimates band gaps. The more advance technique called GW approximation was applied in order to correct the band gap calculation. Our GW correction provided the band gap of 1.56 eV, which is consistent with 1.69 eV from Huang et al. [5]. The discrepancy of about 0.13 eV may be due to the shift between the Sn s- and the Br p-levels, which are slightly different between using pseudopotentials and LMTO [20]. As described in Methodology, the calculation within GW approximation applied in large systems requires very large computational resource. Thus, we used the difference between LDA and GW band gaps of bulk CsSnBr3, which is 1.2 eV, as a GW correction to LDA band gap of surface structures. The structural properties and band gap with GW correction of a pristine α-CsSnBr3 are represented in Table 1. The electronic band structure and partial density of states (PDOS) of the pristine α-CsSnBr3 can be virtually represented in Fig. 2. α-CsSnBr3 has a direct band gap (1.55 eV) at R symmetry point as shown in Fig. 2(a). As seen from Fig. 2(b), the PDOS analysis indicates that Br p- and Sn p-orbitals are the main contribution to valence band maximum (VBM) and conduction band minimum (CBM) respectively. These results and the calculated band structure reported with PDOS from Huang et al. [5] are in good agreement. For surface structures, there were two clean surfaces (undoped) for CsBr and SnBr2 termination. For each kind of termination, we defined two impurity structures, i.e. surface and bulk defective structures. This gives a total of six structures, i.e. clean surface with CsBr termination, bulk doping of CsBr termination, surface doping of CsBr termination, clean surface with SnBr2 termination, bulk doping of SnBr2 termination,
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx Table 1 The lattice constants and band gap (Eg) with GW correction of pristine CsSnBr3, and all supercell structures. The lattice constant, c of supercell structures were defined by the averaged thickness (10 unit cells) along z-direction from bottom to top of the structures. %Sx, %Sy, and %Sz are the calculated strains in x, y, and z directions. %S = 100 × (surface lattice constant−bulk lattice constant) / bulk lattice constant. The lattice constants (strain) a (%Sx) and b (%Sy) are equal to each other for all structures. Lattice parameters (Å) calculated using PBE
Ref. CsSnBr3 Our CsSnBr3c Model 1c Model 2c Model 3c Model 4c Model 5c Model 6c
a (%Sx)
c (%Sz)
5.804a 5.802 5.788 (−0.24) 5.786 (−0.28) 5.783 (−0.33) 5.786 (−0.28) 5.780 (−0.38) 5.781 (−0.36)
5.804a 5.802 5.836 (0.59) 5.819 (0.29) 5.821 (0.33) 5.874 (1.24) 5.872 (1.21) 5.899 (1.67)
Eg (eV) with GW
1.69b 1.56c 1.74 1.67 1.71 1.76 1.55 1.68
a
Ref [19] experimental value. Ref [5], DFT calculation using FP-LMTO with LDA and QSGW. Our calculation using pseudopotential with PBE for structural relaxation and GW for band gap correction. b c
and surface doping of SnBr2 termination, which were defined as model 1–6 respectively. Their structural and electronic properties are also presented in Table 1. The calculated lattice constants reported in Table 1 indicate that both CsBr and SnBr2 terminated (001) surfaces do not only cause a strain in z direction but also in x and y directions. Although it has been expected that the lattice constants of the clean surface structures (model 1 and 4) in x and y directions (a and b lattice constants) should not differ from their unit cell values because of the complete periodic boundary condition, the coupling between the out-of-plane strain (Sz) and in-plane strain (Sx, Sy) results in the change of in-plane lattice constants. The largest strain was found in model 6 since the dopant (I atom) moved away from the surface after a structural relaxation. The results from Table 1 also reveal that all surface structures experience crystal symmetry change from cubic to tetragonal lattice. In addition, the difference in the net force applied on each atom, based on the distance from the surface, leads the atoms to different environment after relaxation (e.g. different bond lengths). Thus, the reasons mentioned above are the main causes for energy band splitting from its degeneracy states in bulk CsSnBr3 band structure, which can be visually illustrated in Fig. 3 compared with that in Fig. 2 (a). Although the symmetry in reciprocal space of the electronic band structure is reduced from three to two dimensions when the surface structure is created, i.e. points R (0.5, 0.5, 0.5) and M (0.5, 0.5, 0.0) reduce to M (0.5, 0.5), the features of the band structures of surface and bulk structures are quite similar, except for the energy band splitting. This implies that the surface structures
3
with sufficiently large thickness preserve almost all bulk properties. Therefore, CsSnBr3 has the potentials to be fabricated as planar heterojunction solar cell, which requires thin film (surface structure) growth. The incorporation of I atom introduces a slight modification in band structures of bulk defective structures (Fig. 3 (a, b)) and surface defective structures (Fig. 3 (c, f)), which are quite similar to those from the clean surface structures (Fig. 3 (a, d)). To further analyse of the change in band gap, we considered the contribution from each atomic orbital. PDOS of all surface structures are presented as shown in Fig. 4. We found that Br-4p and Sn-5p orbitals were still the main contribution for VBM and CBM, respectively. This behavior does not change from that of the bulk CsSnBr3. In Fig. 4, the contributions from I-5s and I-5p orbitals in doped systems were combined with those from Br-4s and Br-4p orbitals, respectively. Considering the PDOS of I-5p and the average PDOS of Br-4p orbitals independently, the Br-4p, which is dominant at the top of valence bands, lies deeper in the valence bands than that of the I-5p as can be seen in Fig. 1 (c), which is an example of model 6. This suggests that I-dopant in surface and bulk structures of α-CsSnBr3 can reduce Eg and improve the optical properties. Furthermore, the spin-orbit coupling (SO) is also found to reduce Eg [5,21], thus it should be included in the calculation in order to get more accurate results, which can be taken into account in future work. It has been quite clear how the induction of I impurity atom into αCsSnBr3 structures leads to the improvement of optical properties. In addition, we found that bulk doping displayed larger change in Eg than surface doping does in both CsBr and SnBr2-terminated structures. The narrowest Eg is found in the case of bulk doping of SnBr2 termination (model 5), where Eg is about 1.55 eV; 0.21 eV less than 1.76 eV of the clean surface with SnBr2 termination. Note that, both clean surface structures yields higher Eg compared with 1.56 eV of pristine CsSnBr3 because of the surface supercell effect. Therefore, our results suggest that I impurity lying deep in the structure (bulk doping) most reduces band gap of CsSnBr3 and allows the material to absorb light in a wider range of wavelength. 4. Conclusion The creation of α-CsSnBr3 (001) surfaces introduces modification on structural and electronic properties. Both CsBr- and SnBr2-terminated surface structures yield the symmetry change from cubic to tetragonal lattice. This structural modification corresponds to the change in electronic properties, in particular the band gap. We found the increasing of band gap for clean surface structures (for both CsBr- and SnBr2 terminations). The incorporation of I foreign atom into α-CsSnBr3 (001) surfaces structures by substituting Br atom lowers band gap. Especially, the bulk doping of I atom into SnBr2-terminated surface structures exhibits
Fig. 2. (a) Electronic band structure and (b) total density of states (TDOS) and partial density of states (PDOS) of pristine α-CsSnBr3. (c) The shift of PDOS of I p-orbital with respected to the averaged PDOS of Br p-orbital which are the main contribution of states to the valence bands.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
4
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx
Fig. 3. Electronic band structures of (a) the clean surface with CsBr termination, (b) bulk doping of CsBr termination, (c) surface doping of CsBr termination, (d) clean surface with SnBr2 termination, (e) bulk doping of SnBr2 termination, and (f) surface doping of SnBr2 termination.
Fig. 4. Total density of states (TDOS) and partial density of states (PDOS) of (a) the clean surface with CsBr termination, (b) bulk doping of CsBr termination, (c) surface doping of CsBr termination, (d) clean surface with SnBr2 termination, (e) bulk doping of SnBr2 termination, and (f) surface doping of SnBr2 termination.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062
S. Pramchu et al. / Surface & Coatings Technology xxx (2016) xxx–xxx
the narrowest Eg. Although the creation of α-CsSnBr3 (001) surfaces tends to increase Eg, the induction of I impurity can be used to adjust its optical property. According to our calculation, effective enhancement of Eg can be achieved by bulk doping. The acquirement of variable band gap will allow the material to absorb light in a wider range of wavelength. Acknowledgements This work was supported by the Development and Promotion of Science and Technology Talents Project (DPST) and the Institute for the Promotion of Teaching Science and Technology, (IPST, Thailand) under Grant No. 30/2557. References [1] K. Heidrich, W. Schafer, M. Schreiber, J. Sochtig, T. Grandke, H.J. Stolz, Electronic structure, photoemission spectra, and vacuum-ultraviolet optical spectra of CsPbCl3 and CsPbBr3, Phys. Rev. B 24 (1981) 5642–5649. [2] I. Chung, B. Lee, J.Q. He, R.P.H. Chang, M.G. Kanatzidis, All-solid-state dye-sensitized solar cells with high efficiency, Nature 485 (2012) 486–489. [3] S. Collavini, S.F. Völker, J.L. Delgado, Understanding the outstanding power conversion efficiency of perovskite-based solar cells, Angew. Chem. Int. Ed. 54 (2015) 9757–9759. [4] M.A. Green, A. Ho-Baillie, H.J. Snaith, The emergence of perovskite solar cells, Nat. Photonics 8 (2014) 506–514. [5] L. Huang, W.R.L. Lambrecht, Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl3, CsSnBr3, and CsSnI3, Phys. Rev. B 88 (2013) 165203. [6] G. Murtaza, I. Ahmad, First principle study of the structural and optoelectronic properties of cubic perovskites CsPbM3 (M = Cl, Br, I), Physica B 406 (2011) 3222–3229.
5
[7] M.A. Ghebouli, B. Ghebouli, M. Fatmi, First-principles calculations on structural, elastic, electronic, optical and thermal properties of CsPbCl3 perovskite, Physica B 406 (2011) 1837–1843. [8] Y.H. Chang, C.H. Park, K. Matsuishi, First-principles study of the structural and the electronic properties of the lead-halide-based inorganic-organic perovskites (CH3NH3)PbX3 and CsPbX3 (X = Cl, Br, I), J. Korean Phys. Soc. 44 (2004) 889–893. [9] L. Hedin, New method for calculating the one-particle green's function with application to the electron-gas problem, Phys. Rev. 139 (1965) A796–A823. [10] S.J. Clark, J.D. Donaldson, J.A. Harvey, Evidence for the direct population of solidstate bands by non-bonding electron pairs in compounds of the type CsMIIX3(MII = Ge, Sn, Pb; X = Cl, Br, I), J. Mater. Chem. 5 (1995) 1813–1818. [11] M. Liu, M.B. Johnston, H.J. Snaith, Efficient planar heterojunction perovskite solar cells by vapour deposition, Nature 501 (2013) 395–398. [12] K.M. Beardmore, N. Grønbech-Jensen, Efficient molecular dynamics scheme for the calculation of dopant profiles due to ion implantation, Phys. Rev. B 57 (1997) 7278–7287. [13] H.J. Limbach, A. Arnold, B.A. Mann, C. Holm, ESPResSo-an extensible simulation package for research on soft matter systems, Comput. Phys. Commun. 174 (2006) 704–727. [14] K.F. Garrity, J.W. Bennett, K.M. Rabe, D. Vanderbilt, Pseudopotentials for highthroughput DFT calculations, Comput. Mater. Sci. 81 (2014) 446–452. [15] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. [16] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13 (1976) 5188–5192. [17] J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23 (1981) 5048–5079. [18] A. Marini, C. Hogan, M. Gruning, D. Varsano, Yambo: an ab initio tool for excited state calculations, Comput. Phys. Comm. 180 (2009) 1392–1403. [19] J. Barrett, S.R.A. Bird, J.D. Donaldson, J. Silver, The Mössbauer effect in tin(II) compounds. Part XI. The spectra of cubic trihalogenostannates (II), J. Chem. Soc. A1971 (1971) 3105–3108. [20] S.K. Bose, S. Satpathy, O. Jepsen, Semiconducting CsSnBr3, Phys. Rev. B 47 (1993) 4276–4280. [21] L. Huang, W.R.L. Lambrecht, Lattice dynamics in perovskite halides CsSnX3 with X = I, Br, Cl, Phys. Rev. B 90 (2014) 195201.
Please cite this article as: S. Pramchu, et al., Surf. Coat. Technol. (2016), http://dx.doi.org/10.1016/j.surfcoat.2016.05.062