1 Introduction

The rate of population growth and increase in industrialization are reflected in the energy demand for day-to-day activities. Due to the number of years required to replenish the fossil fuels and the effects they pose to the environment, the search for viable renewable energy resources is of very importance. Solar energy is one of the most promising sources due to its availability. Currently, our market is dominated by silicon solar cells. These cells are suffering from the high cost in production and installation which leads to a long payback time in many areas and hence in one way or another tends to lower their widespread use.

Efforts have been made to find cheaper materials to replace silicon. Perovskite materials have recently gained popularity due to their higher power conversion efficiency (PCE) as compared to silicon [1,2,3]. The term ‘organic-metal-halide pervoskites’ describes materials of the formula ABX3 where A stands for an organic cation, B for metal ion and X is a halide (Cl, Br, I). The hybrid perovskites are peculiar due to their lower cost, possession of strong optical absorption, high charge carrier mobility, and low temperature vapor assisted solution based processing; the cells based on perovskites have also a high power conversion efficiency, a good potential to attain a stable structure with long carrier-diffusion length [4,5,6]. Kojima et al. [7] were the first who reported that perovskites solar cells possess as high PCE as 3.9%. Later it was reported on even greater efficiencies of lead perovskite solar cells: 6.5% [8], 17.9% [9,10,11] then to over 22.7% [12,13,14].

Lead perovskite materials have drawn significant attention of researchers because of the high ability to convert the energy from the sun to electricity as compared to silicon materials. In the other fields of research, the perovskites have been widely applied in electrodes [15], high temperature superconductors [16], wearable electronics [17], optoelectronics (sensors, LEDs) [16, 18], fuel cells and as oxygen carriers [19, 20] and thermoelectric materials [21]. The toxicity issue of lead among other issues has been a challenge in commercializing the lead perovskites and so banned from numerous technical applications in many countries [13, 22]. Alternatives to Pb, such as Sn, Ge, Cu, Bi, and Sb, have been explored [9, 13, 22]. Tin-based perovskites have shown excellent mobility in transistors [23] which gives them an opportunity to be explored more for solar cell applications. Both tin and lead belong to the same group all having similar valence configuration. Tin has shown some exceptional properties like having a smaller effective mass of holes as compared to lead and narrower bandgap which is useful in more photons absorption [24, 25]. A study by Umari and coworkers [25] has shown that CH3NH3SnI3 has high potential in delivering high photocurrent density due to its reduced band gap when compared to CH3NH3PbI3.

Different phases of the CH3NH3SnI3 perovskite have been investigated including the cubic [22, 26,27,28,29], tetragonal [9, 19, 25, 26, 30, 31] and orthorhombic (O-phase) [32,33,34]. From the experimental data, the phase transitions are discovered through the temperature dependence of the single-crystal resistivity [35] as well as from the photoluminescence and absorption spectra measured in the temperature range between 8 and 295 K [36], the CH3NH3SnI3 phase transitions occur at ~ 110 K, O-phase to tetragonal, and at ~ 275 K, tetragonal to cubic.

The characteristics of each phase are of importance because of phase transformations in the perovskite when subjected to different temperatures as observed for the methylammonium lead perovskite [36,37,38,39,40,41]. This study aimed at investigation of structural, electronic and thermodynamic properties of the O-phase of the methylammonium tin perovskite using different theoretical approaches to understand the photovoltaic performance of the material. The O-phase was chosen due to the results of the experimental study by Peng and Xu [24] that the power conversion efficiency of the O-phase CH3NH3SnI3 solar cells was higher compared to that of the tetragonal.

2 Methodology

Simulation of methylammonium tin iodide (CH3NH3SnI3) was done using the Quantum ESPRESSO Software package (QE) [42]. The Crystallographic Information Files of CH3NH3SnI3 were obtained from the Crystallography Open Database [43, 44] and Materials Project [45] which are free databases for crystal structures. The input files for QE were generated as described by the software manual [42]. The initial data for this simulation were generated through convergence tests on the structure done by self-consistent field (SCF) calculations to determine the convergence of the plane wave cut-off (ecutwfc), lattice parameters as well as the charge density cut-off (ecutrho) with the total energy. The ultrasoft pseudopotentials were employed with three different exchange–correlation (XC) functionals, i.e. Perdew, Burke and Ernzerhof (PBE) [46], Local Density Approximation (LDA) [47], and Perdew-Burke-Ernzerhof revised for solids (PBEsol) [48]. The ecutwfc and ecutrho were obtained through convergence tests as 50 with 450 Ry, 60 with 600 Ry and 70 with 490 Ry, for the LDA, PBE, and PBEsol functionals, respectively.

Brillouin zone sampling was performed as described by Hinuma et al. [49] and Setyawan and Curtarolo [50] for orthorhombic structures. The cell relaxation (cell optimization) was conducted as described by the Quantum ESPRESSO input file [42, 51] following the Broyden-Fletcher-Goldfarb-Shanno algorithm. The cell parameters and atomic positions of the structure were relaxed with each XC functional to a force convergence threshold of 1.0E-04 Ry/Bohr and energy convergence threshold of 1.0E-08 Ry which were enough to obtain a relaxed structure [42, 51]. Additionally, the ultrasoft pseudopotentials from QE database corresponding to the three exchange–correlation functionals (LDA, PBE, and PBEsol) were used for the band structures and density of states calculation.

3 Results and discussion

3.1 Structural parameters

An orthorhombic phase of CH3NH3SnI3 with 48 atoms per cell was considered. Both the original structure from the database (before optimization) and optimized structures were simulated using the same values for ecutwfc and ecutrho to check the relevance of optimizing structures before simulation. The software, VESTA [52] and XCrySDen [53] were used to view the structures before and after optimization. The structure contains a network of corner-sharing of [SnI6] octahedrons with the Sn-site cations and iodide anions, and the organic cation [CH3NH3]+ which is located in between the octahedral corners (Fig. 1). The lattice parameters before and after optimization are compared as listed in Table 1. There was no noticeable deformation of the structures during the structural relaxation, only a slight change can be observed on the lattice parameters and volume of the cell.

Fig. 1
figure 1

The unit cell of the orthorhombic phase of CH3NH3SnI3 visualization by VESTA [52] as balls and sticks (a) and polyhedral style (b)

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Table 1 The calculated lattice parameters and energy gap of the orthorhombic phase of CH3NH3SnI3 hybrid halide perovskite
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The relationship between the energy and volume of the orthorhombic perovskite cell is represented by the energy-volume diagram (Fig. 2); the PBE XC functional results to the minimum energy at the volume 1011.44 Å3 (Table 1).

Fig. 2
figure 2

Energy–volume diagram for the orthorhombic CH3NH3SnI3 cell using PBE

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3.2 Electronic properties

The electronic structures of the hybrid halide perovskites are of crucial factors that need to be explored because these materials have the potential application as a light-harvesting medium. The calculated band structures of the non-optimized and optimized orthorhombic CH3NH3SnI3 crystals along the high-symmetry lines in the first Brillouin zone are presented in Figs. 3, 4, 5 and 6.

Fig. 3
figure 3

The band structure and PDOS of original orthorhombic CH3NH3SnI3 simulated with the PBE XC functional

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Fig. 4
figure 4

The band structure and PDOS of optimized orthorhombic CH3NH3SnI3 simulated with the LDA XC functional

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Fig. 5
figure 5

The band structure and PDOS of optimized orthorhombic CH3NH3SnI3 simulated with the PBE XC functional

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Fig. 6
figure 6

The band structure and PDOS of optimized orthorhombic simulated with the PBEsol XC functional

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The orthorhombic crystal has a direct bandgap at Γ symmetry points with different calculated bandgap energies from the LDA, PBE, and PBEsol DFT functionals. The Fermi levels for the three exchange–correlation functionals are all located between the valence band maxima and the conduction band minima of the material. They were tuned to zero at the valence band maxima for proper visualization of the bandgap. As is seen, the different values of Eg result from the LDA, PBE, and PBEsol DFT functionals. The bandgap energies for the optimized CH3NH3SnI3 structure, to the best accuracy of the XC functionals, are obtained: 1.12 eV (PBE) and 0.98 eV (PBEsol), which are comparable to the experimental data 1.2–1.35 eV [29, 44]. The LDA functional brings to the Eg = 0.46 eV which is much lower than experimental. This result is not surprising because generally, the LDA XC functional from standard DFT has been found to underestimate the bandgap energies of solid-state semiconductors and insulators by about 40% [55, 56] which originates from assigning physical meaning to the Kohn–Sham energy levels rather than from intrinsic errors of the DFT methods [57]. For the non-optimized O-phase, the PBE and PBEsol functionals result in the bandgaps 0.88 eV and 0.82 eV, respectively, these values are substantially underestimated that apparently indicates the need to relax the crystal structure before calculating electronic properties. It is interesting to note that other DFT studies [24, 32, 34, 54] of the CH3NH3SnI3 orthorhombic structure conducted using different XC functionals reported bandgap values in a broad range, between 0.6 and 1.7 eV (Table 1).

3.3 Density of states

The total projected density of states (TPDOS) and the projected density of states (PDOS) of the orthorhombic CH3NH3SnI3 were calculated using the projwfc.x code implemented in the QE package. The PDOS displays the interaction of the orbitals for interpretation of the bonding mechanisms between the atoms in the system (Figs. 3, 4, 5, 6, right-hand side). A higher density of states can be seen distributed in the valence band of the perovskite which indicates that the CH3NH3SnI3 perovskite belongs to the family of semiconductors. The analysis provides a better understanding of the bandgap variations which is influenced by the electronic states of the Sn and I atoms. The 5p-states of the I atoms are the main contributors to the valence band maxima with a slight overlapping with the 5s-states of tin. On the other hand, the conduction band is populated by the 5p-states of Sn atoms responsible for formation of the conduction band minima with small contribution from the 5p-states of the iodine atoms. In general, the location of the Fermi level in between the valence band and conduction band is governed by the electron density of the p-states of tin and iodine atoms in the perovskite.

3.4 Thermodynamic properties

The energy of decomposition reaction and enthalpy of formation of photovoltaic materials are essential in determining the stability of materials when subjected to moisture, light, and heat. Both tin and lead halide perovskites basing on methylammonium experience a rapid conversion to the halides under the conditions of high humidity [58, 59].

The decomposition of the CH3NH3SnI3 into the solid state products may proceed as follows:

$${\text{CH}}_{3} {\text{NH}}_{3} {\text{SnI}}_{3} \left( {\text{s}} \right) = {\text{CH}}_{3} {\text{NH}}_{3} {\text{I}}\left( {\text{s}} \right) + {\text{SnI}}_{2} \left( {\text{s}} \right).$$
(1)

The energy of this reaction ΔrE was found through the total energies E of the components:

$$\Delta_{{\text{r}}} E = E\left( {{\text{CH}}_{3} {\text{NH}}_{3} {\text{I}}} \right) + E\left( {{\text{SnI}}_{2} } \right){-}E\left( {{\text{CH}}_{3} {\text{NH}}_{3} {\text{SnI}}_{3} } \right).$$
(2)

The total energies E were computed for the relaxed structures of the participants using the three DFT XC functionals (Table 2). As is seen, the XC functional affects significantly the calculated values of ΔrE: − 22 kJ mol−1 (LDA), 37 kJ mol−1 (PBE) and 9 kJ mol−1 (PBEsol). It is known that the orthorhombic CH3NH3SnI3 is stable at temperature below 110 K [35, 36], hence the result from PBE seems most reasonable.

Table 2 Thermodynamic characteristics of decomposition reaction (1)
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Based on the ΔrE, the enthalpy of formation of the O-phase perovskite can be determined through the enthalpies of formation of the precursors:

$$\Delta _{{\text{f}}} H {^\circ }\left( {{\text{CH}}_{3} {\text{NH}}_{3} {\text{SnI}}_{3} ,{\text{s}},0\,{\text{K}}} \right) = \Delta _{{\text{f}}} H {^\circ }\left( {{\text{CH}}_{3} {\text{NH}}_{3} {\text{I}},{\text{s}},0\,{\text{K}}} \right) + \Delta _{{\text{f}}} H {^\circ }\left( {{\text{SnI}}_{2} ,{\text{s}},0\,K} \right){-}\Delta _{{\text{r}}} H {^\circ }\left( {0\,{\text{K}}} \right).$$
(3)

The reference values are available: ΔfH° (SnI2, s, 0 K) =  − 152.4 kJ mol−1 [60] and ΔfH° (CH3NH3I, s, 298 K) =  − 200.7 kJ mol−1 [61]. Assuming that correction on lattice vibration energies is negligible for the reaction (1), we accept ΔrH° (0 K) ≈ ΔrE. In addition, we suggest that the enthalpy increment H° (298) − H° (0) for CH3NH3I does not exceed few kJ mol−1. Similar assumptions were opinioned by Ciccioli, Latini [62] for the decomposition of lead perovskites CH3NH3PbX3(s) = CH3NH3X(s) + PbI2(s), X = Cl, Br, I. Thus we obtained the enthalpy of formation of the O-phase tin perovskite CH3NH3SnI3 (Table 2). As it was discussed in the previous sections, the PBE XC functional outperformed the other two in evaluation of the electronic properties, therefore we consider the ΔrH° (0 K) = 37 kJ mol−1 and ΔfH° (CH3NH3SnI3, 0 K) =  − 390 kJ mol−1 to be reliable values.

It is worth to compare these results with the literature data for the lead perovskite. For the tetragonal phase of CH3NH3PbI3, the enthalpy of decomposition reaction ΔrH° (298 K) = 34.5 ± 1.0 kJ mol−1 was determined by solution calorimetry [59]. Using the enthalpy of formation ΔfH° (PbI2, s, 298 K) =  − 176 kJ mol−1 [60] the enthalpy of formation of the lead perovskite can be found as ΔfH° (CH3NH3PbI3, s, 298 K) =  − 411 kJ mol−1. Taking into account the phase transition enthalpy from tetragonal to orthorhombic 3 kJ mol−1 [63] and neglecting the enthalpy increment H° (298) − H° (0), we estimated the ΔfH° (CH3NH3PbI3, O-phase, 0 K) ≈ − 414 kJ mol−1. Compared to this value, our result for the enthalpy of formation of the tin perovskite (− 390 kJ mol−1) is in a good accordance. Moreover, it is interesting to note that the difference in ΔfH° between tin and lead perovskites (24 kJ mol−1) appeared to be almost equal to that between SnI2 and PbI2 (23 kJ mol−1), this equality also advocates correctness of our result.

4 Conclusion

Different exchange–correlation functionals LDA, PBE, and PBEsol have been used to study the structural, electronic and thermodynamic properties of the O-phase of the CH3NH3SnI3 perovskite. The PBE XC functional outperformed the LDA and PBEsol in estimating the electronic and thermodynamic properties of the perovskite. It was found that for the optimized structure, the bandgap determined by the PBE XC functional (1.12 eV), was much closer to the experimental value (1.2 eV) when compared to the other two. In addition, importance of the crystal structure relaxation procedure, before calculating electronic properties, was corroborated. From the projected density of states, it is observed that the valence band is mostly occupied with 5p-electrons of the iodine atoms and the conduction band with 5p-electrons of the tin atoms. Considering the thermodynamic characteristics of the decomposition reaction, the methylammonium tin iodide perovskite is confirmed to be stable material at low temperature that is in accordance with literature data on phase transformations in the crystals.