Substitution induced band structure shape tuning in hybrid perovskites (CH₃NH₃Pb_1−xSn_xI₃) for efficient solar cell applications

Abstract

Organic–inorganic hybrid perovskite compounds such as CH₃NH₃PbI₃ hold a great potential for low cost photovoltaic devices. Though CH₃NH₃PbI₃ possesses fundamental properties favorable for solar energy harvesting, environmentally safe materials with higher energy efficiency are needed for practical applications. Replacement of lead by tin is a promising solution and investigating the fundamental properties of lead and tin mixed halides is essential. In this article, we have reported electronic and optical properties by employing Density Functional Theory based first principles calculations of Sn doped methyl ammonium lead halide, CH₃NH₃Pb_1−xSn_xI₃ (x = 0, 0.25, 0.5, 0.75, 1.0). Our results reveal that tin doping narrows the optical band gap allowing absorption of visible light up to 850 nm. Tin doping at Pb sites primarily affects the composition and nature of the valence band maximum. Tin 5p induced electronic states are highly delocalized in nature and are likely to improve the mobility and possible exciton diffusion lengths of holes. Based on the results of this study, 50% Sn doping could to be useful for enhanced performance of perovskite based photovoltaics.

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1. Introduction

The renewable energy quest has taken the front-seat for the last few years as one of the most challenging problems in the scientific community. The spreading of industrialization in accordance with population growth triggers the search for a practical source of renewable energy to replace fossil fuels. Among all the possible renewable energy sources, solar energy has come out as the most promising. Crystalline silicon based solar cells are the most widely used in the field of photovoltaics. But their economic feasibility is still a bottleneck for the use of silicon-based solar cells in the long run, which necessitates finding more economic alternatives to silicon solar cells.

The organic–inorganic hybrid perovskites have opened new avenues to develop low cost and high efficiency photovoltaic devices.¹ Perovskites with the general formula MAX₃ (M = CH₃NH₃; A = Pb, Sn; X = I, Br, or Cl) have attracted significant attention as efficient light harvesters.^2,3 In particular, CH₃NH₃PbI₃ has been intensely studied over past two years for solar cell applications. CH₃NH₃PbI₃ has a direct band gap value of 1.4–1.6 eV, band energies favorable for transferring photoexcited charges across metal/semiconductor interfaces, and possess long range exciton diffusion lengths (∼200 nm).^4–8 Recent advances demonstrate that mixed halides such as CH₃NH₃PbI₂X (X = Br, Cl) could have exciton diffusion length up to a micrometer lengths.⁹ Solar cells based on the hybrid perovskites have shown efficiencies more than 15%, claiming these materials as potential candidates for next generation solar devices.¹⁰ Lead based perovskite solar cells are relatively new devices and the research work in these materials is focused on understanding the materials properties and improving the efficiency of energy conversion. Such perovskite materials are highly sensitive and decompose on the exposure to moisture or air, henceforth posing serious issues about their stabilities.¹¹ Further, CH₃NH₃PbI₃ undergoes phase transformation at 50 °C, which affects its inherent electronic properties. Most importantly, lead content in these solar harvesters is always a serious threat to the sustainable environment and human health. Therefore, efforts are needed to reduce or replace lead in these materials and further enhance their energy conversion efficiency and stability for commercial applications. Therefore, profound understanding of the fundamental optical and electronic properties is crucially important to design new materials based on hybrid perovskites.

Both lead and tin belong to the same group in the periodic table. Both cations have a lone pair of electrons and exist in M²⁺ as well as M⁴⁺ oxidation state. In the most stable form, these cations take M⁴⁺ oxidation state, while M²⁺ is considered as a metastable state. The experimental and theoretical work so far has shown that organic inorganic mixed perovskites could be crystallized using lead as well as tin. Further, Sn based materials could offer certain advantages such as lower effective mass for hole (high mobility of holes), lower band gap values for enhanced light absorption. Recent report on Sn based perovskite is really promising and opens up the possibilities for more such investigations regarding these systems.¹² Density Functional Theory (DFT) based electronic structure calculations are extremely useful to design and predict the properties of new materials systems. Solid solution could be useful in combining the useful properties of both lead and tin, enhancing the performance of the solar cell devices.

In this work, we have reported the electronic structure of solid solution of tetragonal perovskite, CH₃NH₃Pb_1−xSn_xI₃ (x = 0, 0.25, 0.50, 0.75, 1.00) using first principles based electronic structure calculations. An extensive study of crystal structure, band structure, optical properties and stability of solid solutions has been discussed. Sn doping in tetragonal CH₃NH₃PbI₃ have been investigated. We find that tin doping in CH₃NH₃PbI₃ systematically reduces its band gap to 0.94 eV and results in increased hole mobility. Our findings provide new insights on the lead and tin based perovskite systems and can be quite useful in development of new materials.

2. Methods

2.1 Computational methods

The electronic structures of hybrid perovskite system CH₃NH₃PbI₃ have been studied by Density Functional theory (DFT) based first principles calculations.^13,14 Throughout the computational modeling CASTEP (CAmbridge Series Total Energy Package) code as implemented in Materials Studio 5.0, has been used extensively.¹⁵ The Generalized Gradient Approximations (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE) is used as the exchange-correlation functional.¹⁶ An energy cutoff of 400 eV is used after checking the convergence criteria. The Monkhorst–Pack k-points mesh of 4 × 4 × 4 and 6 × 6 × 6 are found sufficient for geometry optimization of the unit cell of CH₃NH₃PbI₃ and CH₃NH₃SnI₃. In the case of Pb doping in pseudocubic CH₃NH₃SnI₃ a k-points mesh of 2 × 2 × 2 has been used. The forces on individual ions in the optimized structure are less than 0.03 eV Å⁻¹ and it has been taken as the force convergence criteria throughout the calculations. The projected density of states (pDOS) calculations is carried out using a denser k-points grid. This is the structure, we have employed our DFT based electronic structure calculations and to envisage the projected density of states and optical spectra. The complete geometry optimization i.e. atomic positions and lattice parameters (a and c) was carried out on the pristine and doped structures.

2.2 Computational models

CH₃NH₃PbI₃ is known to exist in tetragonal phase at ambient temperature and pressure. Fig. 1a and b show the crystal structure of tetragonal CH₃NH₃PbI₃ (space group no. 140, I4/mcm) and tetragonal CH₃NH₃SnI₃ (space group no. 99, P4mm). For CH₃NH₃PbI₃ the phase change from tetragonal to cubic (high symmetry) and from tetragonal to orthorhombic (low symmetry) occurs at 323 K and 140 K respectively.^13,14,17,18 The tetragonal phase has been widely studied and used in the solar harvesting devices. Similar to lead perovskite, CH₃NH₃SnI₃ is known to exist in three different phases in different temperature ranges.¹⁸ Stoumpos et al. reported a detailed study on phase changes in hybrid perovskites where CH₃NH₃SnI₃ single crystals, where tetragonal phase (pseudocubic phase) with lattice parameters, of a = 6.2017 Å, c = 6.2035 Å is stable at ambient conditions.¹⁸ Further, the authors also report a mixed phase (CH₃NH₃Pb_0.54Sn_0.46I₃) belonging to the tetragonal phase with space group no. 140.¹⁸ Therefore, in the current work we have considered tetragonal crystal structure (a = 8.8 Å, c = 12.6 Å) as starting geometry for all the systems studied. Further, the use of single phase forms a common basis to study the substitutional doping of Sn in Pb based perovskite system. CH₃NH₃SnI₃ is also known to be a light harvester and holds promise for environmental friendly solar devices.¹⁸ It is proposed that the mixed perovskites may benefit from the lower band gap values due to presence of Sn, while excellent transport properties due to presence of Pb. To study the electronic structure of pristine CH₃NH₃SnI₃, pseudocubic phase is also investigated and results are compared to tetragonal system. It is known that methyl ammonium groups have multiple degrees of freedom in low symmetry structures. However, for the purpose of simplicity we have fixed the movements of methyl ammonium ion in the lattice.

Fig. 1 Crystal structure of tetragonal CH₃NH₃PbI₃ seen from 101 and 001 directions. (Color code: black lead, brown iodide, grey carbon, blue nitrogen, and white hydrogen).

3. Results

3.1 Crystal structure

The optimized lattice parameters of CH₃NH₃PbI₃ a = 9.1.85 and c = 13.39 Å are in good agreement with the experimental reports as well as other DFT studies.¹⁸ The lattice parameters are approximately 5% larger than the experimental system, which is commonly observed in DFT studies. The average bond lengths of Pb–I in PbI₆ octahedra were 3.25 Å and tilting angle of I–Pb–I is found to be 178.33°. It has been seen that when Sn is substituted at Pb site, the cell volume is decreased along with the decrement of both a and c values. The decrease in lattice parameters agree well with the ionic radii of the cations viz. Pb and Sn and with the experimentally reported lattice parameters of CH₃NH₃PbI₃ and CH₃NH₃SnI₃ belonging to tetragonal phase. Further, substitution of Sn in CH₃NH₃PbI₃ has been resulted in increased formation energy. The increment in the total energy is linear with the doping concentration. It is noted that lead halide has lower energy than corresponding tin halide.

3.2 Density of states (DOS)

Several computational studies have been reported on hybrid perovskites.^19,20 Earlier study shows the effective masses are favorable for solar harvesting.²¹ In particular, relativistic GW calculations with spin orbit coupling have been applied to CH₃NH₃PbI₃.²² Relativistic approach yields the correct values of effective mass of electrons and holes. Further, studies have shown that effects of spin orbit coupling (SOC) on the band structure are significant and SOC incorporation in DFT calculations places the band energies at correct locations.²³ In the present work the focus is on exploring new efficient material systems. In this case, relativistic consideration in band structure calculations could be computationally expensive. Our aim is to shed light on the electronic and optical properties of new materials systems which would be useful in experimental designing. Therefore, we have carried out calculations using GGA-PBE functional. In the case, perovskite lead halide, the band gap values obtained by GGA-PBE are well comparable to the experimental values.

Fig. 2 shows the density of states of CH₃NH₃PbI₃. The calculated band gap of 1.65 eV agrees well with the experimental value as well as with the other DFT reports. Partial density of states (PDOS) analysis shows that VB is mainly contributed by I 5p while the contributions to CB are predominantly by Pb 6p. Site decomposed DOS show the contributions of methyl ammonium (MA) group in the valence band is significantly less as compared to that of iodine. Further, MA induced energy states are located deep in the CB at around 4.5 eV and not in the CBM. The density of states (DOS) analysis shows that in the valence band maximum, no significant overlap between Pb 6p and I 5p exists. This indicates weak bonding between Pb and I in PbI₆ octahedra. CH₃NH₃PbI₃ has a direct band gap where, the maxima and minima occur at Γ (0.0, 0.0, 0.0) point in the reciprocal space, as been depicted in the band structure plots (Fig. 6a).

Fig. 2 Total and site decomposed density of states (DOS) of tetragonal CH₃NH₃PbI₃ (dotted black total, green d, blue p, red s).

Fig. 3 shows the total density of states (DOS) plots of Sn doped CH₃NH₃PbI₃. The DOS plots show that Sn induced energy states have been appeared above the VBM changing its shape. Sn doping decreases the band gap value of CH₃NH₃PbI₃ and the decrease in band gap is proportional to the doping concentration. However, two clear trends are seen from the data. Sn doping up to 50% results in larger narrowing of the band gap, as compared to those more than 50%. It is noted that the effect of Sn doping on the phase of the perovskite is not considered in this study. Earlier experimental reports show that tetragonal phase could be obtained up to 50% Sn doped in lead halide.¹⁸

Fig. 3 Total density of states (DOS) of CH₃NH₃Pb_1−xSn_xI₃ (x = 0.25, 0.50, 0.75, and 1.0) (dotted black total, green d, blue p, red s).

Sn induced energy states appear as a shoulder to the VB and are mainly composed of 5p orbitals. The width and number of states increase with the increase in concentration thereby reducing the effective band gap value and increasing the visible light absorption. The effect of doping of Sn on the band gap values of CH₃NH₃PbI₃ is shown in Fig. 4. Fig. 5 shows the site decomposed DOS in Sn doped perovskite. It is clear that Sn 5s energy states appear above the VBM, significantly changing its shape. With the increase in concentration, Sn 5s contributions in the VBM have been increased. Further, Sn 5p energy states appear in the CBM, overlapping with Pb 6p energy states. The contributions of Sn 5p in the CBM are significantly greater than that of Sn 5s in the VBM. Both Pb and Sn show a similar trend in terms of band composition (CB dominated by Pb/Sn p orbitals) and lesser overlap with iodine 5p energy states.

Fig. 4 Calculated band gap values of CH₃NH₃Pb_1−xSn_xI₃ (x = 0.0, 0.25, 0.50, 0.75, and 1.0).

Fig. 5 Partial density of states (DOS) highlighting the contributions of Sn in CH₃NH₃Pb_1−xSn_xI₃ (x = 0.25, 0.50, and 0.75). Color code (dotted black total, green I 5p, red Pb 6p, black Pb 6s, yellow Sn 5s, blue Sn 5p).

3.3 Band structure

The valence band structure of all the systems has been investigated in detail to understand the effect of Sn doping on the electronic properties of the considered hybrid perovskites. The band structure of the pristine CH₃NH₃PbI₃ shows significant fluctuations in the CB, while the VB is relatively flat. The shape of bands in CH₃NH₃PbI₃ indicates that the electrons are lighter than the holes. However, when Sn is substituted at Pb site, the VB of the doped halide gradually becomes more fluctuating as seen in Fig. 6.

Fig. 6 Band structure plots of CH₃NH₃Pb_1−xSn_xI₃ (x = 0.0, 0.25, 0.50, 0.75, and 1.0), showing changes in the shape of VB.

In this work, we have qualitatively predicted the effective mass of hole and electron from the shape of the valence band and conduction band. The effective mass of the carrier (electron/hole) can be determined by solving the eqn (2), which originates from the dispersion relation at the band maxima (or minima) as approximated by the parabola (eqn (1))

E_n(k⃑) = α₁k_x² + α₂k_y² + α₃k_z² (1)

The eigenvalue of the tensor is an inverse of the effective mass and the eigenvector is the direction of the effective mass. Hence, one can scan through all possible k-point of the band structure in order to find the values of the effective mass. Therefore, the nature of the valence band and the conduction band is quite important in order to have the qualitative argument about the effective mass since the value depends on the curvature of the specific band.

The minor changes in the shape of the CB occur upon Sn doping. The shape of the bands clearly shows that Sn doping significantly qualitatively reduces the effective mass of the holes, while the effective mass of the electrons remains unchanged. It is known that the effective mass plays a critical role in the exciton diffusion length of photoexcited charges, which in turn favors the separation of electrons and holes. In the case of hybrid perovskites, longer diffusion length is the key to high energy conversion efficiency. The results of band structure analysis clearly show that the mixed tin and lead halides offer lower effective mass for both electrons and holes. Earlier experimental reports suggest that mixed are could be stable up to 50% doping. Therefore, mixing of tin and lead is beneficial for high performance photovoltaic.

3.4 Band edge alignment and optical spectra

The analysis of DOS indicates that Sn doping pushes the VB hybrid of perovskite to more negative values into the band gap. Fig. 7 shows the estimated band alignment of the doped hybrid perovskites, based on the DOS position of Sn and band gap values. Such band alignment is favorable for TiO₂ or grapheme interface, which are currently used.⁷ As CB potential is not changed significantly, the thermodynamics of electron transfer from light harvester to electron receiver such as TiO₂, is not affected. Fig. 8 shows the theoretically predicted optical absorption spectra of Sn doped systems. The absorption spectra of pristine lead halide agree well with the previously reported results.^24,25 Strong absorption peaks around 550 nm and 700 nm appear in the spectrum, which correspond to near band gap value of this phase. It is observed that absorption peak shifts to higher wavelength values as Sn doping concentration increases. Sn doping enhances the absorption peak around 700 nm significantly. The absorption spectra clearly indicate that Sn doping increase the visible light absorption, which could be favorable for increasing solar cell performance.

Fig. 7 Estimated band alignment of MAPbI₃, CH₃NH₃Pb_1−xSn_xI₃ (x = 0.25, 0.50, and 0.75), and MASnI₃.

Fig. 8 Estimated optical absorption spectra of CH₃NH₃Pb_1−xSn_xI₃ (x = 0.0, 0.25, 0.50, 0.75, and 1.0).

4. Conclusions

We have studied the effect of Sn doping, CH₃NH₃Pb_1−xSn_xI₃ (x = 0.25, 0.50, and 0.75), on the optical and electronic properties of methyl ammonium lead halide based of DFT based electronic structure calculations. Our results show that Sn doping is favourable for band gap narrowing, and extending visible light response and absorption of photons up to 850 nm. In addition to changing the composition in the hybrid perovskite system, Sn doping also changes the shape of valence band maximum by producing extra energy states above the VBM and is responsible for lowering the effective mass of holes (delocalized energy states than Pb). This improves the hole mobility that leads to the exciton diffusion length increment, which is beneficial for charge separation in these type of hybrid materials. The prime outcome of this work is to find the optimum doping concentration of Sn–Pb, which is 50% in order to achieve a perovskite based photovoltaic with higher efficiencies. The focus of this study is to see the fundamental reasoning behind the qualitative effective mass changing from the perspective of the valence and conduction band nature, with respect to the Sn substitution of Pb. From the practicality concerned, specially regarding the stability issue, one can play with the halogen substitution with other halogens or superhalogens for that matter along with reasonable power conversion efficiency. The organic part of the hybrid perovskite can also be replaced with completely inorganic functional owing to the enhanced stability and efficiency both at the same time. All these possibilities open up an extensive research with the ongoing feedback between theory and experiment.

Acknowledgements

SC and RA would like to acknowledge the Carl Tryggers Stiftelse for Vetenskaplig Forskning (CTS), Swedish Research Council (VR) for financial support. CJR acknowledges Brazilian agencies CAPES and CNPq. ZC acknowledges financial support from the National Research Foundation (NRF) Singapore through its Campus for Research Excellence and Technological Enterprise (CREATE) program SNIC, HPC2N and UPPMAX are acknowledged for providing computing time.

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