Effect of surface termination on electronic and optical properties of lead-free tin-based eco-friendly perovskite solar cell: a first principal study

The lead (Pb)-based halide perovskites have been reported to be promising materials for photovoltaic applications; however, the presence of toxic lead in them concerns the environmental and health issues. In this work, we have, therefore, studied the lead-free and non-toxic tin-based halide perovskite, CsSnI3, which is an eco-friendly material with high power conversion efficiency, thus, being a potential candidate for photovoltaic applications. We have investigated the influence of CsI and SnI2-terminated (001) surfaces on structural, electronic and optical properties of lead-free tin-based halide perovskite CsSnI3 from the first principal calculations, based on density functional theory (DFT). The calculations of electronic and optical parameters are performed under the parameterisation of PBE_Sol for exchange–correlation functions conjugated with modified- Beche-Johnshon (mBJ) exchange potential. The optimised lattice constant, the energy band structure and the density of states (DOS) have been calculated for the bulk and different terminated surface structures. The optical properties of CsSnI3 are computed in terms of the real and imaginary part of absorption coefficient, dielectric function, refractive index, conductivity, reflectivity, extinction coefficient and electron energy loss. The photovoltaic characteristics for the CsI-termination are found to be better than the bulk and SnI2-terminated surfaces. This study reveals that optical and electronic properties can be tuned by selecting proper surface termination in halide perovskite CsSnI3. The CsSnI3 surfaces exhibit semiconductor behaviour with a direct energy band gap and a high value of absorption power in the ultraviolet and visible region, rendering these inorganic halide perovskite materials important for the eco-friendly and efficient optoelectronic devices.


Introduction
The photovoltaic solar cell (PVSC) materials have been emerging as breakthrough materials in renewable energy generation because of their low cost and high conversion efficiency of power (Wang et al. 2022a, b;Jiyuan et al. 2022;Kim et al. 2020;Sheng et al. 2021;Zhou et al. 2014).As far as the environmental and health issues are concerned, the renewable energy is the best alternative as it reduces the air, water and soil pollution which are severe threats for the environment.The organic-inorganic lead-based halide perovskite solar cell have suitable photovoltaic properties, such as high value of carrier mobility, long range charge diffusion length, high absorption coefficient, tuneable direct band gap and high-power conversion efficiency (Li et al. 2017;Zarenezhad et al. 2020).However, the high toxicity of lead contained in them has been the main concern for the environmental and health issues.Due to higher water solubility, the lead-based perovskites slowly accumulate in food chain and then in the human body.Also, their instability against the moisture, rain, heat, oxygen, electric field and light affects their performance adversely (Wang et al. 2017;Kim et al. 2016;Soufiani et al. 2016;Hailegnaw et al. 2015;Dong et al. 2016).Moreover, the pure organic perovskite solar cells are intrinsically unstable for outdoor applications due to the fragmentation of their organic components (Wang et al. 2021;Azmi et al. 2020).For the environment friendly and highly efficient optoelectronic devices, the elaboration of lead-free pure inorganic perovskite solar cells is highly recommended.The similar elemental analogue and a non-toxic and eco-friendly element Sn is the most suitable replacement for Pb in the perovskite structure.As per the literature survey, though there are lots of other emergent Pbfree perovskites too, however, most of them face limitations as compared to the Sn-based perovskites (Yang et al. 2017).Likewise, the Bi-based PVSCs are also Pb-free perovskites, used in the solar cell applications, but they are reported to suffer from low Jsc.Furthermore, other Bi-based perovskites, i.e.A 3 Bi 3 I 9 (A: K, Rh, NH 4+ ) family have also been well investigated, which have a 2-D type structure (Lehner et al. 2015;Sun et al. 2016a, b); however, no reported application has been found in the PVSCs of these 2-D type materials.Furthermore, another Pb-free perovskite, i.e.CsGeI 3 is reported to be also suitable for the fabrication of solar cells because of its utmost ideal bandgap of 1.6 eV, but, unfortunately, CsGeI 3 -based solar cell suffers from poor efficiency of 0.20% with a low Voc (Yang et al. 2017).Now coming to another Pb-free perovskite family, i.e. the organic-inorganic perovskite MAGeX 3 (X: Cl, Br, I) family, the MAGeI 3 amongst them is reported to be the most potential perovskite for fabrication of solar cells due to its properties being similar to the MAPbI 3 perovskite.However, the Ge 2+ is reported to be more sensitive to oxygen than the Sn 2+ , which is not appropriate for the practical applications (Sun et al. 2016a, b).Antimony-based perovskite Cs 3 Sb 3 I 9 having a band gap of 2.05 eV has also been explored.Though the DFT results indicate that the valence band maximum (VBM) and the condensed band minimum (CBM) of Cs 3 Sb 3 I 9 are quite similar to the MAPbI 3 perovskite family, though it has suffered from deep trap states, resulting in a poor performance from the point of view of its device applications (Yang et al. 2017).
Further, the divalent cations Sr 2+ and Ca 2+ are also able to form perovskites, which are chemically more stable than the Sn 2+ and the Ge 2+ ; however, both the CH 3 NH 3 SrI 3 and CH 3 NH 3 CaI 3 perovskites have been reported to have a large band gap (above 3.5 eV), which render them unsuitable for the solar cell-based devices (Jacobsson et al. 2015;Uribe et al. 2016).Tin-based perovskite solar cell has witnessed tremendous focus in the past years.Raghvendra et al. (2021) studied the effect of relative permittivity (ε r ), carrier lifetime (τ) and thickness on the performance of solar cells.The maximum efficiency was obtained for high τ (> 50 ns).They show that with optimised absorber properties, power conversion efficiency (PCE) of 17.33% was achieved.Shubham et al. (2021) studied a core-shell ZnO nanorod-based lead-free perovskite solar cell.Various factors affecting the performance of solar cells, like the length and diameter of the ZnO nano-rod core, perovskite shell thickness, and thickness of perovskite cap layer were investigated by them for device optimisation; The defect density of states in the perovskite absorber layer and the effect of interface defect density on the performance of the cell are also studied.They reported power conversion efficiency of 14.50%, the open-circuit voltage (V OC ) of 0.96 V.They also analysed the effect of the inclination of nano-rods on the performance of the cell.By optimising the device parameters, they achieved a power conversion efficiency of 21.27% and V OC of 0.97 V at an inclination of 10-degree tilt with respect to the incident light.
Thus, it can be concluded that the Sn-based perovskites may be good candidates to replace the Pb-based perovskites as they show the opto-electronic properties similar to the Pb-based perovskite and possess additional advantages like higher carrier mobility, lower optical bandgaps (1.2-1.4 eV) and lesser toxicity than the Pb-based perovskites.These factors make them potential contenders for the lead-free perovskite applications (Wang et al. 2021).Also, some recent studies have shown that inorganic perovskite CsSnI 3 has superior intrinsic thermal stability, higher absorption at shorter wavelength, high value of hole mobility, and high value of melting point and relatively easier to be synthesised (Wang et al. 2022a;Yua et al. 2022;Lin et al. 2021).
Usually, the surface termination and dimensionality of materials influence their electronic and optical properties.Recent studies on inorganic-organic perovskite surfaces have shown that surface termination is a key factor that affects their electronic and optical properties to a great extent (Xiao et al. 2017;Liu et al. 2016;Keil et al. 2017).Based on hybrid density functional theory (DFT) calculations on CsPbX 3 nanostructures, Di Liberto et al. (2021) reported that the role of surface termination is a key aspect in determining their electronic properties.Also, they considered the quantum size (thickness) of the 2D slabs and showed that these nanostructures exhibit significant quantum size effects, and the band gap was found to increase by decreasing the thickness of the slabs.Such type of effect has been observed experimentally also both in the 2D nanostructures and the 0D ones, such as the nano-platelets, the nano-cubes and the dots.
A survey of the literature reveals that pure inorganic halide perovskite surface terminations are quite less studied systems (Zhuo-Liang et al. 2018).In view of the above discussed facts, we were motivated to study the effect of CsI and SnI 2 -terminated (001) surfaces on the structural, electronic and optical properties of the lead-free and non-toxic tin-based halide perovskite CsSnI 3 from the first principal calculation based on DFT.The results show that CsSnI 3 in the bulk and surfaces exhibits semiconducting behaviour with a direct energy band gap and a high value of absorption power in the ultraviolet and the visible range.The study also reveals that optical and electronic properties of this tin-based organic halide perovskite can be tuned by selecting proper surface termination, rendering it an important system for the photovoltaic and opto-electronic devices.

Computational details
We have chosen the cubic CsSnI 3 system in bulk form which exhibits pm-3 m space group symmetry.The nonpolar (001) surfaces of CsSnI 3 were chosen for the study due to the fact that these comprise of alternate of stacking up of the CsI and SnI 2 planes.The different terminated (001) surfaces of CsSnI 3 are constructed by using Structureditor programme invoked in WIEN2k code.The full potential linearised augmented plane wave (FP-LAPW) is used to set out the core valence interaction within the framework of DFT.The exchange correlations have been treated using the Perdew, Burke and Ernzerof (PBE-Sol) within the generalised gradient approximation (GGA).This approximation potential was corrected employing an advance technique known as modified-Beche-Johnshon (mBJ) exchange potential.The Muffin Tin sphere radii (R MT ) of Cs, Sn and I were taken to be 2.5 a.u. to avoid the possibility of charge leakages.The R MT K max was chosen to be 7, where R MT is the smallest muffin tin radius.The energy threshold value between the core and the valence energy states was taken to − 6 Ry.The value of Fourier expression (G max ) was set equal to 12 a.u.We constructed CsI-termination and SnI 2 -termination (001) surfaces in two different slabs and also added the vacuum of 30 Å to avoid the possibility of any interaction with the adjacent slabs.The calculations for the bulk and the (001) surfaces were performed with electron charge 10 −5 e, and 10 −4 Ry energy and 1 mRy force minimisation for the self-consistence force convergence.

Structural Properties
The structural parameters such as the ground state energy (E 0 ) and the lattice constant (a 0 ) of the perovskite CsSnI 3 have been obtained by optimisation of the unit cell energy as a function of the unit cell volume.In the optimisation process, the total energy of the unit cell of bulk CsSnI 3 is obtained by varying the unit cell volume and then plotted against corresponding energy according to Murnaghan's equation of state: In the above equation, E 0 represents the minimum ground state energy corresponding to 0 K, B represents the bulk modulus, B p is the pressure derivative bulk modulus and V 0 is the equilibrium volume.
The optimisation curve for the bulk CsSnI 3 is displayed in Fig. 1.The obtained values of lattice constant (a), the bulk modulus and the ground state energy E o are found to be in good agreement with the reported theoretical values (Kamat et al. 2017).The optimised value of lattice constant (6.128Å) was used for the calculation of electronic and optical properties of the CsI-termination and the SnI 2 -terminated (001) surfaces.The bulk CsSnI 3 crystallises in the cubic structure within the Pm-3 m space group symmetry.Unit cell of the bulk material consists of 5 atoms with Cs and Sn occupying (1) 1 The optimisation curve for bulk CsSnI 3 crystal structure the (1/2,1/2,1/2) and (0,0,0) positions, respectively, and I occupying the (0, 1/2, 0), (1/2, 0, 0) and (0, 0, 1/2) sites, respectively.The CsI-termination and SnI 2 -terminated (001) surfaces of CsSnI 3 have a tetragonal structure.The unit cells of the CsI-termination (001) surface of CsSnI 3 have six atoms (2Cs, 1Sn, 3I) and the SnI 2 -termination surface consists of eight atoms (2Cs, 2Sn, 4I).
The crystal and surface structures of CsSnI 3 for the bulk and the (001) surface for CsI-termination and SnI 2 -termination are shown in Fig. 2.

Electronic properties
The electronic properties of the bulk as well as the CsItermination and SnI 2 -termination (001) surfaces of CsSnI 3 are analysed in terms of DFT and band structure.The band structure diagrams for the bulk, the CsI-termination and the SnI 2 -termination (001) surface of CsSnI 2 are plotted in Fig. 3.In the band structure plots, the energy (E) versus wave vector (K) corresponding to the high symmetry points X, Y, V and Г within the first Brillouin zone boundary have been plotted.Figure 4   SnI 2 -terminated (001) surfaces are found to be 1.21 eV and 1.07 eV, respectively.It can be seen that the values of band gap in both the surfaces show an increment as compared to their bulk counterparts.Generally, the DFT calculations have been found to show remarkable variations in the value of band gaps as the band gap highly depends upon the type of exchange-correlation potentials used in the DFT calculations.For example, Liu and Zhang (2020) studied the optoelectronic properties of CsMI 3 (M = Ge, Sn, Pb) using the DFT calculations over gradient approximation GGA within the Perdew-Burke-Ernzerhof (PBE) and found the band gap to be 0.44 eV for CsSnI 3 perovskite.Traoré et al. (2019) found the value of band gap to be 0.03 eV and 1.21 eV for CsSnI 3 by applying local density approximation (LDA) and Tran-Blaha modified Becke-Jonhnson (TB-mBJ) potential, respectively.However, in our case, the value of band gap is found to be 0.82 eV for the bulk CsSnI 3 through the PBE_Sol method with mBj exchange potential.
The increase of band gap in surface termination of CsSnI 3 is due to decrement in volume as compared to the bulk state of CsSnI 3 .Additionally, in case of the surface terminations, which have thickness of a few nano-metres, the band gap is also increased on surface termination due to the quantum confinement effect, in comparison to their bulk state.It is also reported that quantum confinement of the electronic particles produces some unique electronic and optical properties in the nano-particles systems that have the prospective to boost the power conversion efficiency of the solar cell (Cao et al. 2020).We have used the mBj exchange potential to calculate the band gap for better results.Our calculated band gap results of bulk sample are in a fair agreement with the reported theoretical results (Zhao et al. 2020).

Optical properties
The optical properties of the samples are described in terms of parameters like dielectric constant, refractive index and electrical conductivity.All these calculated parameters are function of energy of electromagnetic radiations.The complex dielectric function, in the form ε = ε1 + iε2, is the most important function and explains the complete response of the material regarding the disturbance caused by the electromagnetic radiations.The complex dielectric function is obtained by the Kramers-Kronig relation, given as: where P represents the component of momentum, ω the complex angular frequency and ε(ω′) represents the dielectric constant, Re and Im represents the real and imaginary part of dielectric function respectively.
The other optical parameters like the extinction coefficient k(ω), the absorption α(ω), the reflectivity R(ω), the conductivity σ (ω), the refractive index n(ω) and the electron energy loss L(ω) can be obtained from the imaginary and real parts of the dielectric constant.All these optical constants are computed by using the corresponding equations, given below: (2) In the above equation, λ is the wavelength, W cv is the transition probability per unit time, and E 0 is the ground state energy and ε 1 (ω) represents the real part of dielectric function.
The energy dependence of the real part of the dielectric function is shown in Fig. 5a.The most important parameter, i.e. the zero-frequency limit ε 1 (0) of this spectrum is calculated, which is the electronic part of the static dielectric constant.The value of the zero-frequency limit ε 1 (0) for the bulk CsSnI 3 is obtained to be 9.20 which decreases remarkably for the CsI-termination and the SnI 2 -terminated (001) surfaces to values 3.4 and 5.25, respectively.It is seen that the value of ε 1 (0) is higher for the bulk and lower for the surfaces showing that energy band gap is inversely related to ε1(0).This signifies that a larger energy band gap has a smaller ε 1 (0) value.The ε 1 (0) spectra of these compounds initially increases from zero-frequency value and reaches to a maximum value.After that, it starts decreasing and after a certain value, it reaches below the zero value.The values below the zero represent a complete attenuation of the incident photon beam.The values of reflectivity R(ω) as a function of frequency for the bulk sample, the CsI-termination and the SnI 2 -terminated (001) surfaces of CsSnI 3 are shown in Fig. 5b.The values of reflectivity at the zero frequency R(0) show a trend similar to the values of ε 1 (0).The variation in reflectivity R(ω) with frequency is also similar to the variation in ε 1 (ω); however, interestingly, the reflectivity becomes maximum where the value of ε 1 (ω) showed the zero value.These negative values of ε 1 (ω) are indicative of metallic nature of the materials.The reflectivity being maximum for the range in which ε 1 (ω) is negative reveals metallic nature of the compounds.The reflectivity spectra indicate that the bulk and the SnI 2 -termination surfaces behave metallic for the energy more than 6.2 eV and 8.9 eV, respectively.But for the CsI-termination surface, the energy range should be more than 10 eV for a metallic behaviour.
Figure 5c shows the variation of the refractive index for the bulk and the (001) surfaces of CsSnI 3 .The refractive index increases from the zero frequency and reaches up to its maximum value of 3.20 for the bulk sample, 2.10 for the CsItermination and 2.7 for the SnI 2 -terminated (001) surface of CsSnI 3 .The variation of refractive index for all the structures starts decreasing beyond a certain maximum value and reaches below the unity for the higher frequency ranges.The values of refractive index being lesser than unity represent the non-linear nature of compounds for the higher frequency range.
The behaviour of energy loss function versus frequency variation is shown in Fig. 5d.These spectra show the energy loss of moving electrons as they travel through the absorber material.The value of energy loss function is minimum for the visible range frequency range, after that it starts increasing for the higher frequency range.
Figure 6a shows the extinction coefficient k(ω) for the bulk sample, the CsI-termination and the SnI 2 -termination (001) surfaces of CsSnI 3 .The values of extinction coefficient at different frequencies are the characteristic of the material that describe how strongly a material absorbs the incident radiation at a particular frequency.The values of extinction coefficient are very low for lower range of frequency indicating that radiation has passed through the visible energy range with minimum energy loss.These graphs also indicate that the CsI-termination surface has lower values of extinction coefficient for the visible region as compared to the bulk and the SnI 2 -termination surface.The observed higher values of k(ω) denote that a considerable absorption has taken place for the higher frequencies range.It can be observed from the graph that there are various maxima and minima of k(ω) for different higher energies range.The absorption coefficient of the bulk sample, the CsI-termination and the SnI 2 -termination (001) surfaces are shown in Fig. 6b.The graph displays the absorption in the energy range 1-13 eV.Ideally, the band gap of materials should lie within the optimal energy range from 0.9 to 1.6 eV, in order to have the efficiency more than 25% (Ju et al. 2017).It can be seen from the graph that (001) surfaces of CsSnI 3 exhibit high values of absorption coefficients in the visible light range (~ 1.6 to ~ 3 eV) as well as that in the ultraviolet energy range (> 5 eV).Thus, the optimal direct energy band gap and higher values of absorption coefficient in the visible and ultraviolet energy range of the CsI-termination (001) surface makes it a promising material for the photovoltaic applications.
Figure 6c represents the graph of the optical conductivity σ(ω) corresponding to different frequencies.The graph shows that the optical conductance starts close to 0.3 eV for the bulk, 0.9 eV for the CsI-terminated (001) surfaces and 0.8 eV for the SnI 2 -terminated (001) surfaces.The behaviour of optical conductivity is similar to that of the absorption coefficient (Fig. 6b).The behaviour of the imaginary part of the dielectric constants of the bulk, the CsI-termination and the SnI 2 -termination (001) surfaces of CsSnI 3 with different frequencies are plotted in Fig. 6d.The imaginary part of the dielectric constant is a measure of dielectric loss or the absorption behaviour of light.The threshold energy of the bulk, the CsI-termination and the SnI 2 -termination (001) surfaces of CsSnI 3 are observed to be 0.6 eV, 1.0 eV and 0.8 eV, respectively.The variation of threshold energy is akin to their variation in calculated energy band gap values.
The calculated band gap value for the bulk CsSnI 3 comes out to be 0.82 eV using the PBE_Sol, however, the values of band gaps of CsI-termination and SnI 2 -terminated (001) surfaces are found to be 1.21 eV and 1.07 eV, respectively.Thus, the band gap is increased in surface-terminated samples in comparison to the bulk state.Since the band gap of surface termination is found to lie in the ideal energy range (1.1-1.6 eV) for solar cell fabrication, it can be concluded that the surface-terminated perovskites are more suitable for the photovoltaic applications.
The Sn-based perovskite may be able to replace the well-studied Pb-based perovskites as they show the optoelectronic properties similar to the later, and additionally, they possess higher carrier mobilities, lower direct optical bandgaps (1.2-1.4 eV), and less toxicity than the Pb-based perovskites, which render them potential contenders for the Pb-free perovskite applications are high optical-absorption coefficients and good stability (Wang et al. 2021).Additionally, the other advantages of the Sn-based perovskites in comparison to the Pb-based perovskites are the costeffectiveness along with the competitive power conversion efficiency and also the suppression in hysteresis behaviour (Xu et al. 2021).

Conclusion
The influence of CsI and SnI 2 -terminated (001) surfaces on structural, electronic and optical properties of leadfree tin-based halide perovskite CsSnI 3 has been studied from the first principal calculations, based on density functional theory (DFT).The optimised lattice constant, the energy band structure and the density of states have been calculated for the bulk and different terminated surface structures.The optical properties of CsSnI 3 are computed in terms of the real and imaginary part of the dielectric functions, the absorption coefficients, the refractive indices, the conductivity, the reflectivity, the extinction coefficient and the electron energy loss.The optical properties of the CsI-termination surface exhibit better suitable photovoltaic characteristics than the bulk and SnI 2 terminated surfaces in the ultraviolet and visible region.This study suggests that the electronic and optical properties of the lead-free and non-toxic tin-based inorganic halide perovskite CsSnI 3 can be tuned by choosing the appropriate surface termination, rendering these inorganic halide perovskite materials important for high performance, safe, eco-friendly and efficient opto-electronic and photovoltaic applications.
displays the partial and total density of states of the bulk CsSnI 3 as well as the CsI-termination and the SnI 2 -termination (001) surfaces.The calculated density of states of the bulk and the (001) surfaces are typical of a semiconductor behaviour.The band structure plot of the bulk CsSnI 3 cubic perovskite structure shows that the bulk samples have a direct energy band gap at the R symmetry point.The calculated value of band gap for the bulk CsSnI 3 comes out to be 0.82 eV using the PBE_Sol.The band structure for the CsI-termination and the SnI 2 -termination surfaces also depict a direct band gap.The values of band gaps for the CsI-termination and

Fig. 2
Fig. 2 The crystal and (001) surface structures of CsSnI 3 a for the bulk, b for the CsItermination, and c for the SnI 2 -termination structure

Fig. 4
Fig. 4 Band structures of the bulk, the CsI-termination and the SnI 2 -termination (001) surfaces of CsSnI 3

Fig. 5
Fig. 5 Calculated values of optical parameters: a real part of dielectric function, b reflectivity, c Refractive Index and d energy loss

Fig. 6
Fig. 6 Calculated optical parameters for the samples: a the extinction coefficient, b the absorption, c the conductivity, and d imaginary part of the dielectric function