Effective Masses and Electronic and Optical Properties of Nontoxic

We calculated the effective masses and electronic and optical properties of CH3NH3SnX3 (X = Cl, Br, I) perovskites as a solar cell absorber using the ...
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Effective Masses and Electronic and Optical Properties of Nontoxic MASnX3 (X = Cl, Br, and I) Perovskite Structures as Solar Cell Absorber: A Theoretical Study Using HSE06 Jing Feng† and Bing Xiao*,‡,§ †

School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States Department of Physics, College of Science and Engineering, Temple University, Philadelphia, Pennsylvania 19122, United States

‡

S Supporting Information *

ABSTRACT: We calculated the effective masses and electronic and optical properties of CH3NH3SnX3 (X = Cl, Br, I) perovskites as a solar cell absorber using the HSE06 hybrid functional. The computed band gaps are direct at the Γ point, ranging from 1.67 to 3.0 eV. The effective masses of carriers and the band gaps decrease from chlorine to iodine. Moreover, their hole masses are comparable to those of CH3NH3PbX3 (X = Br and I) phases. The optical dielectric constant does not decrease monotonically when going from X = Cl to Br to I for CH3NH3SnX3 perovskites. Under a small isotropic compressive stress, the photon absorption efficiency of CH3NH3SnX3 perovskites is slightly improved due to the reduction of the fundamental band gap.

1. INTRODUCTION The solar cells based on hybrid organic−inorganic halide perovskite (e.g., CH3NH3PbX3, X = Cl, Br, I) as light absorbers are upcoming new players in the field of third-generation photovoltaics. 1−6 In the past 2 years, pervoskite-type methylammonium lead halides emerged as light harvesters for mesoscopic heterojunction solar cells, reaching a surprisingly high energy conversion efficiency of about 16%, comparable to that of the commercial silicon solar cells.7−9 References 10−12 have developed different technologies to make sandwich-type absorbers, exhibiting the direct band gap, large absorption coefficient, and high carrier mobility. The previous investigations of the physical properties (e.g., electronic structure and optical properties) of hybrid organic−inorganic perovskites to some extent explained why they are so promising for solar energy conversion.13−16 As we know, lead poisoning is a type of metal poisoning and a medical condition in humans and vertebrates caused by increased levels of the heavy metal lead in the body; moreover, lead interferes with a variety of body processes and is toxic to many organs and tissues, including the heart, bones, intestines, kidneys, and reproductive and nervous systems.17 However, all of these advanced materials contain the toxic element lead, which would eventually hinder the commercialization of the products in the market. Tin is in element the same group as lead, and it would be interesting to study the effects of replacing the Pb in methylammonium lead halides by Sn. In this report, we have investigated the effective masses of hole and electron at the Γ point and the electronic and optical properties of nontoxic methylammonium tin halide (MASnX3, MA= CH3NH3, X = Cl, Br, I) compounds under © 2014 American Chemical Society

small isotropic stress and at the equilibrium geometries using the range-separated hybrid functional HSE06.18

2. DETAILS AND METHODS The calculation details and crystal structures of orthorhombic MASnX3 (X = Cl, Br, and I) are presented in the Supporting Information. Similar to MAPbX3 (X = halogens), MASnX3 also exhibits a very rich phase diagram as a function of temperature, i.e., the crystal structure goes from cubic, tetragonal, orthorhombic, and monoclinic to triclinic class by cooling.19−24 The complicated phase transition behaviors of MASnX3 structure is attributed to the disordering of (CH3NH3)+ cations and the distortions of (SnX3)− octahedra at finite temperature.19−22,24 For example, in the high-temperature cubic phase, the orientations of (CH3NH3)+ cations are completely disordered. In the same phase, the SnX6 structural unit has perfect cubic symmetry. By lowering the temperature, the tilting and distortion of SnX6 octahedral create the local potential wells for the cations, suppressing the dynamical disordering of (CH3NH3)+ cations. As a result, the MASnX3 (X = Cl, Br, and I) structures with symmetry lower than tetragonal class show the ordered orientation of (CH3NH3)+ structural units. Experimentally, it was found that CH 3 NH 3 SnX 3 compounds crystallize into monoclinic phase at low temperature.23 Hao et al.25 reported a tetragonal MASnX3 (X = Br and I) phase at room temperature. However, the unit cell of Received: June 30, 2014 Revised: August 4, 2014 Published: August 6, 2014 19655

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and co-workers25 measured the optical band gaps of MASnI3‑xBrx samples in tetragonal phase, and the values were found to be between 1.30 eV (CH3NH3SnI3) and 2.15 eV (CH3NH3SnBr3). The computed fundamental band gaps of orthorhombic MASnI3 and MASnBr3 in our paper are slightly larger than the reported values for tetragonal structures in ref 25. Experimentally, the various defects dominate the electronic and solar energy harvesting properties of MASnX3 compounds.30,31 Using the computed band dispersions, the effective hole and electron masses in the three principal directions are evaluated for each orthorhombic MASnX3 phase by HSE06. For the computational details, one may refer to ref 27. The results are given in Table1. From the data shown in Table 1, the effective masses of either hole or electron in orthorhombic MASnX3 (X = Br and I) are generally similar to those of corresponding orthorhombic MAPbX3 (X = Br and I) phases.27 The tetragonal MAPbX3 (X = Br and I) phases have smaller effective masses of holes than orthorhombic MASnX3 and MAPbX3 structures. Roughly speaking, the mobility of carriers in orthorhombic MASnX3 is less satisfactory than that of the tetragonal MAPbX3 structure for photovoltaic purposes. The anisotropies in the effective mass of hole at the Γ point are shown in Figure 2 for both MASnX3 and MAPbX3 in orthorhombic phase. Besides MAPbI3, the effective masses of the hole of the remaining compounds show relatively weak directional dependences. For orthorhombic MAPbI3, the strong anisotropy in hole effective mass is mainly caused by its unusual heavy hole along the Γ (0 0 0)−Y (0 1/2 0) line in the Brillouin zone.27 The spherical averaged effective mass of hole or electron at the Γ point is given by

monoclinic phase deviates from the orthorhombic crystal class very slightly.24,26 Therefore, one can use an orthorhombic cell to approximate the realistic structure. Figure 1 shows the orthorhombic crystal structure of CH3NH3SnX3 (X = Cl, Br, I), which is built from CH3NH3PbX3 in our previous work.27

Figure 1. Crystal structure of orthorhombic CH3NH3SnX3 (X = Cl, Br, I) perovskites.

3. RESULTS AND DISCUSSIONS The optimized lattice constants of CH3NH3SnX3 (X = Cl, Br, and I) structures are given in Table S1 (Supporting Information). Since the atomic radius of halogen increases from Cl to I, the lattice constants also increase from CH3NH3SnCl3 to CH3NH3SnI3 in the same order. On the other hand, the lattice constants of MASnX3 are smaller than those of MAPbX3, because the ionic radius of Sn2+ is smaller than in Pb2+. For hybrid organic−inorganic tin or lead halides, the van der Waals interactions play an important role in their equilibrium geometries. In our calculations, we employed the PBE+D2 method, in which dispersion forces are accounted for by using semiempirical pairwise interactions.28 The previous works27,29 indicated that the PBE+D2 only captures the van der Waals interactions qualitatively. The equilibrium geometries of MASnX3 structures are usually slightly improved over PBE calculations. The band structures and densities of states of all MASnX3 (X = Cl, Br, and I) compounds are shown in Figures S1 and S2 (Supporting Information). Starting from the PBE+D2 geometries, the HSE06 was used throughout this paper for calculating electronic structures. All orthorhombic MASnX3 structures exhibit the direct band gap at the Γ point. The band gaps are in range from 1.7 eV (MASnI3) to 2.8 eV (MASnCl3), which are very similar to those of orthorhombic MAPbX3 (X = Cl, Br, and I) compounds (1.6−2.3 eV).27 Hao

m* =

1 4π

2π

∫0 ∫0

π

M *(θ , φ) sin θ dθ dφ

(1)

M *(θ , φ) =

1 S1 sin 2 θ cos2 φ + S2 sin 2 θ sin 2 φ + S3 cos2 θ

(2)

where θ and φ are azimuthal and polar angles in spherical coordinates, respectively. Si represents the inverse of the effective mass of the i principal direction, i.e., S1 = 1/m[100] * , S2 = 1/m[010] * , and S3 = 1/m[001] * . The calculated values for hole and electron are given in Table.1. We can see the spherical averaged effective masses of hole and electron decrease from MASnCl3 to MASnI3, which show the same ordering as the decreasing of band gap, implying that the Sn−I bonds of (SnI3)− anions in MASnI3 show stronger covalent character than those of Sn−Cl and Sn−Br bonds in MASnCl3 and MASnBr3, respectively. As seen from Figure S2 (Supporting Infromation), the electronic densities of states of orthorhombic MASnX3 (X = Cl, Br and I) are more or less similar to each other. The top of the valence band is dominated by the 5s shell of Sn2+. Meanwhile, the bottom of conduction band is attributed to the 5p orbital of the same atom. The occupied p states of halogens are far below

Table 1. Calculated Effective Masses of Holes and Electrons of CH3NH3SnX3 (X = Cl, Br, I) Perovskites [100] CH3NH3SnCl3 CH3NH3SnBr3 CH3NH3SnI3

[010]

[001]

spherical average

m*e

m*h

m*e

m*h

m*e

m*h

m*e

m*h

1.94 5.88 3.74

0.63 0.65 0.59

13.19 0.94 0.81

1.41 1.27 1.14

0.58 6.25 5.77

0.55 0.55 0.53

4.06 3.15 2.65

1.17 1.11 1.03

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Under such growth conditions, the surface of the as-grown MASnX3 bulk material is always terminated with X atoms (Cl, Br, and I). The Sn atoms near the surface are coordinated by six other X atoms, the same chemical environment as those in the bulk MASnX3 crystal structure, implying that the Sn2+ state is preserved.34,35 On the other hand, using SnX2 (X = Cl, Br, and I) as the precursor for the synthesizing of MASnX3 (X = Cl, Br, and I) is an effective way to stabilize the Sn2+ ion in either the relevant aqueous solutions or the solid-state reactions method.36,37 In the subsequent production of Sn-based pervoskite solar cell, the entire heterojunction structure consisting of MASnX3 and other materials must be sealed in the module. We should note that the SR (scalar relativistic) effects have been included properly in the construction of the standard tin norm-conserving type pesudopotential (NCPP) in this calculation. The remaining nonrelativistic effect turns on the spin−orbital coupling (SOC) interaction, which is not available in the current CASTEP code using NCPPs. The effects of SOC on the band dispersions and effective mass of carriers are more significant in MAPbX3 compounds than MASnX3 in our case. We expect that including SOC will split the bottom of the conduction band at the Γ point into p1/2 and p3/2 states, creating the heavy and light electron pockets. Meanwhile, the degeneracy at the top of valence band at the same k point remains the same, except the electronic band is more dispersive due to SOC. From the previous studies of hybrid organic− inorganic pervoskites with DFT+SOC methods,14,38,39 we can see the fundamental band gap and effective masses of hole or electron are usually reduced. In Table 2, we show the calculated nonzero diagonal components of optical dielectric tensor for each orthorhombic MASnX3 (X = Cl, Br, and I) structure. The results are compared to those of MAPbI3. For the orthorhombic class, the three principal diagonal elements in the dielectric tensor are supposed to be different from each other. It is found that the values in the [100] and [001] directions are very close to each other for three MASnX3 structures. Meanwhile, in the [010] direction, the tensor component is obviously smaller than for the other two directions. As can be seen from Figure 1, in the orthorhombic MASnX3 (X = Cl, Br, and I), the rigid (SnX3)− anions form the uniform three-dimensional network in the crystal structure. As a result, the anions contribute equally to the three principal optical dielectric elements. Therefore, the observed anisotropy in the optical dielectric tensor is mainly attributed to the orientation of (CH3NH3)+ cations. In these structures, the principal rotation axis of (CH3NH3)+ cation is aligned in the [101] direction or parallel to the x−z plane. This structural feature distinguishes the component of the optical dielectric tensor in the [010] direction from the other two principal directions.

Figure 2. Anisotropies in the effective hole mass at the Γ point along different directions in the first irreducible Brillouin zone for orthorhombic MASnX3 and MAPbX3 (X = Br and I). The highsymmetry k-points are indicated in the graphs by the Greek letters.

the Fermi level. The upper part of the conduction band of all MASnX3 (X = Cl, Br and I) mainly consists of the antibonding states of organic (CH3NH3)+ cations. A detailed analysis of the chemical bonding mechanisms of those hybrid organic− inorganic pervoskites can be found in refs 13, 14, 22, 29, 32, and 33. Practically, the main difficulty of the fabrication of solar cells using MASnX3 (X = Cl, Br, and I) is that, unlike Pb2+ ion, Sn2+ ion is unstable. It can be easily oxidized into Sn4+ state by oxygen existing in the environment. Therefore, the stringent controlling of oxygen is required during the preparation of MASnX3 material. One possible way to efficiently eliminate the oxidation of Sn2+ ion in MASnX3 (X = Cl, Br, and I) bulk materials is to grow the materials in halogen-rich conditions.

Table 2. Computed Non-Zero Diagonal Elements of the Optical Dielectric Tensor (ε∞), the Average Value (ε∞ ave), and the Fundamental Band Gap (Γ → Γ) of Orthorhombic CH3NH3SnX3 (X = Cl, Br, and I) by HSE06 at the Equilibrium Cell Volume

a

ε∞

CH3NH3SnCl3

CH3NH3SnBr3

CH3NH3SnI3

CH3NH3PbI3a

ε∞ xx ε∞ yy ε∞ zz ε∞ ave Eg (eV)

8.64 4.30 9.96 7.63 2.8

6.07 4.84 5.95 5.62 2.0

10.63 5.82 10.10 8.85 1.7

5.28 4.73 5.23 5.08 1.6

The corresponding values of CH3NH3PbI3 are also given. 19657

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Stress exists in the synthesis, fabrication, and application of multilayered photovoltaics or materials used on flexible polymer substrates.5 In our calculations, we apply the small hydrostatic pressure in different magnitudes (±2.0 GPa) to perovskite MASnX3 (X = Cl, Br, and I) structures. The influences of isotropic external pressure on the electronic structure and optical properties of those compounds can be calculated very conveniently by HSE06. The band gap deformation potential is obtained from the expression given below

The average optical dielectric tensor and the fundamental band gap of each MASnX3 structure are also given in Table 1. Since the band gap of MASnX3 is decreased in the order of Cl, Br, and I, the average optical dielectric constant is supposed to be increased in the same sequence. Clearly, our conjecture is not true for MASnBr3. The main reason can be traced back to the calculation of the optical dielectric constant. Generally, the three principal components of the optical dielectric tensor are obtained using the following expression40 εij∞(ω → 0) 2 3

2e ℏ =1+ 2 2 π m

∑∫d k 3

Eg (V ) = c + αV ln V

⟨v , k|pi |c , k⟩⟨c , k|pj |v , k⟩

v ,c

where Eg(V) is the fundamental band gap computed from HSE06 at volume V, c is a fitting parameter, and αV defines the band gap deformation potential at a specific k point, referring to the Γ point in our case. It has been reported that the hybrid organic−inorganic pervoskites usually have positive αV, implying that the fundamental band gaps increase with the increasing of the cell volume.43 In Figure 3, the band gap versus

[Ec(k) − Ev(k)]3 (3)

|⟨c , k|pi |v , k⟩|2 ∝

m2Eg me*

(6)

(4)

where e is the element charge, ℏ is the reduced Planck constant, and m is the mass of free electron; |c,k⟩ and |v,k⟩ are the Bloch states of the conduction and valence bands, and their eigenenergies are given by Ec(k) and Ev(k), respectively. The wave vector in the first Brillouin zone is denoted by k. The effective “optical” mass m*e is defined for the conduction electrons.41 The momentum component in the i direction is given by pi. Equation 4 is derived from the effective mass sum rule.42 Assuming that the conduction and valence bands show very weak dependence upon k wave vector, then the relationship between optical dielectric constant and other quantities such as electron effective mass and band gap can be written as ε(ω → 0) ∝ 1 +

2e 2ℏ3 1 π 2 me*Eg 2

(5)

Figure 3. Band gap deformation potentials of orthorhombic MASnX3 (X = Cl, Br, and I) compounds computed from HSE06 at the Γ point.

From eq 5, we can see that the optical dielectric constant is large for the material with small band gap and light electron effective mass. From Tables 1 and 2, one can clearly see that the effective masses of conduction electrons at the Γ point of MASnBr3 in the [100] and [001] directions are significantly larger than those of MASnCl3 in the same directions. In the [010] direction, the latter structure has a much bigger electron effective mass than former one does. It might be reasonable to conclude that the heavy electron effective masses of MASnBr3 significantly reduce the two components of the optical dielectric tensor in the [100] and [001] directions, resulting in an overall smaller optical dielectric constant than that of MASnCl3. Meanwhile, MASnI3 has the smallest band gap among the three perovskites, and it also has less heavy effective masses for electrons than MASnBr3. Thus, it gives the largest optical dielectric constant. Although the band gap of MAPbI3 is comparable to that of MASnI3, the optical dielectric constant of the former structure is considerably smaller than that of latter one. The effective mass of conduction electrons of MAPbI3 is actually smaller than that of MASnI3.27 One possible explanation is that the electronegativity of Pb (1.87) is smaller than that of Sn (1.92), indicating that the Pb−I bond has stronger ionicity than the Sn−I bond. It is known that the dielectric constant is usually small for an ionic solid.

cell volume data and the corresponding fitting curves by eq 6 are shown for MASnX3 (X = Cl, Br, and I) structures. We can see that the band gap deformation potentials of them are all positive. The values are increased from Cl− to I−. This trend is opposite to the change of fundamental band gap from MASnCl3 to MASnI3. The results presented here imply that for some of MASnX3 or MAPbX3 compounds, the compressive stress improves the solar energy conversion efficiency, because the band gap can be reduced to match the solar energy spectrum. In order to confirm this conjecture, we calculate the optical absorption spectra of orthorhombic MASnX3 (X = Cl, Br, and I) phases by HSE06 at different hydrostatic pressures. The results are shown in Figure 4 along with profiles of Si crystal and orthorhombic-MAPbI3. Clearly, all orthorhombic MASnX3 (X = Cl, Br, and I) phases exhibit stronger photon absorption in the green−red region of the visible-light spectrum than Si and MAPbI3. At the short wavelength, the response of MASnX3 (X = Cl, Br, and I) structures to photons is more prominent than those of the latter two materials. Under compression, the photon adsorption is enhanced for the whole visible-light spectrum in the cases of MASnCl3 and MASnBr3. Since MASnI3 already has the smallest direct band gap among the three MASnX3 compounds, the isotropic compressive stress slightly deteriorates the photon absorption in the long wavelength part of the visible-light spectrum. 19658

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determined both by the effective mass of conduction electrons and band gap, implying that it does not always increase monotonically with the decreasing of band gap. Under the low hydrostatic pressure, MASnX3 compounds show the positive band gap deformation potential. Therefore, their band gaps can be engineered to match the visible light spectrum. As a result, the photon absorption is also improved by applying the small isotropic compressive stress to orthorhombic MASnX 3 materials.

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ASSOCIATED CONTENT

S Supporting Information *

Details of the methods used and some additional properties of the MASnX3 (X = Cl, Br, and I) compounds in this work. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +1-215-900-4820. E-mail: [email protected]. Present Address §

Department of Physics, College of Science and Engineering, Barton Hall A205, Temple University, Philadelphia, PA 19122. Author Contributions

J.F. provided the idea and calculated the properties, and B.X. participated in the discussion and wrote the main part of the paper. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Research financed by the National Scholarship Council under Grant No. 201208530028.

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REFERENCES

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Figure 4. Comparison of the absorption spectra of CH3NH3SnX3 (X = Cl, Br, I) perovskites with those of single crystal Si and CH3NH3PbI3 compounds in the visible light spectrum.

4. CONCLUSIONS The electronic and optical properties of orthorhombic CH3NH3SnX3 (X = Cl, Br, I) perovskites are studied by the first principle calculations using the HSE06 hybrid functional. The calculated direct band gap of methylammonium tin halides ranges from 1.67 to 3.0 eV at the Γ point. The evaluated effective masses of electrons and holes at the same k-point of them are comparable to those of orthorhombic MAPbX3 (X = Br and I) materials. The anisotropies in the effective mass of electron at the Γ point are relatively weak for MASnX3 (X = Cl, Br, and I) compounds. The optical dielectric constant is 19659

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