First principles study of structural, electronic and optical properties of Cs-doped CH3NH3PbI3 for photovoltaic applications

Accepted Manuscript First principles study of structural, electronic and optical properties of Cs-doped CH3NH3PbI3 for photovoltaic applications Ankur Taya, Priti Rani, Jyoti Thakur, Manish K. Kashyap PII:

S0042-207X(18)31415-5

DOI:

https://doi.org/10.1016/j.vacuum.2018.12.008

Reference:

VAC 8424

To appear in:

Vacuum

Received Date: 31 July 2018 Revised Date:

23 October 2018

Accepted Date: 3 December 2018

Please cite this article as: Taya A, Rani P, Thakur J, Kashyap MK, First principles study of structural, electronic and optical properties of Cs-doped CH3NH3PbI3 for photovoltaic applications, Vacuum (2019), doi: https://doi.org/10.1016/j.vacuum.2018.12.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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First Principles study of structural, electronic and optical properties of Cs-doped CH3NH3PbI3 for photovoltaic applications Ankur Taya1,†, Priti Rani1, Jyoti Thakur2 and Manish K. Kashyap1 2

Department of Physics, Kurukshetra University, Kurukshetra-136119 (Haryana), India

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Department of Physics and Astrophysics, University of Delhi, New Delhi-110007, India

ABSTRACT

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Corresponding author’s e-mail: †[email protected]

Hybrid halide perovskites (HHPs) based solar cells have revolutionized the photovoltaic

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landscape by demonstrating the power conversion efficiencies (PCE) exceeding 22% at a low cost. Through first-principles pseudopotential calculations, we have investigated the structural, electronic and optical properties of Pb-based HHP, CH3NH3PbI3 (MAPbI3) and analyzed the effect of incorporating inorganic Cs+ at methyl ammonium (MA+) cation site in MAPbI3. Our results reveal that 12.5% of Cs-doping slightly enhances the absorption coefficient of MAPbI3, making it a promising candidate for highly efficient perovskite solar cells. This optical

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absorption is decided by the tradeoff between widening of the band gap and increase of DOS in sub-VBM region on Cs-doping. Further, the compositional degradation of MAPbI3 can be

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prevented with this doping and the solar cells based on it can be used for the longer time.

Keywords: DFT; pseudopotential; solar cells

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PACS: 71.15.Mb; 71.15.Dx; 84.60.Jt

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1. Introduction Hybrid halide perovskites (HHPs) have emerged as a very promising candidate for absorber layer in third generation solar cells. Since introduction in 2009 by Kojima et al [1] in liquid electrolyte based dye-sensitized solar cells (DSSCs), these materials have shown

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tremendous potential owing to their excellent photovoltaic response. Over the course of past few years, HHPs have taken the solar cell technology by storm as the solar cells based on these materials have exceeded the photon conversion efficiency (PCE) to 23.3% [2] till date from 3.8% [1] in 2009. Such exponential rise in the PCE has never been witnessed before in any other

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existing solar cell technology. Due to the enormous value of research interests in this field, current performance of HHP solar cells is expected to increase substantially with an aim to make

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these a commercial reality [3]. The factors that make HHP solar cells advantageous are their easy fabrication from the liquid phases [4,5] and the efficiency which can be tuned by controlling their structural order and composition [6,7].

HHPs have standard AMX3 perovskite structure, where X is the halide anion (Cl-, Br-, I-), M is the metal cation (Ge, Sn, Pb), while the remaining position A is taken by an organic molecule, generally methylammonium, CH3NH3 (MA) and formamidinium, HC(NH2)2 (FA) etc.

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Among numerous hybrid perovskites, a group of halides having the stoichiometry of MAPbX3 (X= Cl-, Br-, I-) is the most widely studied. From these, MAPbI3 has been extensively applied owing to its ideal properties such as direct bandgap of 1.55 eV [8], high level of defect self regulation [9], small exciton binding energy [10], excellent charge carrier mobility [11-13] and

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long charge carrier diffusion length [14-15]. Furthermore, MAPbI3 possesses several key properties which are likely to give rise to highly efficient and defect-tolerant solar absorbers [16].

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Despite these advantages, MAPbI3 based solar cells have failed to be commercialized due to lack of its intrinsic long term stability [17,18] and compositional degradation. Additionally, MAPbI3 is unstable against light and heat due to its low crystallization energy [19-21]. Although ample efforts have been put by scientific community, both experimentally and theoretically in MAPbI3 yet addressing its long-term stability has always been a hurdle [22]. So there is an imperative need to look for new HHP materials that are stable and efficient in ambient environmental conditions. It is established that the properties of the materials are closely related to their electronic structures so an intuitive strategy to achieve stability in the HHP absorber layer is to replace the 2

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cation A by suitable doping without compromising the excellent photovoltaic properties. Interestingly, the size of A cation is limited by the Goldschmidt tolerance factor [23]. Considering that, the structure of the HHP materials can be modulated by partial or full substitution of cation A with suitable cations like FA+ and Cs+ without destroying the Pb-I

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octahedral arrangement. Such strategies have been used experimentally in achieving more stable HHP based solar cells. For instance, Choi et al [22] demonstrated that with partial Cs doping at A site in the MAPbI3 perovskite light absorber, resulting CsxMA1-xPbI3 (x = 0.1) perovskite devices exhibit 40% enhancement in PCE i.e. from 5.51% to 7.68%, on account of increase in short-

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circuit current density and open-circuit voltage via increased light absorption. Niu et al [24] provided the detailed study on the thermal stability of Cs-doped MAPbI3 film and fabricated

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solar cells from spin coating method. They showed that Cs doping enhances the device performance by suppressing perovskite degradation and the best solar cells with PCE of 18.1% are obtained for 9% of Cs doping.

A lot of experimental efforts have been put in understanding physical properties of Csdoped MAPbI3 but to the best of our knowledge, the theoretical investigations are rather limited on these materials. In this work, first principles calculations were carried to systematically

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examine the geometry, electronic structure and optical properties of Cs-doped tetragonal MAPbI3 perovskite. To provide the further insight into the fundamental mechanism behind experimental observations, here we report on Cs:MAPbI3 as an alternative light absorber to MAPbI3. Furthermore, the relationship between structural, electronic and optical properties of pure and

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doped MAPbI3 have also been investigated.

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2. Computational Details

The first principles calculations of pure and Cs:MAPbI3 were carried out using the plane

wave density functional theory (DFT) formalism, as implemented in the VASP code [25], using the electron exchange−correlation functional proposed by Perdew-Burke-Ernzerhof (PBE) [26,27]. The electron−ion interaction was described by projector augmented wave (PAW) method [28]. A basis set cutoff was taken as 400 eV and the reciprocal space was sampled by the Monkhorst-Pack [29] k-point grid of 4×4×4 and integrated over with a Gaussian smearing. The present systems were relaxed with conjugate-gradient algorithm until all the forces on the atoms become < 0.05 eV/Å. The optical properties were evaluated with the help of frequency 3

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dependent complex dielectric function; ε ( x ) = ε 1 ( x ) + ε 2 ( x ) in the independent particle approximation i.e. the excitonic effects and the local-field corrections were neglected. Quite large numbers of bands were taken into account in dielectric properties calculations to include

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the high frequency effects of interband transitions. The imaginary part of the ε (x) can be computed with the help of first order time dependent perturbation theory in the simple dipole approximation. In the long wavelength limit, the imaginary part is given by

ε 2 ( x) =

2eπ Ωε 0

rr

∑

2

ψ KCB u .r ψ KVB δ ( E KCB − E KVB − ω )

K ,CB ,VB

(1)

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where ω is the frequency of electromagnetic (EM) radiation in energy unit. Ω represents the

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volume of the supercell and ε 0 is the free space permitivity. CB and VB represent, respectively, r r conduction band and valence band. u and r denote the polarization vector of electric field of EM wave and position vector, respectively [30]. The real and imaginary parts of the dielectric function are related to each other by Kramers-Kronig relation

ε 1 (ω ) = 1 +

1

∞

dω ′ε π∫ 0

2

1   1 (ω ) +   ω′ − ω ω′ + ω 

(2)

Absorption coefficient α(ω) can be deduced from ε(ω) via simple relations as given in the

VESTA [33] program.

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3. Results and Discussion

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reference [31,32]. All schematic representations of the crystal structures were generated using

MAPbI3 adopts a tetragonal structure with space group I4/mcm at room temperature [34]. Interestingly, a tetragonal unit cell of MAPbI3 consists of 4 units of MAPbI3 with each Pb atom

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coordinates with six I-atoms (four in equatorial and two in apical direction). It has been confirmed experimentally that at the room temperature, the dipolar organic MA+ cation reorients quite rapidly [0.5-14 ps] inside the PbI6-octahedron cage [35-38]. However, for computation, the MA+ cations have to be relaxed to fix orientations in such a way that there is minimum steric hindrance in the hybrid halide perovskite system. We used experimental lattice parameters [39] as the input parameters of our DFT calculations and subsequently obtained the optimized local structure of MAPbI3 by applying the structural relaxation, the top view of which is depicted in Fig. 1.

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Fig. 1. Top view of unit cell of tetragonal MAPbI3 (space group 140: I4/mcm) In order to obtain 12.5% of Cs doping, a 2×1×1 supercell containing 8 formula units of MAPbI3 was formed and one MA+ ion was replaced by Cs+ within the supercell (Fig. 2). Since the environment of MA+ cation is uniform so any of the MA+ ions can be chosen for doping with

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Cs+. The Goldschmidt tolerance factor (t) is calculated using

t=

RA + RX

2 (R M + R X )

(3)

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where RA, RM and RX are the effective radii of the ions in the perovskite AMX3 [40]. The value of t for Cs:MAPbI3 is 0.8985, which is well within the permissible limit for stable perovskite

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structure [41]. Moreover, doping concentration beyond 12.5% has been avoided as increased Cs content would have increased the value of bandgap, which is undesirable as we want to retain the excellent electronic and optical properties of the MAPbI3 as absorber layer in PSCs besides enhancing its stability by introducing Cs.

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Fig. 2. Schematics for introducing 12.5% of Cs-doping in MAPbI3 along with relaxed structures of MAPbI3 and Cs:MAPbI3. (Grey/Purple/Brown/Blue/Pink/Turquoise sphere represents Pb/I/C/N/H/Cs atom)

The optimized lattice parameters of pure and Cs:MAPbI3 obtained after relaxation are

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listed in the Table 1 which are in good agreement with experimental values [39] and other theoretical data [42]. The slight overestimation in the calculated lattice parameters as compared to experimental data is expected behavior in GGA formalism. However, the deviation in volume with respect to experimental data is less than 5% in case of MAPbI3. The incorporation of Cs in

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MAPbI3 doesn’t have remarkable impact on the lattice parameters. But the hydrogen bonding existing between the H-atoms of MA+ cation and Iodine framework get reduced significantly which in turn increases the tilting of PbI6-octahedra. On measurement, we found that the

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minimum bond lengths of H-bond in Cs:MAPbI3 is 2.651 Å which is greater than that in MAPbI3 (2.627 Å), indicating that the strength of H-bonding gets reduced in doped lattice. Further, the average equatorial Pb-I-Pb angle gets increased from 152.10 to 153.97 on 12.5% of Cs-doping in MAPbI3. Therefore, the increase in tilt w.r.t. host MAPbI3 is 1.87 . On the other hand, the minimum bond length Pb-I covalent bonds decreases from 3.207 Å to 3.175 Å on this doping which yields the better strength of Pb-I bonds and the stability of Cs:MAPbI3 gets enhanced over pure MAPbI3. In this way, compositional degradation of MAPbI3 can be prevented and the solar cells based on it can be used for the longer time. 6

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Table I : Calculated lattice parameters of MAPbI3 and Cs:MAPbI3 MAPbI3 a = b (in Å)

Cs:MAPbI3 c (in Å)

a = b (in Å)

c (in Å)

8.90

13.16

8.91

13.16

Experiment [39]

8.85

12.64

-

-

Theory [40]

8.89

12.70

-

[39] Stoumpos et al, [42] Yun et al

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This work

-

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To explore the electronic structures of MAPbI3 and to see how Cs+ cation mixing affects the electronic properties of MAPbI3, the analysis of total density of states (DOS) was performed for both compounds. 12.5% of Cs doping drastically modifies the DOS in the energy region, -6.5

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eV to -8 eV. Importantly, the DOS in sub - valence band maximum (VBM) region that is of interest for photovoltaic applications and as a result of cation mixing this DOS get enhanced in the region up to 0.5 eV below the VBM as evident from inset of Fig 3. Our findings are in line with the recent results obtained in the case of Cs-doped FAPbI3 by Yi et al [43]. The magnitude of band gap of absorber material is very crucial as it is related to the maximum voltage of the PV device and determines the optical absorption [42]. The fundamental band gap (Eg) between the

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VBM and conduction band minimum (CBM) for MAPbI3 is 1.58 eV, which is in good agreement with the experimental value of 1.55 eV [8] as compared to previous theoretical work [44] where value of Eg = 1.63 eV was reported. Although DFT-PBE is known to underestimate the band gap in most of the materials but quite a peculiar situation seems to exist for Pb-based perovskites, for

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which standard PBE functionals estimate the band gaps in good agreement with corresponding experimental values [7, 45]. Interestingly, this agreement is just due to a fortuitous cancellation

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of the errors. The underestimated bandgap due to PBE is counterbalanced by enhanced band gap owing to non-involvement of SOC in Pb-based materials which brings the bandgap values in closer agreement with experimental data. Since DFT-PBE without SOC provides a semiquantitatively correct picture of Pb-based perovskites, making us confident that employed methodology is suitable to investigate the MAPbI3 and Cs:MAPbI3, the subject of this study. The value of Eg gets increased from 1.58 eV to 1.62 eV after Cs doping. Further, we have tested 8.3% and 25% Cs doping also in MAPbI3 within 3×1×1 and 1×1×1 supercells of MAPbI3, respectively. It is observed that the band gap for 8.3%/ 12.5% case comes out to be 1.60/1.68 eV. It is

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observed from here that there is no benefit of increasing the Cs-content in MAPbI3 beyond

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12.5% as the band gap rises above the optimal value for photovoltaics.

Fig. 3. Calculated TDOS of MAPbI3 and Cs:MAPbI3 at GGA level of theory

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To explain the above observations and to understand the bonding mechanism between the atoms of the Cs:MAPbI3, the analysis of partial density of states (PDOS) was performed. From panel 2, 3 and 4 of Fig. 4, it can be elucidated that the VBM is constituted of combination of Pb-

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6s and I-5p states. Further, the inset of panel 6 of this figure also indicates a small contribution from Cs atom in the vicinity of EF which leads to a small shift of 0.04 eV in the band gap of the doped case w.r.t. host MAPBI3. The noticeable contribution of Cs is observed at ~ -7.5 eV in the

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occupied region. Therefore, addition of Cs in MAPBI3 doesn’t bring any modest change in the band gap and optical response. On the other hand, the CBM is formed by the empty Pb-6p states along with a residual contribution from I-5p states. The first quantitative contribution ascribed to the MA+ cation is 5 eV deep in valence. The incorporation of Cs against CH3NH3 decreases the number of H-atoms and hence the overall strength of H-bonds between H and I gets reduced to some extent. Thus, in turn, increases the tilting of PbI6-octahedra and the coupling between Pb-6s and I-5p states becomes stronger which subsequently increases the band gap of resultant compound slightly. The Fig. 5 shows the electronic charge density isosurfaces in the upper valence

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band and the lower conduction band. The delocalization of electronic charge on Cs-atom is clearly

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visible here.

Fig. 4. Calculated Partial DOS (PDOS) of Cs:MAPbI3 at GGA level of theory

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Fig. 5: Charge density isosurfaces of (a) the upper valence band and (b) the lower conduction band of Cs:MAPbI3.

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The electronic band structure of Cs:MAPbI3 along high symmetry points of the Brillouin zone is reported in the Fig. 6. The direct bandgap of 1.62 eV is obtained along the Г- Г direction. It is stressed here that the direct bandgap from the dispersed Pb-6s/ I-5p valence bands to Pb-6p conduction bands plays an essential role in the superior PV performance of the PSCs and all the

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by central cation.

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visible light absorption takes place in the inorganic cage structure with almost no light absorption

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Fig. 6. Bandstructure of Cs:MAPbI3 along some high symmetry points of the Brillioun zone

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Optical absorption of the materials is fundamentally determined by two factors. One is the transition matric elements between the VB and CB states, and another is their DOS. The former measures the probability of each photoelectric transition and the latter determines the total number of possible photoelectric transitions. Thus, the optical absorption between of these

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materials is closely related to their electronic structures. The edge transition in both the compounds comes from mixed Pb-6s, I-5p to Pb-5p states. The intra-atomic transition

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probability is high which accounts for the higher value of absorption coefficient in both as compared to other commonly used PV materials [44]. Moreover, the value of absorption coefficient in Cs:MAPbI3 is higher than that of MAPbI3 in the visible energy range i.e. from 1.62 eV to 3.25 eV [46] making it one of the potential candidates for the absorber layer in PSCs (Fig. 7). The optical absorption is decided by the tradeoff between widening of the band gap and increase of DOS in sub-VBM region at a particular doping concentration. For 12.5% of Cs doping in MAPbI3, increased DOS in the sub-VBM accounts for the increased absorption coefficient.

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Fig. 7. Absorption coefficient of MAPbI3 and Cs:MAPbI3

4. Conclusion

Using first principles calculations we have shown that mixed inorganic-organic

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perovskites obtained by incorporating 12.5% of Cs into MAPbI3 can be potential candidate for absorber layer in HHP solar cells. This result is an outcome of the DFT calculations performed by using projector augmented wave (PAW) method under GGA exchange-correlation potentials. Our results elucidate that due to the decrease in H-bonding on incorporating Cs in MAPbI3, the

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increased octahedral tilting not only provides the stability to the compound but also increases its bandgap of MAPbI3 from 1.58 eV to 1.62 eV. Moreover, an enhanced value of absorption

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coefficient was observed in the visible light region for the Cs:MAPbI3. In the nutshell, Cs-doing offers an alternative way to avoid the compositional degradation of MAPbI3 at no cost of optical absorption and the photovoltaic performance of MAPbI3 based solar cell device can be extended for a longer time.

Acknowledgements A.T. would like to acknowledge the financial support from Universities Grant Commission (UGC), New Delhi (India) in the form of a junior research fellowship (JRF). The computations

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in this work were performed on National Param Yuva facility (NPSF) of CDAC-Pune (India). The work is supported by DST-SERB, New Delhi vide grant no. EMR/2016/007380.

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Figure Captions

Fig. 1. Top view of unit cell of tetragonal MAPbI3 (space group 140: I4/mcm) Fig. 2. Schematics for introducing 12.5% of Cs-doping in MAPbI3 along with relaxed structures

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of MAPbI3 and Cs:MAPbI3. (Grey/Purple/Brown/Blue/Pink/Turquoise sphere represents Pb/I/C/N/H/Cs atom)

Fig. 3. Calculated TDOS of MAPbI3 and Cs:MAPbI3 at GGA level of theory

Fig. 4. Calculated Partial DOS (PDOS) of Cs:MAPbI3 at GGA level of theory

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Fig. 5: Charge density isosurfaces of (a) the upper valence band and (b) the lower conduction band of Cs:MAPbI3. Fig. 6. Bandstructure of Cs:MAPbI3 along some high symmetry points of the Brillioun zone

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Fig. 7. Absorption coefficient of MAPbI3 and Cs:MAPbI3

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Highlights •

Reduced H-bonding due to Cs-doping in MAPbI3 increases the structural stability. Direct bandgap (1.62 eV) of Cs:MAPbI3 is suitable for visible light

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•

absorption in solar cells. •

Cs-doing avoids the compositional degradation of MAPbI3 at no cost of

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optical absorption.

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