Superior Photovoltaic Properties of Lead Halide Perovskites: Insights

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Feature Article

Superior Photovoltaic Properties of Lead Halide Perovskites: Insights from First-Principles Theory Wan-Jian Yin, Tingting Shi, and Yanfa Yan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp512077m • Publication Date (Web): 06 Feb 2015 Downloaded from http://pubs.acs.org on February 9, 2015

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The Journal of Physical Chemistry

Superior Photovoltaic Properties of Lead Halide Perovskites: Insights from First-Principles Theory Wan-Jian Yin, Tingting Shi, and Yanfa Yan* Department of Physics and Astronomy, and Wright Center for Photovoltaic Innovation and Commercialization, The University of Toledo, Toledo, Ohio 43606, USA

ACS Paragon Plus Environment

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ABSTRACT

Organic-inorganic methylammounium lead halide perovskites have recently emerged as promising solar photovoltaic absorbers. In this feature article, we review our theoretical understanding of the superior photovoltaic properties, such as the extremely high optical absorption coefficient and very long carrier diffusion length of CH3NH3PbI3 perovskites through first-principles theory. We elucidate that the superior photovoltaic properties are attributed to the combination of direct band gap p-p transitions enabled by the Pb lone-pair s orbitals and perovskite symmetry, high iconicity, large lattice constant, and strong antibonding coupling between Pb lone-pair s and I p orbitals. We show that CH3NH3PbI3 exhibits intrinsic ambipolar self-doping behavior with conductivities tunable from p-type to n-type via controlling the growth conditions. We show that the p-type conductivity can be further improved by incorporating some group IA, IB, or VIA elements at I-rich/Pb-poor growth conditions. However, the n-type conductivity cannot be improved under thermal equilibrium growth conditions through extrinsic doping due to the compensation from intrinsic point defects.

KEYWORDS: Photovoltaic properties; perovskite; semiconductor; absorption; defect; doping


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1. INTRODUCTION The organic-inorganic lead halide perovskites such as CH3NH3PbX3 (X= Cl, Br, I) have shown enormous potential for producing low-cost and high efficiency thin-film solar cells. Since the first application of CH3NH3PbI3 in dye-sensitized solar cells (DSSCs) by Miyasaka et al., the efficiency of lead halide perovskite-based thin-film solar cells have increased rapidly from 3.8% for a CH3NH3PbI3-based DSSC in 2009 to 20.1% for a planar CH3NH3PbI3-based thin-film solar cell in 2014.1-16 Such rapid progress has nerve been seen before in the history of solar cell development. Studies have shown that the rapid improvement on cell efficiency is mainly due to the fact that lead halide perovskite absorbers exhibit superior photovoltaic properties such as extremely high optical absorption coefficient8,17 and super long carrier diffusion lengths.10-11 For example, the reported experimental absorption coefficient of a CH3NH3PbI3 thin film has shown a value of about 105 cm-1, which is nearly one order of magnitude higher than that of GaAs.18 The high optical absorption coefficient enables high efficiency lead halide-based thin film solar cells with rather thin absorbers, typically less than 500 nm.

Polycrystalline lead halide

perovskite thin films have shown exceptionally long carrier diffusion lengths, which in the very best case can be as high as 1µm11, even for the films grown at low temperature by wet chemical synthesis. It seems that the grain size and grain boundaries do not significantly affect adversely the carrier diffusion length, indicating that polycrystalline lead halide perovskit thin films may exhibit photovoltaic properties as good as their single-crystal counterparts. As a result, thin-film solar cells based on CH3NH3PbI3-xClx perovskites have achieved open-circuit voltage (VOC) as high as 1.13 V.16 The VOC deficient, defined by Eg/q – VOC, for CH3NH3PbI3-xClx–based solar cells is smaller than that of the best CIGS cells and is approaching to that of the best c-Si and epitaxial sing-crystal GaAs thin-film solar cells.19


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Beside the rapid increase in efficiency, the understanding of the fundamental mechanisms concerning the superior photovoltaic properties of lead halide perovskites has also made important progress. Before the first report of lead halide perovskite-based solar cells, the electronic properties of lead halide perovskites has been studied using density-functional theory (DFT).20,21 After the report of lead halide perovskite-based solar cells, more theoretical investigations were carried out.22-44 Most of these investigations have focused on the electronic and optical properties. Using DFT calculations, we have revealed the possible origins for the high optical absorption coefficients and long carrier diffusion lengths for halide perovskites.37,38 The exceptionally long carrier diffusion length and high VOC observed in polycrystalline films strongly indicate that point defects and grain boundaries are not causing significant non-radiative recombination. Through comprehensive calculations of energy levels of point defects and grain boundaries and the formation energies of point defects under various growth conditions, we have found rather unique defect properties in lead halide perovskites, i.e., all dominating defects in lead halide perovskites do not create deep levels. This discovery has recently been confirmed by other research groups both in theory39-43 and experiments45,46. In this feature article, we review our recent progress on the understanding of the superior photovoltaic properties of CH3NH3PbI3 through DFT calculations. We explain in detail the roles of the Pb lone-pair s orbitals and the perovskite symmetry for the exceptionally high optical absorption coefficients. We further elucidate the impacts of the antibonding coupling between Pb lone-pair s and I p orbitals, the high ionicity, and the large lattice constant on the defect properties in CH3NH3PbI3. Moreover, we provide strategies for doping lead halide perovskite absorbers. We reveal that improved p-type conductivity for CH3NH3PbI3 can be realized by incorporating of group IA, IB, or VIA elements such as Na, K, Rb, Cu, and O at I-rich/Pb-poor


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growth conditions. We further show that the n-type conductivity of CH3NH3PbI3 is more difficult to be improved via extrinsic doping due to the compensation from intrinsic point defects. Our results suggest that non-equilibrium growth conditions and/or processes may be required to produce good n-type CH3NH3PbI3 halide perovskites. The understanding of the origins for the superior photovoltaic properties and doping properties of lead halide perovskites provide guidance for designing new absorber materials or engineering the current perovskite materials for even more improved device performance. 2. COMPUTATIONAL DETAILS The calculations reported in this article were carried out by using the VASP code with the standard frozen-core projector augmented-wave (PAW) method.47,48 The cut-off energy for basis functions was 400 eV. The general gradient approximation (GGA) was used for exchangecorrelation.49 Atomic positions are relaxed until all the forces on atoms are below 0.05 eV/Å. It has been discussed that it is important to include the effect of spin-orbital coupling (SOC) in DFT calculations of the electronic and optical properties of lead halide perovskites due to the strong relativistic effect of Pb. 26-30 However, SOC-GGA significantly underestimates the band gap of halide perovskites. For example, the calculated SCO-DFT band gap is about 0.6 eV for CH3NH3PbI3, much smaller than the experimental gap of 1.56 eV. To correct the band gap underestimation, hybrid functional such as the Heyd−Scuseria−Ernzerhof (HSE06) functional, need to be used.50 The most advanced calculation approach is to use SOC-GW calculation.28 However, so far, both SOC-HSE and SOC-GW calculations are very time consuming and can only be feasible for calculations with small unit cells. In our study, most calculations require the use of large super cells. For these calculations, it is not possible to consider SOC-HSE or SOCGW. Fortunately, it is known that the errors of using GGA and non-SOC are cancelled with each


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other in occurrence.25

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The defect properties predicted by non-SOC-GGA calculations are

confirmed by experiments.46 Our recent results show that the calculated optical absorption spectrum of CH3NH3PbI3 using non SOC-GGA can match well with experimental results measured by spectroscopic ellipsometry (unpublished results). Therefore, non-SOC-GGA is so far a reasonable and efficient approximation for the calculation of optical properties and defect physics of CH3NH3PbI3. At finite temperatures, CH3NH3PbI3 may exhibit three phases, the cubic (α), tetragonal (β), and orthorhombic (γ) phases, as shown in Figures 1(a), 1(b), and 1(c), respectively. Transitions between those structures at finite temperature often happen in most perovskites.51,52 It was reported that the α to β to γ phase transitions happen at 330 K and 160 K, respectively.53 In α phase, all the octahedra formed by Pb and I atoms are oriented along the same direction. In β and γ phases, some of the octahedra rotate to different directions. The large solid boxes and the small dashed boxes in Figs. 1(b) and 1(c) indicate the relationship between the unit cells of α, β and γ phases and the unit cells of the α phase. The α phase has a Pm 3 m point symmetry, whereas the point symmetries for β and γ phases are I4/mcm and Pnma-2.

Figure 1. Atomic structures for (a) α phase, (b) β phase, and (c) γ phase CH3NH3PbI3.


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The rotation of Pb-I octahedra does not change significantly the electronic properties of CH3NH3PbI3. Figures 2(a), 2(b), and 2(c) show the calculated band structures for α, β, and γ phases, respectively, using DFT with non-SOC-GGA calculations. For better comparison, the band structure of α phase is calculated with a (

2× 2×2)

supercell. The main differences

between these band structures are the slight splitting of the conduction band minimum (CBM) and valence band maximum (VBM) caused by the decreased symmetries. This suggests that the Pb-I-Pb bond angle distortions do not change significantly the electronic structures. We therefore anticipate that the electronic, optical, and defect properties should be very similar for these three phases. Therefore, in this article, only the α phase is used for calculations of electronic, optical, and defect properties of CH3NH3PbI3.

(a)

(b)

α phase

(c)

β phase

γ phase

Figure 2. Calculated band structure for (a) α phase, (b) β phase, and (c) γ phase CH3NH3PbI3. The α phase is calculated using the same tetragonal supercell as for β and γ phases. Adapted with permission from ref 37. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.


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The point defect calculations were based on a (4×4×4) host supercell with the Γ point. The supercell contains 768 atoms. With this large supercell size, both VBM and CBM are folded to the Γ point. Our test calculations indicate that the use of (4×4×4) host supercell with the Γ point provides reliable results. It is noted that the main characteristics of the conduction and valence bands of CH3NH3PbI3 produced by SOC and non-SOC DFT calculations do not change significantly. Because the defect levels, especially the shallow acceptor/donor levels, are mostly derived from either the upper valence or the lower conduction bands, it is reasonable to expect that the calculated shallow energy levels using non-SOC should not exhibit significant errors. The errors for deep levels could be large, but these defects are not important for doping. Grain boundaries (GBs) are modeled using supercells containing two identical GBs with opposite arrangements. The atomic structures of GBs in halide perovskites are adopted from the atomic structures of the same GBs in perovskite oxides, which have been determined by atomicresolution transmission electron microscopy.54 The calculation of the transition energies and formation energies of defects include the following:55,56 We first calculate the total energy E(α, q) for a supercell containing defect α in charge state q, then calculate the total energy E(host) of the same supercell without the defect, and, finally, calculate the total energies of the involved elemental solids or gases at their stable phases. The defect formation energy also depends on the atomic chemical potentials µi and the electron Fermi energy EF. From these quantities, the defect formation energy, ∆Hf(α, q), can be obtained by:

∆Hf(α, q) = ∆E(α, q) + Σ niµi + qEF

(1)

where ∆E(α, q) = E(α, q) – E(host) + Σ niE(i) + qεVBM(host). EF is referenced to the VBM of the host. µi is the chemical potential of constituent i referenced to elemental solid/gas with


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energy E(i). ni is the number of elements, and q is the number of electrons transferred from the supercell to the reservoirs in forming the defect cell. The transition energy for the defect α from q charge state to q' charge state, εα(q/q'), can be obtained by:

εα(q/q') = [∆E(α, q) – ∆E(α, q')] / (q' - q).

(2)

The formation energy of a charged state is then given by:

∆Hf(α,q) = ∆Hf(α,0) – qε(0/q) + qEF ,

(3)

where ∆Hf(α,0) is the formation energy of the charge-neutral defect and EF is the Fermi level with respect to the VBM. 3. RESULTS AND DISCUSSIONS 3.1. Origin for the high optical absorption coefficient We first discuss the origin of the extremely high optical absorption coefficient for CH3NH3PbI3 perovskite. The optical absorption of a semiconductor at photonic energy hω is directly

2π h

correlated with

∫

2

2

v Hˆ | c

8π

r

(

r

)

δ Ec (k ) − Ev (k ) − hω d 3k ,57 where 3

v Hˆ | c is

the

transition matrix from states in the valence band (VB) to states in the conduction band (CB) and the integration is over the whole reciprocal space. For simplicity, the transition matrix v Hˆ | c can be considered independent of k and the absorption formula is approximately

2π v Hˆ | c h

2

r

r

∫ 8π δ ( E (k ) − E (k ) − hω ) d k , where the second term is the joint density of 2

3

c

3

v

states (JDOS) at energy hω . Therefore, the optical absorption of a semiconductor is fundamentally determined by the transition matrix and JDOS. The JDOS is related to the density


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of states (DOS) of the CB and VB, which depend on the atomic orbitals that form the CB and VB. Figures 3(a) and 3(b) show the schematic of the transitions responsive for the optical absorptions of two representative conventional photovoltaic absorber materials, Si and GaAs. From the JDOS point of view, the CB and VB of Si are more preferred than that of GaAs, because the s bands are more dispersive than the p bands. However, Si has an indirect gap. The transitions between the VB and CB edges require the assistant of phonons, leading to a rather inefficient optical absorption near the band edge. The ideal situation for efficient optical absorption is to combine the characteristics of Si and GaAs, i.e., to have p-p transitions and a direct band gap. The p-p transitions can only be possible for compound semiconductors containing cation elements that exhibit lone pair s electrons, such as Ge(2), Sn(2), Pb(2), Sb(3), and Bi(3). For example, SnS, PbS, Sb2Se3, Bi2S3, etc. are compound semiconductors with p-p transitions. Unfortunately, these compounds usually have low symmetry and therefore indirect band gaps. However, lead halide perovskites not only have p-p transitions, but also have direct band gap, leading to highly efficient optical absorptions as depicted in Fig. 3(c). Therefore, lead halide perovskites are expected to exhibit high optical absorption coefficient, due to the Pb lonepair s orbitals and the perovskite symmetry.

Figure 3. The schematic optical absorption of (a) Si, (b) GaAs, and (c) CH3NH3PbI3 perovskite.


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To evaluate the high optical absorption of halide perovskites, the optical absorption coefficients of two representative absorbers, CH3NH3PbI3 and GaAs, are calculated. Our results shown in Figure 4(a) confirm that the JDOS of CH3NH3PbI3 is significantly higher than that of GaAs. The trend of JDOS is consistent with the calculated optical absorption coefficients shown in Figure 4(b). It is seen that in the visible light regions, the absorption coefficients of CH3NH3PbI3 are nearly one order of magnitude higher than that of GaAs. As the visible light range accounts for the major usable portion of the full solar spectrum, high visible light absorption is critical for achieving high efficiency solar cells. Other commonly studied solar cell absorbers such as CdTe, CIGS and CZTSS have similar chemical characters in their CBs58,59 as GaAs. Therefore, they are expected to exhibit weaker optical absorption above the absorption edge than CH3NH3PbI3.

(a)

(b)

(c)

Figure 4. Calculated (a) JDOS, (b) optical absorption, and maximum efficiency as a function of thickness for CH3NH3PbI3 and GaAs. Adapted with permission from ref 37. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.

The optical absorption coefficient strongly affects the quantum efficiency of a solar cell, which is not considered in the well-known Shockley-Queisser limit.60 For a real solar cell, the theoretical maximum efficiency depends on the thickness of the absorber layer. After taking the absorption coefficient and absorber layer thickness into consideration, we have calculated the


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maximum efficiencies of representative light absorbers as a function of the thickness of the absorber layers following the method proposed by Yu et al.61 As shown in Figure 4(c), the calculated maximum efficiencies for CH3NH3PbI3 are much higher than that of GaAs for any given thickness. CH3NH3PbI3 is capable of achieving high efficiencies with very thin absorber layers. For example, with a 300 nm CH3NH3PbI3, the solar cell can have a maximum efficiency up to 21%, while it is only 13% for a GaAs-based solar cell. A recent simulation by Filippetti et al.62 has taken the consideration of carrier concentration and minority carrier lifetime. Similar results have been obtained. 3.2. Origin for the exceptionally long carrier diffusion length Small effective masses for electrons and holes. The carrier diffusion length is typically determined by the effective masses (m*), non-radiative recombination, and scattering of carriers. The effective masses for electrons and holes are determined by the dispersion of the edges of −1

2 CBs and VBs, and can be approximately described by m* = h2  ∂ ε2(k )  , where ε (k ) are the

 ∂k 

energy dispersion relation functions described by band structures. CB and VB edges with larger dispersions result in smaller effective masses. The CBMs of conventional thin-film solar cell absorbers (p-s semiconductors), such as GaAs and CdTe, are mostly contributed by cation s and anion s orbitals, whereas the VBMs are mostly contributed by anions’ p characters. High-energylevel s orbitals are more delocalized than low-energy-level p orbitals. Consequently, the electron effective mass is smaller than hole effective mass in the p-s semiconductors. As discussed above, Pb atoms exhibit 6s2 electron configurations in lead halide perovskites. The lower CBs of Pb halide perovskites are mainly derived from the unoccupied Pb p orbitals.


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The upper VBs are mainly halogen p orbitals mixing with a small component of Pb s states. Therefore, the electronic structure of CH3NH3PbI3 is inverted as compared to conventional p-s semiconductors. However, the cation Pb p orbital has a much higher energy level than anion p orbitals. Therefore, the lower CBs of lead halides are expected to be more dispersive than the upper VBs in conventional p-s semiconductors. Furthermore, because Pb lone-pair s orbitals are close in energy to the filled I p orbitals, there is strong s-p coupling, making the upper VB of CH3NH3PbI3 very dispersive. Therefore, in lead halide perovskites, the effective masses are smaller for holes than for electrons, which is contrary to the conventional p-s semiconductors. Benign defect properties. The non-radiative recombination and carrier scattering are often caused by defects that generate deep gap states. The defects include both point defects and structural defects such as grain boundaries. We found that lead halide perovskites exhibit unique defect properties that have not seen in other semiconductors, i.e., grain boundaries and dominant point defects do not create deep levels and are therefore electrically benign. Some point defects generate deep gap states, but these defects have high formation energies and their concentrations are expected to be low in synthesized lead halide perovskite thin films. We further found that these unique defect properties are attributed to the strong Pb lone-pair s – halogen p antibonding coupling, the ionic characteristics, and the large lattice constants. We first provide a qualitative understanding on the basic electronic structure and unique defect properties of CH3NH3PbI3 based on the atomic orbital theory, which has been successfully used to predict the oxygen energy levels in oxides.63 Our discussions are lying on two facts: (i) The energy bands are formed by atomic orbital mixing (either through ionic or covalent interactions or in-between) between bonded atoms; (ii) The defect levels of both point and structural defects are formed due to the breaking or addition of bonds, namely, dangling bonds


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and wrong bonds. In this way, we can unravel the atomic origin of defect levels starting from basic electronic structure of the host material. The formation of the CB and VB of CH3NH3PbI3 is depicted in Figure 5(a). As discussed above, the CB of CH3NH3PbI3 is mainly derived from the empty Pb p orbital. Due to the ionic characteristic of CH3NH3PbI3, the covalent antibonding coupling between Pb p and I p is not strong. Therefore, the CBM should not be much higher than the atomic Pb p states. Therefore, the energy difference between the CBM and the Pb p atomic orbital is not large, as shown Fig. 5(a). The VB of CH3NH3PbI3 is mainly derived from I p states with small components of Pb s states. Because of the strong Pb s–I p antibonding coupling, the VBM is above the I p atomic orbital level, as shown in Fig. 5(a). When a cation vacancy is formed, the defect state created by this cation vacancy is composed of the surrounding anion dangling bonds. For an I vacancy in CH3NH3PbI3, the defect state is formed by the Pb dangling bonds surrounding the I vacancy. The defect state will therefore lie in between the Pb p atomic orbital level and the CBM of CH3NH3PbI3, as shown in Fig. 5(b). Because the difference between the Pb p atomic orbital level and the CBM of CH3NH3PbI3 is small as discussed above, the I vacancy level should be close to the CBM, forming a shallow donor state (Dd). For a Pb vacancy, the defect state is formed by the I dandling bonds surrounding the Pb vacancy, and therefore it should be between the VBM and the I p atomic orbital level. As discussed earlier, due to the strong Pb s – I p antibonding coupling, the VBM is higher in energy than the I p atomic orbital level, as shown in Fig. 5(a). Therefore, the Pb vacancy level should be below the VBM, forming a shallow acceptor (Da). The formation of defect states of antisite defects are from either cation-cation or anion-anion wrong bonds. The formation of defects states of interstitial defects can also be derived from either dangling bonds or wrong bonds, depending on the defect configuration. Wrong bonds could create deep gap states. For example, Pb p – Pb p


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and I p – I p wrong bonds in CH3NH3PbI3 may create deep levels, as shown in Fig. 5 (c). The CWS and AWS* states could be deep in the band gap. CWS denotes cation-cation wrong bond state and AWS denotes anion-anion wrong bond state. The asterisk denotes the corresponding antibonding state.

Figure 5. Schematics depicting the formation of (a) VBM and CBM, (b) donor-like and acceptorlike defects from cation and anion vacancies; and (c) defects from cation-cation and anion-anion wrong bonds.

To confirm the above general picture, we have calculated the transition levels for all possible point defects in CH3NH3PbI3: CH3NH3, Pb, and I vacancies (VMA, VPb, VI), CH3NH3, Pb, and I interstitial (MAi, Pbi, Ii), CH3NH3 on Pb and Pb on CH3NH3 cation substitutions (MAPb, PbMA) and four antisite substitutions, CH3NH3 on I (MAI), Pb on I (PbI), I on CH3NH3 (IMA), and I on Pb (IPb). The calculated transition energies for these point defects are shown in Figure 6. It is seen that all the vacancy defects and most interstitial defects exhibit rather shallow transition energy levels. The defects that generate deep levels are IMA, IPb, Pbi, MAI and PbI. These defects are mostly cation or anion antisite defects, except for Pbi. The results are consistent with the picture shown in Fig. 5. We found that the reason why Pbi creates deep gap states is due to the


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crystal field splitting of Pb p orbital at interstitial site, which pulls Pb pz orbital below px/py orbital. As discussed above, the reason why VPb and MAPb are shallow acceptors is attributed to strong s-p antibonding states at the VBM of CH3NH3PbI3. Without Pb s lone-pair orbitals, the VBM should be derived only from I p orbitals. The s-p antibonding coupling between Pb lone pair s and I p orbitals pushes the VBM up to a higher level so that the acceptors are generally shallower than in the case without strong s-p antibonding coupling. The shallow nature of MAi and VI is due to the high ionicity of CH3NH3PbI3. A MAi has no covalent bonding with Pb-I framework and therefore does not create additional gap states.

Figure 6. Calculated transition energy levels of donor-like and acceptor-like point defects in CH3NH3PbI3. Adapted with permission from ref 37. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.

The electrical properties of a semiconductor are determined by the dominant point defects formed in the semiconductor. Therefore, to determine which of the above point defects may


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dominate the electronic properties of CH3NH3PbI3, we have calculated the formation energies of the defects considered above. As shown in section 2, the formation energy of a point defect depends on the chemical potentials of constituent elements. In thermodynamic equilibrium growth conditions, the chemical potentials are constrained in ranges that promote the growth of CH3NH3PbI3 and exclude the formation of secondary phases such as PbI2 and CH3NH3I. Therefore, the chemical potentials should satisfy:55,56

µCH NH + µ Pb + 3µ I = ∆H (CH 3 NH 3 PbI 3 ) = −5.26 eV 3

3

(6)

where µi is the chemical potential of the constitute element referred to its most stable phase and ∆H(CH3NH3PbI3) is the formation enthalpy of CH3NH3PbI3. For µCH3 NH3 , we used bodycentered-cubic phase of CH3NH3 following Cs. To exclude the possible secondary phases of PbI2 and CH3NH3I (rock-salt phase), the following constrains must also be satisfied.

µCH NH + µ I < ∆H (CH 3 NH 3 I ) = −2.87 eV

(7)

µPb + 2µI < ∆H (PbI2 ) = −2.11 eV

(8)

3

3

The chemical potentials of Pb and I satisfying eqs (6) (7) (8) are shown as the middle red region in Figure 7. This narrow and long chemical range indicates the growth conditions for synthesizing CH3NH3PbI3 phase in the equilibrium conditions. The narrow but long chemical potential range indicates that the growth conditions should be carefully controlled to form the desirable CH3NH3PbI3 perovskite phase. The small chemical range is consistent with the calculated small dissociation energy of CH3NH3PbI3, only 0.27 eV, as defined by E(CH3NH3I) + E(PbI2) − E(CH3NH3PbI3).


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Figure 7. Calculated chemical ranges for forming CH3NH3PbI3 (middle red region), PbI2 (upper right yellow region), and CH3NH3I (left blue region). Three representative points A(µMA= −2.87 eV, µPb= −2.39 eV, µI= 0 eV), B(µMA= −2.41 eV, µPb= −1.06 eV, µI= −0.60 eV), and C(µMA= −1.68 eV, µPb= 0 eV, µI= −1.19 eV) were used for calculating the formation energies of point defects. Adapted with permission from ref 38. Copyright 2014 AIP Publishing LLC.

To evaluate the dependence of formation energies of point defects on the chemical potentials of the constituent element, we have chosen three representative points, A (I-rich/Pb-poor), B (moderate), C (I-poor/Pb-rich), shown in Figure 7. Their formation energies of the considered point defects as a function of Fermi level position at chemical potential A, B, and C are shown in Figures 8(a), 8(b), and 8(c), respectively. For clarity, only the defects with low formation energies are shown in solid color lines. The defects with high formation energies are shown by light-gray lines. At chemical point A, i.e., I-rich/Pb-poor, CH3NH3PbI3 should be intrinsically ptype., because the Fermi level is close to the VBM. At chemical point B, i.e., moderate, CH3NH3PbI3 should be intrinsic (low conductivity). At chemical point C, i.e., I-poor/Pb-rich, CH3NH3PbI3 should be intrinsically good n-type, as te Fermi level is close to the CBM. In CH3NH3PbI3, the dominant defects are donor MAi and acceptor VPb, which have comparable formation energies. The low formation energy of VPb in CH3NH3PbI3 is due to the energetically


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unfavorable s-p antibonding coupling, which resembles the p-d antibonding coupling in CIS59. The fully occupied antibonding state between Pb s and I p coupling does not gain electronic energy thus tend to break bond and form a vacancy. The lower formation energy of MAi could be explained by its weak interaction with the Pb-I framework. The Fermi level is pined by the formation of these two shallow defects. A recent report has demonstrated that the conductivity of CH3NH3PbI3 can be tuned from p-type to n-type by modifying the growth conditions.46

Figure 8. Calculated formation energies of point defects as a function of Fermi level at three chemical potential points, (a) A, (b) B, and (c) C, shown in Figure 7. Adapted with permission from ref 38. Copyright 2014 AIP Publishing LLC.

It is seen that the defects that have low formation energies, such as MAi, VPb, MAPb, Ii, VI, and VMA, have transition energies less than 0.05 eV above (below) the VBM (CBM) of CH3NH3PbI3. On the other hand, all the defects that create deep levels, such as IPb, IMA, Pbi, PbI, have high formation energies. Because only the defects with deep levels are responsible for nonradiative recombination, these formation energies strongly indicate that CH3NH3PbI3 should intrinsically have low non-radiative recombination rate.


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In polycrystalline semiconductor absorbers, grain boundaries could also create deep levels and increase the non-radiative recombination rate. In conventional inroganic solar cell absorbers such as GaAs, CIGS, CZTS, and CdTe, intrinsic GBs create deep levels in band gaps and are considered detrimental for solar cell performance. Recent theoretical studies have shown that cation-cation and anion-anion wrong bonds are mainly responsible for the deep gap states.64-66 We have therefore calculated the electronic properties of GBs in CH3NH3PbI3 perovskite. Because there are no experimental data available for atomic structure of GBs in CH3NH3PbI3, we have adopted the atomic structures of GBs determined in perovskite oxides by atomic-resolution transmission electron microscopy.54 To maintain the periodicity, each supercell contains two identical GBs, which are oriented in the opposite directions. Figure 9 shows the atomic structure of a supercell containing two identical Σ5(310) GBs. The atomic structure is adopted from the same GB in perovskite SrTiO3. To investigate the consequence of interaction between the two GBs in the supercell, supercells with various widths between the two GBs are constructed. When the distance between the GBs reaches 38.32 Å, the interaction between the two GBs becomes negligible. The fully relaxed GB structure is shown in Figure 9. Some Pb and I atoms in the boundary regions that have dangling bonds or wrong bonds are labeled. The Pb1-Pb1’, I1-I1’, I2I2’, I3-I3’ distances are 4.870, 4.636, 4.856, and 3.776 Å, respectively. This is mainly due to the large lattice constant of CH3NH3PbI3. Such large distances indicate that there are no strong wrong Pb-Pb and I-I bonding. The GBs contain mainly Pb and I dangling bonds, Pb-I-Pb wrong bond angles, and extra bonds (Pb2). As discussed above, Pb and I dangling bonds should generate only shallow levels. Therefore, the GBs are expected to be electrically benign.


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Figure 9. The structural model of Σ5(310) GBs in CH3NH3PbI3. Two identical GBs are included the supercell to enable the periodicity. Adapted with permission from ref 37. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.

Our DOS analysis indeed shows that the GBs in CH3NH3PbI3 are intrinsically electrically benign. Figure 10(a) shows the comparison of the calculated total DOS of a supercell containing CH3NH3PbI3 bulk and a supercell containing two Σ5(310) GBs with opposite arrangements. The two DOS are almost identical in the band gap regions, indicating that the GBs do not generate any states in the band gap of CH3NH3PbI3. The benign GB properties could be explained by the shallow nature of point defects formed by dangling bonds. We have further plotted the partial DOS of Pb and I atoms such as Pb1, Pb2, I1, I2, I3, I4, I5, and I6 in the Σ5(310) GB regions and Pb3 and I7 atoms in bulk region (Figure 10(b)-10(e)). It is seen that no gap states are observed. We have also considered Σ3(111) GB, another common GB in perovskites. Likewise, no gap state is observed. Such completely benign GB behavior has not been seen in GaAs, CdTe, CuInSe2, and Cu2ZnSnSe4.64-66 The benign GB properties in CH3NH3PbI3 are consistent with its shallow defect feature in point defects.


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Figure 10. (a) Calculated total DOS of a supercell with CH3NH3PbI3 bulk and a supercell containing two Σ5(310) GBs. (b)-(e) Partial DOS of selected atoms near GB planes. The partial DOS are enlarged for clarity. Adapted with permission from ref 37. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.

3.3. Doping properties of CH3NH3PbI3 High efficiency CH3NH3PbI3 perovskite thin-film solar cells typically use expensive and unstable hole transport material (HTM)2,2’,7,7’-tetrakis-(N,N-di-p-methoxyphenylamine)9, 9’-spirobifluorene (spiro-OMeTAD)6,7,14,16. CH3NH3PbI3 solar cells using non-spiro-OMeTAD HTM layers such as CuSCN,

67,68

NiO,

67

and CuI69 or no HTM layers15,70-72 have exhibited

poorer performance than the cells using spiro-OMeTAD HTM layers. However, spiro-OMeTAD is not preferred for commercial manufacturing. An alternative approach to achieve low-cost and stable hole transport materials is to dope CH3NH3PbI3 p-type. Furthermore, if CH3NH3PbI3 can be doped both p-type and n-type, p-n junction based solar cell structures, which have been the case for most inorganic solar cells, may be realized.


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We have considered external doping using group IA IB, IIA, IIB, IIA, VA and VIA elements. For group IA and IB elements, we considered K, Na, Rb, and Cu on interstitial sites (Nai, Ki, Rbi, and Cui) as donors and on Pb sites (NaPb, KPb, RbPb, and CuPb) as acceptors. For group IIA and IIB elements, we considered Sr, Ba, Zn, and Cd on MA site (SrMA, BaMA, ZnMA, and CdMA) as donors and on Pb site (SrPb, BaPb, ZnPb, and CdPb) as neutral defects. For group IIIA and VA elements, we considered Al, Ga, In, Sb and Bi, on Pb sites (AlPb, GaPb, InPb, SbPb, and BiPb) as potential donors. For group VIA elements, we considered O, S, Se, and Te on I sites (OI, SI, SeI, and TeI) as potential acceptors.

Figure 11. Calculated transition energy levels of considered extrinsic dopants. Adapted with permission from ref 44. Copyright 2014 American Chemical Society.

The calculated transition energy levels of shallow donors and acceptors are shown in Figure 11. For donors, the transition energy levels are referenced to the CBM of CH3NH3PbI3, whereas the levels are references to the VBM for acceptors. It is seen that interstitial group-IA and -IB elements, Nai, Ki, Rbi, and Cui, are shallow donors. Group-IIA elements such as Sr and Ba


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occupying MA sites are also shallow donors. They are neutral defects when they occupy Pb sites. Our calculations revealed that ZnMA, CdMA, AlPb, GaPb, and InPb are deep donors. Therefore, these dopants are not considered. BiPb and SbPb are shallow donors with transition energy levels of -0.17 eV and -0.19 eV, respectively. The calculated transition energy levels of NaPb, KPb, RbPb, and CuPb are -0.026 eV, 0.014 eV, 0.020 eV, and 0.084 eV, respectively. The calculated transition energy levels for OI, SI, SeI, and TeI are -0.076 eV, 0.021eV, 0.070eV, and 0.128eV, respectively. The negative transition energies for NaPb and OI mean that their levels are below the VBM, indicating spontaneous ionizations.

Figure 12. Calculated total DOS and partial DOS from acceptors of OI, SI, SeI, and TeI. The DOS of the acceptors are enlarged by 500 times. Adapted with permission from ref 44. Copyright 2014 American Chemical Society.

A shallow transition energy level typically corresponds to a delocalized defect state, while a deep level is related to a localized defect state. The localization of a defect states can be viewed


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from the total and partial DOS plots. For example, Figure 12 shows the calculated total DOS and partial DOS of supercells containing OI, SI, SeI, and TeI. It is seen clearly that the O p state is very delocalized with strong coupling to the valence band of CH3NH3PbI3. However, the p states of S, Se, and Te show clear narrow peaks, indicating more localization. The trend is consistent with the trend of the energy position of the atomic p-orbitals of the O, S, Se, and Te. Therefore, OI has the shallowest level and TeI has the deepest level. The electrical properties of semiconductors depend on the Fermi levels, which are determined by the formation of both intrinsic and extrinsic defects. To evaluate the extrinsic doping properties of CH3NH3PbI3, we have calculated the formation energies of the above dopants as a function of Fermi level under two representative growth conditions: I-rich/Pb-poor and I-poor/Pb-rich. To calculate the formation energies of dopants, the chemical potentials of considered dopant elements must satisfy additional constrains to exclude the formation of dopant-related secondary phases. For example, for doping using group IA elements such as Na, K, and Rb, we exclude the possible secondary phases of NaI, KI, and RbI. Therefore, the following constrains must also be satisfied: µNa + µI < ∆H(NaI) = -2.59 eV, µK + µI < ∆H(KI) = -3.01 eV, and µRb + µI < ∆H(RbI) = -3.03 eV. Similar constrains are considered to exclude the formation of other possible dopant-related secondary phases, for examples, CuI, SrI2, BaI2, SbI3, BiI3, PbO, PbS, PbSe, and PbTe. Figures 13(a) and 13(b) show the calculated formation energies as functions of Fermi levels for group IA and IB dopants at I-rich/Pb-poor and I-poor/Pb-rich growth conditions, respectively. The dashed line shows the intrinsic defects with the lowest formation energies. At I-rich/Pb-poor condition (Fig. 13(a)), acceptors NaPb, KPb, RbPb, and CuPb have much lower formation energies than the donors, Nai, Ki, Rbi, and Cui. Therefore, the majority of these


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dopants should occupy Pb sites and dope CH3NH3PbI3 p-type. The compensation from intrinsic donor defect, MAi, is very weak. For Na and K doping, the Fermi levels are pinned below the VBM, indicating degenerate p-type doping. For Cu doping, the Fermi level is pinned by the CuPb (0/-1) transition, which is about 0.09 eV above the VBM. For Rb doping, the Fermi level is pinned at about 0.06 eV above the VBM by RbPb and MAi. Therefore, I-rich/Pb-poor growth conditions, group 1A and 1B doping should lead to improved p-type conductivities as compared to undoped CH3NH3PbI3. At I-poor/Pb-rich growth conditions (Fig. 13(b)), the compensations from intrinsic donor defects and extrinsic acceptor defects become strong. For Na, K, and Rb doping, the Fermi levels are pinned at 1.02 eV, 1.26 eV, and 1.31 eV by NaPb, KPb, RbPb and MAi, respectively. For Cu doping, the Fermi level is pinned by the intrinsic defects, MAi and VPb. Therefore, at I-poor/Pb-rich growth conditions, group IA and IB doping would lead to more insulating CH3NH3PbI3 as compared to the undoped ones.

Figure 13. Calculated formations energies as functions of the Fermi levels for group IA and IB dopants at (a) I-rich/Pb-poor and (b) I-poor/Pb-rich conditions. Adapted with permission from ref 44. Copyright 2014 American Chemical Society.


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We further found that doping with Sr, Ba, Sb, and Bi does not improve the n-type conductivity of CH3NH3PbI3 as compared to undoped material grown at the same growth conditions. This is largely due to the factor that the dopant related defects have higher formation energies than the dominant intrinsic defects MAi and VPb, which pin the Fermi levels. For Sr and Ba doping, the acceptors of SrMA and BaMA have higher formation energies than the neutral defects of SrPb and BaPb. This could be due to a number of reasons. First, the s-p antibonding coupling is energetically unfavorable.73,74 When a Pb is substituted by a Sr2+ or Ba2+, the energetically unfavorable s-p antibonding coupling is eliminated, leading to energetically favorable substitutions. Secondly, Sr and Ba are isovalent to Pb. While SrMA and BaMA introduce electrons to the conducton band, SrPb and BaPb do not. Thirdly, SrPb and BaPb may introduce less lattice strain than SrMA and BaMA due to less size mismatch. Therefore, group IIA element doping should not influence the electrical conductivity of CH3NH3PbI3 due to the strong compensation effects from intrinsic defects, particularly VPb and MAi. For doping with group VIA elements, we found that only O may improve the p-type conductivity of CH3NH3PbI3 under I-rich/Pb-poor growth conditions. Other group VIA elements such as S, Se, and I do not improve the p-type conductivity of CH3NH3PbI3. Figures 14(a) and 14(b) reveal the calculated formation energies as functions of Fermi levels for group-VIA elements on I sites at I-rich/Pb-poor and I-poor/Pb-rich conditions, respectively. The chemical potentials for O, S, Se, and Te are constrained to avoid the formation of secondary phases of PbO, PbS, PbSe, and PbTe. The calculated formation enthalpies are -2.96 eV, -1.16 eV, -1.25eV and -0.96eV for PbO, PbS, PbSe, and PbTe, respectively. The dashed lines show the intrinsic defects with the lowest formation energies. It is seen that at I-rich/Pb-poor growth condition (Fig. 14(a)), the Fermi level for doping with O is pinned at the top of VBM by MAi and OI. Therefore,


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the p-type conductivity is expected to be better than intrinsic CH3NH3PbI3 grown at the same growth condition (Fermi level is pinned by MAi and VPb at ~0.1 eV above VBM). An interstitial O atom at the site that binds to two H atoms of a MA molecule has the lowest energy. This configuration resembles an interstial O in Si. Similarly the O interstitial in MAPbI3 does not produce any gap states and therefore is a neutral defect. At I-poor/Pb-rich condition, the doping is strongly compensated by the formation of intrinsic point defects. Therefore, for doping using group VIA elements, only O leads to improved p-type conductivity at I-rich/Pb-poor conditions as compared to intrinsic CH3NH3PbI3 grown at the same conditions.

Figure 14. The calculated formation energies as functions of Fermi levels for group VIA dopants at (a) I-rich/Pb-poor and (b) I-poor/Pb-rich. Adapted with permission from ref 44. Copyright 2014 American Chemical Society.


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4. CONCLUSION We have reviewed our understanding of the superior photovoltaic properties of CH3NH3PbI3 through first-principles theory calculations. We have elucidated that the extremely high optical absorption coefficient is due the perovskite symmetry and the direct band gap p-p transitions enabled by the Pb lone-pair s orbitals. The long carrier diffusion length is attributed to the unique defect properties, i.e., the dominant point defects in CH3NH3PbI3 only produce shallow levels and GBs are electrically benign. Such unique defect properties are due to the large lattice constant, ionic characteristics, and strong antibonding coupling between Pb lone-pair s and I p orbitals. We have shown that CH3NH3PbI3 can be made with electrical conductivity from a good p-type to a good n-type via tuning the growth conditions. We have also shown that Na, K, Rb, and O doping at I-rich growth conditions can improve the p-type conductivity. However, n-type conductivity cannot be improved through extrinsic doping due to strong compensations from intrinsic defects.

AUTHOR INFORMATION Corresponding Author Yanfa Yan; Email: [email protected]; Tel: (1) 419 530 3918 ACKNOWLEDGMENT This work was supported by the U.S. Department of Energy (DOE) SunShot Initiative under the Next Generation Photovoltaics 3 program (DE-FOA-0000990) and Ohio Research Scholar Program. This research used the resources of the Ohio Supercomputer Center and the National


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Biographies: Wan-Jian Yin received his B.S. in Physics (2004) and Ph.D. in Theoretical Physics (2009) from Fudan University, China. He joined the National Renewable Energy Laboratory (NREL) as postdoctoral researcher in 2009. He is currently holding a joint position of research associate in NREL and research assistant professor in University of Toledo. His research interests include energy-related materials and defect physics in semiconductors.

Tingting Shi received Ph. D. (2014) from The University of Toledo, USA. She has studied in National Renewable Energy Laboratory for one year before coming to University of Toledo. She has been working on computational study of photovoltaic materials.


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Yanfa Yan has been an Ohio Research Scholar Chair and Professor in the Department of Physics and Astronomy at The University of Toledo, since 2011. Previously, he was a Principal Scientist at the National Renewable Energy Laboratory. He earned his Ph. D. in Physics from Wuhan University. His expertise includes theoretical study of electronic properties and defect physics of semiconductors and nanoscale characterization of microstructures, interfaces, and defects in thinfilm photovoltaic materials. He is a Fellow of the American Physical Society.


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Calculated charge density map revealing the antibonding coupling nature between Pb s-I p orbitals 101x100mm (200 x 200 DPI)


Superior Photovoltaic Properties of Lead Halide Perovskites: Insights

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