Letter pubs.acs.org/JPCL
Anomalous Alloy Properties in Mixed Halide Perovskites Wan-Jian Yin,*,†,‡ Yanfa Yan,*,‡ and Su-Huai Wei*,† †
National Renewable Energy Laboratory, Golden, Colorado 80401, United States Department of Physics & Astronomy and the Wright Center for Photovoltaics Innovation and Commercialization, The University of Toledo, Toledo, Ohio 43606, United States
‡
ABSTRACT: Engineering halide perovskite through mixing halogen elements, such as CH3NH3PbI3−xClx and CH3NH3PbI3−xBrx, is a viable way to tune its electronic and optical properties. Despite many emerging experiments on mixed halide perovskites, the basic electronic and structural properties of the alloys have not been understood and some crucial questions remain, for example, how much Cl can be incorporated into CH3NH3PbI3 is still unclear. In this Letter, we chose CsPbX3 (X = I, Br, Cl) as an example and use a first-principle calculation together with clusterexpansion methods to systematically study the structural, electronic, and optical properties of mixed halide perovskites and find that unlike conventional semiconductor alloys, they exhibit many anomalous alloy properties such as small or even negative formation energies at some concentrations and negligible or even negative band gap bowing parameters at high temperature. We further show that mixed-(I,Cl) perovskite is hard to form at temperature below 625 K, whereas forming mixed-(Br,Cl) and (I,Br) alloys are easy at room temperature. SECTION: Energy Conversion and Storage; Energy and Charge Transport
L
reduced short circuit current due to the large band gap of CH 3 NH 3 PbBr 3 and CH 3 NH 3 PbBr 3−x Cl x . Mixed halide CH3NH3PbI3−xBrx26 could be used to create colorful solar cell design for energy-saving buildings. The consecutive band gap range of mixed halide perovskites CH3NH3PbI3−xClx, CH3NH3PbI3−xBrx and CH3NH3PbBr3−xClx could also be used for application in multijunction solar cells.33,35,36 Recently, solar cells based on light harvester CH3NH3PbI3−xBrx have reached the efficiency of 17.9% in early 2014,2 which holds the current certified record.37 These facts show that to achieve efficiency over 20% or even comparable to crystalline silicon (25%), one of the promising options is to finely tune the properties of archetypal CH3NH3PbI3 by mixing Br or Cl. Even though many experiments have demonstrated that Br and Cl can effectively tune the electronic properties and cell performance of CH3NH3PbI3, there are still many unclear issues: (i) The atomic ratio of Cl in CH3NH3PbI3−xClx was previously assumed to be up to one-third as the ratio in precursors.8,28 However, subsequent experiments24,38 show that its atomic ratio is less than 4% and the existence of Cl is to help release of excess CH3NH3+ during growth process,39 which explains the previous puzzle that the Cl addition almost does not change the band gap of CH3NH3PbI3. Thus, the miscibility of Cl in CH3NH3PbI3 should be studied in more detail. (ii) For CH3NH3PbI3−xBrx, Noh26 et al. reported that even though the stability of the solar cell was improved, initial cell efficiency decreased a little. In contrast, Suarez et al.33 reported that the
ead halide perovskites have recently revolutionized the photovoltaic field1−10 because this class of materials exhibit several superior properties for solar cell application, including proper band gap and band alignment,11−16 strong optical absorption,17 balanced electron and hole mobility,14,15,17−19 good charge transport,20,21 and benign topological defect properties.17,19,22,23 Meanwhile, lead halide perovskite solar cells can be economically processed by low-temperature solution methods and the compositional elements are earth abundant. Solar cells based on the archetypal halide perovskite, methylammonium lead triiodide (CH3NH3PbI3), have achieved high efficiency over 15%.7 Chemical managements of compositional elements,24−30 especially for halogen ions, have been verified as effective methods to refine the properties of CH3NH3PbI3. Mixing multiple halogen elements seems leading to at least three beneficial effects. The first is increasing the stability. In the seminal work of Lee et al.,8 iodide-chloride mixed-halide perovskites CH3NH3PbI3−xClx were found to be remarkably stable when processing in air compared to CH3NH3PbI3. Noh et al.26 also demonstrated that mixing 20%−29% Br into CH3NH3PbI3 would greatly improve the solar cell stability while keeping the efficiency. The second is e n h an ci n g t h e c a r r i e r t r a n s p o rt . M i xe d h a l i d e s CH3NH3PbI3−xClx demonstrated much longer electron−hole diffusion length than CH 3 NH 3 PbI 3 . 24 , 31 −3 4 Besides CH3NH3PbI3−xClx, improved carrier mobility and reduced carrier recombination rates were also observed in CH3NH3PbI3−xBrx33 and CH3NH3PbBr3−xClx.35 The third is band gap tuning. CH3NH3PbBr336 (CH3NH3PbBr3−xClx35) has demonstrated good photovoltaic performance and reached open circuit voltage as high as 1.3 eV (1.5 eV) with slightly © XXXX American Chemical Society
Received: September 6, 2014 Accepted: October 4, 2014
3625
dx.doi.org/10.1021/jz501896w | J. Phys. Chem. Lett. 2014, 5, 3625−3631
The Journal of Physical Chemistry Letters
Letter
Figure 1. (a) α phase, (b) β phase, and (c) γ phase of the halide perovskite. (d), (e), and (f) are top views of (a), (b), and (c) along [001] direction, respectively. The arrows in (e) and (f) indicate the distortion directions of the halogen ions away from the α phase.
Table 1. Calculated Lattice Constants and Band Gaps of the Three Phases of CH3NH3PbX3 (X = I, Br, Cl) Are Compared with the Experimental Onesa lattice constant (Å) phase
symmetry
PBE
α β
Pm3m ̅ I4/mcm
a = 6.39 a = 8.80, c = 12.99
γ
Pbnm
a = 8.84, b = 8.77, c = 12.97
α
Pm3̅m
a = 6.04
β γ
I4/mcm Pbnm
a = 8.28, c = 12.25 a = 8.32, b = 8.29, c = 12.15
α β γ
Pm3m ̅ I4/mcm Pbnm
a = 5.78 a = 7.93, c = 11.71 a = 7.94, b = 7.95, c = 11.66
relative energy (meV) PBE
HSE +SOC
0 −100
1.53 1.57
0.46 0.77
1.14 1.60
−50
1.46
0.59
1.43
0
1.93
0.89
1.92
−59 −19
−92 −44
1.98 1.81
1.13 0.91
2.11 1.86
CH3NH3PbCl3 0 0 −52 −53 −12 −16
0 −65 −18
2.40 2.47 2.27
1.33 1.57 1.31
2.57 2.77 2.47
PBE
CH3NH3PbI3 a = 6.31,45 6.2858 0 0 a = 8.85,45,58 8.88,24 12.6724 c = −93 −127 12.64,45 a = 8.84,58 b = 8.56,58 c = −38 −55 12.58,58 CH3NH3PbBr3 a = 5.94,26 a = 5.95,40 0 0 −60 −21 a = 5.7040
band gap (eV) PBE +SOC
exp
PBE +SOC
HSE +SOC
exp
1.52,45 1.559
2.23,25 2.32,36 2.29,26,33 2.3540
3.1140
a Because the CH3NH3 molecule is noncentrosymmetric, for α phase, the calculated pseudocubic lattice constant is defined by a = V1/3 and for β phase, a = 1/2(a + b). The relative total energy (meV/formula), referred to α phase, is also given. For HSE+SOC, a 43% portion of exact-exchange is chosen to reproduce the band gap of β phase CH3NH3PbI3 as in ref 19.
electronic and energetic properties of mixed-halide perovskites. We have found that halide perovskites exhibit anomalous alloy properties that are different from conventional semiconductors. In conventional semiconductor alloys, the physical properties P(x), such as band gap Eg(x) and formation energy ΔH(x), of alloy A1−xBx usually deviates from the averaged value P̅(x) = (1−x)P(A)+xP(B) of constituents solids A and B. Both experiment and theory for isovalent semiconductor alloys show that the deviation ΔP̅ ( x) = P(x) − P̅ ( x) can approximately be described by ΔP̅(x) = βx(x − 1), where β is a composition independent parameters. For formation energies [ΔH(A1−xBx) = E(A1−xBx) − (1 − x)E(A) − xE(B)], the interaction parameter Ω = β is usually positive,
electron−hole recombination rate of CH3NH3PbI3 decreased by mixing Br and open circuit voltage (Voc) increased, which is similar to Cl addition. (iii) For CH3NH3PbBr3−xClx, Edri et al.35 reported that Cl is hard to mix in CH3NH3PbBr3 as that in CH3NH3PbI3. However, a previous study of Kitazawa et al.40 show that CH3NH3PbBr3 and CH3NH3PbCl3 are fully mixable and similar results are recently found for CH3NH3SnX3.41 So far, there is no systematic theoretical study for a mixed-halide perovskite, and the origin of different miscibility behaviors between different types of mixed halides is not clear. In this Letter, we use first-principle calculations42 together with Monte Carlo simulations based on cluster expansion methods (CEM)43,44 to systematically study the structural, 3626
dx.doi.org/10.1021/jz501896w | J. Phys. Chem. Lett. 2014, 5, 3625−3631
The Journal of Physical Chemistry Letters
Letter
Figure 2. Formation energies of mixed halide CsPbX3 (X = I, Br, Cl). There are 1250 structures considered for each CsPb(I1−xBrx)3, CsPb(I1−xClx)3, or CsPb(Br1−xClx)3 alloy. The red circles (blue plus) indicate the formation energies of structures calculated by first-principle calculations (ECI fitting). The black cross points indicate the extra ones predicted by the parameter-fitted Ising Hamiltonian (1).
is the high temperature phase. Our calculated lattice constants, relative energies and band gaps of CH 3 NH 3 PbI 3 , CH3NH3PbBr3, and CH3NH3PbCl3 with three phases are shown in Table 1. The calculated results are in good agreement with experimental results. Here, we choose β phase for the study of mixed-halide perovskites as β phase is the roomtemperature phase of CH3NH3PbI3 in experiments. For studying mixed-halide perovskites alloys, we will use CsPbX3 (X = I, Br, Cl) as example to avoid complication in CH3NH3PbX3 due to the different orientation of organic molecule CH3NH3. The formation energies of 1250 symmetry-nonequivalent structures up to 20 atoms per supercell for alloy CsPbI3−xBrx, CsPbI3−xClx, and CsPbBr3−xClx are calculated through Isinglike Hamiltonian (1) based on CEM47,48 and are enumerated in Figure 2. In conventional alloy, the formation energies are positive and generally follow parabolic convex curve. Here, we find that some alloy structures have almost zero or even negative formation energies, especially for CsPbI3−xBrx and CsPbBr3−xClx. Moreover, we find that a particularly stable alloy structure exists at concentration x = 1/3 with formation energies obviously lower than other structures as shown in Figure 2. The crystal structure of this stable alloy is shown in Figure 3a. Previous DFT-GGA calculations28 using the same tetragonal cell found that in CH3NH3PbI2Cl, Cl favors apical sites as shown in Figure 3b. Here, using structure searching by MC methods, we find that for CsPbI2Cl, the new structure relaxation pattern in Figure 3a is more stable by as much as 60 meV per formula than similar structure in Figure 3b. It is interesting to investigate why such a particularly stable structure exist at x = 1/3. As discussed before, in conventional isovalent semiconductor alloy A1−xBx, the formation energies are positive and generally follow ΔH = Ωx(1 − x). The positive formation energy is mostly attributed to the strain energy by which the ideal A and B bulk are stretched or compressed to the lattice constant of alloy A1−xBx. Usually, bulk with small lattice constant has larger bulk modulus, which means that it is
because formation of alloys cost strain energy when there is a size difference between A and B. For band gap (Eg), the bowing parameter b = −β is usually positive because the reduced local symmetry in the alloy environment usually increases the intraband coupling inside the conduction band as well as inside the valence band, thus narrowing the band gap. However, we have found that mixed-halide perovskites have anomalous alloy properties. Due to strong ionic properties, the ordered structure of CsPbX3−xYx (X, Y = I, Br, Cl; X has larger size than Y) at x = 1 has considerable Coulomb energy gain, and thus, its formation energy significantly deviates from the parabolic curve. This behavior may help to stabilize ordered mixedhalogen perovskite alloys at this particular composition. Furthermore, the miscibility gap temperature (TMG), which is defined as critical temperature that alloys can be fully mixable, is estimated by calculating formation energies of alloys based on special-quasirandom-structures (SQS). We find that the TMG’s of CsPbI3−xClx, CsPbI3−xBrx, and CsPbBr3−xClx are 625, 223 and 116 K respectively. Considering that halide perovskites are usually grown by solution-based method at relatively low temperature (below 400 K), both CsPbI 3−x Br x and CsPbBr3−xClx can be fully mixable, whereas CsPbI3−xClx is more difficult to mix. The results are in consistent with experimental observations. The crystal structure of archetypal halide perovskite CH3NH3PbI3 changes with temperature from α phase (>330 K, Pm3̅m symmetry), β phase (150−330 K, I4/mcm symmetry) to γ phase (
