Junke Jiang1, Chidozie K Onwudinanti2, Ross A Hatton3, Peter A Bobbert1,1, Shuxia Tao1. 1. Center for Computational Energy Research, Department of Applied Physics, and Molecular Materials and Nano Systems, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. 2. Center for Computational Energy Research, DIFFER-Dutch Institute for Fundamental Energy Research, De Zaale 20, 5612 AJ Eindhoven, The Netherlands. 3. Department of Chemistry, University of Warwick, CV4 7AL Coventry, U.K.
Abstract
Because of its thermal stability, lead-free composition, and nearly ideal optical and electronic properties, the orthorhombic CsSnI3 perovskite is considered promising as a light absorber for lead-free all-inorganic perovskite solar cells. However, the susceptibility of this three-dimensional perovskite toward oxidation in air has limited the development of solar cells based on this material. Here, we report the findings of a computational study which identifies promising Rb y Cs1-y Sn(Br x I1-x )3 perovskites for solar cell applications, prepared by substituting cations (Rb for Cs) and anions (Br for I) in CsSnI3. We show the evolution of the material electronic structure as well as its thermal and structural stabilities upon gradual substitution. Importantly, we demonstrate how the unwanted yellow phase can be suppressed by substituting Br for I in CsSn(Br x I1-x )3 with x ≥ 1/3. We predict that substitution of Rb for Cs results in a highly homogeneous solid solution and therefore an improved film quality and applicability in solar cell devices.
Because of its thermal stability, lead-free composition, and nearly ideal optical and electronic properties, the orthorhombic CsSnI3 perovskite is considered promising as a light absorber for lead-free all-inorganic perovskite solar cells. However, the susceptibility of this three-dimensional perovskite toward oxidation in air has limited the development of solar cells based on this material. Here, we report the findings of a computational study which identifies promising Rb y Cs1-y Sn(Br x I1-x )3 perovskites for solar cell applications, prepared by substituting cations (Rb for Cs) and anions (Br for I) in CsSnI3. We show the evolution of the material electronic structure as well as its thermal and structural stabilities upon gradual substitution. Importantly, we demonstrate how the unwanted yellow phase can be suppressed by substituting Br for I in CsSn(Br x I1-x )3 with x ≥ 1/3. We predict that substitution of Rb for Cs results in a highly homogeneous solid solution and therefore an improved film quality and applicability in solar cell devices.
Organic–inorganic
hybrid halideperovskite solar cells (PSCs)
have attracted strong attention in the past few years and are becoming
one of the most promising types of emerging thin-film solar cells.[1−4] In less than a decade, the power conversion efficiency (PCE) of
PSCs has increased from 3.8% in 2009 to 22.7% in 2017.[5,6] Despite the high efficiency of PSCs, two challenges currently hinder
their upscaling toward practical applications.[7] One issue is the long-term instability of PSCs, which is mainly
caused by the intrinsic thermal instability of hybrid perovskite materials.[8−13] Encouragingly, it has been demonstrated recently that mixing the
cations or replacing the organic cation with an inorganic cation can
improve thermal stability and photostability (e.g., substituting FA
for MA in MAPbI3, Rb for Cs in CsSnI3, and Cs
for MA in MAPbI3; MA stands for CH3NH3, and FA stands for NH2CHNH2).[7,14,15] The other concern is the well-documented
toxicity of lead (Pb), which is particularly problematic because lead
halide perovskites decompose into lead compounds that have significant
solubility in water.[16] Consequently, an
intensive research effort focused on finding air-stable lead-free
perovskites suitable as the light-harvesting semiconductor in PSCs
is now underway.[9,17−20]Among the various alternatives
to lead, tin (Sn) is regarded as
a promising substitute because Sn-based hybrid perovskites have been
shown to exhibit outstanding electrical and optical properties, including
high charge carrier mobilities, high absorption coefficients, and
low exciton binding energies.[21−23] Theoretical predictions by Even
et al.[24] and Chiarella et al.[25] also confirmed the promising properties of Sn
perovskites, such as suitable band gaps and favorable effective mass.
However, Sn-based perovskites also have drawbacks, which have limited
their application in efficient PSCs.[1,23,26−29] The primary challenge is the susceptibility of tin
toward oxidation from the +2 to the +4 oxidation state upon exposure
to ambient air, which, in the case of CsSnI3, ultimately
results in the formation of Cs2SnI6, whose relatively
weak light absorption across the visible spectrum is undesirable for
a photoabsorber.[22,30−33] Consequently, to date, there
has been much less research effort directed at the advancement of
tin halide PSCs than their lead analogues, and their PCE has remained
below 10%.[27,28] Recently, a PCE as high as 9.0%
in PSCs was achieved using single-crystalline FASnI3, made
by mixing a small amount of two-dimensional (2D) Sn perovskites with
three-dimensional (3D) FASnI3 in which the organic FA molecules
are oriented randomly,[34] an approach that
promises further improvement.As compared to hybrid organic–inorganic
Sn perovskites,
all-inorganic Sn perovskites could have the advantage of improved
thermal stability while maintaining favorable optical and electronic
properties for photovoltaic (PV) applications.[35,36] For example, γ-CsSnI3 is a p-type semiconductor
with a high hole mobility,[21,37] a favorable band gap
of ∼1.3 eV, a low exciton binding energy, and a high optical
absorption coefficient.[38,39] There have been a few
attempts to fabricate solar cells using γ-CsSnI3 as
a photoactive layer, but their maximum efficiency was still low. In
2012, Chen et al.[40] first used CsSnI3 to fabricate a Schottky contact solar cell, which achieved
a PCE of 0.9%. In 2014, Kumar et al.[41] achieved
a PCE of 2.02% by forming the perovskite from a solution under Sn-rich
conditions, using SnF2 as the source of excess Sn, an approach
that reduces the density of Sn vacancy defects. In 2016, Wang et al.[19] achieved a PCE of 3.31%. By removing the electron-blocking
layer in a simplified inverted solar cell architecture and using the
additive SnCl2 instead of SnF2, Marshall et
al.[22] achieved the highest PCE to date
of 3.56%, together with exceptional device stability under continuous
illumination without device encapsulation. However, the PCE of γ-CsSnI3-based solar cells is still significantly lower than those
of their hybrid organic–inorganic Sn and Pb perovskite counterparts,
primarily because of the lower open-circuit voltage. The most important
challenges are therefore to develop ways to increase the open-circuit
voltage and to stabilize tin halide perovskites toward oxidation in
air. The oxidation instability manifests as a phase transition from
the photoactive black orthorhombic (γ) phase to a photoinactive
2D yellow (Y) phase upon exposure to water vapor, which spontaneously
converts to the weakly absorbing one-dimensional Cs2SnI6,[22] leading to difficulties in
controlling the morphology and quality of the perovskite film.In Pb halide perovskites, the strategy of mixing cations or anions
has been widely used to improve the stability and PV performance of
PSCs.[12,42−47] In contrast, explorations of the mixing of cations and anions in
all-inorganic Sn-based perovskites are scarce.[7,48−50] Recently, the electronic structure variation of γ-CsSnI3 by mixing A-site cations (e.g., mixing Cs and Rb) has been
investigated by Jung et al.[7] However, the
relative stability of the structures as compared to the Y phase was
not investigated. To our knowledge, the amalgamated effect of exchange
of both the A-site metal cation and the halide anion in completely
inorganic tin perovskites has not been investigated.In this
paper, we present a theoretical study of the impact of
cation and anion mixing (Rb/Cs cation exchange and Br/I anion exchange)
in all-organic γ-CsSnI3 using the density functional
theory (DFT)-1/2 method [the local density approximation (LDA)-1/2
version],[51−54] taking into account the spin–orbit coupling (SOC) effect.
We focus on the evolution of the electronic properties as well as
the thermal and structural stabilities when substituting Br for I
and Rb for Cs in γ-CsSnI3. We predict that 3D perovskites
with the composition RbCs1–Sn(BrI1–)3, where 0 ≤ x,y ≤ 1, are direct band gap semiconductors
with band gaps in the range 1.3–2.0 eV. Importantly, our results
indicate that substitution of Br for I in CsSnI3 can prevent
the unwanted γ-to-Y phase transition, evidenced by the favorable
formation energies of the γ phase over the Y phase. In addition,
calculations of the free energy of mixing and the prediction of phase
diagram demonstrate that further substitution of Rb for Cs in CsSn(BrI1–)3 can improve the mixing thermodynamics, which is expected
to improve the film-forming properties. Our predicted trends in the
thermodynamic stability and band gaps provide a guideline to develop
more efficient and stable lead-free all-inorganic perovskites for
PSCs.
Computational Methods and Structural Models
The initial
structure optimizations are performed using DFT as
implemented in the Vienna ab initio simulation package (VASP).[55,56] The Perdew, Burke, and Ernzerhof (PBE) functional within the generalized
gradient approximation is used.[57] The outermost
s, p, and d (in the case of Sn) electrons are treated as valence electrons,
whose interactions with the remaining ions are modeled by pseudopotentials
generated within the projector-augmented wave method.[58,59]Figure shows the
crystal structures and cells used in the DFT calculations. Unit cells
with 20 atoms (four ASnX3 units) are used for all structures
using a 1 × 1 × 1 cell for the γ and Y phases and
2 × 2 × 1 supercells for the α phase. In the structural
optimization, the positions of the atoms as well as the cell volume
and cell shape are all allowed to relax by setting ISIF = 3. An energy
cutoff of 500 eV and 4 × 4 × 8, 6 × 4 × 6, and
4 × 10 × 2 k-point meshes (α, γ,
and Y phase structures, respectively) are used to achieve an energy
and force convergence of 0.1 meV and 2 meV/Å, respectively. The
subsequent electronic structure calculations were performed using
an efficient approximate quasi-particle DFT method, namely, the DFT-1/2
method. The DFT-1/2 method stems from Slater’s proposal of
an approximation for the excitation energy, a transition-state method,[60,61] to reduce the band gap inaccuracy by introducing a half-electron/half-hole
occupation. Teles et al.[51−54] extended the method to modern DFT and particularly
to solid-state systems. Recently, we successfully applied this method
in predicting accurate band gaps of metal halide perovskites.[62] The computational effort is the same as for
standard DFT, with a straightforward inclusion of SOC when coupled
with VASP. In this work, we extend the use of the DFT-1/2 method with
the same settings (CUT values of 2.30, 3.34, and 3.76 for Sn, I, and
Br, respectively, with half-ionized p orbitals) to alloys of CsSnI3 when mixing Cs with Rb and I with Br. The physical insights
of why Sn p and halide I or Br p orbitals are both half-ionized are
demonstrated in Figure S1.
Figure 1
Top (a–c) and
side (d–f) views of the cubic (α, Pm3m), orthorhombic (γ, Pnma), and yellow phase (Y, Pnma) of ASnX3 (A = Cs and Rb and X = Br and I).
Top (a–c) and
side (d–f) views of the cubic (α, Pm3m), orthorhombic (γ, Pnma), and yellow phase (Y, Pnma) of ASnX3 (A = Cs and Rb and X = Br and I).We calculated the free energy[7,63] of mixing
for each
composition according to the expressionwhere ΔU and ΔS are the internal energy
and entropy of mixing, respectively,
and T is the absolute temperature. The internal energy
of mixing of RbCs1–SnX3 is then calculated via the formulawhere ERb, ERbSnX, and ECsSnX are the total energies of
RbCs1–SnX3, RbSnX3, and CsSnX3, respectively.The internal energy of mixing of ASn(BrI1–)3 is calculated
using the formulawhere EASn(Br, EASnBr, and EASnI are the total energies of ASn(BrI1–)3, ASnBr3, and ASnI3, respectively.The
entropy of mixing is calculated in the homogeneous limit according
to the formulawhere kB is the
Boltzmann constant.We plot the phase diagram by using the generalized
quasi-chemical
approximation (GQCA)[63,64] code developed by Walsh et al.[63] to further investigate the thermodynamic properties
of γ-ASnX3. The phase diagram offers insight into
the critical temperature for mixing and into the stability of the
solid solution for typical temperatures at which perovskites are synthesized.On the basis of the size of the cells for calculations, we have
considered seven (ASn(BrI1–)3, x = 0, 1/6, 1/3,
1/2, 2/3, 5/6, and 1) and five (RbCs1–SnX3, y = 0, 1/4, 1/2, 3/4, and 1) concentrations of A cations and X anions,
respectively. For the γ phase structures, all possible configurations
(2, 4, and 2 for y = 1/4, 1/2, and 3/4, respectively) of substituting
Rb for Cs were considered. Owing to the large number of possible configurations
of substituting Br for I (22, 139, 252, 139, and 22 possible configurations
for x = 1/6, 1/3, 1/2, 2/3, and 5/6, respectively),
we have considered only two possible configurations for each concentration
of Br, namely, the two extreme cases with most negative and least
negative ΔH. From Figure S2 and Table S1, the formation energy
of configuration 3 is the most negative, whereas that of configuration
7 is the least negative. This indicates that the Br ions tend to sit
as close as possible to each other and to form as many bonds as possible
with Sn ions. We use this strategy to select two extreme configurations
for all other Br–I alloys considered in this work.
Results and Discussion
Before studying the mixing of A cations and X anions in ASnX3, we first performed calculations for the four pure compounds:
CsSnI3, CsSnBr3, RbSnI3, and RbSnBr3. The calculated lattice parameters of orthorhombic (γ)
ASnX3 are shown in Table . Those of other polymorphs including cubic α,
tetragonal β, and Y phase structures are listed in Table S2. The optimized lattice parameters are
in good agreement with experiments, with a slight overestimation of
lattice constants by about 1%, and with other theoretical results
(differences within 0.1%).[7,38,49,65−68] It should be noted here that
the predicted lattice parameters of α-CsSnI3 and
γ-CsSnI3 in our previous work are smaller because
of the use of LDA, which slightly underestimates the lattice parameters.[62] In this work, PBE is used, resulting in a slight
overestimation of lattice parameters. Consequently, the predicted
band gap of γ-CsSnI3 (1.36 eV) in this work (will
be discussed in the next paragraph) is slightly higher compared to
that of previous work (1.34 eV).[62]
Table 1
Lattice Constants (in Å) Obtained
by DFT and Band Gap Energies E (in eV) Obtained with the DFT-1/2 Method Including SOC Compared
to Experimental Data and Theoretical Predictions Based on Hybrid and
GW Methods
material
lattice constants (this work)
lattice constants (experimental)
lattice constants (other theoretical work)
Eg DFT-1/2 + SOC
Eg (experimental)
Eg + SOC
γ-CsSnI3
8.99, 12.52, 8.63
8.69, 12.38, 8.64a
8.94, 12.52, 8.69b
1.36
1.27c
1.34 (GW0)d
γ-RbSnI3
8.91, 12.28, 8.47
8.93, 12.28, 8.47b
1.55
1.13 (HSE06)b
γ-CsSnBr3
8.36, 11.79, 8.22
1.72
1.83 (GW0)d
γ-RbSnBr3
8.38, 11.55, 7.98
2.01
Reference (38).
Reference (7).
Reference (49).
Reference (68).
Reference (38).Reference (7).Reference (49).Reference (68).The calculated band gaps of γ-CsSnI3 and γ-CsSnBr3 are 1.36 and 1.72 eV, respectively,
in excellent agreement
with reported experimental measurements[49] (1.27 and 1.75 eV) and GW0 calculations[68] (1.34 and 1.83 eV). There are no experimental reports known
to us of the band gap of either RbSnI3 or RbSnBr3. Only theoretical results from HSE06 for γ-RbSnI3 and PBE for α-RbSnBr3 are found to be 1.41 and
0.57 eV, respectively.[7,69] Our predicted band gap for γ-RbSnI3 is 1.55 eV. Substituting Br for I in γ-RbSnI3 further increases the band gap to 2.01 eV.It is worth noting
that although CsSnBr3 is reported
to have the α structure at room temperature, the actual atomic
arrangement at finite temperature (due to the dynamic disorder of
the ions in the lattice)[70] resembles that
of the γ phase. Consequently, it is not surprising that predicted
band gaps using α structures are always significantly smaller
than those measured experimentally.[7,24,71,72] Therefore, in this
work, we always report band gaps calculated using γ phases.
RbSnI3 has been reported to exist in a nonperovskite 2D
Y phase structure owing to the small cationic size of Rb+.[38,66] Nevertheless, for comparison with the alloys
RbCs1–SnI3, the band gaps of RbSnI3 in a 3D γ
phase are also predicted. In addition, all band gaps of α structures
are also provided in the Supporting Information in Table S2 and Figure S3 for comparison. The calculated effective
masses of the electrons and holes at the G point
for γ-ASnX3 are given in Table S3.Figure shows the
computed band gaps for the γ phases of ASn(BrI1–)3 and RbCs1–SnX3 perovskites, whereas the band gaps of the other structures
are shown in Figure S4. In general, the
band gap increases with increasing percentage of Br in ASn(BrI1–)3 and Rb in RbCs1–SnX3. From Figure a and Table S4, generally, the band gaps change because of the variations in both
volume and lattice distortion. However, the changes in cell volume
have more pronounced effects on the band gaps than the changes in
lattice distortion, that is, octahedral tilting. The reduction of
the cell volume is responsible for the widening of the band gap in
ASn(BrI1–)3 or RbCs1–SnX3 solid solutions with an increased
Br or Rb percentage. For the band gap variations with the same Br
or Rb percentage in ASn(BrI1–)3 or RbCs1–SnX3 solid solutions,
there is no certain relationship found between the degree of lattice
distortion (i.e., the degree of octahedral tilting, which is the tilting
angle difference |Δθ̅|)[4] and band gaps.
Figure 2
Calculated band gaps of (a) γ-ASn(BrI1–)3 and (b)
γ-RbCs1–SnX3 perovskites. The dashed lines are guides to
the eye.
Calculated band gaps of (a) γ-ASn(BrI1–)3 and (b)
γ-RbCs1–SnX3 perovskites. The dashed lines are guides to
the eye.It is well-known that for single-junction
and multijunction solar
cells, the Shockley–Queisser limit suggests optimal band gap
ranges of 0.9–1.6 and 1.6–2.0 eV, respectively, for
achieving a maximum PCE.[23,73] The band gaps of CsSn(BrI1–)3 are almost completely in the optimal range (1.30–1.55
eV) for single-junction PSCs. When substituting Rb for Cs in CsSn(BrI1–)3, the band gaps of RbSn(BrI1–)3 increase by 0.2–0.3
eV as compared to their Cs counterparts, making RbSn(BrI1–)3 (x > 1/3) ideal as a wide-band gap material
for
tandem solar cells in conjunction with narrow-band gap semiconductors
such as Si or CsSn(BrI1–)3. The changes in band gap when mixing
Rb and Cs cations are much smaller than those when mixing I and Br.
This is true for all values 0 ≤ y ≤
1 and also for different structures with a fixed y. The band gaps of RbCs1–SnBr3 (1.71–2.01 eV) and RbCs1–SnI3 (1.36–1.55 eV) are in the ideal range for tandem and
single-junction solar cells, respectively.In addition to the
band gap, another key property for the application
of mixed inorganic perovskites in PSCs is their structural stability.
CsSnI3 has two coexisting polymorphs (the γ and Y
phases) at room temperature, which both belong to the Pnma space group. Although both phases have similar free energies and
stable phonon modes, a transition from the black γ phase to
the yellow Y phase has been observed in ambient conditions.[7,38,74] Oxidation of Sn2+ to
Sn4+ spontaneously occurs after the transformation of the
γ phase to the Y phase.[75]Because
of the different crystal structure and electronic properties
of the Y phase (i.e., a 2D structure and an indirect band gap of 2.6
eV), the unwanted phase transition from γ to Y can considerably
decrease the efficiency of a solar cell.[14,22,75−77] In addition, the Y phase
will spontaneously react with O2 when exposed to air, resulting
in Cs2SnI6 with a face-centered cubic structure.[30,32] Therefore, we focus here on the evolution of the stability of the
γ and Y phases upon gradual substitution of Br for I and Rb
for Cs. The results of our calculations for other structures are given
in Figure S5.The formation energy
of ASnX3 is defined as ΔH = EASnX – EAX – ESnX, where EASnX, EAX, and ESnX are
the total energies of ASnX3, AX, and SnX2, respectively.
Here, a negative value of ΔH represents favorable
formation of ASnX3 perovskites.
The more negative ΔH, the more stable the corresponding
structure. It can be clearly seen in Figure that all perovskites considered exhibit
good thermal stability, with large negative ΔH values. Figure also
shows the effect of ion mixing on the stability of the γ phase
with respect to the Y phase.
Figure 3
Formation energy (ΔH)
of (a) ASn(BrI1–)3 and (b) RbCs1–SnX3 perovskites for
the γ and Y
phases. Because of the large number of possible configurations for
each substitution concentration x of Br in ASn(BrI1–)3, we only show in (a) the results for the two configurations
with the most negative and least negative ΔH.
Formation energy (ΔH)
of (a) ASn(BrI1–)3 and (b) RbCs1–SnX3 perovskites for
the γ and Y
phases. Because of the large number of possible configurations for
each substitution concentration x of Br in ASn(BrI1–)3, we only show in (a) the results for the two configurations
with the most negative and least negative ΔH.For CsSnI3, the formation
energies of the γ and
Y phases are the same. However, with the increase of Rb concentration,
the structural instability of RbCs1–SnI3 becomes increasingly
pronounced. Consequently, upon exposure to air, the rate at which
the perovskite oxidizes is predicated to increase with an increasing
Rb concentration.[75] The substitution of
Rb for Cs seems to facilitate the formation of the Y phase, as now
evidenced by the more negative formation energy of the Y phase than
the γ phase. It should be mentioned that the formation energies
are both negative for RbSnI3 in both γ and Y phases.
However, the formation energy of the Y phase is relatively more negative,
indicating that the Y phase is more favorable than the γ phase.
Indeed, the instability of the γ phase is in agreement with
the experimental observation of RbSnI3 only existing in
a 2D yellow phase.[75] On the contrary, for
CsSnBr3, the formation energy of the Y phase is much less
negative than that of the γ phase (by 0.06 eV), indicating that
the γ phase is more stable than the Y phase. The substitution
of Rb for Cs results in a slight decrease (to 0.04 eV) in the energy
differences between the two phases, with the γ phase still being
favored.The formation energies of mixing Cs and Rb in RbCs1–SnI3 or
RbCs1–SnBr3 follow a perfect linear relation (Figure b), indicating favorable mixing
thermodynamics. However, substitution of Br for I (Figure a) shows an unusual trend as
a function of x: the curves show first a decrease
and then an increase, with a valley point at x =
1/3 in both CsSn(BrI1–)3 and RbSn(BrI1–)3. When x < 1/3, the most negative ΔH of
the γ phase for each concentration is relatively more positive
than or nearly equal to the most negative ΔH of the Y phase, which indicates that the Y phase is favored over
the γ phase. When x = 1/3, the most negative
ΔH of the γ phase is clearly more negative
than the most negative ΔH of the Y phase, whereas
the least negative ΔH of the γ phase
is almost equal to the most negative ΔH of
the Y phase. When x > 1/3, all ΔH of the γ phase for each concentration are more negative
than
those of the Y phase, which means that the γ phase is stabilized.
For RbCs1–SnI3 or RbCs1–SnBr3, mixing Cs and Rb does not change
the stability of the γ phase with respect to the Y phase (Figure b). For RbCs1–SnI3, the Y phase is always favored when mixing Rb and Cs, whereas for
RbCs1–SnBr3, the opposite is true. We conclude that the addition
of Br to RbCs1–SnI3 tends to stabilize the favorable γ phase
and suppress the transformation to the Y phase. The critical Br concentration
is about one-third. This prediction calls for an experimental validation.As shown in Figure , very different trends are observed for mixing of cations (Rb and
Cs) and anions (I and Br) in γ-CsSnI3. For a deeper
insight, we have investigated the different mixing thermodynamics
by calculating the Helmholtz free energy of mixing. Details of the
calculations can be found in the Computational Methods and Structural
Models section. Results of these calculations are shown in Figure S6. On the basis of the Helmholtz free
energies, we plot the phase diagram for γ-ASnX3 by
using the GQCA[63] code, as shown in Figure .
Figure 4
Predicted phase diagrams
of (a) γ-CsSn(BrI1–)3, (b) γ-RbSn(BrI1–)3, (c) γ-RbCs1–SnBr3, and (d) γ-RbCs1–SnI3 solid solutions. The purple and pink
lines are binodals and spinodals,
respectively. The dashed horizontal lines indicate room temperature
(300 K). In (b), the gap between the horizontal line and the critical
miscibility temperature is the miscibility gap in γ-RbSn(BrI1–)3. A thermodynamically stable solid solution can be formed
only in the white region.
Predicted phase diagrams
of (a) γ-CsSn(BrI1–)3, (b) γ-RbSn(BrI1–)3, (c) γ-RbCs1–SnBr3, and (d) γ-RbCs1–SnI3 solid solutions. The purple and pink
lines are binodals and spinodals,
respectively. The dashed horizontal lines indicate room temperature
(300 K). In (b), the gap between the horizontal line and the critical
miscibility temperature is the miscibility gap in γ-RbSn(BrI1–)3. A thermodynamically stable solid solution can be formed
only in the white region.For CsSn(BrI1–)3, the critical temperature is 291 K
(see Figure a), indicating
that the mixing of anions (I and Br) is favorable at room temperature
(300 K). However, for RbSn(BrI1–)3 at 300 K, a miscibility gap is found
in the composition region between x1 =
0.33 and x2 = 0.70 (see Figure b). The pure compounds RbSnI3 and RbSnBr3 are not miscible inside the miscibility
gap under equilibrium conditions, leading to the formation of two
phases with Br concentrations x1 and x2. Meanwhile, the alloy has spinodal points
at the compositions x1′ = 0.40 and x2′ =
0.62 at room temperature. Thus, in the intervals x1 < x < x1′ and x2′ < x < x2, a metastable
phase can occur, showing small fluctuations in composition. The predicted
critical temperature (the temperature above which the solid solution
is stable for any composition) is 312 K, which is significantly lower
than the critical temperature of 343 K predicted for the MAPb(BrI1–)3 perovskite.[63] This indicates that,
although mixing of Br and I is not favored slightly below (for CsSn(BrI1–)3) or around (for RbSn(BrI1–)3) room temperature,
the phase segregation in these alloys is less significant than that
in MAPb(BrI1–)3 perovskites.A uniform mixture can be synthesized
either through control of
the deposition kinetics or by annealing above the critical miscibility
temperature. The uniform mixture tends to segregate below the critical
temperature, but this segregation is a very slow process.[63] The inclusion of smaller cations often provides
an improvement, overcoming kinetic barriers and changing the local
critical temperature. For example, smaller cations such as Cs and
Rb were introduced in (FA/MA)Pb(I/Br)3 and were shown to
have a positive effect on the structural and photostability of state-of-the-art
PSCs.[8,10,13,78] Indeed, we predict that mixing of Rb and Cs in RbCs1–SnX3 is very favorable at room temperature. For RbCs1–SnBr3 and RbCs1–SnI3, the phase diagrams show that mixing
of cations (Rb and Cs) is favorable at temperatures above 118 and
137 K, respectively (see Figure c,d). Our prediction of the critical miscibility temperature
of 137 K of RbCs1–SnI3 is in good agreement with the result
of 140 K calculated by Jung et al.[7] The
slight difference of the predicted critical temperature could be caused
by the small variation in energies per cell due to the differences
in computational settings (energy cutoff value, k-point grid, version,
and implementation of VASP codes) in DFT calculations. The critical
temperatures of mixing of Rb and Cs in RbCs1–SnX3 are much
lower than those of mixing of Br and I in ASn(BrI1–)3. Therefore,
additional mixing of Cs and Rb in ASnIBr1– is predicted to bring down
the critical temperature for mixing of Br and I below room temperature,
suppressing phase segregation and resulting in better material quality
for PV applications.
Conclusions
In summary, the effects
of cation (Cs and Rb) and anion (I and
Br) mixing in all-inorganic tin halide perovskites have been investigated
with DFT-based calculations. Using standard DFT for structure optimization
and the DFT-1/2 method with SOC for band structure calculations, we
studied the evolution of the structural, thermodynamic, and electronic
properties as a function of the extent of substitution of Rb for Cs
and Br for I. We predict that CsRb1–Sn(BrI1–)3 perovskites
have direct band gaps in the range of 1.3–2.0 eV. The alloys
with high I and Cs concentrations are well suited for highly efficient
single-junction PSCs, whereas those with high Rb and Br concentrations
are suitable as wide-band gap materials for tandem PSCs. Importantly,
we found that substitution of Br for I can suppress the unwanted γ-to-Y
phase transition. The critical concentration for stabilization of
the γ phase with respect to the Y phase in CsRb1–Sn(BrI1–)3 is x = 1/3. Furthermore, phase diagrams based on the free energy
of mixing show that a solid solution of Br and I is thermodynamically
possible around and slightly above room temperature for CsSn(BrI1–)3 and RbSn(BrI1–)3, respectively. Finally, substitution
of Rb for Cs to ASn(BrI1–)3 is predicted to decrease the critical
temperature to well below room temperature, enabling the formation
of highly homogeneous solid solutions for improved solar cell performance.
Our predictions regarding the stabilization of the γ phase and
the use of five elements in RbCs1–Sn(BrI1–)3 as an efficient
and stable light absorber for PSCs call for experimental exploration.
Authors: Zhiping Wang; David P McMeekin; Nobuya Sakai; Stephan van Reenen; Konrad Wojciechowski; Jay B Patel; Michael B Johnston; Henry J Snaith Journal: Adv Mater Date: 2016-12-01 Impact factor: 30.849