Criticality of Symmetry in Rational Design of Chalcogenide

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Letter

Criticality of Symmetry in Rational Design of Chalcogenide Perovskites Abdulrahiman Nijamudheen, and Alexey V. Akimov J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02589 • Publication Date (Web): 23 Dec 2017 Downloaded from http://pubs.acs.org on December 24, 2017

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The Journal of Physical Chemistry Letters

Criticality of Symmetry in Rational Design of Chalcogenide Perovskites A. Nijamudheen and Alexey V. Akimov* Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, NY 14260-3000

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Abstract Chalcogenide perovskites constitute an emerging class of promising photovoltaic materials that are stable and less toxic than popular lead-halide perovskites. Transition metal and chalcogenide doping are the possible strategies for improving the photovoltaic properties of these materials via the band gap engineering. At the same time, doping can facilitate nonradiative charge carrier recombination in these materials, adversely affecting their photovoltaic properties. We report a systematic study of electronic structure and nonadiabatic dynamics in transition metal and chalcogenide doped barium-zirconium-sulfide-based perovskites. The potential of these doping strategies to modulate the performance of photovoltaic materials is explored. Through the detailed analysis of the factors affecting the dynamics, we illustrate how symmetry (both structural and orbital) and decoherence can be critical to furnishing the most favorable properties. The noted factors of symmetry and decoherence may provide new rational design principles for efficient photovoltaics.

TOC GRAPHICS


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Solar energy harvesting is a promising strategy to generate clean and sustainable electrical energy and chemical fuels. In 2009, Miyasaka and co-workers have demonstrated the applicability of hybrid organic-inorganic perovskite (HOIP) materials to solar energy conversion.1 This work stimulated the interest of many researchers in lead-halide-based perovskites, MAPbX3, where MA is methylammonium, X = I, Br. These efforts have led to a dramatic increase of the solar-to-electrical energy conversion efficiency from 3.8% in the original HOIP/TiO2 single junction interface to that beyond 22% in a thoroughly designed multilayer photovoltaic (PV) architecture.2–4 Although the lead-halide perovskites are simple to synthesize and are composed of cheap and abundant precursor materials, they are also sensitive to moisture and heat. Being ionic salts, the materials are unstable in the presence of water. The decomposition of lead-halide perovskites leads to a release of toxic lead cations (Pb+2), raising the environmental concerns.5,6 A number of approaches have been undertaken to mitigate these problems of HOIP. Partial substitution of Cs7,8 with organic cations can improve stability of the resulting organic-inorganic perovskites without adversely affecting their optoelectronic properties. The stability of perovskites can be improved by organizing them in low-dimensional structures and interfacing with other materials.9–15 The chalcogenide perovskites, ABX3 (A = Ca, Ba, Sr; B = Ti, Zr, Hf; and X = O, S, Se;) have been recently proposed as moisture-resistant alternative to the conventional HOIP materials.16 The computational studies have suggested favorable optoelectronic properties of chalcogenide perovskites such as near-optimal electronic bandgaps (< 2.0 eV) and large solar absorption coefficients. Barium-zirconium sulfide, BaZrS3 (BZS) was identified as one of the most promising candidates for efficient PV, based on the following criteria: (1) it can be easily synthesized and is Pb-free; (2) it has a direct bandgap of ~1.76 eV, near the maximum of the



solar radiation spectrum; (3) it has large carrier mobility; (4) it is composed of cheap, non-toxic, Earth-abundant elements. By doping the original BZS, one can tune the properties of the resulting materials to reach maximal PV performance. This strategy has been demonstrated recently by Meng, et al.17 who have systematically tuned the BZS bandgap from 1.76 eV for the undoped composition down to 1.47 eV for the 10% Ti-doped BZS (BaZr1-xTixS3, x = 0.1). They showed that the bandgap reduction significantly increases the optical absorption efficiency of the material. Very recently, Perera, et al.18 have used the anion alloying to synthesize oxy-sulfide perovskites, BaZr(S1-xOx)3 with x = 0 - 1.0 (further referred to as BZSO) by the sulfurization of BaZrO3. Their experimental study showed that the optical and electronic properties of the perovskites can be tuned by the anion doping as well. Although chalcogenide perovskites have been known for long time, it was not until recently when they have attracted interest as the potential PV materials. Therefore, the studies of this class of perovskites are still scarce. A recent study has investigated the temperature and pressure dependent vibrational properties and the pressure dependent absorption properties of BaZrO3.19 It is known that the details of the photoexcited charge carrier dynamics are among the most important factors that determine the overall power conversion efficiency in solar cells.20 To improve the efficiency of PV materials, it is desirable to decelerate the nonradiative relaxation of hot electrons and hot holes and slow down their recombination at the band edges. The excited state dynamics in HOIP has been a topic of recent interest both from experimental and theoretical perspectives.21–29 Using the first principles nonadiabatic molecular dynamic (NAMD) simulations, Madjet et al.30 have concluded that the halide mixing (Br or Cl for I) in HOIP can suppress the hot carrier thermalization. Long and Prezhdo have rationalized the effects of


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grain boundary, dopants, moisture, and local electric order.31–34 Zheng et al.35 suggested that the Rashba spin-orbit couplings can increase the lifetimes of excited states in HOIP. At the same time, the excited states dynamics in the promising class of chalcogenide perovskites remains poorly understood. We are not aware of any such studies. Thus, it is critical to investigate this aspect of these materials if they are to be used for PV applications. In this work, we undertake a systematic investigation of the nonadiabatic dynamics of the photogenerated charge carriers in BZS and its derivatives designed by transition metal or chalcogenide doping. To study the effect of transition metal doping, we replace 12.5 or 25% of Zr in the parent BaZrS3 by Ti or Hf. Similarly, the effect of anionic doping is investigated by substituting 50% of S in BZS by O or Se. We correlate the peculiarities of electronic structure in these systems with the details of excited states dynamics. By using NA-MD coupled with the Kohn-Sham density functional theory (KS-DFT), we investigate the electron-hole recombination dynamics in chalcogenide perovskites. We unravel how the factors such as excitation energy, time derivative nonadiabatic coupling (NAC), and decoherence affect the recombination timescales in chalcogenide perovskites. Here, we study the idealized defect-free, pristine and doped systems, focusing on the qualitative structure/composition-properties relationships existing in such systems. It should be kept in mind that the presence of defects may alter the overall dynamics in materials, as has been suggested by a number of studies.26,36–39 Since the structure and composition of materials affect their symmetry on both the molecular and electronic structure levels, it is possible to relate the observed trends to the fundamental concepts of symmetry and decoherence. In this work, we emphasize the role of such factors in modulating the PV properties of chalcogenide perovskites.



All structures are fully optimized by employing plane wave DFT methods with PBE functional40 and projector-augmented wave (PAW)41 pseudopotentials. The ground state molecular dynamics is integrated for 3.2 ps using velocity Verlet integration scheme and the time step of 1 fs. The density of states (DOS) and NACs used in NA-MD simulations are computed using the PBE+U methodology,42,43 which partially fixed the delocalization errors of the pure PBE functional. The Quantum Espresso software is used to perform the electronic structure calculations.44 To identify systematic trends, we have considered the following systems (Figure 1): BaZrS3 (BZS), BZS with 12.5% or 25% Ti doping (BaZr1-xTixS3, x = 0.125 or 0.25, BZTS), BZS with 12.5% or 25% Hf doping (BaZr1-xHfxS3, x = 0.125 or 0.25, BZHS), BZS with 50% sulfur substitution by oxygen (BaZrS1.5O1.5, BZSO) or selenium (BaZrS1.5Se1.5, BZSSe). Starting with a 1×2×1 supercell of BZS in distorted perovskite phase, the atom replacement strategy is utilized to generate the transition metal doped and mixed-chalcogenide perovskites. The lattice parameters of the optimized BZS unit cell agrees very well with the previously reported values18 (Table S1). The Ti and Hf substitution of Zr induces only inconsequential changes in the lattice parameters, since the cations have relatively small sizes comparable to one another. When half of the S atoms in BZS are replaced by O to form BZSO, the simulation cell volume decreases significantly. This is expected because the ionic radius of oxygen is notably smaller than that of sulfur. Similarly, the substitution of S with Se causes the increase of the size of ZrS3Se3 octahedra and the lattice parameters. When several configurations are possible (e.g. when 2 Zr atoms are replaced in the 25% metal-doped BZS), all inequivalent structures are considered and the most stable ones are identified. Our calculations suggest that the structures with two metal dopant atoms placed next to each other have the smallest energy (see the SI, Figure S1). Such


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atoms form the nanoscale islands of the different phase (e.g. BTS or BHS). Because of the limited size of our simulations cells, this statement is given only as a conjecture and should be further investigated with larger unit cells. It should be noted that the qualitative trends in excited states dynamics found in this work depend strongly on the composition of the BZS-derived materials and are expected to be mildly affected by the details of the dopant distribution. The electronic structure of the studied chalcogenide perovskites is conveniently represented by the projected density of states (pDOS), which provides information about the magnitudes of electronic band gaps and the orbital compositions (Figure 1). Our DFT+U calculations predict a direct bandgap of 1.78 eV for BZS (Table S2), which agrees with our hybrid-DFT calculations (1.81 eV) and the previously reported values (~1.8 eV).17,18 The DFT+U delivers the best compromise between the accuracy of hybrid functionals and the computational efficiency of pure functionals. Therefore, the DFT+U approach is utilized also for the NA-MD and other related calculations. Further numerical details and the DFT methods benchmarks are summarized in the SI. The pDOS indicates that the valence band maximum (VBM) and conduction band minimum (CBM) of BZS are represented by the S 3p and Zr 4d orbitals, respectively (Figure 1, panels a, d, h). Consequently, the substitution of Zr by Ti atoms decreases the bandgap, because the atomic Ti 3d orbitals are lower in energy than the Zr 4d orbitals. The Ti 3d orbitals therefore push the CBM to the lower energies, reducing the gap (Figure 1, panels b, c). In BZTS with 12.5% and 25% Ti doping, the bandgap is reduced to 1.56 and 1.33 eV, respectively. Thus, Ti doping has the potential for a systematic bandgap tuning in BZS. On the contrary, the atomic Hf 5d orbitals have higher energy than Zr 4d. As the result, they appear high in the CB of the doped BZS and do not affect the bandgap (Figure 1, panels e, f). Therefore, it is expected that such doping will not affect electron-hole recombination strongly, but may affect the cooling rates of “hot”



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electrons.30,45–48 The VB edge states of the BZS are composed mostly of the S 3p states and remain practically unaffected by the Ti or Hf doping. The anion doping affects the VB states, which is similar to the effect of cation doping on the CB states. In BZSO, the O 2p orbitals that are lower in energy than the S 3p orbitals are located deep in the VB, yet the interaction between O and S orbitals of the VB is non-vanishing. This results in the shift of the CBM in BZSO by 0.15 eV, thereby reducing the gap to 1.63 eV (Figure 1, panel g). The 4p orbitals of Se are higher in energy than 3p orbitals of S, so in BZSSe they constitute the VBM. In addition, their interaction with 3p orbitals of S raises the VBM toward the vacuum level. The bandgap of BZSSe is reduced down to 1.45 eV (Figure 1, panel i). Thus, the anion doping is another effective strategy for the bandgap engineering in BZS.

(a)

(b)

(c)

(d)

(e)

(f)


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(g)

(h)

(i)

Figure 1. Optimized geometries and the projected density of states (pDOS) calculated from PBE+U method for doped and undoped perovskites. (a, d, h) BZS, (b) BZTS (12.5%), (c) BZTS (25%), (d) BZHS (12.5%), (e) BZHS (25%), (g) BZSO, and (i) BZSSe. The bandgaps in eV are shown. Both the cation and anion doping are viable strategies of band gap tuning, however it is important to evaluate them from the point of view of their effect on the charge carrier lifetimes. If, for instance, a certain doping approach leads to a favorable energy gap, but increases the recombination rates, it may deteriorate the material’s photovoltaic efficiency since both the photocurrent and photovoltage may be compromised. The overall efficiency of solar energy converting material depends on many factors, such as asbsorption coefficient (e.g. optical absorption spectra) of the material, its chemical stability, its tendency to form defects, and others. These factors may or may not be affected by the elemental doping. The present work assesses the materials only from the point of view of their electron-hole recombination timescales, which is one of the rate-limiting steps that contribute to the overall PV performance. Indeed, “hot” holes/electrons usually thermalize to the edge states (conduction band edge for electrons and valence band edge for holes) within several hundreds of femtoseconds to several picoseconds. The lifetime of the “hot” carrier becomes insufficient for their efficient injection into the



photovoltaic circuit electrodes. On the contrary, electrons and holes relaxed to the band edges are significantly longer-lived and their fate has larger effect on the success of charge collection. One can further conclude that because of the rapid charge carrier thermalization, the position of the optical absorption maximum can be regarded as a generally less important factor than the lifetime of the edge states. This work only focuses on the factors that are related to recombination of the edge state. A comprehensive evaluation of the multiple factors, more sophisticated criteria may be needed, which is beyond the scope of the present work. To reveal the role of orbital and molecular symmetry in the electron-hole recombination dynamics, we have computed the nonradiative relaxation times of the lowest excited states in a number of systematically-designed BZS-derived compositions. The NA-MD methodology based on the quantum-classical decoherence-induced surface hopping (DISH)49 and the time-domain DFT methods as implemented in the open-source PYXAID package50,51 are utilized. The chosen methodology describes the dynamics of nuclei classically, although using the DFT-level forces. We ensure the accuracy in describing vibrations by utilizing the converged k-points meshes (see the SI, Section S8) to compute the nuclear dynamics of the system. We found that the 3×2×2 kpoints grid delivers the best compromise between accuracy and computational efficiency (SI, Section S8). We also apply the same DFT methodology to compute the vibrational spectrum of the BZS (SI, Figure S3). Although previous studies of the IR spectra are not available for the direct comparison, the recent work of Gross et al.19 reported Raman spectra with the frequencies of the same order of magnitude. The electrons and the properties that require wavefunctions (e.g. NAC) are treated quantummechanically at the DFT level. The electronic states are approximated by the 1-electron KS orbitals that correspond to the ground state-converged density. This approximation has been


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widely used in many works.29,52–59 The approach may be not as accurate as the rigorous TD-DFT or many-body methods for excited states, but is critical for computational feasibility of the calculations. It should be regarded as the NA-MD approach formulated in an orthonormal diabatic basis. Thus, the emphasis of the obtained results is on the qualitative trends and not so much on the quantitative results. The electronic transitions are handled via a stochastic hopping procedure (DISH), which ensures a proper energy partitioning between the electronic and nuclear degrees of freedom and accounts for electronic decoherence via non-empirically derived time-dependent decoherence times. These times depend both on the intrinsic coherent dynamics of electronic states and pure dephasing times. The latter are computed non-empirically using the optical response function formalism. The decoherence correction is important for obtaining reasonable estimates of the electronic transition times. In general, it slows down electronic relaxation dynamics, reflecting the quantum Zeno effect, which manifests itself when the intrinsic coherent dynamics is “probed” (observed) by the external environment. Further conceptual and computational details can be found in the SI. The dynamics is computed within a reduced space of the 1-electron Konh-Sham states around the edge states. Although we focus on the recombination of the edge states, the near-edge electronic facilitate the transitions according to a thermally-assisted recombination mechanism. To account for such effects, we have considered all the orbitals that have energy greater than EVBM – (2.5 × kBT) and less than ECBM + (2.5 × kBT) (EVBM, ECBM = energy of VBM and CBM, respectively; kB = Boltzmann constant, and T = 300 K) (Table S3). Thus, the electron-hole pairs that can carry up to 5 units of thermal energy are included in the dynamics. Since the nuclear



dynamics is sampled by the isothermal ground state molecular dynamics, the occurrence of such pairs is expected with the Boltzmann probability on the order of e −5 ≈ 7 × 10−3 . The computed dynamics of non-radiative electron-hole recombination of BZS-derived materials is summarized in Figure 2a. The time-evolution of the ground state population recovery due to the relaxation of the lowest energy excited state (corresponding to a HOMOLUMO transition) is shown. The recombination times are computed by fitting the time-dependent state populations with an exponential function (Figure S2). The population changes presented in Figure 2a are small, which prompted us for unprecedentedly large number of surface-hopping trajectories of 200,000 to ensure statistical reliability of the computed dynamics (Table S4). Using this large number of trajectories gives a minimally-resolved population change to be on the order of 5 × 10−6 per time step. Hence, the 3 ps NA-MD run with the 1 fs nuclear integration timestep would allow us to resolve the recombination timescales of about 0.01 × 1 × 109 fs = 10ns with a 1% uncertainty. The NA-MD calculations employed here rely on classical path approximation that neglects electron-nuclear back-reaction effects. However, the structural rigidity of perovskites suggests that such effects may be negligible. Yet another factor that may need a further consideration is the concentration of the charge carriers, which is significantly increased in the present computational setup in comparison to realistic conditions. Handling such effects may need significantly large systems, that would push the computational costs beyond the present-day practical limits. It is therefore expected that the computed rates may be overestimated with respect to the experimentally-derived ones. However, the qualitative trends are largely defined by the intrinsic electronic structure properties of the materials, so it is assumed that the found trends would be weakly-dependent on the charge carrier concentration.


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We find that in BZS, the recombination occurs on the timescale of 6.84 ns. The replacement of 12.5% of Zr with Ti accelerates the recombination by a factor of ~9, making it 0.75 ns in BZTS (12.5%). When the percentage of Ti doping is further increased from 12.5 to 25%, recombination timescale reduces down to 0.23 ns. On the contrary, the Hf doped perovskites show comparatively slower recombination: 5.72 and 5.08 ns in the 12.5% and 25% Hf doped systems, respectively. In the mixed-chalcogenide perovskites, BZSO and BZSSe, the nonradiative electron-hole recombination occurs on the timescales of 1.18 and 3.72 ns, respectively, notably faster than in BZS. The timescales are summarized in Table 1.

(a)

(b)

Figure 2. Recombination (a) and dephasing (b) dynamics in metal- and chalcogenide-doped BZS. To understand trends in the recombination timescales, we compute the factors that can modulate the quantum transition rates: the nonadiabatic couplings, pure dephasing times, and energy gaps. Decoherence between electronic subsystems induced by the electron-phonon coupling is neglected in the original fewest switches surface hopping (FSSH) scheme.60 When



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the decoherence is significantly faster than the electronic transition rate, the FSSH can overestimate the latter by several orders of magnitude.59,61 Quantum Zeno effect rationalizes the slow electronic transition rates in several solid-state systems, where the decoherence occurs in ultrafast timescales.54,62–65 Simple FSSH may fail when modeling slow electron-hole recombination. Therefore, we use DISH to compute the rates of electronic transitions.49 In the present approach, the decoherence times are expressed in terms of pure-dephasing induced by the electron-phonon scattering. To obtain the pure dephasing times, the dephasing functions are first computed (Figure 2b) via the linear response function formalism,66 as detailed elsewhere.67 The

dephasing functions are fitted to a Gaussian, e

1 t  −   2τ 

2

, to yield the dephasing times. The calculated

pure-dephasing times may be verified experimentally from the homogeneous luminous linewidths.55,68 The NAC between electronic states is obtained by applying the numerical approach of Hammes-Schiffer and Tully64.

[ (

) (

)

(

) (

)]

r  dt  1 r r r r r r r r dij  t +  = φi r ; R(t ) φ j r ; R(t + dt ) − φi r ; R(t + dt ) φ j r ; R(t ) . 2  2dt 

(

(1)

)

r r r r Here, φi r ; R(t ) is the KS orbital of index ݅ at time ‫ ;ݐ‬r and R (t ) represent the electronic and nuclear coordinates, respectively. In general, small excitation energy, large NAC, and slow dephasing all facilitate fast electronhole recombination. These quantities are summarized in Table 1, together with the computed recombination timescales. The NAC and dephasing times summarized in Table 1 represent the values that are averaged over all ground and excited states included in the active space by taking a Boltzmann distribution. The Boltzmann averaged NAC and dephasing times in different perovskites follow qualitatively similar trends compared to the NAC between the HOMO and


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LUMO states and the dephasing times corresponding to HOMO → LUMO transitions in these systems. To facilitate the discussion of the observed trends, the systems are grouped in three homological series, with the BZS present in each of them as a reference. In the first two series, we vary the metal (Ti and Hf) doping percentage: 0%, 12.5%, 25%. In the third series, the chalcogenide nature is varied in the row: O, S, Se (in the order they appear in the chalcogenide series of periodic table).

Table 1. The computed recombination times, average NAC, dephasing times, and band gaps in studied chalcogenide perovskites. System

Recombination

Average

Variance

Dephasing

time, ns

NAC, meV

in NAC

BZS

6.84

0.74

0.49

30.68

1.78

BZTS (12.5%)

0.75

1.30

1.10

12.08

1.56

BZTS (25%)

0.23

1.66

2.84

12.96

1.33

BZS

6.84

0.74

0.49

30.68

1.78

BZHS (12.5%)

5.72

0.96

0.49

12.54

1.73

BZHS (25%)

5.08

0.79

0.28

28.60

1.74

BZSO

1.18

1.13

0.87

13.97

1.63

BZS

6.84

0.74

0.49

30.68

1.78

BZSSe

3.72

0.65

0.29

18.38

1.45


time, fs

Band eV

gap,


In the first series (Ti doping), one can clearly observe that the increase of the Ti doping percentage causes the band gap reduction and the NAC increase. The dephasing becomes more rapid in the Ti-doped BZS and does not depend on the percentage of Ti. The recombination timescales suggest that a large NAC and a small bandgap play the dominant role in the dynamics in this series. Although fast dephasing can contribute to slow dynamics, the combined effects due to large change in the magnitudes of both NAC and bandgaps lead to overall fast dynamics. It also appears that dephasing is affected strongly by the symmetry of the unit cell – once the symmetry is broken, the dephasing time decreases abruptly. The trends in NAC magnitudes in Ti-doped BZS can be understood from the points of view of energy gap and orbital symmetries. First, our electronic structure calculations (Figure 1) indicate that the band gap decreases gradually as the percentage of Ti doping increases. The derivative coupling vector can be expressed via the energy gap and the expectation value of the Hamiltonian derivative starting directly from the (time-dependent) Hellman-Feynman theorem and considering the wavefunction to be time-dependent. As a consequence of the theorem, the nonadiabatic couplings are inversely proportional to the magnitude of the energy gap. This relationship has been also demonstrated explicitly in a recent computational study.70 The effect can be attributed to the relative energies of atomic d-states in Ti and Zr. Second, the symmetries of the frontier orbitals involved in the recombination process change qualitatively when the BZS is doped with Ti (Figure 3, a-c). The VBM of BZS has a large contribution of S 3pz orbitals, whereas the CBM is represented by Zr 4dxy orbitals, positioned perpendicular to the 3pz states. The NAC between two states quantifies how fast one orbital changes in time with respect to another, which can be quantified by the time-overlaps of the corresponding orbitals,

φi (t ) φ j (t + dt ) , as defined by Eq. 1. The KS orbitals can be represented as a superposition of


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( )

( )

( ) ( )

r r r r atomic-orbital-projected basis functions, χ k R(t ) : φi (t ) = φi R(t ) = ∑ ck R(t ) χ k R(t ) . If the KS k

orbitals are dominated by a single atomic-like term, χ 0 , the mixing-originating time-dependence

( )

r of the orbital (via the ci R(t ) terms) gets weaker. The only dependence of the overlaps that is

( )

r left is the implicit one, via the χ R(t ) . The qualitative analysis of φi (t ) φ j (t + dt ) is then

( ) (

)

r r reduced to that of χ i R (t ) χ j R (t + dt ) . In special cases, dictated by symmetry of orbitals and atomic motions, this integral may be vanishing. Indeed, the overlap of pz and dxy orbitals remains zero even, when the center of one of them is displaced along x, y, or z direction. Thus, the composition of the frontier orbitals and their symmetry are the likely factors that reduce the NAC in BZS down to 0.74 meV. On the contrary, in BZTS, the Ti atoms polarize the CBM orbitals along z direction (Figures 3b and 3c, upper panels), destroying the translational invariance of the atomic-orbital overlaps,

( ) ( r

r

)

χ i R(t ) χ j R(t + dt ) . Now, although the VBM is still dominated by the 3pz orbitals of sulphur, the CBM states are represented by a superposition of the Ti 3dxz and Zr 4dxz states, leading to

( )

r two effects. First, the time-dependence is reintroduced via the superposition coefficients, ci R(t )

. Second, the overlaps of the pz and dxz orbitals are no longer zero, when the centers are displaced from each other. Together, the two effects maximize the time-overlap φi (t ) φ j (t + dt ) , leading to the increased NACs of 1.30 and 1.66 meV in 12.5%- and 25%-doped samples, respectively. In order to understand how NAC varies along the trajectory, we calculate the variance in NAC for all systems (see SI for the methods). We find the values of 0.49, 1.10, and 2.84 for the variance in average NAC for BZS, BZTS (12.5%), and BZTS (25%), respectively. It indicates that along



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with an increase in average NAC, the fluctuation in NAC magnitude also increases with respect to the Ti doping. To recapitulate, the Ti-doping introduces two competitive effects. On the one hand, it decreases the band gap, increasing the efficiency of the solar energy harvesting. On the other hand, it facilitates the recombination of photogenerated charge carriers, decreasing the photocurrent and photovoltage.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Figure 3. Charge density plots of the LUMO (top) and HOMO (bottom) orbitals in; (a) BZS, (b) BZTS (12.5%), (c) BZTS (25%), (d) BZHS (12.5%), (e) BZHS (25%), (f) BZSO, and (g) BZSSe. In the second homological series (Hf doping), the band gaps vary slowly and are comparable to each other, showing only a little dependence on the Hf concentration. We observe a relatively weak change of the recombination timescales due to Hf doping, however it goes seemingly contradictory with the NAC magnitudes and energy gaps. This makes us conclude that decoherence plays the dominant role in these compositions. The computed dephasing time is significantly smaller in BZHS (12.5%) than in BZS or BZHS (25%): 12.54 fs vs 30.68 and 28.60


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fs, respectively. This effect correlates with the observed increase of the recombination times in the 12.5% Hf doped BZHS. Both the NAC and energy gap suggest that the recombination should be significantly faster in the 12.5% BZHS than in BZS or BZHS (25%), yet it is not observed. In the latter system, the NAC is larger than in BZS, but the band gap and dephasing is comparable. Therefore, the larger NAC leads to faster recombination than in BZS. Although fluctuations in the magnitude of NAC is slightly larger in BZHS (12.5%) than in BZHS (25%) (0.49 vs 0.28), it is similar to that found in BZS (0.49). It is illustrative to discuss the trends observed in other computed properties. In BZHS, the NAC between the frontier orbitals is smaller than in BZS. Analogously to the BZTS, this effect is understood from the point of view of atomic orbital energies and symmetries (both atomic and orbitals). Since the Hf 5d orbitals are higher in energy than Zr 4d, they contribute only to the high energy CB states. The frontier orbitals are practically unchanged with respect to BZS (Figure 3, panels d and e). This results in the energy gap being practically unaffected and in the minimized orbital overlap (similar to BZS). The non-monotonic behavior of the NACs and dephasing times in the BZHS as the function of Hf percentage is somewhat surprising. At the present point, we attribute it to the symmetry of the unit cells, which eventually affects the details of the dynamics. Indeed, the reference BZS structure comprises a regular motif of Zr-SZr units. In the 25% Hf-doped BZS, the symmetry is lowered, but one can see a combination of both Zr-S-Zr and Hf-S-Hf motifs. On the contrary, in the 12.5% Hf doped BZS, this local atomic bonding regularity is broken: one find the Hf-S-Zr motif, which in their turn may lead to faster vibrational modes than any of the Zr-S-Zr or Hf-S-Hf (as simply follows from the 3-body harmonic oscillator problem). Such changes can induce increase in the dephasing rates and hence slow down the dynamics. Thus, the asymmetry of the local atomic bonding pattern (termed here



“molecular symmetry”) can directly affect the pure dephasing and overall recombination dynamics. It should be noted that such situation is likely to occur in the doped or defected systems. The defects or dopants can therefore act as the centers for slow recombination by changing the dephasing dynamics of the localized electronic states. This may be used as the design principle for dephasing engineering. The photogenerated charge carriers in mixed-chalcogenide perovskite, BZSO undergo a recombination on the timescale of 1.18 ns. The faster relaxation in BZSO compared to BZS is understood on the basis of larger NAC and smaller excitation energy in the former. The increase of the coupling in BZSO can be attributed to the changed nature of the VBM (Figure 3f, bottom panel). The orbital still preserves the S 3p character, but it is slightly bent and diffuse, allowing for increased overlap with the CB state. In BZSSe, the recombination occurs on the order of 3.72 ns, despite having a small NAC (0.65 meV) and shorter dephasing time (18.38 fs). BZSSe shows smallest magnitudes of average NAC and the variance in NAC among all perovskites studied. We conclude that the major factor determining the recombination rates in BZSSe is its smaller excitation energy (1.45 eV) compared to BZS. It is interesting to note that in this case the significantly decreased energy gap dominates notably over the fast dephasing and small NACs to accelerate the recombination of the charge carriers. In summary, we have investigated the electronic properties and excited state dynamics in a novel class of perovskites (chalcogenide perovskites) by using time-domain DFT and NA-MD calculations. Our study reveals a number of trends in the properties relevant to photovoltaic performance of chalcogenide perovskites as the function of chemical modification via elemental doping. Specifically, substitution of Zr with Ti or S with O or Se leads to a significant reduction of the bandgaps, indicating that the solar energy absorption may be maximized using the doped


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systems. Concurrently, the same modifications lead to the increase of the non-radiative recombination timescales, changing them from 6.84 ns in BZS to 1.18/3.72 ns in BZSO/BZSSe and to 0.23 ns in 25% Ti-doped BZTS. In BZTS, the fast recombination occurs due to two reasons: smaller excitation energy and larger NAC compared to BZS. The large NAC in Ti doped systems results from favorable overlaps of metal 3d/4d orbitals in LUMO with the S 3p orbitals in HOMO. Such orbital interactions are minimized in BZS by symmetry and gradually increase as the symmetry is broken in the doped systems. We emphasize that a lower symmetry of atomic motifs (e.g. Hf-S-Zr versus Hf-S-Hf or Zr-S-Zr) can increase the magnitude of NACs and facilitate dephasing. Although Hf doping only leads to an inconsequential change in the magnitude of excitation energy and an increase in NAC, a notable reduction in the decoherence time furnishes slow electron-hole recombination. This finding suggests that it may be possible to improve performance of PV materials by engineering decoherence dynamics. In this work, we have illustrated how the computed recombination timescales depend on the key parameters (NAC, energy gap, and decoherence). We analyze how these terms depend on the details of molecular and orbital symmetry. We utilize the term “symmetry” in a broad sense to distinguish between highly ordered (e.g. BZS) structures and less ordered ones (e.g. doped BZS). We demonstrate that in the Ti-doped BZS series, addition of every Ti atom induces the appearance of a “stripe” of Ti-aligned CB orbitals with particular ordering with respect to the VB ones. A similar effect is observed with the VB orbitals, when an anion doping is utilized. Next, we relate the local symmetries in the atomic motifs like Hf-S-Hf vs. Hf-S-Ti to the dephasing times, and hence to the recombination timescales. Thus, the essential properties affecting electron-nuclear dynamics can be understood from the point of view of molecular and orbital symmetries.



Associated Content Supporting Information. The SI in PDF form comprises: the details of methodologies and computational setups, table of relaxed cell-parameters of perovskites, comparison of the bandgaps obtained using different methods, geometries and relative energies of different configurations of BZTS (25%), phonon spectrum of BZS, comparison of results from different NA-MD calculation setups, and fittings of recombination dynamics data. Additionally, the setup files used for various stages of simulations are attached as separate txt files. The main SI file contains (section 9) a brief description of the details of each setup file.

Author Information Corresponding Author * Email: [email protected] Twitter: @AkimovLab

Notes The authors declare no competing financial interests.

Acknowledgements A.V.A. acknowledges the financial support from the University at Buffalo, SUNY startup package and from the SEED RENEW project. A.N. thanks Brendan Smith and Ekadashi Pradhan for help with the Python scripting used in the data analysis. A.V.A and A.N. acknowledge Prof. Michel Dupuis for useful discussion of the computational results. The computational facility is provided by the Center for Computational Research at the University at Buffalo, SUNY.

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Orbitals on the Choice of Density Functional: Pure vs Hybrid. J. Phys. Chem. A 2016, 120, 9028–9041.


Criticality of Symmetry in Rational Design of Chalcogenide

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