Ferroelectric Materials for Solar Energy Conversion: Photoferroics RevisitedKeith T. Butler,1 Jarvist M. Frost,1 and Aron Walsh1, a)

Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Claverton Down,Bath BA2 7AY, UK

(Dated: 23 December 2014)

The application of ferroelectric materials (i.e. solids that exhibit spontaneous electric polarisation) in solarcells has a long and controversial history. This includes the first observations of the anomalous photovoltaiceffect (APE) and the bulk photovoltaic effect (BPE). The recent successful application of inorganic andhybrid perovskite structured materials (e.g. BiFeO3, CsSnI3, CH3NH3PbI3) in solar cells emphasises thatpolar semiconductors can be used in conventional photovoltaic architectures. We review developments inthis field, with a particular emphasis on the materials known to display the APE/BPE (e.g. ZnS, CdTe,SbSI), and the theoretical explanation. Critical analysis is complemented with first-principles calculationof the underlying electronic structure. In addition to discussing the implications of a ferroelectric absorberlayer, and the solid state theory of polarisation (Berry phase analysis), design principles and opportunitiesfor high-efficiency ferroelectric photovoltaics are presented.

I. INTRODUCTION

Ferroelectrics are a class of materials that display spon-taneous electric polarisation. This is due to the break-ing of centrosymmetry of the crystallographic unit cell,and may be varied by the application of physical, chem-ical or mechanical bias. Ferroelectric materials have ex-tensive potential technological applications, due to thepossibility of coupling the ferroelectric response withother properties. Applications include memory storagemedia1,2, field effect transistors and ferroelectric random-access memory3,4. The coupling of ferroelectricity andmagnetism has led to an extremely fertile area of re-search, ‘multi-ferroics’, with potential use in emergentspintronic technologies5–7. An important realised tech-nological function of ferroelectrics is the coupling of me-chanical response to electric field, applied in both sensorsand actuators.

Light-to-electricity energy conversion in ferroelectricswas envisioned 35 years ago by V. M. Fridkin, who imag-ined a “photoferroelectric crystal” as a potential solarcell8. In the following decades the development of fer-roelectric based photovoltaic (PV) devices has mostlyremained the preserve of academic research. Industryadoption is hampered by low quantum efficiencies of de-vices, as well as poor bulk conductivity of common ferro-electric materials. Further, the theoretical description ofpolar properties in bulk materials remained incompleteuntil formalisation in the modern theory of polarisation9.There have been significant recent advances in ferroelec-tric photovoltaics10, most notably in devices based onoxide and halide perovskites.

In this perspective we consider a class of systems wherethe ferroelectric effect and photo-response are intimatelylinked: photoferroics. We will outline the ferroelectricand photovoltaic action, followed with an examination ofthe application of ferroelelectrics to solar cells, discuss

a)Electronic mail:a.walsh@bath.ac.uk

several proposed models for enhanced PV performanceobserved in ferroelectric materials, and consider contem-porary research into photoferroics. We will investigatea historically important but latterly overlooked class ofphotoferroic materials, the antimony chalcohalides. Theperspective concludes with a consideration of new direc-tions for materials design, and how ferroelectric materialscan be applied in novel device architectures to improvephotovoltaic performance.

II. THE FERROELECTRIC EFFECT

Pyroelectric crystals possess a net dipole moment (P)in their primitive unit cell, and therefore exhibit spon-taneous polarisation. They generate a transient voltagewhen heated (hence ‘pyro’) due to changes in lattice po-larisation arrising from thermal expansion. All pyroelec-tric materials must adopt a non-centrosymmetric crystalstructure, with an asymmetric (negative) electron densityaround the (positive) nuclei. These asymmetric chargedensity crystals are necessarily described by polar crys-tallographic point groups (10 out of the 32 groups), wheremore than one site is unmoved by every symmetry oper-ation. This excludes all cubic crystals, and other highsymmetry space groups. The electric dipole resultingfrom the ionic positions is defined as:

Pionic =∑i

qiui (1)

where qi and ui represent the ion charge and position,and the sum is over all atoms in the unit cell.

Ferroelectrics can be defined as the subgroup of pyro-electric materials in which the equilibrium structure hasno net dipole above a certain temperature. The orienta-tion of spontaneous dipoles below this transition temper-ature can be manipulated by the application of an electricfield—ferroelectric materials exhibit a polarisation whichis dependent on the history of applied field (hysterisis).The first report of ferroelectricity was from Valasek, who

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In many cases the polar structure of a ferroelectric ma-terial may be obtained from non-polar polymorphs bya small mechanical strain, temperature change, or evena variation in carrier concentration. The free energiesof the polar and non-polar polymorphs of a crystal aregenerally quite close (several meV per atom). A criti-cal temperature exists (the Curie temperature, TC) atwhich the free energies of both phases are degenerate.The polar (lower symmetry) structure is usually the lowtemperature ground state.

When a material is in its pyroelectric phase it com-monly consists of domains – regions of homogeneous po-larisation – that differ only in the direction of the po-larisation. For greater detail on the ferroelectric (andrelated piezoelectric) effect, several excellent text booksare available8,12,13.

A. Modern theory of polarisation

The interpretation of crystal polarisation was funda-mentally altered 25 years ago by the modern theory ofpolarisation9,14,15. The classical polarisation resultingfrom the position of charged ions in a lattice is well de-fined (Equation 1), while the calculation of electric po-larisation from periodic electronic wavefunctions poseda major theoretical challenge. There is no unique wayto separate the charge density into finite regions of welldefined polarisation. By recasting the problem from realto reciprocal space, and applying Berry phase analysis16

to the change in phase of the electronic wavefunctionsummed over all wavevectors, an intrinsic polarisationcan be directly and unambiguously computed for a peri-odic material.

Berry’s Geometric phase analysis has been applied innumerous studies revealing hitherto unknown aspects offerroelectric materials. For electronic structure calcula-tions such analysis requires a relatively low-cost post-processing of pre-computed electronic structure and ionpositions. The total change in polarisation for a (ferro-electric) transition can now be defined as a sum of theionic and electronic components:

∆P = ∆Pionic + ∆Pelectronic. (2)

Recent applications include unusual ferroelectric in-stabilities in fluoroperovskites17, highlighting the impor-tance of covalent bonding in the piezoelectric responseof BaTiO3

18, as well as the discovery of new classes ofproper and improper ferroelectrics19,20. The approachhas also been applied to the study of less traditional solid-state materials such as metal-organic frameworks21,22.Building upon the work of von Baltz and Kraut23, Rappeand co-workers were able to calculate the so-called shift-current contribution to photovoltaic performance24,25. Inthe field of hybrid halide perovskites, Berry phase analy-

sis has been used to demonstrate the possibility of molec-ular tuning of the electric polarisation26.

III. THE PHOTOVOLTAIC EFFECT

In a semiconducting material, the absorption of pho-tons with energies above the band gap (hν ≥ Eg) resultsin the promotion of electrons from the valence band tothe conduction band. The process generates hole (valenceband, effective positive charge) and electron (conductionband, negative charge) carriers. In a typical materialthese excited carriers will decay back to the ground-state,energy being conserved by the emission of light (photons,radiactive decay) or heat (phonons, non-radiative decay).The photovoltaic effect occurs where an asymmetry inthe electric potential across the material (or selectiveelectrical contacts) results in a net flow of photogener-ated electrons and holes: a photocurrent. In one of theearliest examples of a solar cell, an asymmetric potentialwas introduced by placing a layer of selenium betweentwo different metallic contacts27. The difference in work-functions of the metals creates the necessary asymmetryand electrically rectifying action, a Schottky barrier.

In the 1950s an alternative method of creating asym-metry for charge separation was discovered. By dopingdifferent regions of a single piece of silicon with phospho-rous and boron, it is possible to establish an asymmetricpotential in a single crystal, the p − n junction. Herethe built-in field gives better rectification, and thereforebetter photovoltaic action. The ideal photovoltaic mate-rial should separate charges as efficiently as possible, withminimal relaxation of the charge carriers from the opticalexcitation, and transport them independently to the con-tacts, thus minimising recombination (the loss pathway)between electrons and holes.

The overall power conversion efficiency (η) of incidentlight power (Pin) to electricity is is proportional to theopen-circuit voltage (Voc), short-circuit current (Jsc) andthe fill-factor (FF ):

η =VocJscFF

Pin, (3)

Voc is the potential difference developed across a cell (inthe light) when the terminals are not connected (no cur-rent flow). This represents the maximum voltage whichcan be generated by the cell. Voc is limited (in a standardsemiconductor junction) by the band gap of the absorberlayer, with additional recombination losses (at open cir-cuit, all photo-generated charges recombine). Jsc is thephoto-current extracted when the voltage across the cellis zero, all generated potential difference is used to ex-tract charge carriers. Jsc is limited by the proportion ofthe solar spectrum absorbed by the active material in adevice. At both Jsc and Voc, no energy is extracted fromthe solar cell. In an idealised device the power genera-tion would equal the product Voc×Jsc. Detailed balancerequires that radiative recombination must occur. Any

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additional recombination is a loss pathway. The realisedpower at the maximum power point on the J − V curveas a fraction of the idealised power is the fill-factor, FF .

Recombination of photo-generated electrons and holeslimits the efficiency of operating solar cells. Recombina-tion can occur directly from valence to conduction band,or via trap states. Trap mediated recombination occurswhen imperfections in the crystal cause a localised den-sity of states within the band gap. Both electrons andholes can become energetically trapped, then recombin-ing with carriers of the opposite sign. Surfaces representa major source of trap states in convential semiconduc-tors, with under-coordinated atoms introducing localisedstates into the gap. Surface effects can be reduced by theinclusion of a passivation layer, to satisfy coordination atthe surface, whilst not conducting charge themselves28,29.Band to band recombination occurs when carriers of op-posite sign encounter each other in the semiconductor.This is reduced by improving the mobility (reducing timein the device) separation (segregating oppositely chargedcarriers with an electric field) or screening of the carriers(reduces recombination cross-section).

There are several photovoltaic architectures which areused to achieve efficient charge separation and trans-portation. p− n homojunctions as outlined above; p− nheterojunctions (e.g. in CdTe cells), which are similarto standard p − n junctions, but consist of two distinctmaterials; p − i − n junctions (e.g. in a-Si cells) havea region of undoped (intrinsic) material between the p−and n− regions. Organic solar cells typically require aheterojunction to efficiently drive the charge separationof tightly bound excitons, sacrificing photon generated.This consists of electron donor and acceptor moleculesin close proximity, with hole- and electron- selective elec-trodes.

IV. FERROELECTRIC PHOTOVOLTAICS

We have outlined common photovoltaic device archi-tectures, which universally rely on charge separation byvariation in material composition. Charge separation dueto the innate crystal field in a homogeneous material isalso possible, which is the process used in some ferro-electric photovoltaics. The crystal polarity creates mi-croscopic electric fields across domains, separating pho-togenerated excitons into free charges, and segregatingthe transport of the free charges to reduce recombina-tion rates.

There are additional potential advantages to such de-vice designs. For example, ferroelectric materials canachieve extremely high open circuit voltages (Voc), unlikea standard photovoltaic cell where Voc is limited by theband gap of the absorber material. The consistency ofthe product of Jsc and Voc is maintained with larger pho-tovoltages being associated with smaller photocurrents.

Recent research into ferroelectric photovoltaic ma-terials has consisted of two mostly independent

strands. Photovoltaic effects have been studied in ox-ide ferroelectrics24,32–35, notably BiFeO3 (BFO), from afundamental physics and materials design perspective.The discovery that hybrid organic-inorganic halide per-ovskites, notably CH3NH3PbI3 (MAPI), can make high-efficiency photovoltaic devices has redirected vast areasof solar energy research36–42. The former has been drivenby both the layer-by-layer control of modern depositiontechniques and the development of the modern theoryof polarisation facilitating a complete description of bulkpolar materials. The latter has been driven by the ex-traordinary empirical performance of MAPI, demonstrat-ing the potential of polar materials.

A. Photoferroic Phenomenology

The photoferroic current (Ji) can be related to ab-sorbed light by the rank three tensor β:

Ji = pjp∗l βijkIo (4)

where Io is the intensity of the absorbed light (assumingisotropic absorption) and pn is the polarisation of themedium, the subscripts ijk correspond to the directionin space. The amplitude of the tensor has the form

where Io is the intensity of the absorbed light (assum-ing isotropic absorption) and pn is the polarisation of themedium in direction n. The amplitude of the tensor hasthe form

βijk = eloζφ(~ω)−1 (5)

where ζ describes the excitation asymmetry, φ is thequantum yield, ~ω is the photon energy. and lo is themean free path of excited carriers and e is the elemen-tary charge. It can be shown43 that the efficiency ofpower conversion from the photoferroic effect can be ex-pressed as :

η = βijkE (6)

where E is the electric field arising from ji

E =Jiσpv

(7)

where σpv is the photoconductivity.Generally, in bulk crystals the values of β and E are

very small. When the size of the sample is of the order oflo, all of the excited carriers contribute to photo-currentand E can become much larger. Within band theory,the length has been estimated to be 10–100 nm44; hence,photoferroic effects are enhanced at the nanoscale. Un-derstanding and controlling lo is an important aspect inthe design of photoferroic device architectures.

In a photoferroic system there is an intricate rela-tionship between photo-response and ferroelectric phasestability (including domain size and distribution). The

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FIG. 1: Models for the bulk photovoltaic effect. a) Asymmetric carrier scattering centres, resulting in a net flowfrom randomly drifting carriers, following Belinicher30. b) Asymmetric potential well at a carrier generation centre;

photogenerated carriers have a preferred direction of exit, following Lines13. c) Relativistic splitting of theconduction band minimum establishes two distinct channels for electron excitation, polarised light promotes

electrons preferentially to one channel, following Fridkin31.

relatively high concentration of photo-generated carriers(electrons and holes) means that the electronic subsystemhas an appreciable effect on free energy close to ferro-electric transition (Curie point). The electron subsystemcan alter the nature of these phase changes, which can beused to experimentally classify a system as a photoferroicas well as to quantify the photoferroic effect.

In general, temperature hysteresis is reduced andCurie-points are lowered in the presence of photo-excitedcharges; the shifts are proportional to carrier concentra-tion, as observed for example in SbSI45. Spontaneouspolarisation as measured, for example by pulsed-field orhysteresis loop methods, is reduced by the presence offree charges due to enhanced screening. Structural defor-mation can be caused by the presence of carriers, withcharges affecting the unit cell volume during the phasetransition. Effective permittivity has a dependence onthe presence and concentration of carriers; the dielec-tric screening is initially increased by increasing carrierconcentration. This outline of the physical manifesta-tions of the photoferroic effect is necessarily limited, fora comprehensive review of these properties, as well as thethermodynamic principles underlying them we refer thereader to V. M. Fridkin’s seminal texts8,44.

Numerous mechanisms have been proposed to explainthe unusual photovoltaic performance of ferroelectric ma-terials. We now describe several of the key models used torationalise experimental phenomena in poly- and mono-crystalline materials.

B. Bulk Photovoltaic Effect (BPE)

Photovoltages in un-doped, single crystal samples ofmaterials have been reported as a bulk photovoltaiceffect (BPE), sometimes referred to as the photogal-vanic effect or non-linear photonics. The earliest re-port was of steady-state photovoltages in single crystalBaTiO3 (BTO) in 195646 and it is only observed in non-centrosymmetric systems. The recorded photocurrents

were closely related to the magnitude and the sign of themacroscopic polarisation of the sample. Subsequently,similar effects were reported in LiNbO3 and LiTaO3

47.More recently there have been a series of studies onBiFeO3 (BFO), with intense interest in its applicationas a photoferroic material in PV devices.

The simplest proposed model for the BPE is based onasymmetric scattering centres in a material30, which isgraphically represented in Figure 1a. If a medium con-tains randomly located, but identically oriented wedges,then, in the absence of external forces, the random diffu-sion and drift of carriers in the medium will eventually setup a net current. Any current established by this mech-anism, however, would be expected to be local and shortlived, constrained by the associated increase in entropy.

Another model, based on asymmetry in the electro-static potential in which electrons and holes diffuse is de-tailed in Figure 1b13. In this case there is anisotropy inthe potential at an absorbing centre, for example, causedby crystal polarisation. Carriers are excited from thestate at E0 to an energy E. If E < V1 the excited elec-tron remains trapped in the potential well. If E >> V2then the carriers move away from the centre isotropically;however, if V1 < E < V2 then carriers moving to theleft are partially scattered by the potential barrier (al-lowing for a certain probability of tunneling) and a netflow of carriers to the right (as indicated in Figure 1)is established. Thus optical absorption in a polar crystalwith aligned asymmetries results in a net current. Thecontribution of this current to the overall photocurrentis maximized when the width of the crystal is similar tothe decay length of the asymmetrically excited carriers43.Due to a decay length of 10 – 100 nm43, as discussed pre-viously, the effect is maximised in ultra-thin films.

A third model relates to the BPE in gyrotropiccrystals31, materials whose valence or conduction bandsare split in reciprocal space by relativistic spin-orbit cou-pling (e.g. so-called Dresselhaus or Rashba splitting48),Figure 1c. A key requirement again is the absence ofcrystal inversion symmetry. In a non-relativistic descrip-

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FIG. 2: Models for the poly-crystalline anomalous photovoltaic effect. Valence and conduction bands are colouredorange and green, respectively. (a) The Dember effect: holes and electron have different mobilities, resulting in a netcharge (with an internal electric field) across the crystal upon carrier generation. (b) Asymmetric aliovalent dopingof a crystal results in an electrostatic potential across a grain. (c) Breaking of centro-symmetry creates a dipole inthe crystal unit cell and can result in ferroelectric domains. (d) If a poly-crystal contains inhomogeneous domains,the gradients in electric potential do not exactly cancel and a voltage is generated across the poly-crystal that may

exceed the band gap of the material.

tion, all valence band electrons have an equal probabilityof being excited by photons. When the bands are split byspin-orbit coupling, the momentum of the excited carrierdepends on its spin. Therefore illumination by polarisedlight results in current flow. Clockwise polarised lightexcites electrons to a state momentum kz > 0 and anti-clockwise polarised light excites electrons to kz < 0, be-cause of the decoupling of the spin channels. The natureof the splitting may be different for electrons and holesdue to the different orbital contributions to the conduc-tion and valence bands. These spin-orbit coupling effectsare larger with heavier elements (e.g. Pb and Bi), andhas been recently demonstrated for the hybrid perovskiteMAPI49,50.

The BPE mechanisms considered above arise from theasymmetric velocities of carriers in the potential of thecrystal lattice. Another important contribution is due tothe asymmetry of the electron density. This results in ex-citation of carriers in one band to another band, which isseparated from the initial one in real space. These “shiftcurrents” have been demonstrated for several materialsincluding BiFeO3

25,BaTiO351 and GaAs52,53, both ex-

perimentally and theoretically. Theoretical results forBaTiO3 demonstrate that for a significant shift currenta material must feature ‘covalent’ bonding that is highlyasymmetric along the current direction24.

C. Anomalous Photovoltaic Effect (APE)

The photovoltage achievable from a semiconductor isgenerally limited by the bandgap of the light absorbingmaterial. Starkiewiz and co-workers first reported ob-servations contravening this general rule on PbS films in194654. Subsequently similar observations were reportedfor polycrystalline CdTe, ZnTe and InP55–57. The com-mon feature was thin films deposited on an angularlyinclined and heated substrate. Reports of photovoltageshundreds and even thousands of times the bandgap werehighly sensitive to the conditions of the samples and wereextremely difficult to reproduce. A coherent model ex-plaining the effect was slow to emerge. An unusual aspectis that the materials mentioned above are not known tobe ferroelectric, e.g. PbS adopts the rocksalt structure,which is stable up to high temperatures58.

The explanations which were put forward generally fallinto three categories: (a) the Dember effect; (b) p−n ho-mojunction domains; (c) ferroelectric domains. All threeexplanations posit an inhomogeneity in the charge distri-bution, which is not fully screened due to the presenceof crystal nano- or micro-structure. The resulting photo-voltage across the material can be additive depending onthe number and type of domains/interfaces present. Themechanisms, outlined in Figure 2, can be summarised asfollows:

(a) In the Dember effect (Figure 2a) photo-generatedcharge carriers are generated inhomogeneously through-out the crystal, forming preferentially at the face exposed

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to the photon source59. Carriers then diffuse through thematerial; however, the difference in effective masses of theelectron and hole carriers means that diffusion occurs atdifferent rates, thus a net polarisation across the materialis developed.

(b) In the p−n junction model (Figure 2b) each crys-tallite is presumed to have an inhomogeneous distribu-tion of p and n type defects or dopants, creating the dif-ference in electric potential necessary to separate chargecarriers in the crystallite54.

(c) In the ferroelectric domain picture (Figure 2c), thecharge carrier separation results from the polarisation ofthe material itself, in the form of the electric fields dueto a ferroelectric domain structure60.

In the above cases the steady-state photovoltage willnot exceed the bandgap of the material. This is becausein a single crystal the depolarisation field would be ex-actly cancelled by the formation of space-charge regionsat the boundaries. In a poly-crystal there can be an ar-ray of alternating interfaces, e.g. AB BA (Figure 2c).If either A or B is pyroelectric then AB and BA junc-tions are not equivalent. In this case the space-chargemay not fully counteract the depolarisation field and theresulting photovoltage can then build up across the poly-crystal resulting in an above bandgap potential difference(Figure 2d)13. Unlike the BPE, which can be defined asan intrinsic bulk response, the APE relies on the nano-and micro-structure of a sample.

V. OXIDE PEROVSKITES

The study of ferroelectrics has been dominated byperovskite-structured metal oxides. These are ternarymaterials of the form ABX3, where the A site in thecrystal lattice is at the centre of a three-dimensional net-work formed by corner-sharing BX6 octahedra. At hightemperature, a high symmetry cubic structure is com-monly observed (where polarisation is forbidden by in-version symmetry), while at lower temperature a rangeof lower symmetry phases can be formed (e.g. tetragonal,rhombohedral and orthorhombic perovskites), which canbe ferroelectric or antiferroelectric. The phase diagramsof these materials are highly complex, with a combina-tion of short and long-range order (see for example recentwork on PbZr1-xTixO3)61.

Most oxide perovskites are wide bandgap insula-tors, and high-temperature conductivity is usually ionic,rather than electronic62,63. For ionic-conducting per-ovskites, aliovalent doping can be performed to in-crease vacancy concentrations (to enhance mass trans-port) rather than electron or hole concentrations. Indeedeven for hybrid halide perovskites, a strong preferencefor ionic compensation of charged point defects has beenpredicted64.

The few demonstrated solar cells based on oxide per-ovskites have poor power conversion. For example it hasbeen shown for single crystal BaTiO3 that the conver-

sion efficiency due to the BPE is limited to ∼ 10−743.Nonetheless there have been recent reports of improvedperformance by decreasing layer thickness and judiciousengineering of domain and electrode interfaces. Whileinitial power conversion efficiencies were in the region of0.5%33,43, there has been recent success up to 8% forBi2FeCrO6

65.One of the major hindrances faced by the oxide mate-

rials are the wide bandgaps, which allow for only a smallfraction of the solar spectrum to be absorbed. Therehave been recent reports of bandgap-engineered materialswith ferroelectric properties and bandgaps appropriatefor efficient solar energy conversion66,67. By controllingthe cation ratio and distribution in the double perovskiteBi2FeCrO6 (Fe and Cr ions are distributed over the per-ovskite B site), the optical band gap could be tuned byseveral eV65.

The authors who first reported above bandgap pho-tovoltages in BiFeO3 dismissed the possibility that thephenomenon has the same origin as the bulk photo-voltaic effect in other single crystals such as BaTiO3 andLiNbO3

32. In this instance the role of domain walls (theinterface between ferroelectric domains) was emphasisedby a series of experiments demonstrating the dependenceof the obtained photovoltage on the domain wall density.They proposed a model building upon theoretical studiesthat demonstrated the presence of built-in electric poten-tial at domain walls68,69. Excitons (electron-hole pairs),which would otherwise be tightly bound in BFO, are sep-arated by the electric field at the domain walls. In thiscase the charge generated at the domain walls acts todepolarise the field in that region, whist the field in thebulk material remains. The imbalance of polarisation isresponsible for the above bandgap photovoltages.

The first model developed for BFO has subsequentlybeen disputed by other groups, who in a series of equallyelegant experiments highlighted the independence of pho-tovoltages on the domain wall density35. The prob-lem of understanding is due to the difficulty in separat-ing bulk photovoltaic and polarisation-dependent mech-anisms. Recent advances in the theory of polarisationmean that deciphering these contributions and interpret-ing experiments with the aid of first principles calcula-tions has become possible. Rappe and co-workers cal-culated the shift-current tensor for BFO25, revealing theanisotropy of the photo-induced currents. Due to distinctexperimental set-ups, the measurements in references32

and35 probe different orientations, which reconciles theinitial disagreement between the studies.

VI. HYBRID HALIDE PEROVSKITES

Hybrid halide perovskites have had a radical impact onsolar energy research in the past two years, motivated bythe highest power conversion efficiencies demonstratedfor a low-temperature solution-processed semiconduc-tor. Since their first reports as PV materials36, devices

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based on these materials have made enormous progress inmesoporous and thin-film configurations37–39,70–73. Therecent highest-efficiency device exceeds 20% light-to-electricity conversion.

Halide perovskites have the same structure as the ox-ide counterparts, with the oxygen anions replaced by ahalide. This change in the formal oxidation state of theanion means that to keep charge neutrality the oxida-tion state of the cations must sum to III (usually by thecombination of monovalent and divalent species).

For CH3NH3PbI3, the upper valence bands are com-posed of I 5p states50,74, which results in a higher en-ergy valence band (lower ionisation potential) than inthe oxide perovskites. The B cation has thus far gener-ally been Pb (with some reports of limited success withSn75), which results in large spin-orbit coupling, lower-ing the conduction band by a significant degree50,76. Thecombined effects of the higher valence band and lowerconduction band means that the optical bandgap of thehalide perovskites are significantly smaller than the ox-ide analogues77, allowing for efficient absorption of whitelight. At the same time, the rich chemistry and physicsassociated with the perovskite structure is maintained.

The distinction for hybrid perovskites is that the Asite cation is an organic molecule as opposed to an inor-ganic ion. This introduces a number of important extradegrees of freedom. The crystal symmetry is directly re-duced; even a cubic arrangement of the BX6 octahedracan result in a net polarisation. The large static electricdipole of the methyl-ammonium (CH3NH3 or MA) ion,used in MAPI is suggested as on contributing factor tocrystal polarisation and PV performance26. The orienta-tional dynamics of the MA have also been implicated aseffecting structural changes in the material78. By vary-ing the size of the organic molecule the bandgap can bemanipulated77. Larger cations cause the break-up of thestructure into 2D layers79–81, the 3D perovskite structureis stable only with a small subset of possible ion choices.

One unusual aspect of the device physics of halide per-ovskite solar cells is significant hysteresis in the photo-voltaic (J–V) response82. Two likely contributing fac-tors are ion diffusion and ferroelectricity. Indeed the firstdirect observation of ferroelectric domains in MAPbI3have just been reported83, and first-principles calcula-tions predict spontaneous electric polarisation similarin magnitude to inorganic perovskites26. A complicat-ing factor is the orientational disorder of the dipolarMA ion, which is sensitive to temperature and latticestrain. Monte Carlo simulations for CH3NH3PbI3 haveshown that a low temperature antiferroelectric structureof twinned dipoles becomes disordered at room temper-ature due to entropy; however, significant short-rangeorder is maintained. This behaviour is consistent withthe low-temperature orthorhombic ordered phase and thedisordered tetragonal and pseudo-cubic structures ob-served around room temperature. The shift-current forMAPI, computed from first-principles, suggests a BPE inthe visible range approximately three times larger than

FIG. 3: Left, view down the (001) direction of thegeneral V-VI-VII structure. Right, schematic of the

ferroelectric structural distortion. The centrosymmetricphase Pnam (upper), has no net polarisation. A shift of

the Sb sub-lattice results in a breaking of the crystalinversion, and a net macroscopic polarisation ∆P ,

Pna21 (lower).

oxide perovskites, and the effect is sensitive to molecularorientation84.

The channels of high and low electrostatic potential as-sociated with the correlation between MA ions may pro-vide efficient diffusion pathways for electrons and holes.The domain behaviour is highly sensitive to the pres-ence of an external electric field. The changes in the 3Delectrostatic potential landscape could be linked to dif-ferences in electron-hole recombination rates under short-circuit and open-circuit conditions, and thus give rise tothe observed hysteretic effect85.

VII. BEYOND PEROVSKITES: CHALCOHALIDES

For much of the early history of photoferroics thearchetypal material for the demonstration of photofer-roic effects was SbSI86–90. This material has two phaseslinked by a ferroelectric distortion. As demonstrated inFigure 3, a small displacement along the z-axis switchesbetween Pnam (centrosymmetric, D2h) and Pna21 (non-centrosymmetric, C2v) structures. The phase behaviourcan be linked to the s2 lone pair electrons associatedwith Sb(III). Similar to Pb(II) and Sn(II), the ion canexhibit a second-order Jahn-Teller instability associatedwith the change from a symmetric to asymmetric coor-dination environment91.

The ferroelectric transition, which results in one phasewith spontaneous polarisation, means that SbSI is anideal candidate material for exhibiting both bulk andpoly-crystalline photoferroic effects. In recent years, thismaterial has been largely overlooked as a potential earth-abundant solar absorber. By applying modern electronicstructure techniques we asses the utility of SbSI as anabsorber layer, and investigate the effects of anion sub-stitution on the electronic properties. SbSI exhibits anoptical band gap of ≈ 2 eV, the value can be tuned bythe choice of chalcogen and halide92.

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FIG. 4: Energy-momentum band structures of SbSI(upper panel), SbSBr, SbSeI (lower panel); all

calculated with GGA-DFT. Valence bands are colouredgold and valence bands are in green. The top of the

valence band is set to 0 eV.

For the calculation of the electronic structure proper-ties of SbSI we compare the results of scalar-relativisticgeneralised-gradient approximation density functionaltheory (GGA-DFT), hybrid-DFT (HSE06) and hybrid-DFT with spin-orbit coupling (HSE06-SOC). The shapeof the bands and the electron and hole effective masses(m∗

e and m∗h) are relatively insensitive to the level of

theory: m∗e=0.21, 0.21, 0.22 and m∗

h=0.27, 0.27,0.34 forGGA, hybrid and hybrid-SOC, respectively. For SbSBrthe electron effective mass from GGA (HSE06) is 0.26(0.23), and for SbSeI the value is 0.52 (0.45). The elec-tronic band gap from GGA (1.51 eV) is smaller thanfor hybrid-DFT (2.14 eV), the further inclusion of spin-orbit coupling reduces the hybrid-DFT value to 1.85 eV.For quantitative predictions of the band gaps, relativisticmany-body electronic structure theory (e.g. the QSGWmethod) would be required50. The electronic and opti-cal band gaps are likely to exhibit a strong temperaturedependence owing to the polar nature of the structuralphase transition.

A. Sb(S/Se)X: electronic band structure

The electronic band structures of SbSI, SbSBr and Sb-SeI are shown in Figure 4. All three are indirect bandgapmaterials and have experimentally reported band gaps of1.88 eV, 2.20 eV and 1.66 eV, respectively93. SbSI hasan indirect gap as the top of the valence band (VBM)lies close to the X point and the bottom of the conduc-tion band (CBM) is at the S point. It should be notedthat the difference between direct and indirect bandgapsis small (0.15 eV); most optical absorption will be direct,and so a thin-film architecture is possible.

Substitution of I by Br results in a change in the elec-tronic band structure. The VBM now occurs between Zand Γ and the CBM at Γ. Substitution of S by Se re-sults in another qualitative alteration of the band gap:the VBM is between gamma and Y in the first Brillouinzone, and the CBM is between Y and T. The value ofthe gap is 1.3 eV, close to optimal for solar radiationabsorption.

We explain this variation in the electronic structurethrough the chemical make-up of the bands. The up-per valence band in all cases is composed of chalcogenand halide p orbitals. The relative contribution from thechalcogen is increased in SbSeI: the lower ionisation po-tential of Se relative to S explains the band engineeringeffect, resulting in a gap narrowing. Subtle changes in thelocal environment of Sb are responsible for the change inband extrema, which can be associated with the compo-sitional dependence of the stereochemical activity of theSb 5s2 lone pair electrons. In contrast, the lower con-duction band is comprised of Sb 5p orbitals, which areaffected by spin-orbit coupling.

The sulpho-halide materials have a small enthalpy dif-ference between the ferroelectric and paraelectric phases(∆E in Table I), indicating that transitions between thetwo phases will be susceptible to the kinds of changes out-lined in Section 4.1. SbSeI has a larger enthalpy differ-ence, the lower energy ferroelectric phase will be ‘locked-in’. Berry phase analysis of the polarisation (∆P in Ta-ble I) indicates that although all three materials have asmaller ∆P than many oxide perovskite structures suchas BFO, they all nonetheless posses significant sponta-neous electric dipole moments.

TABLE I: Results of scalar-relativistic GGA-DFTcalculations. Band gap (Eg in eV), electron and hole

effective masses (m∗e, m∗

h), lattice parameters (a, b, c in

A), polarisation (∆P in µC/cm2) andferroelectric/paraelectric phase energy difference (∆E in

meV per f.u.).

Eg m∗e m∗

h a, b, c ∆P ∆ESbSI 1.51 0.21 0.27 8.5, 10.2, 4.0 11 59SbSBr 1.57 0.26 0.57 8.2, 9.8, 3.9 17 2SbSeI 1.29 0.52 0.24 8.3, 11.7, 4.1 10 376

9

FIG. 5: High-efficiency charge separation using aSbSI/SbSBr heterojunction. The band energies of the

materials are aligned in a type II offset. The bulkpolarisation is in the same direction, so the carriers,

which split at the interface, are swept in oppositedirections.

VIII. TOWARDS HIGH-EFFICIENCY SOLAR ENERGYCONVERSION

While the main recent focus for solar cells based on fer-roelectrics has been on metal oxides, with limited spectralresponse in the visible range, the consideration of polarchalcogenide and halide semiconductors opens up severalnew avenues for fundamental research.

Considering the case of the Sb chalcohalides, the ef-fective masses of the charge carriers in all of the mate-rials (Table I) suggest high mobility will be possible ingood quality crystals with low defect concentrations. Theclosely matched lattice parameters, and the systematicband offsets resulting from chemical substitution, meanthat these are ideal candidates for semiconductor hetero-junctions. For example, epitaxial growth of SbSBr onSbSI, with aligned polarisations. In this configurationthe combination of type II band offset (driven by thechemistry of the halide ions) and parallel electrical fieldscould be employed to design efficient charge separationstructures; sweeping carrier of opposite charge in oppo-site directions. Such a device is shown schematically inFigure 5.

There is a great opportunity for exploring similar ef-fects in other families of materials. For instance, a re-cent review of metal-organic ferroelectrics highlightedmany hybrid metal halide and metal formate compoundsthat exhibit ferroelectric transitions, with chemical andstructural similarities to the hybrid halide perovskitesystems94. Mixed anion inorganic compounds, includingoxychalcogenides, oxypnictides and chalcopnictides, are

of particular interest as the lower symmetry associatedwith the multi-component systems, coupled with polar-isation driven by the electronegativity differences of theconstituent anions, ensures that the materials will exhibitcomplex behaviour. A grand challenge is to identify ma-terials with properties similar to the hybrid perovskites (i.e. light absorption, conductivity, dynamic polarisa-tion, and ease of fabrication), but where Pb is replacedby a more sustainable element.

Another application of ferroelectric materials in PVis for tuning band offsets. The energy offset at junc-tions between materials is a major source of efficiencyloss in PV devices95,96, ideally there should be Ohmiccontact between materials27. Absolute electron energiesare known to be highly sensitive to external and internaldipoles97. Moreover, the relative positions of valence andconduction bands has previously been shown to dependon surface and interface dipoles98,99. Simple oxide layersand surface effects have been shown to affect electron en-ergies by as much as 1 eV100,101, this effect could be evenlarger from a thin film of a polar material, and wouldallow for the application of alternative, cheaper contact-ing materials in a range of PV architectures, for examplereplacing In2O3 for organic101 and CdTe102 devices andreplacing silver in silicon PV103.

In summary, the bulk properties of ferroelectric mate-rials are important for solar cells, in particular, influenc-ing electron-hole separation and band alignment. Beyondthese macroscopic effects, photoferroic processes can besignificantly enhanced at the nanoscale. Understandingand quantifying the interplay between charge carrier dis-tributions, ion transport, and polar structural domainswill provide a major challenge for scientists and engi-neers in this field. Furthermore, the interface betweenpolar domains can be as critical as the bulk polarisationitself: the field of domain wall engineering is growing,with many novel and unexpected optoelectronic proper-ties associated with extended defects. To paraphrase V.M. Fridkin, Let us hope that ferroelectric photovoltaicswill have a bright future for solar energy generation.

IX. ACKNOWLEDGEMENTS

The work has been funded by EPSRC GrantsEP/K016288/1, EP/M009580/1 and EP/J017361/1,with support from the Royal Society and ERC (Grant277757). We acknowledge membership of the UK’s HPCMaterials Chemistry Consortium, which is funded by EP-SRC grant EP/L000202.

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