Photochemistry on a polarisable semi-conductor: what do we understand today?

Ferroelectricity is a phenomenon in which a crystal exhibits two or more stable configurations in the absence of an electric field and can be shifted from one to another state by the application of electric field. The most studied and frequently applied ferroelectric materials are those with perovskite-type structures with general formula ABO₃, which A and B are cations such as Pb²⁺/Ba²⁺/Sr²⁺, Zr/Ti and O is oxygen anion O²⁻.

Piezoelectricity is a phenomenon in which a crystal can be polarised by the application of mechanical stress. Conversely when an electric field is applied across a piezoelectric crystal, it will change its dimensions to either expand or contract. Therefore, application of pressure to a piezoelectric crystal between two electrodes causes a charge to flow in one direction. The sign of piezoelectric charge or the direction of strain is the same as the direction of applied mechanical and electrical fields respectively.

The regions of a ferroelectric crystal with uniformly oriented polarisation are called ferroelectric domains and the plane separating two domains is called a domain wall. Unpoled ferroelectric materials tend to form multiple domains because a single domain crystal would produce an electric depolarising field. This is very unfavourable from an energetic point of view and to produce uni-polar ferroelectric materials energy must be supplied in the form of the process of poling. Thus, during synthesis, a ferroelectric crystal forms into separate domains so that the equilibrium energy level between the domain walls and the electrostatic self-energy of the crystal is achieved [38]. It can be said that the general ferroelectric domain structures in equilibrium is a result of minimising the overall deformation and the electrostatic energy;where W_M is the elastic energy, W_E is the electric energy, W_DW is the domain wall energy and W_S is the surface energy.

Those domains whose polarisation vector points in +z direction are ‘up’(c⁺) domains, domains whose polarisation vector points in −z direction are ‘down’(c⁻) domains and the domains in ±x or ±y direction, i.e. lies on the surface plane are lateral domains (a). The boundaries separating a–c domains are called 90° boundaries, and those separating c⁺–c⁻ domains are 180° boundaries (the name implies the angle between the polarisation vectors in adjacent domains). Figure 5 depicts various domains and domain boundaries. In the tetragonal structure crystal, both 180 and 90° domain walls can form in the crystal; however, the formation mechanism is slightly different. The formation of both 180 and 90° domain walls can minimise the depolarisation field by compensating for the surface charge in an unpoled ferroelectric ceramics, but only the formation of the 90° domain wall can release the elastic energy stored in the crystal. The motion and interaction of domain walls significantly affects the piezoelectric, mechanical and optical properties of the structure [39]. To be able to predict and control the domain wall kinetics, their physical and electrical properties need to be thoroughly understood and accurately determined.

In semiconducting ferroelectric thin films the coupling between polarisation and space charges leads to the formation of charge double layers at 90° domain walls, which are decorated by defects such as dopants, oxygen vacancies [40]. There is no such charge layer formation in 180° walls.

Over the years there have been extensive and exhaustive studies that have focused on the formation and static properties of domains in bulk crystalline ferroelectrics by polarising optical microscopy, etching and surface decoration [41, 42]. These methods have a disadvantage in that they have a low spatial resolution of the order of 1 μm. Under certain circumstances resolution below 10 nm can be achieved by SPM [27]. Domain related topographic features are characterised by contact and intermittent mode [43‐48] and electrostatic properties above the surface by electrostatic force microscopy [49, 50].

Traditionally ferroelectrics have been regarded as insulators following the Devonshire–Ginsburg–Landau theory [51]. The band gap of ferroelectric materials is large, e.g. for PZT type materials it is around 3.2–3.7 eV [52‐54], and for BaTiO₃ it is around 3.2 eV. Variations in the band gap, especially for PZT and other complex perovskite materials, arise due to variations in processing conditions and other external factors and as such there is yet to be a definitive E_g that is widely accepter for PZT. Under equilibrium situations the materials can be treated as insulators, however, under the influence of sufficiently high energy radiation the non-equilibrium that develops follows basic semi-conductor theory. Furthermore the large concentration of structural defects acting as doping centres, the presence of Schottky barriers at contacts, and large leakage currents are characteristic properties of a semiconducting material. Therefore these materials can also be considered, and treated, as wide band gap semiconductors [55]. A non-doped PZT film, i.e. as close as possible to stoichiometric composition is a p-type semiconductor according to defect chemistry. Indeed the chemistry of the PZT produces some interesting effects; due to the oxygen vacancy accumulation an oxygen deficient layer, which is about 30 nm thick, n-type conductivity arises in the region close to the surface, whereas bulk remains p-type [56]. According to Mihara et al. [57] the n-type layer appears during the crystallisation annealing of films at high temperatures in the range 500–700 °C because of the volatilisation of lead oxide from the film composition.

In ferroelectric materials the displacement of a body centred cation, e.g. in a cubic perovskite BaTiO₃ the displacement of Ti³⁺, gives rise to a dipole in the unit cell. The interactions between dipoles in unit cells cause polarisation alignment resulting in a polarisation bound charge at the surface of the block of ceramic. This polarisation charge affects surface topography, chemical reactivity, optical and electronic properties of ferroelectric surfaces and interfaces, and this is clearly demonstrated by phenomena such as ferroelectric electron emission [58, 59], polarisation dependent work function [60], metal photodeposition [32, 61].

On an oriented BaTiO₃ crystal, the atomic polarisation may be directed either perpendicular or parallel to the plane of the surface whereas on an unoriented BaTiO₃ crystal the atomic polarisation may be directed randomly. This atomic polarisation induces a surface charge σ which is:where σ is surface or polarisation charge, P is polarisation vector, n is unit vector normal to the surface. This induced surface charge may be compensated by free charge carriers and defects in the bulk (internal screening) and/or by the surface adsorption of charged molecules from the environment (external screening) [16] as shown in Fig. 6.

The first suggestion about the existence of surface layer was given by Kanzig [62] on the basis of experiments performed on BaTiO₃. It was observed that a strong electric field of 10⁴–10⁶ V/cm and a low dielectric constant could be observed in the volume of the surface layer. It was then shown that the surface layer is not a foreign film but is a surface region of the crystal in which dielectric saturation and piezoelectric compression occur because of strong electric field [63]. Through detailed investigation of properties and nature of the surface layer Treibwasser [64] modelled it as a Schottky barrier.

Further results have been completed to compare the electric potential, space charge density, defect density and polarisation in the surface layer to the bulk [40] of a ferroelectric material. It should be noted that there are expected significant differences in the behaviour of materials as they are reduced in thickness as the region of space layer approaches the thickness of the sample. In the case of PZT (30:70) samples approaching 50 nm in thickness will exhibit space charge characteristics almost throughout the sample thickness as the individual space charge layers at each interface are around 23 nm [65]. It is also interesting to note to that the stoichiometry of the sample can influence the space charge layer. However, this should not be counterintuitive as there is also a variation in the spontaneous polarisation as the stoichiometry changes. The measurements have been taken along the line AA′ in the BaTiO₃ slab (as shown in Figs. 7 and 8). A depletion layer of approximately 100 nm thickness is observed near the Pt electrodes, accompanied by a voltage increase of 1.4 V across the depletion layers [40]. The space charge density is at a maximum near the electrodes and is ≅0 in the bulk. The large electric field in the depletion layer drives the diffusion of defects including oxygen vacancies, especially during annealing at high temperatures where the thermal energy enables the efficient movement of defects and ions into low energy positions within the crystal lattice.

In a ferroelectric material the width of the space charge layer is dependent on the composition of elements that constitute the material [65]. When investigating a set of metal–Pb(Zr, Ti)O₃–metal samples with different Zr/Ti ratios (from 92/8 to 20/80) and variation in the width of surface layer δ along with other quantities like saturation polarisation P_s, static dielectric constant ε_st hole concentration p(T), apparent built-in potential V_bi′, effective space charge density in the depleted layer N_eff, potential barrier ϕ_B is observed. The evaluated values are shown in Table 1.

The quality of the ferroelectric film is an important factor which contributes to the thickness of the surface layer. As defect density has an impact on the photochemical properties [66] of the ferroelectric material that has been processed in different ways could be expected to show some differing photochemical effects. When a sample has been made by processes such as sol–gel [67] then a very different defect density and structure through out the thickness of the thin film exists compared to MBE grown material. The interaction between the density and nature of defects, in the material and the internal depolarisation field leads to the development of the space charge layer. The depth to which the space charge layer penetrates is determined by how many mobile carriers are available to screen the depolarisation field. Therefore a material with a large spontaneous polarisation and few defects will generate a wide space charge layer, increasing the defect density, and with that the number of available carriers, reduces the width of the space charge layer [68]. If the ferroelectric is processed using low temperature sol–gel type mechanisms then there are different defect structures compared to material that has been processed at higher temperatures using standard ceramic processing techniques.

When dealing with materials at the nanoscale there is an interest in how the dimensions affect the fundamental properties of the material. This is also true for a ferroelectric and there has been some detailed work investigating the impact of cross sectional thickness on various parameters. Of particular interest here is the impact on the depolarisation of the ferroelectric and the influence that reducing the thickness of the thin film has. In a short review Scott [69] discusses finite size effects. It is well known that the spontaneous polarisation it at a maximum at the surface of the ferroelectric and decays to zero towards the centre. A key question is what is the dimension required for the spontaneous polarisation to decay and do nanostructured ferroelectrics allow this?

The influence of size on a ferroelectric when treated as a semi-conductor, can be seen in Table 1. The surface layer can vary from 33 to 3 nm depending on the composition (these values are for various PZT compositions). It is routine to make ferroelectric samples that are 10–100 nm in the z-direction. This would mean that for many ferroelectric compositions there would be an interaction between the SCL at both interfaces, as a result of the depolarisation field decaying across the thickness of the film. As a thin film ferroelectric would normally be grown on a conducting substrate there will be pinning of the Fermi levels of electrode and ferroelectric. In essence there is likely to be a strong influence of the depolarisation field on the surface photochemistry in thin film ferroelectric systems.

The impact of an interface between a traditional semiconductor and solution or secondary phase has long since been established [70]. After the interface has come to equilibrium there has been a movement of free carriers that is the result of drift due to local concentration gradients. The band bending that is found in the semiconductor is a direct result of the drift of mobile carriers across the interface. There are, however, some fundamental differences when dealing with a material that has an internal field due to displacement of ions in the crystal lattice, in other words a ferroelectric material. These materials, while exhibiting n or p-type behaviour do not generate bent bands in the same way as a traditional semiconductor—the need to screen the spontaneous depolarisation is too high and so the band bending is determined by this need.

The internal screening caused by free charge carriers or defects in the bulk causes ‘band bending’ at the surface of the ferroelectric material [71]. On a surface with positive polarity, the positive polarisation charge is screened by free electrons, negatively ionised acceptors or defects in the bulk and/or adsorption of negative ions from the air (as shown in Fig. 9). Similarly on the surface with negative polarity the negative polarisation charge is screened by free holes, positively ionised donors, defects and/or adsorption of positive ions from the atmosphere. The intrinsic screening gives rise to an internal electric field which causes band bending in the near surface region, resulting in the formation of depletion and accumulation layers, as shown in Fig. 9.

It is generally true that for perovskites such as BaTiO₃ and PbTiO₃ as well as the more complex systems such as PbZr_xTi_(1−x)O₃ (PZT) that E_v is the top of the valence band and is associated with oxygen 2p orbitals and E_c is bottom of conduction band associated with titanium, or A/B 3d orbitals. E_f is the Fermi level and E^bb is the energy associated with band bending that is introduced either due to the field developed due to crystal distortion associated with ferroelectric behaviour or contact with. The density of states for the ferroelectric materials varies with the composition and also the processing parameters of the materials.

The electrostatic properties of the ferroelectric surface play a significant role in its behaviour under various conditions. As the polarisation charge is always screened when at equilibrium, and in any environment that is not high vacuum, through a variety of mechanisms a screening charge equivalent to surface charge density is present. This screening charge is of opposite polarity to the polarisation charge. In this section we will discuss the following cases that have been previously highlighted as applicable to the surface of a ferroelectric material [72];

A completely unscreened surface is a very unfavourable energy state. This state is unlikely to occur under ambient conditions and can be observed only in vacuum. This is due to the presence of water in all normal circumstances and the associated screening through interactions with the dipoles in the water and development of stable interface layers. There will also be a number of ionic constituents in water on the ferroelectric surface that are a result of partial dissolution of the ferroelectric or in the water itself. These components will interact with the surface of the ferroelectric to form a Helmholz layer to further screen the surface charge. Over-screened surfaces may occur and have been observed during bias induced domain switching [73] but are not likely in ambient conditions at equilibrium. The most likely state of ferroelectric surfaces, when in ambient environments such as in air and at equilibrium, is the partially or completely screened surface. This is due to the adsorption of water molecules and salts on them as described to refute the possibility of an unscreened surface. The charge distribution on this type of surface can be given in terms of the uncompensated charge component: Δσ = σ_pol − σ_s [72]. The results that have been obtained for potential and electric field measurements on unscreened and completely screened surfaces are shown in Fig. 10. The non-contact measurements have been performed with the tip surface separation set to between 10 and 100 nm. At this distance from the surface the electrostatic interaction of the material being investigated can be accurately measured and recorded. Therefore the impact of screening on the ferroelectric surface can be determined.

The sign and magnitude of surface potential on a ferroelectric surface are not only dependent on polarisation charges, but they depend on the intricate balance between the polarisation and screening charges. An extreme case could be surface polarisation reversal due to the sorption of highly polarised long chain hydrocarbons on the surface of a ferroelectric akin to the behaviour of detergent molecules in an oil and water mix. In the case of the ferroelectric the balance is due to the availability of carriers (from within the sample) and the variation in the space charge layer that forms. The exact shape and dimensions of the space charge layer depend on a number of factors that are material and in some cases sample specific. It has been shown that photo deposition of silver can occur on both positive and negative domains on PZT when it is [100] orientated, but that silver only deposits on PZT [111] when it is positively charged [74]. This is due to variations in the density of states and also in the variation in the remnant polarisation of the sample, which impacts the shape of the space charge layer and screening processes. It is clear from Fig. 10 that above the unscreened surface the surface potential varies linearly and reciprocally with domain size whereas the electric field is domain size independent. Above the completely screened surface the electric field varies linearly and reciprocally with domain size and the surface potential is domain size independent.

The surface potential measured by scanning surface potential microscopy [75] on a ferroelectric surface is smaller and of opposite sign than the polarisation charge [76].

The grain boundary (GB) is a region which separates crystallographically coherent areas in crystalline solids. GBs act as barriers for the charge transport of carriers in materials showing ionic/electronic conduction. The GB effect has been studied for a variety of n-type semiconducting ceramics [77, 78]. For n-type semiconducting ceramics negatively charged GB states are compensated by positively charged donor centres in the bulk close to the GB. This creates a depletion of the negatively charged mobile carriers in a layer of the width d_GB symmetrically surrounding all grain boundaries, and leads the formation of depletion layers. From the electronic point of view these depletion layers can be described as two Schottky diodes back to back. In perovskite type alkaline earth titanates a highly resistive GB layer has been observed [79‐81]. In acceptor, p-type, doped alkaline earth titanates the GB states are electrically active and are positively charged due to donor centres. These are compensated by negative space charged acceptor dopants from the bulk close to the GB. The positive charge in the GB creates a depletion region of mobile positively charged carriers, holes and oxygen vacancies. This depletion space charge layer can be considered as two back to back Schottky barriers. This model was introduced by Chiang and Tagaki [82].

With the core of the GB heavily positively charged, the outer region becomes depleted of electrons. This gives rise to a depletion region around the GB core and causes band bending at the GB as shown in Fig. 12. The depletion region has a space charge which is greatest at the core of the GB and reduces as it moves into the grains [83, 84]. The impact of grain boundaries on the semi-conducting nature of a ferroelectric have recently been studied by Jones and Dunn [85] using UV irradiation of PZT surfaces and the growth of Ag clusters through reduction of silver cations. The grain structure of highly heterogeneous PZT(30/70) was found to have a significant impact on the rate of growth of sliver clusters, see Fig. 11. During UV irradiation electron–hole pairs are generated in the film due to interactions with incoming photons. The combination of band bending and positive electric field present at the GB causes the electrons to migrate towards it as shown in Fig. 12. Due to this migration there is an increased availability of electrons for metal reduction at the grain boundaries than at the surface of the grain away from the boundaries. A table of the relative rates of deposition can be seen in Table 2.

Conduction in solids is dependent upon the mobilities and concentrations of both ionic defects (interstitial ions and vacancies) and electronic charge carriers (electrons and holes) through the bulk and along and across interfaces such as grain boundaries, electrode contacts and surfaces [86]. It has been shown by Maier [86] in 1993, that both conductive mechanisms: ionic and electronic, may be modelled using analogous methods and that both mechanisms, and their dependence on environmental parameters such as temperature and partial pressure, participate in the overall reactivity of many materials, including ferroelectrics.

Electronic conduction can be activated through the optical transition of electrons from valence to conduction band but, as quantised light particles. Incident photons must have energies exceeding that of the material’s band gap. This limiting factor is referred to as the fundamental absorption and in BaTiO₃ for example, only energies greater than the band gap (E_g) value of ~3.15 eV at room temperature [87] are productive, with each photon producing one electronic charge (q) at a voltage of:where h is Planck’s constant and v_g the band gap frequency. Therefore, the beneficial range of incident spectral wavelengths is limited by the value of the band gap.

Ionic conduction mechanisms rely on the transport of interstitial ions and vacancies which are also subject to a minimum energy requirement that is referred to as free activation energy. It has been shown by Franklin [88] that the enthalpies of vacancy formation in elemental solids are approximately proportional to their absolute melting points with results ranging from a fraction of one eV (e.g. Ar, Xe) to over 2 eV (Mo), whilst the free enthalpy change caused by the introduction of an oxygen defect is in the order of 1 eV, or 100 kJ mol⁻¹ [89].

Defect concentrations can be manipulated via thermal excitation or doping and the introduction of intermediate donor or acceptor impurity levels within the band gap can influence the level of energy required for electron and hole transitions across the gap [90]. These intermediate states can behave as non-radiative Schockley Hall Read (SHR) generation-recombination centres or Auger type traps.

While SHR generation-recombination enables electrons and holes to recombine and thus navigate the potential barrier to produce an additional current flow mechanism via thermal exchange, recombination at deep Auger trap sites is non-radiative and reduces carrier densities whilst trapping the energy within deep lying energy bands. However, Auger rates decrease exponentially with increasing bandgap values and become more or less inconsequential for bandgaps above ~1.5 eV [91]. It should also be noted however that heavy doping results in a narrowing of the bandgap.

In all photochemical reactions the kinetics of the process plays an important role. While the thermodynamics of the system may be favourable the rate at which the products are formed is determined by the complex interaction of the surface and near boundary layers. As has been discussed earlier this is very complex for a ferroelectric surface that is screened by counter ions as the inherent REDOX couple (e.g. reduction on a c⁺ surface) requires the participation of M⁺ species in solution. The development of a screening layer that is composed of species that are effectively of an opposite charge to those required for the reaction means that any REDOX chemistry must occur through either local tunnelling or a disruption of the local double layer interface [92]. What is interesting is that although there are a number of inhibiting features to the REDOX chemistry at the surface of a ferroelectric there is also a strong driving force—the internal dipole—that enables the reactions to proceed. It has been shown that reduction of highly charged cations with large negative reduction potentials can be achieved on ferroelectric surfaces, an example of which is the reduction of Al³⁺ to Al⁰ on LiNbO₃.

It is possible to describe the reactions occurring on the surface of the ferroelectric using classical interpretations of the kinetics at an interface. As demonstrated by Bard and Faulkner [93], for a classic metal electrode reaction:where k_f and k_b are the rate constants of the forward and backward reactions, respectively, n is the electron concentration and e the electron charge. At equilibrium, this system is characterised by the Nernst equation:where E ⁰′ is the formal potential (a calculated value for each half cell measured across the complete cell), F is Faraday’s charge on one mole of electrons, and \( C_{\text{O}}^{ * } \) and \( C_{\text{R}}^{ * } \) the bulk concentrations of oxidation and reduction species.

The overall current across a cell (i) under external bias is the sum of both forward cathodic (i_c) and backward anodic (i_a) currents and is dependant upon the surface area (A) and surface concentrations at distance from the surface 0 and time, t, i.e. C(0,t):In heterogeneous materials, such as metal-semiconductor junctions, this kinetic behaviour is influenced by interfacial potential differences as previously discussed, and influenced by the development of local double layer interactions. The dependence of the rate constants k_f and k_b on these influences can be expressed as: where f = F/RT, and k ⁰ and α are adjustable, phenomenological parameters evaluated by experiment called the intrinsic or standard rate constant, which is the value of k_f and k_b at E ^0′, and the transfer coefficient which is a measure of symmetry of the energy barrier:thus, for symmetrical intersections Φ = θ, and α = ½.

As previously mentioned however, most chemical processes occur over multiple steps. In cases where one of these steps is slower than the others, this step controls the overall process rate and as such is the rate-determining step, for example in perovskites, such as BaTiO₃, holes have particularly slow mobilities [94] and are less likely to tunnel through any barrier such as that presented by a double layer. In these situations the number of electrons effected by the rate-determining step (n_a) must be distinguishable from the overall number of electrons involved in the overall process of converting one mole of reactant (n), where n_a ≤ n:For non-equilibrium potentials, boundary resistance or overpotential (η) is produced by polarisation (non-spontaneous) and mass transfer pseudoresistances:where R_ct is the charge transfer resistance and R_mt,c and R_mt,a the mass transfer resistance for anodic and cathodic ions, respectively.

The reaction rate (v) at an electrode surface is proportional to the faradaic current:Thus, surface reactivity tends to be determined via current–voltage (I–V), capacitance–voltage (C–V), or photoresponse–wavelength (I–λ) characteristics. This result shows why in the case of a poled ferroelectric material it is possible for the ferroelectric dipole to influence the surface photochemistry. The local field in the ferroelectric can influence (either beneficially or adversely depending on the dipole) the photocurrent that is generated.

For surface electrochemistry to take place the standard reaction potential (U ⁰), corresponding to the sum of the energy requirements for the transfer of the participating defect species, must be exceeded to accommodate the fugacities of the products and the overvoltages of the electrodes. For semiconducting electrodes, the Fermi level of the electrode corresponds to its surface potential. Thus, the flat-band potential (U_fb) of the electrode, which is itself sensitive to the pH of the electrolyte at an approximate rate of 0.059 V per pH unit [95], and to absorption of certain solutes [96, 97] must exceed the required reaction potential and will define the ‘activation’ or ‘switch on’ potential of the reaction.

For example, as Fushima and Honda [13] in 1972 first demonstrated, the decomposition of water requires a potential increase of 1.23 V at the anodic surface to manifest oxidation (O), corresponding to the transfer of two electrons from oxygen to hydrogen. If the reaction were carried out in a single absorption step, for a typical metal-semiconductor electrode this reaction can be calculated to require photons with energies exceeding ~1.48 eV. However, as Tomkiewicz and Fay [98], in 1979 note, although 60% of solar radiation meets this criterion, water is not transparent in the extreme spectral regions and so an additional agent, or sensitiser, is used as a reaction intermediary, absorbing solar energy and delivering it to the water creating a stepped reaction, see Fig. 13.

In general therefore, photolysis may be optimised via manipulation of both the chemical and electrical electrode surface potentials.

In a typical cell configuration, using an n-type photoanode and a p-type photocathode, overall cell efficiency is limited by the least efficient electrode. Under short circuit operation, such as would be the case in a ‘wireless’ cell, the overall energy requirements may be summarised: where V_Bp and V_Bn are the band bending voltages at the p and n semiconductors, respectively, x is the required reaction potential and the inequality expressed in Eq. 16 equals the sum of the overvoltages at the two interfaces.

It is well know that for a standard semiconductor the photovoltage cannot exceed the band gap of the semiconductor. In practice several features combine to mean that the photovoltage is lower than the band gap of the semi-conductor, these include parasitic losses, and losses associated with local defects in the semi-conductor. The only exception has been semiconductor heterostructures that have been textured to give a series of p–n junctions which break this fundamental rule. One group of materials that break this rule when treated homogeneously are ferroelectric materials. Anomalously high photovoltages (APV) have been reported from ferroelectric Rochelle salt crystal as early as 1939 by Brady and Moore [99]. It has been shown that APV’s in the order of 40 V can be obtained from BaTiO₃ [100] under ideal circumstances which far exceed the band gap of 3.2 eV. The source of the APV comes from an interaction of phase transition, internal dipole and interaction with the incoming radiation.

Later, whilst researching barium titanate and lithium niobate, respectively, both Chynoweth [101] in 1955 and Chen [102] in 1967 recorded weak but steady, underlying photocurrents in each ferroelectric crystal when under illumination with no external bias and heated through temperatures rising from below, to well above, their individual Curie temperatures. Open circuit voltages were eventually measured in single domain barium titanate crystal [103] and found to be fractional relative to the ~3.15 eV band gap [104]. Similarly less than band gap photovoltages were also observed in unpoled ceramic barium titanate [105]. These photovoltages were linked to the presence of potential variations within the crystal, supporting Kanzig’s [62] in 1955 proposal that there exists temperature independent, space charge or barrier layers at crystal surfaces induced by extrinsic ionic conduction at impurity concentrations nearing 10¹⁸ cm⁻³. According to Kanzig, in ferroelectric crystals fields of 10⁵ or 10⁶ V cm⁻³ are enough to generate saturation polarisation within this surface layer, creating a potential difference of approximately 1 V between surface and bulk, and the resulting piezoelectric strain is structurally inelastic, prevailing despite bulk phase changes resulting from above Curie temperatures.

In contrast, Glass et al. [106] reported high photovoltages in doped single crystal LiNbO₃ and Brody later reported greater than band gap photovoltages of several hundred volts per centimetre in poled ceramic BaTiO₃ + 5 wt% CaTiO₃, Pb(Zr_0.65, Ti_0.35)O₃ and other ferroelectric ceramics [107‐109] which were shown to be linearly proportional to both the sample length and the remnant polarisation and were observed only below the Curie temperature. Ionue et al. [110] recorded photovoltages three times larger than the bandgap for Lead Strontium Zirconate Titanate with directed polarisation fields in opposite directions to the photocurrent.

A mechanism, based on similar behaviour observed in semiconductor materials such as thin polycrystalline semiconductor films of Cadmium telluride [111] and striated zinc sulphide crystals [112], where the potential differences across individual crystallites, having the same origins as single crystal surface barrier layers, create multiple smaller than band gap voltages that add up in series across the whole was proposed, in 1975, by Brody and Crowne [89] with the total voltage written as:where P_s is the spontaneous polarisation, S is the length of the space charge region, N₀ is the number of crystal grains, ε_s is the dielectric constant of the space charge region, ε_b is the dielectric constant of the bulk and L is the particle size.

Following Fujishima and Honda’s demonstration that TiO₂ could be used as a photocatalyst without itself decomposing [13], others went on to demonstrate similar reactive stability in further metal oxide electrodes such as SnO₂ [113] and WO₃ [114], until in 1975 Mavroides et al. [115], closely followed in 1976 by Wrighton et al. [116] reported small currents resulting in H₂ evolution at SrTiO₃ electrodes under zero applied voltage in basic electrolytes. In the same year Nasby and Quinn [14] and a Japanese team, Okuda et al. [117] went on to compare the behaviour of single crystal and ceramic BaTiO₃ and SrTiO₃ electrodes, respectively, reporting similarly repeatable and stable current–voltage characteristics with both single crystal and ceramic electrodes producing small photoinduced currents under short circuit conditions. Both teams reported that SrTiO₃ was more photosensitive than BaTiO₃. Nasby and Quinn [14] also noted that their results demonstrated “the blocking character of depletion layer formation indicated by negligible dark current with anodic polarisation”, and that increasing the pH of the electrolyte increased the turn-on voltage under illumination, dopant concentrations and flat-band potential indicating the applicability of the Mott-Schottky relation:By 1985 Inoue et al. were experimenting with ferroelectric substrates such as LiNbO₃ [118], PZT and BaTiO₃ [119] beneath Pt/TiO₂ thin films producing semiconductor–metal–ferroelectric junctions attempting to combine the reactivity of TiO₂ with the spatial separation of charge carriers provided by the ferroelectric substrate. They showed that film conductivity increased to a maximum at thicknesses of 50–100 nm while any influence of the underlying perpendicularly poled ferroelectric substrate vanished for film thicknesses above 200 nm. For film thicknesses of <50 nm the semiconductor carrier densities are too low to be affected by the polarisation field. Polarisation-direction dependence, with positively polarised surfaces facilitating photoexcited semiconductor electron transport towards chemically active sites on the Pt metal and negatively polarised substrates opposing this outcome and therefore producing negligible photoconductivity, was directly attributed to the presence of anomalous photovoltaic effects. The influence of poled ferroelectric substrates was shown to disappear as a result of phase transition above their Curie temperatures [35]. In 2002 Kalinin et al. [1] carried out research that supported the significance of semiconductor properties in the ferroelectric BaTiO₃ during the photodeposition of metals.

Hanson et al. [66] published work showing that the local reactivity on ferroelectric surfaces depends on relative densities of polarisation charges, adsorbed charges and surface states as well as the polarisation itself. Photochemical reduction of silver ions on the surface of a domain-patterned LiNbO₃ template resulted in silver decoration of 180° domain walls rather than of positive domains as would be expected. This effect was explained by Hanson et al. as a combination of inhomogeneous distribution of the electric field in the vicinity of the domain wall and low conductivity of the template material. Dunn et al. [35] have proposed that extreme band bending due to a build up of charge at the surface, can bring the flat-band region close enough to the surface to allow carriers to tunnel through the space charge region and thus reach active reaction sites.

Indeed the interest in ferroelectric photochemistry is now moving away from perovskite materials such as BaTiO₃ and PZT and growing to cover a wider spectrum of ferroelectric materials. New areas of study include polymeric ferroelectric systems such as poly(vinylidene fluoride) [120] and more widely LiNbO₃. What is particularly interesting in the case of LiNbO₃ is the variation in the details about the published results. When the work relating to perovskite materials is reviewed there are no publications that demonstrate homogenous wire like structures that are being formed on the ferroelectric surface. In all cases the material that formed on the surface has done so from discrete nucleation sites. The reasons for this are that in materials such as PZT and BaTiO₃ the spontaneous polarisation is among the largest for ferroelectric materials.

Certainly when compared to materials such as LiNbO₃ there are significant, an order of magnitude or greater, differences in the spontaneous polarisation. So what does this mean? In essence for the materials with a large spontaneous polarisation the inner Helmholtz layer is extremely tightly bound to the surface. This means that in order for local REDOX chemistry to occur there must be a local disruption, as noted earlier, in this layer. Therefore it is on regions of defect that the initial nucleation takes place [92]. For a material, such as LiNbO₃, the inner layer is not as tightly bound as the spontaneous field is lower. This then means that it is possible for there to be a more homogeneous nucleation of growing material on the surface of the ferroelectric. There is likely to be more solvated ions (cations for reduction over a positive domain) close to the surface than in the case of a strongly bound layer. The early discussion over the use of LiNbO₃ showed a variety of growth mechanisms which when considered in the light of spontaneous polarisation and power of incident radiation can be found to be mutually supportive [66, 121‐123]. A further anomaly of LiNbO₃ is the low electron affinity found for LiNbO₃, as shown in Fig. 14. This means that when high energy photons are used to irradiate the surface it is possible the produce electrons from both the c⁺ and c⁻ domain surfaces. The low spontaneous polarisation and low electron affinity combine to make some extremely effects on the material.