Nanoscale excitonic photovoltaic mechanism in ferroelectric BiFeO 3 thin films

We report an electrode-free photovoltaic experiment in epitaxial BiFeO3 thin films where the picosecond optical absorption arising from carrier dynamics and piezoelectric lattice distortion due to the photovoltaic field are correlated at nanoscale. The data strongly suggest that the photovoltaic effect in phase-pure BiFeO3 originates from diffusion of charge-neutral excitons and their subsequent dissociation localized at sample interfaces. This is in stark contrast to the belief that carrier separation is uniform within the sample due to the lack of center of symmetry in BiFeO3. This finding is important for formulating strategies in designing practical photovoltaic ferroelectric devices.We report an electrode-free photovoltaic experiment in epitaxial BiFeO3 thin films where the picosecond optical absorption arising from carrier dynamics and piezoelectric lattice distortion due to the photovoltaic field are correlated at nanoscale. The data strongly suggest that the photovoltaic effect in phase-pure BiFeO3 originates from diffusion of charge-neutral excitons and their subsequent dissociation localized at sample interfaces. This is in stark contrast to the belief that carrier separation is uniform within the sample due to the lack of center of symmetry in BiFeO3. This finding is important for formulating strategies in designing practical photovoltaic ferroelectric devices.

distortion is measured using the time-resolved X-ray diffraction (TRXRD) technique under ambient conditions at beam line 7ID-C of the Advanced Photon Source.Optical excitation was provided by 400 nm, 50 fs laser pulses synchronized to the X-ray pulses with an adjustable time delay.Incident X-ray pulses with photon energies of 10 or 12 keV and pulse duration of 100 ps were used.The highest pump laser fluence was 5 mJ/cm 2 .
We employ phase-pure epitaxial (0 0 1)-oriented bismuth ferrite (BFO) thin films of 4, 20, and 35 nm grown on SrTiO 3 (STO) and 35 nm grown on (LaAlO 3 ) 0.3 (Sr 2 AlTaO 3 ) 0.7 (LSAT) substrates by reactive molecular-beam epitaxy. 23The phase purity and high epitaxy quality of the samples were verified by the X-ray reciprocal space mapping where the 4 nm film is tetragonal and the thicker films are monoclinic. 24All samples have a single domain in the sample normal direction with an in-plane domain size of 400, 40, and 40 nm for the 4, 20, and 35 nm thick samples, respectively.The pump photon energy is below the bandgaps of STO (3.2 eV) and LSAT (5 eV), thus the photo response of the substrates is negligible.For the 35-nm samples, the one grown on LSAT was used for optical measurements and the one grown on STO for the x-ray measurements.We measured no difference in the dynamics between samples with different substrates.Experimentally, piezoelectric effects are reported for BFO films below 6 nm at 8 pm/V and drop to zero at 3 nm. 25Therefore, it is reasonable to assume all our samples are ferroelectric.
The generation and subsequent transport of charge carriers form an optical absorption band in a BFO following the excitation by photons with an energy larger than the direct bandgap at 2.6-2.7 eV. 23The absorption spectrum spans from 1.7 to 2.5 eV, peaked at about 2.3 eV.The spectrum varies as a function of the sample thickness due to the different strain status in these films. 22The relaxation of the photo-induced absorption band over time has a stretched exponential decay [Figs.The decay of the absorption is due to carrier removal from the system through recombination or dissociation.The lifetime of the carrier can be expressed as 1/τ OD = 1/τ B + 1/τ s , where τ B and τ S are due to the recombination/dissociation in the bulk and at the sample surfaces, 26 where we have τ S = Z/s + ( Z π ) 2 /D, with Z as the sample thickness, s as the surface quenching velocity, and D as the diffusion coefficient, respectively.Clearly, a strong thickness dependence indicates that τ B τ S and within our resolution, τ OD = τ S , i.e., carrier quenching is dominated by surface/interface effects.Further analysis shows that τ OD is quadratically dependent on the film thickness [see Fig. 2(a)], indicating quenching is much faster than diffusion in these samples.Thus, the carrier dynamics is dominated by their diffusion.This largely rules out the possibility that the carriers are locally trapped entities as previously speculated. 22tretched exponential decay is associated with a diffusion system with traps (in our case, self-trapping), which can be described by a diffusion model using a time-dependent diffusion constant. 27The one-dimensional diffusion equation, widely applied in describing the carrier dynamics in excitonic photovoltaic devices, 28 can be written as Here N is the carrier density, and D(t) = Dt −γ is the diffusion coefficient with 1 > γ > 0, where γ is a measure of the trap energy distribution. 27The initial and boundary conditions are In these equations, L is the optical absorption length, 14 z = 0 is the interface between the film and air, z = Z is at the film/substrate interface, and s is the surface quenching velocity.The equation can be solved by adjusting D and γ while fitting to the measured OD time dependence so that OD(t) ∝ ∫ N(z, t)dz.As shown in Fig. 2 Correlated to the TAS results, a thickness dependence of the film structural distortion was also observed in the TRXRD measurement, shown in Fig. 2(a) for the shift of the (0 0 2) BFO diffraction peak, or the average strain.Note that the strain has a longer relaxation time because heating also contributes to the expansion of the lattice with a much longer time scale. 16The diffraction peak after the laser excitation shifts to lower diffraction angle indicating the expansion of the lattice [Fig.3(a)].The thickness dependence is consistent with the TAS data.As discuss earlier, it also rules out any localized, non-diffusive effect as the dominant origin of the lattice distortion as previously speculated. 18,29o reveal the structure distortion mechanism, we performed a measurement of the time-dependent strain profile, i.e., the depth-dependent lattice distortion.This is accomplished by measuring the diffraction intensity distribution along a large range of reciprocal space [Fig.3(a)], which is the convolution of the phase distribution of the reflected X-ray along the film depth due to the distortion of the individual unit cell layer. 30,31The strain profile is first retrieved using the Gerchberg-Saxton algorithm, followed by a six-point spline algorithm fitting the phase and the layer-by-layer occupancy of the BFO unit cell. 30,31The fitting to the data, as shown in Fig. 3(b) for the 35 nm film, provides an excellent agreement to the measured diffraction intensity distribution and a detailed strain profile, a significant improvement over the results published previously. 17It shows that the depth-dependent strain profile as a function of time after the photoexcitation [Fig.3(c)] is linearly dependent on the strain profile before the photo excitation Here ε 0 (z) is the strain profile before the laser excitation.Both β(t) and α(t) are correlated to the shift of the diffraction peak.
After excluding other candidate effects, 17 the time-dependent strain profile is consistent with a piezoelectric response of the film to a spatially homogeneous but time-dependent electric field across the film depth, i.e., the screening field.This can be shown by rewriting Eq. ( 4) as follows: where d 33 (z) ∝ ε 0 (z) is the piezoelectric coefficient, ε th (t) ∝ β(t) is a homogeneous strain over the sample that can be attributed to heating, 16 and E(t) ∝ α(t) is a spatially homogenous screening field due to free carriers accumulated (destroyed) at the interfaces from the dissociated laser generated excitons.Note that though d 33 is commonly used as a constant, it is both a function of the external electric field in lead zirconate titanate (PZT) 32,33 and the strain in the BFO, as analyzed before. 17,34he spatial uniformity of the screening field E(t) across the film implies that the film behaves like a planar capacitor, indicating that there is no significant presence of free carriers in the bulk of the film, i.e., photocarriers remain charge neutral entities before their arrival at the interfaces.These carriers dissociate at the interfaces, and electron and holes are separated by the polarization field to and fitted (black thin lines) strain profiles using Eq. ( 4) at different delays, in comparison with that before the optic excitation (dotted line).The lower strain side is determined to be the air/film interface based on the relaxation of epitaxial strain.The fitting overlaps with the data within the thickness of the line in (b) and (c).RLU: reciprocal lattice unit referencing to the STO substrate.Note that we added 4 monolayers (∼1.6 nm) at the air/substrate interfaces to accommodate the roughness (partial occupancy), where the retrieved strain may contain larger uncertainties.form the screening field, a completely different scenario from the BPE.To confirm this, we simulate the piezoelectric response of the film due to BPE using a self-consistent one-dimensional particle-incell model 35 for the 35 nm film.Equal number of holes and electrons is generated, filling the space following the laser deposition profile p(z) ∝ exp(−z/L).To simulate the internal polarization field, a hypothetic constant bias field E 0 = 1 MV/cm (screened by the surface charges, the remaining field can be much smaller) is applied to generate a peak strain of 0.5% that is comparable to the data (for a d 33 = 50 pm/V with a dielectric constant of 50 14 ).We use nominal mobility for the electrons and holes of 7 × 10 −5 and 5 × 10 −5 m 2 V −1 s −1 , respectively.The carriers are absorbed when they reach the boundaries.Figure 4 is a case with a carrier density of 1.5 × 10 18 cm −3 (absorption fluence of 0.005 mJ/cm 2 ) where the bulk charge separation causes ±50% modulation of the field inside the film.The resulting strain profile, and thus the diffraction intensity distribution, is however completely different from the experimental observation [Figs.mechanism in our experiment.Note that this model is not intended to describe the BFO material.The case for Dember field 36 is not applicable because the polarization field would drive electrons and holes, if present in the bulk, to opposite directions.
The difference of nanoscale piezoelectric response between the bulk and interface charge separation effects is transient and thus can only be revealed via a time-resolved measurement with nanoscale spatial resolution.The difference disappears once a steady current is established, and electrons and holes mix homogeneously in the film.
One plausible structure of the charge-neutral carrier can be inferred from the spectral feature at 1.8-2.4eV in Fig. 1.This spectral structure has been identified as the electronic origin of the photostriction effect in the thin film BFO 16 and more recently the origin of photovoltaic effect in BFO single crystals. 37It has been interpreted as a characteristic of a self-trapped charge transfer (CT) exciton with a hole in the O-2p orbitals and an extra electron in the Fe-3d orbitals. 38Such a self-trapped CT exciton in oxides has been discussed as an inherent material property 38,39 of which the hopping is facilitated by the lattice distortion.The dissociation of the exciton at the interfaces can be due to local band bending, 40 band line up, 41 defects, 42 or pre-existing free carriers.Such localized exciton dissociation is consistent with the well-documented domain wall and interface effects, [9][10][11][12] but the details remain to be understood.Note that due to the charge neutrality of CT excitons, the diffusion dynamics is not dependent on the sample polarization.The piezo effect due to the screening of the depolarization field by dissociated carrier always enhances the polarization field and is not dependent on the poling of the film either.Some of the surface quenching processes may be dependent on the polarization, but our present technique is not capable of resolving such dependence.
For bulk samples, the exciton mechanism is not directly observable due to the limited exciton diffusion length.However, even in a macroscopic sample, excitons need not traverse the whole sample to generate free carriers-they only need to diffuse far enough to reach entities such as grain boundaries, defects, or electrodes to generate free carriers which in turn can be separated by the internal polarization field.This would lead to the appearance as if the bulk contributed to the photovoltaic effect homogeneously.Physical pictures of a bulk effect based on such micro/nano processes have been proposed before 1,11,13,43 but lack the evidence of corresponding carrier and photovoltaic field dynamics.The role of the interplay between the excitons and the light field in generating the shift current remains to be understood.
Note that our samples have no electrodes, preventing us from performing some of the standard photovoltaic measurements.However, it is worth mentioning that the strain dynamics in our experiments serve as a location-sensitive nanoscale field sensor.This allows the corroboration of the field distribution with the carrier dynamics on a picosecond time scale with nanometer resolution, which cannot be achieved in a conventional photovoltaic measurement of the photovoltage or current.The nanoscale excitonic mechanism opens a new perspective for understanding the photovoltaic effect in ferroelectric materials and may lead to very different design strategies for practical devices.
FIG. 1. TAS of the photo-induced optical density as a function of absorption photon energy and time.Note the different time scale in the (a)-(c).The nominal fluence used are 5.5, 5.5, and 4.7 mJ/cm 2 for the 4, 20 and 35 nm films.
(b), the observed OD dynamics is closely reproduced by the fitting.The spatiotemporal carrier diffusion maps are shown in Figs.2(c)-2(f).

FIG. 3 .
FIG. 3. (a) Diffraction intensity as a function of delay along the truncation rod around the (0 0 2) diffraction peak for a 35 nm BFO thin film, interpolated from measurement at time ∆t = −0.3,0, 1, 2, 4, 6, and 10 ns.(b) Measured (red thick lines) and fitted (black thin lines) diffraction amplitude |A| at different delays.(c) Corresponding retrieved (red thick lines)and fitted (black thin lines) strain profiles using Eq.(4) at different delays, in comparison with that before the optic excitation (dotted line).The lower strain side is determined to be the air/film interface based on the relaxation of epitaxial strain.The fitting overlaps with the data within the thickness of the line in (b) and (c).RLU: reciprocal lattice unit referencing to the STO substrate.Note that we added 4 monolayers (∼1.6 nm) at the air/substrate interfaces to accommodate the roughness (partial occupancy), where the retrieved strain may contain larger uncertainties.
FIG. 4. Comparison of strain effects in a 35 nm film due to BPE with experiment data.(a) Position-velocity diagram of the holes (positive speed) and electrons (negative speed) at different times (indicated in the legend in nanoseconds) after the impulsive excitation; (b) the corresponding fields due to charge separation by the internal field of E 0 = 1 MV/cm; and (c) simulated (0 0 2) diffraction pattern (blue) due to the lattice response to the field in (b) in comparison with the experiment (red line) and the retrieval (black thin line) data.