Short-circuit photocurrent due to bulk photovoltaic effect displays an oscillatory dependence on the polarization state of light. Here, we explore how the ferroelectric polarization direction in h-LuMnO3 crystals affects the oscillating short-circuit photocurrent. It is shown that after prepoling the crystal at saturation, at remanence, the direction and amplitude of photocurrent oscillations are no longer dictated by prepoling voltage but are largely modulated by polarization back-switching, here ruled by the imprint field. Thus, the light polarization dependence of photocurrent is also ruled by the imprint field. The impact of these effects on the determination of the Glass coefficients of the material is discussed.

Bulk photovoltaic effect (BPE) occurs in non-centrosymmetric materials.1–4 In recent years, interest on BPE has been renewed mainly because the open circuit voltage is not limited by the bandgap of the absorber, but can be orders of magnitude larger.5 BPE is governed by optically induced excitations between ground and excited states, most commonly assumed to be the valence and conduction bands, although the contribution of in-gap states to BPE has been reported.6 The BPE photocurrent under illumination of a linearly polarized light is given by JBPE,iGijkejek, where JBPE,i denotes the BPE photocurrent density measured along the i direction and ej,k are the light polarization components along the j and k directions.7 The symmetry of the Glass tensor {Gijk} collects the point symmetry of the studied material,8 and the values of its elements which depend on photon energy, are dictated by specific features of the electronic band structure.9 As a result, there is a genuine dependence of short circuit current density (Jsc) on polarization of the incoming photons.

Determination of the Gijk elements involves measuring Jsc along different directions (i,j,k) when the sample is illuminated with light of a given wavelength (λ) at different incidence angles (θ) with respect to the normal to sample surface and different polarization angles (φ). Typically, oscillating Jsc(θ,φ) behavior is observed, whose details depend on the symmetry-related structure, illumination configuration, and the values of the Gijk elements.

When measuring Jsc in ferroelectric materials, several contributions may exist and be entangled. Other than JBPE, drift photocurrent (JE) arising from internal fields of various sources [i.e., Schottky (Ebi), depoling (Edep), imprint (Eim), etc.] and a diffusion term (JD) associated with photoinduced charge gradients may coexist and contribute to the measured Jsc.10,11 Discerning these different contributions to Jsc (=JBPE + JE + JD), particularly JBPE and JE, requires knowing the ferroelectric polarization P state when Jsc is measured.12 This seemingly simple requirement, in practice, could be difficult to achieve. Indeed, the presence of Edep and Eim may hinder, keeping the polarization at saturated state,13,14 and at remanence, when Jsc is measured, polarization back-switching may have occurred leading to a ferroelectric multidomain state or even reversing the overall polarization.15 As reversing the ferroelectric P is equivalent to a spatial inversion, JBPE should change its sign with equal magnitude because the {Gijk} tensor is odd (see details in the supplementary material, S1).8,16,17 Similarly, JE can be changed upon reversing P as the depoling field/Schottky barriers are modulated.18,19 Therefore, the amplitude of the observed JBPE oscillations may not be as expected for a fully polarized sample. Moreover, in general, at oblique incidence, the intensity of light transmitted and reflected at any interface should also depend on the polarization state (π or σ) of the incoming light (Fresnel coefficients), thus producing a modulation of Jsc20,21 irrespectively of the origin of the photocurrent.

Here, we address this issue by measuring Jsc in uniaxial ferroelectric single crystals. Hexagonal h-LuMnO3 is a room-temperature narrow-gap ferroelectric,22,23 where the polarization axis is along the hexagonal c-axis, either pointing up or down. It will be shown that the Jsc magnitude and its dependence on light polarization Jsc(φ) are largely affected by the back-switching effect. More precisely, imprint governs the back-switching as evidenced by polarization retention measurements, performed on crystals displaying opposite imprint directions, which translates into the amplitude of Jsc(φ). Consequently, the quantitative extraction of the Glass coefficients can be severely hampered.

We report data on two single crystals (I and II) of h-LuMnO3 (LMO) around 100 μm thick with its hexagonal c-axis along the perpendicular to the largest surface. Crystals I and II were selected to display opposite imprint direction (see below). Pt contacts were deposited on top of the crystals (Pttop, 7 nm thick, with transparency at 405 nm around 50%) forming capacitor structures labeled as En (n = 1, 2, 3, …).24 The bottom side of the crystals was fully covered by continuous Pt contact (Ptbot, 7 nm thick). Details on experiments are included in the supplementary material, S2.

Figure 1(a) depicts the I(V) curves recorded on illustrative capacitors (E1, E2, and E3) on crystal-I. Data show obvious current peaks indicating polarization switching at coercive voltages (Vc+ and Vc). The polarization P(V) loops are shown in Fig. 1(b). The saturation polarization is about 9 μC/cm2, which is somewhat larger than typically found in hexagonal manganites.18,25,26 Of interest here is that the IV loops clearly reflect an imprint field (loops are shifted toward negative voltages), which indicates the presence of an internal field pointing downward [Fig. 1(c)]. From Fig. 1(b), we obtain Eim [= (Vc+ + Vc)/2)] of −2.22 V, −3.21 V, and −4.26 V for E1, E2, and E3, respectively. It is worth noticing that the loops in Figs. 1(a) and 1(b) have been collected at 1 kHz without delay time.

FIG. 1.

(a) IV curves and (b) corresponding polarization P(V) loops collected using the Dielectric Leakage Current Compensation (DLCC) mode at 1 kHz, in capacitors E1,2,3 (crystal-I). (c) Sketch of the Pt/LMO/Pt sample, the illumination geometry, and the direction of the imprint field. (d) Dependence of the Jsc on the light polarization angle φ and on the sign of the prepoling voltage V+/− (crystal-I). (e) Data from (d) vertically shifted to emphasize the dependence of the amplitude of oscillations on V+/−. (f) Jsc measured after V+, in capacitors E1,2,3 (crystal-I). In (d)–(f), solid lines are fits using Eq. (1) to experimental data (symbols).

FIG. 1.

(a) IV curves and (b) corresponding polarization P(V) loops collected using the Dielectric Leakage Current Compensation (DLCC) mode at 1 kHz, in capacitors E1,2,3 (crystal-I). (c) Sketch of the Pt/LMO/Pt sample, the illumination geometry, and the direction of the imprint field. (d) Dependence of the Jsc on the light polarization angle φ and on the sign of the prepoling voltage V+/− (crystal-I). (e) Data from (d) vertically shifted to emphasize the dependence of the amplitude of oscillations on V+/−. (f) Jsc measured after V+, in capacitors E1,2,3 (crystal-I). In (d)–(f), solid lines are fits using Eq. (1) to experimental data (symbols).

Close modal

The short-circuit photocurrent along the hexagonal axis is monitored while rotating the light polarization angle φ, with an incidence angle of θ ≈ 45° [Fig. 1(c)]. Data corresponding to electrode E1 [Fig. 1(d)] have been collected after prepoling the sample with V+/− = ± 60 V. We first note in Fig. 1(d) the characteristic oscillations of Jsc(φ) that are typically but disputably taken as fingerprints of BPE. Data can be fitted using the following equation, as predicted by the BPE theory:8,27,28

Jsc(φ)=Azcos2(φ+φ0)+Bz,
(1)

where the subindex z signals that photocurrent is measured along z-axis (out of plane), and φ0 (≤ 5°) is a phase shift related to experimental uncertainties. Data in Fig. 1(d) also evidence a dependence of background current [Bz(V+) > Bz(V)] and of amplitude (Az) of the Jsc(φ) oscillations on the sign of the voltage V+/− used to write the capacitor. The amplitude variation [Az(V+) > Az(V)] can be better appreciated in Fig. 1(e) where data have been vertically shifted to match at φ = 90°. In Fig. 1(f), we show the Jsc recorded in three capacitors after prepoling with V+. Clearly, the background current and the amplitude of oscillations vary similarly among electrodes but with Az/Bz ≈ 0.1 almost constant among various capacitors.

In Fig. 1(d), the sign of Jsc is independent of the sign (+/−) of the prepoling voltage. We notice that the observed Eim, evident in the I(V) and P(V) loops in Figs. 1(a) and 1(b), may have promoted a fast-preferential back-switching of the polarization before Jsc is recorded. We remark recording that the whole Jsc(φ) [Figs. 1(d)–1(f)] sweep takes τ ≈ 162 s, which may be much longer than the required polarization back-switching time. To get information on the dynamics of the back-switching process, we have recorded polarization loops with a delay time τd = 1 s, between polarization writing and reading as shown in Fig. 2.

FIG. 2.

(a) Voltage pulse trains used to determine the remanent polarization in τd = 1 s, after V or V+ writing pulses. (b)–(d) Polarization loops and retention in τd = 1 s in capacitors E1,2,3 (crystal-I), respectively.

FIG. 2.

(a) Voltage pulse trains used to determine the remanent polarization in τd = 1 s, after V or V+ writing pulses. (b)–(d) Polarization loops and retention in τd = 1 s in capacitors E1,2,3 (crystal-I), respectively.

Close modal

The methodology to measure the remnant relaxation polarization Pr,rel and Pr,rel+ (retention) after saturation with V and V+ is illustrated in Fig. 2(a). A V(t) pulse sequence consisting of four bipolar triangular excitation signals (1 and 2, and 3 and 4) is applied to Pttop with a delay time τd (1 s) between them. Pr,rel is the polarization value after 1 s delay of negative prepoling, determined from the P(V) loop recorded during pulse 2. Similarly, Pr,rel+ is the polarization after 1 s delay of positive prepoling, determined from the P(V) loop recorded during pulse 4. Positive values of polarization correspond to polarization pointing down (toward Ptbot) and negative for polarization pointing up (toward Pttop). Similar information is extracted from positive-up-negative-down (PUND) measurements (supplementary material, S3).

Data for devices E1,2,3 [Figs. 2(b)–2(d)] reveal that in all cases, Pr,rel has the same sign as Pr,rel+, implying that polarization written with V has switched back to downward within τd = 1 s, mimicking Pr,rel+. As expected, as Eim increases from E1 to E3 the polarization difference of Pr,rel+ and Pr,rel decreases. Additional experiments indicate that longer delay (up to 1000 s) does not reveal further switching back (see the supplementary material, S4). Therefore, when Jsc(φ) is recorded, the polarization always points down irrespectively on the writing voltage, as dictated by Eim. Accordingly, Az(V+) > Az(V) and Bz(V+) > Bz(V), and Jsc is positive as observed.

Crosscheck experiments have been performed using crystal-II where the P(V) loops indicate that Eim is pointing upward [Fig. 3(a)], and consistently, back-switching favors upward Pr,rel [Fig. 3(b)]. The Jsc(φ) data [Figs. 3(c) and 3(d)] show that the impact of polarization is reversed compared to data of crystal-I (Fig. 1), that is, Az(V) > Az(V+) and Bz(V) > Bz(V+). The fact that here, Jsc is still positive also denotes the presence of additional terms, probably related to a diffusion term due to non-homogenous illumination and/or a non-switchable drift contribution due to a pinned electric field.

FIG. 3.

(a) I(V) and P(V) loops and (b) retention in τd = 1 s in crystal-II. (c) Raw Jsc (φ) and (d) the same data shifted to better visualize the change of amplitude; solid lines are fits using Eq. (1) to experimental data (symbols).

FIG. 3.

(a) I(V) and P(V) loops and (b) retention in τd = 1 s in crystal-II. (c) Raw Jsc (φ) and (d) the same data shifted to better visualize the change of amplitude; solid lines are fits using Eq. (1) to experimental data (symbols).

Close modal

The δPr,rel=|Pr,rel+Pr,rel2| is the difference of polarization measured at remanence after writing with V+/−. It is to be expected that any polarization contribution to Az and Bz should be encapsulated by δPr,rel. To assess this hypothesis, we plot in Fig. 4(a) the δAz = |Az(Pr,rel+) − Az(Pr,rel)| vs δPr,rel collected from 20 capacitors (crystal-I), all having the same imprint sign. Data show that the contrast of amplitude (δAz) of Jsc(φ) oscillations increases when reducing the back-switching (larger δPr,rel). A similar trend can be appreciated in Fig. 4(b) where δBz = |Bz(Pr,rel+) − Bz(Pr,rel)| vs δPr,rel is plotted. In short, both Az and Bz change when reversing the polarization, and the stronger the retention of the pre-polarized states (bigger δPr,rel), the larger the contrasts in δAz and δBz.

FIG. 4.

Contrast of the oscillation (a) amplitudes (δAz) and (b) backgrounds (δBz) of Jsc(φ) vs the difference of remanent polarization (δPr,rel) after V+/− writing, collected in 20 capacitors in crystal-I. Sketches represent the polarization at saturation of (c) P+ (blue), (d) P (green) domains in the absence of back-switching, and (e) the polarization at remanence in the presence of back-switching, favoring P+ state. Blue arrows indicate the polarization direction, the yellow arrow denotes the imprint direction, black arrows represent the propagation direction (k) of the light, and red arrows illustrate a π-polarized light (Eπ).

FIG. 4.

Contrast of the oscillation (a) amplitudes (δAz) and (b) backgrounds (δBz) of Jsc(φ) vs the difference of remanent polarization (δPr,rel) after V+/− writing, collected in 20 capacitors in crystal-I. Sketches represent the polarization at saturation of (c) P+ (blue), (d) P (green) domains in the absence of back-switching, and (e) the polarization at remanence in the presence of back-switching, favoring P+ state. Blue arrows indicate the polarization direction, the yellow arrow denotes the imprint direction, black arrows represent the propagation direction (k) of the light, and red arrows illustrate a π-polarized light (Eπ).

Close modal

Several mechanisms may contribute to the photocurrent as observed in h-LuMnO312 and other materials.29 As the background term Bz may contain all these contributions, the role of ferroelectric P on Bz is difficult to discern. In contrast, understanding the dependence of the amplitude of oscillations on P appears at first sight simpler. Indeed, Az reflects the sensitivity of the photoresponse to light polarization, and it is expected to provide a genuine fingerprint of BPE weighted by any Fresnel contribution. However, the observation that Az depends on writing voltage (Figs. 1 and 3), implies that it is not simply determined by the symmetry of the crystal, but it is also affected by fine details of the polarization state of the sample when measurements are performed. As different capacitors on a given crystal have slightly different imprint fields [Figs. 1(a) and 1(b)], it is expected that the polar state of the sample under the electrodes, when Jsc is measured at remanence, may differ from one capacitor to another. If so, the differences of Az after V+/− writing, δAz = Az(V+) − Az(V), could be a fingerprint and a reflection of the polarization retention, or in other words, a measure of the fraction of domains that may have switched back.

To better understand the rationale behind, we recall that BPE photocurrent is given by

JBPE,i+=I0αjkGijk+ejek,
(2)

where I0 is the light intensity of a given wavelength, αjk is the absorption coefficient, and Gijk is the third rank Glass tensor.8,27 In Eq. (4), the suffixes (i, j, k) refer to (x, y, z) cartesian coordinates of the polarization components of the incoming light. We take the z-axis along the polar c-axis of h-LMO. As reported elsewhere,12,28 the oscillations of JBPE(φ) in h-LuMmO3 of Fig. 1 can be well described by Eq. (2). The super index (+) emphasizes that the actual values of the tensor elements correspond to a net shift of positive ionic charges along the negative direction of z-axis, say P+, and under this circumstance, JBPE,z+ is measured.

When polarization is fully reversed (P), preserving illumination conditions, Eq. (2) transforms to

JBPE,i=I0αjkGijkejek,
(3)

and JBPE,z is measured. Polarization reversal in h-LuMnO3 corresponds to a spatial inversion like a mirror (m ⊥ c) symmetry transformation. Therefore (see the supplementary material, S1),

Gijk=Gijk+.
(4)

Equations (3) and (4) imply that under P reversal, JBPE,z should display similar oscillations of the same amplitude but reversed sign than JBPE,z+, that is, Jsc(φ) should be phase-shifted by 90°. Under partial polarization back-switching, where the sample is in a mix state of polarization, the JBPE,z would be the weighted sum of the JBPE,i+/ contributions.

Data of crystal-I [Figs. 1(d) and 1(e)] show that after V+/− writing, the current direction remains unperturbed. Only a relatively small change of amplitude (≈ 5%) is observed. This implies that when Jsc is measured (τd > 1 s), the polarization written with V has been partially switched back to P+ state, in which case Pr is also downward but with a smaller magnitude than the fully stable Pr+ (Fig. 2), thus the measured Jsc written with V keeps the same sign but smaller value than Jsc+ written with V+. This process is sketched in Figs. 4(c)–4(e). It is expected to have opposite Jsc for downward and upward polarization states, respectively [Figs. 4(c) and 4(d)]. Instead, due to the presence of imprint, the final state can be a mixture of up and down domains impacting on the Jsc sign and magnitude. Thus, the presence of Eim is instrumental triggering the switching-back process and accounts for the observed dependence of Jsc(φ) on the polarization state of crystal.

On the contrary, in crystal-II, where the upward Eim favors P, Jsc+ is smaller than Jsc because the magnitude of real upward Pr+ is smaller than fully switched Pr. However, the measured Jsc+/− is always positive (Fig. 3), and data show that the BPE-predicted phase shift of Jsc(φ) compared with crystal-I is absent. Therefore, it follows that an additional contribution to Jsc(φ) that does not change its sign under a mirror transformation should also coexist. As shown in BiFeO3,30 defect-related in-gap states in the ferroelectric may conspicuously affect the actual symmetry of Gijk7 while preserving the cosinusoidal cos2φ dependence. The observation that the measured photocurrent differs among electrodes on the sample already indicates the importance of defects and/or impurities in the photovoltaic response, as already found in BiFeO3.31 Finally, additional contributions to Jsc(φ) may originate from dichroism, as recently reported in BiFeO332 although earlier experiments indicated that this is not the case in LuMnO3.28 Even more, the polarization-dependent light transmittance (Fresnel) at the interfaces could impact both the BPE and drift or diffusion currents by adding a cos2φ contribution to the measured Jsc(φ) photovoltaic current. Its inspection is beyond the scope of this work.

Finally, we recall that the extraction of the Glass coefficients from the measured magnitude of Jsc(φ) relies on the assumption that the measured photocurrent is dominated by bulk photovoltaic response, potentially affected by polarization back switching as demonstrated above. However, other effects such as drift photocurrent associated with band alignment at interfaces and/or diffusion photocurrent associated with photocarrier gradients contribute to the light-polarization insensitive background Jsc. Their presence, which precludes accurate extraction of some of the Gijk elements, can be minimized by using optimized metallic electrodes and thin films.

In summary, the short circuit photocurrent Jsc in ferroelectric materials, measured at zero V-bias and, thus, at remanence, is largely affected by the polarization history of the sample and the presence of polarization back-switching and depoling processes. By measuring the dependence of Jsc(φ) on the polarization of light, we have observed that the amplitude of cos2φ oscillations depends on the polarization state of the ferroelectric at remanence, and thus, it is sensitive to the polarization back-switching. It follows that accurate extraction of the intrinsic Glass coefficients of the material, related to the amplitude of Jsc(φ) oscillations, is challenging. As back-switching is typically more relevant in thin films, dedicated attention is required toward quantitative understanding of BPE. Moreover, data have been analyzed based on the assumption that BPE controls Jsc(φ). However, it is worth noticing that similar Jsc(φ) oscillations (≈ cos2φ) depending on the light polarization could be expected in the case of Fresnel controlled transmittance of π and σ light at top interfaces, and thus, a similar ferroelectric polarization dependent Jsc(φ) could appear since the Schottky barriers at interfaces and depoling field are related to ferroelectric polarization. Disentangling both effects remains to be solved.

See the supplementary material for the Glass tensor (BPE) reversal upon switching the ferroelectric polarization, experimental methodology, PUND and retention measurements.

Financial support from the Spanish Ministry of Science and Innovation (10.13039/501100011033), through the Severo Ochoa FUNFUTURE (No. CEX2019-000917-S); the TED2021-130453B-C21 (AEI/FEDER, EU), PID2020-118479RB-I00 (AEI/FEDER, EU), and PID2019-107727RB-I00 (AEI/FEDER, EU) projects; and from CSIC through the i-LINK (No. LINKA20338) program is acknowledged. Project supported by a 2020 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. Y.S. is financially supported by China Scholarship Council (CSC) through No. 201806410010. The work of Y.S. has been done as part of her Ph.D. program in Materials Science at Universitat Autònoma de Barcelona.

The authors have no conflicts to disclose.

Yunwei Sheng: Data curation (lead); Formal analysis (lead); Investigation (lead); Writing - original draft (lead). Ignasi Fina: Conceptualization (equal); Writing - review & editing (equal). Marin Gospodinov: Methodology (equal). Josep Fontcuberta: Conceptualization (equal); Supervision (lead); Writing - review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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