# Depletion region width of a ferroelectric heterostructure interface by surface potential measurements under illumination

Antoine Bagard, Chenyue Hu, Xavier Henning, Thomas Fix, Marc Lenertz, Aziz Dinia, Silviu Colis, Mircea Rastei

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Antoine Bagard, Chenyue Hu, Xavier Henning, Thomas Fix, Marc Lenertz, et al., Depletion region width of a ferroelectric heterostructure interface by surface potential measurements under illumination. Physical Review Materials, 2025, 9 (12), pp.123801. 10.1103/8ctp-3531. hal-05459346

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Depletion region width of a ferroelectric heterostructure interface by surface potential measurements under illumination

A. Bagard,¹ C. Hu,¹ X. Henning,¹ T. Fix,² M. Lenertz,¹ A. Dinia,¹ S. Colis,¹ and M. V. Rastei¹,*

¹Institut de Physique et Chimie des Matériaux de Strasbourg, CNRS, Université de Strasbourg, 23 Rue du Loess, F-67034 Strasbourg, France

²ICube Laboratory, CNRS, Université de Strasbourg, 23 Rue du Loess, 67037 Strasbourg, France

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(Received 3 September 2025; revised 23 October 2025; accepted 10 November 2025; published 1 December 2025)

Optimizing the band gap of ferroelectric oxides is crucial for enhancing light absorption in specific spectral ranges. In thin-film heterostructures, however, light absorption is also strongly influenced by interfacial properties. Bismuth ferrite-chromite (BFCO) thin films for instance, behave as a p-type semiconductor due to intrinsic cationic bismuth vacancies. When epitaxially grown on niobium-doped $SrTiO_3$, a p-n-like junction forms with a characteristic depletion region. In this work, we present a nondestructive approach to determine the depletion region width using surface photovoltage (SPV) measurements. Kelvin probe force microscopy under illumination was applied to BFCO films of varying thicknesses. A distinct transition in the SPV response at 67 ± 5 nm identifies the depletion region width and the extent of band bending. These results are corroborated by macroscopic SPV measurements with a Kelvin probe setup. From the depletion width, the acceptor concentration in BFCO, primarily attributed to bismuth vacancies, was estimated to be ~0.01% of the total number of Bi atoms in the ideal lattice. This method provides a powerful and noninvasive route to probe depletion widths and carrier concentrations in complex ferroelectric heterostructures.

DOI: 10.1103/8ctp-3531

## I. INTRODUCTION

Thin-film oxides are usually grown on single-crystal substrates using chemical or physical deposition techniques [1,2]. Often, this process creates an active interface with many fascinating physical properties [3–6]. A canonical example is the emergence of planar conductivity in oxide interfaces despite that both materials are bulk insulators [7,8]. Furthermore, as for traditional semiconductors, oxide heterostructures also demonstrate appealing charge transport properties perpendicular to the interface [9–11]. This includes photovoltaic effects in which the generated photovoltage is linked to both the material’s intrinsic polarization and its inherently asymmetric crystal structure [12–16]. In such cases, the depletion region width arising from interface electronic band alignments is expected to play a key role.

Based on their spontaneous and directional polarization, thin films of ferroelectrics, such as polyvinylidiene fluoride, $HfO_2$-based materials, or perovskites, e.g., $BiTiO_3$ and $BiFeO_3$ [17–19], hold promise for multiple future applications [20]. However, a limitation of these materials for use in the visible spectral range is related to their large band-gap values. In this context, a double perovskite $Bi_2FeCrO_6$ (BFCO) was introduced as a more optimal band-gap ferroelectric [21,22]. Slightly lower band-gap values, typically ranging from 1.5 to 2.5 eV depending on the synthesis conditions, have therefore been frequently reported into the literature [23–27].

In addition, similarly to $BiFeO_3$ [28–30], $Bi_2FeCrO_6$ thin films have been shown to behave as a p-type material due to inherent presence of Bi vacancies that act as shallow acceptor

levels [16]. This means that a p-n-like junction forms if the substrate has an n-type character. This is, indeed, the case when a $Bi_2FeCrO_6$ thin film is grown on a niobium-doped $SrTiO_3$ (NSTO) substrate, i.e., a common substrate used to ensure a good epitaxial growth while simultaneously having a conductive bottom electrode [16,22–26]. However, despite its importance for many physical properties, the depletion region of BFCO/NSTO junctions requires study. In particular, depletion width is expected to impact the photovoltaic response, as it determines the region where the electric field is strong enough to separate photocarriers [16]. Moreover, it is well known that the depletion width can lead to quantitative values for dopant concentration. Indeed, depletion width and acceptor concentration in p-type semiconductors are linked through the following equation for a heterojunction [31,32]:

$$W_p = \sqrt{\frac{2\epsilon_1\epsilon_2V_{bi}N_d}{qN_a(\epsilon_1N_a + \epsilon_2N_d)}}, \quad (1)$$

where $W_p$ corresponds to the depletion region width in the p-type material; $\epsilon_1$ and $\epsilon_2$ are the dielectric permittivity of p-type (BFCO) and n-type (NSTO) material, respectively; $V_{bi}$ is the built-in voltage; $q$ is the elementary charge; $N_d$ and $N_a$ are the effective donor and acceptor concentrations in the n- and p-type material, respectively. A similar equation can be found for the depletion region width in the n-type material [31].

For many systems the doping concentration is a known parameter, typically obtained by Hall effect measurements. A simple calculation thus leads to a value of the depletion region width [33–35]. Nevertheless, in the case of BFCO, and also for other ferroelectric films, obtaining the doping concentration through Hall effect measurements is complicated, as the electrical conduction is usually too low and, moreover, the

<footnote>*Contact author: mircea.rastei@ipcms.unistra.fr</footnote>
<figure><img src="image_4.png" /><figcaption>FIG. 1. (a) Schematic of Kelvin probe force microscopy (KPFM) experiments on a thin film of Bi₂FeCrO₆ (BFCO) of thickness *t* larger than the depletion region width *W*<sub>p</sub>, deposited on a Nb-doped SrTiO₃ (NSTO) substrate. Blue arrows correspond to the laser radiation used for SPV measurements. The laser power can be controlled outside the microscope. (b), (c) Representations of band bending with and without illumination. Green segments highlight the amplitude of surface photovoltage (SPV) induced by light. For a fixed laser power, a larger signal is expected if the depletion region is directly exposed to the light (*t* < *W*<sub>p</sub>).</figcaption></figure>

material polarization could have an effect on the measurement
[25]. Alternative methods for evaluating the depletion region
width or carrier density [36] are therefore beneficial for study-
ing the photovoltaic response and transport properties in such
thin-film heterostructures.

One possible approach to determine the width of a de-
pletion region is by measuring the surface potential. Indeed,
because of the electronic band bending taking place at the
interface, a change of surface potential is expected upon op-
tical absorption in the depletion region [37]. To measure the
surface potential across a junction with a high spatial reso-
lution, Kelvin probe force microscopy (KPFM), a mode of
atomic force microscopy (AFM), can be used [38]. This has
successfully been done for lateral configurations [39–41] or
nanowires of semiconductors with different doping profiles
along the long axis [42–44]. However, these configurations
are not the most common. For thin films grown on substrates,
samples must be sectioned and scanned in cross section,
perpendicular to the interface [45–47]. One issue with this
method is that cutting exposes the junction, creating a surface
where the potential can differ. In the present work, we use
KPFM to measure the surface photovoltage (SPV) directly at
the surface of BFCO thin films grown on a NSTO substrate
(Fig. 1). The most important result is that the SPV value, as
a function of film thickness, exhibits a transition that is at-
tributed to the width of the depletion region (Wp). In addition,
the found Wp value and Eq. (1) yield to an acceptor concen-
tration of about 0.01% of the total number of Bi atoms, in
agreement with expected values for a bismuth ferrite structure
[28–30].

It is noteworthy that, in heterostructure junctions, several
factors can cause the SPV measured under strong illumina-
tion to differ from the built-in potential, including band-gap
mismatch, interfacial trap density, and, in particular, Fermi-
level pinning. Such pinning effects limit changes in band
bending, leading to a smaller SPV amplitude. However, as in
the present work the estimation of the depletion region width
is not directly derived from the SPV magnitude but rather
from its relative variation as a function of film thickness, a
lower-bound estimate of the effective acceptor density can still
be obtained.

II. EXPERIMENTAL DETAILS

BFCO thin films with different thicknesses were epitaxi-
ally grown on Nb-doped STO (001) substrates (from Codex
International). The value of Nb concentration was 0.7 wt%.
The films were obtained by pulsed laser deposition using a
KrF excimer laser presenting a 248-nm wavelength. Twelve
samples of varying thicknesses, deposited at different times
under closed deposition conditions, were used in this study.
The deposition procedure details and structural characteriza-
tions were previously reported [16,24,26,48]. The thickness of
each film was estimated by x-ray reflectivity.

AFM experiments were performed with a customized
Icon Microscope from Bruker coupled to a supercontinuum
laser source (Fianium SC-400-4 from NKTPhotonics) and a
monochromator. KPFM measurements were realized with a
Si probe covered with a conductive gold layer of about 50 nm
(PPP-NCHAu from Nanosensors). The cantilever stiffness
is of ≈40 N m⁻¹. The amplitude modulation KPFM (AM-
KPFM) mode was used, as the potential signal is relatively
strong. The monochromator was set to λ = 450 nm and a
bandwidth of 10 nm. A beam splitter allows us to permanently
control the laser power received by the sample. For SPV
experiments, the slow scan axis was disabled. The speed of
fast scan axis was set to 2 s per line (8 ms per pixel), leading
to a good signal-to-noise ratio. Note that the fast scan axis
is vertical. The power of the laser was increased every 35 s
by 1/10th of the maximum power (Pmax) using a power mod-
ulator. The SPV signals were recorded in the form of images
(256 scan lines) [see, for instance, Fig. 2]. The signal was then
vertically averaged to obtain the SPV variation as a function
of laser power, as exemplified in Fig. 2(c) for four films of
different thicknesses. Analyses carried out in different areas
of the samples showed good consistency, suggesting that the
films are uniform. All films were measured in the as-grown
state, with no prior electrical poling, to reduce the impact of
polarization on the depletion region width.

Surface potential experiments were also realized at a
macroscopic scale, using a Kelvin probe system (KP Technol-
ogy APS03) with a 2-mm-diameter gold tip. The sample was
illuminated by a white halogen light source at different inten-
<figure><img src="image_5.png" /><figcaption>FIG. 2. (a) Topography image of a BFCO/NSTO sample. (b) KPFM potential image while gradually increasing the laser power. Each vertical stripe corresponds to 35 s at a constant laser power. The 100-nm scale corresponds to the vertical direction, which is the fast-scan axis. (c) SPV variation for samples of various thicknesses, obtained by vertically averaging the signal from images as shown in panel (b). (d) SPV variation with laser power obtained by averaging the last nine lines of each stripe, revealing a logarithmic change.</figcaption></figure>

sities. Signal calibrations were made on gold and aluminum reference samples.

### III. RESULTS AND DISCUSSIONS

#### A. KPFM experiments and SPV signal

When a depletion region is illuminated with light of a high enough energy ($h\nu \ge E_g$), hole-electron pairs are created. Due to the built-in electric field in the band-bending region, charge carriers can separate. A direct consequence is that valence and conduction bands become flatter [Figs. 1(b)-1(c)]. This induces a modification of KPFM potential even for an interface buried into the sample [37]. The SPV signal is defined as the potential difference with and without light: $SPV = V_{light} - V_{dark}$. This effect was also found to hold for a buried interface, provided that the oxide film is thin enough, i.e., thinner than the absorption length and/or carrier diffusion length. As the latter is likely larger than the film thickness, the absorption length appears to be a critical factor capable of changing the SPV signal by reducing the amount of light reaching the interface. According to the Beer-Lambert law, films thicker than the depletion region are thus allowing a linearly smaller amount of light to reach the depletion region. A decrease of the SPV signal is hence expected for films thicker than the depletion region width.

A topographic image of a BFCO/NSTO sample is shown in Fig. 2(a). Small rectangular grains are seen, in agreement with an epitaxial growth along the [001] direction. The samples are therefore not perfectly flat, presenting a degree of roughness [16,24]. Nevertheless, the surface potential image [Fig. 2(b)]

reveals a homogeneous signal due to longer range electrostatic interactions involved in KPFM as compared to van der Waals forces used for topography. Each signal stripe in Fig. 2(b) corresponds to a constant laser power. The laser power was gradually increased from left to right. Vertical averaged signals as a function of the laser power are shown in Fig. 2(c) for samples presenting different thicknesses.

#### B. Variation of SPV signal with laser power

Time-averaged variations of the SPV signal with laser power for different samples are shown Fig. 2(d). It can be seen that each curve follows a logarithmic behavior. The flattening of the interfacial electronic bands induced by photoexcited carriers is indeed expected to saturate as the bands become flatter, an effect described by the following equation [37]:

$$SPV(P) = \frac{\eta k_B T}{q} \ln\left(\frac{cP}{R_0} + 1\right), \quad (2)$$

where $\eta$ is a parameter varying between 0.5 and 2 reflecting how efficiently photogenerated carriers contribute to the surface photovoltage, $k_B$ is the Boltzmann's constant, $T$ is the temperature, $q$ is the electron charge, $c$ is the efficiency of the electron-hole separation, $P$ is the light power, and $R_0$ is the bulk-to-surface flow of electrons under dark conditions [37,49].

While SPV($P$) logarithmic variations are understood based on light-induced band-flattening effects, BFCO film thickness seems to play an additional role. As seen in Figs. 2(c) and 2(d), SPV values are slightly increasing with film thickness ($t$) up to $t = 70$ nm. Interestingly, the SPV signal is considerably smaller for the film thickness of 82 nm. For a better visualization of this effect, the SPV values corresponding to the maximum laser power ($P = 797$ µW) are traced in Fig. 3 for all investigated films. A change in the SPV trend can be observed around $t = 67 \pm 5$ nm, despite slight deviations from the general behavior shown by the red lines in Fig. 3,

<figure><img src="image_6.png" /><figcaption>FIG. 3. SPV signal measured at the maximal laser power ($P = 797$ µW) for BFCO samples of different thicknesses. Red lines are a guide for the eye. The depletion (red) and bulk (blue) regimes correspond to band-bending and flat-band regions illustrated in Fig. 1.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>FIG. 4. SPV variations obtained by normalizing all data with respect to the maximum value for each power. A behavior similar to that in Fig. 3 is seen regardless of the laser power. A change of regime can be observed around 70 nm for all laser powers. Error bars for each data point correspond to the standard deviation of the averaged signal.</figcaption></figure>

such as the 40-nm sample, which exhibits a somewhat lower SPV value.

This finding remains consistent when analyzing the signals for the other laser power values. Thus, normalized SPV values are shown in Fig. 4 for four laser powers. Normalization was performed by scaling all data taken at a fixed power by the corresponding SPV maximum value. All curves show a similar drop of signal around the same thickness, i.e., estimated above at $t = 67 \pm 5$ nm. In addition, the thickest sample ($t = 88$ nm) shows that the SPV value is reduced by almost half compared to samples with a thickness of around $t = 60$ nm, indicating, as expected, a significant optical absorption in the flat-band region of the BFCO film [Fig. 1(b)]. Note that the error bars represent the standard deviation of the averaged signal, determined from the last eight scan lines of each scanning interval (vertical stripe) recorded at a fixed laser power. This procedure ensures that a steady-state response is achieved for each laser power, i.e., at the end of a vertical stripe [Figs. 2(b) and 2(c)].

Indeed, in the case of samples thicker than the depletion region width, i.e., $t > W_p$, a flat-band (bulk-like) region forms where light is absorbed but charge separation does not directly occur due to the reduced electric field. Light absorption in this region follows a Beer-Lambert-like law, meaning that the light intensity decreases linearly with thickness. As a result, less light reaches the p-n junction, where the SPV signal is generated, leading to a reduced signal in thicker samples, consistent with the observed decreasing trend. For fully depleted samples ($t < W_p$), a slight increase in the SPV with thickness is observed, likely because the active region for charge separation expands [50].

Another interesting aspect that can be observed in Fig. 4 is that all data collapse rather well on similar values for the three largest laser powers, whereas for $P = 79.7$ µW they are slightly lower (light blue data points). While our data are not enough to trigger a definitive conclusion, it might nevertheless

suggest that photosaturation of the depletion region at such a low laser power value has not yet been reached [37].

### C. Kelvin probe measurements

A verification of local KPFM observations was realized at a larger scale by a macroscopic Kelvin probe setup as described in Sec. II. Figure 5 shows the Kelvin probe signals while switching on and off the light. The measured surface potential under dark conditions was used as a reference, i.e., zero SPV signal. Importantly, while the SPV values for $t < 70$ nm are rather close, a clear signal drop is measured for the film of $t = 82$ nm, in strong agreement with KPFM results described above. Moreover, the fact that the macroscopic Kelvin probe SPV values are obtained with a white light illumination generalizes even more our findings. While this is not surprising considering that the BFCO is developed as a low-band-gap material, it suggests that macroscopic SPV experiments can be a useful technique for optimizing thin-film thicknesses for photovoltaic applications if realized as a function of wavelength.

### D. Dopant concentration

Assessing the depletion region width is important for understanding the extension of interface electric fields and the size of the region where photocarriers can separate in photovoltaic systems. Yet, according to Eq. (1), the depletion region width can be used to calculate the acceptor concentration ($N_a$) through the following second-order polynomial:

$$N_a^2 + \frac{\epsilon_2}{\epsilon_1} N_d N_a - \frac{2N_d \epsilon_2 V_{bi}}{q W_p^2} = 0. \quad (3)$$

Using $\epsilon_1 \approx 80\epsilon_0$ [22] and $\epsilon_2 \approx \epsilon_{SrTiO_3} \approx 330\epsilon_0$ [51–53], with $\epsilon_0 = 8.854 \times 10^{-12}$ F m$^{-1}$, and the donor concentration $N_d$ in NSTO (0.7 wt. % representing 1.4 at. %), which is $N_d = 0.014C_A = \frac{5}{V_{STO}} = 1.2 \times 10^{27}$ m$^{-3}$ with $C_A$ being the atomic density of $SrTiO_3$ and $V_{STO}$ the volume of the cell of $SrTiO_3$ (cubic cell with $a = 0.39$ nm [54]), the equation can be numerically solved for $N_a$. We used $V_{bi}$ calculated from the difference of Fermi levels $E_{F1}$ and $E_{F2}$ ($V_{bi} = \frac{E_{F1}-E_{F2}}{q} = 0.98$ V [16]).

<figure><img src="image_8.png" /><figcaption>FIG. 5. SPV measured with a Kelvin probe setup under white light illumination, revealing a signal drop for the thickest film of 82 nm, in agreement with the local KPFM findings.</figcaption></figure>
There are two solutions for Eq. (3), of which only the positive one has physical meaning:

$$N_a = \frac{-\frac{\epsilon_2}{\epsilon_1} N_d + \sqrt{\left(\frac{\epsilon_2}{\epsilon_1} N_d\right)^2 + \frac{8N_d \epsilon_2 V_{bi}}{q W_p^2}}}{2} \quad (4)$$

Considering the depletion region width $W_p = 67$ nm as found above, Eq. (4) gives $N_a = 1.9 \times 10^{18} \text{ cm}^{-3}$, which is consistent with Bi vacancies in BFO systems [28,30]. Moreover, assuming that only Bi vacancies participate as acceptors and using the fact that there is one Bi atom per cell, it is possible to estimate the doping concentration. Thus, taking into account the lattice parameters ($a = 0.3901$ nm and $c = 0.3954$ nm in the tetragonal approximation [23]) and the total number of Bi atoms of $N_{Bi} = 1.7 \times 10^{28} \text{ m}^{-3}$, the vacancies represent 0.01 at.%. This value is also coherent with the p-type character of BFCO films [16,48] and the fact that Bi atoms are known to be the most volatile during the nonequilibrium deposition process [55,56]. Note, however, that Eq. (3) assumes an ideal junction without significant interfacial defect levels and therefore provides a lower-bound estimate of the acceptor concentration. If a certain number of defect states, such as trapping or recombination centers, are present, the measurable effect of acceptors is reduced. As a result, the acceptor concentration will be higher than the value estimated here.

## IV. SUMMARY AND CONCLUSION

We presented a nondestructive method to estimate the depletion region width in oxide thin-film heterostructures, based on the analysis of the surface photovoltage (SPV) response in samples with varying thicknesses. The evolution of the SPV signal with film thickness provides direct information on

the extent of the depletion region. The method was demonstrated on BFCO films grown on Nb-doped $SrTiO_3$ (NSTO) substrates, which form a p-n junction at the interface. When the depletion region is directly exposed to light, the SPV response remains nearly constant, whereas films thicker than the depletion width show progressively reduced SPV values due to absorption in the flat-band region. From this analysis, the depletion width of BFCO/NSTO heterostructures was determined to be $67 \pm 5$ nm. Complementary Kelvin probe measurements confirmed the KPFM results, thereby validating the approach across both local and macroscopic scales. Furthermore, from the depletion width, the acceptor concentration in BFCO—primarily attributed to bismuth vacancies—was estimated to be 0.01% of the total Bi atoms. This result provides a quantitative estimate of the acceptor concentration in BFCO, particularly valuable given the difficulty of applying Hall effect measurements to such low-conductivity ferroelectric films.

## ACKNOWLEDGMENTS

We thank N. Beyer and L. Schlur for technical assistance. We acknowledge the Interdisciplinary Thematic Institute EUR QMat (Grant No. ANR-17-EURE-0024) as part of the ITI 2021-2028 program supported by the IdExUnistra (Grant No. ANR-10-IDEX-0002) and the SFRI STRAT'US (Grant No. ANR-20-SFRI-0012) through the French Programme d'Investissement d'Avenir.

## DATA AVAILABILITY

The data that support the findings of this article are not publicly available. The data are available from the authors upon reasonable request.

[1] J. A. Oke and T.-C. Jen, Atomic layer deposition and other thin film deposition techniques, J. Mater. Res. Technol. 21, 2481 (2022).

[2] M. Dawber, K. M. Rabe, and J. F. Scott, Physics of thin-film ferroelectric oxides, Rev. Mod. Phys. 77, 1083 (2005).

[3] R. C. Cammarata, Surface and interface stress effects in thin films, Prog. Surf. Sci. 46, 1 (1994).

[4] N. Reyren, S. Thiel, A. D. Caviglia, L. F. Kourkoutis, G. Hammerl, C. Richter, C. W. Schneider, T. Kopp, A. S. Retschi, D. Jaccard, M. Gabay, D. A. Muller, J. M. Triscone, and J. Mannhart, Superconducting interfaces between insulating oxides, Science 317, 1196 (2007).

[5] A. Brinkman, M. Huijben, M. van Zalk, J. Huijben, U. Zeitler, J. C. Maan, W. G. van der Wiel, G. Rijnders, D. H. Blank, and H. Hilgenkam, Superconducting interfaces between insulating oxides, Nat. Mater. 6, 493 (2007).

[6] W. Li, J. E. Kleibeuker, R. Wu, K. H. L. Zhang, C. Yun, and J. L. MacManus-Driscoll, Insulating-to-conducting behavior and band profile across the $La_{0.9}Ba_{0.1}MnO_3/Nb: SrTiO_3$ epitaxial interface, Phys. Rev. B 96, 165103 (2017).

[7] A. Ohtomo and H. Y. Hwang, A high-mobility electron gas at the $LaAlO_3/SrTiO_3$ heterointerface, Nature (London) 427, 423 (2004).

[8] M. Basletic, J.-L. Maurice, C. Carrétéro, G. Herranz, O. Copie, M. Bibes, É. Jacquet, K. Bouzehouane, S. Fusil, and A. Barthélémy, Mapping the spatial distribution of charge carriers in $LaAlO_3/SrTiO_3$ heterostructures, Nat. Mater. 7, 621 (2008).

[9] K. G. Rana, T. Yajima, S. Parui, A. F. Kemper, T. P. Devereaux, Y. Hikita, H. Y. Hwang, and T. Banerjee, Hot electron transport in a strongly correlated transition-metal oxide, Sci. Rep. 3, 1274 (2013).

[10] H. Chen and A. Millis, Charge transfer and emergent interfacial phenomena, J. Phys.: Condens. Matter 29, 243001 (2017).

[11] H. Y. Hwang, Y. Iwasa, M. Kawasaki, B. Keimer, N. Nagaosa, and Y. Tokura, Emergent phenomena at oxide interfaces, Nat. Mater. 11, 103 (2012).

[12] V. M. Fridkin, Bulk photovoltaic effect in noncentrosymmetric crystals, Cryst. Rep. 46, 654 (2001).

[13] Z. Wang, S. Shu, X. Wei, R. Liang, S. Ke, L. Shu, and G. Catalan, Flexophotovoltaic effect and above-band-gap photovoltage induced by strain gradients in halide perovskites, Phys. Rev. Lett. 132, 086902 (2024).

[14] D. F. Pan, G. F. Bi, G. Y. Chen, H. Zhang, J. M. Liu, G. H. Wang, and J. G. Wan, Polarization-dependent interfacial coupling modulation of ferroelectric photovoltaic effect in PZT-ZnO heterostructures, Sci. Rep. 6, 22948 (2016).
[15] A. Abdelsamie, L. You, L. Wang, S. Li, M. Gu, and J. Wang, Crossover between bulk and interface photovoltaic mechanisms in a ferroelectric vertical heterostructure, *Phys. Rev. Appl.* **17**, 024047 (2022).

[16] X. Henning, L. Schlur, L. Wendling, T. Fix, S. Colis, A. Dinia, M. Alexe, and M. V. Rastei, Interfacial photovoltaic effects in ferroelectric Bi₂FeCrO₆ thin films, *Phys. Rev. Mater.* **9**, 024403 (2025).

[17] X. Chen, X. Han, and Q.-D. Shen, PVDF-Based ferroelectric polymers in modern flexible electronics, *Adv. Electron. Mater.* **3**, 1600460 (2017).

[18] Y.-C. Liu, B.-C. Chen, C.-C Wei, S.-Z. Ho, Y.-D. Liou, P. Kaur, R. Rahul, Y.-C. Chen, and J.-C Yang, Thickness-dependent ferroelectricity in freestanding Hf₀.₅Zr₀.₅O₂ membranes, *ACS Appl. Electron. Mater.* **6**, 8617 (2024).

[19] N. Nuraje and K. Su, Perovskite ferroelectric nanomaterials, *Nanoscale* **5**, 8752 (2013).

[20] A. Fernandez, M. Acharya, H.-G. Lee, J. Schimpf, Y. Jiang, D. Lou, Z. Tian, and L. W. Martin, Thin-film ferroelectrics, *Adv. Mater.* **34**, 2108841 (2022).

[21] P. Baettig and N. A. Spaldin, *Ab initio* prediction of a multiferroic with large polarization and magnetization, *Appl. Phys. Lett.* **86**, 012505 (2005).

[22] R. Nechache, C. Harnagea, A. Pignolet, F. Normandin, T. Veres, L.-P. Carignan, and D. Ménard, Growth, structure, and properties of epitaxial thin films of first-principles predicted multiferroic, *Appl. Phys. Lett.* **89**, 102902 (2006).

[23] R. Nechache, C. Harnagea, S. Li, L. Cardenas, W. Huang, J. Chakrabarty, and F. Rosei, Bandgap tuning of multiferroic oxide solar cells, *Nat. Photon.* **9**, 61 (2015).

[24] M. V. Rastei, F. Gellé, G. Schmerber, A. Quattropani, T. Fix, A. Dinia, A. Slaoui, and S. Colis, Thickness dependence and strain effects in ferroelectric Bi₂FeCrO₆ thin films, *ACS Appl. Energy Mater.* **2**, 8850 (2019).

[25] D. S. Walch, Y. Yun, N. Ramakrishnegowda, L. Mühlenbein, A. Lotnyk, C. Himcinschi, and A. Bhatnagar, Resistive switching in ferroelectric thin films and impact on the photovoltaic effect, *Adv. Electron. Mater.* **8**, 2200276 (2022).

[26] A. Quattropani, D. Stoeffler, T. Fix, G. Schmerber, M. Lenertz, G. Versini, J. L. Rehspringer, A. Slaoui, A. Dinia, and S. Colis, Band-gap tuning in ferroelectric Bi₂FeCrO₆ double perovskite thin films, *J. Phys. Chem. C* **122**, 1070 (2018).

[27] Z. Tang, X.-C. Lai, J. Fang, L. Feng, D.-J. Yao, L. Zhang, Y.-P. Jiang, Q.-X. Liu, X.-G. Tang, Y.-C. Zhou, and J. Gao, A reversible positive and negative photoconductivity behavior modulated by polarization effect, *Appl. Phys. Lett.* **125**, 241106 (2024).

[28] Q. Xu, M. Sobhan, Q. Yang, F. Anariba, K. Phuong Ong, and P. Wu, The role of Bi vacancies in the electrical conduction of BiFeO₃, *Dalton Trans.* **43**, 10787 (2014).

[29] T. R. Paudel, S. J. Jaswal, and E. Y. Tsymbal, Intrinsic defects in multiferroic BiFeO₃ and their effect on magnetism, *Phys. Rev. B* **85**, 104409 (2012).

[30] T. Rojac, A. Bencan, B. Malic, G. Tutuncu, J. L. Jones, J. E. Daniels, and D. Damjanovic, BiFeO₃ ceramics: Processing, electrical, and electromechanical properties, *J. Am Ceram. Soc.* **97**, 1993 (2014).

[31] S. M. Sze, *Physics of Semiconductor Devices*, 2nd ed. (Wiley, New York, 1981).

[32] A. Rockett, *The Materials Science of Semiconductors* (Springer, Boston, 2008).

[33] M. S. Islam, M. A. Hussain, and A. F. Alkhateeb, Fabrication of pn junction arrays with highly successful grown n-Si microneedles by using low temperature VLS method, *J. Micromech. Microeng.* **31**, 055008 (2021).

[34] T. Sugino, T. Itagaki, and J. Shirafuji, Formation of pn junctions by bonding of GaAs layer onto diamond, *Diamond Relat. Mater.* **5**, 714 (1996).

[35] E. Barrigón, O. Hultin, D. Lindgren, F. Yadegari, M. H. Magnusson, L. Samuelson, L. I. M. Johansson, and M. T. Björk, GaAs nanowire pn-junctions produced by low-cost and high-throughput aerotaxy, *Nano Lett.* **18**, 1088 (2018).

[36] P. W. Turner, J. P. V. McConville, S. J. McCartan, M. H. Campbell, J. Schaab, R. G. P. McQuaid, A. Kumar, and J. M. Gregg, Large carrier mobilities in ErMnO₃ conducting domain walls revealed by quantitative Hall effect measurements, *Nano Lett.* **18**, 6381 (2018).

[37] L. Kronik and Y. Shapira, Surface photovoltage phenomena: Theory, experiment, and applications, *Surf. Sci. Rep.* **37**, 1 (1999).

[38] W. Melitz, J. Shen, A. C. Kummel, and S. Lee, Kelvin probe force microscopy and its application, *Surf. Sci. Rep.* **66**, 1 (2011).

[39] B.-Y. Tsui, C.-M. Hsieh, P.-C. Su, S.-D. Tzeng, and S. Gwo, Two-dimensional carrier profiling by Kelvin-probe force microscopy, *Jpn. J. Appl. Phys.* **47**, 4448 (2008).

[40] R. Nowak, D. Moraru, T. Mizuno, R. Jablonski, and M. Tabe, Potential profile and photovoltaic effect in nanoscale lateral pn junction observed by Kelvin probe force microscopy, *Thin Solid Films* **557**, 249 (2014).

[41] K. Shirota, D. Takeuchi, H. Kato, T. Makino, M. Ogura, H. Okushi, and S. Yamasaki, Potential profile evaluation of a di-amond lateral p-n junction diode using Kelvin probe force microscopy, *Phys. Stat. Solidi a* **212**, 2589 (2015).

[42] S. Vinaji, A. Lochthofen, W. Mertin, I. Regolin, C. Gutsche, W. Prost, F. J. Tegude, and G. Bacher, Material and doping transitions in single gaas-based nanowires probed by Kelvin probe force microscopy, *Nanotechnology* **20**, 385702 (2009).

[43] A. Minj, A. Cros, T. Auzelle, J. Pernot, and B. Daudin, Direct assessment of p-n junctions in single GaN nanowires by Kelvin probe force microscopy, *Nanotechnology* **27**, 385202 (2016).

[44] S. R. McKibbin, J. Colvin, A. Troian, J. V. Knutsson, J. L. Webb, G. Otnes, K. Dirscherl, H. Sezen, M. Amati, L. Gregoratti, M. T. Borgström, A. Mikkelsen, and R. Timm, Operando surface characterization of InP nanowire p-n junctions, *Nano Lett.* **20**, 887 (2020).

[45] A. Doukkali, S. Ledain, C. Guasch, and J. Bonnet, Surface potential mapping of biased pn junction with Kelvin probe force microscopy: Application to cross-section devices, *Appl. Surf. Sci.* **235**, 507 (2004).

[46] J. Lee and J. Kong, Potential dip in organic photovoltaics probed by cross-sectional Kelvin probe force microscopy, *Nanoscale Res. Lett.* **13**, 228 (2018).

[47] T. Nakamura, N. Ishida, K. Sagisaka, and Y. Koide, Surface potential imaging and characterizations of a GaN p-n junction with Kelvin probe force microscopy, *AIP Adv.* **10**, 085010 (2020).
[48] X. Henning, K. Alhada-Lahbabi, D. Deleruyelle, B. Gautier, L. Schlur, T. Fix, S. Colis, A. Dinia, and M. V. Rastei, Oxygen vacancy effects on polarization switching of ferroelectric Bi₂FeCrO₆ thin films, *Phys. Rev. Mater.* **8**, 054416 (2024).

[49] M. A. Reshchikov, M. Foussekis, A. A. Baski, Surface photovoltage in undoped *n*-type GaN, *J. Appl. Phys.* **107**, 113535 (2010).

[50] L. Kronik, M. Leibovitch, E. Fefer, V. Korobov, and Y. Shapira, Electronic characterization of heterojunctions by surface potential monitoring, *J. Electron. Mater.* **24**, 893 (1995).

[51] N. Nepomniashchaia, V. Vetokhina, D. Chvostova, Z. Bryknar, M. Tyunina, and A. Dejneka, Effect of doping SrTiO₃ with Nb studied with wide-range spectroscopic ellipsometry, *J. Appl. Phys.* **134**, 034102 (2023).

[52] R. C. Neville, B. Hoeneisen, and C. A. Mead, Permittivity of strontium titanate, *J. Appl. Phys.* **43**, 2124 (1972).

[53] A. M. Kamerbeek, Charge and spin transport in Nb-doped SrTiO₃ using Co/AlOₓ spin injection contacts, Ph.D. thesis, University of Groningen, 2016.

[54] M. Lebeda, J. Drahokoupil, S. Kamba, S. Svoboda, V. Smola, B. Dabrowski, and P. Vlčák, Lattice parameters and bulk modulus of SrTi₁-xMnxO₃ perovskites: A comparison of exchange-correlation functionals with experimental validation, *Comput. Condens. Matter.* **43**, e01030 (2025).

[55] A. J. E. Rettie, S. Mozaffari, M. D. McDaniel, K. N. Pearson, J. G. Ekerdt, J. T. Markert, and C. B. Mullins, Pulsed laser deposition of epitaxial and polycrystalline bismuth vanadate thin films, *J. Phys. Chem. C* **118**, 26543 (2014).

[56] H. Yuan, S. Pal, C. Forrester, Q. He, and J. Briscoe, Understanding the impact of Bi stoichiometry towards optimised BiFeO₃ photocathodes: Structure, morphology, defects and ferroelectricity, *J. Mater. Chem. A* **12**, 17422 (2024).