Linear Electro-Optic Modulation in Electrophoretically Deposited Perovskite Nanocrystal Films

Abstract

We report the observation of a linear electro-optic (EO) response in CsPbX₃ (X = Cl, Br, I) perovskite nanocrystal (NC) films fabricated via electrophoretic deposition (EPD). Under an alternating electric field, the EPD films exhibit clear linear EO modulation of transmitted light intensity, indicating the formation of an anisotropic medium through field-induced NC alignment. In contrast, spin-coated NC films show no measurable linear EO response, underscoring the critical role of structural anisotropy introduced by EPD. All EPD samples exhibit a decreasing EO response with increasing modulation frequency, consistent with the involvement of slow ion migration dynamics. The halide composition influences EO behavior, with Br/Cl mixed-composition films maintaining the highest EO response at elevated frequencies, and Br-based NCs showing stronger EO signals than their Cl counterparts, while Bi-doped CsPbBr₃ films exhibit quenched photoluminescence yet retain a measurable but weaker EO response, underscoring the trade-off between defect-induced nonradiative recombination and EO activity. These results highlight the potential of EPD-assembled perovskite NCs for reconfigurable EO applications by tailoring composition and microstructure.

1. Introduction

Metal halide perovskite NCs, particularly those with the formula CsPbX₃ (X = Cl, Br, I), have emerged as promising materials for a wide range of optoelectronic applications due to their excellent photophysical properties, such as high absorption coefficients [1], size- and composition-tunable bandgaps [2], and efficient photoluminescence [3]. While extensive efforts have been devoted to developing these materials for light-emitting diodes, lasers, photodetectors [4,5], and solar cells [6], their potential for active optical modulation remains relatively underexplored. In contrast, conventional electro-optic (EO) materials such as LiNbO₃ and BaTiO₃ are widely used in modulators but suffer from high fabrication costs, limited scalability, and integration challenges with silicon photonics, which motivates the search for low-cost, solution-processable EO-active alternatives.

Among optical modulation techniques, the linear EO effect—or Pockels effect—holds particular significance, as it enables ultrafast, low-power modulation of light by applying an electric field [7,8]. In bulk perovskites, a Pockels response is typically forbidden due to their centrosymmetric crystal structures. However, when reduced to the nanoscale and assembled into aligned ensembles, symmetry breaking can occur, potentially giving rise to a nonzero second-order nonlinear optical response. Despite this possibility, realizing a robust Pockels response in halide perovskites has been challenging. Bulk perovskites are centrosymmetric, which forbids second-order nonlinear effects, while solution-processed films usually consist of randomly oriented NCs that average out local asymmetry. In addition, parasitic effects such as ionic migration and defect states often obscure the intrinsic χ² response, complicating the interpretation of experimental results.

Previous studies have reported electro-optic (EO) responses in halide perovskites, but the results remain inconsistent and sometimes controversial. In several cases, the observed signals were later attributed to extrinsic effects such as ionic migration, interfacial fields, or electric-field-induced χ³ processes rather than a genuine Pockels response. Many apparent SHG or χ⁽²⁾ signals were later shown to originate from multiphoton photoluminescence or second-harmonic-like signals generated via electric-field-induced χ³ processes [9]. In other cases, hysteretic responses initially interpreted as ferroelectric were instead attributed to ionic migration and frequency-dependent conductivity [10]. Moreover, reported EO coefficients vary by orders of magnitude depending on sample preparation and measurement conditions [11]. These conflicting findings highlight the need for systematic approaches to achieve reliable symmetry breaking and to clarify the intrinsic EO activity in perovskite nanomaterials.

Here, we explore this possibility using colloidal CsPbX₃ NCs deposited via EPD, a technique that allows for field-directed assembly of charged NCs into compact films with potential dipole alignment [12,13]. Unlike conventional spin-coated films, which tend to form randomly oriented structures [14], EPD enables long-range ordering and preferential dipole orientation under applied fields, breaking the inversion symmetry required to activate the linear EO effect [15,16]. Building on these considerations, in this work, we aim to investigate the linear electro-optic (EO) behavior of CsPbX₃ nanocrystal (NC) films prepared via electrophoretic deposition (EPD). We focus on demonstrating that EPD can induce nanocrystal alignment and macroscopic symmetry breaking, leading to a measurable linear EO effect, examining how the halide composition and Bi³⁺ doping influence EO activity, and analyzing the frequency dependence of EO modulation to assess the role of ionic migration in enhancing the response.

In this work, we demonstrate clear linear EO responses in EPD films of CsPbX₃ NCs under DC bias, while no such response is observed in spin-coated control samples. By tuning the halide composition and introducing Bi³⁺ as a dopant, we examine how the chemical environment and ionic mobility influence EO behavior. In particular, we observe a strong frequency dependence on EO modulation, especially in iodide-rich and Bi-doped samples, suggesting that ion migration contributes to the EO response at low modulation frequencies. These findings provide new insight into the interplay between structural asymmetry, ion dynamics, and nonlinear optical properties in perovskite NCs, and point to EPD as a scalable strategy for fabricating EO-active nanomaterials.

2. Results

Cesium lead halide perovskite NCs with various halide compositions—CsPbCl₃, CsPbBr₃, Bi-doped CsPbBr₃, and Bi-doped CsPbI₃—were synthesized using a conventional hot-injection method [1]. In a typical procedure, cesium oleate was first prepared by dissolving Cs₂CO₃ in oleic acid and octadecene (ODE). This solution was swiftly injected into a hot mixture of PbX₂ (X = Cl, Br, I) or a combination of PbX₂ and BiX₃ (for Bi doping), oleylamine (OAm), and oleic acid (OA) in ODE at temperatures between 160 and 180 °C under an inert atmosphere. The rapid injection induced burst nucleation, followed by short growth times (<60 s), yielding monodisperse NCs. The resulting NCs were purified by repeated cycles of precipitation with methyl acetate and redispersion in hexane or toluene. Bi doping was achieved by substituting a small fraction of PbX2 (typically 5–10 mol%) with BiX₃, which preserved the NC morphology but led to significant photoluminescence (PL) quenching [17,18]. This complete quenching of PL can be attributed to the formation of mid-gap trap states associated with Bi³⁺ ions, which serve as efficient nonradiative recombination centers and suppress band-edge emission. Similar mechanisms of PL suppression by Bi-induced defect states have been reported in halide perovskites [19]. Although Bi³⁺ doping is introduced, XRD patterns and optical spectra confirm that the 3D CsPbX₃ perovskite structure is maintained, with no evidence of formation of a 0D A₃B₂X₉ phase.

Mixed-halide compositions, including CsPbBrxCl_3−x and CsPbBrxI_3−x, were synthesized via a post-synthetic anion exchange strategy [20]. This was carried out by directly mixing two types of pre-formed NCs (e.g., CsPbCl₃ with CsPbBr₃ for CsPbBr_xCl_3−x, or CsPbBr₃ with CsPbI₃ for CsPbBr_xI_3−x) in nonpolar solvents under ambient conditions (e.g., toluene). Anion exchange occurred spontaneously within minutes, resulting in alloyed, single-phase perovskite NCs rather than a physical mixture of two distinct compositions. This ensured structural homogeneity and avoided dual emission that would otherwise indicate incomplete exchange. By adjusting the ratio of the two parent NCs, the emission peak of the mixed-halide NCs could be finely tuned between those of the pure-halide endpoints [21,22]. Importantly, no dual-emission behavior was observed, confirming uniform halide redistribution across the NC ensemble. The resulting spectra exhibited narrow emission linewidths and maintained high photoluminescence quantum yields, consistent with previously reported halide-exchanged CsPbX₃ NCs [20].

The optical properties of the synthesized NCs are summarized in Figure 1. The absorption spectra exhibit well-defined excitonic features, which red-shift systematically from ~400 nm (CsPbCl₃) to ~680 nm (CsPbI₃) as the halide composition changes. Undoped NCs display intense (Figure 1a,b), narrow PL peaks corresponding to band-edge recombination, indicative of high crystallinity and uniformity. The emission peaks of mixed-halide NCs fall between those of their parent compositions and can be precisely modulated by the mixing ratio (Figure 1c,d), confirming successful anion exchange and compositional tunability. In contrast, Bi-doped CsPbBr₃ and CsPbI₃ NCs show strong absorption but completely quenched PL (Figure 1e,f), implying that Bi incorporation introduces mid-gap trap states or enhances nonradiative decay pathways.

NC thin films were fabricated using an EPD technique, selected not only for its ability to produce uniform coatings but also for its potential to promote orientational alignment of NCs—an essential condition for realizing linear EO (Pockels) effects. Previous studies have suggested that lead halide perovskite NCs can possess small intrinsic dipole moments, originating from lattice distortions, asymmetric surface terminations, or non-centrosymmetric crystal facets [23,24,25]. However, in conventional film-processing methods such as spin-coating, the NCs are randomly oriented [26] and their dipole moments average out at the macroscopic scale, thus suppressing net polarization.

EPD offers a promising route to overcome this limitation by leveraging an externally applied electric field to induce both migration and alignment of the NCs during film formation. The deposition system consisted of an indium tin oxide (ITO)-coated glass substrate as the anode and a copper plate as the cathode, arranged in a parallel configuration with a spacing of 1~2 mm. The NCs were dispersed in toluene to form a stable colloidal solution. Due to the native surface ligands—oleic acid and oleylamine—the NCs carried a slight negative charge in this nonpolar solvent, enabling their electrophoretic motion toward the positively biased ITO electrode under a DC electric field (typically 500 V).

As the electric field was applied, the NCs migrated and deposited uniformly onto the ITO surface, forming continuous films over a deposition time of 30 min. The field-assisted assembly is expected to promote partial alignment of the NC dipoles along the field direction, potentially generating a net macroscopic polarization in the film. After deposition, the films were rinsed with clean toluene to remove unbound particles and dried under nitrogen. Compared to conventional solution-processing methods, EPD enables not only high-quality film formation but also enhanced structural anisotropy, both of which are expected to be critical for observing and optimizing linear EO modulation in perovskite NC systems [27,28].

According to previous studies, the morphology and surface roughness of thin films can affect their optoelectronic properties [29]. Therefore, in this study, to exclude the impact of film morphology and surface roughness on the film’s properties, we used Atomic Force Micros-copy (AFM) to characterize the surface of the film, obtaining the following data: the arithmetic mean roughness (Ra) value is 14.9594 nm, and the root mean square roughness (Rms) value is 19.1496 nm, indicating that the surface has some roughness but is generally smooth. To provide a more intuitive representation of the film’s morphology and roughness, we have included the following AFM images, as shown in Figure S1. From the images, it can be observed that the film surface exhibits some undulations but is overall relatively flat. These data demonstrate that our film has a relatively uniform and flat surface morphology, with surface roughness within an acceptable range. These results suggest that our film preparation process is effective and excludes the influence of film morphology and surface roughness on the film’s optoelectronic properties, thus meeting the experimental requirements.

To characterize the linear EO response of the electrophoretically deposited perovskite NC films, we adopted a free-space optical setup inspired by the improved Teng-Man method, as modified by Yoshito Shuto et al. [30]. A linearly polarized He-Ne laser (λ = 632.8 nm) was used as the light source. Although 1550 nm is the standard telecom wavelength, prior studies have demonstrated that 632.8 nm is effective and representative for evaluating EO coefficients in thin films [31,32].

In the setup, the laser beam first passed through a polarizer oriented at 45° with respect to the x-axis in the XOY plane, producing equal components of s- and p-polarized light. The beam was then directed at an oblique angle θ onto the film sample, which had the following configuration: ITO/SiO₂/perovskite NCs/SiO₂/ITO. A thin SiO₂ insulating layer was introduced between the NC film and the ITO electrodes to suppress current flow while maintaining an electric field across the active layer. Both ITO layers faced the NC film and were connected to a function generator providing an AC electric field normal to the film surface (along the z-axis). Under these low-voltage, high-frequency conditions, any Joule heating is negligible, confirming that the measured linear EO signal arises from the Pockels effect rather than thermal effects.

Due to the birefringent nature of the film under an applied electric field, a phase difference (Δφ_sp) arose between the s- and p-polarized components of the transmitted light. Since the induced modulation was small, Δφ_sp was computed using a linearized differential expression derived from the full birefringent phase equation. A Soleil–Babinet compensator was used to finely adjust the phase delay φ_sb between the two polarization components. The beam then passed through an analyzer oriented orthogonally to the input polarizer and was detected by a photodiode (PDA). The modulated signal was sent to a lock-in amplifier synchronized with the signal generator to extract the modulation amplitude.

When φ_sp + φ_sb = π/2, the relationship between the induced phase shift and output signal intensity simplifies to:

$$∆{\varphi }_{sp}={\displaystyle \frac{I_m}{I_c}}$$

(1)

The r₃₃ coefficient was then calculated using:

$$r_{33}={\displaystyle \frac{\mathsf{\lambda }{I}_m}{\pi I_c{U}_z}}\left[{\displaystyle \frac{r_{13}}{r_{33}}}\left({\displaystyle \frac{{n_o}^3\sqrt{{n_e}^2-{\mathrm{s}\mathrm{i}\mathrm{n}}^2\mathsf{\theta }}}{n_e}}-{\displaystyle \frac{{n_o}^4}{\sqrt{{n_o}^2-{\mathrm{s}\mathrm{i}\mathrm{n}}^2\mathsf{\theta }}}}\right)+{\displaystyle \frac{n_o{n}_e{\mathrm{s}\mathrm{i}\mathrm{n}}^2\mathsf{\theta }}{\sqrt{{n_e}^2-{\mathrm{s}\mathrm{i}\mathrm{n}}^2\mathsf{\theta }}}}\right]$$

(2)

where I_m and I_c are the modulation and carrier light intensity amplitudes, and U_z is the applied voltage.

The linear EO properties of electrophoretically deposited perovskite NC films were characterized by measuring the modulation strength under a fixed modulation frequency of 1 kHz, where all samples exhibited a linear increase in signal amplitude with applied voltage, confirming the linear EO effect, as shown in Figure 2.

The effective Pockels coefficient r₃₃ was extracted at various modulation frequencies under a constant 5 V bias. In Bi-doped CsPbCl₃, the r₃₃ value exhibited a sharp decline from 0.036 pm·V-1 to approximately 0.002 pm·V-1 with increasing frequency, corresponding to an 18-fold reduction (Figure 2a). Pristine CsPbCl₃ also showed a frequency-dependent decay, with r₃₃ decreasing from 0.486 to 0.168 pm·V-1 (around 3-fold) (Figure 2b). In I-doped CsPbBr₃ (i.e., CsPbBr_xI_3−x), the coefficient initially decreased from 2.108 pm·V-1 to 1.035 pm·V-1, followed by a moderate increase and stabilization around 1.6 pm·V-1 at frequencies above 20 kHz (Figure 2c). Similarly, Bi-doped CsPbBr₃ showed a reduction in r33 from 6.765 to ~3.6 pm·V-1 (Figure 2d), while pristine CsPbBr₃ decreased from 5.706 to ~3.0 pm·V-1 (Figure 2e). Notably, in the mixed halide system CsPbBr_xCl_3−x, a remarkably high r33 value of 103.415 pm·V-1 was observed at low frequency, which rapidly declined and stabilized around 25 pm·V-1 between 20 kHz and 60 kHz (Figure 2f).

These comparative results between doped and pristine films not only highlight the distinct frequency-dependent trends, but also allow for further insight into the role of Bi incorporation. Despite PL quenching, the EO response of Bi-doped films remained measurable, although it was clearly weaker than that of undoped counterparts. This indicates that EO modulation is primarily determined by structural symmetry and nanocrystal alignment, rather than by radiative recombination efficiency. However, the introduction of Bi-related defects likely increases scattering and trap-assisted recombination pathways [33], thereby reducing the effective nonlinear polarization and lowering the EO coefficient. A side-by-side comparison reveals that undoped CsPbBr₃ films exhibit bright PL with strong EO activity, while Bi-doped films show quenched PL and only a weakened EO response, highlighting the trade-off between defect formation and EO performance.

The high EO response observed at low frequencies, especially in halide-alloyed compositions, is likely attributed to field-induced ionic migration, which can significantly enhance polarization under slowly varying electric fields [34,35,36]. However, at higher frequencies, the ionic response becomes ineffective due to its sluggish kinetics, leading to a rapid drop in modulation efficiency and a transition to purely electronic contributions to the EO effect [35,37]. The observed linear EO response is a clear indication of broken centrosymmetry at the film scale, likely induced by partial alignment of the NCs during electrophoretic deposition. Notably, control experiments using spin-coated NC films—which lack such field-driven alignment—show no detectable linear EO response under the same measurement conditions, highlighting the critical role of EPD in enabling second-order EO activity in perovskite NC assemblies.

Notably, the high r₃₃ value observed at a low frequency in CsPbBrxCl_3−x is primarily attributed to the enhanced field-induced polarization of partially aligned nanocrystals in the EPD film. While parasitic effects such as interfacial charge accumulation, electric double layers, or capacitive coupling could potentially contribute, several factors suggest a dominant Pockels-type origin: the measurements were performed under low AC voltages (≤5 V) with frequencies above 1 kHz, no physical instability or electrochemical reactions were observed, and the cross-polarized detection with lock-in amplification effectively suppresses background signals. These conditions collectively minimize non-χ² contributions, verifying that the measured high r₃₃ reflects genuine linear EO modulation rather than artifacts.

To further probe the non-centrosymmetric nature of the electrophoretically deposited perovskite NC films, we conducted SHG measurements on CsPbBr₃ and CsPbCl₃ samples. Clear SHG signals were observed from both films, as shown in Figure 3, confirming the presence of a non-centrosymmetric component in the macroscopic structure [38]. This result suggests that the EPD process not only facilitates the formation of EO-active films but also introduces a degree of asymmetry in the ensemble of NCs, potentially through field-assisted assembly or interfacial effects. The detection of SHG—absent in centrosymmetric media—supports the intrinsic nonlinearity observed in linear EO measurements and reinforces the hypothesis that symmetry breaking during film formation is crucial for the emergence of both χ²-related effects [39]. Notably, the SHG response was reproducible and stable under moderate excitation conditions [40], implying robust structural characteristics introduced by the EPD method.

Although this study primarily focuses on the electro-optic modulation applications of CsPbX₃ perovskite nanocrystal films, these materials inherently possess excellent photophysical properties, granting them significant potential in the field of photodetection. CsPbX₃ perovskite nanocrystals exhibit characteristics such as high absorption coefficient, size- and composition-tunable bandgap, and highly efficient photoluminescence, all of which are fundamental requirements for constructing high-performance photodetectors. By comparing with the outstanding performance of FeBHT photodetectors [41], we can infer the versatile potential of this material system in photodetection. The high absorption coefficient and efficient photoluminescence of CsPbX₃ nanocrystals indicate their excellent light-harvesting capability, which is analogous to the role of FeBHT materials as light-absorbing layers in photodetectors. Considering the superior photoelectric conversion efficiency of CsPbX₃ perovskites, with appropriate device design and optimization—such as through controlling nanocrystal alignment and interface engineering—they are expected to achieve high responsivity and specific detectivity comparable to FeBHT in photodetectors. Regarding stability, although the stability of organic–inorganic hybrid perovskites has been a persistent challenge, all-inorganic cesium lead halide perovskites (e.g., CsPbBr₃) generally demonstrate better environmental stability compared to hybrid perovskites [42], enabling the development of long-term stable photodetectors.

3. Conclusions

In summary, we demonstrate linear EO modulation in EPD films of CsPbX₃ (X = Cl, Br, I) perovskite NCs, made possible by field-assisted dipole alignment during deposition, which breaks centrosymmetry across the ensemble. All samples exhibit a decreasing EO response with increasing modulation frequency, indicating that ion migration contributes significantly at lower frequencies but is suppressed at higher frequencies. Notably, the Br/Cl-alloyed NC films show the highest EO modulation under high-frequency driving fields. In contrast, CsPbCl₃ based samples show a negligible EO response, likely due to the absence of dipole formation or suppressed alignment. Spin-coated films also lack EO modulation, highlighting the importance of electric-field-guided assembly in generating nonlinear optical activity. These results reveal the critical roles of dipole alignment and ionic behavior in tuning the EO properties of perovskite NCs, providing valuable insights for designing next-generation nanomaterial-based EO devices.