Halide perovskites have revolutionized photovoltaics with their exceptional optoelectronic properties, primarily optimized through interfacial engineering in solar cells. However, as performance approaches the theoretical limits of conventional p-n junction physics, there is a pressing need to explore alternative photovoltaic mechanisms. This study investigates the flexo-photovoltaic (FPV) effect—a bulk photovoltaic effect (BPVE) driven by strain gradients—in methylammonium lead halide perovskites (MAPbBr3 and MAPbI3). The research demonstrates that these materials exhibit an FPV effect orders of magnitude larger than the benchmark oxide SrTiO3 and, crucially, can generate photovoltages exceeding their own bandgap under sufficient strain gradients. This work suggests that strain gradient engineering could provide a new functional paradigm for enhancing the performance of halide perovskite devices beyond traditional limits.
Understanding the flexo-photovoltaic effect requires grounding in fundamental symmetry principles and existing photovoltaic mechanisms.
A net directional flow of photo-generated charge carriers (photocurrent) requires the breaking of spatial inversion symmetry. In conventional solar cells, this symmetry breaking occurs at the p-n junction interface, separating electron-hole pairs.
In certain non-centrosymmetric (e.g., piezoelectric) crystals, spatial inversion symmetry is broken intrinsically within the bulk material. Illumination can generate a steady-state photocurrent, known as the bulk photovoltaic effect, without the need for a junction. The shift current, a major mechanism, can be described phenomenologically.
Flexoelectricity is a universal property where a strain gradient ($\nabla \epsilon$) induces a polarization ($P$) in any dielectric material: $P_i = \mu_{ijkl} \frac{\partial \epsilon_{jk}}{\partial x_l}$, where $\mu$ is the flexoelectric tensor. Bending a crystal creates such a gradient, breaking symmetry and enabling a strain-gradient-driven BPVE, i.e., the flexo-photovoltaic effect. This effect is theoretically possible in any material under bending.
Single crystals of MAPbBr3 (MAPB) and MAPbI3 were synthesized. Commercial SrTiO3 (STO) single crystals served as a flexoelectric benchmark. Symmetric capacitor structures were fabricated by depositing identical Au electrodes on opposite faces of the crystals.
Crystals were mechanically bent to apply a controlled strain gradient. Lateral illumination (405 nm LED for MAPB, 365 nm for STO) ensured that interface-related photovoltaic contributions from the two symmetric electrodes canceled out, isolating the bulk effect. Photovoltage was measured as a function of bending curvature (strain gradient) and light intensity (up to 1000 LUX).
Halide Perovskites >> SrTiO3
> Bandgap Achievable
FPV + Native BPVE
The measured flexo-photovoltaic effect in MAPbBr3 and MAPbI3 was found to be orders of magnitude larger than that in the reference oxide SrTiO3. This highlights the exceptionally strong coupling between strain gradients and charge separation in halide perovskites, attributed to their high dielectric constants and ionic mobility, which enhance flexoelectric coefficients.
A landmark finding is that for sufficiently large applied strain gradients, the generated photovoltage can exceed the material's bandgap voltage ($V_{ph} > E_g / e$). This violates the traditional Shockley-Queisser limit for single-junction solar cells, which is based on junction physics, and demonstrates the fundamentally different and potentially superior ceiling of bulk-effect-based energy conversion.
In MAPbI3, the flexo-photovoltage was superimposed on a pre-existing, hysteretic native bulk photovoltage. This hysteresis is consistent with the material's electrically switchable macroscopic polarization, suggesting a coupling between ferroelectric (or ferroelectric-like) domains and the photovoltaic response. The effects are additive, showcasing the potential for multi-mechanism enhancement.
The flexo-photovoltaic current density $J_{FPV}$ can be phenomenologically linked to material properties and experimental parameters:
$J_{FPV} \propto \beta \cdot I \cdot \nabla \epsilon$
Where $\beta$ is a material-specific FPV coefficient encapsulating the flexoelectric tensor and charge carrier transport properties, $I$ is the light intensity, and $\nabla \epsilon$ is the strain gradient. The open-circuit photovoltage $V_{oc}$ is related to this current and the sample's internal resistance. The condition for above-bandgap photovoltage implies that the product $\beta \cdot \nabla \epsilon$ in these perovskites can be large enough to drive carriers against a potential difference greater than $E_g/e$. The hysteretic response in MAPbI3 suggests a time-dependent polarization $P(t)$ that modifies the internal field: $J_{total} \propto (\beta_{FPV} \cdot \nabla \epsilon + \gamma \cdot P(t)) \cdot I$, where $\gamma$ is a coupling coefficient.
Framework for Evaluating Novel PV Mechanisms:
Case Study Application: Applying this framework to the presented paper clearly shows its execution: symmetric structures isolated the bulk effect, bending controlled $\nabla \epsilon$, STO provided a benchmark, and the discovery of >$E_g$ $V_{oc}$ was a result of limit testing. The hysteretic behavior prompted an investigation into the native polarization state.
This isn't just an incremental efficiency bump; it's a paradigm attack on the Shockley-Queisser limit. The authors have effectively weaponized a material's mechanical deformation—a factor typically considered a reliability nightmare—to generate photovoltages that theoretically shouldn't be possible in a single-phase material. They've moved the battle for higher efficiency from the nano-engineering of interfaces to the macro- and micro-engineering of strain fields. The implications are profound: if the ceiling for single-junction Si is ~29%, and for perovskites is ~31%, a mechanism unbound by detailed balance opens a new, undefined ceiling.
The logic is razor-sharp and reductionist. 1) Need new PV physics beyond junctions. 2) Bulk effects like BPVE are an alternative. 3) Flexoelectricity can induce a BPVE (FPV) in any bendable material. 4) Halide perovskites are champion PV materials and known to be highly flexoelectric. 5) Therefore, test their FPV. 6) Result: It's monstrously large and can break the bandgap voltage barrier. The chain of reasoning is airtight, transforming a theoretical curiosity (FPV in oxides) into a potentially disruptive technology in the hottest PV material family.
Strengths: The experimental design is elegant in its simplicity for isolating the effect. The >$E_g$ result is a headline-grabbing, unambiguous validation of the concept's potential. Using STO as a benchmark provides crucial context. The observation of additivity with native polarization in MAPbI3 hints at a rich playground for multi-physics optimization.
Flaws & Gaps: This is a single-crystal, fundamental science study. The elephant in the room is practical implementation. How do you introduce large, controlled, and stable strain gradients into a thin-film solar cell on a flexible substrate without causing fatigue or fracture? The paper is silent on power conversion efficiency (PCE) metrics—generating a high voltage is one thing, but extracting useful power (current x voltage) is another. The stability of the effect under continuous illumination and mechanical cycling is completely unaddressed, a critical omission for any real-world application.
For researchers: The immediate next step is to demonstrate this in thin films. Partner with groups skilled in strain engineering (e.g., using mismatched substrates, core-shell nanoparticles, or patterned stressor layers). Measure the full J-V curve and report a FPV-contributed PCE. Explore other hybrid perovskites and 2D variants which may have even higher flexoelectric coefficients.
For investors: This is a high-risk, high-reward, early-stage bet. Do not expect commercial devices in the next 5 years. However, fund the teams that are tackling the materials integration and mechanical engineering challenges. The IP around methods for embedding designed strain gradients into PV modules could be immensely valuable if the efficiency claims hold up at scale.
For the industry: View this as a long-term strategic option. Continue optimizing interfacial perovskite solar cells (PSCs) for near-term deployment, but allocate a small, agile R&D team to track and experiment with bulk-effect concepts. The potential payoff—a solar cell with a fundamentally higher efficiency limit—justifies a portfolio approach.