The authors interpret this joint behavior as evidence that the apparent scaling is shaped by an evolving, nonequilibrium environment in the perovskite lattice, rather than solely by competition among static recombination pathways. In a common analysis, PL intensity is fitted to a power law, I PL proportional to P β , where P represents excitation power and β is the scaling exponent. Classical recombination theory links limiting values to carrier-loss processes: first-order trap or surface recombination can yield β near 2 at low excitation, direct bimolecular radiative recombination gives a slope near 1 at higher densities, and nonradiative Auger recombination can produce sublinear behavior when carrier densities become very high.

Intermediate exponents can occur when several mechanisms overlap, so superlinearity alone does not identify one uniquely defined process. That ambiguity matters because metal halide perovskites combine strong light absorption, long carrier diffusion lengths, tunable bandgaps and comparatively low nonradiative losses. Their soft lattices also support strong carrier–phonon coupling, dynamic disorder, anharmonic motion and comparatively slow vibrational dissipation.

These traits make them promising absorbers and emitters, but they also mean that photoexcited carriers relax in a material environment that may not remain static. The study therefore asks whether β can behave as an effective, condition-dependent observable rather than a direct label for recombination order. The researchers propose a phenomenological description in which energy deposited into the lattice through carrier–phonon interactions creates transient, spatially heterogeneous states that remain coupled to the evolving electronic system.

Power-dependent PL measurements on MAPbI3 films revealed intermediate superlinear scaling across the measured range, but β varied systematically with excitation conditions. At room temperature, increasing the excitation wavelength from 375 to 405 and 560 nm increased β. The corresponding optical penetration depths rose from about 22 to 31 and 67 nm, respectively.

Short-wavelength light therefore places more weight on the illuminated surface, where surface-associated losses, local defects and energetic disorder can influence relaxation, whereas longer wavelengths sample more of the film interior. This spatial shift could alter trap filling, carrier redistribution and the balance between surface and bulk losses. However, the accompanying time-resolved PL results showed that deeper excitation also lengthened delayed emission, linking the scaling behavior to the temporal recovery of carriers rather than only to where they were initially generated.

Temperature supplied another constraint. Under both 405 and 560 nm excitation, β increased as the films cooled from 293 to 180 K. The trend is compatible with a distributed-trap picture: reduced thermal escape can keep carriers in trap states longer and change the apparent PL slope under Shockley–Read–Hall statistics.

Yet cooling also changes how excitation energy moves among phonons, vibrational modes and structural degrees of freedom. The measurements remained above MAPbI3’s reported tetragonal-to-orthorhombic transition near 163 K, excluding that low-temperature phase transition as the primary origin of the observed trend. The authors’ interpretation instead allows trap-mediated carrier dynamics and temperature-dependent lattice relaxation to evolve concurrently, with changes in detrapping, vibrational redistribution and energy dissipation all affecting the environment in which radiative recombination occurs.

Prolonged illumination separated brightness from scaling even more clearly. After 10 minutes of continuous illumination, MAPbI3 emitted more light across the measured excitation range, while its fitted exponent decreased from β = 1.42 to β = 1.36. Thus, stronger absolute emission did not mean that the response had moved toward a more quadratic dependence on excitation.

The emission maximum also underwent a small systematic redshift while its linewidth changed only modestly, an observation consistent with an alteration of the energetic environment from which radiative recombination occurred. The source does not assign this behavior to a single microscopic cause; possible contributors include trap occupation, ionic redistribution, local structural relaxation, strain and carrier–lattice interactions. What the measurements establish is that prolonged excitation changes both the measured output and its dependence on excitation power.

Illumination history remained important after the excitation was removed. Measurements on FA 0.8 MA 0.2 PbI 3 showed that PL levels and normalized temporal trajectories after 30 and 60 minutes in the dark still reflected earlier illumination under 405, 520 and 620 nm excitation. The persistence far beyond the photocarrier lifetime indicates that some material degree of freedom survives electronic recombination.

The authors do not claim that a single “stored lattice energy” reservoir has been directly observed. Instead, the response may reflect coupled evolution of defects, ions, local structure and vibrational redistribution, none of which can be separated conclusively by the reported measurements. The persistence of the response after dark storage therefore provides evidence for a slowly evolving material state, while leaving its microscopic composition unresolved.

Time-resolved PL supplied the clearest link between steady-state scaling and carrier recovery. Pulsed measurements used 375 or 405 nm light, an approximately 1 MHz repetition rate, a 256 ps channel width and a 972.8 ns observation window. Biexponential fits separated a fast component from a slower emissive component, with the slow lifetime reaching roughly 100 ns in the longest fitted cases.

At room temperature under 405 nm excitation, both the slow lifetime and the ratio of slow to fast amplitude increased with excitation density. Cooling produced the same changes, while deeper 405 nm excitation generated longer-lived and more prominent delayed emission than 375 nm excitation. These trends differ from the straightforward lifetime shortening often associated with increasing bimolecular or Auger recombination at higher carrier density.

The slow component instead became longer-lived and more prominent under the same conditions that strengthened the intermediate steady-state superlinearity. The proposed framework treats the measured PL as a combination of a conventional radiative term and a second contribution associated with the evolving lattice environment. In the phenomenological expression given by the researchers, I PL ( P ) = K 1 P 2 + ε K 2 P μ , with ε representing the state-dependent contribution and μ expected between first- and second-order limits.

The coefficients are not independently measured microscopic quantities, and the authors do not use their amplitudes for quantitative comparisons among conditions. Instead, the model captures how a changing balance between ordinary free-carrier emission and delayed, lattice-conditioned recovery can produce apparent β values that do not settle at a single fixed order. The framework does not discard trap-assisted recombination; rather, it proposes that trapping, detrapping and radiative recovery can themselves occur within a photoexcited environment whose vibrational and structural degrees of freedom continue to evolve.

The interpretation remains a framework rather than a direct microscopic identification. The experiments did not image the proposed nonequilibrium regions or measure their intrinsic relaxation times, and they do not show that phonon recycling alone causes the effect. Conventional diffusion also appears too fast to account for minute-scale illumination memory: using MAPbI3’s reported thermal diffusivity of about 2.8 × 10 −7 m 2 s −1 , diffusive times for 10–100 nm structures are roughly 0.4 nanoseconds to 40 nanoseconds, much shorter than the observed history effects.

The proposal instead concerns coupled vibrational, structural and electronic degrees of freedom. Its clearest expected applicability is to soft hybrid perovskites with effectively quadratic free-carrier recombination; in strongly doped, minority-carrier-limited or exciton-dominated systems, the authors expect the mechanism to weaken or disappear. For perovskite researchers, the practical implication is that a single β value cannot safely be treated as an intrinsic measure of radiative efficiency or defect tolerance: it must be interpreted alongside excitation wavelength, temperature, illumination history, spatial generation profile and time-resolved dynamics.

Persistent superlinear PL in soft metal halide perovskites is therefore consistent with radiative recovery occurring inside a photoexcited environment that continues to evolve, making β a window onto coupled carrier–lattice relaxation rather than a fixed verdict on which recombination channel dominates.

Subject of Research: Excitation-dependent photoluminescence superlinearity and carrier–lattice relaxation in MAPbI3 perovskite thin films.

Article Title: Persistent Photoluminescence Superlinearity Beyond Static Recombination Physics in Metal Halide Perovskites

Article References: Ghasemi, M., Li, Q., Jia, B., & Wen, X. (2026). Persistent Photoluminescence Superlinearity Beyond Static Recombination Physics in Metal Halide Perovskites. Advanced Science, Article e78378. https://doi.org/10.1002/advs.78378

Image Credits: AI Generated

DOI: 10.1002/advs.78378

Keywords: metal halide perovskites, MAPbI3, photoluminescence, superlinear scaling, carrier–lattice coupling, nonequilibrium relaxation, time-resolved luminescence, trap-mediated recombination, illumination history, soft lattices, Persistent, Superlinearity

The team, led by Zeinab PourMohammadi, Fatemeh Dehghan Nayeri, and Rouhollah Azimirad, focused on a heterojunction device that sandwiches the archetypal perovskite methylammonium lead iodide, known as MAPbI3, on top of p-type silicon. Silicon remains the backbone of the photovoltaic and optoelectronic markets thanks to its abundance, stability, and excellent electronic properties, but forming traditional silicon junctions requires high-temperature doping processes and sophisticated equipment. Pairing silicon with metal halide perovskites offers a cheaper, low-temperature alternative. MAPbI3, a crystalline material with the general ABX3 perovskite formula, brings direct-bandgap light absorption, low exciton binding energy, long carrier diffusion lengths, and simple solution processing to the partnership. In principle, the combination should harness the best of both materials.

In practice, however, the marriage has a persistent flaw. When silicon and perovskite are pressed directly against each other, mismatched energy band alignment creates a poor electrical contact. Photoexcited charge carriers recombine at the interface before they can be collected, squandering the very light the device is meant to detect. The standard remedy is a buffer layer, a thin film that bridges the two dissimilar materials and smooths out the energetic landscape. Previous studies have tested metal oxides such as tin dioxide, gallium oxide, and titanium dioxide in this role, each with its own trade-offs between dark current, recombination, and tunneling efficiency.

The new study takes a different route by turning to PEDOT:PSS, the workhorse hole-transport polymer of the perovskite world. This material is a polymer electrolyte with a split personality: positively charged PEDOT is highly conductive but water-insoluble, while negatively charged PSS is insulating but acts as a surfactant that lets PEDOT disperse in water. The two components naturally form a micelle-like structure, with conductive PEDOT cores wrapped in nonconductive PSS shells. Crucially for the new work, the arrangement of these components is not fixed. During spin-coating, the denser, hydrophobic PEDOT phase settles toward the bottom of the film while the hydrophilic PSS-rich phase accumulates at the surface, and a mild 120-degree-Celsius bake does not remix them.

The researchers exploited this segregation with an elegantly simple modification: instead of depositing a single PEDOT:PSS layer spun at 2000 rpm, they applied two consecutive coatings, first at 1500 rpm and then at 2000 rpm, with no chemical additives of any kind. Each new spin-coating cycle exposes the PSS-rich surface to water, which partially washes it away and replaces it with the conductive PEDOT-rich phase. With every additional layer, the stack becomes richer in PEDOT at the bottom and leaner in insulating PSS, driving down sheet resistance without a proportional increase in thickness. The resulting bilayer measured about 100 nanometers total, barely thicker than the roughly 90-nanometer single layer, yet its conductivity was inferred to be substantially higher.

The benefits rippled far beyond simple conductivity. Scanning electron microscopy revealed that perovskite films grown on the modified bilayer contained far fewer pinholes than films grown on pristine PEDOT:PSS, which itself performed worse than bare silicon in this respect. The explanation lies in surface physics: multiple coatings increase the roughness of the polymer layer, and according to the Wenzel equation, roughness enhances wettability. Better wetting lowers the energy barrier for perovskite nucleation, creating more nucleation sites and a more complete, pinhole-free film. Pinholes matter enormously because they introduce trap states and shunt paths that degrade carrier lifetime and cause leakage, so suppressing them directly improves device quality.

Structural analysis told a consistent story. X-ray diffraction confirmed the tetragonal MAPbI3 phase in all samples, with the characteristic (110) preferred orientation, but films grown on PEDOT:PSS interlayers showed sharper peaks and larger crystallites. Using the Williamson-Hall method, the team extracted crystallite sizes of about 99 nanometers for films on both pristine and modified PEDOT:PSS, compared with only 55 nanometers for perovskite grown directly on silicon, which also carried a compressive microstrain. Larger grains mean fewer grain boundaries, less carrier scattering, and less recombination. Notably, the telltale diffraction peaks of residual lead iodide, prominent in the silicon-only sample, were strongly suppressed by the interlayer, suggesting the acidic polymer promotes complete conversion of precursors into the perovskite phase, a factor linked to better device stability.

Optical and electrical measurements sealed the case. Photoluminescence from the perovskite was strongly quenched on the interlayer samples, indicating efficient extraction of photoexcited carriers by the built-in electric field at the heterojunction, with the modified layer outperforming all alternatives. A blue shift in the emission peak further hinted at reduced trap density near the band edges. Under 530-nanometer laser illumination at a modest intensity of 0.3 milliwatts per square centimeter, all devices showed rectifying behavior from the built-in field, but the champion device with the modified interlayer delivered a photocurrent roughly 170 times greater than the interlayer-free control at a reverse bias of 5 volts. The device achieved a responsivity of 0.78 amperes per watt and a detectivity of 4.9 times ten to the eleventh Jones, figures that compare competitively with recent perovskite-based photodetectors, many of which required far more elaborate fabrication.

The authors are careful to frame the work as a proof of concept. Direct carrier-lifetime measurements were not performed, and long-term stability testing remains a key direction for future investigation, particularly because the hygroscopic nature of PEDOT:PSS is a known degradation risk for MAPbI3 devices. Even so, the bilayer design offers two plausible stability advantages: the reduced PSS content should make the polymer less hydrophilic, and the denser perovskite film should limit moisture ingress into the bulk. If those predictions hold up, the implications are significant. A photodetector that combines silicon’s maturity with perovskite’s optical prowess, assembled from solution at room temperature with a modification as simple as spinning the same material twice, points toward scalable, low-cost hybrid optoelectronics in which the trade-off between performance and processability is decisively rebalanced.

Subject of Research: Enhancement of silicon/MAPbI3 heterojunction photodetectors using a modified bilayer PEDOT:PSS interlayer

Article Title: Improving photodetection ability of Si/MAPbI 3 heterojunction by using modified PEDOT:PSS interlayer

Article References: PourMohammadi, Z., Nayeri, F. D., & Azimirad, R. (2026). Improving photodetection ability of Si/MAPbI3 heterojunction by using modified PEDOT:PSS interlayer. Results in Optics, Article 101177. https://doi.org/10.1016/j.rio.2026.101177

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101177

Keywords: photodetector, perovskite, silicon, PEDOT:PSS, MAPbI3, heterojunction, interlayer, spin coating, responsivity, detectivity, thin films, optoelectronics