Persistent Photoluminescence Superlinearity Beyond Static Recombination Physics in Metal Halide Perovskites

Researchers studying metal halide perovskites have found that a familiar optical measurement—how photoluminescence intensity rises with excitation strength—does not behave like a fixed indicator of recombination order in these materials. In MAPbI3 thin films, the intensity repeatedly followed an intermediate power law with an exponent above one, but the exponent changed reproducibly with excitation wavelength, temperature, illumination history and carrier density. Time-resolved measurements showed that the conditions producing stronger superlinearity also increased the lifetime and relative strength of delayed emission.

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