Resonant Multiple-Phonon Absorption Causes Efficient Anti-Stokes Photoluminescence in CsPbBr₃ Nanocrystals

Abstract

Lead halide perovskite nanocrystals, such as CsPbBr 3 , exhibit efficient photoluminescence (PL) up-conversion, also referred to as anti-Stokes photoluminescence (ASPL). This is a phenomenon where irradiating nanocrystals up to 100 meV below gap results in higher energy band edge emission. Most surprising is that ASPL efficiencies approach unity and involve single-photon interactions with multiple phonons. This is unexpected given the statistically disfavored nature of multiple-phonon absorption. Here, we report and rationalize near-unity anti-Stokes photoluminescence efficiencies in CsPbBr 3 nanocrystals and attribute them to resonant multiple-phonon absorption by polarons. The theory explains paradoxically large efficiencies for intrinsically disfavored, multiple-phonon-assisted ASPL in nanocrystals. Moreover, the developed microscopic mechanism has immediate and important implications for applications of ASPL toward condensed phase optical refrigeration.

Thermal Activation of Anti-Stokes Photoluminescence in CsPbBr3 Perovskite Nanocrystals: The Role of Surface Polaron States

“…These trends further indicate the complex spectral dependence of quantum yield for ASPL. This data appears to be consistent with observations made by Zhang et al of decreases in the efficiency of up-conversion as excitation is detuned from the band edge of surface-deposited CsPbBr 3 NC samples . Additionally, the smooth exponential decay in ASPL suggests a continuum of sub-gap states, as opposed to a single discrete electronic state assisting in up-conversion.…”

“… ,, However, when excitation is further red-shifted, the much smaller cross section for two-photon absorption becomes relatively significant, so that the power law for up-converted photoluminescence gains superlinear character. As reported by Grandados del Águila et al, and observed in studies in our laboratory (see Figure S4), two photon up-conversion starts to become significant when exciting between 150 and 200 meV below-gap. , When sub-gap excitation decreases in energy there is an exponential decrease in ASPL intensity (see Figure A). For excitation energy with small detuning, where two-photon process does not contribute, throughout the spectral region known as the Urbach tail, it is reasonable to expect that the spectral-dependent decrease in ASPL intensity may simply be proportional to the exponential decrease in absorbance.…”

“…The prevalence of polarons in perovskites has been widely discussed, ,, and polarons have previously been proposed as assisting in CsPbBr 3 NC up-conversion. ,, Previous measurements have identified distortions of the PbBr 6 octahedral as being most often associated with polaron formation. ,, Though it is difficult to ascribe a single phonon mode to the up-conversion mechanism as the Δ E s which are attained are much greater than any single phonon-mode measured in CsPbBr 3 NCs. Therefore, several researchers have proposed that up-conversion is the result of a multiphonon process. , Prior studies have suggested that STEs are the particular class of MGP states that facilitate ASPL up-conversion in CsPbBr 3 NCs . STEs are localized distortions in the crystal lattice, induced by light, that stabilize bound excitons in ionic materials with strong electron–phonon coupling.…”

“…Although optical cooling has been demonstrated in CsPbBr 3 NCs, there remains a lack of understanding regarding the ASPL mechanism, so the theoretical cooling limits and possible paths toward optimization are unclear. Initial models of ASPL in CsPbBr 3 and other semiconductor nanostructures that show ASPL have assumed that sub-gap optical excitation promotes photocarriers to a mid-gap state, followed by thermalization to the conduction or valence band edge that is mediated via electron–phonon coupling. , The energy gains possible during ASPL are greater than any single phonon mode that has been measured in CsPbBr 3 NCs so it is believed to be a multiphonon process. , The precise nature of the sub-gap state which assists ASPL is disputed. Though there is evidence that shallow defect states or surface states associated with dangling bonds, energetically within the band gap, can promote ASPL in similar material systems, ,,,, our previous research has shown that ASPL efficiency increased by as much as a factor of 3 when CsPbBr 3 NCs were treated post-synthetically to reduce trap states and defects .…”

The Impact of Partial Carrier Confinement on Stimulated Emission in Strongly Confined Perovskite Nanocrystals

“…An aspect of lead halide perovskites that attracts extensive interest is the strong coupling between charge carriers and the crystal lattice. Several studies have argued that electron–phonon coupling in lead halide perovskites leads to the formation of small polarons, i.e., a composite quasi-particle consisting of a charge carrier and a local lattice distortion. − Considering the Frölich interaction, which assigns electron–phonon coupling to Coulomb interactions between charge carriers and the lattice ions as the most important contribution, polaron formation was first interpreted in terms of displacements of the organic cations . Later work, however, highlighted the coupling of charge carriers with the inorganic sublattice and related polaron formation to distortions of the PbX 6 octahedra. ,, This interpretation accounts for the rapid, sub-picosecond polaron formation , and agrees with changes of the X-ray absorption spectrum after photoexcitation. , Interestingly, both time-resolved X-ray absorption spectra and several computational studies indicated a marked difference in localization between a large electron-polaron and a small hole-polaron. − Moreover, it was argued that this distinction is preserved in an electron–hole pair or excitonthe typical unit formed by photoexcitationand this finding was related to the smaller-than-expected electron–hole recombination rate in lead halide perovskites …”