Hot carrier cooling mechanisms in halide perovskites

Barium stannate (${\mathrm{BaSnO}}_{3}$) is an emerging perovskite oxide with promising properties for many potential applications. One of the most outstanding properties is the high-room-temperature electron mobility. The extraordinary superior electronic transport performance has attracted great attention but the research is limited by semiempirical assumptions. In this work, the first-principles calculations are employed to study the electronic transport of ${\mathrm{BaSnO}}_{3}$ by solving the Boltzmann transport equation (BTE) with full information on electron, phonon, and electron-phonon interactions taken into account. The mode-resolved analyses of scattering rates show that the longitudinal optical (LO) phonons dominate the scattering processes not only at low but also at high carrier concentrations. As a consequence, the energy relaxation time approximation significantly underestimates the solution of BTE due to the divergent coupling coefficient of electrons and LO phonons. The drift and Hall mobilities are calculated in the framework of BTE in the presence of electric and magnetic fields. At low concentration limits, the room-temperature drift and Hall mobilities are 357 and $418\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, respectively, while the Hall factor is temperature dependent with values between 1.06 and 1.17 in the temperature range of 100 K to 800 K. In the doping system with carrier concentration above $1\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, the upper limit of drift mobility is $377\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ at room temperature, and the Hall factor becomes smaller than 1, which cannot be revealed by the formula under the isotropic parabolic assumption at all, indicating the importance of magnetic transport calculation from ab initio based BTE.

Hot-carrier solar cells can achieve higher efficiency by utilizing excess carrier energy before thermalization. The hot-phonon bottleneck delays phonon decay and allows their reabsorption by carriers, delaying carrier cooling and retaining excess energy. This study investigates the hot-phonon bottleneck effect and biphasic cooling dynamics in CsPb(Cl/Br)3 perovskite quantum dots. We modeled time-resolved emission spectra to analyze carrier cooling dynamics. At high carrier densities, the cooling curves revealed two distinct phases. Phase I, driven by Fröhlich interactions, exhibits cooling times independent of carrier density, indicating a constant average number of longitudinal optical (LO) phonon emission per carrier. Similarly, phase II, influenced by the hot-phonon bottleneck, also displayed cooling times unaffected by carrier density. However, the overall average cooling time increased with increasing carrier density due to a fluence-dependent amplitude for phase II. Increased LO phonon lifetimes at high carrier densities facilitate their reabsorption by carriers, delaying cooling. These findings elucidate the dual-phase cooling dynamics and, more importantly, their carrier-density-independent rates, offering critical insights into slow carrier cooling necessary for hot-carrier solar cell advancement.

The hot phonon bottleneck (HPB) effect has been proposed as one of the main phenomena behind the slow cooling in metal halide perovskites. Even though consensus has been reached regarding its existence, open questions remain concerning the HPB's specific applicability and potential regarding hot carrier solar cell (HCSC) applications. We present a full investigation using ensemble Monte Carlo simulations of the HPB effect in metal halide perovskites (MHP). After describing the HPB effect in detail, we quantify how the HPB effect can extend carrier cooling times by orders of magnitude. We show how the HPB effect depends on carrier concentration, longitudinal optical (LO) phonon lifetime, and LO phonon frequency and connect these findings to how MHPs should be tuned concretely. Using ensemble Monte Carlo simulations, we can accurately model the interplay between carrier-phonon and carrier-carrier interactions up to high carrier density, yielding precise predictions regarding the HPB effect. This study provides important insights into the governing dynamics behind the HPB effect and shows how cooling times can be extended far beyond the phonon lifetime. Furthermore, it contributes to the discussion on cooling times in MHPs and their suitability for HCSC applications.

Organic–inorganic halide perovskite has emerged as the front-runner of absorber materials for highly efficient solar cell in recent years. The incorporation of metallic (Au, Ag) nanoparticles (NPs) within the perovskite contributes to the effective tuning of their optoelectronic properties via enhancing the channels of solar energy transfer and promoting carrier transport. Placing a dielectric shell over the metal NP further enhances the carrier mobility and reduces the carrier recombination in the semiconductor material. Here, we have extensively investigated the effect of the Au@CZTS core–shell nanocrystal (NC) on hot carrier (HC) cooling dynamics and excited carrier recombination dynamics in bulk MAPbI3−X Cl X perovskite using femtosecond transient absorption spectroscopy with a temporal and spectral resolution of 120 fs and 0.8 nm respectively. The HC cooling dynamics indicates the formation of longitudinal optical (LO) phonons within the first 0.6 ps and a delayed conversion of LO phonons to longitudinal acoustic (LA) phonons from 8 ps to 15.9 ps due to the incorporation of the Au@CZTS core–shell NC in bulk perovskite. Further, the investigation of carrier recombination dynamics shows that at a fixed pump fluence of 3.19 μJ cm −2 the rate constants decrease nearly 1 order of magnitude for (a) Auger recombination (from 1.2 × 10−32 cm6 s−1 to 1.7 × 10−34 cm6 s−1), (b) band-to-band recombination (from 8 × 10−14 cm3 s−1 to 8 × 10−15 cm3 s−1) and (c) trap state recombination (from 5.5 × 108 μs−1 to 5 × 107 μs−1) after the modification of bulk perovskite by Au@CZTS core–shell NC. Delayed conversion of LO phonons to LA phonons confirms the presence of an enhanced ‘hot phonon bottleneck’ effect in modified bulk perovskite. Lowering of the recombination rate constants provides an opportunity for developing high-performance perovskite-based photovoltaics.

Hot-carrier cooling processes of perovskite materials are typically described by a single parabolic band model that includes the effects of carrier-phonon scattering, hot phonon bottleneck, and Auger heating. However, little is known (if anything) about the cooling processes in which the spin-degenerate parabolic band splits into two spin-polarized bands, i.e., the Rashba band splitting effect. Here, we investigated the hot-carrier cooling processes for two slightly different compositions of two-dimensional Dion–Jacobson hybrid perovskites, namely, (3AMP)PbI4 and (4AMP)PbI4 (3AMP = 3-(aminomethyl)piperidinium; 4AMP = 4-(aminomethyl)piperidinium), using a combination of ultrafast transient absorption spectroscopy and first-principles calculations. In (4AMP)PbI4, upon Rashba band splitting, the spin-dependent scattering of hot electrons is responsible for accelerating hot-carrier cooling at longer delays. Importantly, the hot-carrier cooling of (4AMP)PbI4 can be extended by manipulating the spin state of the hot carriers. Our findings suggest a new approach for prolonging hot-carrier cooling in hybrid perovskites, which is conducive to further improving the performance of hot-carrier-based optoelectronic and spintronic devices.

Slow hot carrier (HC) cooling resulting from hot phonon bottleneck has been widely demonstrated in metal halide perovskites. Although manipulating HC kinetics in these materials is of both fundamental and technological importance, this task remains a daunting challenge. Here, via interfacial engineering, i.e., epitaxial growth of Cs4PbBr6 on CsPbBr3 nanocrystals (NCs), we have revealed an obvious shortening of HC cooling times, evidenced by transient absorption and ultrafast PL spectra. Collaborated with the longitudinal optical (LO) phonon model, theoretical calculations verify the breaking of the hot phonon bottleneck in CsPbBr3@Cs4PbBr6 and identify the interfacial electron-LO phonon coupling as the leading mechanism for the observed large tuning of HC cooling times. Especially, the participation of LO phonons from Cs4PbBr6 enables the efficient Klemens channel for hot phonon decay. Our findings establish an effective method to tailor HC dynamics in perovskite NCs, which could be conducive to improving the performance of optoelectronic applications.

Evidence of auger heating in hot carrier cooling of CsPbBr3 nanocrystals

Dynamic screened scattering rate of polar optical phonons has been calculated for electrons in the central valley of GaN at moderate carrier concentrations around 3 24 10 2 m x. Our calculations used the Lindhard formalism with Fermi-Dirac distribution and with neglecting the collisional damping.Also, for simplicity nonparabolicty and the coupling between various electrons and hole have been neglected.The inverse of the dielectric function showed antiscreening peak at small phonon wave vector at carrier temperature 77 K and 300K.The screened scattering rate is strongly enhanced at low electron temperature and high carrier concentrations.This is due to antiscreening property of inverse dielectric function which appears in both emission and absorption screened optical phonons.The principle purpose of this study is too showing how the various parameters, such as carrier concentrations and carrier temperature, could change the shape of dynamic screened scattering rate of polar optical phonons.

Micro-Raman imaging measurements of $n$-type $4H\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}$ crystals with graded donor concentration were carried out, and spatial distributions of the free carrier concentration, carrier mobility, and longitudinal optical (LO) phonon damping were obtained from a line shape analysis of the LO phonon-plasmon coupled (LOPC) mode. The damping of free carriers and optic phonons was determined as a function of free carrier density. We obtained an empirical relationship between carrier concentration and relative Raman shift of the LOPC mode, which is in close agreement with the relationship calculated for the damping-free coupled mode. It is found that the LO phonon damping deduced from the analysis increases linearly with carrier concentration. This LO mode behavior is mainly attributed to the interaction of the LO phonon and ionized impurities (free electrons).

A clear understanding of excited carrier relaxation to their equilibrium state via carrier-phonon, carrier-carrier interaction etc. is always required for the advancement of perovskite based device performance. Organic/inorganic lead halide perovskite have shown remarkable slow hot carrier cooling properties. Herein, we investigate the effect of hot phonon and Auger heating on hot carrier relaxation dynamics in Methyl-ammonium lead iodide-chloride (CH3NH3PbI3-XClX or mixed halide) perovskite using transient absorption spectroscopy. The reduced energy-loss rate on sub-picosecond time scale clearly shows the non-equilibrium build-up of longitudinal optical and acoustic phonon modes (carrier-phonon interaction) at low pump excitation (1018 cm-3). However at high pump excitation (1019 cm-3), dominating Auger heating process (carrier-carrier interaction) further reduces the energy-loss rate by more than two order of magnitude and delays the carrier relaxation process to tens of picoseconds which makes perovskite as a promising candidates in hot carrier photovoltaic.

The hot carrier cooling dynamics in the C-excitonic state of monolayer MoS2 is slowed down by the hot phonon bottleneck and Auger heating effects, as exploited by ultrafast transient absorption spectroscopy. The hot carrier cooling process, determined by the hot phonon bottleneck, can be prolonged through rising the excitation photon energy or increasing the absorbed photon flux. By inducing the Auger heating effect under higher absorbed photon flux, the hot carrier lifetime also increases at the low excitation photon energy. When these two effects are combined under higher excitation photon energy and higher absorbed photon flux, the hot phonon bottleneck is gradually weakened because of Auger recombination. In addition, the similar hot carrier phenomenon can be observed in A/B excitonic states owing to the same physical mechanism. Our work establishes a solid photophysics foundation for 2D transition-metal dichalcogenide applications in advanced energy conversion, optical quantum communication, quantum technology, etc.

Transition metal dichalcogenides (TMDs) have shown outstandingsemiconducting properties which make them promising materials fornext-generation optoelectronic and electronic devices. These propertiesare imparted by fundamental carrier–carrier and carrier–phononinteractions that are foundational to hot carrier cooling. Recenttransient absorption studies have reported ultrafast time scales forcarrier cooling in TMDs that can be slowed at high excitation densitiesvia a hot-phonon bottleneck (HPB) and discussed these findings inthe light of optoelectronic applications. However, quantitative descriptionsof the HPB in TMDs, including details of the electron–latticecoupling and how cooling is affected by the redistribution of energybetween carriers, are still lacking. Here, we use femtosecond pump–push–probespectroscopy as a single approach to systematically characterize thescattering of hot carriers with optical phonons, cold carriers, anddefects in a benchmark TMD monolayer of polycrystalline WS2. By controlling the interband pump and intraband push excitations,we observe, in real-time (i) an extremely rapid “intrinsic”cooling rate of ∼18 ± 2.7 eV/ps, which can be slowed withincreasing hot carrier density, (ii) the deprecation of this HPB atelevated cold carrier densities, exposing a previously undisclosedrole of the carrier–carrier interactions in mediating cooling,and (iii) the interception of high energy hot carriers on the subpicosecondtime scale by lattice defects, which may account for the lower photoluminescenceyield of TMDs when excited above band gap.

Observations of the hot-phonon bottleneck, which is predicted to slow the rate of hot carrier cooling in quantum confined nanocrystals, have been limited to date for reasons that are not fully understood. We used time-resolved infrared spectroscopy to directly measure higher energy intraband transitions in PbS colloidal quantum dots. Direct measurements of these intraband transitions permitted detailed analysis of the electronic overlap of the quantum confined states that may influence their relaxation processes. In smaller PbS nanocrystals, where the hot-phonon bottleneck is expected to be most pronounced, we found that relaxation of parity selection rules combined with stronger electron-phonon coupling led to greater spectral overlap of transitions among the quantum confined states. This created pathways for fast energy transfer and relaxation that may bypass the predicted hot-phonon bottleneck. In contrast, larger, but still quantum confined nanocrystals did not exhibit such relaxation of the parity selection rules and possessed narrower intraband states. These observations were consistent with slower relaxation dynamics that have been measured in larger quantum confined systems. These findings indicated that, at small radii, electron-phonon interactions overcome the advantageous increase in energetic separation of the electronic states for PbS quantum dots. Selection of appropriately sized quantum dots, which minimize spectral broadening due to electron-phonon interactions while maximizing electronic state separation, is necessary to observe the hot-phonon bottleneck. Such optimization may provide a framework for achieving efficient hot carrier collection and multiple exciton generation.

Hot phonon bottleneck (HPB), one of the dominant effects for tuning hot carrier (HC) cooling, has been extensively studied in lead halide perovskites (LHP), and most attention has been devoted to its role in those photovoltaic devices. However, behaviors of HPB in strongly confined systems and its influence on optical gain remain obscure. Herein, by monitoring state-resolved relaxation in strongly confined CsPbBr3 quantum dots (QDs), we discover a discrete cooling process of HCs and demonstrate that their elongation, induced by HPB, primarily occurs during the intraband relaxation from the first excited (1P) to the lowest (1S) states. Moreover, a threshold-like character of HPB in LHP QDs, where the energy dissipation rate significantly drops only beyond a certain carrier density, could be ascribed to the nonadiabatic interaction by coupling with ligand vibrations. Remarkably, HPB has been found to trigger the formation of a giant optical gain (6000 cm–1) near the second absorption peak, and spectral analysis indicates its origin from population inversion at the higher-transition or 1P state. Our findings could strengthen the understanding of photophysics in LHP QDs and guide the development of efficient and broadband lighting applications.

The electron-phonon interaction controls the intrinsic mobility of charges in metal halide perovskites, and determines the rate at which carriers lose energy. Here, the carrier mobility and cooling dynamics were directly examined using a combination of ultrafast transient absorption spectroscopy and optical pump, THz probe spectroscopy, in perovskites with different lead and tin content, and for a range of carrier densities. Significantly, the carrier mobility in the ``hot phonon bottleneck'' regime, where the LO phonon bath keeps carriers warm, was found to be similar to the mobility of cold carriers. A model was developed that provides a quantitative description of the experimental carrier cooling dynamics, including electron-phonon coupling, phonon-phonon coupling and the Auger mechanism. In the Pb and Sn alloy the duration of the hot carrier regime was extended as a result of the slower decay of optical phonons. The findings offer an intuitive link between macroscopic properties and the underlying microscopic energy transfer processes, and suggest new routes to control the carrier cooling process in metal halide perovskites to optimize optoelectronic devices.