Reflectivity Effects on Pump-Probe Spectra of Lead Halide Perovskites: Comparing Thin Films versus Nanocrystals

Mechanism of Hot-Carrier Photoluminescence in Sn-Based Perovskites

Metal halide perovskites have shown exceptionally slow hot-carrier cooling, which has been attributed to various physical mechanisms without reaching a consensus. Here, experiment and theory are combined to unveil the carrier cooling process in formamidinium (FA) and caesium (Cs) tin triiodide thin films. Through impulsive vibrational spectroscopy and molecular dynamics, much shorter phonon dephasing times of the hybrid perovskite, which accounts for the larger blueshift in the photoluminescence seen at high excitation density for FASnI3 compared to CsSnI3 is reported. Density functional theory investigations reveal that the largest contribution to the blueshift is accounted by a giant, dynamic band-filling effect in Sn-based perovskites, which in turn can explain the cooling disparity with the Pb-based counterparts. Several years after the first experimental observations, here a deeper understanding of the cooling mechanism of these materials is provided. Design principles for hot-carrier materials, which may be useful for future implementations of hot-carrier solar cells are further provided.

Quantum-State Renormalization in Semiconductor Nanoparticles

A single photoexcited electron-hole pair within a polar semiconductor nanocrystal (SNC) alters the charge screening and shielding within it. Perturbations of the crystal lattice and of the valence and conduction bands result, and the quantum-confinement states in a SNC shift uniquely with a dependence on the states occupied by the carriers. This shifting is termed quantum-state renormalization (QSR). This Perspective highlights QSR in semiconductor quantum wires and dots identified in time-resolved transient absorption and two-dimensional electronic spectroscopy experiments. Beyond the interest in understanding the principles of QSR and energy-coupling mechanisms, we pose the contributions of QSR in time-resolved spectroscopy data must be accounted for to accurately identify the time scales for intraband relaxation of the carriers within SNCs.

Polarization dependent exciton-plasmon coupling in PEA2PbI4/Al and its application to perovskite solar cell

This paper reports the strong coupling between Al nanostructure and two-dimensional (2D) layered perovskite PEA2PbI4 (PEPI) films. The high exciton binding energy of 118 meV and long carrier lifetime of 216 ps are characterized from the 2D PEA2PbI4 film, which indicates that the excitons in perovskite are robust and can couple to metal plasmons. The ordinary and extraordinary optical dispersions are revealed from the anisotropic 2D perovskite. The transmission spectra of PEA2PbI4/Al nanoparticle arrays are simulated under different polarization excitations, and the typical anti-crossing behaviors originating from exciton-plasmon strong coupling are demonstrated. We found that compared with transverse magnetic (TM) polarization, transverse electric (TE) polarization excitation is more conducive to the realization of exciton-plasmon coupling with a larger Rabi splitting. Furthermore, the PEA2PbI4/Al nanoparticle arrays are proposed, which present polarization-dependent local electrical field enhancement due to the exciton-local surface plasmon polariton coupling. Additionally, it is noticed that the proposed plasmonic structure increases the photo-generation rate inside the active material with improved current density. Therefore, the 2D proposed plasmonic design increases the power conversion efficiency (PCE) with an enhancement of 3.3% and 1.3% relative to the planar structures for TE and TM polarizations, respectively. This study provides a deeper understanding of polarized exciton-plasmon coupling properties, promoting the development of the field of plasmon and providing guidance for the design and preparation of efficient optoelectronic devices.

Quantitative Complex Refractive Index Changes in Thin Films: A Pump-Probe Spectroscopy Analysis Approach

Photoexcitation induces intricate changes in both the real and imaginary components of the complex refractive index of thin film materials, which is essential for interpreting transient spectral features. Here, we employ a Kramers-Kronig-based analytical approach to elucidate light-induced changes in the complex refractive index from transient transmission spectra of thin films. Using gold-perovskite films as model systems, we conduct experimental measurements of transient transmission spectra for both individual gold and perovskite films, as well as for the bilayer heterostructure. Our analysis reveals significant changes in the refractive index and absorption for these systems. Notably, we observe negligible photocarrier transfer between the gold and perovskite layers based on transient spectroscopic analysis. These findings have implications for the design and optimization of bilayer heterostructures in optoelectronic applications. This work highlights the importance of spectroscopic techniques in studying the photophysical properties of heterostructure films.

Transient Absorption Spectroscopy of Films: Impact of Refractive Index

Transient absorption spectroscopy is a powerful technique to study the photoinduced phenomena in a wide range of states from solutions to solid film samples. It was designed and developed based on photoinduced absorption changes or that photoexcitation triggers a chain of reactions with intermediate states or reaction steps with presumably different absorption spectra. However, according to general electromagnetic theory, any change in the absorption properties of a medium is accompanied by a change in the refractive properties. Although this photoinduced change in refractive index has a negligible effect on solution measurements, it may significantly affect the measured response of thin films. In this Perspective paper, we examine why and how the measured responses of films differ from their expected "pure" absorption responses. The effect of photoinduced refractive index change can be concluded and studied by comparing the transmitted and reflected probe light responses. Another discussed aspect is the effect of light interference on thin films. Finally, new opportunities of monitoring the photocarrier migration in films and studying nontransparent samples using the reflected probe light response are discussed. Most of the examples provided in this article focus on studies involving perovskite, TiO2, and graphene-based films, but the general discussion and conclusions can be applicable to a wide range of semiconductor and thin metallic films.

Charge carrier dynamics and transient spectral evolutions in lead halide perovskites

Lead halide perovskites (LHPs) have emerged as promising materials for solar cell applications due to their unique photophysical properties. Most of the crucial properties related to solar cell performance such as carrier mobility, diffusion length, recombination rates, etc. have been estimated using ultrafast spectroscopic methods. While various methods have been developed to prepare and fabricate high-quality perovskite films for photovoltaic applications, understanding the charge carrier dynamics is also crucial at each stage of the charge generation, cooling, and recombination processes. Using femtosecond (fs) transient absorption (TA) spectroscopy, various stages of charge carrier dynamics in perovskite materials could be monitored. In this article, we focus on some of the recent experimental developments related to charge carrier dynamics in perovskites and discuss the current understanding of (1) exciton dissociation, (2) charge carrier thermalization, (3) hot carrier cooling, and (4) electron-phonon coupling along with some of the crucial spectral emergence in the pump-probe experiments of LHP materials.

Thermalization and relaxation mediated by phonon management in tin-lead perovskites

Understanding and control of ultrafast non-equilibrium processes in semiconductors is key to making use of the full photon energy before relaxation, leading to new ways to break efficiency limits for solar energy conversion. In this work, we demonstrate the observation and modulation of slow relaxation in uniformly mixed tin-lead perovskites (MASnxPb1-xI3 and CsSnxPb1-xI3 nanocrystals). Transient absorption measurements reveal that slow cooling mediated by a hot phonon bottleneck effect appears at carrier densities above ~1018 cm-3 for tin-lead alloy nanocrystals, and tin addition is found to give rise to suppressed cooling. Within the alloy nanoparticles, the combination of a newly introduced high-energy band, screened Fröhlich interaction, suppressed Klemens decay and reduced thermal conductivity (acoustic phonon transport) with increased tin content contributes to the slowed relaxation. For inorganic nanocrystals where defect states couple strongly with carriers, sodium doping has been confirmed to benefit in maintaining hot carriers by decoupling them from deep defects, leading to a decreased energy-loss rate during thermalization and an enhanced hot phonon bottleneck effect. The slow cooling we observe uncovers the intrinsic photophysics of perovskite nanocrystals, with implications for photovoltaic applications where suppressed cooling could lead to hot-carrier solar cells.

A roadmap to decipher ultrafast photophysics in two-dimensional nanomaterials

Atomically thin two-dimensional (2D) semiconductors are extensively investigated for optoelectronic applications that require strong light-matter interactions. In view of such applications, it is essential to understand how (photo)excitation alters the non-linear optical response of these materials under high carrier density conditions. Broadband transient absorption (TA) spectroscopy is by now a widely used tool to study the semiconductor physics in such highly excited systems. However, the complex interplay between different many-body interactions in 2D materials produces highly congested spectral information and an ensuing non-trivial non-linear photo-response, thereby masking the desired intrinsic photophysics. Herein, we outline a concise roadmap for analyzing such congested datasets based on examples of TA analysis of various 2D materials. In particular, we emphasize the synergy between an initial qualitative understanding of the transient photo-response based on line shapes and their derivatives and a consequent quantitative spectral deconvolution backed by such insights.

Quantum entanglement control of electron-phonon systems by light irradiation

We numerically study the dynamics of quantum entanglement between interacting electron-phonon and qubit-spin systems under photoirradiation, employing a model of multiple spins and boson modes. The interplay of the antiferromagnetic exchange and electron-phonon interactions provides us with a phase diagram, wherein each phase is characterized by the ground state property of the electron-phonon system. Light irradiation of the electron-phonon system facilitates the generation of quantum entanglement, according to the spin configuration and the phonon state in the ground state. Analyses using the quantum mutual information and the singular values of the reduced density matrix indicate that the quantum mechanical effect of the irradiated light appears in the state of the material.

Broadband Optical Phase Modulation by Colloidal CdSe Quantum Wells

Two-dimensional (2D) semiconductors are primed to realize a variety of photonic devices that rely on the transient properties of photogenerated charges, yet little is known on the change of the refractive index. The associated optical phase changes can be beneficial or undesired depending on the application, but require proper quantification. Measuring optical phase modulation of dilute 2D materials is, however, not trivial with common methods. Here, we demonstrate that 2D colloidal CdSe quantum wells, a useful model system, can modulate the phase of light across a broad spectrum using a femtosecond interferometry method. Next, we develop a toolbox to calculate the time-dependent refractive index of colloidal 2D materials from widely available transient absorption experiments using a modified effective medium algorithm. Our results show that the excitonic features of 2D materials result in broadband, ultrafast, and sizable phase modulation, even extending to the near infrared because of intraband transitions.

Multipulse Terahertz Spectroscopy Unveils Hot Polaron Photoconductivity Dynamics in Metal-Halide Perovskites

Hot carriers in metal-halide perovskites (MHPs) present a foundation for understanding carrier-phonon coupling in the materials as well as the prospective development of high-performance hot carrier photovoltaics. While the carrier population dynamics during cooling have been scrutinized, the evolution of the hot carrier properties, namely mobility, remains largely unexplored. Here we introduce novel ultrafast visible pump-infrared push-terahertz probe spectroscopy to monitor the real-time conductivity dynamics of cooling carriers in methylammonium lead iodide. We find a decrease in mobility upon optically re-exciting the carriers, as expected for band transport. Surprisingly, the conductivity recovery is incommensurate with the hot carrier population dynamics measured by infrared probe and exhibits a negligible dependence on the hot carrier density. Our results reveal the importance of localized lattice heating toward the hot carrier mobility. This collective polaron-lattice phenomenon may contribute to the unusual photophysics of MHPs and should be accounted for in hot carrier devices.

Hot Carrier Dynamics and Charge Trapping in Surface Passivated β-CsPbI3 Inorganic Perovskite

Thermodynamically stable CsPbI₃ inorganic perovskite has achieved high efficiency exceeding 20% with surface defect passivation, but a thorough understanding on the photophysics properties of surface passivated CsPbI₃ inorganic perovskite is still lacking. Herein, we have used transient absorption spectroscopy to investigate the photophysical properties of β-CsPbI₃ perovskites with and without passivation. The results indicate that the carrier trapping process has become slower because of the reduced deep defects that were varied to shallow defects due to surface passivation. The bimolecular recombination of β-CsPbI₃ was also accelerated because of the improved carrier mobility after healing surface defects by passivation agents. Moreover, the efficient defect passivation can also elongate the hot carrier lifetime from 0.26 to 0.37 ps by impeding the charge trapping process. Our findings reveal that the defects passivation is beneficial to enhance defect tolerance, improve carrier transport, and slow down the hot carrier cooling for developing high-performance photovoltaics.

Unusually Strong Biexciton Repulsion Detected in Quantum Confined CsPbBr3 Nanocrystals with Two and Three Pulse Femtosecond Spectroscopy

Transient absorption measurements were conducted on pristine and monoexciton saturated CsPbBr₃ nanocrystals varying in size within the regime of a strong quantum confinement. Once the difference spectra were translated to absolute transient changes in absorption cross section, a single exciton is shown to completely bleach the band edge absorption peak and induce a new absorption roughly two times weaker ∼100 meV to the blue. Difference spectra obtained during Auger recombination of biexciton demonstrate that the addition of a second exciton, rather than double the effect of a first, bleaches the blue-induced absorption band without producing a net stimulated emission at the band edge. Accompanied by high time resolution transient absorption spectra pumping at the lowest exciton band, these results identify the blue-induced absorption as the second transition to 1S_e1S_h which is shifted in energy due to unusually strong and promptly rising biexciton repulsion. Possible mechanisms giving rise to this repulsion and prospects for applying it to enhance optical gain applications of these particles are discussed.

Engineering bandgap of CsPbI3 over 1.7 eV with enhanced stability and transport properties

Potential multijunction application of CsPbI₃ perovskite with silicon solar cells to reach efficiencies beyond the Shockley-Queisser limit motivates tremendous efforts to improve its phase stability and further enlarge its band gap between 1.7 and 1.8 eV. Current strategies to increase band gap via conventional mixed halide engineering are accompanied by detrimental phase segregation under illumination. Here, ethylammonium (EA) in a relatively small fraction (x < 0.15) is first investigated to fit into three-dimensional CsPbI₃ framework to form pure-phase hybrid perovskites with enlarged band gap over 1.7 eV. The increase of band gap is closely associated with the distortion of Pb-I octahedra and the variation of the average Pb-I-Pb angle. Meanwhile, the introduction of EA can retard the crystallization of perovskite and tune the perovskite structure with enhanced phase stability and transport properties.

Electronic States Modulation by Coherent Optical Phonons in 2D Halide Perovskites

Excitonic effects underpin the fascinating optoelectronic properties of 2D perovskites that are highly favorable for photovoltaics and light-emitting devices. Analogous to switching in transistors, manipulating these excitonic properties in 2D perovskites using coherent phonons could unlock new applications. Presently, a detailed understanding of this underlying mechanism remains modest. Herein, the origins of the carrier-phonon coupling in 2D perovskites using transient absorption (TA) spectroscopy are explicated. The exciton fine structure is modulated by coherent optical phonons dominated by the vibrational motion of the PbI₆ octahedra via deformation potential. Originating from impulsive stimulated Raman scattering, these coherent vibrations manifest as oscillations in the TA spectrum comprising of the generation and detection processes of coherent phonons. This two-step process leads to a unique pump- and probe-energy dependence of the phonon modulation determined by the imaginary part of the refractive index and its derivative, respectively. The phonon frequency and lattice displacement of the inorganic octahedra are highly dependent on the organic cation. This study injects fresh insights into the exciton-phonon coupling of 2D perovskites relevant for emergent optoelectronics development.

Visualizing Ultrafast Electron Transfer Processes in Semiconductor-Metal Hybrid Nanoparticles: Toward Excitonic-Plasmonic Light Harvesting

Recently, it was demonstrated that charge separation in hybrid metal-semiconductor nanoparticles (HNPs) can be obtained following photoexcitation of either the semiconductor or of the localized surface plasmon resonance (LSPR) of the metal. This suggests the intriguing possibility of photocatalytic systems benefiting from both plasmon and exciton excitation, the main challenge being to outcompete other ultrafast relaxation processes. Here we study CdSe-Au HNPs using ultrafast spectroscopy with high temporal resolution. We describe the complete pathways of electron transfer for both semiconductor and LSPR excitation. In the former, we distinguish hot and band gap electron transfer processes in the first few hundred fs. Excitation of the LSPR reveals an ultrafast (<30 fs) electron transfer to CdSe, followed by back-transfer from the semiconductor to the metal within 210 fs. This study establishes the requirements for utilization of the combined excitonic-plasmonic contribution in HNPs for diverse photocatalytic applications.

Quantitative Electrochemical Control over Optical Gain in Quantum-Dot Solids

Solution-processed quantum dot (QD) lasers are one of the holy grails of nanoscience. They are not yet commercialized because the lasing threshold is too high: one needs >1 exciton per QD, which is difficult to achieve because of fast nonradiative Auger recombination. The threshold can, however, be reduced by electronic doping of the QDs, which decreases the absorption near the band-edge, such that the stimulated emission (SE) can easily outcompete absorption. Here, we show that by electrochemically doping films of CdSe/CdS/ZnS QDs, we achieve quantitative control over the gain threshold. We obtain stable and reversible doping of more than two electrons per QD. We quantify the gain threshold and the charge carrier dynamics using ultrafast spectroelectrochemistry and achieve quantitative agreement between experiments and theory, including a vanishingly low gain threshold for doubly doped QDs. Over a range of wavelengths with appreciable gain coefficients, the gain thresholds reach record-low values of ∼1 × 10-5 excitons per QD. These results demonstrate a high level of control over the gain threshold in doped QD solids, opening a new route for the creation of cheap, solution-processable, low-threshold QD lasers.

Observation of Charge Generation via Photoinduced Stark Effect in Mixed-Cation Lead Bromide Perovskite Thin Films

Extensive transient absorption studies on hybrid organic-inorganic lead halide perovskites have elucidated many optical properties important for their device performance. Despite the enormous progress, the derivative shaped photoinduced absorption feature in transient spectra that is above the bandgap has many explanations, including the photoinduced Stark effect, where the bandgap is blue shifted due to a local electric field generated by charges. In this work, we employ broad band transient absorption and two-dimensional electronic spectroscopy (2DES) to examine the early transient events after photoexcitation of [CH(NH₂)₂]_0.83Cs_0.17PbBr₃ (FA_0.83Cs_0.17PbBr₃). 2DES resolves a photomodulation feature at the excitation energy of the exciton, suggesting the presence of a dipole field created by a polaron pair shifting the exciton transition to higher energies. As this polaron pair dissociates over 200 fs, the exciton transition shifts to higher energies over the same time scale, evidenced by the 2DES diagonal energy spectra. Given that the observations are well explained in terms of the Stark effect, our work provides extra grounds to support the Stark effect assignment of the above-gap photoinduced absorption. Furthermore, our study reports on the time scale of charge generation, contributing to the fundamental understanding of mixed-cation lead bromide perovskite photophysics.

Hot Carrier Dynamics in Perovskite Nanocrystal Solids: Role of the Cold Carriers, Nanoconfinement, and the Surface

Carrier cooling is of widespread interest in the field of semiconductor science. It is linked to carrier-carrier and carrier-phonon coupling and has profound implications for the photovoltaic performance of materials. Recent transient optical studies have shown that a high carrier density in lead-halide perovskites (LHPs) can reduce the cooling rate through a "phonon bottleneck". However, the role of carrier-carrier interactions, and the material properties that control cooling in LHPs, is still disputed. To address these factors, we utilize ultrafast "pump-push-probe" spectroscopy on LHP nanocrystal (NC) films. We find that the addition of cold carriers to LHP NCs increases the cooling rate, competing with the phonon bottleneck. By comparing different NCs and bulk samples, we deduce that the cooling behavior is intrinsic to the LHP composition and independent of the NC size or surface. This can be contrasted with other colloidal nanomaterials, where confinement and trapping considerably influence the cooling dynamics.

Dark Subgap States in Metal-Halide Perovskites Revealed by Coherent Multidimensional Spectroscopy

Metal-halide perovskites show excellent properties for photovoltaic and optoelectronic applications, with power conversion efficiencies of solar cell and LEDs exceeding 20%. Being solution processed, these polycrystalline materials likely contain a large density of defects compared to melt-grown semiconductors. Surprisingly, typical effects from defects (absorption below the bandgap, low fill factor and open circuit voltage in devices, strong nonradiative recombination) are not observed. In this work, we study thin films of metal-halide perovskites CH₃NH₃PbX₃ (X = Br, I) with ultrafast multidimensional optical spectroscopy to resolve the dynamics of band and defect states. We observe a shared ground state between the band-edge transitions and a continuum of sub-bandgap states, which extends at least 350 meV below the band edge). We explain the comparatively large bleaching of the dark sub-bandgap states with oscillator strength borrowing from the band-edge transition. Our results show that upon valence to conduction band excitation, such subgap states are instantaneously bleached for large parts of the carrier lifetime and conversely that most dark sub-bandgap states can be populated by light excitation. This observation helps to unravel the photophysical origin of the unexpected optoelectronic properties of these materials.

Ultrafast and large optical nonlinearity of a TiSe2 saturable absorber in the 2 μm wavelength region

The non-equilibrium state of correlated electron materials is crucial for both scientific research and practical applications in optoelectronic and photonic devices. Because of the weak optical nonlinearity of most materials even under a dense optical excitation, it is desirable to achieve a significant nonlinear optical response with ultrafast and large optical nonlinearity utilizing a common material. Here, an ultrafast response and large optical nonlinearity induced by non-equilibrium electrons in typical transition metal dichalcogenides, TiSe2, are investigated in the 1.55-2.0 μm wavelength region. Significantly, we observe an ultrafast transient dynamics of 491 femtoseconds as well as a large optical nonlinearity with a saturable coefficient of -0.17 cm GW-1 (1.55 μm) and -0.10 cm GW-1 (2.0 μm). Upon increasing pump fluence, TiSe2 exhibits an enhanced bleaching response amplitude up to 563%. Furthermore, a stable Q-switched fiber laser in the 2.0 μm wavelength region is achieved by employing the TiSe2-saturable absorber. The findings offer the potential design to enhance the optical nonlinearity via non-equilibrium electrons for advanced photonic devices.

Hot carrier extraction in CH3NH3PbI3 unveiled by pump-push-probe spectroscopy

Halide perovskites are promising materials for development in hot carrier (HC) solar cells, where the excess energy of above-bandgap photons is harvested before being wasted as heat to enhance device efficiency. Presently, HC separation and transfer processes at higher-energy states remain poorly understood. Here, we investigate the excited state dynamics in CH₃NH₃PbI₃ using pump-push-probe spectroscopy. It has its intrinsic advantages for studying these dynamics over conventional transient spectroscopy, albeit complementary to one another. By exploiting the broad excited-state absorption characteristics, our findings reveal the transfer of HCs from these higher-energy states into bathophenanthroline (bphen), an energy selective organic acceptor far above perovskite's band edges. Complete HC extraction is realized only after overcoming the interfacial barrier formed at the heterojunction, estimated to be between 1.01 and 1.08 eV above bphen's lowest unoccupied molecular orbital level. The insights gained here are essential for the development of a new class of optoelectronics.

Ultrafast carrier dynamics of metal halide perovskite nanocrystals and perovskite-composites

Perovskite nanocrystals (NCs), especially those based on cesium lead halides, have emerged in recent years as highly promising materials for efficient solar cells and photonic applications. The key to realization of full potential of these materials lies however in the molecular level understanding of the processes triggered by light. Herein we highlight the knowledge gained from photophysical investigations on these NCs of various sizes and compositions employing primarily the femtosecond pump-probe technique. We show how spectral and temporal characterization of the photo-induced transients provide insight into the mechanism and dynamics of relaxation of hot and thermalized charge carriers through their recombination and trapping. We discuss how the multiple excitons including the charged ones (trions), generated using high pump fluence or photon energy, recombine through the Auger-assisted process. We discussed the harvesting of hot carriers prior to their cooling and band-edge carriers from these perovskite NCs to wide band-gap metal oxides, metal chalcogenide NCs and molecular acceptors. How perovskites can influence the charge carrier dynamics in composites of organic and inorganic semiconductors is also discussed.

Cooling dynamics of electrons in MAPbBr3 probed in the deep-UV

Transient absorption in the Visible and in the deep-UV is performed on MAPbBr3 thin films with 3.1 eV pump excitation. The UV probe can access higher order transitions in the material exploring different high-symmetry points of the Brillouin zone. Uncorrelated electron-hole pairs are generated within the instrument response function of 150 fs. The photobleaching at 3.3 eV shows that electron cooling happens in ~ 1 ps.

Refractive index change dominates the transient absorption response of metal halide perovskite thin films in the near infrared

Perovskite films have an uncommon, previously unreported transient absorption response in the NIR, which is caused by a change in the refractive index.

Using Bulk-like Nanocrystals To Probe Intrinsic Optical Gain Characteristics of Inorganic Lead Halide Perovskites

Following the introduction of perovskites for photovoltaic solar energy conversion, the use of these materials as a general purpose optoelectronic material for displays, lighting, and lasing has been explored. However, while reports on stimulated emission and lasing by perovskites show great promise, a comprehensive quantification of their optical gain characteristics is lacking. Here, we measure gain coefficients, clarify the gain mechanism, and explore the gain dynamics of colloidal CsPbBr₃ nanocrystals by deploying a unique combination of broadband transient absorption and ultrafast fluorescence spectroscopy. Opposite from current literature, we show that optical gain in such nanocrystals is supported by stimulated emission from free carriers, and not from excitons or biexcitons. Importantly, we demonstrate that the concomitant gain coefficients and thresholds agree with literature results reported for perovksite thin films. Finally, we show that, even in the case of fully inorganic lead halide perovskites, a cooling bottleneck hampers the development of net stimulated emission at high excitation density. Based on these results, we propose that bulk-like colloidal nanocrystals in general offer a unique testbed to quantify optical gain of novel photonic materials and in particular for lead halide perovskites.