# Simultaneous Electronic and Thermal Signatures in Pump-Probe Spectroscopy of Semiconductor Nanocrystal Films

Francesco de Bellis, Matias Feldman, Ilaria Delbono, Sébastien Royer, Yoann Prado, Hervé Cruguel, Emmanuelle Lacaze, Emmanuel Lhuillier, James Utterback

► To cite this version:

Francesco de Bellis, Matias Feldman, Ilaria Delbono, Sébastien Royer, Yoann Prado, et al. Simultaneous Electronic and Thermal Signatures in Pump-Probe Spectroscopy of Semiconductor Nanocrystal Films. Nano Letters, 2025, 10.1021/acs.nanolett.5c00326. http://dx.doi.org/10.1021/nl50326f

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# Simultaneous Electronic and Thermal Signatures in Pump-Probe Spectroscopy of Semiconductor Nanocrystal Films

Francesco De Bellis,¹ Matias Feldman,¹ Ilaria Delbono,¹ Sébastien Royer,¹ Yoann Prado,¹ Hervé Cruguel,¹ Emmanuelle Lacaze,¹ Emmanuel Lhuillier,¹ James K. Utterback¹*

¹ Sorbonne Université, CNRS, Institut des NanoSciences de Paris, 75005 Paris, France.

*Correspondence to: james.utterback@sorbonne-universite.fr

## Abstract

Thermal contributions are typically ignored in optical spectroscopy of semiconductor nanomaterials. However, such considerations are important for an accurate interpretation of spectroscopy measurements. Here, we identify signatures of transient photoinduced heating in optical pump-probe signals of colloidal semiconductor nanocrystal films. We find that lattice heating following excitation above the band gap or at high fluences leads to a significant temperature-induced transient signal that impacts three aspects of pump-probe measurements: the transient spectra, relaxation kinetics, and spatiotemporally-resolved carrier diffusivity. The effects are general across nanocrystal core material, appearing in both CdSe and PbS quantum dot films. This study proposes several methods for distinguishing simultaneous electronic and thermal contributions to transient measurements as well as guidelines for how to avoid misassignments. On the other hand, we discuss the ability to track both electronic and thermal transport as a largely missed opportunity that can be leveraged.

<figure><img src="image_2.png" /></figure>

## Keywords

Colloidal semiconductor nanocrystals, pump-probe spectroscopy, charge transport, thermal transport, artifacts, relaxation kinetics
**Spectral contributions of transient heating.** We first demonstrate how a thermal contribution might manifest itself in pump-probe signals at visible wavelengths. Throughout this work, we study films of colloidal CdSe (bandgap around 635 nm) and PbS (bandgap around 990 nm) quantum dots (Figure 1a,b, S1), prepared by spin coating on glass coverslips and ligand exchanged to render the films electrically conductive (see Methods). To obtain the effective spectral changes caused by a rise in temperature, we measure the electronic ground state reflectance contrast spectrum R of the NC films as a function of temperature T in steady state (Figure 1c,d) and calculate the change relative to room temperature (Figure 1e,f): $\Delta R/R|_{thermal} = [R(T_0 + \Delta T) - R(T_0)]/R(T_0)$, where $T_0 = 20$ °C. Increasing the temperature leads to a small redshift and broadening of the ground state spectral features (Figure 1c,d). The differential spectral changes $\Delta R/R|_{thermal}$ (Figure 1e,f) are largest in the vicinity of the electronic resonances (Figure 1a,b). This is seen most clearly in the case of the CdSe NC film, whose band gap transition is in the measured wavelength range (Figure 1a,c). The magnitude of the heating-induced relative reflectance change per unit Kelvin is around $d(\Delta R/R)/dT = -8 \times 10^{-4} \text{ K}^{-1}$ at the largest peak corresponding to the band gap transition of CdSe NCs.<sup>32</sup> The PbS NC film exhibits similar behavior, however, the sample has broader features at visible wavelengths (i.e., above band edge) and thus has temperature-induced changes that are less distinct and lower in amplitude (Figure 1b,d,f). The peak magnitude is smaller for PbS than CdSe in this range, reaching $d(\Delta R/R)/dT = -2 \times 10^{-4} \text{ K}^{-1}$. The key observation here is that the differential temperature spectrum remarkably resembles a typical transient reflection/absorption spectrum.

To directly demonstrate the commonalities between temperature-induced spectral changes and electronic carrier spectra, we perform transient reflection spectroscopy on the same NC films. Figure 1g and 1h respectively show the transient reflection spectra of the CdSe and PbS NC films over 100 ps to 50 ns after photoexcitation with 405 nm wavelength light pulses. The CdSe NC film exhibits well-resolved spectral features corresponding to the ground state bleach of the first electronic transition (Figure 1g). The signal has an initial decay component with a few-ns half-life (Figure 1g, inset), typical of CdSe NC charge carrier relaxation,<sup>7,9,37</sup> and the spectrum evolves, redshifting and narrowing over time (Figure 1g). For the PbS NC film, the transient reflection spectra contain more broad features (Figure 1h) as the band gap lies in the near-infrared beyond the range measured here. The signal decays with a half-life of tens of nanoseconds as is consistent with charge carrier relaxation for PbS NCs with ethanedithiol ligands (Figure 1h, inset).<sup>38</sup> Strikingly, the transient reflection spectra of both CdSe and PbS NC films in Figure 1g,h appear very similar to the respective temperature-induced difference spectra in Figure 1e,f.
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Spectral signatures of heating and electronic excitation in nanocrystal films. (a,b) Steady-state visible absorption spectrum of (a) CdSe and (b) PbS nanocrystal films at 20 °C. Insets: Transmission electron micrographs of nanocrystal samples with native ligands. (c,d) Temperature-dependent reflectance contrast spectra of (c) CdSe and (d) PbS nanocrystal films. (e,f) Steady-state change in reflection spectrum as a function of temperature relative to 20 °C for (e) CdSe and (f) PbS nanocrystal films. (g,h) Pump-probe transient reflection spectra of (g) CdSe and (h) PbS nanocrystal films after excitation with 405 nm light pulses at the indicated time delays, normalized to the peak amplitudes for comparison of spectral shapes over time. Data were collected at room temperature. Insets: Un-normalized transient reflection spectra to monitor decay kinetics. The pump fluence was about 100 µJ cm⁻², resulting in estimated temperature rises of about 1 and 4 K for the CdSe and PbS nanocrystal films, respectively (see SI).</figcaption></figure>

We propose that the photoexcited transient spectra can be explained as having both electronic and thermal contributions. The predominant assignment of pump-probe signals to excited-state charge carrier populations is of course very well established, at least on timescales shorter than the band edge carrier lifetime.⁷,¹⁰,³⁹ However, transient heating could also make up a fraction of the signal. The transient reflection spectra of the CdSe NC film most closely match the temperature-induced difference spectra for pump-probe time delays >10 ns. This corresponds to a time window after a significant fraction of the charge carriers are expected to have decayed from the excited state. As heat dissipation is slow (discussed in detail below), the relatively fast decay of charge carriers may give way to a lingering transient heating signal. In this picture, the transient reflection signal is dominated by electronic excitation at early times and transitions to being
dominated by heat at late times. We focus on qualitative comparisons of the electronic and thermal
signals here because while the steady-state spectra used a macroscopic spot size and incoherent
lamp, the pump-probe data was collected with a microscopic laser spot. Moreover these signals
are sensitive to—and can even change sign with—local film thickness and focal position.<sup>14,40</sup> That
said, transient electronic excitation (e.g. band edge bleach) signals of NC films and other thin film
materials are commonly in the range of ~10<sup>-3</sup>. With d(Δ*R*/R)/dT being in the range measured here,
transient heating of even 1 K could contribute a significant fraction of the signal, and our detection
limit is about an order of magnitude lower than this. While our experiments do not yield a direct
measure of the absolute temperature change, we estimate that excitation above the band gap at 405
nm at the fluences used should locally heat the CdSe and PbS NC films by about 1 and 4 K,
respectively (Table S1). We estimate that Auger-mediated heating likely contributes an additional
≈0.5 K and ≈0.02 K, respectively, for the data in Figure 1 (Table S1). These magnitudes are
consistent with previous reports by Guzelturk et al. that used a more direct, electron diffraction-
based probe of the lattice temperature.<sup>29</sup> These estimates suggest that the thermal signal would be
on the order of magnitude measured in the experiments at late times.

**Thickness dependence of heat dissipation timescale.** We investigate how charge and thermal carriers can be distinguished through the distinct dependence of their relaxation kinetics on film thickness. Charge carrier recombination is not typically influenced by the thickness of a NC film,⁴¹ provided that the substrate is not electronically active and the film is sufficiently multilayer so as to not affect the dimensionality of transport. In contrast, heat dissipation occurs via transfer to the substrate, making its characteristic timescale increase with increasing film thickness. To access the pump-probe decay kinetics as a function of local film thickness, we perform correlative spatially-resolved transient reflection spectroscopy and AFM (Figure S2). We examine transient reflection time traces for a range of CdSe and PbS NC film thicknesses, comparing near-band gap to above-band gap excitation (Figure 2). We focus on the late tens-to-hundreds of nanoseconds time window corresponding to the regime where pump-probe spectra resemble temperature-induced differences discussed above and where slower transport is observed as discussed below. We note that the thickness-dependent deviation should only emerge after the thickness-independent charge carrier signal has decayed by a large enough extent. Both NC compositions exhibit decay kinetics that are independent of thickness after near-bandgap excitation at low fluence (Figure 2a,b), as expected. In contrast, after excitation well above the bandgap at 405 nm, the decay timescale becomes longer with increasing film thickness (Figure 2c,d). This effect appears more dramatic in the case of the PbS NC film, for which 405 nm places the pump photon energy further in excess above the band gap than for CdSe NCs. Alternatively, exciting near the band gap but with high fluence also results in film thickness dependent relaxation kinetics, again with slower relaxation for increasing thickness (Figure 2e,f).

The above behavior is consistent with a temperature-induced transient reflectance change dominating at late times following photoexcitation of hot carriers or Auger-mediated heating. Our estimates for the temperature jump based on film absorbance, heat capacity and the respective excitation conditions support this interpretation (indicated in each panel of Figure 2, Table S2). To further test this hypothesis, we perform two-dimensional finite element simulations of heat dissipation (see Methods) and extract the decay curves of the spatially integrated temperature rise of the film (Figure 2g). The time scale of thermal relaxation increases with film thickness (Figure 2h), and the variation is apparent over the same time window seen in the pump-probe experiments. The thickness dependence of the pure thermal relaxation signal in Figure 2g is likely stronger than the pump-probe data in Figure 2c-f because it only accounts for a fraction of the overall amplitude,
dominating only at late times after sufficient charge carrier relaxation. To intuitively rationalize the thickness dependent heat dissipation kinetics, we consider two analytical limits: diffusion-limited and interface-limited heat transfer. When heat transfer across the film-substrate interface is limiting, the characteristic timescale is given by $\tau_{\text{interface}} = \rho C_p L/h$, where $\rho$ is the NC film density, $C_p$ its specific heat capacity, $L$ the film thickness, and $h$ the interfacial thermal conductance. We find that $\tau_{\text{interface}}$ ranges from 20 to 300 ns for NC film thicknesses of 80 to 550 nm for reasonable input parameters (Figure 2h, see SI). In the diffusion limited regime, the characteristic timescale of heat dissipation is $\tau_{\text{diff}} = L^2/D$, where $D$ is the thermal diffusivity. Assuming $D = 150 \text{ nm}^2 \text{ ns}^{-1}$ (this value is discussed below), we find $\tau_{\text{diff}}$ ranges from 40 ns to 2 $\mu$s for the same thickness range (Figure 2h). We note that the true thermal dissipation kinetics in NC films likely lie between these two extremes as the ratio of bulk and interfacial thermal conductances, $hL/k$ (where $k$ is the film thermal conductivity), is $\approx 1-10$ (see SI). Indeed, the finite element simulations yield relaxation times that lay between the two analytical limits (Figure 2h). These thickness-dependent time scales are consistent with those observed for late-time relaxation of the NC film after above-bandgap excitation or high fluence. Taken together, these findings support the picture of a photoinduced heating signal that decays by thermal dissipation to the substrate and dominates at late times after charge-carrier relaxation.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Thickness dependence of heat dissipation timescale. (a-f) Pump-probe time traces for (a,c,e) CdSe and (b,d,f) PbS nanocrystal films collected in locations of the local thicknesses</figcaption></figure>
indicated in the legends. We compare pulsed excitation (a,b) with photon energies near the band gap at low fluence, (c,d) with photon energies above the band gap at low fluence, and (e,f) at photon energies near the band gap at high fluence. The specific pump wavelengths and fluences are indicated for each figure panel. The estimated temperature jumps due to the sum of both hot carrier excitation and Auger-mediated heating, calculated using the absorbance and fluence, are indicated for each figure panel and detailed in Table S2. All CdSe data sets were collected using probe pulses with a wavelength of 775 nm. All PbS data sets were collected using probe pulses with a wavelength of 635 nm. (g) Finite element simulations of heat dissipation decay curves for different film thicknesses. (h) Characteristic time scale of heat dissipation as a function of film thickness for different heat transfer models. The finite element simulations are characterized by the half-life of the temperature relaxation curve, the diffusion-limited heat transfer timescale is given by $\tau_{\text{diff}} = L^2/D$, and the characteristic timescale of nanocrystal film-substrate interface-limited heat transfer is given by $\tau_{\text{interface}} = \rho C_p L/h$. Here we took representative values of $D = 150 \text{ nm}^2 \text{ ns}^{-1}$, $\rho = 4000 \text{ kg m}^{-3}$, $C_p = 500 \text{ J kg}^{-1} \text{ K}^{-1}$, and $h = 10 \text{ MW m}^{-2} \text{ K}^{-1}$. See SI for details on simulations and dissipation time estimates.

**Dual signals in transient microscopy of carrier diffusion.** To optically probe carrier diffusion in these NC films, we use spatiotemporally-resolved transient reflection microscopy—also known as stroboscopic optical scattering microscopy (stroboSCAT) in the configuration implemented here.<sup>14,15</sup> Such pump-probe techniques have previously been used to resolve electronic carrier transport in semiconductor NC assemblies<sup>42–44</sup> and, separately, thermal transport in metallic NC systems.<sup>28,45,46</sup> In this experiment, we optically generate a diffraction-limited carrier density profile and track its evolution in space and time by imaging the resulting change in reflectance ($\Delta R/R$) of a wide-field probe light pulse (Figure 3a,b, see Methods on stroboSCAT). Following the standard analysis of such data, we fit the carrier profiles to a Gaussian of standard deviation $\sigma$ as a function of time $t$ to obtain mean-squared expansion curves, $\sigma^2(t) - \sigma^2(t_0)$ (Figure 3c,d).

The choice of excitation wavelength results in a striking difference in the observed transport. For excitation with photon energies close to the bandgap, transport is initially relatively fast and exhibits subdiffusive behavior ($\sigma^2(t) - \sigma^2(t_0) \propto t^\alpha$ with $\alpha < 1$), suggestive of electronic transport in polydisperse and/or disordered NC films.<sup>47</sup> Accordingly, the instantaneous diffusion coefficient obtained by calculating $D_{\text{eff}}(t) = [\sigma^2(t) - \sigma^2(t_0)]/2t$ decreases over time from about $1 \times 10^4 \text{ nm}^2 \text{ ns}^{-1}$ down to around $1 \times 10^3 \text{ nm}^2 \text{ ns}^{-1}$ (Figure 3e,f), consistent with previous reports for similar systems.<sup>42,43,47,48</sup> Excitation further above the bandgap, in contrast, yields transport that appears to be significantly slower (Figure 3e,f). At late times the transport becomes diffusive (linear mean-squared expansion, $\alpha = 1$) with a diffusion coefficient of $1–2 \times 10^2 \text{ nm}^2 \text{ ns}^{-1}$—occurring specifically over the tens-to-hundreds of nanoseconds time window corresponding to the regime of thickness-dependent relaxation kinetics (Figure 2). This diffusion coefficient is in good agreement with the expected thermal diffusivity of these NC films estimated using the Hasselman-Johnson Maxwell-Euken effective medium approximation of $100 \text{ nm}^2 \text{ ns}^{-1}$ (see SI for details) and previous reports for similar systems.<sup>36,46,49–51</sup> These features occur in both CdSe and PbS NC films (Figure 3c,d), suggesting a common mechanism.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Thermal artifacts in transient microscopy of carrier diffusion. (a,b) Representative stroboSCAT time series for (a) CdSe and (b) PbS nanocrystal films at the indicated pump wavelengths and pump-probe time delays. Each frame is normalized to the maximum of the absolute value of the profile peak for visualization purposes, so the noise artificially appears amplified as time increases. (c,d) Mean-squared displacement curves $\sigma^2(t) - \sigma^2(t_0)$ for the (c) CdSe and (d) PbS nanocrystal films at the indicated pump wavelengths and fluences. The corresponding estimated temperature rises are summarized in Table S3: $\Delta T_{\text{CdSe 405 nm pump}} \approx 0.3$ K; $\Delta T_{\text{CdSe 635 nm pump}} \approx 0.005$ K; $\Delta T_{\text{PbS 405 nm pump}} \approx 9$ K; $\Delta T_{\text{PbS 775 nm pump}} \approx 0.1$ K. Because the signal is longer lived after hot carrier excitation (Figure 2), the transport behavior can be monitored out to longer time delays. All CdSe data sets were collected using probe pulses with a wavelength as of 775 nm. All PbS data sets were collected using probe pulses with a wavelength of 635 nm. (e,f) Instantaneous diffusion coefficient versus time $t$ for (e) CdSe and (f) PbS nanocrystal films calculated from panels (c) and (d), respectively, using the expression $D_{\text{eff}}(t) = [\sigma^2(t) - \sigma^2(t_0)]/2t$.</figcaption></figure>

We attribute the above behavior of pump-wavelength dependent carrier diffusion measurements to the contribution of photoinduced heating to the signal. In this picture, excitation near the band gap at low fluence generates minimal heating (Table S3) such that the signal is dominated by electronic transport up until the population profile decays. In the case of above-band gap excitation, the generation of hot carriers results in significant lattice heating (Table S3) such that the transient signal contains both electronic and thermal contributions. These two overlapping profiles expand according to their distinct diffusivities and transport regimes, causing the overall
profile to appear to expand at an effective rate that lies somewhere between the two true populations. However, at late times the temperature-induced reflectance change starts to dominate the signal amplitude and the extracted mean-squared expansion curve simply reports on the thermal transport.

To illustrate this effect, we generate synthetic carrier profiles that diffuse with realistic parameters based on the experimentally measured transport and relaxation. We simulate relative initial amplitudes ranging from all-electronic to all-thermal profiles with selected intermediate values (Figure 4a-c, see SI for details). The two profiles sum to give the overall profile at each time delay (Figure 4d). As the changes in temperature are small compared to room temperature and the electronic and thermal transport properties do not significantly change over such a range,³⁶,⁵² we assume a linear sum of the electronic and thermal components with fixed respective parameters. Following the typical spatiotemporal data analysis, we fit the profiles to a single Gaussian function with floating amplitude and width to extract decay kinetics (Figure 4e) and mean-squared expansion curves (Figure 4f). The simulated behavior closely resembles the experimental carrier diffusion data for the various excitation conditions (Figure 4f versus Figure 3c,d), lending weight to the picture of combined electronic and thermal contributions.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Simulation of effect of two carrier populations underlying carrier diffusion measurements. Simulated $\Delta R/R$ profiles for (a) electronic carriers only, (b) transient thermal signal only, and (c) equal initial amplitudes of both electronic and thermal signals. (d) Representative case showing underlying thermal and electronic carrier profiles and their sum at a time delay of 10 ns for 50/50 electronic/thermal initial amplitudes. (e) Extracted amplitude time trace and (f) mean-squared expansion curve obtained by fitting profiles to a single Gaussian function. The indicated $A_{0,el}$ and $A_{0,th}$ are the input relative initial amplitudes of the electronic and thermal components. The electronic signal has a 10 ns single exponential decay while thermal dissipation has 50 ns half-life but with a diffusive power-law tail. The charge carrier transport is subdiffusive with $\alpha = 0.5$ while the thermal profile is diffusive with $D_{th} = 200 \text{ nm}^2 \text{ ns}^{-1}$. The all-electronic and all-thermal simulations serve as references, exhibiting the input fast yet subdiffusive electronic transport and slow, diffusive thermal transport.</figcaption></figure>
In the striking case where the thermal contribution is small at early times but outlives the electronic contribution, the simulations show a dramatic shrinking in the mean-squared expansion curve (Figure 4f). This occurs as the fit transitions from detecting mostly electronic to mostly thermal profile widths. We can experimentally reproduce such behavior when exciting at the band gap with sufficient fluence to generate Auger-mediated heating (Figure 5), and the behavior is mildly present for low-fluence above-bandgap excitation (Figure 3). In this scenario, the wider profile of the short-lived fast-moving species (charges) decays, giving way to the sharper profile of the longer-lived slowly-diffusing species (heat) that was underlying the former (Figure 4d).<sup>18,53,54</sup> Under such conditions the electronic and thermal transport regimes can be clearly distinguished with a single measurement (Figure 5). Interestingly, the time-dependent charge carrier diffusivity and thermal diffusivity in these samples have a ratio of ≈100 at 100 ps that falls to <10 approaching 100 ns. This suggests a time-dependent thermoelectric figure of merit that has important performance implications.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Mean-squared displacement curve at high fluence band gap excitation. Mean-squared expansion curve of a CdSe NC film excited near the bandgap with 635 nm light pulses and probed at 775 nm. We plot $\sigma^2(t) - \sigma^2(t_0)$ using a $t_0$ of 500 ps to isolate the time window after Auger recombination is complete. The pump fluence was 3 mJ cm$^{-2}$ per pulse—much higher than the fluence of 20 $\mu$J cm$^{-2}$ used for the data presented in Figure 3. We estimate a temperature rise of a few Kelvin due to Auger recombination under these conditions. Dashed lines show plots of $\sigma^2(t) - \sigma^2(t_0) = Kt^\alpha$ for $\alpha = 0.3$ and $\alpha = 1$ for visual reference of the log-log plot slopes corresponding to initial relatively fast subdiffusive regime and relatively slow diffusive transport, respectively.</figcaption></figure>

***Implications of dual electronic and thermal signatures.*** We expect dual electronic and thermal signals to be a common occurrence in the pump-probe spectroscopy of nanomaterials as the processes of photoinduced heating and temperature-dependent spectral responses are general. For instance, here we found similar results for both CdSe and PbS quantum dots, speaking to the likely pervasiveness of transient heating signals. The relative contributions, however, will vary with material dependent—and possibly size dependent—optical, thermal, and thermo-optical parameters. While our measurements used a transient reflection-based detection geometry, similar signals are expected in transient absorption data (though with different weights) as they are causally related by the Kramers–Kronig transformation. We focused on transient signals here, but the temperature-induced spectral changes affect steady-state measurements as well.

Our findings have important implications for the interpretation of pump-probe spectroscopy experiments of NCs. Pump-probe spectra and relaxation kinetics are most commonly attributed to electronic processes, but the presence of thermal signals would make some such interpretations erroneous. This in turn raises problems for relating such data to functional
performance metrics such as quantum efficiency or diffusion length. We consider that behavior
such as slow transport and long-lived signals would commonly be modeled in terms of trap-limited
processes. However, thermal relaxation can also exhibit similar timescales and non-exponential
kinetics, meaning care must be taken to not conflate the two. While some of the observations of
the present work could be modeled by invoking trapping, characteristics such as increasing lifetime
with film thickness and the late-time transport matching the thermal diffusivity are strongly
suggestive of a thermal origin. At the very least, we propose that trapping and thermal effects
should both be considered as alternative mechanisms for explaining pump-probe dynamics.

Our study provides guidelines for how to identify and control the relative weights of
electronic and thermal carriers in pump-probe spectroscopy. The transient thermal contribution is
enhanced by three experimental conditions explored here: (1) excitation above the bandgap
followed by hot carrier-lattice equilibration; (2) high fluences that lead to Auger heating; (3) use
of thicker films that slow down heat dissipation to the substrate. Such conditions could either be
minimized to isolate electronic carriers or maximized to explicitly study thermal dynamics. These
experimental parameters could also be considered as tests for thermal contributions, as was done
here. Other strategies could be implemented, such as choice of substrate to control heat dissipation.
Note that for colloidal NCs in solution, heat dissipation to the solvent occurs on a ~10² ps
timescale.³⁴ Alternatively, if the electronic and temperature induced spectra exhibit clear
differences, their relative weights can be tuned by judicious choice of probe wavelength.²⁴,²⁵ The
use of spatiotemporally-resolved measurements here aided in differentiating electronic and
thermal signals by their distinct transport characteristics. We also note that some features seen here
should not be present in PL-based methods that selectively track radiative
recombination.¹⁶,⁴⁷,⁵³,⁵⁵,⁵⁶

Moreover, pump-probe techniques like transient absorption or reflection can exploit the
phenomena explored here by accessing thermal transport and dissipation. The nanoscale thermal
transport properties of NC assemblies are important for their implementation as virtually all
applications either generate heat as a byproduct or deliberately utilize it. We were able to access
the local thermal diffusivity and heat dissipation timescale of the two semiconductor NC films,
something that is typically done using a transducer layer without spatiotemporal resolution.³⁶ This
implies future opportunity for using well established visible pump-probe techniques that are
typically used for charge-carrier dynamics to also study thermal dynamics. The ability to
simultaneously measure charge carrier and thermal transport with one technique is promising,
especially for investigating electron-phonon energy transduction and for characterization of
thermoelectrics.
**ASSOCIATED CONTENT**

**Supporting Information**

Methods, Absorption spectra in solution, Estimation of photoinduced temperature jump, Correlative AFM and transient reflectance microscopy, Effective medium approximation of nanocrystal film thermal diffusivity, Estimation of heat dissipation timescale, Simulations of overlapping electronic and thermal contributions.

**AUTHOR INFORMATION**

**Competing interests**

The authors declare no competing interests.

**ACKNOWLEDGMENTS**

J.K.U. is grateful to Milan Delor and Raj Pandya for useful discussions about the experimental setup, Florent Margaillan and Thierry Barisien for access to optical components, and Mathieu Bernard for laser lab installations. This work was supported by the Emergence Research Programme and the Institute of Materials Science (iMAT) of Alliance Sorbonne Université. This work was supported by French state funds managed by the Agence Nationale de la Recherche through the grants PV-SCOPE (ANR-24-CE50-5726), Emap (ANR-23-CE50-0025), DIRAC (ANR-24-ASM1-0001). The project was supported by ERC grant AQDtive (grant n°101086358).
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SUPPORTING INFORMATION
for

# Simultaneous Electronic and Thermal Signatures in Pump-Probe Spectroscopy of Semiconductor Nanocrystal Films

Francesco De Bellis,¹ Matias Feldman,¹ Ilaria Delbono,¹ Sébastien Royer,¹ Yoann Prado,¹ Hervé Cruguel,¹ Emmanuelle Lacaze,¹ Emmanuel Lhuillier,¹ James K. Utterback¹*

¹ Sorbonne Université, CNRS, Institut des NanoSciences de Paris, 75005 Paris, France.

*Correspondence to: james.utterback@sorbonne-universite.fr

## Table of Contents

<table><tr><td>I. Methods</td><td>S2</td></tr><tr><td>II. Estimation of Transient Temperature Jump</td><td>S7</td></tr><tr><td>III. Correlative AFM and Transient Reflection Microscopy</td><td>S10</td></tr><tr><td>IV. Estimation of Nanocrystal Film Thermal Diffusivity</td><td>S11</td></tr><tr><td>V. Estimation of Heat Dissipation Timescale</td><td>S11</td></tr><tr><td>VI. Simulation of Overlapping Electronic and Thermal Contributions to Carrier Diffusion</td><td>S12</td></tr><tr><td>VII. References</td><td>S14</td></tr></table>
# I. METHODS

## Materials

Se (Alfa Aesar 99%), CdO (Alfa Aesar 99.95%), lead oxide (PbO, Strem Chemicals, 99.999%), HgCl₂ (Sigma Aldrich, 99.5%), NaOH (VWR Normapur), hexamethyldisilathiane (TMS₂S, Sigma Aldrich, synthesis grade), 1,2-ethanedithiol (EDT, Fluka, 98%), myristic acid (Alfa Aesar 90%), oleic acid (OA, Alfa Aesar 90%), mercaptoethanol (Thermo scientific, 98%), methanol (VWR Normapur), ethanol (VWR, >99.9%), acetonitrile (ACN, VWR technical), toluene (VWR rectapur), octadecene (ODE, Acros Organics, 90%), N,N-dimethylformamide (DMF, VWR rectapur).

## Preparation of Cd(Myr)₂

In a 100 mL three neck flask, 2.56 g of CdO and 11 g of myristic acid are degassed under vacuum for 30 minutes at 70 °C. Under nitrogen flow, the mixture is heated up to 200 °C until the solution becomes colorless, then maintained for 30 min at 200 °C. Then, the temperature is decreased to 65 °C and 50 mL of methanol is added to solubilize the excess myristic acid. The mixture is stirred for 30 minutes. Then, the dispersion is introduced into 3 centrifuge tubes, sonicated and centrifuged. The washing procedure is repeated at least three times. The cadmium myristate is dried overnight under vacuum.

## Preparation of 0.5 M Cd(OA)₂

In a 250 mL three-necked round-bottomed flask equipped with a rubber septum, a temperature probe and a condenser, 6.42 g of CdO (0.05 mol) and 100 mL of oleic acid is introduced and the mixture is heated at 180 °C until the formation of a yellow clear solution. Then, the reaction is cooled immediately to 120 °C (heating the solution too long at high temperature can degrade the Cd(OA)₂) and is degassed at this temperature (P < 3.0 × 10⁻¹ mbar) to remove the water formed during the first step. Then, the heating mantle is removed and the solution is aliquoted while still warm into several 15 mL vials before the formation of a solid at room temperature.

## Preparation of 0.1 M Se-ODE

In a 100 mL three-necked flask, 46.7 mL of ODE are degassed at room temperature for 30 min. Meanwhile, a suspension of 393 mg of Se (4.98 mmol) in 3 mL of ODE is prepared. After degassing, the atmosphere is switched to nitrogen and the temperature is raised to 170 °C. The suspension is added gradually, waiting for the complete dissolution of the Se between each addition. Once all the Se is completely dissolved in the ODE, the solution is heated for 1 h at 215 °C. The solution turns orange-red to yellow. The solution is cooled down to room temperature and transferred to the glove box.

## CdSe nanocrystal (NC) growth

The synthesis is based on a previous report.¹ In a 100 mL three-necked flask, 340 mg of Cd(Myr)₂ (0.6 mmol) and 15 mL of ODE is degassed at room temperature for 30 min. Then, the reaction is put under nitrogen and heated to 250 °C. Meanwhile, a suspension of Se (48 mg, 0.608 mmol) in 4 mL of ODE is prepared. At 250 °C, 2 mL of this solution is rapidly injected (suspension is sonicated just before injection). Immediately after the injection, the temperature controller is set at 240 °C and the reaction is heated for 5 min. After this time, 400 µL of oleic acid was added and the temperature controller is set to 260 °C. At 260 °C, 4 mL of oleylamine is added and the reaction mixture is heated for 10 min. Meanwhile, 4 mL of Cd(OA)₂ at 0.5 M and 20 mL of Se-ODE at 0.1 M are mixed. 22 mL of the mixture is injected with a 20 mL syringe with a flow rate of 10 mL h⁻¹. Then, the reaction is left to cool down to room temperature. The reaction mixture is split into 4 centrifuge tubes and the round-bottomed flask is rinsed with ethanol, which is distributed between
the 4 tubes. The particles are precipitated by adding ethanol in each tube. The mixtures are centrifuged (11000 rpm, 5 min). The supernatants are discarded and the pellets are assembled into 10 mL of hexane. The CdSe cores are washed twice with ethanol. The mixture is centrifuged (11000 rpm, 5 min). The supernatant is discarded and the pellet is dispersed in 10 mL of toluene.

### CdSe film deposition and ligand exchange

A ligand exchange solution is prepared with 15 mg of HgCl₂ dissolved in 9 mL of DMF, to which 1 mL of mercaptoethanol is added. 500 µL of NC solution (with a concentration of 50 mg mL⁻¹ in toluene) is mixed with 500 µL of the ligand exchange solution and 5 mL of hexane. Then, 500 µL of DMF is added and the mixture is sonicated and mixed. The NCs undergo a phase transfer from the apolar phase to the DMF phase. The clear apolar phase is discarded using a pipette and two more rounds of cleaning via hexane are performed. Once the apolar phase is removed, the NCs are precipitated by adding a few drops of toluene and centrifuging at 6000 rpm for 3 min. A pellet forms, which is then redispersed in 200 µL of DMF. Then, the ink is spin-coated on the sample at 3000 rpm for 150 s to obtain the film.

### PbS nanocrystal synthesis

The procedure is inspired from Hines *et al.*² 0.94 g of PbO is introduced in a 100 mL three-neck flask with 4 g of OA and 20 g of ODE. The flask is degassed under vacuum at 110 °C for 2 hours. Meanwhile, in an air-free glove box, a mixture of 720 µL of TMS₂S and 20 mL of ODE is prepared in a 20 mL vial, then 10 mL is introduced into a syringe. The atmosphere of the flask is switched to Ar and the temperature is set equal to 110 °C. The TMS₂S solution is quickly injected and the solution turns dark. After 1 min, the reaction is stopped by removing the heating mantle and dipping the three-neck flask in a water bath. The NCs are then precipitated by addition of ethanol. The formed pellet is redispersed in hexane. A second step of cleaning is repeated. Finally, the pellet is redispersed in toluene with a 50 mg mL⁻¹ concentration. The solution is centrifuged to remove any colloidalily unstable material. Finally, the solution is filtered with a 0.22 µm PTFE filter.

### PbS film deposition and ligand exchange

100 µL of PbS NCs are spin coated at 2000 rpm. The film is then dipped in a 1% by volume solution of EDT in acetonitrile for 30 s before being rinsed 10 s in pure acetonitrile. Spinning is continued for 60 s to dry the film. The deposition is repeated 3 times to build film thickness.

### Atomic force microscopy (AFM)

AFM of the same NC film regions measured by spatially-resolved transient reflectance spectroscopy was performed using an NX20 AFM (Park Systems) equipped with a PPP-NCHR 10M non-contact cantilever (Park Systems). Images were collected in non-contact mode. Images were flattened and corrected using Gwyddion.³ Film thickness was determined by comparing the height relative to the glass substrate.

### Optical microscopy

Optical microscopy images were collected on the stroboSCAT setup (see below) using a white-light light emitting diode (LED) (MNWHL4, ThorLabs) that was equipped with an adjustable collimating lens (SM1U25-A, ThorLabs) and driven by a LED driver (T-Cube LEDD1B, ThorLabs).

### Absorption spectroscopy

UV-visible absorption was performed using a JASCO V-730 spectrometer, while the infrared spectrum was acquired using a Nicolet IS50 Fourier Transform InfraRed spectrometer in total attenuated reflection configuration.
<figure><img src="image_8.png" /><figcaption>**Figure S1.** Absorption spectra of colloidal nanocrystal solutions. (a) CdSe nanocrystals with oleate ligands in toluene. (b) PbS nanocrystals with oleate ligands in toluene.</figcaption></figure>

## Transmission electron microscopy

A drop of diluted NC solution in hexane was drop-casted on to a copper grid covered with an amorphous carbon film. The grid was degassed overnight under a secondary vacuum. Imaging was conducted using a JEOL 2010 transmission electron microscope operated at 200 kV.

## Temperature-dependent reflectance contrast spectroscopy

Broadband emission from a stabilized tungsten-halogen lamp source (SLS201L/M, Thorlabs) was coupled into a SMA fiber patch cable and collimated with a parabolic mirror (RC02SMA-P01, Thorlabs) then focused onto the sample to give a ≈5 mm spot size. The angle of incidence was 10°. The sample was mounted vertically in a Peltier based heating stage (LTS120, Linkam) to control the temperature. The reflected light output was fiber-coupled to a linear CMOS-based single grating spectrometer (VIS, Ultrafast Systems, USA) equipped with a 16-bit digitizer (ADC-10-USB, Ultrafast Systems, USA) that was calibrated using a mercury lamp. Spectra were collected by averaging 100,000 frames at 700 µs exposure per frame.

The temperature dependent spectra were collected for the samples on their glass coverslip substrates as well as for a bare glass coverslip. The dark count-corrected reflectance contrast relative to a blank glass coverslip substrate is first calculated, $RC(T) = [R_{sample}(T) - R_{substrate}(T)]/R_{substrate}(T)$, then the difference spectra are calculated as $\Delta R/R_{thermal} = [RC(T_0 + \Delta T) - RC(T_0)]/RC(T_0)$ with $T_0 = 20 °C$ (Figure 1).

## Transient reflection spectroscopy

The experimental setup for transient reflection spectroscopy measurements was built with inspiration from a previously described instrument developed by the Delor Lab⁴ with some modifications. White-light probe pulses with a ≈50 ps pulse width were obtained from a supercontinuum laser (Fianium-15, NKT Photonics) coupled into an acousto-optic tunable filter (SuperK Varia, NKT Photonics). For spectroscopy measurements, the filter was set to allow a wavelength window of 500–800 nm. The pump pulses were generated by a 405 nm wavelength laser diode (LDH-D-C-405, PicoQuant) with a <100 ps pulse width. The laser diode head was controlled by the PDL 828-S “SEPIA II” laser driver equipped with an SLM 828 module and a SOM 828-D oscillator (PicoQuant). The two laser sources were synchronized by triggering the PicoQuant laser diode driver using a pulse train synchronization signal from the supercontinuum laser after being delayed with a digital delay generator (DG645, Stanford Research Systems) that has a <25 ps jitter. We used a pulse repetition rate of 500 kHz, controlled using the built in variable repetition rate of the supercontinuum source. The pump was modulated at 1 kHz using the gating capabilities of the PicoQuant driver. The probe beam was expanded to a diameter of ≈10 mm using a pair of parabolic mirrors while the pump beam had a ≈2 mm diameter. The pump and probe
beams were overlapped using a dichroic mirror. They were then directed into a home-built inverted microscope featuring 50/50 beamsplitter (BSW10, Thorlabs) and a high numerical aperture (1.4 NA) oil-immersion objective (Leica HC PL APO 63×/1.40 NA). Samples were mounted in a microscope slide format holder and controlled by a three-axis piezo-controlled nano-positioning stage (BIO3, PiezoConcept). The pump spot size at the sample plane was 30 µm while the probe spot was smaller at 5 µm. Both the pump and probe light reflected from the sample were collected through the same objective used for focusing, passed through the 50/50 beam splitter and fiber-coupled to a high-speed linear CMOS-based single grating spectrometer (VIS, Ultrafast Systems, USA) equipped with a 16-bit digitizer (ADC-10-USB, Ultrafast Systems, USA) that was calibrated using a mercury lamp. Here, the spectrometer was triggered at 1 kHz, synched to the modulation of the pump. Transient reflection spectra were generated by taking the difference between pump-on and pump-off raw pixel intensities, normalized to the raw pump-off intensities, yielding $\Delta R/R$ spectra. Pump-on and pump-off spectra were distinguished using the intensity from the reflected pump, spectrally separated from the wavelength range of interest. Each spectrometer acquisition was integrated for 700 µs (corresponding to thousands of pulses), 10,000 frames were averaged, and this was repeated multiple times for each time delay. Data acquisition was implemented in LabVIEW 2022 64-bit. All experiments were performed at room temperature, in this case 293 K.

## stroboSCAT measurements

The experimental setup for stroboSCAT measurements of spatiotemporally-resolved carrier diffusion was previously described in detail⁵ and was based on an instrument developed by Delor et al.⁶ Briefly, the home-built microscope used an inverted microscope configuration with a 1.4 numerical aperture oil-immersion objective. Two laser diodes were used at a time for pump and probe sources, including combinations of center wavelengths of 405 nm, 635 nm and 775 nm (LDH-D-C-405, LDH-D-C-640, LDH-D-C-780, PicoQuant), and were operated by drivers from PicoQuant to control the pump-probe time delay. The durations of these laser pulses are <100 ps. We used a laser repetition rate of 500 kHz, with the pump modulated at 660 Hz. Both the pump and probe were spatially filtered through pinholes, the probe beam passed through a wide-field lens, the two beams are overlapped using a dichroic mirror and reflected into the objective by a 50/50 beamsplitter. This leads to an overlapped near-diffraction-limited pump and wide-field probe illumination. Probe light reflected from the sample was collected through the same objective, isolated with a band-pass filter and focused onto a CMOS camera, triggered at 660 Hz by the laser driver. The pixel calibration was done using a 1951 USAF Pattern resolution target (R3L1S4PR, Thorlabs), giving 28 nm/pixel. stroboSCAT images are generated by taking the difference between pump-on and pump-off raw pixel intensities, normalized to the raw pump-off intensities, yielding $\Delta R/R$ contrast images as a function of time delay. Data acquisition was implemented in LabVIEW 2022 64-bit. Data analysis and plotting were performed using ImageJ, Igor Pro, and Python. To obtain the relaxation and mean-squared expansion curves, each $\Delta R/R$ image of a given stroboSCAT time series is fitted to a normalized Gaussian profile function with a common center and floating amplitudes and widths. By normalizing the Gaussian function, the amplitude represents the spatially-integrated amplitude, thereby giving the population decay traces. The width of the Gaussian $\sigma$ versus time $t$ is used to obtain the mean squared expansion, $\sigma^2(t) - \sigma^2(t_0)$.

The pump fluence was found by measuring the power arriving at the sample—using a microscope slide format power sensor (S171C, Thorlabs) and power meter (PM100D, Thorlabs)— and the pump spot size by imaging its reflection. The spot sizes when using 405, 635 and 775 nm wavelength sources were 300, 460 and 540 nm at FWHM, respectively. These spot sizes are consistent with the differences in diffraction limit for the respective wavelengths. The fluences for each measurement are indicated in their respective figures. Experiments were conducted at 293 K.
Finite element simulations of heat dissipation

COMSOL Multiphysics® 6.0 (COMSOL Inc., Los Angeles, CA) finite element software was used to simulate heat transport in an effective NC films. The simulations were conducted using the built-in Heat Transfer in Solids module. To render the simulations computationally feasible, we reduce the geometry to two dimensions, including the in-plane (parallel to the substrate) and out-of-plane (perpendicular to the substrate) thermal transport. Simulation geometries were constructed using a simplified rectangular region with the bulk thermal properties of a composite NC–ligand film. We used a density of 4000 kg m⁻³, heat capacity of 500 J kg⁻¹ K⁻¹, and thermal conductivity of 0.3 W m⁻¹ K⁻¹ as representative parameters lying in the range of values calculated for CdSe and PbS NC films, which are quite similar to each other (see Section IV of the SI for more details). The bottom of the composite film was in contact with glass while the top was in contact with air. We take a layer conductance of 10 MW m⁻² K⁻¹ based on reports of polystyrene film-sapphire interfaces as a proxy for a typical organic film-glass interface, and neglect any heat transfer to the air. The lateral size of the film and width of the glass substrate were large enough to avoid edge effects in the thermal transport. 300 K was used as the ambient reference temperature, and simulations were initialized using a Gaussian profile (sigma = 180 nm) of elevated temperature with a peak of 310 K (ΔTmax = 10 K), reflecting the experimental conditions. We assumed a constant temperature profile in the vertical direction within the film, consistent with a film thickness smaller than the attenuation length of the pump beam. The mesh was constructed using a “fine” element size. The finite element simulation solves the heat equation (Fourier’s law) using a quadratic Lagrange discretization to calculate the time dependence of the temperature profile with a relative tolerance of 0.0001. The simulated temperature profiles as a function of time were treated analogously to the pump-probe microscopy data, fitting to a time dependent amplitude multiplied by a normalized Gaussian function over time. By using a normalized Gaussian, the time dependent amplitude corresponds to the spatially-averaged transient reflectance signal like what is reported in Figure 2.
## II. ESTIMATION OF TRANSIENT TEMPERATURE JUMP

In estimating the pump-induced lattice temperature jump in our experiments we consider two heating mechanisms: thermalization of hot carriers and Auger-mediated heating. The total temperature jump after Auger recombination is taken to be $\Delta T_{\text{total}} = \Delta T_{\text{ph}} + \Delta T_{\text{Auger}}$.

### Photon energy contribution to film temperature jump ($\Delta T_{\text{ph}}$)

We assume that the excess energy of hot charge carriers is all converted to heating of the lattice with a negligible electron/hole heat capacity compared to the NC lattice and film heat capacity. The pump-induced lattice temperature jump can be estimated using the excess energy above the bandgap: $\Delta T_{\text{ph}} = U_{\text{excess}}/C$, where $U_{\text{excess}}$ is the excess photon absorbed energy above the bandgap per unit volume and C is the volumetric heat capacity of the NC film. We estimate $U_{\text{excess}}$ based on the pump fluence ($J_0$), photon energy ($E_{\text{ph}}$) relative to the band gap ($E_g$), and optical attenuation length ($\alpha^{-1}$): $U_{\text{excess}} = (E_{\text{ph}} - E_g) \times J_0 (1 - e^{-\alpha L}) / E_{\text{ph}} L$. Similar calculations to estimate the temperature jump in NC films were validated by more direct measurements of transient lattice temperature.⁷,⁸,¹⁰

For the heat capacity, we use the average mass density—$\rho = \rho_{\text{NC}}\rho_{\text{NC}} + (1 - \rho_{\text{NC}})\rho_{\text{L}}$, where $\rho_{\text{NC}}$ is the volume fraction of the NC core and $\rho_{\text{NC}}$ and $\rho_{\text{L}}$ are the densities of the NC core and ligand, respectively—and the mass-weighted specific heat capacity—$C_p = m_{\text{NC}}C_{\text{NC}} + (1 - m_{\text{NC}})C_{\text{L}}$, where $m_{\text{NC}}$ and $1 - m_{\text{NC}}$ are the mass fractions of the NC core and the ligand, respectively, and $C_{\text{NC}}$ and $C_{\text{L}}$ are the NC core and ligand specific heat capacities, respectively—and we use them to calculate $C = \rho C_p$. We assume bulk values for the densities and heat capacities of CdSe, PbS, and ethanedithiol. The NC core volume fraction is estimated assuming FCC packing of spheres with 6 and 3 nm diameters for CdSe and PbS, respectively, and 0.5 nm long ligands¹¹—this is likely a slight overestimate as the packing is more likely to be disordered, but the error introduced is expected to be small compared to other parameters and we only report estimates to one significant figure in the end. The attenuation length at a given wavelength of the NC films was estimated by measuring the absorption spectra $A(\lambda)$ (Figure 1a,c) and using the average film thickness measured by AFM. The attenuation length is then defined as $\alpha^{-1}(\lambda) = L/A(\lambda)$. We note that the reported fluences use the local (peak) fluence of the Gaussian pump spot for spectrally resolved measurements since the small probe spot only contains signal from that spatial region (Figure 1), and the $2\sigma$ definition for the diffraction-limited experiments (Figure 2,3,5). However, the temperature jumps are reported at $1\sigma$ as this better represents the average temperature measured.

The results of the estimations appear in Table S1, S2 and S3.

### Auger-mediated heating contribution to film temperature jump ($\Delta T_{\text{Auger}}$)

As an estimate for Auger-mediated heating, we find the fraction of NCs within the excitation volume that absorb 2 or more photons ($P_{N \ge 2}$). We assume that Auger recombination has unity efficiency, that Auger recombination leads to hot carriers with a combined energy equal to $E_g$, that all of that energy is converted to heat, and that the electron and hole heat the lattice equally with negligible heat capacity compared to the lattice. We treat all NCs having absorbed 2 or more photons as if they only absorbed 2. $P_{N \ge 2}$ is calculated by finding the average number of photons absorbed per NC, $\langle N \rangle = J_0(1 - e^{-\alpha L}) / E_{\text{ph}} n L$—where n is the NC number density per unit volume— and assuming a Poisson distribution, $P_N$. Under these assumptions the Auger-mediated hot carrier energy density is $U_{\text{Auger}} = E_g P_{N \ge 2} n$. Then the Auger-mediated heating contribution to film temperature jump after the timescale of Auger recombination is $\Delta T_{\text{Auger}} = U_{\text{Auger}}/C$.

The results of the estimations appear in Table S1, S2, and S3. The estimated temperature jumps are consistent with those expected based on previous direct measurements of photoheating in NC films.⁸,¹⁰
<table><caption>Table S1. Estimated temperature jump due to photoexcitation in Figure 1</caption><thead><tr><th></th><th>E<sub>g</sub><br>(eV)</th><th>E<sub>ph</sub><br>(eV)</th><th>J<sub>0</sub><br>at<br>peak<br>(μJ cm<sup>-2</sup>)</th><th>Fraction of<br>energy<br>exceeding<br>bandgap,<br>E<sub>ph</sub> - E<sub>g</sub><br>E<sub>g</sub></th><th>α<sup>-1</sup><br>(nm)</th><th>U<sub>excess</sub><br>at<br>peak<br>(J m<sup>-3</sup>)</th><th>C<br>(J m<sup>-3</sup> K<sup>-1</sup>)</th><th>ΔT<sub>ph</sub><br>at<br>peak<br>(K)</th><th>⟨N⟩</th><th>P<sub>N≥2</sub></th><th>n<br>(nm<sup>-3</sup>)</th><th>U<sub>Auger</sub><br>at<br>peak<br>(J m<sup>-3</sup>)</th><th>ΔT<sub>Auger</sub><br>at<br>peak<br>(K)</th></tr></thead><tbody><tr><td>CdSe<br>405 nm<br>pump</td><td>1.94</td><td>3.06<br>(405 nm)</td><td>100</td><td>0.37</td><td>5 × 10<sup>2</sup></td><td>3 × 10<sup>6</sup></td><td>2.8 × 10<sup>6</sup></td><td>1</td><td>0.9</td><td>0.22</td><td>5<br>× 10<sup>-3</sup></td><td>1.5<br>× 10<sup>6</sup></td><td>0.5</td></tr><tr><td>PbS<br>405 nm<br>pump</td><td>1.25</td><td>3.06<br>(405 nm)</td><td>100</td><td>0.59</td><td>3 × 10<sup>2</sup></td><td>2 × 10<sup>6</sup></td><td>2.2 × 10<sup>6</sup></td><td>4</td><td>0.2</td><td>0.02</td><td>3<br>× 10<sup>-2</sup></td><td>5<br>× 10<sup>5</sup></td><td>0.02</td></tr></tbody></table>

<table><caption>Table S2. Estimated temperature jump due to photoexcitation in Figure 2</caption><thead><tr><th></th><th>E<sub>g</sub><br>(eV)</th><th>E<sub>ph</sub><br>(eV)</th><th>J<sub>0</sub><br>at 2σ<br>(μJ cm<sup>-2</sup>)</th><th>Fraction of<br>energy<br>exceeding<br>bandgap<br>E<sub>ph</sub> - E<sub>g</sub><br>E<sub>g</sub></th><th>α<sup>-1</sup><br>(nm)</th><th>U<sub>excess</sub><br>at 1σ<br>(J m<sup>-3</sup>)</th><th>C<br>(J m<sup>-3</sup> K<sup>-1</sup>)</th><th>ΔT<sub>ph</sub><br>at 1σ<br>(K)</th><th>⟨N⟩</th><th>P<sub>N≥2</sub></th><th>n<br>(nm<sup>-3</sup>)</th><th>U<sub>Auger</sub><br>at 1σ<br>(J m<sup>-3</sup>)</th><th>ΔT<sub>Auger</sub><br>at 1σ<br>(K)</th></tr></thead><tbody><tr><td>CdSe<br>405 nm<br>pump</td><td></td><td>3.06<br>(405 nm)</td><td>20</td><td>0.36</td><td>5 × 10<sup>2</sup></td><td>6 × 10<sup>5</sup></td><td></td><td>0.2</td><td>0.2</td><td>0.02</td><td></td><td>3<br>× 10<sup>4</sup></td><td>0.05</td></tr><tr><td>CdSe<br>635 nm<br>pump</td><td>1.95</td><td></td><td>7</td><td></td><td></td><td>≈0</td><td>2.8 × 10<sup>6</sup></td><td>≈0</td><td>0.06</td><td>0.002</td><td>5<br>× 10<sup>-3</sup></td><td>1<br>× 10<sup>4</sup></td><td>0.005</td></tr><tr><td></td><td></td><td>1.95<br>(635 nm)</td><td>1000</td><td>0</td><td>1 × 10<sup>3</sup></td><td>≈0</td><td></td><td>≈0</td><td>8</td><td>≈1</td><td></td><td>6<br>× 10<sup>6</sup></td><td>2.5</td></tr><tr><td>PbS<br>405 nm<br>pump</td><td></td><td>3.06<br>(405 nm)</td><td>200</td><td>0.59</td><td>3 × 10<sup>2</sup></td><td>1 × 10<sup>7</sup></td><td></td><td>8</td><td>0.35</td><td>0.05</td><td></td><td>1<br>× 10<sup>6</sup></td><td>0.6</td></tr><tr><td>PbS<br>775 nm<br>pump</td><td>1.25</td><td></td><td>24</td><td></td><td></td><td>3 × 10<sup>5</sup></td><td>2.2 × 10<sup>6</sup></td><td>0.1</td><td>0.09</td><td>0.004</td><td>3<br>× 10<sup>-2</sup></td><td>1<br>× 10<sup>5</sup></td><td>0.04</td></tr><tr><td></td><td></td><td>1.60<br>(775 nm)</td><td>2000</td><td>0.22</td><td>8 × 10<sup>2</sup></td><td>2 × 10<sup>7</sup></td><td></td><td>10</td><td>3</td><td>0.82</td><td></td><td>2<br>× 10<sup>7</sup></td><td>10</td></tr></tbody></table>
<table><caption>Table S3. Estimated temperature jump due to photoexcitation in Figure 3</caption><thead><tr><th></th><th>E<sub>g</sub><br>(eV)</th><th>E<sub>ph</sub><br>(eV)</th><th>J<sub>0</sub><br>at 2σ<br>(μJ cm<sup>-2</sup>)</th><th>Fraction of<br>energy<br>exceeding<br>bandgap<br>E<sub>ph</sub> - E<sub>g</sub><br>E<sub>g</sub></th><th>α<sup>-1</sup><br>(nm)</th><th>U<sub>excess</sub><br>at 1σ<br>(J m<sup>-3</sup>)</th><th>C<br>(J m<sup>-3</sup> K<sup>-1</sup>)</th><th>ΔT<sub>ph</sub><br>at 1σ<br>(K)</th><th>⟨N⟩</th><th>P<sub>N≥2</sub></th><th>n<br>(nm<sup>-3</sup>)</th><th>U<sub>Auger</sub><br>at 1σ<br>(J m<sup>-3</sup>)</th><th>ΔT<sub>Auger</sub><br>at 1σ<br>(K)</th></tr></thead><tbody><tr><td>CdSe<br>405 nm<br>pump</td><td>1.95</td><td>3.06<br>(405 nm)</td><td>20</td><td>0.36</td><td>5 × 10<sup>2</sup></td><td>6 × 10<sup>5</sup></td><td>2.8 × 10<sup>6</sup></td><td>0.2</td><td>0.2</td><td>0.02</td><td>5<br>× 10<sup>-3</sup></td><td>3<br>× 10<sup>4</sup></td><td>0.05</td></tr><tr><td>CdSe<br>635 nm<br>pump</td><td></td><td>1.95<br>(635 nm)</td><td>7</td><td>≈0</td><td>1 × 10<sup>3</sup></td><td>≈0</td><td></td><td>≈0</td><td>0.06</td><td>0.002</td><td></td><td>1<br>× 10<sup>4</sup></td><td>0.005</td></tr><tr><td>PbS<br>405 nm<br>pump</td><td>1.25</td><td>3.06<br>(405 nm)</td><td>200</td><td>0.59</td><td>3 × 10<sup>2</sup></td><td>1 × 10<sup>7</sup></td><td>2.2 × 10<sup>6</sup></td><td>8</td><td>0.35</td><td>0.05</td><td>3<br>× 10<sup>-2</sup></td><td>1<br>× 10<sup>6</sup></td><td>0.6</td></tr><tr><td>PbS<br>775 nm<br>pump</td><td></td><td>1.60<br>(775 nm)</td><td>24</td><td>0.22</td><td>8 × 10<sup>2</sup></td><td>3 × 10<sup>5</sup></td><td></td><td>0.1</td><td>0.09</td><td>0.004</td><td></td><td>1<br>× 10<sup>5</sup></td><td>0.04</td></tr></tbody></table>

Summary of variable definitions used in Tables S1, S2, and S3.

*Eg*: Band gap energy

*Eph*: Pump photon energy

*J0*: Pump fluence

*α⁻¹*: Photon attenuation length

*L*: Nanocrystal film thickness

*Uexcess*: Excess absorbed energy due to absorption of photons above the band gap

*UAuger*: Excess energy generated by Auger recombination

*C*: Volumetric heat capacity of NC film

*⟨N⟩*: Average number of electron-hole pairs excited per nanocrystal

*P<sub>N≥2</sub>*: Probability of a nanocrystal absorbing two or more photons

*n*: Number density of nanocrystals in film per unit volume

*ΔT<sub>ph</sub>*: Photon energy contribution to film temperature jump

*ΔT<sub>Auger</sub>*: Auger heating contribution to film temperature jump
### III. CORRELATIVE AFM AND TRANSIENT REFLECTION MICROSCOPY

<figure><img src="image_9.png" /></figure>

**Figure S2. Correlated AFM and optical mapping of CdSe and PbS NC films for thickness dependence.** (a) Optical reflectance image and (b) AFM of CdSe NC film, where regions with local thicknesses of 80, 250 and 400 nm are indicated. (c-h) Optical reflectance images (left-hand column) and AFM (right-hand column) collected for the same regions of a PbS NC film, with indicated locations for thicknesses of 100 nm (c,d), 300 nm (e,f), and 550 nm (g,h). Locations where pump-probe measurements were performed are indicated with circles, roughly to scale with sub-micron pump spot size.
## IV. ESTIMATION OF NANOCRYSTAL FILM THERMAL DIFFUSIVITY

To estimate the expected thermal diffusivity of our NC films for comparison to the data, we use the Hasselman Johnson Maxwell Euken (HJ-ME) effective medium approximation (EMA) which has been established to work well in the case of NC solids.¹¹⁻¹³ In this case, the effective thermal conductivity of the composite medium, $k_{eff}$, is given by

$$k_{eff} = k_{ligand} \frac{\frac{k_{NC}}{k_{ligand}} + \frac{2k_{NC}}{rh_{NC-ligand}} + 2 + 2\varphi_{NC} \left( \frac{k_{NC}}{k_{ligand}} - \frac{k_{NC}}{rh_{NC-ligand}} - 1 \right)}{\frac{k_{NC}}{k_{ligand}} + \frac{2k_{NC}}{rh_{NC-ligand}} + 2 - \varphi_{NC} \left( \frac{k_{NC}}{k_{ligand}} - \frac{k_{NC}}{rh_{NC-ligand}} - 1 \right)},$$

where $k_{ligand}$ is the ligand thermal conductivity, $k_{NC}$ the NC core thermal conductivity, $r$ the NC core radius, $h_{NC-ligand}$ the NC–ligand interfacial conductance, and $\varphi_{NC}$ the NC volume fraction. Then, the effective diffusivity of the composite medium can be calculated as $D_{eff} = k_{eff}/\rho C_p$, where $\rho$ is the density and Malen and coworkers showed that, specifically, the mass-weighted average specific heat capacity $C_p$, is appropriate for NC arrays.¹¹

Assuming bulk thermal parameters of the NC and ligand, $h_{NC-ligand} = 200 \text{ W m}^{-2} \text{ K}^{-1}$ as expected for a high density of thiolate ligands,¹¹,¹²,¹⁴,¹⁵ and FCC packing with 0.5 nm NC–NC spacing due to short ligands, we find for the CdSe NC film that $\rho = 3900 \text{ kg m}^{-3}$, $C_p = 720 \text{ J kg}^{-1} \text{ K}^{-1}$, and $\varphi_{NC} = 0.58$, and for the PbS NC film $\rho = 4100 \text{ kg m}^{-3}$ and $C_p = 520 \text{ J kg}^{-1} \text{ K}^{-1}$, and $\varphi_{NC} = 0.47$. This in turn leads to the estimate that both the CdSe and PbS NC films should have a thermal diffusivity of about $100 \text{ nm}^2 \text{ ns}^{-1}$. This value is in agreement with the diffusion coefficient of $100–200 \text{ nm}^2 \text{ ns}^{-1}$ found for the NC films using stroboSCAT at late times when exciting well above the bandgap (Figure 3).

## V. ESTIMATION OF HEAT DISSIPATION TIMESCALE

To evaluate the regime of thermal dissipation, we estimate the ratio of bulk and interfacial thermal transport as $hL/k$, where $h$ is the interfacial thermal conductance between the film and the substrate, $L$ the material thickness, and $k$ is the thermal conductivity. As the NC film is in contact with the glass substrate via the ligand layer, we take a layer conductance of $5–10 \text{ MW m}^{-2} \text{ K}^{-1}$ based on reports of polystyrene film–sapphire interfaces as a proxy for a typical organic film–glass interface.¹⁶ The film thickness $L$ here ranges from 80 to 550 nm overall. The NC film thermal conductivity $k$ estimated using the effective medium approximation above is $0.2–0.3 \text{ W m}^{-2} \text{ K}^{-1}$. This places $hL/k$ in the range of 1–12. In this case the kinetics of heat dissipation lie between the simplified limits of exponential interfacial transfer and bulk thermal diffusion.

Here we do not examine the detailed heat dissipation kinetics, but we find the order of magnitude of the characteristic time by considering the two limits with the knowledge that the true time scale will lie between the two. In the limit that thermal dissipation of the NC film is limited by interfacial heat transfer across the film–substrate interface, the characteristic timescale is given by $\tau_{interface} = \rho C_p L/h$, where $\rho$ is the NC film density, $C_p$ its specific heat capacity, $L$ the thickness of the film, and $h$ the interfacial thermal conductance. Using the values listed above for all parameters, we find that $\tau_{interface}$ ranges from 20 to 300 ns for NC film thicknesses of 80 to 550 nm. In the diffusion limited regime, the characteristic timescale of heat dissipation is $\tau_{diff} = L^2/D$, where $D$ is the thermal diffusivity. Assuming $D = 150 \text{ nm}^2 \text{ ns}^{-1}$ to be consistent with the data and the calculation above, we find $\tau_{diff}$ increases from about 40 ns to 2 µs for the same thickness range.

Finite element simulations of the heat dissipation process yield time constants that lay between these two analytical limits (Figure 2h).
## VI. SIMULATION OF OVERLAPPING ELECTRONIC AND THERMAL CONTRIBUTIONS TO CARRIER DIFFUSION MEASUREMENTS

This section elaborates on the methods and interpretation surrounding Figure 4 of the main text. To demonstrate the impact of having two carrier populations underlying the measured transient reflection profile in stroboSCAT, we generate synthetic data and perform analysis as usual. Consider photoexcitation using a Gaussian beam that generates both a charge carrier profile and a transient temperature increase with the same initial spot size. We take the resulting total transient reflection signal $\Delta R/R$ to be the weighted sum of two normalized Gaussians as a function of position $x$ and time $t$:

$$ \frac{\Delta R}{R}(x, t) = A_{el}(t) \frac{\exp[-x^2/2\sigma_{el}^2(t)]}{\sqrt{2\pi\sigma_{el}^2(t)}} + A_{th}(t) \frac{\exp[-x^2/2\sigma_{th}^2(t)]}{\sqrt{2\pi\sigma_{th}^2(t)}}, $$

where $A_{el}$ and $A_{th}$ are the time-dependent amplitudes of the electronic and thermal components, respectively, and $\sigma_{el}$ and $\sigma_{th}$ are the time-dependent standard deviations of the Gaussian profiles for the electronic and thermal components, respectively. This formulation is meant to be an empirical representation of the linear relative reflectance change broken down into differential components for each transient species,

$$ \frac{\Delta R}{R}(x, t) = \frac{1}{R_0} \left[ \left( \frac{\partial R}{\partial T} \right) \Delta T(x, t) + \sum_i \left( \frac{\partial R}{\partial n_i} \right) \Delta n_i(x, t) \right], $$

where $T$ is temperature and $n_i$ is the carrier density in state $i$.

We seek an approximate yet realistic set of parameters for illustration purposes. For the decay kinetics, we assume that the electronic signal decays as a single exponential with a lifetime of 10 ns. The thermal dissipation was taken to have a 50 ns half-life but with a power law tail to reflect slow, diffusive thermal dissipation limited by a substrate. We assume that the charge carriers undergo subdiffusive transport, $\sigma_{el}^2(t) = \sigma_0^2 + Kt^\alpha$, where $K$ is an empirical prefactor taken to be 32,000 $\text{nm}^2 \text{ ns}^{-1/2}$ such that the mean-squared expansion is $1 \times 10^4 \text{ nm}^2$ at 0.1 ns for $\alpha = 0.5$ to approximate the CdSe NC data after bandgap excitation in Figure 3. The thermal signal is assigned diffusive transport with $\sigma_{th}^2(t) = \sigma_0^2 + 2D_{th}t$ with $D_{th} = 200 \text{ nm}^2 \text{ ns}^{-1}$ to reflect the diffusivity found at late times in Figure 3. The initial distribution was given $\sigma_0 = 180 \text{ nm}$ to approximate the real data. Synthetic data sets were generated with these parameters for different relative initial amplitudes of the electronic and thermal components, $A_{0,el}$ and $A_{0,th}$. No noise was included. We highlight profiles for three cases for illustration proposes: $A_{0,el} = 1$ and $A_{0,th} = 0$ (Figure 4a, “all electronic”); $A_{0,el} = 0$ and $A_{0,th} = 1$ (Figure 4b, “all thermal”); $A_{0,el} = A_{0,th} = 0.5$ (Figure 4c, “50/50 electronic/thermal”).

These synthetic data were treated just as spatiotemporal data is typically analyzed, fitting the profiles to a single Gaussian function with floating amplitude and width to extract decay kinetics (Figure 4e) and mean-squared expansion curves (Figure 4f). The all-electronic and all-thermal simulations serve as references, exhibiting the expected fast yet subdiffusive electronic transport and slow, diffusive thermal transport. However, in the case when both species contribute significantly to the amplitude, the extracted mean-squared expansion curve lies part way between the two true populations on early timescales, and matches the thermal transport curve at late times when the slowly-decaying thermal signal dominates the signal amplitude. The mean-squared
expansion curve can even appear to contract as the wider electronic profile decays and gives way
to the temperature profile that has not yet had a chance to diffuse as far.

This simulated behavior closely resembles the experimental carrier diffusion data for the
various excitation conditions explored in the manuscript, lending weight to the picture of combined
electronic and thermal contributions discussed in the main text.

It is tempting to fit the experimental and theoretical carrier profiles to the sum of two
species to extract them. Unfortunately, fitting to the sum of two Gaussians with a common center
and similar widths is unstable with no unique solution even with no noise. Note that the ineptitude
of the single-population fit in the case of theoretical 50/50 electronic/thermal signal is not obvious
by eye as deviations from a perfect fit are minor (Figure 4c). Thus, distinguishing the two
distributions for all times is unreliable. However, if we force one of the Gaussians (i.e., thermal)
to have diffusive transport and fix its diffusion coefficient to that extracted at late times, the
transport of the other competent generally reproduces the simulated electronic contribution for
times when its amplitude is significant. This gives some hope for future refinements of the analysis
of such cases to isolate the different contributions, perhaps by imposing further constraints, the use
of principal component analysis, or machine learning. However, we note that for the real data, it
is not clear if the thermal transport is truly diffusive over all timescales.¹⁷ Motivated by the success
of the empirical analysis done without recourse to underlaying assumptions about the data in the
scope of this work, we do not pursue this specific analysis in the present work.
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