Hot carrier redistribution, electron-phonon interaction, and their role in carrier relaxation in thin film metal-halide perovskites

Temperature dependent (4–295 K) photoluminescence and transmission spectra are analyzed to study the effect of changing the different components of a perovskite compound, be it $A, B$, or $X$. Four different films are compared: $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3, \mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3, \mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, and $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$. The low temperature results highlight the changes that occur, especially underlying ones that are easily masked at room temperature. The overall Stokes shift is of similar magnitude at room temperature for the three Pb only based samples. This is governed by the interaction strength ${\mathrm{\Gamma }}_{\mathrm{LO}}$, phonon energy $E_{\mathrm{LO}}$, and exciton binding energy $E_{\mathrm{ex}}$. One exception to this behavior is the Sn based $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$ film, which shows a lack of Stokes shift between the absorption and photoluminescence. However, the strong absorption (more than 100 meV) below the band gap is indicative of an excitonic feature that has a large density of states. Transient absorption measurements confirm the trends observed in continuous wave (CW) measurements; the three Pb only films all show the convolution of an excitonic feature within 20 meV of the band gap as a contributing factor to the photobleach along with a region of high energy photoinduced absorption (PIA). However, the behavior for the Sn based film is notably different (just as it is in the CW measurements) with an unusual low energy PIA and a lack of high energy PIA. The large unusual low energy PIA is attributed to the large sub-band-gap absorption observed in the CW transmission/absorption measurements. Notably, regardless of interchanging components, the slow cooling of carriers in metal-halide perovskites shows little effect of ${\mathrm{\Gamma }}_{\mathrm{LO}}, E_{\mathrm{LO}}$, and $E_{\mathrm{ex}}$. As such, here it is proposed that while the initial cooling of carriers is attributed to LO phonons, the overall cooling of carriers is dominated by the intrinsic low thermal conductivity of all metal-halide perovskites, which limits the dissipation of acoustic phonons in these systems.

Figure 1

Temperature dependent PL from 4.2 to 295 K for (a) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$, (b) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, (c) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, and (d) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$, respectively.

Figure 2

FWHM from 4.2 to 295 K for (a) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$, (b) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, (c) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, and (d) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$, respectively. The purple solid line is the fit to the data with the contributions of the various coupling parameters as described in Eq. (1) shown in red for ${\mathrm{\Gamma }}_0$ plus ${\mathrm{\Gamma }}_{\mathrm{LA}}$, green for ${\mathrm{\Gamma }}_{\mathrm{LO}}$, and blue for ${\mathrm{\Gamma }}_{\mathrm{imp}}$. Please note in panel (b) that ${\mathrm{\Gamma }}_{\mathrm{imp}}$ overlays ${\mathrm{\Gamma }}_{\mathrm{LA}}$.

Figure 3

(a) Comparison of the temperature dependence of the peak PL energy (black circles) and the energy from the transmission spectra (red circles) for (a) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$, (b) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, (c) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, and (d) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$ from 4.2 to 295 K. Shaded regions correspond to the extent of FWHM. The insets show PL (black) and absorbance (red) spectra for 4 K (upper) and 295 K (lower).

Figure 4

Transient absorption measurement of $\mathrm{\Delta }A$ as a function of energy at room temperature for delay times ranging from 0 to 3000 ps for (a) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$, (b) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, (c) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, and (d) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$. Transient absorption measurement of $\mathrm{\Delta }A$ as a function of energy at room temperature for specific (ps) delay times (e) 0.1 (purple), 0.5 (red), 1 (green), 10 (orange), and 100 (blue) for $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$ and (f–h) 0.5, 1, 10, and 100 for (f) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, (g) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$, and (h) $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$.

Figure 5

$T_c$ as a function of delay time at room temperature for $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}_3$ (black), $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$ (red), and $\mathrm{F}\mathrm{A}\mathrm{Pb}{\mathrm{I}}_3$ (green).

Figure 6

(a) $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$ transient absorption spectra of $\mathrm{\Delta }A$ as a function of energy at room temperature for delay times ranging from 2 to 50 ps. (b) Carrier density dependence of $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$ room temperature transient absorption spectra for a delay time of 2 ps. (c) Room temperature CW carrier density dependence for $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$. (d) Cooling rate curves for carrier densities of 2 and $32\times {10}^{14}{\mathrm{cm}}^{-2}$ for $\mathrm{F}\mathrm{A}\mathrm{M}\mathrm{A}\mathrm{Pb}\mathrm{Sn}{\mathrm{I}}_3$.