Low threshold and efficient multiple exciton generation in halide perovskite nanocrystals

Abstract

Multiple exciton generation (MEG) or carrier multiplication, a process that spawns two or more electron-hole pairs from an absorbed high-energy photon (larger than two times bandgap energy E_g), is a promising way to augment the photocurrent and overcome the Shockley-Queisser limit. Conventional semiconductor nanocrystals, the forerunners, face severe challenges from fast hot-carrier cooling. Perovskite nanocrystals possess an intrinsic phonon bottleneck that prolongs slow hot-carrier cooling, transcending these limitations. Herein, we demonstrate enhanced MEG with 2.25E_g threshold and 75% slope efficiency in intermediate-confined colloidal formamidinium lead iodide nanocrystals, surpassing those in strongly confined lead sulfide or lead selenide incumbents. Efficient MEG occurs via inverse Auger process within 90 fs, afforded by the slow cooling of energetic hot carriers. These nanocrystals circumvent the conundrum over enhanced Coulombic coupling and reduced density of states in strongly confined nanocrystals. These insights may lead to the realization of next generation of solar cells and efficient optoelectronic devices.

Fig. 1

Size-dependent bandgaps and biexciton lifetimes of FAPbI₃ NCs. a Normalized PL spectra of FAPbI₃ NCs in toluene with different sizes (emission peak positions are listed in Supplementary Table 1) and the FAPbI₃ polycrystalline bulk-film counterpart. b Bandgap energies (black dots) as a function of the edge length of FAPbI₃ NCs together with fitting using Supplementary Eq. (1) (red solid line). The vertical blue dashed line indicates the position of exciton Bohr diameter (D_x). Error bars correspond to the NC size distribution and uncertainty in the measurements of TA spectra. c Biexciton Auger-lifetime (black circles) as a function of NC volume. The horizontal and vertical error bars correspond to the NC size distribution and the uncertainty in the fitting procedure, respectively. The red square is obtained from ref. (Fang et al)

Fig. 2

MEG QY determination from TA dynamics. a Normalized (norm.) band-edge PB dynamics under different pump photon energies with <N₀> = 0.24 in 7.5 nm-sized FAPbI₃ NCs. Inset shows the similar measurements for the bulk-counterpart with pump fluence of 2 × 10¹⁷ cm⁻³. TA dynamics generated by photon energy of (b) 1.51E_g and (c) 2.70E_g for 7.5-nm sized NCs with different average number of absorbed photons per NC <N₀>. Solid black lines are single exponential in (b) and biexponential fittings in (c), respectively. d–f R_POP as a function of <N₀> under photon energies below and above MEG threshold for three different sized FAPbI₃ NCs. R_POP is determined by the PB intensity ratio at the beginning of pump excitation at a delay time of 2 ps to that at a delay time of 4 ns and fitted with Eq. (1) (solid lines). The error bars in d–f represent the uncertainties in the determination of TA amplitudes in the fitting procedure of TA dynamics

Fig. 3

MEG threshold and slope efficiency determination. a MEG QY as a function of relative pump photon energies (hν/E_g) for FAPbI₃ NCs of different edge lengths and bulk-counterpart. b Comparison of MEG QY vs. hν/E_g with PbSe NCs (from ref. ) and PbS NCs (E_g = 1.3 eV) as a reference measured using the same setup. The error bars in a, b represent the uncertainties in the MEG QY fitting procedure. c Detailed balance calculations for maximum PCEs under AM1.5 solar illumination as a function of material E_g for different MEG thresholds. The Shockley–Queisser limit is denoted as SQ

Fig. 4

Slower hot-carrier cooling in smaller FAPbI₃ NCs. a Schematic for hot-carrier cooling (left) below MEG threshold and (right) above the MEG threshold. b Normalized band-edge PB dynamics in colloidal 7.5 nm-sized FAPbI₃ NCs and their bulk-counterpart (inset) under different pump wavelengths. The dashed lines are single exponential fits. c Band-edge PB buildup-time of FAPbI₃ NCs (7.5 nm (blue circles); 12.9 nm (red triangles)), polycrystalline bulk-film (black square), and PbS NCs (yellowish-brown diamonds) measured at different pump photon energies. Gray region indicates the energies below ideal MEG threshold of 2E_g. d Hot-carrier cooling time as a function of converted real excess energies of carriers in FAPbI₃ NCs. The error bars in (c) and (d) represent the uncertainty in the fitting procedure for the rise time