Spectator Exciton Effects in Nanocrystals III: Unveiling the Stimulated Emission Cross Section in Quantum Confined CsPbBr3 Nanocrystals

Abstract

Quantifying stimulated emission in semiconductor nanocrystals (NCs) remains challenging due to masking of its effects on pump-probe spectra by excited state absorption and ground state bleaching signals. The absence of this defining photophysical parameter in turn impedes assignment of band edge electronic structure in many of these important fluorophores. Here we employ a generally applicable 3-pulse ultrafast spectroscopic method coined the "Spectator Exciton" (SX) approach to measure stimulated-emission efficiency in quantum confined inorganic perovskite CsPbBr₃ NCs, the band edge electronic structure of which is the subject of lively ongoing debate. Our results show that in 5-6 nm CsPbBr₃ NCs, a single exciton bleaches more than half of the intense band edge absorption band, while the cross section for stimulated emission from the same state is nearly 6 times weaker. Discussion of these findings in light of several recent electronic structure models for this material proves them unable to simultaneously explain both measures, proving the importance of this new input to resolving this debate. Along with femtosecond time-resolved photoluminescence measurements on the same sample, SX results also verify that biexciton interaction energy is intensely attractive with a magnitude of ∼80 meV. In light of this observation, our previous suggestion that biexciton interaction is repulsive is reassigned to hot phonon induced slowdown of carrier relaxation leading to direct Auger recombination from an excited state. The mechanism behind the extreme slowing of carrier cooling after several stages of exciton recombination remains to be determined.

Figure 1

(A) Linear absorption and PL spectra of 6 nm CsPbBr₃ NCs. (B) TEM image of them with the mentioned average edge-length.

Figure 2

(A) Time resolved PL specta of 6 nm CsPbBr₃ under high intensity photoexcitation resulting in ⟨N₀(max)⟩ = 3.5. At early delays broadened PL resulting from high multiexcitons is noted. The broadening at the blue energy side converges to the steady state emission spectrum rapidly leaving a distinct long-lived red shoulder decaying on a longer time scale. (B) TRPL at ⟨N₀(max)⟩ = 1.4: Lowering in pump intensity eliminates blue extended PL, with a distinct red shoulder which converges on a similar time scale to the steady state emission as in (A), depicted in orange shading. (C) TRPL spectra recorded at 15 ps (black circles) and 50 ps (blue circles) at ⟨N₀(max)⟩ = 3.5. The latter, and the difference spectrum which is presented in red circles, are both fit to Gaussian functions presented as solid blue and red lines, respectively. The difference of peak positions between red and blue curves estimates a biexciton binding energy of 80 meV. Inset to panel C presents a schematic potential energy diagram clarifying rationale for estimating Δ_XX.

Scheme 1. “Spectator Exciton” Experiment

A strong above band gap saturation pulse excites the whole sample with at least a single exciton. 50 ps after that, once all the excited particles have relaxed to a single BE exciton, a weak chopped pulse is introduced to further excite the NCs. The time resolved changes are then followed by a variably delayed broadband probe.

Figure 3

(A) Pump–probe spectra of 6 nm CsPbBr₃ NCs at different delays after pumping with weak 400 nm laser pulse producing ⟨N₀⟩ = 0.1. (B) Same as (A) under intense 400 nm photoexcitation leading to ⟨N₀⟩ = 6. (C) Difference spectrum accumulated over the process of Auger recombination from data in (B) (green minus blue curve).

Figure 4

Comparison of TA measurements after weak 400 nm excitation, without (black) and with (Red) spectator excitons at a series of designated pump–probe delays (A–C). Biexciton recombination is compensated for by multiplying it by e^kτ where k is the Auger rate and τ the PP delay Panel D presents buildup of BE bleach signal associated with hot carrier relaxation following 400 nm excitation with (λ_Probe = 498 nm) and without SX (λ_Probe = 484 nm). The exponential fits indicate that carrier cooling is unaffected by SX presence. (E) Comparison of difference cross sections.

Scheme 2. Schematic Illustration of Two Possible Outcomes of Band Edge Irradiation on SX Saturated NCs

Photoexcitation results in a biexciton as depicted to the right. This reverts within tens of ps to a single exciton through Auger recombination (A.R.). Alternatively, irradiation stimulates emission (S.E.) to the stable ground state depicted left.

Figure 5

(A) Spectral evolution in an SX experiment with band edge pumping. Diminishing of the red bleach signal though Auger leaves a long-lived residual consisting of an inverted replica of the single exciton TA. (B) Integrated SE yield as obtained from the inverted signal intensity as a function of band edge pump wavelengths (tracking different portions of CW PL; Figure S7). (C) Transient difference absolute cross section spectra compared with the absorption cross section of a single particle (black). The difference cross section per particle without SX at PP delay of 2 ps is shown in red, compared with that obtained with SX at a delay of 100 ps (blue). In Magenta is the stimulated emission cross section (*10) calculated on the basis of these spectra. See SI for details.

Figure 6

Comparison of the apparent absorption cross sections of a ground state NC, one containing one, and one containing two relaxed excitons, for (A) 6 nm CsPbBr₃ and (B) 5 nm CsPbBr₃. In both cases, no net gain is observed at any wavelength under single excitation of the NCs, while a large gain is obtained in doubly excited case. The purely absorptive cross-section is depicted as well, clearing of the effects of stimulated emission obtained by the SX method.