Universal Size-Dependent Stokes Shifts in Lead Halide Perovskite Nanocrystals

Abstract

Size-dependent photoluminescence Stokes shifts (Δ<i>E</i>_s) universally exist in CsPbX₃ (X = Cl^-, Br^-, or I^-) perovskite nanocrystals (NCs). Δ<i>E</i>_s values, which range from ∼15 to 100 meV for NCs with average edge lengths (<i>l</i>) from approximately 13 to 3 nm, are halide-dependent such that Δ<i>E</i>_s(CsPbI₃) > Δ<i>E</i>_s(CsPbBr₃) ≳ Δ<i>E</i>_s(CsPbCl₃). Observed size-dependent Stokes shifts are not artifacts of ensemble size distributions as demonstrated through measurements of single CsPbBr₃ NC Stokes shifts (⟨Δ<i>E</i>_s⟩ = 42 ± 5 meV), which are in near quantitative agreement with associated ensemble (<i>l</i> = 6.8 ± 0.8 nm) Δ<i>E</i>_s values (Δ<i>E</i>_s ≈ 50 meV). Transient differential absorption measurements additionally illustrate no significant spectral dynamics on the picosecond time scale that would contribute to Δ<i>E</i>_s. This excludes polaron formation as being responsible for Δ<i>E</i>_s. Altogether, the results point to an origin for Δ<i>E</i>_s, intrinsic to the size-dependent electronic properties of individual perovskite NCs.