Two-Photon Absorption of ZnS Quantum Dots: Interpreting the Nonlinear Spectrum

We report a quantitative wavelength-resolved analysis (460–600 nm) of the two-photon absorption (2PA) cross-section of water-soluble MPA-capped ZnS quantum dots (QDs). For that, we employed the open-aperture Z-scan technique using an amplified femtosecond laser system operating at low repetition rate (1 kHz). MPA-capped ZnS QDs with size distribution centered at ca. 3.8 nm were synthesized using the one-step aqueous procedure. The molar absorptivity of the lowest energy one-photon transition from ZnS QDs (1S3/2(h) → 1S(e)) was estimated in ∼6.5 × 104 M–1 cm–1. Nonlinear spectroscopic data showed that ZnS QDs present 2PA in the region between 4.15 and 4.35 eV (2hν) due to the 1S1/2(h1) → 1P3/2(e) low energy transition. Furthermore, two 2PA bands centered at 4.68 and 5.25 eV (2hν), associated with higher energy excitonic transitions, were also observed. The 2PA cross-section values along the entire spectral region measured (2hν = 4.15 to 5.4 eV) are in the order of 102 Goeppert–Mayer units. By means of a theoretical model based on parabolic effective-mass approximation, proposed by Fedorov et al. [Phys. Rev. B 1996, 54, 8627–8632], we modeled the 2PA cross-section spectrum and observed strong qualitative and quantitative correlation between experimental and theoretical results. In addition, using this model, we observed that the ZnS QDs present a 2PA band centered at 4.05 eV that corresponds to the lowest energy 2PA allowed excitonic transition (1P1/2(h1) → 1S3/2(e)). Theoretical results of the 2PA cross-section as a function of the ZnS QDs diameter, based on Fedorov's model, are also reported.