The two-photon absorption, 2PA, cross sections of PbS quantum dots, QDs, are theoretically and experimentally investigated and are shown to be enhanced with increasing quantum confinement. This is in contrast to our previous results for CdSe and CdTe QDs where the reduced density of states dominated and resulted in a decrease in 2PA with a decrease in QD size. Qualitatively this trend can be understood by the highly symmetric distribution of conduction and valence band states in PbS that results in an accumulation of allowed 2PA transitions in certain spectral regions. We also measure the frequency nondegenerate 2PA cross sections that are up to five times larger than for the degenerate case. We use a k·p four-band envelope function formalism to model the increasing trend of the two-photon cross sections due to quantum confinement and also due to resonance enhancement in the nondegenerate case.

The influence of quantum confinement on the one- and two-photon absorption spectra (1PA and 2PA) of PbS and PbSe semiconductor quantum dots (QDs) is investigated. The results show 2PA peaks at energies where only 1PA transitions are predicted and 1PA peaks where only 2PA transitions are predicted by the often used isotropic k x p four-band envelope function formalism. The first experimentally identified two-photon absorption peak coincides with the energy of the first one photon allowed transition. This first two-photon peak cannot be explained by band anisotropy, verifying that the inversion symmetry of the wave functions is broken and relaxation of the parity selection rules has to be taken into account to explain optical transitions in lead-salt QDs. Thus, while the band anisotropy of the bulk semiconductor plays a role in the absorption spectra, especially for the more anisotropic PbSe QDs, a complete model of the absorption spectra, for both 1PA and 2PA, must also include symmetry breaking of the quantum confined wave functions. These studies clarify the controversy of the origin of spectral features in lead-salt QDs.

Lead (II) oxide powder (PbO, 99.999%), Bis (trimethylsilyl) sulfide (TMS), Oleic acid (OA, technical grade 90%), 1-Octadecene (ODE, technical grade 90%), and anhydrous Toluene were purchased from Sigma-Aldrich. Distilled Acetone was purchased from Caledon Lab. Bistrimethylsilylselenide (TMSe>97%) was purchased from Gelest. ODE was degassed by pre-pumping at 80oC for 16 hours. QDs synthesis:The QDs were synthesized and purified using standard air-free techniques in two-neck flask equipped with magnetic stirrer, thermocouple, and heating mantle.Lead oleate stock solution (SS) used for PbS and PbSe synthesis was prepared by pumping the mixture of 4.0 mmol of PbO (0.9 g), 9.5mmol of OA (2.67 g) and 18.8 mmol of ODE (4.73 g) at 100oC for 16 hours. The sulfur or selenium precursors were prepared in a Nitrogen-filled Glove box. A mixture of 4.5 mL of SS and 15 mL of ODE was pre-pumped at 100 0 C for 30 min for each synthesis. The sulfur or selenium precursors were quickly injected at a certain temperature. Than the heater then was turned off without removing the heating mantel and the reaction flask was let to cool down slowly.

We calculate the spectrum of three-photon absorption (3PA) in zinc blende semiconductors using Kane's four-band model. We apply this to ZnSe and measure the 3PA spectrum using femtosecond pulses, obtaining excellent agreement. The spectrum shows the apparent onset of 3PA from the split-off band and also shows quantum interference between the several possible evolution pathways when exciting carriers from valence to conduction band.

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