Tracing spatial confinement in semiconductor quantum dots by high-order harmonic generation

We report here on results of systematic experimental-theoretical investigation of high-order harmonic generation (HHG) in layers of CdSe semiconductor quantum dots of different sizes and a reference bulk CdSe thin film. We observe a strong decrease in the efficiency, up to complete suppression of HHG with energies of quanta above the band gap for the smallest dots, whereas the intensity of below band gap harmonics remains weakly affected by the dot size. In addition, it is observed that the suppression of the above gap harmonics is enhanced with increasing the driving wavelength. These systematic investigations allow us to develop a simple physical picture explaining the observed suppression of the highest harmonics: the discretization of electronic energy levels seems to be not the predominant contribution to the observed suppression but rather the confined dot size itself, causing field-driven electrons to scatter off the dot's walls. The reduction in the dot size below the classical electron oscillatory radius and the corresponding scattering limits the maximum acceleration by the laser field. Moreover, this scattering leads to a chaotization of motion, causing dephasing and a loss of coherence, therefore suppressing the efficiency of the emission of highest-order harmonics. Our results demonstrate a regime of intense laser-nanoscale solid interaction, intermediate between the bulk and single-molecule response, and are crucial for nanophotonic platforms aiming at control over high-order harmonic properties and efficiency.

Figure 1

Experimental setup: NDFG: noncollinear difference frequency generation module, providing tunable mid-IR pulses by DFG between the signal and idler waves; FROG: frequency-resolved optical gating apparatus for pulse characterization. The lens on the stage with a mid-IR CCD camera was used for focus beam profile characterization. A white-light source with a 50× removable infinity-corrected objective (not shown), a lens, and a CCD camera were used as an imaging system for the on-site sample diagnostic.

Figure 2

(a) TEM images of quantum dots of different sizes used in this investigation. Acquisition was either carried out in scanning TEM mode using a high-angle annular detector or in TEM bright-field mode. (b) Statistical size distribution for 4 nm QDs. The analysis of the TEM images results in a mean diameter of 4.2 nm, which is in good agreement with the diameter of 4 nm determined from the position of the first excitonic transition in the absorption spectra. (c) SEM image of a layer of 4.2 nm dots deposited on a Si substrate.

Figure 3

Measured HHG spectra in different size QDs for (a) 3.72 $\mu \mathrm{m}$ and (b) 4.74 $\mu \mathrm{m}$ laser wavelength at a fixed intensity. The dashed line marks the band gap determined from photoemission/photoabsorption measurements.

Figure 4

Intensity dependence of the harmonic's yield for the 3.72 $\mu \mathrm{m}$ laser wavelength: (a) for the 4.4 nm size QDs and (b) 2.2 nm size QDs. Intensity dependence of the harmonic's yield for the 4.74 $\mu \mathrm{m}$ laser wavelength: (c) for the 4.4 nm size QDs and (d) 2.2 nm size QDs.

Figure 5

The slope of the laser intensity dependence of the harmonic's yield as a function of harmonic order in the range of laser intensities $0.4–1\mathrm{TW}\mathrm{c}{\mathrm{m}}^{-2}$ for (a) 3.75 $\mu \mathrm{m}$ and (b) 4.74 $\mu \mathrm{m}$ laser wavelength

Figure 6

Ellipticity dependence of the harmonic's yield. (a) The spectrogram for the reference film and (b) the spectrogram for 2.2 nm QDs. Note the logarithmic scale of the spectral intensity. Spectrally integrated harmonic yield for (c) the reference film and (d) 2.2 nm size QDs. The laser wavelength is 4.74 $\mu \mathrm{m}$.

Figure 7

FWHM of ellipticity dependence in HHG for (a) 3.75 $\mu \mathrm{m}$ and (b) 4.74 $\mu \mathrm{m}$ laser wavelength and different dot diameters. The laser intensity is fixed at $0.5\mathrm{TW}\mathrm{c}{\mathrm{m}}^{-2}$.

Figure 8

(a) Visual representation of 272-atom ${\mathrm{Cd}}_{136}{\mathrm{Se}}_{136}$ quantum dot (diameter 2.16 nm) with spatial structure as it would be as a cut from bulk (upper image) and the energetically optimized structure (lower image). The histograms show the distribution of interatomic distances between Cd and Se atoms; (b) electronic energy structure of ${\mathrm{Cd}}_{136}{\mathrm{Se}}_{136}$ quantum dot with optimized geometry and (c) ${\mathrm{Cd}}_2{\mathrm{Se}}_2$ molecule. The blue levels are fully occupied and form in the bulk valence band(s), whereas the red levels show unoccupied states and form conduction bands. The inset in (b) shows a close-up of the bottom of the conduction band. The bar shows the scale of the laser quanta energy 0.26 eV, corresponding to the 4.72 $\mu \mathrm{m}$ wavelength.

Figure 9

(a) Modeled electric field (in atomic units) in the laser pulse. (b) HHG spectra for the bulk (wine curve) and 64 atoms QD (violet curve). The spectra are normalized to their maxima.

Figure 10

Simulated dipole acceleration spectra in QDs of different sizes for (a) 3.75 $\mu \mathrm{m}$ and (b) 4.75 $\mu \mathrm{m}$ laser wavelengths. The irregular structure of the spectrum is the consequence of scattering at the walls; see in the text.

Figure 11

Dynamics of selected trajectories with zero initial velocity and different initial positions within the well for (a) 4 nm diameter dots and (b) 2 nm diameter dots. The phase of the laser field oscillations is defined as $\phi =\omega t/\pi$ where $\omega$ is the laser frequency. The trajectories leaving the well correspond to particles stochastically heated to energies above the work function $V_0$.

Figure 12

Kinetic energy at different electron trajectories, moving at a given moment of time within the emission region, for different dot diameters and driven by (a) 3.75 $\mu \mathrm{m}$ and (b) 4.75 $\mu \mathrm{m}$ laser wavelength.

Figure 13

(a) UV/vis absorption (bottom panel) and normalized photoluminescence spectra (top panel) of CdSe QDs of different sizes used in this investigation dispersed in toluene. (b) Tauc plots for different sizes of CdSe QDs derived from absorption spectra of particles dispersed in toluene and (c) normalized photoluminescence spectra of different sizes of CdSe QDs deposited in the layer.

Figure 14

(a) UV/vis absorption spectra and (b) Tauc plot of the bulk CdSe layer.

Figure 15

XRD patterns of CdSe QDs of different sizes.

Figure 16

XRD of bulk CdSe layer.

Figure 17

TEM images and size distribution of different sizes of CdSe QDs shown by blue, green, yellow, and red (border of the images and histograms).

Figure 18

SEM images of CdSe QDs of sizes 2.2 nm (blue), 3 nm (green), 4 nm (yellow), and 8.2 nm (red). The 2 and 3 nm sized QDs are below or just at the limit of the resolution of the instrument.

Figure 19

(a) AFM image of 4 nm QD. (b) Thickness determination curve of the QD layers, where thickness is calculated from the bottom of the scratch (at 0) to the top of the surface.