Phonon-assisted radiative recombination of excitons confined in strongly anisotropic nanostructures

The influence of acoustic phonons on the emission spectra of quantum dashes (QDashes), that are quasi-zero-dimensional epitaxial nanostructures with significant shape anisotropy, is investigated both experimentally and theoretically. Photoluminescence (PL) spectra of single InAs/InGaAlAs/InP (001) QDashes exhibit sidebands of the main emission peak, clearly indicating the contribution of phonon-assisted emission to the exciton luminescence, which dominates the PL line shape at higher temperatures (between 50 and 100 K, usually). By utilizing the independent boson model we perform systematic and comprehensive studies of the influence of the overall geometry of quantum confinement on this spectral feature in an uncommon quantum system. A comparison of the experimental data and the results of modeling have confirmed the existence of two types of states differing in the spatial confinement and symmetry within one sample, i.e., typical for large elongated objects or characteristic for smaller and more symmetric structures. The latter are supposed to correspond to local widenings or zigzag bends present in some of the dashes and acting as additional localization centers, which confine excitons in a much smaller volume and decrease effectively the resulting in-plane anisotropy. Those observations evidence a nontrivial spatial character of the quantum confinement in these structures. They are consistent with our previous polarization-resolved study on the QDash ensemble and correlate well with the exciton decay times, and the spectral-diffusion-dominated line broadenings at low temperatures reflecting the effect of electric field fluctuations on the excitons of a different spatial extension. Finally, we demonstrate a pronounced suppression of phonon-induced decoherence for such strongly elongated nanostructures.

Figure 1

Temperature dependence of the μPL spectra of single InAs/InP QDashes originating from the sample with a nominal dash size of $100\times 20\times 3.5{\mathrm{nm}}^3$ in the range of 5–90 K.

Figure 2

Temperature dependence of the FWHM of two representative lines from the spectra in Fig. 1. Dashed lines are a guide to the eye. Inset: μPL spectra of line 1 for selected temperatures, normalized to the integrated intensity.

Figure 3

Wave-function localization length $l_x$ dependence on the physical length of the QDash based on the eight-band $\mathbf{k}·\mathbf{p}$ calculations.

Figure 4

(a) Calculated single exciton PL spectra of $100\times 16\times 3.0{\mathrm{nm}}^3$ InAs QDash, normalized to the integrated intensity for various temperatures with ${\sigma }^{\mathrm{SD}}$ = 0.1 meV. For clarity, the energy positions of emission lines are shifted horizontally. (b) Temperature dependence of the full width at half maximum of the exciton line.

Figure 5

Calculated phonon spectral densities for a $100\times 16\times 3.0{\mathrm{nm}}^3$ InAs QDash at various temperatures, assuming exciton interaction with acoustic phonons via (a) deformation potential and (b) piezoelectric effect.

Figure 6

Calculated temperature dependence of the exciton emission line FWHM for two lengths of a QDash: (a) $L$ = 100 nm and (b) $L$ = 25 nm and a set of cross sections $D$×$H$ ranging from 8 × 1.5 up to $24\times 4.5{\mathrm{nm}}^2$. (c) and (d) Analogous dependencies of FWHM are presented for two extreme cross sections and ${\sigma }^{\mathrm{SD}}$ in the range of 0.1 to 0.5 meV. (e) Calculated temperature dependence of the exciton emission line FWHM of typical InAs QDashes with cross-section dimensions $D\times H=16\times 3.0{\mathrm{nm}}^2$ and a set of lengths $L$ ranging from 25 to 125 nm. (f) Analogous dependencies of FWHM are presented for two extreme lengths and ${\sigma }^{\mathrm{SD}}$ in the range of 0.1 to 0.5 meV.

Figure 7

Temperature dependence for the four exciton PL emission lines FWHM. Black squares represent experimental data obtained for QDashes originating from the sample with nominal dashes size of $100\times 16\times 3.0{\mathrm{nm}}^3$. Color solid lines are modeled curves for fixed values of $D\times H=16\times 3.0{\mathrm{nm}}^3$ and lengths $L$ equal to 20 nm in the case of (a) and (b) and 100 nm in the case of (c) and (d). Different colors represent different values of ${\sigma }^{\mathrm{SD}}$ in the ranges 0.08–0.14 and 0.18–0.25 meV for (a), (b) and (c), (d), respectively. Decay times ${\tau }_D$ are determined from time-resolved experiments performed as in Ref. [24].