Electronic shell structure and carrier dynamics of high aspect ratio $\mathrm{InP}$ single quantum dots

Systematic excitation-power-density dependent and time-resolved single-dot photoluminescence studies have been performed on type-I $\mathrm{InP}∕{\mathrm{Ga}}_{0.51}{\mathrm{In}}_{0.49}\mathrm{P}$ quantum dots. These dots are rather flat and therefore exhibit larger than normal single-dot ground-state transition energies ranging from 1.791 to $1.873\mathrm{eV}$. As a result of their low height, the dots have a very high aspect ratio (ratio of width to height) of approximately $27:1$. In general, even at high excitation power densities, the dots with ground-state transition energies above $1.82\mathrm{eV}$ exhibit only $s$-shell emission, while the larger dots exhibiting ground-state emission below $1.82\mathrm{eV}$ tend to exhibit emission from several (in some cases up to eight) shells. Calculations indicate that this change is due to the smaller dots having only one confined election level while the larger dots have two or more. Time-resolved investigations indicate the presence of fast carrier relaxation and recombination processes for both dot types, however, only the larger dots display clear interlevel relaxation effects as expected. The temporal behavior has been qualitatively simulated using a rate equation model. Also, in a more detailed analysis, the fast carrier relaxation is described on the basis of a quantum kinetic treatment of the carrier-phonon interaction. Finally, the dots display a clear single-photon emission signature in photon statistics measurements.

Figure 1

(Color online) (a) $1\mathrm{\mu }{\mathrm{m}}^2$ AFM image of uncapped $\mathrm{InP}$ QDs grown using the same growth parameters that were used to produce the capped QDs. Please note that the height dimension of the image is highly magnified with respect to the lateral dimensions. (b) QD height versus lateral size for the uncapped QDs. The line through the data points is a linear fit to the data and has a slope of 0.037 (1/27). This implies that the average aspect ratio is $27:1$. In other words, for a $1\mathrm{nm}$ change in QD height there is an associated $27\mathrm{nm}$ change in the QD lateral dimensions. (c) QD ensemble PL emission spectrum from nominally identical capped QDs recorded at $4\mathrm{K}$ and an excitation power density of $4\mathrm{W}∕{\mathrm{cm}}^2$ $\left(2P_0\right)$. The markers indicate the GS (biexciton) emission energy of the 18 single QDs that have been investigated to date.

Figure 2

(Color online) (a) PL spectra recorded at $4\mathrm{K}$ as a function of PD from QD1 (left graph) and QD2 (right graph). At low PDs both sets of spectra display clear excitonic emission features, namely, an exciton and a biexciton, however, at high PDs QD2 also displays a clear shell structure, whereas no such structure is apparent from QD1. At $100P_0$, a good fit of the QD2 PL spectrum may be achieved using ten Lorentzian peaks. (b) Schematic illustration of the proposed band structure of QD1 and QD2, with the former proposed to have only one confined electron shell while the latter is proposed to have several. Please note that the schematic drawing is intended to sketch the confinement situation and the resulting states without referring to the spatial directions. The interlevel energy spacing for both electrons and holes depends primarily on the lateral size of the quantum dot in question while the wetting layer and barrier states are defined along the growth direction.

Figure 3

(Color online) (a) PL intensity versus time taken at $4\mathrm{K}$ for both the $X$ and $XX$ emission of QD1 at different PDs. (b) PL intensity versus time for the $S$ $\left(XX\right)$, $P$, and $D$ emission from QD2 recorded at moderate PDs, and (c) the $S$, $P$, and $D$ emission from QD2 taken at $60P_0$. The delay of the maximum peak intensities at high PDs is thought to be due to delayed filling from higher-lying levels. (d) Curves generated using Eq. (1) which closely reproduce the related $60P_0$ data for the investigated shells. Where necessary the curves have been shifted vertically for clarity.

Figure 4

(Color online) Calculation using Eq. (2) of the temporal evolution of the $s$-shell and the $p$-shell PL signals from $\mathrm{InP}$ dots at $10\mathrm{K}$ following the excitation of carriers in the wetting layer. To mimic the finite temporal resolution of the experiment, a convolution of the theoretical result with a Gaussian $(\mathrm{FWHM}=35\mathrm{ps})$ was performed. Please note that for better visibility the PL signal for the $p$-shell has been shifted vertically.

Figure 5

(Color online) QD1 and QD2 $XX$ autocorrelation measurements recorded at moderate PDs (upper and lower graphs, respectively). Both graphs display the unambiguous signature of single-photon emission, thereby implying that the source of the emission in each case is a single QD.