Excitation intensity dependence of photoluminescence spectra of SiGe quantum dots grown on prepatterned Si substrates: Evidence for biexcitonic transition

The pumping intensity ($I$) dependence of the photoluminescence (PL) spectra of perfectly laterally two-dimensionally ordered SiGe quantum dots on Si(001) substrates was studied. The PL results from recombinations of holes localized in the SiGe quantum dots and electrons localized due to the strain field in the surrounding Si matrix. The analysis of the spectra revealed several distinct bands, attributed to phonon-assisted recombination and no-phonon recombination of the excitonic ground state and of the excited excitonic states, which all exhibit a linear $I$ dependence of the PL intensity. At approximately $I\ge 3\text{W}{\text{cm}}^{-2}$, additional bands with a nearly quadratic $I$ dependence appear in the PL spectra, resulting from biexcitonic transitions. These emerging PL contributions shift the composite no-phonon PL band of the SiGe quantum dots to higher energies. The experimentally obtained energies of the no-phonon transitions are in good agreement with the exciton and biexciton energies calculated using the envelope function approximation and the configuration interaction method.

Figure 1

Atomic force micrographs of the samples (a) $S1$ (pit period 300 nm) and (b) $S2$ (pit period 170 nm). The scanned area was $1.5\times 1.5\mu \mathrm{m}$ for both samples. The average height of the QDs in sample $S1$ ($S2$) is 15.3 (15) nm and the QD base diameter is 122.8 (118) nm.

Figure 2

Measured (open squares) and fitted (red curve) PL spectrum of the sample $S1$ for (a) $I=0.25\mathrm{W}{\mathrm{cm}}^{-2}$, (b) $I=0.49\mathrm{W}{\mathrm{cm}}^{-2}$, and (c) $I=4.94\mathrm{W}{\mathrm{cm}}^{-2}$. The residual error (blue curve) has been multiplied by a factor of 2. The individual GL profiles are attributed to phonon replicas (dotted curves), excitonic ($X_0,X_1$, broken curves), and biexcitonic ($X{X}_0$, full curve) states. The calculated values of the energies of the excitonic (biexcitonic) states for the model dome-shaped dot (see Fig. 5) blueshifted by 1 meV are displayed by dashed (solid) vertical lines. The inset of panel (c) shows the calculated probability densities (contours of $|{\Psi }^2|=0.1{\mathrm{nm}}^{-3}$) of the hole ground state (blue), ${\Delta }_{xy}$ (green), and ${\Delta }_z$ (red) electron ground states and their location within the dot (its surface is represented by the light green surface) as obtained by the nextnano$++$ simulation suite (Ref. 31).

Figure 3

Measured PL spectra (the values of the pumping intensity are given next to the right vertical axis) for samples (a) $S1$ and (b) $S2$. Dashed (solid) vertical lines correspond to the resonance energies $E_0$ of the fitted GL profiles attributed to excitons (biexcitons). The dotted vertical line in (b) corresponds to the detector cutoff energy of 780 meV.

Figure 4

Excitation intensity ($I$) dependence of the oscillator strength ($F_i$) normalized to the respective squared resonance energies $E_{0,i}$ and divided by the oscillator strength $F_{X_0}$ of the no-phonon transition with the lowest value of $E_0$, i.e., of the $X_0$ profile, for the no-phonon transition GL profiles in the sample $S1$ (a) and in the sample $S2$ (b). The sums of $F_i$ of the phonon replicas are displayed by open triangles. The thick lines represent fits of the measured data to the linear functions $a_1{I}^{a_2}$ and the thin ones are guides to the eye. Note, that due to the linearity of the normalization factor $F_{X_0}$ with respect to $I$, quadratic (linear) powers of $I$ appear as linear (constant) functions. The graphs in the insets show the $I$ dependence of the FWHM of the fitted Gaussian lines. The same symbols as in the main diagram are used except for the dependencies of the profiles with the lowest value of $E_0$, which are displayed by open circles.

Figure 5

A cut through the simulation space for the SiGe QD of sample $S1$ ($S2$), containing its vertical axis. The QDs were approximated by cylindrically symmetric cones with the dimensions shown in the figure. The Ge content inside the QD varies linearly from 0.277 (0.34) at the base of the cone to 0.43 (0.49) at its apex. The dotted rectangle denotes the space where the Schrödinger equation was solved and the grid spacing was set to 0.5 nm.