Optical response of (InGa)(AsSb)/GaAs quantum dots embedded in a GaP matrix

The optical response of (InGa)(AsSb)/GaAs quantum dots (QDs) grown on GaP (001) substrates is studied by means of excitation and temperature-dependent photoluminescence (PL), and it is related to their complex electronic structure. Such QDs exhibit concurrently direct and indirect transitions, which allows the swapping of $\mathrm{\Gamma }$ and $L$ quantum confined states in energy, depending on details of their stoichiometry. Based on realistic data on QD structure and composition, derived from high-resolution transmission electron microscopy (HRTEM) measurements, simulations by means of $\mathbf{k}·\mathbf{p}$ theory are performed. The theoretical prediction of both momentum direct and indirect type-I optical transitions are confirmed by the experiments presented here. Additional investigations by a combination of Raman and photoreflectance spectroscopy show modifications of the hydrostatic strain in the QD layer, depending on the sequential addition of QDs and capping layer. A variation of the excitation density across four orders of magnitude reveals a 50-meV energy blueshift of the QD emission. Our findings suggest that the assignment of the type of transition, based solely by the observation of a blueshift with increased pumping, is insufficient. We propose therefore a more consistent approach based on the analysis of the character of the blueshift evolution with optical pumping, which employs a numerical model based on a semi-self-consistent configuration interaction method.

Figure 1

Set of samples studied in this work: $S_{\mathrm{w}/\mathrm{o}}$ represents the structure without QDs (only GaAs interlayer), $S_{\mathrm{with}}$ with ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x{\mathrm{As}}_y{\mathrm{Sb}}_{1-y}$ QDs on top of the GaAs layer, and $S_{\mathrm{cap}}$ with an additional GaSb capping layer above the QDs.

Figure 2

(a) Material distribution profile taken by EDX along the growth direction for all elements present in sample $S_{\mathrm{cap}}$, and averaged over the area highlighted by the yellow dashed curve of (d). In the QD area, between the vertical positions of 30 and $40\mathrm{nm}$ in the cut, a substantial increase of In, As, Sb and a reduction of P are observed. (b) HRTEM micrograph clearly showing a single QD with truncated-pyramid shape (highlighted in yellow). The inset (c) shows a schematic of the investigated sample, while inset (d) shows the estimated composition of Ga and As around the QD depicted in (c). (e) displays, from top to bottom: cross-section HRTEM image of $S_{\mathrm{cap}}$ and three EDX concentration profiles measured at the same time: red for P, white for As, and blue for In. HRTEM images were taken under strong-beam bright field condition using the (200) reflection perpendicular to the growth direction.

Figure 3

Raman spectra taken at room temperature of samples $S_{\mathrm{cap}}$ (red), $S_{\mathrm{with}}$ (blue), $S_{\mathrm{w}/\mathrm{o}}$ (green), and bulk GaAs (grey). The dashed lines show the reference bulk GaAs TO and LO phonon modes [71]. Calculated hydrostatic strain components ${\epsilon }_{\mathrm{H}}$ for each sample are also indicated. A label IF corresponds to the interface Raman band.

Figure 4

PR spectra at room temperature of samples $S_{\mathrm{w}/\mathrm{o}}, S_{\mathrm{with}}$, and $S_{\mathrm{cap}}$. Solid lines indicate best fits to Aspnes' TDFF [80]. Corresponding critical point energies and broadening factors are shown in the Table 3.

Figure 5

Comparison of the experimentally obtained transition energies for the excitation density $D=0.1\mathrm{W}/{\mathrm{cm}}^2$, for samples $S_{\mathrm{with}}$ (a) and $S_{\mathrm{cap}}$ (b) (symbols). The corresponding theoretical values for transitions from $\mathrm{\Gamma }$ and $L$ electrons (located in QD) to $\mathrm{\Gamma }$ holes, obtained by $\mathbf{k}·\mathbf{p}$ approximations (solid lines), are also displayed. The red dashed lines represent the transitions energies between $X_{xy}$ electrons and $\mathrm{\Gamma }$ holes (both quasiparticles located in IL), extracted from band edges. The slash-dot vertical lines indicate the concentrations where theory matches the experimental data. Sketches of the corresponding QD areas are also depicted for reader's guidance.

Figure 6

PL of samples $S_{\mathrm{w}/\mathrm{o}}$ (green curve), $S_{\mathrm{with}}$ (blue), and $S_{\mathrm{cap}}$ (red) measured at $15\mathrm{K}$, and excitation density of $10\mathrm{W}/{\mathrm{cm}}^2$. As reference, the background emission from GaP substrate is also shown (black curve) and multiplied by a factor of 70, to facilitate comparison.

Figure 7

PL spectra of $S_{\mathrm{w}/\mathrm{o}}$ for excitation densities $D$ of 100 and $0.1\mathrm{W}/{\mathrm{cm}}^2$ (symbols) and fits (red solid curves) by Eqs. (7) (left) and (6) (right). Individual transitions are highlighted in different colours. The vertical dashed lines indicate the energy positions of the observed energy transitions at $100\mathrm{W}/{\mathrm{cm}}^2$ (see labels of individual bands on the top.

Figure 8

$E_{\mathrm{phon}}$ for individual phonon-broadened bands from fits by Eq. (6) as a function of $D$ (symbols). Bulk phonon frequencies of GaAs (gray solid line), GaP (dashed orange) listed in Table 4. Violet dotted lines represent multiphonon frequencies from both GaAs and GaP.

Figure 9

Transition energies from fits by Eq. (7) (full symbols) and (6) (empty symbols) as a function of $D$. Lines represent fits by Abramkim et al. model (8).

Figure 10

Integrated PL intensity of individual bands obtained by fits by Eq. (6) as a function of excitation density $D$ (symbols) fitted in three regions by $I\propto D^{\gamma }$. The exponents $\gamma$ are added in legend.

Figure 11

$S_{\mathrm{w}/\mathrm{o}}$. (a) measured PL at $D=30{\mathrm{Wcm}}^{-2}$ between 15 and 100 K. Inset (b) shows the best fit of emission energy of $O_X^{\mathrm{IL}}$–$O_{3\mathrm{R}}^{\mathrm{IL}}$ (symbols) as a function of temperature by the Varshni Eq. (9), solid curve [modified Varshni Eq. (11), dashed curve] model. In the inset (c), we give integrated PL intensities of individual transitions $O_X^{\mathrm{IL}}$–$O_{3\mathrm{R}}^{\mathrm{IL}}$ (symbols) fitted by the Boltzmann model, Eq. (12) (solid curves), with the high temperature activation energies $E_2$ shown in the inset.

Figure 12

PL spectra (points) of samples $S_{\mathrm{with}}$ (a) and $S_{\mathrm{cap}}$ (b) for $D=100$ and $0.05\mathrm{W}/{\mathrm{cm}}^2$ fitted by sum of five Gaussian bands. Individual transitions are shadowed and for estimation of their energy shift the vertical lines are added in positions of transition energies observed at $100\mathrm{W}/{\mathrm{cm}}^2$. Labels of bands are given at the top.

Figure 13

$S_{\mathrm{with}}$. (a) Band scheme of ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$ QD calculated using nextnano$++$ [83, 84] along with single-particle eigenenergies (dotted lines). (b) Detail of the band scheme with showing also recombination paths (solid arrows with transition energies in meV) and escape energies (values in meV) observed in temperature dependent PL. (c) Integrated PL intensity of individual transitions (symbols) fitted by linear dispersion in log-log scale, corresponding slopes are given in the legend. (d) Emission energy of individual transitions (symbols) vs $D$; values of absolute blueshifts are in the inset. Solid (dashed) curves represent fits by Eq. (8) with $\beta =0$ ($\beta \ne 0$).

Figure 14

$S_{\mathrm{with}}$. (a) Measured PL at $D=2\mathrm{W}{\mathrm{cm}}^{-2}$ for temperatures between 15 and 100 K. In inset (b) we show the emission energy of $W_{\mathrm{\Gamma }}^{\mathrm{QD}}$–$W_X^{\mathrm{IL}}$ (symbols) as a function of temperature fitted by the Varshni Eq. (9), solid curve, [modified Varshni Eq. (11), dashed curve] model. In inset (c), integrated PL of individual transitions $W_{\mathrm{\Gamma }}^{\mathrm{QD}}$–$W_X^{\mathrm{IL}}$ (symbols) fitted (solid curves) by the Boltzmann model, Eq. (12) is shown along with the high temperature activation energies $E_2$.

Figure 15

$S_{\mathrm{cap}}$. (a) PL spectra for $D=20{\mathrm{Wcm}}^{-2}$ for temperatures between 15 and 100 K. The results in (b) and (c) are given in the same way as in Fig. 14.

Figure 16

$S_{\mathrm{cap}}$. (a) Calculated band scheme of a ${\mathrm{In}}_{0.2}{\mathrm{Ga}}_{0.8}{\mathrm{As}}_{0.8}{\mathrm{Sb}}_{0.2}$ QD using nextnano$++$ [83] simulation suite with single-particle eigenenergies indicated by dotted lines. (b) Detail of the band scheme with indicated emission recombination paths (solid arrows with transition energies in meV) and escape energies (values in meV) found from temperature dependent PL. (c) Integrated PL intensity of individual transitions (symbols) fitted by linear dispersion in a log-log scale, corresponding slopes for segments are given in the inset. (d) Emission energies of individual transitions (symbols) vs excitation density $D$. Values of absolute blueshifts are given in the inset. Solid (dashed) lines represent fits by Eq. (8) with $\beta =0$ ($\beta \ne 0$).

Figure 17

From left to right we show the polar graphs of $C\left(\theta \right)$ for samples (a) $S_{\mathrm{w}/\mathrm{o}}$, (b) $S_{\mathrm{with}}$, and (c) $S_{\mathrm{cap}}$, respectively. Individual bands of PL spectra for each sample are represented by different symbols, consistently with labeling in previous figures.