Effect of Sb incorporation on the electronic structure of InAs quantum dots

On the basis of optical characterization experiments and an eight band $kp$ model, we have studied the effect of Sb incorporation on the electronic structure of InAs quantum dots (QDs). We have found that Sb incorporation in InAs QDs shifts the hole wave function to the center of the QD from the edges of the QD where it is otherwise pinned down by the effects of shear stress. The observed changes in the ground-state energy cannot merely be explained by a composition change upon Sb exposure but can be accounted for when the change in lateral size is taken into consideration. The Sb distribution inside the QDs produces distinctive changes in the density of states, particularly, in the separation between excitation shells. We find a 50$\%$ increase in the thermal escape activation energy compared with reference InAs quantum dots as well as an increment of the fundamental transition decay time with Sb incorporation. Furthermore, we find that Sb incorporation into quantum dots is strongly nonlinear with coverage, saturating at low doses. This suggests the existence of a solubility limit of the Sb incorporation into the quantum dots during growth.

Figure 1

Normalized PL spectra obtained with excitation powers of 0.04, 0.4, and 4 W/cm${}^2$ overlapped with the PLE spectra. The corresponding detection energies are indicated on the right corner of each spectrum. The PL power dependence signal has been measured at $T$ $=$ 20 K, and the PLE powder dependence signal has been measured at $T$ $=$ 16 K.

Figure 2

Photoluminescence energy evolution with Sb concentration in the top half of the QD. The vertical error bars correspond to the PL FWHM, and the horizontal error bars correspond to the uncertainty margin of the Sb concentration measurements reported in Ref. 18. Results are compared with the $kp$ calculated energy for QDs with two different diameters ($F_{\mathrm{QD}}$ $=$ 15 and $F_{\mathrm{QD}}$ $=$ 20 nm).

Figure 3

Calculated optical absorption spectra. The spectrum of the bottom panel corresponds to the QD without Sb, the one of the middle panel corresponds to a QD with 20$\%$ Sb distributed homogenously, and finally, that of the top panel corresponds to a QD with 20$\%$ Sb in the upper half and 10$\%$ in the lower half. For the spectrum in black (red), a homogeneous (inhomogeneous) broadening of 1 (10) meV is assumed. These results correspond to a QD of 8-nm height and 15-nm diameter. The spectra are computed from 14 electron and 14 hole states.

Figure 4

Electron and hole wave functions calculated using a lens-shaped QD. The diameter of the QD is 20 nm. We consider a factor 2 difference in the Sb concentration between the top and the bottom halves as input.