Photoluminescence pressure coefficients of $\mathrm{InAs}∕\mathrm{GaAs}$ quantum dots

We have investigated the ground exciton energy pressure coefficients of self-assembled $\mathrm{InAs}∕\mathrm{GaAs}$ quantum dots by calculating 21 systems with different quantum dot shape, size, and alloying profile using the atomistic empirical pseudopotential method. Our results confirm the experimentally observed significant reductions of the exciton energy pressure coefficients from the bulk values. We show that the nonlinear pressure coefficients of the bulk InAs and GaAs are responsible for these reductions, and the percentage of the electron wave function on top of GaAs atoms is responsible for the variation of this reduction. We also find a pressure coefficient versus exciton energy relationship which agrees quantitatively with the experimental results. We find linear relationships which can be used to get the information of the electron wave functions from exciton energy pressure coefficient measurements.

Figure 1

The band-edge energies [$E\left({\Gamma }_{6c}\right)$ and $E\left({\Gamma }_{8v}\right)$] of (a) bulk InAs and (b) GaAs and their direct band gap $E_g({\Gamma }_{8v}-{\Gamma }_{6c})$ under hydrostatic pressure.

Figure 2

The PL pressure coefficient $\left(E_0^{\prime }\right)$ vs $E_0\left(0\right)$ (PL energy) and comparison with experiments. The $E_0\left(0\right)$ is the zero-pressure exciton energy which equals the single-particle electron-hole gap minus the electron-hole Coulomb interaction. The experimental results are Li et al. (Ref. 7), Ma et al. (Ref. 2), Manjon et al. (Ref. 3), and Itskevich et al. (Refs. 5 and 6). We also included one previously calculated result from Williamson et al. (Ref. 8).

Figure 3

(a) $E_{\mathrm{CBM}}$ as a function of ${\sum }_{\mathrm{at}}{W}_{\mathrm{at}}{E}_c\left(\mathrm{at}\right)$; (b) $E_{\mathrm{CBM}}^{\prime }$ as a function of ${\sum }_{\mathrm{at}}{W}_{\mathrm{at}}{E}_c^{\prime }\left(\mathrm{at}\right)$.

Figure 4

(a) The relationship between $E_0^{\prime }\left(0\right)$ and $x$ (the percentage of the electron state in GaAs); (b) the relationship between $E_0\left(0\right)$ and $x$.