Pressure effects on neutral and charged excitons in self-assembled ($\mathrm{In},\mathrm{Ga})\mathrm{As}∕\mathrm{GaAs}$ quantum dots

By combining an atomistic pseudopotential method with the configuration-interaction approach, we predict the pressure dependence of the binding energies of neutral and charged excitons: $X^0$ (neutral monoexciton), $X^{-}$ and $X^{+}$ (charged trions), and $X{X}^0$ (biexciton) in lens-shaped, self-assembled ${\mathrm{In}}_{0.6}{\mathrm{Ga}}_{0.4}\mathrm{As}∕\mathrm{GaAs}$ quantum dots. We predict that (i) with applied pressure the binding energy of $X^0$ and $X^{+}$ increases and that of $X^{-}$ decreases, whereas the binding energy of $X{X}^0$ is nearly pressure independent. (ii) Correlations have a small effect in the binding energy of $X^0$, whereas they largely determine the binding energy of $X^{-}$, $X^{+}$, and $X{X}^0$. (iii) Correlations depend weakly on pressure; thus, the pressure dependence of the binding energies can be understood within the Hartree-Fock approximation and it is controlled by the pressure dependence of the direct Coulomb integrals $J$. Our results in (i) can thus be explained by noting that holes are more localized than electrons, so the Coulomb energies obey $J^{\left(hh\right)}>J^{\left(eh\right)}>J^{\left(ee\right)}$.

Figure 1

Pressure dependence of (a) binding energies ${\Delta }_{\mathrm{CI}}\left({\chi }^q\right)$ as obtained from the many-particle, configuration-interaction method, (b) Coulomb-energy component $J_{00}^{\left(\mu {\mu }^{\prime }\right)}$, and (c) correlation-energy components $\delta \left({\chi }^q\right)$. (See text for definitions.)

Figure 2

(Color) LUMO $\left[{\psi }_0^{\left(e\right)}\right]$ and HOMO $\left[{\psi }_0^{\left(h\right)}\right]$ wave functions at 0.2, 1.3, and 2.4 GPa. The outline of the dot is present as a light shadow. The (red) isosurface encloses 75% of the charge, the in-plane (bottom) contour plot is taken at 1 nm above the dot’s base and the out-of-plane contour plot bisects the dot. The LUMO wave function becomes more confined as pressure increases—see the how the wave function penetrates less into the barrier above of the dot as pressure increases; whereas the HOMO wave functions are almost independent of pressure.