Excitons, biexcitons and trions in self-assembled (In,Ga)As/GaAs quantum dots: Recombination energies, polarization and radiative lifetimes versus dot height

We calculate the height dependence of recombination energies, polarization and radiative lifetimes of the optical transitions of various excitonic complexes: neutral excitons (X^0), negatively- (X^-) and positively-charged (X^+) trions, and biexcitons (XX^0) in lens-shaped, self-assembled In_0.6Ga_0.4As/GaAs quantum dots. By using an atomistic pseudopotential method combined with the configuration-interaction method, we predict the following. (i) The recombination energy of the lowest transition of X^- blue-shifts as height increases, whereas that of X^+ red-shifts. Remarkably, the recombination of XX^0 shows a red-shift at small heights, reaches a maximum shift, and then blue-shifts for taller dots. (ii) Changes in dot height lead to a bound-to-unbound crossover for X^-, X^+ and XX^0. (iii) When considering the [110] and [1\bar{1}0] directions, the lowest transitions of X^0 and XX^0 manifest [110] vs [1\bar{1}0] in-plane polarization anisotropy that switches sign as a function of height as well as alloy randomness. $X^-$ and $X^+$ show transitions with negligible polarization anisotropy regardless of height. (iv) The ground state of X^0 is split in a low-energy pair that is forbidden (dark) and a high-energy pair that is allowed; thus, at T=0K the radiative lifetime \tau(X^0) is long (~ ms) due to the dark exciton. On the other hand, at T=10K, \tau(X^0) decreases moderately as height increases and its magnitude ranges from 2-3ns. The ground state of X^- and X^+, and that of XX^0 is allowed (bright); so, \tau(X^-), \tau(X^+) and \tau(XX^0) are fast (~ ns) even at T=0K. These radiative lifetimes depend weakly on height. In addition, \tau(X^-) ~ \tau(X^+) ~1.1ns, while \tau(XX^0)~0.5ns$. We compare our predictions with available spectroscopic data.