Optical and theoretical investigations of small InP quantum dots in ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{P}$

We have studied small InP quantum dots in a GaInP matrix theoretically and experimentally. Using low-temperature photoluminescence spectroscopy in conjunction with six band $\mathbf{k}\cdot \mathbf{p}$ calculations, including direct and exchange interactions, we show that the dot size is a crucial parameter that determines whether the dot is neutral or charged with electrons in the nominally undoped n-type host material. For a small enough quantum dot, the conduction-band ground state is positioned above the Fermi level and the dot remains neutral. However, as soon as the dot is large enough for the conduction-band ground state to be located below the Fermi level the dot is charged. Furthermore, we show that, for neutral quantum dots, the position of the bi-exciton emission line with respect to the exciton emission line depends on the size of the quantum dot and that the bi-exciton emission can be on either side of the exciton emission: for the smallest dots the bi-exciton emission is always at higher energy than the exciton emission but for larger dots the ordering is the opposite with the exciton emission line on the high-energy side.