Fine Structure of Highly Charged Excitons in Semiconductor Quantum Dots

An exciton in a symmetric semiconductor quantum dot has two possible states, one dark and one bright, split in energy by the electron-hole exchange interaction. We demonstrate that for a doubly charged exciton, there are also two states split by the electron-hole exchange, but both states are now bright. We also uncover a fine structure in the emission from the triply charged exciton. By measuring these splittings, and also those from the singly charged and doubly charged biexcitons, all on the same quantum dot, we show how the various electron-hole exchange energies can be measured without having to break the symmetry of the dot.

Figure 1

Gray-scale plot of the photoluminescence versus gate voltage for a single dot from sample $A$ at 4.2 K. White corresponds to 0 counts, black to 4000 counts on the detector. The excitons are labeled with $X$ standing for exciton, $2X$ for biexciton, with excess charge as the suffix. Dotted lines mark charging events. The unlabeled emission at 1.288 eV is related to $2X^0$, but its exact origin is presently unknown. The power of the 850 nm laser was chosen so that the biexciton features are clearly visible. Above a voltage of about 0.05 V, the wetting layer (WL) loads with electrons.

Figure 2

Main figure: level diagrams for the initial and final states of a doubly charged exciton $X^{2-}$ in a QD. The states shown are the hole $s$ state, the electron $s$ state and the electron $p_x$ state. Electrons (holes) are shown with solid (open) arrows; an up-arrow (down-arrow) denotes spin up (spin down). The pseudospin is used for the hole. The two initial states differ in energy by the electron-hole exchange interaction $\Delta$. There are three possible final states: (a) $S,S_z=1,0$; (b) $1,1$; and (c) $0,0$. State (c) is split from (a) and (b) by electron-electron exchange, $\Delta (ee)$. The inset shows a typical $X^{2-}$ emission spectrum from a dot from sample $B$. The transitions are labeled with (a), (b), (c) to denote the final state, as in the level diagrams.

Figure 3

(a) $X^{1-}$, (b) $X^{2-}$, (c) $X^{3-}$ emission spectra for dot I from sample $B$ at 4.2 K. The voltages applied to generate the various excitons are labeled in each case. Also shown are (d) $2X^{1-}$ and (e) $2X^{2-}$ emission spectra for a dot from sample $A$ at 4.2 K. Symbols are experimental data, and lines are fits to Lorentzian line shapes.