Extended excitons and compact heliumlike biexcitons in type-II quantum dots

We have used magnetophotoluminescence measurements to establish that InP/GaAs quantum dots have a type-II (staggered) band alignment. The average excitonic Bohr radius and the binding energy are estimated to be 15 nm and 1.5 meV, respectively. When compared to bulk InP, the excitonic binding is weaker due to the repulsive (type-II) potential at the heterointerface. The measurements are extended to over almost 6 orders of magnitude of laser excitation powers and to magnetic fields of up to 50 T. It is shown that the excitation power can be used to tune the average hole occupancy of the quantum dots and hence the strength of the electron-hole binding. The diamagnetic shift coefficient is observed to drastically reduce as the quantum dot ensemble makes a gradual transition from a regime where the emission is from (hydrogenlike) two-particle excitonic states to a regime where emission from (heliumlike) four-particle biexcitonic states also becomes significant.

Figure 1

(Color online) (Inset) Three representative spectra from the InP/GaAs QD ensemble taken under different conditions. Y:magnetic field $B=0$, laser power $P\sim {10}^{-4}\text{W}{\text{cm}}^{-2}$, $\text{Z}1:B=0$, $P\sim 85\text{W}{\text{cm}}^{-2}$, $\text{Z}2:B=50\text{T}$, $P\sim 85\text{W}{\text{cm}}^{-2}$. The relative amplitudes have been arbitrarily scaled. (main figure) The measured peak shift as a function of magnetic field at the excitation power of about ${10}^{-4}\text{W}{\text{cm}}^{-2}$. (solid line) Fit to Eq. (1) (dotted lines) Eqs. (1a, 1b) plotted separately. The crossover from Coulombic confinement to magnetic confinement occurs at 5.9 T and corresponds to an effective Bohr radius of 15 nm. The extrapolation of the linear slope measured at high field to zero field gives the binding energy, $E_B=1.5\text{meV}$.

Figure 2

(Color online) Schematic depiction of an exciton in bulk material and heterostructured QDs with type-I and type-II band alignment. Material combination “B/A” has type-I alignment (e.g., InAs/InP and possibly InP/InGaP) whereas “B/C” has type-II band alignment (e.g., InP/GaAs). Type-I confinement results in a decrease in the exciton radius and an increase in the exciton binding energy. For QDs with type-II band alignment, the exciton binding should be weaker and the radius larger compared to the bulk InP values and the emission energy can be smaller than the band gaps of either of the two materials.

Figure 3

(Color online) (a) The magnetic field-dependent shift of the emission peak at different excitation powers—0.0001, 0.39, 0.9, 32, and $85\text{W}{\text{cm}}^{-2}$. Pulsed field measurements, which allow for only a short photon accumulation time, could only be performed at high powers. (b) Dependence of the PL energy on the excitation power measured at 4.2 K $\left(B=0\right)$. (c) The diamagnetic shift coefficient $\left(\Gamma \right)$. (d) The biexciton fraction roughly inferred from (c) using Eq. (2). ${\rho }_{xx}/{\rho }_x$ was assumed to be 0.6, which is close to the ratio of hydrogen to helium radii. (e) The exciton reduced mass. The dotted lines in (c), (d), and (e) are just to guide the eye.