Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements

The radiative and nonradiative decay rates of InAs quantum dots are measured by controlling the local density of optical states near an interface. From time-resolved measurements, we extract the oscillator strength and the quantum efficiency and their dependence on emission energy. From our results and a theoretical model, we determine the striking dependence of the overlap of the electron and hole wavefunctions on the quantum dot size. We conclude that the optical quality is best for large quantum dots, which is important in order to optimally tailor quantum dot emitters for, e.g., quantum electrodynamics experiments.

Figure 1

(Color online) (A) Decay of the spontaneous emission recorded at $1.20\mathrm{eV}$ for two different distances to the interface of $z=109\mathrm{nm}$ (green/light gray, upper curve) and $z=170\mathrm{nm}$ (blue/dark gray, lower curve). The solid red/gray lines are biexponential fits resulting in ${\Gamma }_{\mathrm{f}}=0.91{\mathrm{ns}}^{-1}$ and ${\Gamma }_{\mathrm{s}}=0.09{\mathrm{ns}}^{-1}$ for $z=109\mathrm{nm}$ and ${\Gamma }_{\mathrm{f}}=1.15{\mathrm{ns}}^{-1}$ and ${\Gamma }_{\mathrm{s}}=0.10{\mathrm{ns}}^{-1}$ for $z=170\mathrm{nm}$. The goodness-of-fit parameters ${\chi }_r^2$ are, respectively, 1.17 and 1.11, close to the ideal value of unity (Ref. 14) verifying the biexponential model. (B) Measured decay rates versus distance $z$ to the GaAs-air interface (squares). Calculated LDOS projected onto a dipole orientation parallel to the interface (solid blue/dark gray line). Calculated LDOS including dissipation at the surface (dashed red/gray line). The inset shows a schematic drawing of the sample. (C) Coefficient of correlation versus the number of data points excluded in the modeling of the data in (B).

Figure 2

(Color online) Left axis: photoluminescence from the inhomogenously broadened ground state measured at $z=281\mathrm{nm}$ (solid line). Right axis: radiative (green/light gray triangles) and nonradiative (blue/dark gray circles) decay rates versus emission energy.

Figure 3

(Color online) (A) Oscillator strength (triangles) and quantum efficiency (squares) versus energy (B) Measured (squares) and calculated (red/gray curve) energy dependence of the overlap of the envelope wavefunctions of electrons and holes.