Size-dependent oscillator strength and quantum efficiency of CdSe quantum dots controlled via the local density of states

We study experimentally time-resolved emission of colloidal CdSe quantum dots in an environment with a controlled local density of states (LDOS). The decay rate is measured versus frequency and as a function of distance to a mirror. We observe a linear relation between the decay rate and the LDOS, allowing us to determine the size-dependent quantum efficiency and oscillator strength. We find that the quantum efficiency decreases with increasing emission energy mostly due to an increase in nonradiative decay. We manage to obtain the oscillator strength of the important class of CdSe quantum dots. The oscillator strength varies weakly with frequency in agreement with behavior of quantum dots in the strong confinement limit. Surprisingly, previously calculated tight-binding results differ by a factor of 5 with the measured absolute values. Results from pseudopotential calculations agree well with the measured radiative rates. Our results are relevant for applications of CdSe quantum dots in spontaneous emission control and cavity quantum electrodynamics.

Figure 1

(Color online) Schematic cross section of the sample used in the measurements. The different layers of the sample are shown together with corresponding thickness and fabrication technique.

Figure 2

Transmission electron micrograph of a CdSe quantum dot with a diameter $D=3.9\text{nm}$. The fringes from the lattice planes are clearly seen. The scale bar is 2 nm.

Figure 3

The distribution in diameter found by analyzing TEM images of 98 quantum dots. The average diameter is 4.1 nm with a standard deviation of 0.5 nm.

Figure 4

(Color online) A schematic picture of the experimental setup. Light from the laser excites the quantum dots in a layered sample inside a nitrogen purged chamber. The emitted light is collimated by a lens L1 with $f=12\text{cm}$, focused by lens L2 with $f=10\text{cm}$ on the entrance slit of a monochromator, and detected by the photomultiplier tube.

Figure 5

(Color online) Emission spectra of CdSe quantum dots in toluene suspension, in a planar sample without silver, and in a planar sample with a silver mirror. The spectra are offset for clarity by 200 and 400 counts/s, respectively. The spectrum in PMMA near the mirror and in toluene is scaled to the spectrum in PMMA on glass by a factor of 0.75.

Figure 6

(Color online) Decay curves of quantum dots at the emission peak at 2.08 eV in PMMA on glass with a top layer of PVA (red circles) and these quantum dots in toluene suspension (blue triangles). The instrument response function (IRF) is indicated by the black line. The peaks in the IRF near 12 and 36 ns are related to the pulse picker of the laser. The decay curves are fitted with a lognormal distribution of decay rates. Residuals are shown in the bottom panel.

Figure 7

(Color online) Lognormal distribution of decay rates of quantum dots in a PMMA layer on glass with a PVA cover layer and for quantum dots in toluene resulting from fits in Fig. 6. The black line shows the delta function distribution for single exponential fit.

Figure 8

(Color online) Decay curves for quantum dot samples with different ${\text{SiO}}_2$ layer thicknesses $z=73\text{nm}$ and $z=166\text{nm}$, respectively, for samples 1 and 2 measured at an emission energy of 2.08 eV. The decay curves are fitted with a lognormal distribution of decay rates. Residuals are shown in the bottom panel.

Figure 9

(Color online) Most frequent decay rate ${\gamma }_{\text{mf}}$ versus distance to the interface for an emission energy of 2.08 eV (circles) and 2.00 eV (triangles). The lines show calculations of the decay rate using the model developed by Chance et al. (Ref. 27).

Figure 10

The angle $\theta$ is the angle between the dark axis of the CdSe quantum dot and the normal to the interface.

Figure 11

(Color online) The decay rate versus the normalized isotropic LDOS for two different emission energies. Data are fitted with a linear function as expected from Fermi’s golden rule.

Figure 12

(Color online) (a) Radiative decay rate (filled circles) determined from the linear fit in Fig. 11 shown versus emission energies. One data point by Brokmann et al. (Ref. 19) is plotted with the open circle. A model for a multilevel exciton from Ref. 34 is shown with a solid line. The dashed line is a tight-binding calculation of radiative decay rate (Ref. 35). The crosses connected with the dotted line are the results from pseudopotential calculations (Ref. 36). (b) Quantum efficiency (circles) and nonradiative decay rate (filled triangles) versus emission energies. The open triangle is the result for nonradiative decay from Ref. 19. (c) Oscillator strength for different emission energies (circles) together with a model describing a strongly confined quantum dot [Eq. (7), dashed line] and results from tight-binding calculations (triangles) (Ref. 38).

Figure 13

(Color online) Relative width of the lognormal distribution versus LDOS for emission energies of 2.08 and 2.00 eV. The lines are linear fits of the data.

Figure 14

(Color online) Measurements of relative width for a homogeneous system $\left(\text{LDOS}=1\right)$ plotted versus the extracted quantum efficiency [see Fig. 12b] together with a linear fit.