Frequency-Dependent Spontaneous Emission Rate from CdSe and CdTe Nanocrystals: Influence of Dark States

We studied the rate of spontaneous emission from colloidal CdSe and CdTe nanocrystals at room temperature. The decay rate, obtained from luminescence decay curves, increases with the emission frequency in a supralinear way. This dependence is explained by the thermal occupation of dark exciton states at room temperature, giving rise to a strong attenuation of the rate of emission. The supralinear dependence is in agreement with the results of tight-binding calculations.

Figure 1

Luminescence decay curve of exciton emission from CdSe nanocrystals at $620\mathrm{nm}\pm 5\mathrm{nm}$ (filled circles). Single-exponential fit (red curve), with background as adjustable parameter, yields a rate of $0.037\pm 0.003{\mathrm{ns}}^{-1}$ and a ${\chi }_r^2$ value of 1.4. A stretched-exponential model yields a rate of $0.036{\mathrm{ns}}^{-1}$ and a $\beta$ value of 0.99. Inset: the background corrected decay curve in a semilogarithmic plot.

Figure 2

Decay rate of emission from CdTe (a) and CdSe (b) nanocrystals. The decay rate is deduced with single-exponential fit (filled black dots), average arrival time (open triangles), and stretched-exponential fit (open squares). The blue lines show the decay rates for a two-level system and pass through the origin [Eq. (2), $\Delta E_j>kT$]. The red curves show the rate according to Eq. (3) and take dark excitonic states into account.

Figure 3

Radiative decay rate from tight-binding calculations (red dots) for CdTe [same experimental data as in Fig. 2a are plotted].