Observation of Size-Dependent Thermalization in CdSe Nanocrystals Using Time-Resolved Photoluminescence Spectroscopy

We report heat dissipation times in semiconductor nanocrystals of CdSe. Specifically, a previously unresolved, subnanosecond decay component in the low-temperature photoluminescence decay dynamics exhibits longer decay lifetimes (tens to hundreds of picoseconds) for larger nanocrystals as well as a size-independent, $\sim 25$-meV spectral shift. We attribute the fast relaxation to transient phonon-mediated relaxation arising from nonequilibrium acoustic phonons. Following acoustic phonon dissipation, the dark exciton state recombines more slowly via LO-phonon assistance resulting in the observed spectral shift. The measured relaxation time scales agree with classical calculations of thermal diffusion, indicating that interfacial thermal conductivity does not limit thermal transport in these semiconductor nanocrystal dispersions.

Figure 1

(a) Temporally and spectrally resolved single exciton PL from a 1.6-nm-radius CdSe NC ensemble at 2.6 K and (b) at 80 K. Here, lower sample temperature results in a faster emission feature as well as a spectral shift to lower energy with time. (c),(d) Time-resolved spectra collected at the indicated temperatures and binned over the indicated time delays reveal a redshift with increasing time at 2.6 K that is not observed at 80 K. Spectra are linearly offset for clarity. The black vertical lines indicate the peak emission amplitude of the 320–340 ps time-binned spectrum. (e),(f) Spectrally resolved PL dynamics become biexponential for shorter PL wavelengths in the case of the lower sample temperature.

Figure 2

“Blue-side” radiative recombination dynamics for CdSe samples with indicated radii generated for the higher energy half of the time-integrated PL spectrum at 2.6 (blue lines) and 80 K (red lines). Traces were scaled to overlap at long time. For every sample, the low-temperature trPL data become biexponential. Also, the decay feature appearing at low temperature becomes increasingly faster with reduced NC radius. Note that the tick mark step size is constant (100 ps) for each data panel and that the measured time window is larger for larger NC size.

Figure 3

The faster decay time derived from biexponential fits of the trPL data in Fig. 2 (squares) exhibits a linear relationship with the NC radius squared (fitted black solid line). Calculations of diffusion-limited (blue dashed line) and interfacial-conductance-limited (gray dotted line, estimated for an interfacial conductance of $4.1\mathrm{MW}/{\mathrm{m}}^2\mathrm{K}$) dissipation suggest that diffusion controls the measured decay times. The inset displays the energy difference between early recombination and emission subsequent to the fast initial decay. The spectral shifts for multiple NC radii are fairly constant and comparable to the 25-meV LO-phonon energy of bulk CdSe (solid red line). Recombination from higher lying states in the CdSe NC exciton fine structure is not apparent, since such emission would exhibit strong size dependence corresponding to ${\Delta }_{db}$ values ranging from 2 to 17 meV for the NC size range probed.

Figure 4

(a) Increasing sample temperature results in a decrease in amplitude of the fast dynamical component, here for a 1.6-nm-radius CdSe NC sample. (b) The ratio of instantaneous PL intensities integrated from $t=0–5\mathrm{ps}$ ($I_{\mathrm{early}}$) and from $t=200–205\mathrm{ps}$ ($I_{\mathrm{late}}$) taken from dynamics such as those shown in (a) for three CdSe NC sizes suggests that Boltzmann populations of low-energy phonons in the NCs eliminates the fast relaxation feature for sufficiently high temperatures. Lines show appropriately scaled thermal partitioning of NCs lacking acoustic phonon excitation, as described in the text. Representative error bars are shown for the 1.30-nm-radius NC sample.