Exciton thermalization and state broadening contributions to the photoluminescence of colloidal PbSe quantum dot films from 295 to 4.5 K

The temperature-dependent photoluminescence (PL) from thick drop-cast films of $\sim 4–5\text{nm}$ diameter PbSe colloidal quantum dots was investigated in the temperature range of 4.5–295 K. Several samples all exhibit single-peak emission with a simple Arrhenius-type decrease in PL yield as temperature increases. The temperature dependence of the Stokes shift and PL line shape are reproducible and can be quantitatively described over the entire temperature range using a relatively simple, yet accurate thermal model, including state broadening. The Stokes shift is completely described by thermalization of the exciton population and the onset of degeneracy below $\sim 100\text{K}$. The variation in linewidth is dominated by the same degeneracy effects below $\sim 100\text{K}$ while above $\sim 125\text{K}$, the variation is controlled by thermal (Lorentzian) dephasing. There is also clear evidence for a substantial and temperature-independent Voigt-type contribution to the state scattering.

Figure 1

The PL spectra of PbSe QDs thick films at different temperatures. Circles of the upper inset shows the T-dep PL peak energy and the dashed line is the absorption peak vs $T$ for PbSe QDs of this size. The lower inset shows the T-dep FWHM and integrated PL intensity.

Figure 2

The absorption spectra of PbSe QDs thick film at different temperatures. The dashed lines are fitted by two Gaussians and a polynomial background. The dotted line is the guide for the eyes. The temperature coefficient of the absorption band edge, $d{E}_g/dT$ is $55\mu \text{eV}/\text{K}$. The spectra are offset for clarity.

Figure 3

(a) Products of Gaussian distribution and Fermi-Dirac occupation factor at 4.5, 80, 200, and 295 K. (b) and (c) show the PL peak energy and FWHM vs temperature, respectively. Circles: experimental results. Dotted lines: $G\left(ϵ,T\right)\times f\left(ϵ,T\right)$. Solid lines: after state broadenings are applied. Squares in (c) show $\left[{ϵ}_c\left(T\right)-\mu \left(T\right)\right]/k_{B}T$ from the model, as a measure of the distribution’s degeneracy. (d)–(f) show PL line shape fittings at 4.5 K, 80 K, and 200 K, respectively. Gray circles are measured PL spectra. Dotted lines: only T-dep Lorentzian broadening is applied. Solid lines: both temperature-independent Voigt and T-dep Lorentzian are applied. All spectra are normalized to 1.

Figure 4

(a) An example of calculated PL peak energy vs $T$ with different values of $n/N$ with all the other parameters identical. The curves correspond to 1, 5, 10, 20, and 40 times $1.3\times {10}^{-4}$, respectively. (b) and (c) show the measured PL spectra at different excitation powers, at 77 K and 295 K, respectively. The spectra correspond to powers of 1, 5, 10, 20, 30, 40, and 50 times $8.4\mu \text{W}$, The dashed lines are guides for the eyes.

Figure 5

Extracted T-dep Lorentzian broadening linewidth vs $T$ for three batches of PbSe QDs. Solid curve is the fit according to a boson scattering model.