Figure 1

(Color online) Schematic of fine structure and exciton-acoustic phonon scattering models applied to an ensemble with an inhomogeneous size distribution. Thick solid (dotted) lines show the convolution of a single NC emission (absorption) spectrum with an inhomogeneous size distribution. Thin lines show single NC emission spectra. (a) Fine structure model. At $T=5\mathrm{K}$, single NC emission is mostly from the dark exciton level, while at $T=300\mathrm{K}$, an oscillator strength weighted Boltzmann distribution leads to emission from higher energy levels. This change in single NC emission causes the Stokes shift to decrease and the ensemble emission linewidth to broaden. (b) Exciton-acoustic phonon scattering model. The single NC absorption and emission have a Prussian helmet shape that consists of a sharp zero phonon line and a broad offset acoustic phonon pedestal, and they are mirror images of one another about the zero phonon line. At higher temperatures, the acoustic phonon pedestal broadens causing both the emission and absorption spectra to broaden. The Stokes shift is temperature independent.Reuse & Permissions

Figure 2

(Color online) [(a) and (b)] Absorption and emission measurements for five samples of QD (655, 605, 585, 565, and 545) at $T=5\mathrm{K}$ and $T=300\mathrm{K}$. Sizes are determined by comparing to literature spectra (Refs. 6, 17, 32). The fit to a series of Gaussians is shown on the absorption spectra. (c) Single NC emission spectra from the same physical batch of 545 NCs used in ensemble measurements.Reuse & Permissions

Figure 3

(Color online) (a) Temperature dependence of the nonresonant Stokes shift for all five of our samples. (b) Ensemble emission linewidth versus temperature. (c) The temperature dependence of the emission wavelength normalized to zero at $T=300\mathrm{K}$. All samples have a hook at low temperatures that is consistent with emission from a dark exciton.Reuse & Permissions

Figure 4

(Color online) (a) Solid lines show the a priori prediction for the temperature dependence of the Stokes shift according to the fine structure theory. The plot assumes that there is a $15\mathrm{meV}$ Stokes shift offset for all sizes and temperatures due to effects other than the fine structure. The fine structure is assumed to look like the solid lines in the lower plot. The dashed lines correspond to a least squares fit of the fine structure to our data. The resulting energy and oscillator strengths are shown with the circles in the lower plot. (b) Repeat of Stokes data. (c) Temperature dependence of Stokes shift according to exciton-acoustic phonon scattering theory for a CdSe core in a $\mathrm{Si}{\mathrm{O}}_2$ matrix based on Ref. 3. [(d) and (e)] Solid line shows the simplified two level a priori theoretical fine structure based on Ref. 6. Circles show the implied energy and oscillator strength from a least squares fit to our experimental data. We vary the magnitude of the temperature independent Stokes contributions. The $R=2.4\mathrm{nm}$ data are skipped because of its unusual properties (see Sec. 2). (f) We fit the $T=5\mathrm{K}$ emission spectrum to a Gaussian to infer the inhomogeneous broadening for $R=1.5\mathrm{nm}$ NCs. We use this to calculate the corresponding absorption spectra ($T=5\mathrm{K}$, $T=300\mathrm{K}$) and emission spectrum $(T=300\mathrm{K})$ using our extracted fine structure.Reuse & Permissions

Figure 5

(Color online) (a) Calculated temperature dependence of an inhomogeneously broadened ensemble linewidth assuming the fine structure implied by a least squares fit to the temperature dependence of the Stokes shift [circles in Figs. 4d, 4e]. The inhomogeneous broadening is assumed to be Gaussian with a width that is chosen to fit the data at $T=5\mathrm{K}$. (b) Repeat of linewidth data. (c) Calculated temperature dependence of the linewidth using exciton-acoustic phonon scattering model.Reuse & Permissions