Size dependent, state-resolved studies of exciton-phonon couplings in strongly confined semiconductor quantum dots

Coherent optical and acoustic phonons are observed in strongly confined CdSe quantum dots using excitonic state–resolved femtosecond pump/probe experiments. These state-resolved time-domain experiments yield the size dependent exciton-phonon couplings for both modes as well as the excitonic state dependent couplings. The size dependences are weak in this regime, but the state dependence is large for the optical phonons via the Fröhlich interaction. The state dependent coupling to optical phonons suggests that the exciton becomes less polar for higher states. The time-domain data are compared to frequency-domain resonance Raman data. The differences between the various experimental results are discussed in terms of intrinsic versus extrinsic coupling and quantified in terms of the state dependent exciton-phonon couplings.

Figure 1

Simultaneous observation of coherent optical and acoustic phonons in a CdSe quantum dot $\left(R=2.7\text{nm}\right)$. (a) A femtosecond pump/probe transient. The inset shows the pump bandwidth relative to the optical-phonon energy. (b) Residual oscillations from the subtraction of the data from the fit. (c) The FFT of the residuals and the fit of the residuals, showing the two coupled modes.

Figure 2

(Color online) State-resolved coherent optical and acoustic phonons in CdSe quantum dots $\left(R=2.7\text{nm}\right)$. (a) Linear absorption spectrum, pump spectra (filled), and probe spectrum (line). (b) Femtosecond pump/probe transient corresponding to the pump spectra in (a). (c) Residual oscillations and fits (gray). (d) The FFTs of the residuals and the fits of the residuals (gray).

Figure 3

(Color online) Size dependence of coherent optical and acoustic phonons in CdSe quantum dots with band-edge pumping. (a) Linear absorption spectra and probe spectra. The arrows correspond to the pump position. (b) Femtosecond pump/probe transients corresponding to the three sizes of quantum dots. (c) Residual oscillations. (d) The FFTs of the residuals.

Figure 4

(Color online) Probe wavelength dependence of oscillation phase. The oscillations arise primarily from frequency modulation. Illustrations of frequency modulated (a) and amplitude modulated (b) spectra. (c) Linear absorption spectrum and the probe spectra. (d) Residual oscillations showing a $\pi /2$ phase shift for the optical phonon. The symbols are the data and the lines are the fits. The gray lines are for guiding the eye. The apparent slope is due to the acoustic phonon.

Figure 5

(Color online) The resonance Raman spectra of CdSe quantum dots $\left(R=2.7\text{nm}\right)$ with three different surface passivations. The quantum dots are normally passivated with ligands such as TOPO and HDA. Pyridine is a known hole acceptor which will polarize the charge distribution. The ZnS shell best passivates the quantum dot, thereby minimizing surface trapping away from the quantized core states.

Figure 6

(Color online) The excitonic state–resolved coupling strengths $\left(S\right)$ to optical and acoustic phonons for a CdSe quantum dot $\left(R=2.7\text{nm}\right)$. The eigenstates and coupling strength $\left(S\right)$ are discussed in the text.

Figure 7

(Color online) The size dependence of the optical- and acoustic-phonon parameters under conditions of band-edge pumping. (a) The size dependent frequencies. (b) The size dependent Huang-Rhys parameter $S$. (c) The size dependent reorganization energy $\lambda$.

Figure 8

Exciton-phonon coupling as probed by resonance Raman spectroscopy. (a) A resonance Raman spectrum simulated from the coupling parameters obtained from the femtosecond experiments. (b) The experimental spectrum of CdSe quantum dots in toluene with their native ligands. (c) Raman correlation functions for the LA and LO modes with a homogeneous linewidth of $5{\text{cm}}^{-1}$ and the equal coupling. The half-Fourier transform of this correlation function gives the Raman intensity. (d) The same correlation functions with a linewidth of $500{\text{cm}}^{-1}$, corresponding to the room-temperature homogeneous linewidths obtained from photon echo experiments (Ref. 8). The LA mode has an attenuated correlation function by the fast electronic dephasing time.

Figure 9

A comparison of the photoluminescence spectra simulated from the intrinsic (time-domain) and extrinsic (frequency-domain) measures of the exciton-phonon coupling strength. (a) The simulated absorption spectrum based upon couplings from the femtosecond data. This spectrum corresponds to a purely homogeneously broadened spectrum—a single dot at room temperature. (b) The same as (a) but with 0.8 meV linewidth in order to show the LA and LO modes. Note that the spectrum is shown on a logarithmic scale with a smaller energy scale to illustrate the phonon progressions. (c) The same as (a), using the couplings from the resonance Raman experiments. (d) The same as (b), using the couplings from the resonance Raman experiments.

Figure 10

(Color online) Illustration of dynamic exciton-phonon coupling which addresses the different quantities measured in time-domain and frequency-domain experiments. (a) The coupling to optical phonons as a function of excitonic state. (b) The populations as a function of time. (c) The population averaged coupling $⟨S\left(t\right)⟩$ is time dependent.