Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement

We report systematic measurements of the dephasing of the excitonic ground-state transition in a series of $\mathrm{InGaAs}∕\mathrm{GaAs}$ quantum dots having different quantum confinement potentials. Using a highly sensitive four-wave mixing technique, we measure the polarization decay in the temperature range from 5 to 120 K on nine samples having the energy distance from the dot ground-state transition to the wetting layer continuum (confinement energy) tuned from 332 to 69 meV by thermal annealing. The width and the weight of the zero-phonon line in the homogeneous line shape are inferred from the measured polarization decay and are discussed within the framework of recent theoretical models of the exciton-acoustic phonon interaction in quantum dots. The weight of the zero-phonon line is found to decrease with increasing lattice temperature and confinement energy, consistently with theoretical predictions by the independent Boson model. The temperature-dependent width of the zero-phonon line is well reproduced by a thermally activated behavior having two constant activation energies of 6 and 28 meV, independent of confinement energy. Only the coefficient to the 6-meV activation energy shows a systematic increase with increasing confinement energy. These findings rule out that the process of one-phonon absorption from the excitonic ground state into higher energy states is the underlying dephasing mechanism.

Figure 1

Combined density of states inferred from room-temperature photoluminescence spectra in a series of InAs quantum dots subject to thermal annealing for 30 s at the indicated temperatures. Curves are vertically displaced for clarity. The first two peaks corresponding to the excitonic ground-state (GS) and first excited-state (ES) transitions are indicated. The wetting layer (WL) and GaAs transitions measured on the dots annealed at 960 °C are also shown.

Figure 2

Time-integrated four-wave mixing field amplitude vs delay time between the exciting pulses on InGaAs QDs with 140-meV confinement energy. Top: zoom over the initial 10-ps delay time for temperatures of 5, 10, 20,…120 K in steps of 10 K. Circularly polarized excitation. Bottom: long delay dynamics at the indicated temperatures. Examples of the dephasing time $T_2$ inferred from an exponential fit according to the indicated function are also shown for the data at 5 and 40 K. Linearly polarized excitation.

Figure 3

Time-integrated field amplitude at 50 K together with an exponential fit of the dynamics at long delay times (dotted line). The initial FWM dynamics divided by the exponential fit, is shown in the inset together with a Gaussian function (dotted line) fitting to the initial decay. The asymptotic value at large delay (dashed line) is used to calculate the ZPL weight, as indicated.

Figure 4

ZPL weight vs lattice temperature for three QD samples with different confinement energies as indicated.

Figure 5

Homogeneous broadening (full width at half maximum) of the ZPL deduced by the dephasing time $T_2$ extracted from the exponential decay of the polarization at long times $(\gamma =2\hslash ∕T_2)$, in four QD samples with different confinement energies as indicated. For clarity, data points (symbols) are shown only for one sample, while interpolating curves are given for the other samples.

Figure 6

Homogeneous broadening of the ZPL vs temperature (square points) in the QDs having 332-meV confinement energy, together with a fit to the data (solid line) according to Eq. (1). The parameters deduced from the fit are indicated. The contribution of the activated term with $E_1\left(E_2\right)$ in Eq. (2) is given as dashed (dotted) line.

Figure 7

Top: zero-temperature extrapolated homogeneous broadening of the ZPL (square symbols) vs confinement energy compared with a curve (solid line) proportional to the inverse square root of the confinement energy $E_{\mathrm{c}}$ times the optical transition frequency $\omega$. Middle (bottom): coefficient $b_1\left(b_2\right)$ of the thermally activated increase of the ZPL width with activation energy $E_1\left(E_2\right)$ vs confinement energy. Dotted lines are guides to the eye. The size of the symbols is equal to or bigger than the error bars of the parameters from the fits.