Polarons in semiconductor quantum dots and their role in the quantum kinetics of carrier relaxation

While time-dependent perturbation theory shows inefficient carrier-phonon scattering in semiconductor quantum dots, we demonstrate that a quantum kinetic description of carrier-phonon interaction predicts fast carrier capture and relaxation. The considered processes do not fulfill energy conservation in terms of free-carrier energies because polar coupling of localized quantum-dot states strongly modifies this picture.

Figure 1

(a) Spectral function of electrons for the lowest WL state at $k=0$ under the influence of polar coupling in the combined QD-WL system (solid line) and without coupling to the QD states (dotted line). For electrons in the QD $p$ shell (b) and $s$ shell (c) full coupling between all states (solid line) is compared to the case without coupling to other QD states (dotted line). Energies are given relative to the continuum edge $E_G$ in units of the phonon energy $\hslash {\omega }_{\mathrm{LO}}$. Vertical lines show the corresponding free-carrier energies. The temperature is $300\mathrm{K}$.

Figure 2

Temporal evolution of the QD population due to carrier-phonon scattering between $p$ shell and $s$ shell for an energy spacing larger than the LO-phonon energy. The solid lines correspond to a quantum-kinetic calculation whereas for the dotted line the Markov approximation is used together with polaronic spectral functions.

Figure 3

Time-evolution of the QD $p$-shell (solid line) and $s$-shell (dashed line) electron population due to carrier capture from the WL including the effect of carrier relaxation between QD shells. If only direct capture processes are considered, the dashed-dotted and dotted lines are obtained for $p$ shell and $s$ shell, respectively.

Figure 4

(a) Spectral function of electrons in the coupled QD-WL system for the $p$ shell (solid line) and $s$ shell (dashed line) using various energy spacings $\Delta E$ between $s$ shell, $p$ shell, and WL $(k=0)$ in units of the LO-phonon energy $\hslash {\omega }_{\mathrm{LO}}$. Vertical lines indicate the positions of the unrenormalized QD states, $E_G$ is the continuum edge of the WL states. The temperature is $300\mathrm{K}$.

Figure 5

Temporal evolution of the QD population due to carrier-phonon scattering between $p$ shell (initially populated) and $s$ shell (initially empty) for different energy spacings $\Delta E$ corresponding to Fig. 4.

Figure 6

Time-evolution of the QD $p$ shell (top) and $s$ shell (bottom) electron population due to carrier capture from the WL including the effect of carrier relaxation between QD shells for different energy spacings $\Delta E$ corresponding to Fig. 4.