Phonon- and Auger-assisted tunneling from a quantum well to a quantum dot

We investigate phonon- and Auger-assisted tunnelings from an adjacent quantum well coupled to a quantum dot by Fermi's golden rule. The filling of quantum-well states is included, and we obtain an average tunneling lifetime depending on the concentration in the quantum well. Depending on the barrier width between the quantum dot and quantum well, both mechanisms can result in a tunneling time of a few to several hundred picoseconds. For the condition of high concentration of carriers in a quantum well, the typical time scale of the net increase of carriers in a quantum dot due to phonon-assisted tunneling can be in sub-picosecond range, which agrees with the recent experimental observation.