Phonon-assisted tunneling of electrons in a quantum well/quantum dot injection structure

We study theoretically phonon-assisted relaxation and tunneling in a system composed of a quantum dot which is coupled to a quantum well. Within the $\mathit{k}·\mathit{p}$ method combined with the Löwdin elimination, we calculate the electron states. We calculate acoustic phonon-assisted relaxation rates between the states in the quantum well and in the quantum dot and study the resulting electron kinetics. We show that transition efficiency crucially depends on the system geometry. We show also that under some conditions, transition efficiency can decrease with the temperature.

Figure 1

The schematic cross section of the system.

Figure 2

The probability density for the ground state and the first excited state (the lowest state in the QW) in the case of neglected strain field (a), (b) and in the presence of strain field (c), (d).

Figure 3

The energies of two lowest states in the system as a function of the distance between the dot and the well.

Figure 4

(a) The capture rate at $T=0$ K and $\mu =15$ meV ($n_e=1.5\times {10}^{11}{\mathrm{cm}}^{-2}$) as a function of the distance between the dot and the well (red solid line) and the contributions to the capture rate due to the DP coupling (green dashed line) and due to the PE coupling (blue dotted line). (b) Temperature dependence of the phonon-assisted relaxation rate at $D=6$ nm as a function of the temperature.

Figure 5

(a) The time evolution of the average number of electrons in the QD at $D=6$ nm and $\mu =10$ meV. (b) The time evolution of the lowest QW state occupation.

Figure 6

The strain-induced potential inside the QW in the QW-QD system for (a) a QD deeply buried in the GaAs, (b) a QD covered only up to its top, (c) a QD on the surface (uncovered). In sets in bottom left corners are schematic cross sections of the system.