Influence of wetting-layer wave functions on phonon-mediated carrier capture into self-assembled quantum dots

Models of carrier dynamics in quantum dots rely strongly on adequate descriptions of the carrier wave functions. In this work we numerically solve the one-band effective mass Schrödinger equation to calculate the capture times of phonon-mediated carrier capture into self-assembled quantum dots. Comparing with results obtained using approximate carrier wave functions, we demonstrate that the capture times are strongly influenced by properties of the wetting layer wave functions not accounted for by earlier theoretical analyses.

Figure 1

Schematic of a quantum dot in the form of a cone on top of a wetting layer. The rotationally symmetric model allows for an efficient two-dimensional numerical solution.

Figure 2

(Color online) Energies of the bound states as function of QD radius, $r_0$. Solid lines denote wetting layer thickness $d=2\mathrm{nm}$ while the dashed lines correspond to $d=4\mathrm{nm}$. The uppermost pair of horizontal, dashed lines define the interval in which capture can take place when $d=2\mathrm{nm}$, while the two lower lines correspond to $d=4\mathrm{nm}$.

Figure 3

(Color online) Radial probability density of the bound state at $r_0=6.25\mathrm{nm}$ and $d=2\mathrm{nm}$. The state has energy $E=370\mathrm{meV}$.

Figure 4

(Color online) Capture times calculated with numerically determined wetting layer wave functions (FEM). Circles indicate capture to a bound state with $m_z=0$ and crosses to a state with $m_z=1$.

Figure 5

(Color online) Capture times for WL thickness $d=2\mathrm{nm}$ into the QD ground state $(m_z=0)$, calculated with the three wetting layer descriptions (FEM, BF, and OBF)

Figure 6

(Color online) Radial probability densities (at $r_0=6.25\mathrm{nm}$ and $z=0\mathrm{nm}$) for the QD state and the three WL states corresponding to magnetic quantum number $m_z=0$ and energies $E_w=E_{\text{dot}}+\hslash {\omega }_{\mathrm{LO}}$.