Polaron relaxation in self-assembled quantum dots: Breakdown of the semiclassical model

We calculate the lifetime of conduction band excited states in self-assembled quantum dots by taking into account LO-phonon-electron interaction and various anharmonic phonon couplings. We show that polaron relaxation cannot be accurately described by a semiclassical model. The contributions of different anharmonic decay channels are shown to depend strongly on the polaron energy. We calculate the energy dependence of the polaron lifetime and compare our results to available experimental measurements of polaron decay time in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots.

Figure 1

(Color online) (a) Full lines: Polaron energies as a function of the electronic energy separation between the $\mid s⟩$ and $\mid p⟩$ levels. Dashed lines: energies of noninteracting $\mid s,1⟩$ and $\mid p,0⟩$ levels. (b) Scheme of the interaction between electronic levels and LO phonon, leading to the polaron formation. Anharmonic coupling with the phonon reservoir and the far-infrared absorption are indicated (see text).

Figure 2

(Color online) Calculated ${\Gamma }^{\mathit{ph}}$ vs the energy: full calculation (solid line); $\mathrm{LA}+\mathrm{LA}$ channel (Klemens channel) in dashed line; $\mathrm{LA}+\mathrm{TA}$ channel in dotted line; $\mathrm{LA}+\mathrm{TO}$ channel in dashed-dotted line; $\mathrm{TA}+\mathrm{LO}$ channel in dashed-double-dotted line $(T=0\mathrm{K})$. Inset: Schematic of the different anharmonic processes.

Figure 3

(Color online) Polaron decay time as a function of the polaron energy: measurements from Ref. 11 in symbols, full calculation (presented in the text) in solid line, calculation involving only the Klemens channel $(\mathrm{LA}+\mathrm{LA})$ in dotted line, and best fit obtained with the semiclassical model in dashed line ($V_{sp\left(\text{fit}\right)}=8\mathrm{meV}$, ${\tau }_{\mathit{LO}}=15\mathrm{ps}$).