Nonresonant tunneling carrier transfer in bilayer asymmetric $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots

Carrier transfer in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ asymmetric quantum dot pairs has been studied by means of continuous-wave and time-resolved photoluminescence in a bilayer $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots system. The dependence of the tunneling time on the thickness of the separation layer is determined and the tunneling time is found to span the range from $250\text{to}2500\mathrm{ps}$. A microscopic model of carrier transfer, including nonresonant electron tunneling from a direct into a cross exciton state, with subsequent generation of two direct excitons in adjacent quantum dot layers, is proposed.

Figure 1

(a) Low excitation density cw PL spectra at $T=10\mathrm{K}$ for $1.8∕2.4$ ML AQDP samples with various spacer thickness. (b) Schematic representation of processes contributing to carrier populations in SQD and LQD ensembles. Photoexcitation of carriers is represented by $G1$ and $G2$, tunneling time for electrons is ${\tau }_T$, and recombination lifetimes are ${\tau }_{R1}$ and ${\tau }_{R2}$ for SQDs and LQDs, respectively.

Figure 2

(a) The normalized PL spectra of a sample with $d_{\mathit{sp}}=40$ ML for different $I_{\mathit{ex}}$. (b) PL peak intensity ratio $I_{\mathit{LQD}}∕I_{\mathit{SQD}}$ of the LQD and SQD PL spectra vs excitation level for various barrier thicknesses. The fit with Eqs. (2) is shown by solid lines.

Figure 3

The $n_1^S$ and $n_2^S$ dependences vs excitation density (a), and the ratio $n_1^S∕n_2^S$ (b) calculated from Eqs. (2) for different tunneling time ${\tau }_T$ and fixed relaxation times for SQDs ${\tau }_{R1}=1.4\mathrm{ns}$ and LQDs ${\tau }_{R2}=1.7\mathrm{ns}$, respectively. The generation rates $G_1$ and $G_2$ are taken equal.

Figure 4

(a) Normalized PL transients for SQDs and LQDs for an AQDP sample with a spacer thickness of 30 ML. The detection energies are 1.25 and $1.094\mathrm{eV}$ for SQDs and LQDs, respectively. (b) Normalized PL transients for SQD for AQDP samples with various spacer thicknesses. The detection energy is at $1.25\mathrm{eV}$. The calculated dependences shown with solid lines where found from the least-squares fit by Eqs. (4, 5) with the correlation parameters $(1-\alpha )$ taken to be 0.95, 0.75, 0.55, and 0.10 for the $d_{\mathit{sp}}=30$, 40, 50, and 60 ML, respectively.

Figure 5

(a) Tunneling time (open circles) deduced from the SQD’s PL transient as a function of barrier width. The solid line is fitted to tunneling times by the least-square method. The data of tunneling times for the similar AQDP systems (closed triangles: Ref. 4; stars: Ref. 12) estimated from cw PL measurements are shown. (b) Comparison of nonresonant electron tunneling times as a function of the effective barrier width observed in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ ADQWs (closed squares: Ref. 20; open triangles: Ref. 21), the $\mathrm{In}\mathrm{Al}\mathrm{As}∕\mathrm{Ga}\mathrm{As}∕\mathrm{In}\mathrm{As}$ AQDP (closed circles: Ref. 19) together with our data (open circles). Dotted lines are guides for the eye.