Ultrafast Carrier Redistribution in Single $\mathrm{In}\mathrm{As}$ Quantum Dots Mediated by Wetting-Layer Dynamics

Optical studies of single self-assembled semiconductor quantum dots (QDs) have been a topic of intensive investigation over the past two decades. Due to their solid-state nature, their electronic and optical emission properties are affected by the particular crystal structure as well as many-body-carrier interactions and dynamics. In this work, we use a master equation for microstates (MEM) model to study the carrier capture and escape from single QDs under optical nonresonant excitation and under the influence of a two-dimensional (2D) carrier reservoir (the wetting layer). This model reproduces carrier dynamics from power-dependent and time-resolved microphotoluminescence experiments. Due to the random nature of the carrier capture and escape processes, when a single QD is pumped with enough excitation power, the carrier redistribution across the available QD microstates produces an effective double-peaked excitonic decay. This double peak is characterized by a first ultrafast (subnanosecond) and a second conventional (approximately nanosecond) decay. The effective transient photoluminescence shape of the population dynamics is governed by the wetting-layer radiative decay and the exciton capture time.

Figure 1

(a) A microstate scheme of all the different charge configurations of a single QD represented by our MEM model. Vertical arrows correspond to single electron capture (downward) and escape (upward). Horizontal arrows correspond to single hole capture (right) and escape (left). Diagonal arrows correspond to the capture of an exciton (downward) and to radiative recombination (upward). (b) The interaction between the QD and the WL carrier reservoir for excitons, electrons, and holes. (c) A single QD microphotoluminescence spectrum as a function of the excitation power, with cw nonresonant pumping configuration at 4 K. The mean excitonic transitions are labeled as neutral exciton ($X^0$), neutral biexciton ($X{X}^0$), negative trion ($X^{-1}$), and positive trion ($X^{+1}$). (d) The experimental integrated intensity as a function of the cw excitation power (colored dots) and the model simulation (continuous lines) for the main excitonic transitions in a double-logarithmic plot. The calculated number of injected carriers at various cw powers is $1.2\times {10}^8$ carriers/s ($0.01\mu \mathrm{W}$), which is estimated considering the $\mathrm{Ga}\mathrm{As}$ capping-layer thickness, the spot size, and the sample QD density. This value is very close to the estimate based on the carrier diffusion length.

Figure 2

Experimental measurement of TRPL (open circles) and model simulation of the time evolution of the population probability (red continuous lines) as a function of the pulsed excitation power for a neutral exciton (X⁰) (a) and a positive trion (X⁺¹) (b). In each case, $P_0=9$ nW (a) and $P_0=8$ nW (b). The output of the model includes the convolution with the system time response.

Figure 3

The time evolution of the neutral-exciton-microstate probability as a function of the pulsed-excitation power as direct output from the model, not including the convolution with the system response. (a) The TRPL simulation for the $X^0$ population. On the right are plots corresponding to the time traces labeled as (i), (ii), and (iii) on the left-hand density plot ($P_0=9$ nW). (b) The TRPL simulation for the $X^{+1}$ population. On the right are plots corresponding to the time traces labeled as (i), (ii), and (iii) on the left-hand density plot ($P_0=8$ nW). (c),(d) The model scheme under pulsed excitation for the neutral-exciton ($X^0$) population. During the first stage after the pulse excitation, the QD population increases very quickly (represented as the red shaded area under the model scheme) and the excitonic transition decay is mostly dominated by the various carrier-capture processes as shown in (c). However, as soon as the mean QD population has decreased due to the carrier-relaxation processes, the $X^0$ population is mostly influenced by its intrinsic radiative decay. The multiple microstate configurations and their own dynamical evolution with the excitation power are manifested as an evolving effective decay, which is observed in each of the QD excitonic transitions.

Figure 4

(a) Microphotoluminescence spectra as a function of the 790-nm cw excitation power in a second quantum dot and its corresponding transition labeling ($P_0=140$ nW). (b) The photon-autocorrelation measurement of the neutral exciton ($X^0$) optical emission as a function of the 790-nm cw excitation power, from the same QD as in (a) ($P_0=280$ nW). The red continuous lines show the best model fit for each power. As the power increases, the single-photon purity, characterized by the $g^{(2)}(0)$ value, changes from 0.02 ($P_0$) to 0.34 ($3\times P_0$) and 0.53 ($12\times P_0$). The top panel shows the model output for comparison.