Temperature behavior of hot carrier dynamics in InP quantum dots

Photoluminescence (PL) kinetics of the InP self-assembled quantum dots is studied under quasiresonant optical excitation in the temperature range 10–100 K. It is found that the PL rise time abruptly drops with increasing temperature. The model calculations based on the rate equations have shown that this drop cannot result from thermostimulated phonon relaxation of the hot carriers. We developed a model assuming that the main reason for variations in the PL kinetics is related to thermal ejection (“evaporation”) of holes from the quantum dots, with a fraction of the dots acquiring negative charge. The model allowed us to describe quantitatively the PL rise as well as the PL decay over the whole temperature range under study. We identified also a number of effects caused by electron evaporation from the quantum dots at temperatures above 60 K. Comparison of the results of the model calculations with the experimental data has allowed us to determine rate parameters of the ejection processes.

Figure 1

(a) PL spectrum of InP QDs plotted vs Stokes shift. $E_{\mathit{exc}}=1765\mathrm{meV}$. Arrows show the spectral points at which the PL kinetics was studied. (b) Phonon density of states spectrum of InP crystal (Ref. 25). Inset shows the PL spectrum measured at high photon energy of excitation.

Figure 2

PL kinetics measured at spectral point TA at different temperatures identified at each curve (noisy curves). For convenience, the curves are translated along the vertical axis. Smooth curves are fits of Eq. (2) to PL kinetics. Note the practically perfect coincidence between the fitting and experimental curves. Dashed curve shows the contribution of the short-lived PL component at $T=50\mathrm{K}$.

Figure 3

Initial part of PL kinetics measured at spectral point $2AC$ at different temperatures identified at each curve. For convenience, the curves are translated along the vertical axis. Dashed line shows the shift of PL pulse maximum with increasing temperature. Inset presents the three-level diagram used in a phenomenological description of PL kinetics.

Figure 4

(a) Temperature behavior of the PL pulse rise time measured at spectral point TA (symbols). The dashed line shows a fit with Eq. (3) made with the model of Ref. 11 (see Sec. 4). Fitting parameters: $E_{\mathit{ph}}=3.2\mathrm{meV},{\tau }_{\mathit{rel}}\left(0\right)=35\mathrm{ps}$. The dotted line is a fit with Eq. (5) based on the phenomenological model (see Sec. 4). Fitting parameters: $A={\left(50\mathrm{K}\right)}^{-3},{\tau }_{\mathit{rel}}\left(0\right)=34\mathrm{ps}$. The solid line is a theoretical curve based on the hole evaporation model (see Sec. 5). The model parameters are given in Table . (b) Same for spectral point $2AC$. Fitting parameters for model of Ref. 11, $E_{\mathit{ph}}=1.9\mathrm{mev},{\tau }_{\mathit{rel}}\left(0\right)=68\mathrm{ps}$; for the phenomenological model, $A={\left(41\mathrm{K}\right)}^{-3},{\tau }_{\mathit{rel}}\left(0\right)=58\mathrm{ps}$. (c) Temperature dependence of the fast PL component decay time measured at spectral points TA (circles) and $2AC$ (triangles). Solid line plots theoretical dependence constructed for the hole evaporation model. The initial part of the graph is approximated by Eq. (15) with parameters $E_{h01}=4\mathrm{meV}$ and ${\gamma }_{\mathit{PL}1}={\left(400\mathrm{ps}\right)}^{-1}$.

Figure 5

The scheme of the processes resulting in QD charging. (See details in Sec. 5.)

Figure 6

(a) PL kinetics measured at $T=50\mathrm{K}$ at spectral point $2AC$ (noisy curve). The solid line shows a theoretical curve calculated with the hole evaporation model as a sum of three PL components plotted below. The curve is convoluted with a Gaussian, 6 ps in halfwidth, which simulates the instrument function of the experimental setup. The inset depicts the rising part of the PL pulse (noisy curve). The long-dashed line reproduces instantaneous pulse rise predicted by the model. The short-dashed line depicts pulse evolution with time for the case of the PL being due to exciton luminescence alone. (b) Temperature dependence of integral intensity of the exciton and trion PL.

Figure 7

(a) Decay rate of long-lived PL component (circles). The solid line is a fit with Eq. (20), ${\gamma }_e^0=3{\mathrm{ps}}^{-1}$. The inset displays schematically the processes involved. (See details in text.) The values of the other parameters used in the calculation are given in Table . (b) Evolution with temperature of the slow PL component measured at spectral point TA and normalized against total PL intensity (symbols). Dashed line—calculation using Eq. (19) and made neglecting electron evaporation $(b=1)$; solid curve—calculation using Eqs. (19, 21), $k_b=180$. (c) The same for spectral point $2AC,k_b=210$. (d) The temperature dependence of integrated PL intensity measured at spectral point $2AC$ (circles) and its fitting with Eq. (20) (solid line), ${\gamma }_e^0=9{\mathrm{ps}}^{-1}$.