Temperature-dependent optical properties of $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots: Independent carrier versus exciton relaxation

We have performed temperature-dependent studies of the photoluminescence properties of a range of $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dot structures. Changes in the temperature dependence of the peak energy and spectral width are governed by thermally stimulated transfer processes and hence depend on the depth of the confining potentials. We have compared our experimental results with detailed calculations based upon correlated electron-hole (exciton) or independent electron-hole relaxation. We conclude that at elevated temperatures the carrier dynamics are governed by independent carrier relaxation.

Figure 1

Photoluminescence spectra of sample Nos. 592 and 617 recorded at a temperature of $T=10\mathrm{K}$ for the highest excitation power density.

Figure 2

Experimental data for the relative photoluminescence peak energy (a), the FWHM of the spectra (b), and the integrated photoluminescence intensity (c) for sample Nos. 617 and 592 at the indicated excitation densities.

Figure 3

Schematic rate equation model (a) and the band DOS diagram (b) for quantum dots. Where $P$ denotes the pumping rate; $W_{nr}$ is the nonradiative recombination rate for charge carriers in the barrier; $W_c$ is the carrier capture rate into quantum dots; $W_e$ is the carrier thermal escape rate; $N_0$ is the concentration of continuum states in the barrier; $n$ is the carrier concentration in the barrier; $D$ is the density of quantum dot states; $m$ is the carrier concentration in quantum dots; $E_g$ is the band gap in the barrier material. The average confinement energies for electron and hole ground states are denoted by $E_m^{\left(\mathrm{e}\right)}$ and $E_m^{\left(\mathrm{h}\right)}$, respectively. CSE and CSH denote continuum states for electrons and holes in the barrier, respectively.

Figure 4

Relative photoluminescence peak energy (a), the FWHM of the spectra (b), and integrated photoluminescence intensity (c) as a function of temperature calculated for sample No. 617 at the low excitation rate of $P={10}^{16}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Open circles and filled boxes correspond to the excitonic and nonexcitonic models, respectively. In addition to the parameters listed in Table the following parameters were specified for this particular sample: $E_m^{\left(\mathrm{e}\right)}=0.15\mathrm{eV}$, $E_m^{\left(\mathrm{h}\right)}=0.15\mathrm{eV}$, $E_0^{\left(\mathrm{e}\right)}=21\mathrm{meV}$, and $E_0^{\left(\mathrm{h}\right)}=10.5\mathrm{meV}$.

Figure 5

Relative photoluminescence peak energy (a), the FWHM of the spectra (b), and integrated photoluminescence intensity (c) as a function of temperature calculated for sample No. 617 at the high excitation rate of $P={10}^{19}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Open circles and filled boxes correspond to the excitonic and nonexcitonic models, respectively. All sample parameters are the same as in Fig. 4.

Figure 6

Relative photoluminescence peak energy (a), the FWHM of the spectra (b), and integrated photoluminescence intensity (c) as a function of temperature calculated for sample No. 592 at the low excitation rate of $P={10}^{16}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Open circles and filled boxes correspond to the excitonic and nonexcitonic models, respectively. In addition to the parameters listed in Table the following parameters were specified for this particular sample: $E_m^{\left(\mathrm{e}\right)}=0.23\mathrm{eV}$, $E_m^{\left(\mathrm{h}\right)}=0.19\mathrm{eV}$, $E_0^{\left(\mathrm{e}\right)}=9.35\mathrm{meV}$, and $E_0^{\left(\mathrm{h}\right)}=5.5\mathrm{meV}$.

Figure 7

Relative photoluminescence peak energy (a), the FWHM of the spectra (b), and integrated photoluminescence intensity (c) as a function of temperature calculated for sample No. 592 at the high excitation rate of $P={10}^{19}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Open circles and filled boxes correspond to the excitonic and nonexcitonic models, respectively. All sample parameters are the same as in Fig. 6.