Temperature dependence of the photoluminescence of self-assembled $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots in pulsed magnetic fields

We have studied the magnetic field $(<50\mathrm{T})$ dependence of the photoluminescence (PL) of self-assembled $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots as a function of temperature $\left(T\right)$. As the temperature is raised from 4.2 up to $80\mathrm{K}$, thermal redistribution causes the PL to be increasingly dominated by dots with a lower PL energy. Magneto-PL demonstrates that these low-energy dots are larger in size only in the growth direction and not in the plane of the sample. At high temperatures $(T>100\mathrm{K})$, a different physical phenomenon emerges: we see an anomalous decrease of the PL shift in magnetic field, which is attributed to field enhancement of the quantum dot barrier potential. This mechanism strongly favors excitons in small dots with a weak PL shift in magnetic field, hence laterally smaller dots increasingly dominate the PL at high temperatures and high fields.

Figure 1

(Color online) The PL energy, $E_{\mathrm{cm}}$, versus magnetic field. The data for $160\mathrm{K}$ have been shifted for clarity. The lines are fits to the data using Eq. (1). At lower temperatures, a crossover from parabolic to linear behavior occurs at $19\mathrm{T}$ (indicated by the arrow), whereas the $160\mathrm{K}$ data are parabolic up to $50\mathrm{T}$. Note that the energy shift is much larger for low temperatures. The inset shows the zero-field PL energy as a function of temperature. For low temperatures, the decrease of the PL energy with temperature is faster than predicted by the Varshni law (Ref. 6) for the InAs band gap (full lines).

Figure 2

(Color online) PL spectra at different magnetic fields for the $B\parallel z$ configuration for (a) 18 and (b) $160\mathrm{K}$. Two PL spectra for the $B\perp z$ orientation at low temperature are also shown in left panel (a). The PL intensity is enhanced when applying a magnetic field, in particular, for the experiments at higher temperatures. The low temperature data have a larger field shift compared to the high temperature data. Additionally, it can be seen that the PL shift with field is larger for the $B\parallel z$ orientation than for the $B\perp z$ configuration.

Figure 3

(Color online) Energy shift between 0 and $50\mathrm{T}$ versus temperature for a magnetic field applied parallel (circles) and perpendicular (triangles) to the growth direction. A strong decrease of the PL shift characterizes the high temperature $(T>100\mathrm{K})$ regime. The inset shows the exciton wave-function extent as a function of temperature following Eq. (1) for $B\parallel z$ and reveals an apparent wave-function shrinkage at high temperatures. For $T>120\mathrm{K}$, the lateral exciton radius becomes so small that the crossover to the high-field regime is at too high a field to be determined reliably. The lines are guides for the eyes.

Figure 4

(Color online) Schematic representation of the electron energy levels of the InAs QDs and GaAs matrix material as they are lifted by the magnetic field. The differential rise in energy levels as a function of $B$ increases the effective barrier height by $0.5–0.7\mathrm{meV}{\mathrm{T}}^{-1}$. The confinement energy $\Delta E_c$, the barrier potential $\Delta E_{\mathit{bp}}$, and the band offset $\Delta E_{\mathit{bo}}$ at $B=0$ are indicated.