Strain-induced $g$-factor tuning in single InGaAs/GaAs quantum dots

The tunability of the exciton $g$ factor in InGaAs quantum dots using compressive biaxial stress applied by piezoelectric actuators is investigated. We find a clear relation between the exciton $g$ factor and the applied stress. A linear decrease of the $g$ factor with compressive biaxial strain is observed consistently in all investigated dots. A connection is established between the response of the exciton $g$ factor to the voltage applied to the piezoelectric actuator and the response of the quantum dot emission energy. We employ a numerical model based on eight-band $\mathbf{k}·\mathbf{p}$ theory to calculate the exciton $g$ factor of a typical dot as a function of strain and a good agreement with our experiments is found. Our calculations reveal that the change in exciton $g$ factor is dominated by the contribution of the valence band and originates from increased heavy hole light hole splitting when applying external stress.

Figure 1

Schematic layout of the device structure. The InGaAs QDs are embedded in an intrinsic GaAs membrane (green). By means of gold thermocompression bonding this membrane is integrated on top of a piezoelectric actuator, which is used to induce additional biaxial compressive strain (indicated by the green arrows) in the QDs by applying a voltage across the piezo. A magnetic field can be applied in the growth direction of the QDs.

Figure 2

Left: PL spectra of a single QD as a function of voltage applied to the piezo, where the exciton (${\text{X}}^0$) and biexciton ($2{\text{X}}^0$) lines are indicated. A linear regression of the emission energy versus the applied voltage is depicted by the dashed lines. Right: PL spectra of the same QD as a function of magnetic field. The dashed lines indicate the shift and splitting of ${\text{X}}^0$ and $2{\text{X}}^0$ as a function of magnetic field. Note that the red highlighted peaks have been enhanced five times to increase the visibility.

Figure 3

Exciton $g$ factor of a single QD as a function of applied voltage (e.g., compressive strain), with the linear regression (solid line) and the error range (red area) indicated.

Figure 4

$g$-factor response to applied voltage versus the emission energy response for both the exciton and biexciton states of several dots. The dashed lines indicate the respective linear fits. The solid lines pair the excitons and biexcitons originating from the same QD. The shaded areas represent the error ranges.

Figure 5

Change in band-edge energy (calculated values including linear regression) of both the conduction and valence band in the bulk (solid) and the QD (dashed) material as a function of applied strain. It reveals an increase of the band gap in both materials, however larger in the bulk material. The blue line shows the change in the splitting between the heavy hole and light hole bands.

Figure 6

Calculated energy for the exciton emissions as a function of applied strain. A linear behavior is found as indicated by the solid line, whose slope $\gamma =2.37\pm 0.04\mu \mathrm{eV}/\mathrm{V}$ agrees well with the experiment.

Figure 7

Top: Calculated hole (open squares) and electron (solid squares) $g$ factor as a function of applied strain. The electron $g$ factor shows a linear increase, however small. The hole $g$ factor has a significantly larger linear strain dependence. The effect agrees with the experiment both qualitatively and quantitatively. Bottom: Composition of the wave function of the hole ground state as a function of the applied strain, revealing that the change in $g$ factor originates from a change in light/heavy hole mixing.