Cross-calibration of GaAs deformation potentials and gradient-elastic tensors using photoluminescence and nuclear magnetic resonance spectroscopy in GaAs/AlGaAs quantum dot structures

Lattice matched GaAs/AlGaAs epitaxial structures with quantum dots are studied under static uniaxial stress applied either along the $[001]$ or $[110]$ crystal directions. We conduct simultaneous measurements of the spectral shifts in the photoluminescence of the bulk GaAs substrate, which relate to strain via deformation potentials $a$ and $b$, and the quadrupolar shifts in the optically detected nuclear magnetic resonance spectra of the quantum dots, which relate to the same strain via the gradient-elastic tensor $S_{ijkl}$. Measurements in two uniaxial stress configurations are used to derive the ratio $b/a=0.241\pm0.008$ in good agreement with previous studies on GaAs. Based on the previously estimated value of $a\approx-8.8$ eV we derive the product of the nuclear quadrupolar moment $Q$ and the $S$-tensor diagonal component in GaAs to be $QS_{11}\approx+0.76\times10^{-6}$ V for $^{75}$As and $QS_{11}\approx-0.37\times10^{-6}$ V for $^{69}$Ga nuclei. In our experiments the signs of $S_{11}$ are directly measurable, which was not possible in the earlier nuclear acoustic resonance studies. Our $QS_{11}$ values are a factor of $\sim$1.4 smaller than those derived from the nuclear acoustic resonance experiments [Phys. Rev. B 10, 4244 (1974)]. The gradient-elastic tensor values measured in this work can be applied in structural analysis of strained III-V semiconductor nanostructures via accurate modelling of their magnetic resonance spectra.