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

Lattice matched GaAs/AlGaAs epitaxial structures with quantum dots are studied at $T=4.2$ K 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 $b/a=0.242\ifmmode\pm\else\textpm\fi{}0.008$ in good agreement with previous studies on GaAs. Based on the previously estimated value of $a\ensuremath{\approx}\ensuremath{-}8.8$ eV we derive the product of the nuclear quadrupolar moment $Q$ and the $S$-tensor diagonal component in GaAs to be $Q{S}₁₁\ensuremath{\approx}+0.758\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ V for $⁷⁵\mathrm{As}$ and $Q{S}₁₁\ensuremath{\approx}\ensuremath{-}0.377\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ V for $⁶⁹\mathrm{Ga}$ nuclei. In our experiments the signs of ${S}₁₁$ are directly measurable, which was not possible in the earlier nuclear acoustic resonance studies. Our $Q{S}₁₁$ values are a factor of $\ensuremath{\sim}1.4$ 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 modeling of their magnetic resonance spectra.