  Quantum devices formed in high-electron-mobility semiconductor
heterostructures provide a route through which quantum mechanical effects can
be exploited on length scales accessible to lithography and integrated
electronics. The electrostatic definition of quantum dots in semiconductor
heterostructure devices intrinsically involves the lithographic fabrication of
intricate patterns of metallic electrodes. The formation of metal/semiconductor
interfaces, growth processes associated with polycrystalline metallic layers,
and differential thermal expansion produce elastic distortion in the active
areas of quantum devices. Understanding and controlling these distortions
presents a significant challenge in quantum device development. We report
synchrotron x-ray nanodiffraction measurements combined with dynamical x-ray
diffraction modeling that reveal lattice tilts with a depth-averaged value up
to 0.04 deg. and strain on the order of 10^-4 in the two-dimensional electron
gas (2DEG) in a GaAs/AlGaAs heterostructure. Elastic distortions in GaAs/AlGaAs
heterostructures modify the potential energy landscape in the 2DEG due to the
generation of a deformation potential and an electric field through the
piezoelectric effect. The stress induced by metal electrodes directly impacts
the ability to control the positions of the potential minima where quantum dots
form and the coupling between neighboring quantum dots.
