Lattice deformation at the sub-micron scale: X-ray nanobeam measurements of elastic strain in electron shuttling devices

The lattice strain induced by metallic electrodes can impair the functionality of advanced quantum devices operating with electron or hole spins. Here we investigate the deformation induced by CMOS-manufactured titanium nitride electrodes on the lattice of a buried, 10 nm-thick Si/SiGe Quantum Well by means of nanobeam Scanning X-ray Diffraction Microscopy. We were able to measure TiN electrode-induced local modulations of the strain tensor components in the range of $2 - 8 \times 10^{-4}$ with ~60 nm lateral resolution. We have evaluated that these strain fluctuations are reflected into local modulations of the potential of the conduction band minimum larger than 2 meV, which is close to the orbital energy of an electrostatic quantum dot. We observe that the sign of the strain modulations at a given depth of the quantum well layer depends on the lateral dimensions of the electrodes. Since our work explores the impact of device geometry on the strain-induced energy landscape, it enables further optimization of the design of scaled CMOS-processed quantum devices.