Lattice Deformation at Submicron Scale: X-Ray Nanobeam Measurements of Elastic Strain in Electron Shuttling Devices

Abstract

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 $\mathrm{Si}/{\mathrm{Si}}_{0.66}{\mathrm{Ge}}_{0.34}$ quantum well by means of nanobeam scanning x-ray diffraction microscopy. We are able to measure $\mathrm{Ti}\mathrm{N}$-electrode-induced local modulations of the strain tensor components in the range of 2--8 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ with about 60-nm lateral resolution. We evaluate that these strain fluctuations are reflected in local modulations of the potential of the $\mathrm{Si}$ 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.