Full Picture of Lattice Deformation in a Ge1 - xSnx Micro-Disk by 5D X-ray Diffraction Microscopy.

Lattice strain in crystals can be exploited to effectively tune their physical properties. In microscopic structures, experimental access to the full strain tensor with spatial resolution at the (sub-)micrometer scale is at the same time very interesting and challenging. In this work, how scanning X-ray diffraction microscopy, an emerging model-free method based on synchrotron radiation, can shed light on the complex, anisotropic deformation landscape within three dimensional (3D) microstructures is shown. This technique allows the reconstruction of all lattice parameters within any type of crystal with submicron spatial resolution and requires no sample preparation. Consequently, the local state of deformation can be fully quantified. Exploiting this capability, all components of the strain tensor in a suspended, strained Ge1 - xSnx /Ge microdisk are mapped. Subtle elastic deformations are unambiguously correlated with structural defects, 3D microstructure geometry, and chemical variations, as verified by comparison with complementary electron microscopy and finite element simulations. The methodology described here is applicable to a wide range of fields, from bioengineering to metallurgy and semiconductor research.

Nanoscale Mapping of the 3D Strain Tensor in a Germanium Quantum Well Hosting a Functional Spin Qubit Device.

A strained Ge quantum well, grown on a SiGe/Si virtual substrate and hosting two electrostatically defined hole spin qubits, is nondestructively investigated by synchrotron-based scanning X-ray diffraction microscopy to determine all its Bravais lattice parameters. This allows rendering the three-dimensional spatial dependence of the six strain tensor components with a lateral resolution of approximately 50 nm. Two different spatial scales governing the strain field fluctuations in proximity of the qubits are observed at <100 nm and >1 µm, respectively. The short-ranged fluctuations have a typical bandwidth of 2 × 10-4 and can be quantitatively linked to the compressive stressing action of the metal electrodes defining the qubits. By finite element mechanical simulations, it is estimated that this strain fluctuation is increased up to 6 × 10-4 at cryogenic temperature. The longer-ranged fluctuations are of the 10-3 order and are associated with misfit dislocations in the plastically relaxed virtual substrate. From this, energy variations of the light and heavy-hole energy maxima of the order of several 100 µeV and 1 meV are calculated for electrodes and dislocations, respectively. These insights over material-related inhomogeneities may feed into further modeling for optimization and design of large-scale quantum processors manufactured using the mainstream Si-based microelectronics technology.