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

Abstract

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 longerranged 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.

Bulk-suppressed and surface-sensitive Raman scattering by transferable plasmonic membranes with irregular slot-shaped nanopores

“…Since the quantum well layers are typically only 10 nm, the use of Raman spectroscopy to extract strain is strongly limited. Previous studies employed high-resolution X-ray diffraction techniques 42 or UV Raman spectroscopy, since using UV light reduces the penetration depth, allowing to collect Raman signals from the sample surface 43 , 44 . Surface-sensitive Raman scattering by PAuM introduced in this work constitutes a promising tool to probe strain in Si quantum well layers, which does not require UV Raman instrumentation.…”

Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields

“…Another quantum foundations experiment afforded by the large Hilbert space is the test of the reality of the quantum state, where the bound on the inadequacy of a purely epistemic view becomes tighter in higher dimensions 54 . The relation between lattice strain and nuclear quadrupole interaction will be exploited to demonstrate nuclear acoustic resonance 25 , and to use the 123 Sb atom as a local probe for strain in semiconductor nanoscale devices 55 . For quantum information processing, an exciting prospect is the encoding of an error-correctable logical qubit in the I = 7/2 nuclear spin 30 .…”

Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity

“…Whereas the anisotropy between g z ′ and g x ′, y ′ is expected from the quantum-well confinement, the additional in-plane anisotropy points to a non-circular confinement of the quantum dot, potentially caused by the interdot barrier breaking the individual quantum-dot symmetry. We suspect that the small but locally varying tilt of with respect to the sample axes is caused by localized strain gradients as imposed by the nanostructured gate electrodes 24 , 30 .…”