  In spin-based quantum information processing devices, the presence of control
and detection circuitry can change the local environment of a spin by
introducing strain and electric fields, altering its resonant frequencies.
These resonance shifts can be large compared to intrinsic spin line-widths and
it is therefore important to study, understand and model such effects in order
to better predict device performance. Here we investigate a sample of bismuth
donor spins implanted in a silicon chip, on top of which a superconducting
aluminium micro-resonator has been fabricated. The on-chip resonator provides
two functions: first, it produces local strain in the silicon due to the larger
thermal contraction of the aluminium, and second, it enables sensitive electron
spin resonance spectroscopy of donors close to the surface that experience this
strain. Through finite-element strain simulations we are able to reconstruct
key features of our experiments, including the electron spin resonance spectra.
Our results are consistent with a recently discovered mechanism for producing
shifts of the hyperfine interaction for donors in silicon, which is linear with
the hydrostatic component of an applied strain.
