High quality factor superconducting resonators on Si/SiGe semiconductor heterostructures

The circuit quantum electrodynamics architecture may allow for the generation of entanglement between spatially separated spin qubits [1]. This approach has introduced the challenge of fabricating high quality factor superconducting resonators on multilayered semiconductor substrates. Here we present electric field simulations which show that 30\% of the resonator electric field resides in the 675$\mu$m thick Si substrate on which the Si/SiGe heterostructure is grown, 55\% resides in the 3 $\mu$m thick SiGe relaxed buffer and 300 nm of Si$_{0.7}$Ge$_{0.3}$ grown above the relaxed buffer, and 15\% resides in the remaining Si/SiGe heterostructure. We evaluate the performance of Nb coplanar waveguide resonators fabricated on top of a strained Si/SiGe quantum well at 4.2 K and 10 mK. The tested resonators exhibit a high quality factor despite the presence of an accumulated two-dimensional electron gas beneath the resonator center pin.\\[4pt] [1] K. D. Petersson \textit{et al.}, Nature {\bf490}, 380-383 (2012).