Measurement of the Low-temperature Loss Tangent of High-resistivity Silicon with a High Q-factor Superconducting Resonator

In this letter, we present the direct loss tangent measurement of a high-resistivity intrinsic (100) silicon wafer in the temperature range from ~ 70 mK to 1 K, approaching the quantum regime. The measurement was performed using a technique that takes advantage of a high quality factor superconducting niobium resonator and allows to directly measure the loss tangent of insulating materials with high level of accuracy and precision. We report silicon loss tangent values at the lowest temperature and for electric field amplitudes comparable to those found in planar transmon devices one order of magnitude larger than what was previously estimated. In addition, we discover a non-monotonic trend of the loss tangent as a function of temperature that we describe by means of a phenomenological model based on variable range hopping conduction between localized states around the Fermi energy. We also observe that the dissipation increases as a function of the electric field and that this behavior can be qualitatively described by the variable range hopping conduction mechanism as well. This study lays the foundations for a novel approach to investigate the loss mechanisms and accurately estimate the loss tangent in insulating materials in the quantum regime, leading to a better understanding of coherence in quantum devices.