Measurement of the Low-Temperature Loss Tangent of High-Resistivity Silicon Using a High- Superconducting Resonator

Abstract

In this paper, we present a direct loss-tangent measurement of a high-resistivity intrinsic (100) silicon wafer in a temperature range from approximately to 1 K, approaching the quantum regime. The measurement is performed using a technique that takes advantage of a high-quality-factor superconducting niobium resonator and allows us to directly measure the loss tangent of insulating materials with a 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, and these are one order of magnitude larger than what was previously estimated. In addition, we discover a nonmonotonic trend in the loss tangent as a function of temperature, which we describe by means of a phenomenological model based on variable-range hopping conduction between localized states around the Fermi energy. We also observe an increasing dependence of the dissipation on the electric field, which can be qualitatively described by the variable-range hopping-conduction mechanism as well. These findings are important for the optimization of quantum devices and for advancing the understanding of their decoherence channels.