  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.
