Measurements of Permittivity, Dielectric Loss Tangent, and Resistivity of Float-Zone Silicon at Microwave Frequencies

Abstract

The complex permittivity and resistivity of float-zone high-resistivity silicon were measured at microwave frequencies for temperatures from 10 up to 400 K employing dielectric-resonator and composite dielectric-resonator techniques. At temperatures below 25 K, where all free carriers are frozen out, loss-tangent values of the order of 2times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> were measured, suggesting the existence of hopping conductivity or surface charge carrier conductivity in this temperature range. Use of a composite dielectric-resonator technique enabled the measurement of materials having higher dielectric losses (or lower resistivities) with respect to the dielectric-resonator technique. The real part of permittivity of silicon proved to be frequency independent. Dielectric losses of high-resistivity silicon at microwave frequencies are mainly associated with conductivity and their behavior versus temperature can be satisfactory described by dc conductivity models, except at very low temperatures