Measurements of complex permittivity of microwave substrates in the 20 to 300 K temperature range from 26.5 to 40.0 GHz
A knowledge of the dielectric properties of microwave substrates at low temperatures is useful in the design of superconducting microwave circuits. Results are reported for a study of the complex permittivity of sapphire (Al2O3), magnesium oxide (MgO), silicon oxide (SiO2), lanthanum aluminate (LaAlO3), and zirconium oxide (ZrO2), in the 20 to 300 Kelvin temperature range, at frequencies from 26.5 to 40.0 GHz. The values of the real and imaginary parts of the complex permittivity were obtained from the scattering parameters, which were measured using a HP-8510 automatic network analyzer. For these measurements, the samples were mounted on the cold head of a helium gas closed cycle refrigerator, in a specially designed vacuum chamber. An arrangement of wave guides, with mica windows, was used to connect the cooling system to the network analyzer. A decrease in the value of the real part of the complex permittivity of these substrates, with decreasing temperature, was observed. For MgO and Al2O3, the decrease from room temperature to 20 K was of 7 and 15 percent, respectively. For LaAlO3, it decreased by 14 percent, for ZrO2 by 15 percent, and for SiO2 by 2 percent, in the above mentioned temperature range.