Determination of the Permittivity of Transmission Lines at Milli-kelvin Temperatures

Many quantum technologies rely heavily on propagation of RF and microwave signals through devices at cryogenic temperatures, and detailed understanding of materials and signal propagation is therefore key to improving the performance of quantum circuits. The properties of dielectric substrate materials used for transmission lines (TLs) such as their permittivity need to be precisely determined to design high performance quantum integrated circuits. In this paper, we discuss a measurement technique for determining the effective permittivity of a TL at mK temperatures. The technique utilizes S-parameter measurements of multiple TLs to reliably extract the effective permittivity of the TL implemented in a substrate material. The technique is demonstrated using measured S-parameters of grounded co-planar waveguide (GCPW) at 296 K and 15 mK. The effective permittivity of the TL at 296 K and 15 mK are determined from measurements and compared. We observed the effective permittivity determinations at 15 mK to be approximately frequency independent and calculated the relative permittivity of Rogers RO4350B material at 15 mK to be 3.64. There is no significant deviation from this relative permittivity value with respect to manufacturer data and from measured data at 296 K.