Complex Permittivity Measurements of Substrates and Thin Films at Millimeter-Wave Frequencies

Dielectric properties (i.e., relative permittivity and loss tangent) describe a material’s response to an applied electric field and are therefore key inputs for the design and modeling of millimeter-wave (30 – 300 GHz) devices. Previously, we benchmarked the agreement among leading laboratories in a round-robin comparison of millimeter-wave dielectric measurements [1], [2] and found that relative permittivity measurements could only agree to within 5 % in the best-case. This means that a material vendor and a device manufacturer could measure the same material and see a 10 % discrepancy in their results, with no recourse to determine which result (if either) is correct. This round-robin directly motivated our development of SI-traceable standards to establish a ‘correct’ answer and improve the overall reliability of material properties data available to researchers. Here, we show the use of split-cylinder resonators and fused silica substrates to develop those standards and their uncertainties. We describe the electromagnetic theory, the key sources of uncertainty, and the limitations of these measurements. Recognizing that not all materials are free-standing sheets, we then extend these split-cylinder resonator measurements from the simple case of homogeneous substrates to the more complicated case of thin films (ranging from ceramics like AlN to polymers like SU-8) on substrates. We extend the theory and uncertainty analysis for this more complicated case, and we discuss the limitations of this approach. This work allows us to deliver reliable material measurements of homogeneous substrates and heterogeneous material stacks with applications in electronics, telecommunications, and quantum computing.