Hybrid Characterization of Nanolitre Dielectric Fluids in a Single Microfluidic Channel Up to 110 GHz

Abstract

In this paper, we present a new “hybrid” method for on-wafer dielectric measurements of nanolitre fluid samples. The first part of the hybrid method uses a technique that extracts the complex relative permittivity of the material used to make microfluidic channels. The extraction is performed with an empty channel measurement, and thus requires no extra deembedding structures. The second part of the hybrid method involves an accurate extraction of the complex relative permittivity of dielectric fluids. The hybrid method uses three different extraction algorithms and calculates their Type B uncertainties within the NIST Microwave Uncertainty Framework. By choosing the calculation algorithm with the smallest uncertainty at each frequency, the hybrid method can achieve accurate measurements of the fluids’ permittivity over a broad bandwidth. One of the three algorithms is a new algorithm based on closed-form equations. A trace-based algorithm is also applied to fluids measurements, for the first time to our knowledge. Through the uncertainty analysis, we found out that these two algorithms should be favored over a traditional least-squares optimization-based algorithm at millimeter wave frequencies, due to their lower sensitivities to probe-placement errors.