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Quantitative Permittivity Measurements of Nanoliter Liquid Volumes in Microfluidic Channels to 40 GHz

We describe the design, fabrication, and evaluation of a new on-wafer measurement platform for the rapid and quantitative determination of the complex permittivity of nanoliter fluid volumes over the continuous frequency range from 45 MHz to 40 GHz. Our measurement platform integrates micrometer-scale poly(dimethylsiloxane) (PDMS)-based microfluidic channels with high-frequency coplanar waveguide (CPW) transmission lines to accurately place small fluid volumes at well-defined locations within planar measurement structures. We applied new on-wafer calibration techniques to accurately determine the scattering parameters of our integrated devices, and we developed a transmission-line model to extract the distributed circuit parameters of the fluid-loaded transmission line segment from the response of the overall test structure. All the necessary model parameters were experimentally determined directly from a single set of measurements without requiring a reference fluid of known permittivity. We extracted the complex permittivity of the fluid under test from the distributed capacitance and conductance per unit length of the fluid-loaded transmission line segment using finite-element analysis of the transmission line cross section. Our measurements show excellent agreement with bulk fluid permittivity determinations for methanol at room temperature and yield consistent results for the extracted fluid permittivity for the same microfluidic channel embedded in multiple CPW transmission lines of different dimensions.