Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer

A simple system, based on a vector network analyzer, has been used with new numerical de-embedding and parameter inversion techniques to determine the relative permittivity (dielectric properties) of materials within the frequency range 750-1100 GHz. Free-space (noncontact), nondestructive testing has been performed on various planar dielectric and semiconducting samples. This system topology is well suited for quality control testing in an industrial setting requiring high throughput. Scattering parameters, measured in the absence of a sample, were used to computationally move the measurement plane to the surface of the samples being characterized. This de-embedding process can be completed much faster than a traditional calibration process and does not require exact knowledge of system geometric lengths. An iterative method was developed for simultaneously determining both sample geometric thickness and electric permittivity, through calculation of theoretical scattering parameters at material boundaries. A constrained nonlinear optimization process was employed to minimize the discrepancy between measured transmission and reflection data with this simulated data, in lieu of a closed-form parameter inversion algorithm. Monte Carlo simulations of parameter retrieval in the presence of artificial noise have demonstrated our method's robustness and superior noise rejection compared with a noniterative method. The precision of derived results has been improved by a factor of almost 50, compared to a closed-form extraction technique with identical input.