A Versatile Approach to Measuring Complex GHz Permittivity of Substrate Supported Polymer Films

Abstract

Polymers have long been used as substrates and dielectric coatings for radiofrequency (RF) applications across a broad range of frequencies. No longer limited to polyolefins and other insulating backbone structures, a wide variety of conjugated, doped, and open-shell polymers and small molecules have been developed with tantalizing electrical properties waiting to be leveraged for low cost, size, weight, and power applications at GHz frequencies. A few isolated examples, such as polymer antennas, have been described, but the larger field of active, organic RF materials has been hindered by a lack of a simple, universally applicable measurement techniques. Values important to RF design, such as conductivity and mobility, are easily measured, but other critical measurements such as complex permittivity prevent rational design and modeling of active RF components made from organic conductors. Existing techniques measure bulk sample coupons inserted into waveguides or at low (kHz-MHz) frequencies, but a broadly applicable GHz solution has remained elusive. We present a broadband method for extracting the complex permittivity of polymeric films at GHz frequencies, employing the X-band (8–12 GHz) as a convenient frequency range. The material under test is deposited at the physical end of a coplanar waveguide where the radiating end effects are measured and analyzed. The complex permittivity is extracted from S11 measurements of the open-end coplanar waveguide by applying a combination of modified Nicolson-Ross-Weir algorithms and a multilayer conformal mapping method using specially derived theoretical relationships. Using this technique, the X-band permittivity of a representative polymer, SU-8, was obtained with >95% agreement to published literature values. The approach is suitable for any solution-processed organic material (polymers, macromolecules, small molecules) and provides a versatile, simple route to broadband RF characterization, key to unlocking the technological potential of these materials.