Measuring the permittivity of fused silica with planar on-wafer structures up to 325 GHz

Fused silica has become an interesting alternative to silicon for millimeter-wave (mmWave) applications. Unfortunately, there are a few reports on the measurement of fused silica's permittivity above 110 GHz that use electrical rather than optical methods. Given that mmWave applications use electrical circuits, additional electrical data would be useful to industry. To test the feasibility of electrical methods, we applied on-wafer techniques based on coplanar waveguide transmission lines to measure the complex permittivity of fused silica to 325 GHz. Our approach used the multiline thru-reflect-line algorithm on the scattering parameter measurements of transmission lines. Our method combined these results with dc measurements of the resistivity of the metals, simulations of the coplanar waveguide cross section, and dimensional metrology. In short, our measurements do not show significant dielectric dispersion for fused silica up to 325 GHz. The resulting complex permittivity was ${ϵ}_r=3.87\pm 0.03$ and a loss tangent $tan\delta <0.005$ from 320 MHz to 325 GHz. To support our conclusions, we performed an uncertainty analysis considering relevant sources of uncertainty. In the broader context, these results show that fused silica is a suitable substrate for mmWave electronics where the loss tangent must be less than 0.005 up to 325 GHz.