Theoretical and Empirical Evaluation of Surface Roughness Effects on Conductivity in the Terahertz Regime

While models for conductivity in the terahertz regime are improving, there is limited data on the effects of submicrometer roughness features on conductivity. We present direct measurements of the effective conductivity of samples with periodic controlled roughness features using an open quasi-optical resonator at 400 and 650 GHz. The empirical results are compared with two closed-form models and a finite-element simulation. We find that the Mie-scattering-based model and finite-element approach are more accurate for samples that are smooth relative to the skin depth. For surface features greater than the skin depth, we found the Hammerstad and Bekkadal model to be a better predictor of effective conductivity. The observed discrepancies identify the need for further advances in theoretical understanding of the underlying physics. The empirical results of this study can be used to benchmark new and improved models of effective conductivity in the terahertz regime.