Simulation and measurement correlation of random rough surface effects in interconnects

We study the effects of three dimensional (3D) random roughness on wave propagation in a parallel plate metallic waveguide with finite conductivity. The surface roughness is characterized as a random process characterized by root mean square (rms) height, correlation length and power spectral density (PSD) function. The second order small perturbation method (SPM2) is applied to compute the coherent wave enhancement factors of absorption. A microstrip line structure is designed for validation of these enhancement factor results. Rough surface height profiles are measured on the substrate and the PSD is extracted. With the PSD we obtain the enhancement factor for the specific surface roughness. The attenuation constant of the microstrip line with rough surface can be estimated using a field solution for a smooth surface and the enhancement factor. The results for waveguides are also compared with the results obtained for a plane wave incident on a metal surface with 3D roughness. Comparison between the estimated and measured attenuation constant shows that the enhancement factor derived by SPM2 gives a better estimation than the standard Hammerstad and Bekkadal equation. The waveguide model gives more accurate enhancement factors than the plane wave model at frequencies above 20 GHz, especially for rough surfaces with rms heights larger than 2 μm.