Copper Roughness Induced Gain for Inductance and Resistance on Stripline Interconnects

This paper presents a method for broadband characterization of copper roughness induced gain factor for resistance and inductance on stripline interconnects. The characterization relies on S-parameter measurements of striplines fabricated with smooth (VLP) and rough (RTF) copper finishing on otherwise identical stack-ups. The VLP and RTF interconnects are each characterized from two-line measurements; then the R, L, G, C parameters for each are extracted under the same Tanδ condition, which yields the copper roughness factor for the inductance and resistance of the RTF interconnects accurately characterized up to 40 GHz. The method also allows to uniquely characterize the permittivity of the dielectric and demonstrates that the increase in inductance due to roughness is considerably larger than that for resistance, which is a necessary condition for a causal model. The experimental characterization shows excellent correlation to a newly introduced generalized causal Hammerstad model, and good correlation to the Huray model, when multiple terms in the expansions are used.