Finite element analysis of skin effect in copper interconnects at 77 K and 300 K

A methodology is presented for calculating normal skin effect in complex geometries using the finite-element method. The results are used to analyze the performance of copper interconnects at 77 K and 300 K for both digital and microwave applications. The analysis includes attenuation per unit length, phase velocity and characteristic impedance as a function of frequency from DC to 10 GHz. It was found that for digital signal propagation, skin effects are important for predicting rise-time degradation for rise-time less than 1.2 times the flight delay, while for larger rise-times, the DC resistance corresponding to the cross-section of the signal line is adequate for explaining the lossy characteristics.<>