Skin effects in narrow copper microstrip in 77 K

Finite-element and circuit simulations have been performed to analyze the performance of copper-polyimide wafer-scale interconnects at 77 K as a function of line width, dielectric thickness, and line length. The copper line width was generally kept equal to the dielectric thickness; this is a realistic geometry which gives a characteristic impedance of about 60 Omega , but one which is difficult to analyze. Finite element simulations were used to extract the frequency-dependent complex impedance which arises from the normal skin effect. This was then fitted to obtain an equivalent circuit which could be used in SPICE simulations. The anomalous skin effect was determined to be unimportant for frequencies below 20 GHz and was not included in the detailed finite-element models. The results have been used to analyze the performance of these lines for digital interconnects and to identify possible applications that would benefit from still lower resistance, such as might be obtainable from the high-temperature oxide superconductors. Skin effects were determined to be important for predicting the response for times less than 1.2 times the time of flight delay, while for larger times the DC resistance corresponding to the cross section of the signal line is adequate.<
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