Modeling Surface Roughness at DC

This paper presents an approach to quantify the effective resistance of a trace at DC by taking metal roughness into account. Algorithms were developed to approximate the resistance variation at 0Hz due to roughness and results were compared with hand calculations, 3D model simulations and measurement. The existing models in the industry are valid only for higher frequencies where skin effect is fully developed. They do not hold true for modeling at DC. In flex designs where the traces are very thin, the surface roughness parameter can be relatively large and can have a significant impact on signal transmission and power delivery of the system at DC.