Numerical Modeling Method
Mathematical estimations account for signal attenuation caused by physical irregularities on the surface of copper traces. The huray roughness model uses a semi spherical approximation of copper nodules to calculate power loss in high speed interconnects at frequencies exceeding ten gigahertz. It replaces older formulas that relied on simple peak to valley distance averages which failed to predict loss in very thin foils accurately.
Theoretical predictions match measured performance more closely with this approach.
Calculation Basis
Power dissipation depends on the surface area increase caused by the recursive structure of the dendritic copper growth. Inputs for the equation include the number of spheres and their radius found through cross sectional analysis of the foil under a scanning electron microscope. This model separates the skin effect loss of a perfectly smooth conductor from the additional losses introduced by the tooth geometry of the electrodeposited metal.
When frequencies rise the current moves closer to the boundary where these geometric effects become the primary cause of signal degradation. The algorithm applies a correction factor based on total surface area density.
Simulation Outcome
Derived correction factors enhance the accuracy of signal integrity tools. Design margins are refined. Reliability is maintained.
