Interfaces groove fractally.

Junctions between dissimilar substances -- for example, between metal and semiconductor -- are ubiquitous in electrical circuitry. An alternating current crossing such a boundary should experience the effect of a resistance and a capacitance. But to get the total impedance offered to the current, as S.H. Liu of Oak Ridge (Tenn.) National Laboratory points out, a physicist also must add in a "mysterious" constant-phase-angle element (CPA), which is somehow related to the roughness of the surface.

In a paper in the July 29 PHYSICAL REVIEW LETTERS, Liu presents an analysis of this relation on the basis of a fractal description of the shapes of such surfaces. Even polished surfaces show long lines of scratches, he points out. He describes the roughness of a given surface in terms of fractals, as a self-similar pattern of grooves within grooves (see illustration). The roughness depends on the stage to which this self-subdividing pattern is taken. Liu can then calculate the CPA from the fractal dimension of the surface, which is defined by the stage of roughness.

Such an interface contributes noise to the signal moving through the circuit. The fractal model of the interface can be represented by an equivalent circuit in which each groove is represented by a partial resistance-capacitance combination. This equivalent circuit would produce noise having the same spectrum as that observed in so-called 1/f noise, which is ubiquitously present in electronic circuits. In consequence, Liu suggests that 1/f noise originates at these interfaces.