On the electrical conductivity of metals with a rough surface

Abstract

ABSTRACT We discuss surface roughness effects on the conduction of electrons in metals using both the quantal Kubo–Greenwood formalism and the semi-classical Fuchs–Sondheimer method. The main purpose here is to compare these methods and clarify a few subtle and widely misunderstood conceptual issues. One of such issues is concerned with the conditions under which the broken translation symmetry along a rough surface may be restored. This symmetry has often been presumed in existing work but not always with proper justifications. Another one relates to the physical meaning of a phenomenological parameter (denoted by p) intuitively introduced in the semi-classical theory. This parameter, called the specularity parameter or sometimes the Fuchs parameter, plays an important role in the experimental studies of surface roughness but has so far lacked a rigorous microscopic definition. The third issue arises as to the domain of validity for the electrical conductivity obtained in those methods. A misplacement of the domain may have resulted in erroneous analysis of surface effects in a variety of electrodynamic phenomena including surface plasma waves.