Electrical resistance across a step of the Si(1 1 1)–Ag surface

A theoretical study on the electrical resistance of monatomic steps of the Si(1 1 1) 3 × 3 –Ag surface is presented. Electronic states of the stepped surfaces are calculated by a tight-binding method. One-dimensional states localized along step edges are found. There is a step-edge state localized at the edges of the lower terrace. The conductance across a step is calculated by the Landauer formalism. The conductance spectra of the surface states are explained by a one-dimensional model of the transmission of Bloch waves. A simple formula for the transmission probability of Bloch waves is derived. The resistance arises from both the difference in Bloch wave numbers and the discontinuity of the logarithmic derivatives of the periodic part of Bloch waves. They are expressed in terms of generalized phase and amplitude which are valid for evanescent waves. The logarithmic derivative of the generalized amplitude is regarded as an imaginary part of the complex wave number.