Statistical properties of local work function on stepped surfaces

Local electrostatic potential of dipole rows along the steps on a solid sur face, generated by the Smoluchowski electron smoothing effect, exhibits lar ge fluctuations in the directions parallel to the surface. We analyze stati stical properties of this potential for the distances above the surface, ra nging from several atomic units to the macroscopic lengths. Complete probab ility density of the potential is evaluated for regularly spaced steps and for randomly distributed steps. Moreover, correlation function of the poten tial, probed at two different points, is analyzed in terms of the probabili ty density for the terrace lengths between two consecutive steps. Several m odels for the latter quantity have been tested, giving rise to various form s of the distance dependence of the potential fluctuation above the surface .