Modeling and measurements of atomic surface roughness.

We present a geometrical model of atomic topography with which to obtain a quantitative assessment of surface roughness. A series of two- and three-dimensional atomic surface roughness equations with sufficiently realistic parameters is developed to permit quantitative comparison with scanning-tunneling microscope and atomic-force microscope (AFM) experimental results. The model is sufficiently simple that one can easily use it to interpret experimental data. Tables are provided with estimated values for two- and three-dimensional rms atomic surface roughness in pure metal crystals and ionic crystals based on the atomic surface roughness equations. We use these roughness equations to determine the roughness of cleaved muscovite mica [essentially, KAl(2)(OH)(2)Si(3)AlO(10)]; the calculated values for both two- and three-dimensional roughness are consistent with those obtained in our AFM measurements. In addition, we demonstrate both theoretically and experimentally that atomic surface roughness is never zero.