Tl. Einstein et al., Terrace-width distributions and step-step repulsions on vicinal surfaces: symmetries, scaling, simplifications, subtleties, and Schrodinger, SURF SCI, 493(1-3), 2001, pp. 460-474
For more than three decades, measurement of terrace width distributions (TW
Ds) of vicinal crystal surfaces have been recognized as arguably the best w
ay to determine the dimensionless strength (A) over tilde of the elastic re
pulsion between steps. For sufficiently strong repulsions, the TWD is expec
ted to be Gaussian, with (A) over tilde varying inversely with the squared
variance. However, there has been a controversy over the proportionality co
nstant. From another perspective the TWD can be described as a continuous g
eneralized Wigner distribution (CGWD) essentially no more complicated than
a Gaussian but a much better approximation at the few calibration points wh
ere exact solutions exist. This paper combines concisely the experimentally
most useful results from several earlier papers on this subject and descri
bes some advancements that are in progress regarding numerical tests and in
using Schrodinger-equation formalism to give greater understanding of the
origin of the CGWD and to give hope of extensions to more general interacti
on potentials between steps. There are many implications for future experim
ents. (C) 2001 Elsevier Science B.V. All rights reserved.