Terrace-Width Distributions and Step-Step Repulsions on Vicinal Surfaces: Symmetries, Scaling, Simplifications, Subtleties, and Schrödinger

Details Terrace-Width Distributions and Step-Step Repulsions on Vicinal Surfaces: Symmetries, Scaling, Simplifications, Subtleties, and Schrödinger Terrace-Width Distributions and Step-Step Repulsions on Vicinal Surfaces: Symmetries, Scaling, Simplifications, Subtleties, and Schrödinger

2000-12-14

arxiv.org/abs/cond-mat/0012274v1

Surface Sci. 493, 460-474 (2001)

Physics

Condensed Matter

Materials Science

13 pages, 2 figures, submitted to Surface Sci., Proc. Int'l Symposium on Surface and Interface-PDSC 2000, Nagoya, Oct. 2000

Scientific paper

For more than three decades, measurement of terrace width distributions (TWDs) of vicinal crystal surfaces have been recognized as arguably the best way to determine the dimensionless strength $\tilde{A}$ of the elastic repulsion between steps. For sufficiently strong repulsions, the TWD is expected to be Gaussian, with $\tilde{A}$ varying inversely with the squared variance. However, there has been a controversy over the proportionality constant. From another perspective the TWD can be described as a continuous generalized Wigner distribution (CGWD) essentially no more complicated than a Gaussian but a much better approximation at the few calibration points where exact solutions exist. This paper combines concisely the experimentally most useful results from several earlier papers on this subject and describes some advancements that are in progress regarding numerical tests and in using Schr\"odinger-equation formalism to give greater understanding of the origin of the CGWD and to give hope of extensions to more general interaction potentials between steps. There are many implications for future experiments.

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