Step-Spacing Distributions Revisited: Curved Crystals Bring Many Opportunities and Challenges to Analysis*

While the properties of vicinal surfaces with close-packed steps are long well understood, recent experiments using curved crystals invite examination of many orientations under the same temperature and other conditions [1]. In addition to having simultaneously a range of geometries, each of which may be preferred for specific epitaxial growth and chemical reactions, one can now test scaling theories of terrace-width distributions (TWDs) based on fundamental theories and the existence of a single characteristic length, the mean terrace width. For close-packed steps, TWDs are well described by a single-parameter Wigner distribution. For fully-kinked steps, the stiffness tends to vanish, and some of the underlying assumptions of that analysis fail [2]. Hence, TWDs typically do not scale. Furthermore, surface states introduce a new length, λ_F, which can confound the scaling analysis. For large terrace widths, a description in terms of quantum well states offers a novel accounting of the TWD. Other subtleties and open questions are discussed.
1. J.E. Ortega et al., New J. Phys. 20 (2018) 073010
2. T.L. Einstein, J. Jpn. Assn. Cryst. Growth 45 (2018) 2-04