The MBE grown Si1−xGex islands on reconstructed high index surfaces, such as, Si(5 5 12), Si(5 5 7) and Si(5 5 3) show a universality in the shape evaluation and the growth exponent parameters, \emph{irrespective} of the substrate orientations and size of the island structures. This phenomena has been explained by incorporating a deviation parameter (ϵ) to the surface barrier term (ED) in the kinematic Monte Carlo (kMC) simulations as one of the plausible mechanisms.
@article{arxiv.1204.0578,
title = {Universality in Shape Evolution of Si$_{1-x}$Ge$_{x}$ Structures on High Index Silicon Surfaces},
author = {J. K. Dash and T. Bagarti and A. Rath and R. R. Juluri and P. V. Satyam},
journal= {arXiv preprint arXiv:1204.0578},
year = {2012}
}