%0 Journal Article %T Universality in Shape Evolution of Si$_{1-x}$Ge$_{x}$ Structures on High Index Silicon Surfaces %A J. K. Dash %A T. Bagarti %A A. Rath %A R. R. Juluri %A P. V. Satyam %J Physics %D 2012 %I arXiv %R 10.1209/0295-5075/99/66004 %X The MBE grown Si$_{1-x}$Ge$_x$ 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 ($\epsilon$) to the surface barrier term ($E_D$) in the kinematic Monte Carlo (kMC) simulations as one of the plausible mechanisms. %U http://arxiv.org/abs/1204.0578v1