Universality in Shape Evolution of Si$_{1-x}$Ge$_{x}$ Structures on High Index Silicon Surfaces

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.