Using lattice kinetic Monte Carlo, we provide a quantitative physically based atomistic model for the selective grown of Si-based materials, and explain {311} facet formation while remaining computationally efficient. Descriptions of the local atomistic configurations critical for the developing of {100}, {110}, {111}, and {311} facets are given. The model also introduces (a) three different microscopic growth rates for local {100} planes, needed to properly simulate the formation of perfect {100} terraces in miscut substrates and (b) a break-up energy to account for bonding during {311} facet formation. The model has been verified against experimental results.