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An atomistic model to account for the formation of facets during solid phase epitaxy regrowth (SPER) is shown. This model relies on a lattice kinetic Monte Carlo approach. The lattice atoms produce different crystalline planes growing with different planar velocities. In particular, the model explains the arrow tip formation during SPER of thin silicon fins typical for fin field effect transistors and the formation of trenches in rectangular-shaped amorphized regions in (001) and (011) silicon, caused by the distortion of the lattice by shear strain and propagated by (111) facets.