Critical thickness for misfit twinning in an epilayer

A Somigliana dislocation dipole model is developed to determine the critical thickness for misfit twin formation in an epilayer with different elastic constants from its substrate. The critical dipole arm length is determined by minimizing the twin formation energy for a given epilayer thickness and lattice mismatch strain, while a zero value of the minimum formation energy determines the critical thickness for misfit twinning. The results obtained by the Somigliana dislocation dipole model are roughly consistent with those by the previous dislocation-based twinning model.