Strain relaxation in heteroepitaxial films by misfit twinning. I. Critical thickness

Based on the dislocation theory of twinning, an analytical solution is given to determine the critical thickness of the misfit twin formation in an epilayer with different elastic constants from its substrate. For a given epilayer thickness and lattice mismatch strain, the twin formation energy should reach its minimum to determine the twin width and a zero minimum formation energy determines the critical thickness for misfit twinning. The effect of elastic mismatch between the epilayer and the substrate on the critical thickness is studied comprehensively, revealing that an elastically soft epilayer has a large critical thickness. Moreover, a misfit-twin-and-perfect-dislocation predominance chart is constructed to predict the predominant regions of misfit twinning and perfect dislocation in the mismatch strain and the specific twin-boundary energy domain. (c) 2007 American Institute of Physics.