The critical thickness was calculated for misfit dislocation formation in an hetero-epitaxial film on a twist-bonded compliant substrate. The boundary between the twist-bonded compliant substrate, and a supporting bulk substrate having a low twist angle, was assumed to be represented by a cross-grid of straight dislocations. The critical thickness corresponded to zero formation energy of a misfit dislocation. The misfit energy comprised the self-energy of the dislocation, the interaction energy between the dislocation and dislocation arrays in the twist boundary and the interaction energy between the dislocation and the mismatch strain. Numerical results for an InGaP film on a twist-bonded GaAs compliant substrate showed that the critical thickness of a film on a twist-bonded compliant substrate was considerably larger than that of a film on a free-standing compliant substrate. This difference in critical thicknesses was attributed to the interaction of misfit dislocations with dislocation arrays in the twist boundary. By comparison with experimental observations, it was shown that the approximation made in the present analysis was valid for compliant substrates having low twist angles.

Critical Thickness of a Heteroepitaxial Film on a Twist-Bonded Compliant Substrate. Y.Obayashi, K.Shintani: Journal of Applied Physics, 2000, 88[1], 105-14