Critical thickness of a heteroepitaxial film on a twist-bonded compliant substrate

The critical thickness for misfit dislocation formation in a heteroepitaxia l film on a twist-bonded compliant substrate is calculated. The boundary be tween the twist-bonded compliant substrate and the supporting bulk substrat e with a low twist angle is assumed to be represented by a cross grid of st raight dislocations. The critical thickness is determined by the zero of th at formation energy of a misfit dislocation which consists of the self-ener gy of the dislocation, the interaction energy between the dislocation and t he dislocation arrays in the twist boundary, and the interaction energy bet ween the dislocation and the mismatch strain. Numerical results for the Inx Ga1-xP film on a twist-bonded GaAs compliant substrate show that the critic al thickness of the film on a twist-bonded compliant substrate is considera bly larger than that of the film on a free-standing compliant substrate. Th is difference in critical thicknesses for the twist-bonded compliant substr ate and the free-standing substrate is due to the interaction of the misfit dislocation with the dislocation arrays in the twist boundary. From the co mparison with the experimental observations in the literature, it is shown that the approximation in the present analysis is valid for the compliant s ubstrates with low twist angles. (C) 2000 American Institute of Physics. [S 0021-8979(00)04413-3].