Elastic energy approach to the strain relaxation mechanism by dislocation splitting and slip in twist-bonded substrates

Abstract

The strain relaxation mechanism by the splitting and slip of a cross grid of dislocations in a heteroepitaxial film on a thin twist-bonded substrate is analytically investigated by considering the energy change due to the slip of the dislocation arrays. In this mechanism, the dislocation arrays resulting from the splitting of a cross grid of screw dislocations in the interface between the twist-bonded substrate and the supporting bulk substrate move toward the interface between the heteroepitaxial film and the twist-bonded substrate so that the mismatch strain is relieved. The energy change consisting of the interaction energy between the dislocation arrays and their images and the interaction energy between the two split dislocation arrays is obtained in the semi-infinite isotropic elastic solid. If the initial screw dislocation arrays dissociate into two partial dislocation arrays, the stacking fault energy must be added in the energy change. The thickness of the twist-bonded substrate at the zero of the energy change becomes the critical thickness at which the strain relaxation mechanism can be operative. The results show that the strain relaxation due to the slip of 60° perfect dislocation arrays does not tend to occur while the strain relaxation due to the slip of 30° partial dislocation arrays is possible if the twist angle is low and if the thickness of the twist-bonded substrate is small. Whether this mechanism was possible in the experiments in the literature is discussed.