Strain relaxation via the splitting and slip of a cross-grid of dislocations in an hetero-epitaxial film, situated on a thin twist-bonded substrate, was investigated analytically by considering the energy changes due to the slip of the dislocation arrays. In this mechanism the dislocation arrays which resulted from the splitting of a cross-grid of screw dislocations, in the interface between the twist-bonded substrate and the supporting bulk substrate, moved towards the interface between the hetero-epitaxial film and the twist-bonded substrate so that the mismatch strain was relieved. The energy change which comprised the interaction energy between the dislocation arrays and their images, and the interaction energy between the 2 split dislocation arrays, was estimated for a semi-infinite isotropic elastic solid. If the initial screw dislocation arrays dissociated into 2 partial dislocation arrays, the stacking-fault energy had to be added onto the energy change. The thickness of the twist-bonded substrate for zero energy change became the critical thickness at which the strain relaxation mechanism could intervene. The results showed that strain relaxation due to the slip of 60° perfect dislocation arrays tended not to occur, while strain relaxation due to the slip of 30° partial dislocation arrays was possible if the twist angle was low and if the thickness of the twist-bonded substrate was small.

Elastic Energy Approach to Strain Relaxation by Dislocation Splitting and Slip in Twist-Bonded Substrates. Y.Obayashi, K.Shintani: Journal of Applied Physics, 2000, 88[10], 5623-9