Strain relaxation via the splitting and slip of a cross-grid of dislocations in an hetero-epitaxial film on a thin twist-bonded substrate was investigated analytically by considering the energy changes which were due to slip of the dislocation arrays. According to 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 consisted of the interaction energy between dislocation arrays and their images and the interaction energy between 2 split dislocation arrays, was obtained 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 to the energy change. The thickness of the twist-bonded substrate, for zero energy change, thus represented the critical thickness at which the strain relaxation mechanism could operate. The results showed that strain relaxation which was due to the slip of 60º perfect dislocation arrays did not tend to occur, whereas strain relaxation which was due to the slip of 30º partial dislocation arrays was possible if the twist angle was small and if the thickness of the twist-bonded substrate was small.

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