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

The strain relaxation mechanism by the splitting and slip of a cross grid o f dislocations in a heteroepitaxial film on a thin twist-bonded substrate i s analytically investigated by considering the energy change due to the sli p of the dislocation arrays. In this mechanism, the dislocation arrays resu lting from the splitting of a cross grid of screw dislocations in the inter face between the twist-bonded substrate and the supporting bulk substrate m ove toward the interface between the heteroepitaxial film and the twist-bon ded substrate so that the mismatch strain is relieved. The energy change co nsisting 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 s crew 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 cr itical thickness at which the strain relaxation mechanism can be operative. The results show that the strain relaxation due to the slip of 60 degrees perfect dislocation arrays does not tend to occur while the strain relaxati on due to the slip of 30 degrees partial dislocation arrays is possible if the twist angle is low and if the thickness of the twist-bonded substrate i s small. Whether this mechanism was possible in the experiments in the lite rature is discussed. (C) 2000 American Institute of Physics. [S0021-8979(00 )01023-9].