A simple derivation of the bulk strain field - MISFIT dislocation equilibrium in semiconductor single heterostructures

The thermodynamic equilibrium between bulk strain field and interface dislocations in lattice mismatched semiconducting single heterostructures, is calculated in a completely solvable two-dimensional model, thanks to a choice of simple physical boundary conditions. The model clearly exhibits a phase transition at a critical misfit or a critical thickness of the epilayer, and allows to separate out from the elastic energy, the core contribution which is left, next, as a parameter. Through a carefull comparison with van der Merwe's and Matthews and Blakeslee's approaches, it is found that all of them turn out to lead to almost identical results. It follows that the widespread agreement of Matthews' theory with number of experimental data holds for all equilibrium theories, and in particular, the present one, as well. The remaining strong discrepancies, on the other hand, are admittedly ascribed to metastable behaviour in growing processes.