Equilibrium critical thickness for misfit dislocations in III-nitrides

The critical thickness gives the transition point between fully strained and relaxed heteroepitaxial films and determines the onset of defect generation, including misfit dislocations, cracks, and V-pits. An important variable in critical thickness calculations concerning misfit dislocations is the dislocation energy. It consists of two contributions: the elastic energy of the bulk material around a dislocation and the energy of the dislocation core. The latter part is often neglected. Recent atomistic calculations have estimated this quantity together with the radius of dislocation cores in wurtzite III-nitrides. The effect of the dislocation core energy on equilibrium critical thickness values for III-nitrides is investigated theoretically and is shown to be significant. The calculated values of the critical thickness are compared with experimentally determined values of the critical thickness for misfit dislocations in the InGaN/GaN system using transmission electron microscopy and x-ray diffraction techniques. A comparison of the present model with experimental observations, together with a wide range of data from the literature for both AlGaN/GaN and InGaN/GaN systems, shows reasonable agreement. Finally, we speculate on a possible reason for differences between theory and experiment.