Threading dislocation interactions in an inhomogeneous stress field: A statistical model

A statistical model is presented to characterize the influence of stress field inhomogeneity on the probability of interactions between threading dislocations in thin films. Any degree of stress field inhomogeneity is shown to increase the likelihood of interactions. However, below a critical level, the effect of stress inhomogeneity is small, while above this level a dramatic effect is observed. The approach taken is applicable to any system of interacting particles with spatially dependent velocities.