A strained layer relaxes plastically when dislocations propagate within the layer, leaving behind an array of misfit dislocations at the layer interface. An analytical model for this process was developed which was based upon the idea that relaxation was frustrated when propagating dislocations were trapped or annihilated by encounters with previously created misfit dislocations or other propagating dislocations. The theory characterized the evolving density of the misfit array and the density of propagating dislocations in terms of a pair of coupled rate equations. The two trapping functions which appeared in these equations were evaluated quantitatively by numerically investigating all possible dislocation-dislocation encounters. Fluctuations in the local stress field driving the individual dislocations were explicitly taken into account when evaluating the trapping functions. Analysis of the rate equations showed that there were two regimes in the strain-relaxation dynamics. Initially, the strain decreases rapidly following a universal dependence on time scaled with the initial dislocation density n0. At a (rescaled) crossover time that increases with n0, the strain levels off from the universal relaxation curve and saturates to an asymptotic residual strain level, which decreases with n0. Microscopically, the present model revealed that the initial fast strain-relaxation regime was dominated by collisions between propagating dislocations, while the slow saturation regime was dominated by the trapping of propagating dislocations by the misfits. In the end, the self-trapping of the propagating dislocations by the misfit array they themselves have generated leaves the layer in a frustrated state with residual strain higher than the critical strain. The predictions of the theory were found to be in good agreement with experimental measurements and with large-scale numerical simulations of layer relaxation.

Dislocation-Interaction-Based Model of Strained-Layer Relaxation. K.W.Schwarz, Y.Tu: Journal of Applied Physics, 2009, 106[8], 083510