Title: Log-normal glide and the formation of misfit dislocation networks in heteroepitaxial ZnS on GaP

Abstract: Scanning electron microscopy (SEM) based electron channeling contrast imaging (ECCI) is used to observe and quantify misfit dislocation (MD) networks formed at the heteroepitaxial interface between ZnS and GaP grown by molecular beam epitaxy (MBE). Below a critical thickness of 15-20 nm, no MDs are observed. However, crystallographic features with strong dipole contrast, consistent with unexpanded dislocation half-loops, are observed prior to the formation of visible interfacial MD segments and any notable strain relaxation. At higher film thicknesses (20 to 50 nm), interfacial MD lengths increase anisotropically in the two orthogonal in-plane <110> line directions, threading dislocation (TD) density increases, and a roughening transition is observed from atomically smooth two-dimensional (2D) to a multi-stepped three-dimensional (3D) morphology, providing evidence for step edge pinning via surface terminating dislocations. The ZnS strain relaxation, calculated from the total MD content observed via ECCI, matches the average strain relaxation measured by high-resolution x-ray diffraction (HRXRD). The MD lengths are found to follow a log-normal distribution, indicating that the combined MD nucleation and TD glide processes must have a normal distribution of activation energies. The estimated TD glide velocity ($v_{g}$) along [$\bar{1}$10] is almost twice that along [110], but in both directions shows a maximum as a function of film thickness, indicating an initial burst of plasticity followed by dislocation pinning.