We propose and investigate a model for the development of cross-hatch surface morphology in growing mismatched layers. The model incorporates two important elements: (i) strain relaxation due to dislocation glide in the layer (film) interior that is also associated with misfit dislocation formation at the film/substrate interface and (ii) lateral surface transport that eliminates surface steps that originated from dislocation glide. A combination of dislocation-assisted strain relaxation and surface step flow leads to the appearance of surface height undulations during layer growth. A Monte Carlo simulation technique was applied to model dislocation nucleation events in the course of strain relaxation. The simulation was used to model the influence of dislocations on film surface height profiles. The surface height displacement was calculated from the analytic elasticity solutions for edge dislocations near a free surface. The results of the modeling predict that the average amplitude of the surface undulations and their apparent wavelength both increase with increasing film relaxation and film thickness. The developed cross-hatch pattern is characterized by an atomically smooth but mesoscopically (lateral dimensions ～0.1-10 μm) rough surface morphology. The conclusions of the model are in agreement with atomic force microscopy observations of cross-hatch surface relief in In_(0.25)Ga_(0.75)As/GaAs samples grown well beyond the critical thickness for misfit dislocation formation.
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