The model developed here describes compressive stress evolution during the growth of continuous, polycrystalline films ͑i.e., beyond the point where individual islands have coalesced into a continuous film͒. These stresses are attributed to the insertion of excess adatoms at grain boundaries. Steady state occurs when the strain energy at the top of the film is balanced by the local excess chemical potential of surface adatmos. Strain gradients associated with this compressive stress mechanism

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... pend on the kinetics of the process. In the absence of grain boundary diffusion, these strain profiles are determined by the ratio of the atom insertion and growth rates. The steady-state strain and the strain evolution kinetics also depend on the two key length scales, the grain size, and the film thickness. The ratio of these two lengths ͑i.e., the grain aspect ratio͒ can also have a significant influence on the thermodynamic driving force for strain evolution if the grain sizes are sufficiently small. The model is fit to existing data for the growth of AlN films. However, more detailed comparisons will require experiments that are specifically designed to test this model.