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Morphological properties of strained epitaxial films are examined through amesoscopic approach developed to incorporate both the film crystallinestructure and standard continuum theory. Film surface profiles and properties,such as surface energy, liquid-solid miscibility gap and interface thickness,are determined as a function of misfit strains and film elastic modulus. Weanalyze the stress-driven instability of film surface morphology that leads tothe formation of strained islands. We find a universal scaling relationshipbetween the island size and misfit strain which shows a crossover from thewell-known continuum elasticity result at the weak strain to a behaviorgoverned by a "perfect" lattice relaxation condition. The strain at which thecrossover occurs is shown to be a function of liquid-solid interfacialthickness, and an asymmetry between tensile and compressive strains isobserved. The film instability is found to be accompanied by mode coupling ofthe complex amplitudes of the surface morphological profile, a factorassociated with the crystalline nature of the strained film but absent inconventional continuum theory.

Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model