The asymmetric effect of stress in the morphological instability of a growing thin film

摘要

Many experiments have shown that films growing under tensile stress and compressive stress have different morphological instability behaviours. Departing from earlier theoretical works, which treated surface diffusion as the only kinetic process for bringing out the morphology change and assumed uniform growth rate along the surface, this paper studies the coupling between the deposition process and surface diffusion, to offer another possible mechanism for the asymmetric effect of stress. A nonlinear kinetic law, in which the activation energy of growth process is modified by local stress, is adopted. Linear stability analysis shows that if the growth rate is enhanced by tensile stress while being slowed by compressive stress, the surface instability, for a growing film under tension, could either be fully suppressed for perturbations of any wavelength, or occurs only when the wavelength is within an intermediate range; if the film is under compressive stress, the instability behaviour is similar to that obtained from considering surface diffusion alone, but with different amplitude on growth rate. Two characteristic lengths, one characterizing the competition between surface energy increase and strain energy reduction and the other representing the competition between surface diffusion and growth process, are identified. The thin film instability behaviour is largely determined by the ratio of these two lengths.