Epitaxial Growth of Thin Films -- a Statistical Mechanical Model

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A theoretical framework is developed to describe experiments on the structure of epitaxial thin films, particularly niobium on sapphire. We extend the hypothesis of dynamical scaling to apply to the structure of thin films from its conventional application to simple surfaces. We then present a phenomenological continuum theory that provides a good description of the observed scattering and the measured exponents. Finally the results of experiment and theory are compared.