Continuum model description of thin film growth morphology

We examine the applicability of the continuum model to describe the surface morphology of a hetero-growth system: compositionally-graded, relaxed GeSi films on (001) Si substrates. Surface roughness versus lateral dimension was analyzed for samples what were grown under different conditions. We find that all samples belong to the same growth class, in which the surface roughness scales linearly with lateral size at small scales and appears to saturate at large scales. For length scales ranging from 1 nm to 100 μm, the scaling behavior can be described by a linear continuum model consisting of a surface diffusion term and a Laplacian term. However, in-depth analysis on nonuniversal amplitudes indicates the breaking of up-down symmetry, suggesting the presence of non-linear terms in the microscopic model. We argue that the leading non-linear term has the form of λ1(∇h) 2, but its effect on scaling exponents will not be evident for length scales less than 1 mm. Therefore, the growth dynamics of this system is described by the Kuramoto-Sivashinsky