Abstract
We examine the applicability of the continuum model to describe the surface morphology of a heterogrowth system: compositionally-graded, relaxed GeSi films on (001) Si substrates. Surface roughness versus lateral dimension was analyzed for samples that 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 of nonuniversal amplitudes indicates the breaking of up-down symmetry, suggesting the presence of nonlinear terms in the microscopic model. We argue that the leading nonlinear term has the form of λ 1 (∇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 equation, consisting of the two linear terms plus λ 1 (∇h) 2 , driven by Gaussian noise. We also discuss the negative coefficient in the Laplacian term as an instability mechanism responsible for large-scale film morphology on the final surface.