  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 $\mu$m, 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
non-universal 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 $\lambda _1(\nabla h)^2$, 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 $\lambda
_1(\nabla h)^2$, driven by a 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.
