A nonlinear stochastic growth equation for the spatiotemporal evolution of
the surface morphology of amorphous thin films in the presence of potential
density variations is derived from the relevant physical symmetries and co
mpared to recent experimental results. Numerical simulations of the growth
equation exhibit a saturation of the surface morphology for large film thic
kness originating from the inclusion of the density inhomogeneities. Furthe
r-more, we argue why moundlike surface structures observed on vapor deposit
ed amorphous films are not the result of the Grinfeld instability.