  We propose a unified moving boundary problem for surface growth by
electrochemical and chemical vapor deposition, which is derived from
constitutive equations into which stochastic forces are incorporated. We
compute the coefficients in the interface equation of motion as functions of
phenomenological parameters. The equation features the Kardar-Parisi-Zhang
(KPZ) non-linearity and instabilities which, depending on surface kinetics, can
hinder the asymptotic KPZ scaling. Our results account for the universality and
the experimental scarcity of KPZ scaling in the growth processes considered.
