We examine the linear stability of a planar, alloy thin film, growing
by a deposition Aux from the vapor. The stability of the film surface
is influenced by stresses generated by both compositional inhomogeneit
y, via a composition dependent lattice parameter, and lattice mismatch
between the film and substrate. The stress generated by the compositi
onal inhomogeneities, which accompany nonplanar interfacial morphologi
es, can be either stabilizing or destabilizing. Under certain conditio
ns, a growing planar film under tensile misfit-strain can be stable, w
hereas a growing film under the same magnitude of compressive strain c
an be unstable. These compositionally generated stresses can also lead
to traveling or standing surface waves and unstable planar surfaces i
n lattice matched films. All of these instabilities can develop via th
e deposition process itself; the wave number dependence of the instabi
lity is different, however, from that in the pure surface diffusion li
mit. We also compare our results with numerous experimental observatio
ns.