We discuss the interplay between chemical ordering and surface roughen
ing during molecular beam epitaxy. We propose microscopic and mesoscop
ic descriptions of homogeneous growth where two types of atoms are dep
osited, and where the interatomic potential energy leads to phase sepa
ration. For deposition rates below a certain threshold value, lamellar
patterns emerge in the thin film, with the concentration modulation o
riented in the growth plane direction. We find that patterning of the
bulk is possible by varying the temperature and the deposition rate, i
n agreement with experimental results.