Experiments have shown that phase separation during the growth of soli
d films by molecular beam epitaxy (MBE) is a phenomenon seen in a vari
ety of systems. We study a MBE process where two types of particles ar
e deposited simultaneously, and where the interatomic potential energy
leads to phase separation. From a microscopic point of view, we descr
ibe the system with a solid-on-solid model augmented by an Ising model
to represent the phase separation. Monte Carlo simulations of this mo
del show that for low deposition rates, a lamellar pattern emerges in
the bulk, with a modulation parallel to the growth plane. We show how
the temperature and the deposition rate can be used to tailor the wave
length of the modulation. The effects of the phase separation on the s
urface morphology create a modulation consisting of steps or grooves a
t the interface between surface domains, which can be seen in the heig
ht-height correlation function and in the surface width. The temperatu
re dependence of the surface width at fixed deposition rate is also pr
esented.