Chemical ordering during surface growth

We study the effects of phase separation on the growth of thin solid films by molecular beam epitaxy. We propose a continuum theory that takes into account the fluctuations of the free surface and the phase separation and explain how bulk lamellar patterns develop from a competition between the surface phase separation and the constant burial of surface domains by the incoming beam. The dependence of the wavelength on the deposition rate is in excellent agreement with previous Monte Carlo results. We demonstrated that the free surface is modulated, with a period that is half the bulk modulation wavelength.