We address the problem of MBE growth in one horizontal and one vertical direction in the presence of Schwoebel barriers. The time-independent growth equation introduced previously is shown to be identical to that for a classical particle in a potential well. We solve this equation using periodic boundary conditions and find time-independent solutions consisting of a periodic array of mounds. We derive the "dispersion relation", i.e. the amplitude as a function of wavelength for these mounds. The equation of motion is derivable from a free energy indicating that there is a most stable ground state, which is independent of the initial conditions. The mounds are marginally unstable and there is a minimum wavelength below which no mounds exist. The wavelength of the mounds coarsens slowly in time according to Λ ∼ t α , with α ≈ 1/4.
No takes yet. Share an insight, caveat, or question.
Hunt et al. (1994) studied this question.