INSTABILITIES IN MBE GROWTH

We address the problem of MBE growth in one horizontal and one vertica l direction in the presence of Schwoebel barriers. The time-independen t growth equation introduced previously is shown to be identical to th at for a classical particle in a potential well. We solve this equatio n using periodic boundary conditions and find time-independent solutio ns consisting of a periodic array of mounds. We derive the ''dispersio n relation'', i.e. the amplitude as a function of wavelength for these mounds. The equation of motion is derivable from a free energy indica ting 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 LAMBDA approximately t(alpha), with alpha almost-equal-to 1/4.