A continuum theory for the deposition and growth of solid films is presented. The theory is developed in a coordinate-independent manner and so incorporates the fully nonlinear physics. The evolution of the film is modeled in three steps. First, the adsorption of atoms in the incident beam is modeled as a ballistic process. Second, the random motion of the adatoms is treated as a diffusive process. Finally, sticking of adatoms to the film occurs as a Poisson process. The resulting system of differential equations is examined in several parameter limits. The diffusively dominated limit appears similar to zone 1 of the structure-zone model. Generically the surface slope develops discontinuities; these ‘‘kinks’’ play the role of grain boundaries. In the ballistically dominated case these kinks may be advected along the surface giving rise to columnarlike microstructures, as is observed in zone 2.
© 1989 The American Physical Society
A. J. Bernoff and S. Lichter, A Continuum Model of Thin Film Deposition," Phys. Rev. B 39 (1989) 10560-10569. doi: 10.1103/PhysRevB.39.10560