A continuum model of kinetic roughening and coarsening in thin films

We present a phenomenological continuum model of film growth based on a ser ies expansion of the deposition flux in powers of the profile gradient, con sideration of the energetics of the film-substrate interface and the enforc ement of Onsager's reciprocity relations. The interfacial term, which opera tes at very small thicknesses, is nonconservative and breaks the +/-h symme try of the remaining terms in the kinetic equation. By virtue of this term, very thin hat films are predicted to be stable within an appropriate range of parameters, and to loose stability and become rough at a well-defined c ritical thickness. This instability effectively provides an island nucleati on mechanism. For thick films, the rate processes envisioned in the model f avor a characteristic slope for the film profile, a feature which is in kee ping with observation for a number of systems including YBCO films. The enf orcement of reciprocity ensures the existance of a kinetic potential and en ables the use of direct methods of the calculus of variations: Within this framework, we provide an explicit construction for the coarsening of the fi lm profile based on a sharp interface approximation. The construction predi cts characteristic exponents for the evolution of grain size and film rough ness which are in close agreement with the observational evidence for YBCO. The predictions of the construction are also born out by numerical tests. (C) 1999 Elsevier Science Ltd. All rights reserved.