Thermodynamic model for the dewetting instability in ultrathin films

Abstract

The spontaneous pattern formation via the classical spinodal dewetting instability in ultrathin films is a nonlinear process. However, the physical manifestation of the instability in terms of characteristic length and time scales can be described by a linearized form of the initial conditions of the film’s dynamics. Alternately, the thermodynamic (TH) approach based on equating the rate of free energy decrease to the rate of frictional loss via viscous dissipation [de Gennes, C. R. Acad. Paris 298, 111 (1984)] can give similar information. Here we have evaluated dewetting in the presence of film-thickness- (h) dependent thermocapillary forces. Such a situation can be found during pulsed laser melting of ultrathin metal films where nanoscale effects lead to a local h-dependent temperature. The TH approach provides an analytical description of this thermocapillary dewetting. The results of this approach agree with those from linear theory and experimental observations provided the minimum dissipation is equated to the rate of free energy decrease. The flow boundary condition that produces this minimum dissipation is when the film-substrate tangential stress is zero. The physical implication of this finding is that the spontaneous dewetting instability follows the path of minimum rate of energy loss.