Surfactant-mediated growth of nonequilibrium interfaces.

A number of recent experiments have showed that surfactants can modify the growth mode of an epitaxial film, suppressing islanding and promoting layer-by-layer growth. Here I introduce a set of coupled equations to describe the nonequilibrium roughening of an interface covered with a thin surfactant layer. The surfactant may drive the system into a novel phase, in which the surface roughness is negative, corresponding to a flat surface. PACS numbers: 68.55 -a, 68.35 Fx, 64.60 Ht Typeset using REVTEX 1 There is much theoretical interest in the statistical properties of nonequilibrium surfaces. The growing interfaces naturally evolve into self-affine structures; the surface morphology and the dynamics of roughening exhibit simple scaling behavior despite the complicated nature of the growth process [1]. In particular, much attention has focused on different models to describe thin-film growth by molecular-beam epitaxy (MBE) [2–6]. Under ideal MBE conditions the primary relaxation mechanism is surface diffusion, which conserves the mass of the film. Experimentally both lattice strain and surface free energy determine whether the film undergoes layer-by-layer growth, islanding, or layer-by-layer growth followed by islanding. In experiments involving growth of Ge on Si(100) surface layer-bylayer growth is limited to 3-4 monolayers (ML) due to the lattice mismatch between Si and Ge and is followed by formation of unstrained Ge islands. It was shown recently that islanding in the Ge/Si system can be suppressed effectively by use of a surfactant monolayer, changing the growth mode from island growth to layer-by-layer growth [7]. Suitable surfactants such as As and Sb strongly reduce the surface free energy of both Si and Ge surfaces and segregate at the surface during growth. A number of subsequent experiments showed that surfactants can change the surface morphology in a wide variety of systems: Sb altered the growth behavior of Ag on Ag(111) [8], antimony was found to change the structure of islands in Ge/Si growth [9] and Te was used as surfactant to sustain layer-by-layer growth of InAs on GaAs(001) [10]. Microscopically, arsenic placed on the surface of Si or Ge lowers the surface tension by eliminating the dangling bond states. But for ordinary surfactants reduced surface tension enhances roughness. The reduced adatom diffusion might change the growth mode, but so far most continuum models with or without surface diffusion predict rough interfaces [2–6,11]. While the microscopic mechanism of As and Ge/Si interaction is much investigated [12], understanding in the framework of continuum growth models is still lacking. In this paper I study the generic problem of nonequilibrium roughening of an interface covered by a thin surfactant layer (see Fig 1). Building on experimental results and general symmetry principles, a set of nonequilibrium equations are proposed to describe the growth