Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface

Growth of thin alumina films on a vicinal NiAl surface

Dramatic changes in the surface morphology have been observed during the oxidation of stepped NiAl(16,14,1) by LEED and STM. The initial sequence of identical (110) terraces is lifted in favor of large, triangular planes, whose mean size is determined by the mismatch-induced stress that accumulates in the thin alumina film. The asymmetry of the original step direction on NiAl(16,14,1) with resp...

Modeling and Control of Epitaxial Thin Film Growth

Thin film deposition is a manufacturing process in which tolerances may approach the size of individual atoms. The final film is highly sensitive to the processing conditions, which can be intentionally manipulated to control film properties. A lattice model of surface evolution during thin film growth captures many important features, including the nucleation and growth of clusters of atoms an...

Operator theory and its applications

Thin film dynamics: theory and applications

This paper is based on a series of four lectures, by the first author, on thin films and moving contact lines. Section one presents an overview of the moving contact line problem and introduces the lubrication approximation. Section two summarizes results for positivity preserving schemes. Section three discusses the problem of films driven by thermal gradients with an opposing gravitational fo...

Amorphous thin film growth: minimal deposition equation

A nonlinear stochastic growth equation is derived from (i) the symmetry principles relevant for the growth of vapor deposited amorphous films, (ii) no excess velocity, and (iii) a low-order expansion in the gradients of the surface profile. A growth instability in the equation is attributed to the deflection of the initially perpendicular incident particles due to attractive forces between the ...