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 surface atoms and the incident particles. The stationary solutions of the deterministic limit of the equation and their stability are analyzed. The growth of the surface roughness and the correlation length of the moundlike surface structure arising from the stochastic growth equation is investigated.