Amorphous thin film growth: Minimal deposition equation

Abstract

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.

Observation and Modeling of Interrupted Pattern Coarsening: Surface Nanostructuring by Ion Erosion

“…This validates the physical relevance of the IC scenario, in particular, in the form that it takes for cases as in [11][12][13][14][15][16]. Specifically, our morphological observations are contrasted with the theoretical approximations given in [12], allowing for a full quantitative description of the experimental dynamics through the continuum model proposed in this reference, to the extent that the pattern behavior can also be accounted for when experimental parameters are changed.…”

“…The former is the celebrated Kuramoto-Sivashinsky (KS) equation [27,28], paradigmatic of spatiotemporal chaos, for which a (disordered) short-range pattern develops with a wavelength that does not coarsen, kinetic roughening occuring at much larger scales [29]. The 1 ¼ 0 case is the ''conserved'' KS equation (CKS), appearing, for dynamics of amorphous thin films [13] and steps on vicinal surfaces [30], for which the linear instability leads to an ordered pattern of paraboloids with uninterrupted coarsening.…”

“…Although in its original formulation IC refers to a pattern that stops growing in ''lateral'' size (') while perpetually increasing in ''vertical'' size (amplitude), more recently other systems have been identified in which an analogous interruption of wavelength and amplitude occur, yielding to kinetic roughening at the largest time and length scales [11,12]. Models with this behavior have been derived for diverse contexts and scales, from amorphous thin film growth [13] to ionbeam nanostructuring [14,15], to patterns on snow fields [16], and belong to a class that remains to date as a theoretical challenge in the identification of the various coarsening scenarios.…”

On the dynamic roughening transition in nanocomposite film growth

“…Another contribution to the increase in roughness may be the strength of the shot noise, which is expected to increase with deposition rate. 21 Figure 2 shows the microstructural evolution of the films 100C0.35Ti-350C0.35Ti and 100C0.55Ti-350C0.35Ti, respectively. During 100 kHz p-dc sputtering, the microstructure shows strong columns but evolves as dense and noncolumnar structure in the onset of 350 kHz p-dc sputtering.…”

Continuum modeling of sputter erosion under normal incidence: Interplay between nonlocality and nonlinearity

“…Assuming that the particle density at the surface of the target material can be basically considered as being constant 18,19 , such a balance equation reads quite generally 20…”