Nonmonotonic roughness evolution in unstable growth

Abstract

The roughness of vapor-deposited thin films can display a nonmonotonic dependence on film thickness, if the smoothening of the small-scale features of the substrate dominates over growth-induced roughening in the early stage of evolution. We present a detailed analysis of this phenomenon in the framework of the continuum theory of unstable homoepitaxy. Using the spherical approximation of phase ordering kinetics, the effect of nonlinearities and noise can be treated explicitly. The substrate roughness is characterized by the dimensionless parameter Q = W0/(k0a 2 ), where W0 denotes the roughness amplitude, k0 is the small scale cutoff wavenumber of the roughness spectrum, and a is the lattice constant. Depending on Q, the diffusion length lD and the Ehrlich-Schwoebel length lES, five regimes are identified in which the position of the roughness minimum is determined by different physical mechanisms. The analytic estimates are compared by numerical simulations of the full nonlinear evolution equation.

Linear growth of thin films under the influence of stress

“…The initial decrease of the roughness is governed by conservative noise roughening. 16,17 The behavior is also similar for increasing correlation lengths .…”

Smoothing and coherent structure formation in organic-organic heterostructure growth

“…4(a), IV) the heterostructure roughens fast and PFP forms large needles (ξ ≈ 370 nm), which is also typical for PFP growth on substrates like SiO 2 [17]. Note, that an increase of the lateral length scale from the first to the second layer, which forms the heterostructure, is a prerequisite for observing a nonmonotonic roughness evolution also within the theoretical framework of [21,22].…”

“…For growth of atomic systems on rough substrates (e.g. InAs buffer layers) it was found using continuum growth theory and kinetic Monte Carlo simulations that under certain conditions the competing mechanisms of smoothing and roughening can lead to a minimum in the roughness evolution even though both materials exhibit step edge-barrier-dominated growth [20][21][22]. In this case, a minimum can occur because of the dependence of the roughening and smoothing rates on the spatial frequency f of the surface modulation.…”

“…We conclude that the mechanism proposed in refs. [20][21][22], which relies on frequency-dependent smoothing and roughening rates, is not applicable in our system.…”

Studying nonlinear effects on the early stage of phase ordering using a decomposition method

“…[9], the study of the early stage of phase ordering has gained renewed interest in recent years [10]- [15]. Another direction that the decomposition method can be useful is in the study of the scaling behavior at early stages of phase ordering [16], a subject of current interest for thin films roughness studies [17].…”