Dynamics of Rough Interfaces in Chemical Vapor Deposition: Experiments and a Model for Silica Films

Abstract

We study the surface dynamics of silica films grown by low pressure chemical vapor deposition. Atomic force microscopy measurements show that the surface reaches a scale invariant stationary state compatible with the Kardar-Parisi-Zhang (KPZ) equation in three dimensions. At intermediate times the surface undergoes an unstable transient due to shadowing effects. By varying growth conditions and using spectroscopic techniques, we determine the physical origin of KPZ scaling to be a low value of the surface sticking probability, related to the surface concentration of reactive groups. We propose a stochastic equation that describes the qualitative behavior of our experimental system.

Relationship between scaling behavior and porosity of plasma-depositedTiO2thin films

“…16 Such an approach has been successfully applied for thin films grown by evaporation, 18 sputtering, 19 thermal CVD, 35 or PECVD. 20,21,24 Here, besides applying this methodology, we will try to correlate the obtained information with the porosity and microstructure of the films.…”

“…16,35 This is defined for two-dimensional images as the radial average of the conjugate product of the Fourier transform of the surface and it provides information about the dependence with the scale of measurement of the surface roughness and the self-affine scaling behavior of the films surface.…”

“…23 Of these, probably the best known are the random deposition model ͑i.e., ␤ = 0.5͒, 23,35 the so called KPZ model ͑i.e., ␤ ϳ 0.22͒ 23,35,36 or others controlled by diffusion like in MBE deposition ͑i.e., ␤ ϳ 0.2͒. 37 The experimental ␤ values obtained in our case are relatively close to theoretical values of 0.5 and 0.25/0.20.…”

Controlling surface morphologies by time-delayed feedback

“…For chemical vapor deposition of silica films, there is some experimental evidence 12 that the lateral growth velocity is related to the temperature, via a temperature-dependent sticking probability. In other words, -and hence effective growth exponents-can be controlled via the temperature.…”

“…Even if such control can only be sustained in a finite window of time, its experimental potential is undiminished since the growth process can simply be terminated when the desired characteristics have been achieved, thanks to today's precise in situ characterization capabilities. Moreover, paradigmatic growth models, such as the KardarParisi-Zhang ͑KPZ͒ equation, 11 find applications in many diverse areas of science, e.g., thin film growth, [12][13][14][15] fluctuating hydrodynamics, 16 driven diffusive systems, [17][18][19] tumor growth in biophysics, [20][21][22] propagating fire fronts, 23 and econophysics. 24 Therefore, broad implications can be expected if methods from control theory can be successfully implemented in this vast context.…”