74,984 research outputs found
Dynamic scaling form in wavelet-discriminated Edwards-Wilkinson growth equation
No full textWe present an analysis of dynamic scaling of the Edwards-Wilkinson growth model from wavelets' perspective. Scaling function for the surface width is determined using wavelets' formalism, by computing the surface width for each wavelet scale, we show that an exact and simple form of the scaling function is obtained. These predictions are confirmed by computer simulation of a growth model described by the EW equation, and by numerical calculations
Scale decomposition of molecular beam epitaxy
No full textIn this work, a study of epitaxial growth was carried out by means of the wavelets formalism. We showed the existence of a dynamic scaling form in a wavelet discriminated linear molecular beam epitaxy (MBE) equation where diffusion and noise are the dominant effects. We determined simple and exact scaling functions involving the scale of the wavelets when the system size is set to infinity. Exponents were determined for both correlated and uncorrelated noise. The wavelet methodology was applied to a computer model simulating linear epitaxial growth; the results showed very good agreement with analytical formulation. We also considered epitaxial growth with the additional Ehrlich–Schwoebel effect. We characterized the coarsening of mounds formed on the surface during the nonlinear phase using the wavelet power spectrum. The latter has an advantage over other methods, in the sense that one can track the coarsening in both frequency (or scale) space and real space simultaneously. Wavelets analysis also provides a quantitative tool for the characterization of the mounded surfaces through its concise scale discrimination. We showed that the averaged wavelet power spectrum (also called scalegram) over all the positions on the surface profile identified the existence of a dominant scale a*, which increases with time following a power law relation of the form a* ~ tn, where n = 1/3
Scale decomposition of unstable growing fronts
No full textWe present results obtained from the wavelet transform of unstable growing fronts. The linear growth equation is transformed using the Hermitian wavelets obtained from recursive shifts and changes in the Gaussian filters. We explore the evolution of the instability at different scales, and at different locations (in the direct space) in the wavelet domain, using a numerical growth model and the experimental example of chemically etched silicon. Wavelet formalism may have an advantage over Fourier methods in the sense that one can track the instability in the location (direct space) and at different scales simultaneously. It also provides a quantitative tool for the characterization of the growing fronts through its concise scale discrimination
Wavelet characterization of the submicron surface roughness of anisotropically etched silicon
No full textThe roughness of etched Si(1 10) surfaces in tetra-methyl ammonium hydroxide has been characterized using the wavelet transform formalism. Wavelet coefficients corresponding to the experimental surface profiles have been calculated and the roughness exponent has been derived using the scalegram method. Its value has been found to be 0.5
Simulation of silicon etching with KOH
No full textAnisotropic chemical etching of monocrystalline silicon in KOH aqueous solution is investigated. The atomic scale model proposed is based on the influence of the OH group on chemical bonds. Etch rate and activation energies are calculated and extended to the complete etch rate polar diagram and compared to available experimental data. Finally, an analytical description of etch rate ratios is proposed
Unstable etching of Si(110) with potassium hydroxide
No full textWe present experimental data for the morphological evolution of Si(110) etched with potassium hydroxide. The observed results are interpreted using a continuum equation. The results reveal the presence of unstable etching which leads to the formation of a columnar structure on the surface. The early stage of the formation of this columnar structure can be explained by a linear theory. This instability is caused by anisotropic surface tension
Atomic scale simulation of silicon etched in aqueous KOH solution
No full textIn this paper we present the theoretical bases of an atomic scale model and the Monte Carlo implementation. We present results for <hk0> oriented surfaces like etching rates, and more detailed results for low-index surfaces such as <100> and <111>. For these two directions we present results concerning the surface morphology and the time evolution of the roughness
Monte Carlo Simulation of wet etching of silicon: Investigation of (111) surface properties
No full textThe etching rate of the Si<111> surface family is of prime importance for micro-fabrication. However, the experimental values of the corresponding etch rate are often scattered and the etching mechanism of <111> surfaces remains unclear. In this paper the Monte Carlo simulation results obtained from etching of Si(111) small size substrates are presented. Simulations were carried out to simulate the behaviour of the <111> surface in contact with strong base aqueous solutions (R - OH). Simulation shows that when etching a small substrate (200 A X 200 A), the etch depth against time curve shows a constant part and a linear part. The former is related to the magnitude of Monte Carlo time steps while the latter corresponds to the evacuation of one sublayer. However, the substrate size fails to impact the etching mechanism which remains unchanged even for an infinite size. The same remark applies to roughness which exhibits a series of alternative peaks
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