Numerical Integrator for Continuum Equations of Surface Growth and Erosion


Numerical Integrator for Continuum Equations of Surface Growth and Erosion

Keller, A.; Facsko, S.; Cuerno, R.

Growth of thin films by physical vapour deposition and erosion of solid surfaces by ion beam sputtering have high relevance in the fields of micro- and nanotechnology. Therefore the theoretical modelling of the surface morphology and its evolution during growth and erosion has received considerable attention. Compared to atomistic models, continuum equations are able to cover a much larger spatial and temporal scale accessing the macroscopic scales at which nontrivial features of the morphological dynamics occur. This is especially relevant for surface erosion which can induce a linear instability of the surface, resulting in the formation of periodic nanoscale patterns.
In this chapter, the software package “Ripples and Dots” is presented which is designed for the numerical integration of continuum equations modelling the surface evolution during ion beam erosion in (2+1) dimensions. These equations are based on the Bradley-Harper (BH) model and often feature in addition to the linear instability also nonlinear and noise terms, e.g. the prominent Kuramoto-Sivashinsky (KS) equation. However, due to the similarity with continuum equations for interface growth the software package can be used as well for studying continuum equations describing thin film growth, like the well known Kadar-Parisi-Zhang (KPZ) equation, the Edwards-Wilkinson (EW) equation, and the linear molecular beam epitaxy (MBE) equation.
Numerical data obtained by integrating various continuum equations for surface erosion is presented and compared to analytical predictions and experimental observations. It is demonstrated that the evolution of the surface morphology observed in the numerical integrations is in good qualitative agreement with experimental results both for normal and oblique ion incidence. In addition, also the special cases of erosion at oblique ion incidence with simultaneous sample rotation and erosion with multiple ion beams are presented.

  • Book chapter
    Sarhan M. Musa: Computational Nanotechnology: Modeling and Applications with MATLAB, Boca Raton: CRC Press, 2011, 978-1439841761, 189-215

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Publ.-Id: 16669