A simple discrete stochastic model for laser-induced jet-chemical etching

Recently developed processes based on laser-induced liquid jet-chemical etching provide efficient methods for high resolution microstructuring of metals. Like in other abrasive techniques (water-jet cutting, laser cutting, ion sputtering etc.) a spontaneous formation of ripples in the surface morphology has been observed depending upon the choice of system parameters. In this paper we present a discrete stochastic model describing the joint action of removal of material by chemical etching and thermally activated diffusion initiated by a moving laser leading to structure formation of a surface. Depending on scan speed and laser power different surface morphologies are observed ranging from rough surface structures to the formation of ripples. The continuum equation associated to the discrete model is shown to be a modified Kuramoto-Sivashinsky equation in a frame comoving with the laser beam. Fourier and wavelet techniques as well as large deviation spectra are used for a characterization of the surfaces.