Patterning by ion-beam sputtering

We review and study pattern formations arising in a sputter-eroded surface. The patterns include nanodots, holes, ripples, and so on. Our study is focused on the theoretical aspect. Several kinetic equations are reviewed first, and then a linearly superposed Kuramoto-Sivashinsky (KS) equation is derived explicitly. The latter equation was introduced for the purpose of illustrating dual ion-beam sputtering (DIBS), where two ion beams are simultaneously projected onto the surface at a grazing angle and cross perpendicular in azimuth. The numerical values of the coefficients of the superposed KS equation are obtained by using the transport of ions in matter (TRIM) algorithm. This shows no linear instability for growing patterns as observed in a recent DIBS experiment. Nanopatterning through the DIBS process is thus beyond the scope of the kinetics under the standard KS equation.