Long-time effects in a simulation model of sputter erosion

A simple (2+1)-dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories. Due to its simple structure, simulations of the model can be performed on time scales where effects beyond the linearized theory become important. Whereas for short times we observe the formation of ripple structures in accordance with the linearized theory, we find a roughening surface for intermediate times. The long-time behavior of the model strongly depends on the surface relaxation mechanism.