Morphology change of the silicon surface induced by Ar${}^{+}$ ion beam sputtering

Two-level modeling for nanoscale pattern formation on silicon target by Ar${}^{+}$ ion sputtering is presented. Phase diagram illustrating possible nanosize surface patterns is discussed. Scaling characteristics for the structure wavelength dependence versus incoming ion energy are defined. Growth and roughness exponents in different domains of the phase diagram are obtained.