Reverse epitaxy of Ge: ordered and facetted surface patterns

Normal incidence ion irradiation at elevated temperatures, when amorphization is prevented, induces novel nanoscale patterns of crystalline structures on elemental semiconductors by a reverse epitaxial growth mechanism: on Ge surfaces irradiation at temperatures above the recrystallization temperature of 250{\deg}C leads to self-organized patterns of inverse pyramids. Checkerboard patterns with fourfold symmetry evolve on the Ge (100) surface, whereas on the Ge (111) surface, isotropic patterns with a sixfold symmetry emerge. After high fluence irradiations these patterns exhibit well developed facets. A deterministic nonlinear continuum equation accounting for the effective surface currents due to an Ehrlich-Schwoebel barrier for diffusing vacancies reproduces remarkably well our experimental observations.