  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.
