  Theoretical continuum models that describe the formation of patterns on
surfaces of targets undergoing ion-beam sputtering, are based on Sigmund's
formula, which describes the spatial distribution of the energy deposited by
the ion. For small angles of incidence and amorphous or polycrystalline
materials, this description seems to be suitable, and leads to the classic BH
morphological theory [R.M. Bradley and J.M.E. Harper, J. Vac. Sci. Technol. A
6, 2390 (1988)]. Here we study the sputtering of Cu crystals by means of
numerical simulations under the binary-collision approximation. We observe
significant deviations from Sigmund's energy distribution. In particular, the
distribution that best fits our simulations has a minimum near the position
where the ion penetrates the surface, and the decay of energy deposition with
distance to ion trajectory is exponential rather than Gaussian. We provide a
modified continuum theory which takes these effects into account and explores
the implications of the modified energy distribution for the surface
morphology. In marked contrast with BH's theory, the dependence of the
sputtering yield with the angle of incidence is non-monotonous, with a maximum
for non-grazing incidence angles.
