Evolution of grating profiles under ion-beam erosion

The faceting phenomenon of ion-beam erosion is used to determine erosion profiles of grating relief patterns on surfaces. The orientation of the planar features formed on an eroding mask are defined in terms of the erosion geometry angles ø and gamma the angle of maximum mask erosion rate over the profile. The geometry required to produce a single facet inclined at any prescribed angle is determined. Expressions are given for the facets generated in the substrate under erosion transverse to the grating stripes, taking into account shadowing effects. The results are illustrated by constructing profiles produced in GaAs by erosion of relief patterns in photoresist and examining the influence of the physical parameters of the mask, divergence of the ion beam, and selection of a different substrate. Profiles observed experimentally confirm the analysis but reveal striking modifications caused by redeposition. These modifications, however, do not involve significant buildup of sputtered material. In contrast to the transverse geometry, significant buildup of redeposited material is observed under erosion parallel to the grating lines. It is shown that buildup does not occur on surfaces that undergo erosion and redeposition simultaneously. Finally, it is shown that even uniformly eroding materials should exhibit facet formation and that the analysis is valid for all materials, regardless of the dependence of erosion rate on angle of incidence.