The growth of topography during sputtering of amorphous solids

Theories of topographic surface development during ion bombardment fall broadly into two categories, one based upon erosion of intersecting planes [1] and the other on a point by point erosion basis [2–4]. A recent paper by Barber et al [5] has shown how, in semiquantitative fashion, an earlier theory by Frank [6] on chemical dissolution or growth of crystals, can be developed to encompass the ion sputtering case. This theory itself is based upon the kinematic wave equation outlined by Lighthill and Whitham [7, 8] and applies to problems of river flooding [7] and traffic flow [8]. In the present communication, the earlier topographic development theories are shown to fit precisely and analytically into the Frank development of the kinematic wave treatment and it is also shown how the occurrence of sharp angled cones formed on surfaces can be analytically and unequivocally predicted.