The development of a general three-dimensional surface under ion bombardment

A general tree-dimensional theory of the development of surface topography during ion etching is presented together with the computational methods used for its visualization. Use of the techniques is illustrated using the example of an elliptical hummock under erosion using ion sources with both uniform and non-uniform ion-current distributions. The analysis is based on the method of characteristics, as in the theory of non-linear waves, and this has several advantages over existing two-dimensional methods including its suitability for numerical manipulation, its extension into three dimensions, and its ease of use with non-uniform beams. The use of the approach is also advantageous in two dimensions and this is considered separately in an Appendix. Areas of application of the methods include the use of ion etching in surface analysis and the microfabrication and micromachining of surface structures on certain electronic devices. The methods may also find application in explaining the effects of more macroscopic surface ablation methods and may also be applicable to the simulation of crystal growth in three dimensions. (author)