Evolution of the Trench

In this chapter we examine a number of physical processes that affect the evolution of the shape of a trench. Etching by neutrals alone is considered first, followed by charged particle effects and behavior. This leads on to charging of the trench walls and the effect of the charging on the charged particles.

The calculation of surface processes from first principles is not feasible at present. Atomistic studies of surface behavior have been widely used, employing accurate interatomic potentials [13,12,11]. Recent attempts to calculate correlation energies, with a view to improving methods such as Density Functional Theory (DFT), are described in Refs. [166]–[168]. For now, however, we stick to phenomenological approaches.

Etching by Neutrals

If the distribution of neutrals is isotropic and uniform and neutrals are responsible for the etching, then each section of the surface is etched at the same rate whatever the position or orientation of the section. If the surface is divided into sections that are all horizontal or vertical then each corner moves at 45° to the vertical. Suppose the distribution is isotropic, and that the density of neutrals varies slowly enough in space so that the sections on each side of any corner etch at roughly the same rate. This means the 45°-rule still holds approximately for each corner even though different corners may move at different rates. The best way to see how this works is to consider a few examples.