Model for ion-initiated trench etching

We model the plasma etching of trenches by Langmuir kinetics for neutral molecules and bombarding ions. The parallel combination of an isotropic etch rate for the neutrals and an anisotropic etch rate for the ions gives an effective etch rate. The ion etch rate is proportional to the normal surface component of the ion energy flux. An approximate analytical expression for the composite etch rate offers a new approach to the computation of etch profiles for these mixed systems. Etch profiles are displayed for three cases: the nearly ion flux-limited regime, an intermediate case, and the nearly neutral-flux limited regime for the trench bottom. The numerical calculation of the etch profiles follows from the integration of three characteristic strip equations which are nonlinear first-order ordinary differential equations (ODE's)