Flux considerations in the coupling of Monte Carlo plasma sheath simulations with feature evolution models

The evolution of two features, a 2-d trench and a circular via exposed to a 3-v ion flux is calculated. The surface flux is calculated using the particle distribution function, obtained from a Monte Carlo sheath simulation. While Monte Carlo sheath simulations are 1-d/2-v (axisymmetric), shadowing on a substrate surface due to topography breaks the axisymmetry and necessitates a 2-d/3-v surface flux calculation. The authors show a methodology for the flux calculation in long trenches and circular vias which adds very little to computational expense over that incurred for a 2-d/2-v flux calculation. Comparison between the trench and the via shows that, as expected, the geometry of a via blocks out more ion trajectories than that of a trench leading to a smaller etch rate in a via. If the flux is calculated in 2-d/2-v phase space, the resulting feature shape is shown to be an artifact of the calculation method. It is also shown that the angular distribution of the particle as well as energy fluxes and the resulting shape of the feature are largely insensitive to the electric field profile assumed for a given sheath voltage