In the microchip manufacturing industry, it is common to need to cut
trenches into a silicon wafer. These trenches have widths on the order of
tens of microns and aspect rations as high as 10 to 1. To cut fine
channels with high aspect ratios, a directed etching process is needed. A
common tool for directed etching of semiconductor wafers is a low-density
plasma discharge. The positively charged ions of the discharge are
accelerated into the surface of the silicon waver via a potential bias.
The ions provide a directed energy at the surface of the wafer, which is
responsible for the generating an anisotropy etching process. These
discharges often have a background gas pressures on the order of 10^(-6)
ATM. A typical chamber in which etching plasma is generated is around
20cm in diameter and from 1 to 10cm in height. At a pressure of 10^(-6)
ATM, the average distance a gas particle will travel before colliding with
another particle is around 5cm. This means that particles inside the
discharge chamber are more likely to collide with the walls of the chamber
than with each other. In particular, the ion distribution function
strongly deviates from a Maxwellian distribution. This implies that a
fluid model is inappropriate for describing the behavior of the ions.
The model that describes the right underlying physics is the Boltzmann
equation. This talk will primarily focus on an efficient numerical
approach for generating solutions to the Boltzmann equation. The model
employs moving phase space meshes to track particle transport over long
distances. The model is applied to the problem of changed particle
transport in low-density etching tools and is compared to the results of a
fluid description.
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