Predictive modelling of gas assisted electron and ion beam induced etching and deposition

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While the field of experimental micrometre scale EBIED / IBIED (“electron beam chemistry” or “ion beam chemistry”) has been growing in recent years, the 3D simulation of these systems at real scales has been non-existent. This type of simulation is important for it is only in three dimensions that interesting asymmetric and patterning phenomena can be tracked. There are a couple of difficulties in these types of simulations. One is solving the diffusion of adsorbate concentrations in the system. Accurate simulation of diffusion on general 2D surfaces is non-trivial, (even on 1D curves), and can require unnatural re-parametrization of the surface (re-meshing). Another difficulty is that simulations have generally been atomistic and limited in scale. The key to providing large scale 3D simulations comes from applying new, mathematically robust, computer-science methods based on implicit surfaces to this field. In this thesis, the issues above are addressed in a couple of different ways. In one case, diffusion over a complex surface was reduced to piecewise axially symmetric equations. Later, implicit methods for solving adsorbate kinetics continuum equations and evolving the surface are implemented, the closest point method and the level set method respectively. The development of the tools themselves is a non-trivial exercise as there are few software libraries for the level set method and none for the closest point method. These tools were then used independently to simulate etching and diffusion, as well as in concert to demonstrate the ability to simulate 3D deposition in the mass transport limited and reaction rate limited regimes.
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