The simulation of topographical manufacturing steps in semiconductor
processing, such as deposition and etching, is still a demanding task for
today's computers. In addition to the surface evolution, the reaction kinetics on the
surface have to be calculated for each time step. While fast
techniques for surface propagation have already been developed and
successfully applied to topography simulations, as, for example, the
sparse field level set method, the efficient determination of the
surface velocity, arising from the local etching or deposition rates,
is still a problem. Although ballistic transport of particles can be
assumed for usual problems, physical models often require the
consideration of coverages, flux-dependent sticking probabilities,
specular reemission, energy- and direction-dependent sputter/etching
yields, etc. Common methods use direct integration to determine
particle fluxes on the surface. However, these methods normally use
simplified models of surface physics, as, for example, the radiosity
method, and scale unfavorably with the size of the simulation domain.
For these reasons, we use the Monte Carlo method in combination with
fast ray-tracing algorithms to override these difficulties. The local
surface velocities are determined by sampling the trajectories and
their interactions with the surface of millions of individual particles.
Smart ray-tracing techniques, such as spatial subdivision and clustering,
are used to efficiently calculate the intersections of particle rays
with the surface. The result of all these techniques is an algorithm
which scales like O(N*log(N)) with surface discretization and
therefore allows large three-dimensional topography simulations.
Furthermore, due to the independence of individual particle
trajectories in the ballistic transport regime, the Monte Carlo flux
calculation can be easily distributed on multi-CPU/core systems. Our
approach has already been successfully applied to simulations of
reactive ion etching and deposition processes.
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