2.1 Existing Topography Simulators

*String/segment-based* algorithms represent the surface as a list of
line segments in two dimensions and as list of polygonal/triangular segments in
three dimensions. Two-dimensional implementations can be found
in [81]
and [44].
Their advantages are a high level of accuracy in representing and moving the
surface as well as an implicit polygonal data format which makes the resulting
geometries easy to be meshed and to be used as input for consequent grid-based
programs. Nevertheless, they need insertion and deletion of segments at corners
and edges and require careful concepts in order to avoid formation of
non-physical loops and self-intersections of the evolving surface. For these
reasons only two three-dimensional implementations of this method can be found,
namely, one by Edward Scheckler [65][80] and one by Eberhard
Bär [6]. Another string-based approach, EVOLVE, has been applied
to many two-dimensional simulations with close relation to equipment scale
considerations and in excellent agreement with experimental
data [78]. For its three-dimensional expansion [34] the
physical modeling parts of EVOLVE were combined with the facet motion algorithm
proposed by Scheckler [64].

Another group of topography programs can be summarized under the term
*Monte Carlo* methods. The geometry representations of these programs
bases primarily on orthogonal grids. Similar to Monte Carlo simulations in
other fields their application focuses on the fundamental physical and chemical
particle-particle and particle-surface interactions on atomistic level and
therefore mainly addresses single process simulation.
The method comprises works by Pelka [52] and very comprehensive works
by Smy, Brett, and Dew [72]. Their approach combines results from the
three-dimensional reactor scale Monte Carlo particle transport simulator
SIMSPUD with the feature scale simulator SIMBAD, thus resulting in interpolated
three-dimensional deposition profiles [69]. This approach is very
closely related to the manufacturing process since it incorporates experimental
data such as target erosion profiles and deals with the evolution of the grain
structure in the deposited films. Monte Carlo models combining particle
transport simulation and surface reaction kinetics for plasma etching processes
are also well established [7] and similarly in [26]
which gives a very complete comparison between two- and three-dimensional
simulations.

Ever since its introduction to modeling of semiconductor
processes [1], the *level set* technique has attracted much
interest for tracking the motion of surfaces.
A very complete compilation of different models for semiconductor topography
simulation with the level set technique is given in [68]. The
importance of this new method is highlighted by the numerous similar
implementations which are emerging,
e.g., [18]
and [53].
Interestingly enough the group at the Center of Integrated Systems at
Stanford University has dropped its segment-based development for
SPEEDIE [4] and now focuses on level set methods [27].

Additionally, several implementations for topography simulators can be found in
the area of *cellular* methods, such as the early implementation of the
cell-removal algorithm [10], and MASTER [39].
From the point of view of the used geometry representation, the approach
presented in this thesis also belongs to this group of cellular simulators. Its
so called structuring element algorithm was first published in [75]. A
very similar pixel-based two-dimensional algorithm followed
in [79].
For the sake of completeness a *shock-tracking*
algorithm [20] with broad applications in simulation of
sputtering processes [22] has to be mentioned.

When talking about success of the different approaches, a look at commercial
packages and the algorithms they use for
topography simulation is helpful.
Avant!^{1}
most recently has released TAURUS, a multi-dimensional process
and device simulation package completely based on level set techniques. Despite
the enthusiasm about level set techniques at academic level, this is still the
only important commercial implementation.
Silvaco^{2}
most recently published a new approach, where mesh generation and topography
simulation is directly coupled [36]. The main goal of the newly
developed technique is to avoid the procedure to extract the zero level for the
level set function, which is not a trivial task for three-dimensional
structures. Furthermore the new technique is intended to circumvent the memory
and CPU time restrictions due to the large number of grid points necessary for
the level set methods.

ISE AG^{3}
relies on PROSIT for its three-dimensional geometry generation. This is a solid
modeling tool for emulating etching and deposition processes, which uses
different models resembling to ``brushes'' used in image processing. Trough a
research project of the European Community ISE closely worked together with
Sigma-C^{4}a German TCAD vendor who provides a complete topography simulation package with
the deposition algorithms from [6] and the etching method
from [39] as well as modules for lithography simulation.

This overview and the many kinds of different approaches it presents underlines that topography simulation can be tackled in many different ways. Each of the methods has specific advantages and drawbacks. People involved in topography simulation should always carefully check different approaches available for best suitability to their needs.

Among all these algorithms cellular methods are renowned for their extraordinary robustness. Further advantages, especially when talking about cellular algorithms for tracking surface movement, are that they implicitly avoid the formation of non-physical loops as observed in segment-based algorithms [24][65] and therefore save efforts of implementing complicated self-intersection detection and delooping methodologies. Thus their coding can be kept very clear, foreseeable, and self-explaining. Finally, when considering only the evolution of the surface, they require no special treatment for emerging voids or sections of material being separated from the bulk, since they are volume-based and need no adding or deleting of segments.

For these reasons a cellular algorithm was the preferred method for this thesis about modeling of etching and deposition processes. I do not state that our cellular algorithm is the only method of choice for any kind of topography simulation. Yet, it was selected for its robustness and, not to forget, for its availability for a quick start for feature scale modeling for etching and deposition processes in semiconductor manufacturing.

- ...
Avant!
^{1} - See
`http://www.avanticorp.com/`. - ...
Silvaco
^{2} - See
`http://www.silvaco.com/`. - ...ISE AG
^{3} - See
`http://www.ise.ch/`. - ...
Sigma-C
^{4} - See
`http://www.sigma-c.de/`.

W. Pyka: Feature Scale Modeling for Etching and Deposition Processes in Semiconductor Manufacturing