3. Solid Modeling and Basic Topography Models

The limits of the available possibilities were exceeded quickly. Joint
projects with industrial partners needed a representation of the geometry
underlying to the deposition in order to be able to compare the
simulation results with the *scanning electron microscopy* (SEM)
cross-sections of the experimentally obtained profiles. It was necessary to
create a series of vias with different diameters and slanted sidewalls. These
slanted sidewalls were especially challenging. I decided for an approach which
allowed generation of an initial simulation domain with an optional
rectangular, square, circular, or elliptic via, and added the possibility for
repeated application of layers patterned with the same geometric
primitives. This allowed the step-wise generation of the slanted via profiles
employing many layers carrying circular patterns with increasing diameter. By
these means, the inherent drawback of the cellular structure for a restricted
and only step-wise resolution of non-orthogonal planes was utilized to define
the slanted sidewalls at the highest accuracy within reach for the cellular
representation. The structures generated in this way (cf. Fig. 6.16)
represent the beginning of a solid modeling program linked to the etching and
deposition simulation by the same data representation and file format. The
program was continuously expanded now allowing for patterns achievable with
combinations of the supplied geometric primitives and including procedures for
cuts and cross-sections in the cellular structure, fast stripping of materials
and simple emulation of CMP as well as of oxidation steps.

As mentioned previously, CMP and oxidation are process steps involving very complex chemical and physical phenomena. The solid modeling program was always intended to work in its strict geometric sense using morphological models to obtain the desired structures instead of exact modeling of the involved physical correlations. This allows fast generation of the desired structures, when only the topography is of significant importance. Moreover the solid modeling tool was designed to work in a non-interactive, step-like, automatic way. Therefore the geometrically based CMP and oxidation steps represent simple plug-ins for completing the tools being at disposal for the overall process recipe.

The algorithms for the geometry and solid modeling operations are straight forward and need no detailed derivation. It is clear that there are some important aspects to be taken care of, but they are mostly related to implementation and programming issues. One example is the need to merge two consequent layers of the same material. This is necessary for a consistent material representation required in order to prevent non-physical separation of a layer repeatedly grown from the same material.

Beyond the geometry operations, explained in Section 3.1 by an illustrative mask generation example, there are some cutting procedures included as auxiliary tools within the solid modeling program. They are used to extract cross-sections of three-dimensional cellular structures, such as in Fig. 6.16 and for partially cutting away material for more clearness in the visualizations, as done, e.g., in Fig. 2.6.

The second part of this chapter will be devoted to basic modules for
*topography simulations* (Section 3.2). For the simulation of
*isotropic* (Section 3.2.1), *anisotropic* (Section 3.2.2), and
*unidirectional* (Section 3.2.3) etching and deposition steps, the modules
rely on the morphological operations based on the structuring element algorithm
introduced in the previous chapter.

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