5.1 Modeling of Resist Development

The resist profile evolving during development is simulated with the cell-based topography algorithm introduced in Section 2.2. The surface advancement is carried out by applying structuring elements at the exposed surface, which successively remove cells of the underlying cellular geometry by switching the material index of the cells from resist (R) to vacuum (0).

Since development corresponds to an isotropic etching process, a sphere is used
as structuring element. In contrast to a common wet etching step, where each
material has a constant etch rate which depends on the selected etchant, the
development rate depends on the grade of polymerization or dissolution of the
*photo-active compound* (PAC) of the resist accumulated during exposure.
Therefore the development rate is inhomogeneous and modeled with spheres of
varying size. Their radius is determined by the local development rate
resulting from lithography simulation multiplied with the time-step (see
Fig. 5.1).

Alternatively to the rate obtained from a precedent exposure simulation the values for the development rate of the single cells were assigned with mathematical expressions. The equations were used for the characterization of typical benchmark examples which directly address specific requirements to be fulfilled for a correct propagation of the surface.

Either way, for resist development after lithography simulation as well as for
the mathematically formulated test cases a sufficiently high number of cells
has to be chosen in order to be able to resolve the strong variations of the
rate originating from standing waves or notching effects during photo-resist
exposure. Such standing wave effects which result from reflective interference
are indicated on the right hand side of Fig. 5.1. We know that the
distance between maxima and minima of the intensity which determines the
development rate is given by /4. For a *deep ultraviolet* (DUV)
illumination wavelength of 248nm and a refractive index of 1.65 for the
photo-resist, this distance is 37nm. For reliable simulations this distance
has to be resolved by at least 10 cells, which leads to a cell density of
300cells/. The lithography examples from Section 5.3 were simulated
with this resolution. The benchmark examples (Section 5.2) have been
scaled to a lower resolution of 200cells/.

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