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5.2 Field Calculation over Planar Topography

Assuming a planar resist the field calculation is considerably simplified.
Various models with different levels of accuracy exist for a planar topography.
The simplest and most basic one is the *vertical propagation model*,
but it incorrectly predicts all lithographic behavior to be completely symmetric
in the focus offset positions. The *scaled defocus approach* overcomes this
drawback as it represents a first-order correction to the vertical propagation
method. The *transfer matrix algorithm* additionally considers the impact
of non-vertical propagation on thin-film interference effects and is thus
the most advanced approach among the analytical models. These three methods
are closely related to the analysis of a stratified medium presented
in Appendix C. Thus all of them neglect scattering effects
due to the lateral inhomogeneity of the resist layer.
The *beam propagation method* overcomes this limitation.
The EM field is modeled by a weakly amplitude-modulated wave traveling
into the resist. Numerical schemes have to be employed to solve the
partial differential equation involved. Although the computational effort is
increased in comparison to the purely analytical models, the performance
is much faster than that of the rigorous EM scattering theory that is
required for a full nonplanar inhomogeneous resist simulation.
In the following four sections
we will briefly sketch each of the methods mentioned.

** Next:** 5.2.1 Vertical Propagation Method
**Up:** 5. Photoresist Exposure/Bleaching Simulation
** Previous:** 5.1.4 Simulation Flow
*Heinrich Kirchauer, Institute for Microelectronics, TU Vienna *

1998-04-17