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The vertical propagation method is the simplest imaging model. It is
derived from the thinfilm theory of Paul Berning [142] and was
introduced into lithography simulation by Frederick Dill [141].
Early versions of the popular lithography simulators PROLITH [107] and
SAMPLE [109] were based on it.
The latent bulk image is obtained by the separation approach

(5.24) 
whereby I_{i}(x, y) denotes the aerial image intensity and
I_{r}(z;t_{k}) is the
standing wave intensity inside the resist at a certain timestep t_{k}.
For the computation of
I_{r}(z;t_{k}) the resist is divided into thin layers over
which the intensity and thus also the refractive index n(z;t_{k}) is
approximately constant. Within one layer a technique similar to that described
in Appendix C is employed to compute the field intensity.
However, the method implicitly assumes that the field propagates only in
vertical direction. For very low numerical apertures and reasonably
thin resists this assumption is valid. It starts to fail when the aerial image
changes or ``defocuses'' as it penetrates into the resist or when the incident
light is appreciably oblique.
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Up: 5.2 Field Calculation over
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Heinrich Kirchauer, Institute for Microelectronics, TU Vienna
19980417