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4.2.1 Defocus
The simplest and most basic aberration type is defocus caused by
a wrong vertical position of the image plane. As discussed in
Chapter 2 the depth of focus is directly related
to the wavelength and the squared reciprocal numerical aperture
(cf. (2.2)). In submicrometer highnumerical aperture
lithography the range over
which the image is adequately sharp is typically less than one micron. Thus
it is extremely difficult to provide an exact positioning
across the entire image field. Problems such as wafer nonflatness,
autofocus errors, leveling errors, lens heating, etc. arise.
In case of a positioning error
the plane waves
do not converge at the wafer. The optical path difference depends on the
orientation of the incident rays.
The aberration function describing defocus
follows from the plane wave decomposition (4.55) and writes to

(4.61) 
whereby
i_{z, nm} = is the
vertical component of the wavevector.
The paraxial approximation valid for almost vertical incident rays, i.e.,
i_{x, n}, i_{y, m}
1, yields the simpler relation
which will subsequently be used to study the impacts of higherorder
aberration types. The obvious effect of defocus is a vertical
shift of the focal point above or below the Gaussian image point
depending on the sign of
. However, if
varies across the lens field, the surface of best
imagery is not planar and the usable depth of focus is correspondingly
reduced [116].
Next: 4.2.2 Power Series Representation
Up: 4.2 Lens Aberrations and
Previous: 4.2 Lens Aberrations and
Heinrich Kirchauer, Institute for Microelectronics, TU Vienna
19980417