We investigate a new technique for high current density beam formation called 3rd order imaging. This technique
has two advantages: 1) increasing the beam current without beam blurring, and 2) producing a desired beam shape, such
as a square or rectangle. Thus, it can significantly decrease writing times in Electron Beam Direct Writing (EBDW).
These advantages are realized by using a patterned beam-defining aperture (PBDA) whose patterned openings work with
the spherical aberration in the objective lens to generate the final beam shape. The PBDA transmits rays if they fall
within the desired shape at the wafer, while blocking rays which would fall outside the desired shape. We have obtained
beam line profiles and two-dimensional beam shapes experimentally. The 3rd-order imaging beam current density is
seven times larger than that of a beam shaped by the conventional aperture. The experimental beam profile and the
calculated result are in good agreement. The experimental two-dimensional shapes reproduce the calculated beam
shapes, thereby verifying the theory of 3rd-order imaging. This technique is a potential solution to break through the
technological impasse of high current density versus high resolution.
We are now investigating a new concept column with the 3rd-order imaging technique, in order to obtain fine resolution
and high current density beams for electron beam direct writing (EBDW) suitable for below 32nm technology nodes.
From the first experimental verification, it is found that the 3rd-order imaging has a benefit of increasing the beam current
compared with conventional Gaussian beam without any beam blurring. However, in order to realize such a column
which can work stably in the sub 32nm technology node generations, it is important to clarify how robust the 3rd-order
imaging is against the mechanical tolerances in column manufacturing.
This paper describes the tolerance analysis for errors of column manufacturing by simulation. The column has an
electron gun with small virtual source and two (Gun and Main) lenses. A patterned beam defining aperture, which
enables the 3rd-order imaging, is set between the 1st and the 2nd lenses. The influences of errors such as concentricity,
offset and tilt between optical parts on the beam shape, beam current density distribution, and beam edge acuity on a
wafer is analyzed for this column. According to these results, the 3rd-order imaging appears to have sufficiently large
allowance compared to the error budget for column manufacturing required in the sub 32nm technology node patterning.
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