The extendibility of 2D-TCC technique to an isolated line of 45 nm width is investigated in this paper. The 2D-TCC
technique optimizes mask patterns placing assist pattern automatically. For 45 nm line patterns, the assist pattern width
generally becomes much smaller than the exposure wavelength of 193 nm. Thus, the impact of the topography of a mask
is examined using an electro-magnetic field (EMF) simulation. This simulation indicates that unwanted assist pattern
printings are brought about by assist patterns with a smaller size than expected by the Kirchhoff's approximation. The
difference, however, can be easily solved by giving a bias to the main pattern in the optimized mask. The main pattern
bias decreases DOF very little. Furthermore, DOF simulated with a thick mask model is roughly the same as that
simulated with a thin mask model. Therefore the topography of the optimized mask does not have an influence on the
assist pattern position of the optimized mask. From these results, we have confirmed that the 2D-TCC technique can be
extended to the optimization of 45 nm line patterns. As one of the notable features, the optimized aperiodic assist pattern
greatly reduces MEEF compared with the conventional periodic assist pattern. To verify the feasibility of the 2D-TCC
technique for 45 nm line, we performed experiment with an optimized mask. Experimental results showed that DOF
increased with the number of assist pattern as simulation indicated. In addition, a defect whose length was twice that of
the assist pattern did not have an influence on CD. From these results we have confirmed that the 2D-TCC technique can
enhance the resolution of 45 nm line and has practical feasibility.
In this paper, a new resolution enhancement technique named 2D-TCC technique is proposed. This method can
enhance resolution of line patterns as well as that of contact hole patterns by the use of an approximate aerial image.
The aerial image, which is obtained by 2D-TCC calculation, expresses the degree of coherence at the image plane of a
projection optic considering mask transmission at the object plane. OPC of desired patterns and placement of assist
patterns can be simultaneously performed according to an approximate aerial image called a 2D-TCC map. Fast
calculation due to truncation of a series in calculating an aerial image is another advantage. Results of mask
optimization for various line patterns and the validity of the 2D-TCC technique by simulations and experiments are
reported.
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