ECE 1406, Homework #3, Due April 22, 2003

1. Problem 2.1, text. Assume that the location of defects is completely random and not correlated from mask to mask (not true in reality).

2. Problem 2.5, text. Note that there may be a typo here since 180 nm technology is not mentioned. Either assume 180 nm is the feature size or that what is meant is 80 nm microprocessor gate width. (which in turn corresponds to 120 nm half pitch)

3. Problem 2.8, text. Assume a numerical aperture of 0.5.

4. Referring to the ASML slide on high NA ArF system for 100 nm node, what is the range of k1 constants highlighted for the 0.75 NA lens?

How does this range compare with the value given in the text?

Using the most advanced illumination and mask technologies to reduce k1 and 157 nm light and a lens with a numerical aperture of 0.85 (as in the new ASML stepper), what would the minimum feature size be for ordinary optical lithography with lenses?

On the left hand side of the slide, the correspondence between illumination and mask technology and the k1 constant is indicated. QUASAR and ANNULAR are ASML names for illumination technologies which enhance high spatial frequency content in the image. Alt PSM, att. PSM and dipole, stand for alternate, attenuated, and dipole phase shift mask technologies. These are not yet used extensively, but might be used in the future. The k1 values associated with the mask technologies are somewhat speculative, but if workable would have obvious advantages.

5. Referring to pages 4 and 5 of the SIA roadmap, look at the 1/2 pitch requirements for the next several years. The pitch corresponds to the center to center distance between adjacent lines (metal or polysilicon, for example), and the 1/2 pitch is approximately equal to the feature size, F, or the resolution Res. that we have been talking about in the text and in class. Note also that the MPU gate in resist is smaller. This number is for the size of the microprocessor gate length as defined in the resist, and is achieved by tuning the process so that smaller lines are produced, even though the half pitch is not reduced.

Using the ASML data on k1, assuming an 0.85 NA 157 nm lens, and looking at the 1/2 pitch figures, comment on what illumination and mask technologies would be required for achieving the 1/2 pitch goals through 2007.

What does yellow on the chart mean? What does red mean?

Can the 2016 goal be achieved with EUV technology, and what lens, mask, and illumination technology might be required - note that this is a big stretch from the current situation!