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Got a Litho Question? Ask the Experts Chris A. Mack, KLA-Tencor
Q How low can k1 be pushed using
Q Now that immersion lithography
off-axis illumination?
seems just around the corner, what is the theoretical limit to the numerical aperture? How high can it go?
A The answer depends on which off-axis illumination you use. Dipole illumination allows you to push the two poles all the way to the edge of the lens (σ = 1), and the pitch resolution will then approach the theoretical limit of k1 = 0.25. There’s a small practical issue that the dipoles cannot have zero radius, and a more practical limit of k1 for dipole is probably about 0.28. Of course, dipole is not very convenient since it can print lines in only one orientation (say, only vertical lines). Quadrupole is an ideal source for dense line/space patterns of Manhattan geometry (vertical and horizontal), but pushing these poles to the edge of the lens means the smallest printable pitch is bigger than that for dipole by the square root of 2. Thus, the theoretical limit for quadrupole is about k1 = 0.35, with a practical limit (assuming a reasonable pole size) of about 0.39. Annular illumination has the same theoretical limit as dipole illumination, but a practical limit closer to that of quadrupole illumination. Lithographers have successfully pushed k1 down to 0.4 using off-axis illumination (usually in conjunction with attenuated phase shifting masks) for many critical layers, but going below that is a serious challenge.
A Without immersion lithography, we all learned that the theoretical limit for numerical aperture (NA) was 1.0. After all, the sine of an angle can never be greater than 1, right? This limit is still true with immersion lithography. The sine of the angle of light times the index of refraction of the media the light is traveling through is an optical invariant, staying the same as the light travels through the lens, through the immersion media, and through the wafer stack (including the resist). Since the sine of an angle can never be greater than 1, the maximum possible value of this invariant (and thus the maximum possible value of the NA) is equal to the smallest refractive index in the wafer side optical path. For 193 nm immersion lithography this will be water, with a refractive index of about 1.45. If new fluids could be engineered with higher refractive indices, this limit could rise. The next limits would be the calcium fluoride (index = 1.50) or fused silica (index = 1.56) of the lithographic lens or the resist itself (with refractive indices in the 1.6 – 1.7 range). Continued materials engineering could conceivably push the numerical aperture above 1.5, but I wouldn’t bet on it. I suspect that the theoretical limit of NA in 193nm immersion lithography (about 1.45) will be approached, with 1.3 – 1.35 as a practical maximum NA.
Do you have a lithography question? Just e-mail lithocolumn@kla-tencor.com and have your questions answered by Chris Mack or another of our experts. Summer 2004
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