In 1979, Electronics magazine reported that stepper lithography would be a passing fancy superseded by direct-write electron beam lithography by the year 1985. It was admitted in a follow-up article, written for that same magazine in 1985, that the demise of optical lithography had been predicted prematurely and that it would take until 1994 for shipments of optical wafer steppers to be of lower volume than those of x-ray step-and-repeat systems. It was expected that optical lithography, once it reached its resolution limit of 0.5 Î¼m, would need to be replaced. Both pronouncements were based upon accepted expert opinion. This book has been written in the year 2005, and optical lithography is still going strong, but there are a number of programs dedicated to developing alternative lithography techniques. It is worth reviewing earlier arguments as to why optical lithography was nearing its end of life, and what arguments are being presented today to justify billions of dollars of investment in new lithography techniques.
10.1 The diffraction limit
The argument that optical lithography has limited resolution is based upon Rayleigh's scaling laws of resolution and depth-of-focus. From Chapter 2, resolution is given by Resolution=k 1 Î» NA , where the prefactors of Eqs. (2.4) and (2.7) are replaced by a general factor k 1 . Similarly, the expression for depth-of-focus can be written as Depth-of-focus=Â±k 2 Î» NA 2 . It has long been recognized that Rayleigh's and equivalent expressions are inexact predictors of resolution, but do correctly capture the trends associated with wavelengths and numerical apertures. Other factors, such as the resist process, are captured by the coefficients k 1 and k 2 . In 1979, the state-of-the-art lens had a resolution of 1.25 Î¼m, a Â± 0.75-Î¼m depth-of-focus, a numerical aperture of 0.28, and imaged at the mercury g-line. This produced values of 0.80 and 0.13 for k 1 and k 2 , respectively. With these values for the coefficients in Eqs. (10.1) and (10.2), the numerical aperture of a g-line lens capable of producing 0.8-Î¼m features would be 0.44, with a Â± 0.3-Î¼m depth-of-focus.
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