In Chapter 2, where the parameter numerical aperture was introduced, it was defined as n sin Î¸, where n is the index of refraction of the medium between the lens and the resist on the wafer, and Î¸ is the half angle subtended by the lens. By geometry, and the fact that light travels in a straight line through homogeneous media, the largest value that Î¸ can reach is 90 deg, so that sin Î¸ must be less than 1.0. The medium between the lens and the resist is typically air, for which n â 1. This implies that the numerical aperture cannot exceed 1.0 in air, creating a limit on resolution for a given wavelength.
It has long been known that resolution in optical microscopy can be enhanced by immersing microscope objective lenses in a liquid that has an index of refraction greater than 1.0. This is not something that can be accomplished by using optics that have been designed for imaging in air, but requires lenses that have been designed specifically for operation using an immersion fluid with a well-defined index of refraction. Nevertheless, such optics have been exploited successfully in optical microscopy for over a century.
The same physics can be used to advantage in lithography. Since sin Î¸ remains constrained by geometry to being less than 1.0, the index of refraction of the medium between the lens and the wafer represents the theoretical upper limit for the numerical aperture. At a wavelength of 193 nm, ultrapure water has an index of refraction of 1.437. Water is also very transparent at ArF wavelengths, so it is a suitable fluid for ArF immersion lithography, where water fills the space between the bottom of the lens and the wafer. The use of water immersion leads to a significant increase in the numerical aperture over the maximum value possible when imaging in air, and hence greatly extends the resolution capability of ArF lithography. With water as an immersion fluid instead of air, the physical limit for numerical apertures increases from 1.0 to 1.437. In this chapter the basic concepts of immersion lithography will be discussed. The remainder of the chapter will then be concerned with what other opportunities there might be to extend optical lithography.