4.5 Optical issues in photolithography  (Page 2/3)

Therefore, improvements in lithography technology translate directly into better, faster, more complex circuits at lower cost.

Having established the importance of the critical dimension it is important to understand what features of a photolithography system impact. The theory behind projection lithography is very well known, dating from the original analysis of the microscope by Abbe. It is, in fact, the Abbe sine condition that dictates the critical dimension:

where the two expressions refer to the limit of a purely coherent illuminating source and purely incoherent source respectively, and λ is the vacuum wavelength of the illuminating light source, n the index of refraction of the objective lens, and Θ refers to the angle between the axis of the lens and the line from the back focal point to the aperture of the entrance of the lens. The quantity in the denominator, n sin( Θ ) is referred to as the numerical aperture or NA. As the degree of coherence can be adjusted in a lithography system, the critical dimension is usually written more generally as:

From this equation, we begin to see what can be done to reduce the critical dimension of a lithography system:

1. Change the wavelength of the source.
2. Increase the numerical aperture (NA).
3. Reduce k ₁ .

Before we discuss how this is accomplished, we must consider one other key quantity, the depth of focus or DOF. The depth of focus is the length along the axis in which a sharp image exists. Naturally a large DOF is desirable for ease of alignment, since the entire dye must with lie within this region. In reality, however, the more meaningful constraint is that the DOF must be thicker than the resist layer so that the entire volume of resist is exposed and can be developed. Also, if the surface morphology of the device dictates that the resist to be exposed is not planar, then the DOF must be large enough so that all features are properly illuminated. Current resists must be 1 µm in thickness in order to have the necessary etch resistance, so this can be considered a minimum value for an acceptable DOF. The depth of focus can also be expressed as a function of numerical aperture and wavelength:

If we desire to minimize the critical dimension simply by making optics of large numerical aperture that we will simultaneously reduce the depth of focus and at a much faster rate owing to the dependence on the square of the numerical aperture.

These two quantities, DOF and CD, provide the direction in lithography and semiconductor processing as a whole. For example, a design with an improved surface planarity or a new resist that is effective at smaller thicknesses would allow for a smaller depth of focus which would in turn allow for a larger numerical aperture implying a smaller critical dimension. The resist, the source wavelength, and the optical delivery system all affect the critical dimension and that further refinements require a multifaceted approach to improving lithography systems. What also must be realized is that, as far as the optical system is concerned, virtually all that can be done with conventional optics has been done and that fundamental restraints on k ₁ have been reached.