In microscopy, one is concerned about the closest distance between two objects that can be resolved in the image. The points of concern are quite different in lithography. A low-contrast image with a shallow-intensity slope can be turned into a sharp edge with the photoresist. As mentioned earlier in Sec. 1.3, the location of this edge is of prime interest and must be quantified against operating parameters of the exposure tool during manufacturing, because it determines the feature size that may be related to circuit-switching speed, leakage, resistance, etc. In addition, the edge position also determines whether the image in a given layer can be effectively overlaid with previous or subsequent layers. The five primary parameters that can be adjusted in the field are exposure dosage, focal position, pattern alignment between layers, magnification, and rotation. The last three parameters are mostly related to overlay. Even though magnification can affect feature size in principle, its effect on overlay is much greater than on feature size. The first two parameters—exposure dosage and focal position—determine the process window of the lithographic system in a mutually dependent way. This mutual dependence and the ability to superimpose simultaneous requirements on different features are captured in the exposuredefocus (E-D) tools that are the backbone of lithography metrics.
4.1 The Resolution and DOF Scaling Equations
Section 2.2 introduced resolution and DOF scaling in projection printing using the proportional relationship to wavelength and inverse proportional relationship to the lens NA without introducing the proportional constant. Equations (3.9) and (3.13) used an arbitrary constant of 0.5 as we provided the physical meaning of these relationships. Here, we finally introduce the resolution and DOF scaling equation with the rigorous proportional constants k1 and k3. We wait until now to do so, because the E-D tools discussed in this chapter can unambiguously determine these proportional constants.