Now that we have provided sufficient background on imaging and tools, the processes to use them and the optimization of these processes are given in this chapter. We start with optimization of the exposure tools, then move on to resist processing, k₁ reduction schemes, and finally the control of critical-dimension (CD) uniformity.

6.1 Optimization of the Exposure Tool

The optimization of an exposure tool involves its numerical aperture (NA), illumination setting, exposure/focus, depth-of-focus (DOF) budget, its components and monitoring of focus, as well as throughput optimization in field size and exposure routing.

6.1.1 Optimization of NA

Most modern exposure tools and steppers allow users to adjust the NA of the imaging lens because the NA cannot be preset in the factory when resolution is extended to the low-k₁ regime. The optimum NA^1,2 is not the highest available setting on the tool, but rather a function of feature size and shape combinations, illumination, etc. It is important to set the NA to the best value at each given imaging environment to take advantage of the capability of the imaging system.

From Eq. (4.3), the resolution scaling equation, sinθ must be sufficiently large to sustain the resolution of a given feature. However, Eq. (4.4) dictates that a large θ reduces DOF. Therefore, in a dry system where the space between the last lens surface and the resist is not immersed in a liquid, the NA of its imaging lens has a medium value whose DOF is maximum. Figure 6.1 shows DOF as a function of NA at σ = 0.82 for 0.20-μm lines separated by 0.20-μm spaces. The DOF is evaluated with the exposure-defocus (E-D) forest methodology covered in Chapter 4, based on 8% EL and CD bounds at ±15 nm. The DOF quickly rises from 0 to 1.04 μm at NA = 0.557, then gradually decreases as NA increases. Figure 6.2 depicts the E-D trees at the NA values evaluated. At NA = 0.455 and below, resolution is too low to support any E-D tree. An E-D tree can be constructed at NA = 0.487, but there is insufficient branch separation to support the E-D window specified for 8% EL.