linewidth tradeoff The rounding of line tips naturally leads to a tradeoff between shrinking the line width (i.e., the width of the line tip) and shrinking the gap between opposite facing tips. As the line width shrinks, the tip radius shrinks. When the line tip is already less than the point spread function (k1~0.6-0.7), the line tip naturally pulls back, increasing the gap between opposite facing tips. The point spread function likewise limits the resolvable distance between the centers of the line tips (modeled as circles). This leads in turn to a tradeoff between reducing cell width and reducing cell height. The tradeoff is avoided by adding a cut/trim mask (see discussion below). Hence, for the EUV-targeted 7nm node, with an 18 nm metal linewidth (k1=0.44 for λ=13.5 nm, NA=0.33), the line tip gap of less than 25 nm (k1=0.61) entails EUV single patterning is not sufficient; a second cut exposure is necessary. Different parts of layout requiring different illuminations When patterns include feature sizes near the resolution limit, it is common that different arrangements of such features will require specific illuminations for them to be printed. The most basic example is horizontal dense lines vs. vertical lines (half-pitch < 0.35 λ/NA), where the former requires a North-South dipole illumination while the latter requires an East-West dipole illumination. If both types are used (also known as cross-quadrupole C-Quad), the inappropriate dipole degrades the image of the respective line orientation. Larger pitches up to λ/NA can have both horizontal and vertical lines accommodated by quadrupole or QUASAR illumination, but diagonally spaced features and elbow features are degraded. In DRAM, the array and periphery are exposed at different illumination conditions. For example, the array could be exposed with dipole illumination while the periphery could use annular illumination. This situation applies to any set of patterns (half-pitch < 0.5 λ/NA) with different pitches or different feature arrangements, e.g., rectangular arrays vs. staggered arrays. Any of the individual patterns is resolvable, but a single illumination cannot be used simultaneously for all of them. The inclusion of both isolated and dense features is a well-known instance of multi-pitch patterning. Subresolution assist features (SRAFs) have been designed to enable the patterning of isolated features when using illumination tailored for the dense features. However, not all pitch ranges can be covered. In particular, semi-dense features may not be easy to include. Specific example: hole arrays For the