layers underneath. Also, the ion masking layer must behave ideally, i.e., blocking all ions from passing through, while also not reflecting off the sidewall. The latter phenomenon would be detrimental and defeat the purpose of the ion masking approach. Trenches as small as 9 nm have been achieved with this approach, using 15 keV Ar+ ion implantation at 15-degree angles into a 10 nm thermal SiO2 masking layer. A fundamental aspect of this approach is the correlation between damage width and damage pitch; both widen at the same time for fixed ion mask height and ion beam angle. Complementary polarity exposures The method of complementary exposures is another way of reducing mask exposures for multiple patterning. Instead of multiple mask exposures for individual vias, cuts or blocks, two exposures of opposing or complementary polarity are used, so that one exposure removes interior portions of the previous exposure pattern. The overlapped regions of two polygons of opposite polarity do not print, while the non-overlapped regions define locations that print according to the polarity. Neither exposure patterns the target features directly. This approach was also implemented by IMEC as two "keep" masks for the M0A layer in their 7nm SRAM cell. Self-aligned blocking or cutting Self-aligned blocking or cutting is currently being targeted for use with SAQP for sub-30 nm pitches. The lines to be cut are divided into two materials, which can be etched selectively. One cut mask only cuts every other line made of one material, while the other cut mask cuts the remaining lines made of the other material. This technique has the advantage of patterning double pitch features over lines at the minimum pitch, without edge placement errors. Cut-friendly layouts are processed with the same minimum number of masks (3), regardless of using DUV or EUV wavelength. EUV multiple patterning possibilities Although EUV has been projected to be the next-generation lithography of choice, it could still require more than one lithographic exposure, due to the foreseen need to first print a series of lines and then cut them; a single EUV exposure pattern has difficulty with line end-to-end spacing control. In addition, the line end placement is significantly impacted by photon shot noise. The existing 0.33 NA EUV tools are challenged below 16 nm half-pitch resolution. Tip-to-tip gaps are problematic for 16 nm dimensions. Consequently, EUV 2D patterning is limited to >32 nm pitch. Recent studies of optimizing