edge roughness in block copolymer patterns is strongly dependent on the interface tension between the two phases, which in turn, depends on the Flory "chi" (χ) parameter. A higher value of χ is preferred for reduced roughness; the interfacial width between domains is equal to 2a(6χ)−1/2, where a is the statistical polymer chain length. Moreover, χN > 10.5 is required for sufficient phase segregation, where N is the degree of polymerization (number of monomer repeats in the chain). On the other hand, the half-pitch is equal to 2(3/π2)1/3aN2/3χ1/6. The fluctuations of the pattern widths are actually only weakly (square root) dependent on the logarithm of the half-pitch, so they become more significant relative to smaller half-pitches. DSA has not yet been implemented in manufacturing, due to defect concerns, where a feature does not appear as expected by the guided self-assembly. Other multi-patterning techniques There have been numerous concerns that multiple patterning diminishes or even reverses the node-to-node cost reduction expected with Moore's Law. EUV is more expensive than three 193i exposures (i.e., LELELE), considering the throughput. Moreover, EUV is more liable to print smaller mask defects not resolvable by 193i. Some aspects of other considered multi-patterning techniques are discussed below. Self-aligned triple patterning (SATP) Self-aligned triple patterning has been considered as a promising successor to SADP, due to its introduction of a second spacer offering additional 2D patterning flexibility and higher density. A total of two masks (mandrel and trim) is sufficient for this approach. The only added cost relative to SADP is that of depositing and etching the second spacer. The main disadvantage of SATP succeeding SADP is that it would only be usable for one node. For this reason, self-aligned quadruple patterning (SAQP) is more often considered. On the other hand, the conventional SID SADP flow may be extended quite naturally to triple patterning, with the second mask dividing the gap into two features. Tilted ion implantation Tilted ion implantation was proposed in 2016 by the University of Berkeley as an alternative method of achieving the same result as spacer patterning. Instead of core or mandrel patterns supporting deposited spacers, an ion masking layer pattern shields an underlying layer from being damaged by ion implantation, which leads to being etched away in a subsequent process. The process requires the use of angled ion beams which penetrate to just the right depth, so as not to damage already processed