is used to directly pattern inter-metal dielectric instead of metal features. The reason is the cut/block locations in the core/mandrel features are already patterned in the first mask. There are secondary features which emerge from the gaps between spacers after further patterning. The edge between a secondary feature and the spacer is self-aligned with the neighboring core feature. 2D SID spacer patterning The use of SID may be applied to 2D arrays, by iteratively adding features equidistant from the previously present features, doubling the density with each iteration. Cuts not requiring tight positioning may be made on this spacer-generated grid. Triangular spacer (honeycomb structure) patterning Samsung recently demonstrated DRAM patterning using a honeycomb structure (HCS) suitable for 20 nm and beyond. Each iteration of spacer patterning triples the density, effectively reducing 2D pitch by a factor of sqrt(3). This is particularly useful for DRAM since the capacitor layer can be fit to a honeycomb structure, making its patterning simpler. Self-aligned quadruple patterning () SADP may be applied twice in a row to achieve an effective pitch quartering. This is also known as self-aligned quadruple patterning (SAQP). With SAQP, the primary feature critical dimension (CD), as well as the spacing between such features, are each defined by either the first or second spacer. It is preferred to have the second spacer define non-conducting features for more flexible cutting or trimming options. Directed self-assembly (DSA) The number of masks used for sidewall spacer patterning may be reduced with the use of directed self-assembly (DSA) due to the provision of gridded cuts all at once within a printed area, which can then be selected with a final exposure. Alternatively, the cut pattern itself may be generated as a DSA step. Likewise, a split via layout may be recombined in pairs. Much progress had been reported on the use of PMMA-PS block copolymers to define sub-20 nm patterns by means of self-assembly, guided by surface topography (graphoepitaxy) and/or surface chemical patterning (chemoepitaxy). The key benefit is the relatively simple processing, compared to multiple exposures or multiple depositions and etching. The main drawback of this technique is the relatively limited range of feature sizes and duty cycles for a given process formulation. Typical applications have been regular lines and spaces as well as arrays of closely packed holes or cylinders. However, random, aperiodic patterns may also be generated using carefully defined guiding patterns. The line