The industry is working to accommodate or minimize these effects, but the possible solutions have significant costs. For example, a paper presented in 2020 predicted substantial increases in dose to print for EUV resists ^[3]. Since EUV tool throughput is slower for higher dose to print, this will increase patterning cost substantially. Using double patterning techniques to print larger features than will be required in the final device will minimize some stochastic effects but will also add significant cost and complexity. There is a need for patterning methods where stochastic effects are minimized or eliminated. One possibility is to use self-organizing materials. These are materials where favorable intra or inter molecular interaction energies are larger than entropic effects, giving structures that self-assemble. By definition, these structures will have less randomness than simple mixtures of molecules. Some such materials have already been demonstrated. The sections below discuss some such materials already demonstrated, their attributes related to semiconductor patterning, and their advantages and limitations. The best-known class of self-organizing materials used for patterning is block co-polymers. These materials consist of two or more polymer chains connected covalently ^[4,5]. The different blocks of polymers self-assemble into distinct domains of different phase whose dimensions are related to the size of the polymer. They have a characteristic length, L0 which is related to the size of the polymer. So far, these materials have been used to create simple repeating patterns, such as arrays of lamellae which can become lines and spaces after etch or arrays of cylinders that can become arrays of holes or pillars after etch. Guide structures are used to line up or “direct” the domains to put them in the right place. This gives rise to the general term “Directed Self-Assembly” (DSA) for this process. Another approach was reported in 2013 ^[6]. It used what are called “bottle brush polymers” which are large rigid polymers that have a cylindrical shape. The cylinders were 3 to 10nm in diameter and 30 to 100nm long. One end of the cylinder was functionalized to reduce surface energy and the other end was functionalized to adhere to a silicon oxide substrate. These materials were then able to give an array of vertical cylinders on the substrate if the spin coating thickness was set at the length of the polymer rods. By including photosensitive cross-linking chemistry, the polymer rods could be cross linked in exposed areas. Since a rod either stays or develops away if not cross linked, this basically gives a pixelated resist, where the size of the pixel is the diameter of the rods. Any feature imaged in this resist can only have a dimension that is a multiple of the cylinder to cylinder spacing along the direction of measurement. The cylinders are not guided into place, so the edge of a feature will depend both on where the edge of the aerial image is and on where the edges of the cylinders happen to fall. This method does not show any reduction of feature size below the aerial image size, but it changes the stochastics considerably. A third approach is called DNA origami ^[7]. This approach takes advantage of the ability to nanoengineer DNA to make two- and three-dimensional objects. In the cited paper, flat rectangles of DNA were designed that each had two small square holes and one larger square holes. The origami was aligned onto a wafer with a patterned hexamethyldisilazane coating (HMDS). An etch process was used to transfer the DNA pattern into the silicon, resulting in 25nm and 12nm holes in the silicon. In all the self-organizing molecule approaches described above, the actual patterned dimension is a function of the molecular size or of the molecular design. This means that stochastic variations in the critical dimension are suppressed. For DSA, the thickness of lamellae or cylinders will determine the dimension of the patterned line or hole, respectively. Random variations in the size of the guide pattern due to stochastic effects will have little influence on the critical dimension. For the bottle brush polymer approach, the width of a patterned feature has to be a multiple of the pitch of the polymeric cylinders. A small variation in the imaging dose will not change the pattern width. For DNA origami, the dimensions of the patterned holes are fixed by the molecular structure. The only lithography involved was patterning guide patterns for the larger DNA rectangles to adhere to. Variations in the pattern size of the guide patterns will not affect the etched hole size. This is different from conventional lithography where the feature size is a function of the imaging dose and is a major benefit for self-assembly methods of patterning On a smaller scale, the roughness at the edge of the patterns will also be different. For DSA, the edge of patterned features will have roughness caused by variations in the locations of boundary molecules. The variations will be determined by the c value of the blocks in the block co-polymer, not by anything in the patterning process for the guide patterns. The roughness of pattern will not get worse as feature sizes shrink, and in fact it may get somewhat smaller in absolute terms if higher c block copolymers are used to pattern the smaller features. For the bottle brush polymers, printed features will have designed in roughness that has the characteristic pitch of the pixels, but smaller scale and larger scale roughness will be absent. The effects of self-assembly on roughness and CD control show promise, but the effect of self-assembly on printed feature position has to be considered. For directed self-assembly, typical processes for reducing critical dimension use pitch multiplication, where some of the DSA blocks are aligned to a guide feature but others fall in between the guide feature. The position of the in-between blocks can vary a little and this adds to any positional errors in the guide features. For the bottle brush polymer approach, the edge of a printed feature will fall along a line of pixel edges closest to the edge of the aerial image, so the printed feature could be as much as half the diameter of a cylinder away from the actual placement of the aerial image. For the DNA approach, the alignment will be dependent on how well the DNA actually aligns to the pattern feature. There should be no further alignment variation due to variations in the DNA since the patterned feature placement with the DNA template is controlled by the molecular structure of the larger template.