In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have... more
In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have verified those statements using a computer. Here we give additional details for one of those lemmas, and we include the original computer programs and data as "ancillary files" accompanying this submission.
ABSTRACT The semiconductor industry is rapidly approaching the limits of 193 nm optical immersion lithography with on chip features of 22 nm planned shortly. The high cost and complexity of extreme ultraviolet lithography is driving a... more
ABSTRACT The semiconductor industry is rapidly approaching the limits of 193 nm optical immersion lithography with on chip features of 22 nm planned shortly. The high cost and complexity of extreme ultraviolet lithography is driving a search for alternative patterning technologies to create structures smaller than 14 nm. One promising alternative is a combination of top-down lithography with the directed self-assembly of block copolymers or blends. As part of an integrated experimental and computational research effort at IBM, we make use of parallel supercomputers, polymer field theory and Monte Carlo calculations to understand and guide the development of new DSA processes, polymers, and patterning designs.
ABSTRACT Immersion lithography for the 32nm node and beyond requires advanced methods to control 193 nm radiation reflected at the resist/BARC interface, due to the high incident angles that are verified under high numerical aperture (NA)... more
ABSTRACT Immersion lithography for the 32nm node and beyond requires advanced methods to control 193 nm radiation reflected at the resist/BARC interface, due to the high incident angles that are verified under high numerical aperture (NA) imaging conditions. ...
Tatsuyuki Nakatani received the BS degree in physics from Tokyo University of Science, Tokyo, Japan, in 1987, and the Ph.D. degree in material engineering from Nagasaki University, Nagasaki, Japan, in 2008. He was with Mazda Motor... more
Tatsuyuki Nakatani received the BS degree in physics from Tokyo University of Science, Tokyo, Japan, in 1987, and the Ph.D. degree in material engineering from Nagasaki University, Nagasaki, Japan, in 2008. He was with Mazda Motor Corporation, Hiroshima, ...
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To investigate possible factors that may be implicated in the poor accommodative responses of individuals with Down syndrome. This article evaluates the effect of age, angular size of target, and cognitive factors on accommodation.... more
To investigate possible factors that may be implicated in the poor accommodative responses of individuals with Down syndrome. This article evaluates the effect of age, angular size of target, and cognitive factors on accommodation. Seventy-seven children with Down syndrome who are participating in an ongoing study of visual development were assessed. One hundred thirty-one developmentally normal children took part in a previous study and provided control data. Accommodation was measured using a modified Nott dynamic retinoscopy technique. Children with Down syndrome showed considerably poorer accommodative responses than normally developing children. No target used in the present study produced an improved response in children with Down syndrome. Age, angular subtense of target, and cognitive factors could not fully account for the poor accommodation in children with Down syndrome. Poor accommodation is a common feature of Down syndrome, regardless of the target used. The etiology o...
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Page 1. Efficiently four-coloring planar graphs Neil Robertson 1 Department of Mathematics The Ohio State University Columbus, Ohio 43210-1174 robertso~math. ohio-state. edu Daniel P. Sanders2 Department of Mathematics ...
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The semiconductor industry is rapidly approaching the limits of 193 nm optical immersion lithography with on chip features of 22 nm planned shortly. The high cost and complexity of extreme ultraviolet lithography is driving a search for... more
The semiconductor industry is rapidly approaching the limits of 193 nm optical immersion lithography with on chip features of 22 nm planned shortly. The high cost and complexity of extreme ultraviolet lithography is driving a search for alternative patterning technologies to create structures smaller than 14 nm. One promising alternative is a combination of top-down lithography with the directed self-assembly of block copolymers or blends. As part of an integrated experimental and computational research effort at IBM, we make use of parallel supercomputers, polymer field theory and Monte Carlo calculations to understand and guide the development of new DSA processes, polymers, and patterning designs.
The directed self-assembly (DSA) of lamella-forming poly(styrene-block-trimethylsilylstyrene) (PS-PTMSS, L0 = 22 nm) was achieved using a combination of tailored top interfaces and lithographically defined patterned substrates. Chemo- and... more
The directed self-assembly (DSA) of lamella-forming poly(styrene-block-trimethylsilylstyrene) (PS-PTMSS, L0 = 22 nm) was achieved using a combination of tailored top interfaces and lithographically defined patterned substrates. Chemo- and grapho-epitaxy, using hydrogen silsesquioxane (HSQ) based prepatterns, achieved density multiplications up to 6× and trench space subdivisions up to 7×, respectively. These results establish the compatibility of DSA techniques with a high etch contrast, Si-containing BCP that requires a top coat neutral layer to enable orientation.
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Directed self-assembly (DSA), which combines self-assembled polymers with lithographically defined substrates, has been considered as a potential candidate to extend optical lithography. In order to assess the capabilities and limitations... more
Directed self-assembly (DSA), which combines self-assembled polymers with lithographically defined substrates, has been considered as a potential candidate to extend optical lithography. In order to assess the capabilities and limitations of DSA as a viable ...
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Tatsuyuki Nakatani received the BS degree in physics from Tokyo University of Science, Tokyo, Japan, in 1987, and the Ph.D. degree in material engineering from Nagasaki University, Nagasaki, Japan, in 2008. He was with Mazda Motor... more
Tatsuyuki Nakatani received the BS degree in physics from Tokyo University of Science, Tokyo, Japan, in 1987, and the Ph.D. degree in material engineering from Nagasaki University, Nagasaki, Japan, in 2008. He was with Mazda Motor Corporation, Hiroshima, ...
Research Interests:
Immersion lithography for the 32nm node and beyond requires advanced methods to control 193 nm radiation reflected at the resist/BARC interface, due to the high incident angles that are verified under high numerical aperture (NA) imaging... more
Immersion lithography for the 32nm node and beyond requires advanced methods to control 193 nm radiation reflected at the resist/BARC interface, due to the high incident angles that are verified under high numerical aperture (NA) imaging conditions. Swing curve effects are exacerbated in the high NA regime, especially when highly reflective substrates are used, and lead to critical dimension (CD)
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In this paper, we employ the self-segregating materials approach used in topcoat-free resists for water immersion lithography to extend the performance of topcoat materials for water immersion and to increase the contact angles of organic... more
In this paper, we employ the self-segregating materials approach used in topcoat-free resists for water immersion lithography to extend the performance of topcoat materials for water immersion and to increase the contact angles of organic fluids on topcoat-free resists for high index immersion lithography. By tailoring polymers that segregate to the air and resist interfaces of the topcoat, high contact
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Directed self-assembly is an emerging technology that to-date has been primarily driven by research efforts in university and corporate laboratory environments. Through these environments, we have seen many promising demonstrations of... more
Directed self-assembly is an emerging technology that to-date has been primarily driven by research efforts in university and corporate laboratory environments. Through these environments, we have seen many promising demonstrations of forming self-assembled structures with small half pitch (<15 nm), registration control, and various device-oriented shapes. Now, the attention turns to integrating these capabilities into a 300mm pilot fab, which
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ABSTRACT This paper will investigate the potential benefits and limitations of increasing the refractive index of the photoresist for water and high-index immersion based lithography. The primary potential benefits are increased exposure... more
ABSTRACT This paper will investigate the potential benefits and limitations of increasing the refractive index of the photoresist for water and high-index immersion based lithography. The primary potential benefits are increased exposure latitude due to restoration of the TM polarization component and improved depth of focus due to a delay in the onset of image-induced top-loss. After first understanding the physical origins of these effects, a series of simulation studies will probe the level of impact they may have for the 32nm and 22nm technology nodes. It is concluded that, although they may provide some process latitude relief, the benefits are minimal for 1.35NA water immersion, especially when weighed against the likely required development effort and cost. The benefits are slightly more compelling for high-index immersion (>1.5 NA), but a high index resist does not appear to be critical, provided the resist is at least as large as the immersion fluid index. A comparable benefit can be achieved with a conventional resist by using polarized illumination (a trend already happening for various reasons) and thinning the resist by ~9% for 1.35NA water immersion and ~15% for 1.55NA high-index immersion. Additionally, increasing the refractive index is typically accompanied by a corresponding increase in absorption. This will be addressed, concluding the limitations of absorption are likely chemical and not optical in nature. High absorption is likely tolerable, provided the chemistry can be engineered to account for exponential intensity decay. The level of difficulty in doing so is addressed.
Three metal-catalyzed vinyl addition copolymers derived from partially fluorinated norbornenes and tricyclononenes have been synthesized and evaluated for use in formulating photoresists for 157 nm lithography imaging. The transparency of... more
Three metal-catalyzed vinyl addition copolymers derived from partially fluorinated norbornenes and tricyclononenes have been synthesized and evaluated for use in formulating photoresists for 157 nm lithography imaging. The transparency of these ...
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ABSTRACT The main concern for the commercialization of directed self-assembly (DSA) for semiconductor manufacturing continues to be the uncertainty in capability and control of defect density. Our research investigates the defect... more
ABSTRACT The main concern for the commercialization of directed self-assembly (DSA) for semiconductor manufacturing continues to be the uncertainty in capability and control of defect density. Our research investigates the defect densities of various DSA process applications in the context of a 300mm wafer fab cleanroom environment; this paper expands substantially on the previously published DSA defectivity study by reporting a defect density process window relative to chemical epitaxial pre-pattern registration lines; as well as investigated DSA based contact hole shrinking and report critical dimension statistics for the phase separated polymers before and after etch, along with positional accuracy measurements and missing via defect density.
ABSTRACT Directed polymer self-assembly which combines lithographically defined substrates and self-assembled polymers has been considered as a potential candidate to extend conventional patterning techniques. In the past few years,... more
ABSTRACT Directed polymer self-assembly which combines lithographically defined substrates and self-assembled polymers has been considered as a potential candidate to extend conventional patterning techniques. In the past few years, successful demonstration of directed self-assembly of block copolymer shows that this method can afford sub-lithographic resolution or enhances dimensional control. However, integration of polymer self-assembly into standard lithographic processes remains a challenge and requires new materials. In this paper, we demonstrate robust and thermally crosslinked underlayer materials which control the orientation of block copolymer assemblies and are compatible with standard lithographic processes. These new materials allow simple integration of perpendicularly oriented polystyrene-b- polymethylmethacrylate (PS-b-PMMA) domains into standard manufacturing processes.
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Extensive pattern customization will be necessary to realize viable circuit patterns from line-space arrays generated by block copolymer directed self assembly (DSA). In pattern customization with regard to chemical epitaxy of lamellar... more
Extensive pattern customization will be necessary to realize viable circuit patterns from line-space arrays generated by block copolymer directed self assembly (DSA). In pattern customization with regard to chemical epitaxy of lamellar block copolymers, quantitative ...
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ABSTRACT Pattern customization is a necessary requirement to achieve circuit-relevant patterns using block copolymer directed self-assembly (DSA), but the edge-placement error associated with customization steps after DSA is anticipated... more
ABSTRACT Pattern customization is a necessary requirement to achieve circuit-relevant patterns using block copolymer directed self-assembly (DSA), but the edge-placement error associated with customization steps after DSA is anticipated to be at the scale of the pattern features, particularly as a result of overlay error. Here we present a new self-aligned approach to the customization of line-space patterns fabricated through chemical epitaxy. A partially inorganic chemical pattern contains a prepattern with pinning lines and non-guiding "blockout" features to which the block copolymer domains are aligned. Pattern transfer results in a line-space pattern with self-aligned customizations directly determined by the prepattern. In the transferred pattern, pinning lines determine the placement of single-line gaps while blockout features determine the placement and size of perpendicular trim across lines. By using designed two-dimensional chemical patterns, this self-aligned, bidirectional customization scheme enables the fabrication of high-resolution circuit-relevant patterns with fewer trim/exposure steps.
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Block copolymer directed self-assembly is an attractive method to fabricate highly uniform nanoscale features for various technological applications, but the dense periodicity of block copolymer features limits the complexity of the... more
Block copolymer directed self-assembly is an attractive method to fabricate highly uniform nanoscale features for various technological applications, but the dense periodicity of block copolymer features limits the complexity of the resulting patterns and their potential utility. Therefore, customizability of nanoscale patterns has been a long-standing goal for using directed self-assembly in device fabrication. Here we show that a hybrid organic/inorganic chemical pattern serves as a guiding pattern for self-assembly as well as a self-aligned mask for pattern customization through cotransfer of aligned block copolymer features and an inorganic prepattern. As informed by a phenomenological model, deliberate process engineering is implemented to maintain global alignment of block copolymer features over arbitrarily shaped,…
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The four-colour theorem, that every loopless planar graph admits a vertex-colouring with at most four different colours, was proved in 1976 by Appel and Haken, using a computer. Here we give another proof, still using a computer, but... more
The four-colour theorem, that every loopless planar graph admits a vertex-colouring with at most four different colours, was proved in 1976 by Appel and Haken, using a computer. Here we give another proof, still using a computer, but simpler than Appel and Haken's in ...