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Journal articles on the topic 'Diblock copolymer (DBC) lithography'

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Author: Grafiati

Published: 14 March 2023

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1

Chervanyov, A. I. "Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks." Polymers 12, no. 8 (July 25, 2020): 1659. http://dx.doi.org/10.3390/polym12081659.

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We investigate the electrical response of the insulating diblock copolymer system (DBC) filled with conductive spherical fillers depending on the affinities of these fillers for copolymer blocks and the interaction between fillers. We demonstrate that the contrast (difference) between the affinities of the fillers for dissimilar copolymer blocks is a decisive factor that determines the distribution of these fillers in the DBC system. The distribution of filler particles, in turn, is found to be directly related to the electrical response of the DBC-particle composite. In particular, increasing the affinity contrast above a certain threshold value results in the insulator-conductor transition. This transition is found to be caused by the preferential localization of the fillers in the microphases of the DBC system having larger affinity for these fillers. The effect of the interaction between fillers is found to be secondary to the described effect of the affinity contrast that dominates in determining the distribution of fillers in the composite. This effect of the inter-particle interactions is shown to be significant only when the affinity contrast and filler volume fraction are sufficiently large.

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2

Permyakova, N. M., T. B. Zheltonozhskaya, V. I. Karpovskyi, R. V. Postoi, V. I. Maksin, S. V. Partsevskaya, L. M. Grishchenko, D. O. Klymchuk, and V. V. Klepko. "Composition of α-tocopheryl acetate with micellar nanocarriers and the possibility of its use as a biologically active additive." Polymer journal 42, no. 4 (December 10, 2020): 292–306. http://dx.doi.org/10.15407/polymerj.42.04.292.

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Based on the asymmetric diblock copolymer (DBC) poly(ethylene oxide)/polyacrylic acid, effective, biocompatible and biodegradable micellar carriers were obtained for the delivery of vitamin E analogue, α-tocopheryl acetate (α-TOCA), in living organisms. The monitoring of the stability of micellar structures of the block copolymer and its composition with α-TOCA over time, in a saline solution and when the pH of the solution changes, was carried out. The stability of DBC micelles over time at pH = 3.5, partial disaggregation of micelles at pH = 9 and an increase in their aggregation in physiological solution were shown. The high stability of the α-TOCA/DBC composition formed in situ in time in the range of pH=3.5-9 and a significant decrease in its solutions of salting out effects in the presence of NaCl were established. The thermodynamic parameters of the process of the micelle formation of the pure α-TOCA in water/ethanol solution (95/5 v/v) as well as the size and morphology of its micellar structures were determined by light scattering and TEM methods. The initial α-TOCA micelles in water/ethanol solution were stable over a wide pH range, but their stability was much lower and the sensitivity to the presence of NaCl was much higher than that of DBC micelles. The dialysis method revealed the gradual release of the drug from the micellar carrier through a semipermeable membrane into the surrounding aqueous and aqueous-saline media. However, the rate and efficiency of α-TOCA release from the DBC micelles in an aqueous medium were significantly lower compared to a similar process of drug release from the pure α-TOCA dispersion. Thus, a possibility of providing of long-term controlled release of α-TOCA in the living organism due to the use of DBC micelles has been proven. Based on in vivo tests of the biological action of the composition on pregnant sows, its high bioavailability, rapid absorption, active participation in metabolic processes and positive effect on the reproductive qualities of sows compared to pure α-TOCA, were displayed, which improves the safety and productivity of newborn piglets. Key words: diblock copolymer, α-tocopheryl acetate, micellar carrier, encapsulation/release, biological action.

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3

Kuech, Thomas F., and Luke J. Mawst. "Nanofabrication of III–V semiconductors employing diblock copolymer lithography." Journal of Physics D: Applied Physics 43, no. 18 (April 21, 2010): 183001. http://dx.doi.org/10.1088/0022-3727/43/18/183001.

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4

Muramatsu, Makoto. "Nanopatterning of diblock copolymer directed self-assembly lithography with wet development." Journal of Micro/Nanolithography, MEMS, and MOEMS 11, no. 3 (July 9, 2012): 031305. http://dx.doi.org/10.1117/1.jmm.11.3.031305.

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5

Kunitskaya, Larisa, Tatyana Zheltonozhskaya, Rostyslav Stoika, and Dmytro Klymchuk. "Compositions of Anticancer Drug with Micellar Nanocarriers and Their Cytotoxicity." French-Ukrainian Journal of Chemistry 5, no. 2 (2017): 103–20. http://dx.doi.org/10.17721/fujcv5i2p103-120.

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Asymmetric diblock (DBC) and triblock (TBC) copolymers contained biocompatible chemically complementary polyacrylamide and poly(ethylene oxide) (PAAm-b-PEO-b-PAAm) or its monomethyl ether (MEPEO-b-PAAm), and also partially hydrolyzed triblock copolymer derivative (TBChydr) were used to create micelles of a special type. The micelles obtained are characterized by small CMCs and large values of the Gibbs micellization energy, thus indicating a high stability of DBC, TBC and TBChydr micelles in aqueous solutions and the capabilities of their use to encapsulate and deliver poorly soluble and/or toxic drugs in living organism. Morphological features and size of DBC and TBC micelles were determined by TEM. The electron images demonstrated spherical micelles of a polymolecular type, monomolecular type and separate micelle aggregates. TBC and TBChydr micelles were used to examine in vitro anticancer activity of their compositions with doxorubicin (Dox). The created micelle systems showed the enhanced cytotoxicity as compared to individual Dox against murine leukemia cells of L1210 line, murine transformed fibroblasts of L929 line and human T-leukemia cells of Jurkat line and allow to achieve a high efficacy at low Dox concentrations (0,1÷3 µg·cm-3) that opens the great prospects for essential decrease in drug dose at chemotherapy.

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6

Park, J. H., J. Kirch, L. J. Mawst, C. C. Liu, P. F. Nealey, and T. F. Kuech. "Controlled growth of InGaAs/InGaAsP quantum dots on InP substrates employing diblock copolymer lithography." Applied Physics Letters 95, no. 11 (September 14, 2009): 113111. http://dx.doi.org/10.1063/1.3224916.

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7

Yoshida, Shinya, Takahito Ono, and Masayoshi Esashi. "Conductive polymer patterned media fabricated by diblock copolymer lithography for scanning multiprobe data storage." Nanotechnology 19, no. 47 (October 29, 2008): 475302. http://dx.doi.org/10.1088/0957-4484/19/47/475302.

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8

Terekhin, V. V., O. V. Dement’eva, A. V. Zaitseva, and V. M. Rudoy. "Diblock copolymer micellar lithography: 1. Intermicellar interactions and pathways for control of monomicellar film structure." Colloid Journal 73, no. 5 (October 2011): 697–706. http://dx.doi.org/10.1134/s1061933x11050152.

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9

Terekhin, V. V., O. V. Dement’eva, and V. M. Rudoy. "Diblock copolymer micellar lithography: 2. Formation of highly ordered nanoparticle ensembles with controlled geometric characteristics." Colloid Journal 73, no. 5 (October 2011): 707–16. http://dx.doi.org/10.1134/s1061933x11050164.

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10

Kim, Honghyuk, Jonathan Choi, Zachary Lingley, Miles Brodie, Yongkun Sin, Thomas F. Kuech, Padma Gopalan, and Luke J. Mawst. "Selective growth of strained (In)GaAs quantum dots on GaAs substrates employing diblock copolymer lithography nanopatterning." Journal of Crystal Growth 465 (May 2017): 48–54. http://dx.doi.org/10.1016/j.jcrysgro.2017.02.046.

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11

Chang, Chun-Chieh, Dan Botez, Lei Wan, Paul F. Nealey, Steven Ruder, and Thomas F. Kuech. "Fabrication of large-area, high-density Ni nanopillar arrays on GaAs substrates using diblock copolymer lithography and electrodeposition." Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena 31, no. 3 (May 2013): 031801. http://dx.doi.org/10.1116/1.4798464.

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12

Dirani, Ali, Fabrice Stehlin, Ihab Dika, Arnaud Spangenberg, Nathan Grumbach, Jean-Louis Gallani, Bertrand Donnio, et al. "Orienting the Demixion of a Diblock-copolymer Using 193 nm Interferometric Lithography for the Controlled Deposition of Nanoparticles." Macromolecular Rapid Communications 32, no. 20 (August 16, 2011): 1627–33. http://dx.doi.org/10.1002/marc.201100399.

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13

Mastari, Marouane, Matthew Charles, Patricia Pimenta-Barros, Maxime Argoud, Raluca Tiron, Anne-Marie Papon, Nicolas Chevalier, et al. "Ge Nano-Heteroepitaxy: From Nano-Pillars to Thick Coalesced Layers." ECS Transactions 109, no. 4 (September 30, 2022): 317–28. http://dx.doi.org/10.1149/10904.0317ecst.

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Ge epitaxy on nanometer-size Ge pillars was studied in a 300 mm industrial Reduced Pressure-Chemical Vapour Deposition tool. A patterning scheme based on diblock copolymer lithography was used to fabricate honeycombed nanometer-sized Si templates for the hetero-epitaxy of Ge nano-pillars. It was highly selective and uniform at 600°C. Thick Ge layers were then grown with a low temperature/high temperature approach on Ge nano-pillars and characterized by Atomic Force Microscopy, X-Ray Diffraction and cross-sectional Transmission Electron Microscopy. A degraded surface morphology, with otherwise similar structural properties was obtained for 2D Ge layers grown on Ge nano-pillars compared to growth on bulk Si. Defects such as stacking faults and twins also formed during the coalescence process.

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14

Borah, Dipu, Cian Cummins, Sozaraj Rasappa, Ramsankar Senthamaraikannan, Mathieu Salaun, Marc Zelsmann, George Liontos, Konstantinos Ntetsikas, Apostolos Avgeropoulos, and Michael Morris. "Nanopatterning via Self-Assembly of a Lamellar-Forming Polystyrene-block-Poly(dimethylsiloxane) Diblock Copolymer on Topographical Substrates Fabricated by Nanoimprint Lithography." Nanomaterials 8, no. 1 (January 9, 2018): 32. http://dx.doi.org/10.3390/nano8010032.

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15

Kim, Honghyuk, Wei Wei, Thomas F. Kuech, Padma Gopalan, and Luke J. Mawst. "Impact of InGaAs carrier collection quantum well on the performance of InAs QD active region lasers fabricated by diblock copolymer lithography and selective area epitaxy." Semiconductor Science and Technology 34, no. 2 (January 14, 2019): 025012. http://dx.doi.org/10.1088/1361-6641/aaf8e8.

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16

Prausnitz, John M. "Thermodynamics of structured fluids. Hard science for soft materials." Pure and Applied Chemistry 72, no. 10 (January 1, 2000): 1819–34. http://dx.doi.org/10.1351/pac200072101819.

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At liquid-like densities, molecules of complex fluids can assume a variety of structures (or positions) in space; when the molecules contain many atoms as, for example, in polymers, that variety becomes very large. Further, when confined to a narrow space, it is possible to achieve structures that are not normally observed. Thanks to recent advances in statistical mechanics and molecular physics, and thanks to increasingly fast computers, it is now possible to calculate a fluid's structure, that is, the positions of molecules at equilibrium under given conditions. Calculation of fluid structure is useful because thermodynamic properties depend strongly on that structure, leading to possible applications for new materials. Three examples illustrate some recent developments; each example is presented only schematically (with a minimum of equations) to indicate the physical basis of the mathematical description. The first example considers the effect of branching on self-assembly (micellization) of copolymers (with possible long-range applications in medicine). The second and third examples consider the effect of confinement on fluid structure: first, crystallization in a narrow, confined space to produce a desired crystal structure (with possible applications for light-emitting diodes) and second, suppression of micellization of a diblock copolymer in a thin film (with possible application in lithography). Whenever possible, theoretical calculations are compared with experimental results.

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17

Cao, Wei, Senlin Xia, Michael Appold, Nitin Saxena, Lorenz Bießmann, Sebastian Grott, Nian Li, Markus Gallei, Sigrid Bernstorff, and Peter Müller-Buschbaum. "Self-Assembly in ultrahigh molecular weight sphere-forming diblock copolymer thin films under strong confinement." Scientific Reports 9, no. 1 (December 2019). http://dx.doi.org/10.1038/s41598-019-54648-3.

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AbstractUltrahigh molecular weight (UHMW) diblock copolymers (DBCs) have emerged as a promising template for fabricating large-sized nanostructures. Therefore, it is of high significance to systematically study the influence of film thickness and solvent vapor annealing (SVA) on the structure evolution of UHMW DBC thin films. In this work, spin coating of an asymmetric linear UHMW polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) DBC is used to fabricate thin films, which are spherically structured with an inter-domain distance larger than 150 nm. To enhance the polymer chain mobility and facilitate approaching equilibrium nanostructures, SVA is utilized as a post-treatment of the spin coated films. With increasing film thickness, a local hexagonal packing of PMMA half-spheres on the surface can be obtained, and the order is improved at larger thickness, as determined by grazing incidence small angle X-ray scattering (GISAXS). Additionally, the films with locally hexagonal packed half-spherical morphology show a poor order-order-poor order transition upon SVA, indicating the realization of ordered structure using suitable SVA parameters.

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18

Alabi, Taiwo R., Dajun Yuan, and Suman Das. "Photopatterneable Block Co-Polymers for Laser Interference Lithography." MRS Proceedings 1412 (2012). http://dx.doi.org/10.1557/opl.2012.1258.

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ABSTRACTWe report on the laser interference patterning of as-spun block copolymer films on silicon and silicon dioxide substrates. Our process involves the use of a pulsed laser light source of 266 nm wavelength and any type of diblock copolymer as a positive tone photoresist, resulting in the generation of sub-micron domains of different geometries and periodicity. This non-solvent based method is robust, and when combined with the inherent nano-scaled periodicity in block copolymers, can produce hierarchical patterns on substrates with potential use in the electronics and semiconductor industries.

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19

Liu, Guangyu, Hongping Zhao, Jing Zhang, Joo Hyung Park, Luke J. Mawst, and Nelson Tansu. "Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography." Nanoscale Research Letters 6, no. 1 (April 15, 2011). http://dx.doi.org/10.1186/1556-276x-6-342.

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20

"InGaAs/InP Quantum Dot Formation Employing Diblock Copolymer Lithography and Selective Growth - Invited Talk." ECS Meeting Abstracts, 2009. http://dx.doi.org/10.1149/ma2009-02/29/2280.

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21

Chevalier, Xavier, Gwenaelle Pound-Lana, Cindy Gomes Correia, Sébastien Cavalaglio, Benjamin Cabannes-Boué, Frederic Restagno, Guillaume Miquelard-Garnier, et al. "Self-organization and dewetting kinetics in sub-10 nm diblock copolymer line/space lithography." Nanotechnology, January 19, 2023. http://dx.doi.org/10.1088/1361-6528/acb49f.

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Abstract In this work, we investigated the self-assembly of a lamellar block copolymer (BCP) under different wetting conditions. We explored the influence of the chemical composition of under-layers and top-coats on the thin film stability, self-assembly kinetics and BCP domain orientation. Three different chemistries were chosen for these surface affinity modifiers and their composition was tuned in order to provide either neutral wetting (i.e. an out-of-plane lamellar structure), or affine wetting conditions (i.e. an in-plane lamellar structure) with respect to a sub-10 nm PS-b-PDMSB lamellar system. Using such controlled wetting configurations, the competition between the dewetting of the BCP layer and the self-organization kinetics was explored. We also evaluated the spreading parameter of the BCP films with respect to the configurations of surface-energy modifiers and demonstrated that BCP layers are intrinsically unstable to dewetting in a neutral configuration. Finally, the dewetting mechanisms were evaluated with respect to the different wetting configurations and we clearly observed that the rigidity of the top-coat is a key factor to delay BCP film instability.

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22

Yoshida, Hiroshi, Hirofumi Kitano, Satoshi Akasaka, Tomohiro Inoue, Mikihito Taknaka, Hirokazu Hasegawa, and Hideki Nagano. "Tailoring Microdomain Orientation in Block Copolymer Thin Films for Lithographic Application." MRS Proceedings 961 (2006). http://dx.doi.org/10.1557/proc-0961-o17-01.

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ABSTRACTBlock copolymer lithography is a promising method for fabricating periodical nano patterns less than 20nm by self-assembly and can be applicable for fabricating patterned magnetic media with recording density over 1Tbit/inch2. We found a simple technique to control the orientation of cylindrical microdomains in thin films. Only by mixing polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymers with the constituent homopolymer (PS or PMMA), we could align the cylindrical microdomains perpendicular to the film surface. The added homopolymer induces conformational entropic relaxation of the block chains in microdomain space and stabilizes perpendicular orientation of hexagonally packed cylindrical microdomains. Thus formed perpendicular cylinders can be readily aligned in a regular array with a grating substrate.

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23

Zhang, Yuan, Simone Raoux, Daniel Krebs, Leslie E. Krupp, Teya Topuria, Jean Jordan-Sweet, Marissa Caldwell, Philip Rice, Delia J. Milliron, and H. S. Philip Wong. "Crystallization Characteristics Of Phase Change Nanoparticle Arrays Fabricated By Self-Assembly Based Lithography." MRS Proceedings 1072 (2008). http://dx.doi.org/10.1557/proc-1072-g08-05.

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ABSTRACTPhase change nanodot arrays were fabricated using self-assembly diblock copolymer template PS-b-PMMA (polystyrene-poly (methyl-methacrylate)) and studied by time resolved X-ray diffraction. The size of the nanodots was less than 15nm in diameter with 40nm spacing. This method is quite flexible regarding the patterned materials, and can be used on different substrates. The crystallization behavior of small scale phase change nanodot arrays was studied for different materials, such as Ge15Sb85, Ge2Sb2Te5 and Ag and In doped Sb2Te. It was found that the nanodots had higher crystallization temperatures compared to their corresponding blanket films and crystallized over a broader temperature range.

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24

Borah, Dipu, Sozaraj Rasappa, Barbara Kosmala, Justin D. Holmes, and Michael A. Morris. "Block Copolymer Self-assembly on Ethylene Glycol (EG) Self-assembled Monolayer (SAM) for Nanofabrication." MRS Proceedings 1450 (2012). http://dx.doi.org/10.1557/opl.2012.1224.

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ABSTRACTNanostructure templates fabrication from P(S-b-MMA) thin films requires precise control of interfacial energies to achieve perpendicular orientation of microdomains to the substrate surface and can be obtained by modifying the oxide layer on silicon with a covalently anchored hydroxyl-terminated random copolymer P(S-r-MMA) termed a “neutral brush”. This commonly employed method enables precise fine-tuning of interfacial energies, but involves a lengthy process, requires starting materials that are commercially available but expensive, and results in a relatively thick under layer that can interfere with subsequent surface processing. We report here the microphase separation behaviour of an asymmetric P(S-b-MMA) diblock copolymer on electronic substrates modified with ethylene glycol (EG) self-assembled monolayer (SAM) as alternative to standard random copolymer brush. The diblock copolymer films deposited on EG SAMs upon thermal annealing spontaneously generates features with sub-lithographic resolution and pitch with perpendicular orientation. Selective etching provides a rapid route for the generation of PS template structures as the PMMA domains are etched at a faster rate. These templates can subsequently be used as etch masks to generate nanoscale features. We use state of the art lithography to generate sub-μm features and within these generate nm sized copolymer templates. Graphoepitaxy method proved a successful approach for the alignment of the microphase separated structures. This method of EG SAM driven self-0assembly provides a simple, rapid, yet tuneable approach for surface neutralization and nanofabrication technique for creating high density nanoscale features for the nanoelectronic industry.

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25

Ramanathan, Muruganathan, Seth B. Darling, Anirudha V. Sumant, and Orlando Auciello. "Self-Assembly of Cylinder-Forming Block Copolymers on Ultrananocrystalline Diamond (UNCD) Thin Films for Lithographic Applications." MRS Proceedings 1203 (2009). http://dx.doi.org/10.1557/proc-1203-j17-15.

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AbstractBlock copolymers (BCPs) consist of two or more chemically distinct and incompatible polymer chains (or blocks) covalently bonded. Due to the incompatibility and connectivity constraints between the two blocks, diblock copolymers spontaneously self-assemble into microphase-separated nanoscale domains that exhibit ordered 0, 1, 2 or 3 dimensional morphologies at equilibrium. Commonly observed microdomain morphologies in bulk samples are periodic arrangements of lamellae, cylinders, or spheres. Block copolymer lithography refers to the use of these ordered structures in the form of thin films as templates for patterning through selective etching or deposition. The self-assembly and domain orientation of block copolymers on a given substrate is critical to realize block copolymer lithography as a tool for large throughput nanolithography applications. In this work, we survey the morphology of cylinder-forming block copolymers by atomic force microscopy (AFM). Three kind of block copolymers were studied: a) poly(styrene-block-ferrocenyldimethylsilane), PS-b-PFS b) poly(styrene-block-methylmethacrylate), PS-b-PMMA and c) poly(styrene-block-dimethylsiloxane) PS-b-PDMS. Block copolymers were dissolved in a neutral solvent for both blocks (toluene) in order to obtain solutions of various concentrations (1 and 1.5 wt %). From these solutions, films were prepared by spin casting on ultrananocrystalline diamond (UNCD) thin film substrates. Results indicate that PS-b-PFS exhibits chemical and morphological compatibility to the UNCD surface in terms of wetting and domain control. A systematic comparison of self-assembly of these polymers on silicon nitride substrates demonstrates that UNCD thin films would require pre-treatment to be considered as a substrate for BCP lithography.

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26

Park, Joo Hyung, Anish Khandekar, Sang-Min Park, Luke Mawst, Thomas Kuech, and Paul Nealey. "Selective GaAs Quantum Dot Array Growth using Dielectric and AlGaAs Masks Pattern-Transferred from Diblock Copolymer." MRS Proceedings 1014 (2007). http://dx.doi.org/10.1557/proc-1014-aa07-15.

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AbstractTo reach the full theoretical potential advantages of ideal Quantum Dots (QDs) for diode lasers and photodetectors, elimination of the wetting layer, which is inherent to self-assembled QDs of Stranski-Krastnow (SK) growth mode, and achieving a uniform mono-modal QD size distribution is needed. The SK QD approach is complicated by the randomness of the QD size distribution and inherent presence of the wetting layer. These factors have been experimentally identified as the underlying cause for low optical gain and high temperature sensitivity in diode lasers which result from carrier leakage out of the QDs into the wetting layer.An alternate approach to QD formation is the use of nanopatterning with diblock copolymers combined with selective MOCVD growth. We utilize cylinder-forming PS-b-PMMA which have the ability of preserving the hole size through the pattern transfer procedures. The combination of diblock copolymer lithography with selective MOCVD growth of the QDs could lead to a higher degree of control over QD shape, size uniformity, and composition over the self-assembly process. Since the SK self-assembly process is not employed, the problematic wetting layer states are eliminated and improved optical gain can be expected. Control over the QD height, shape, and strain, also allows for the design of increased energy spacing between ground and excited QD states and hence a wider control or selection of the emission wavelengths. Since the QD strain is decoupled from the size, the process also has potential for achieving longer wavelength emission compared with SK QDs. On a GaAs substrate, hexagonally arranged uniform size QD arrays have been fabricated. The QD patterning is prepared by dense nanoscale diblock copolymer lithography, which consists of perpendicularly ordered cylindrical domains of polystyrene-block-poly(methylmethacrylate) (PS-b-PMMA) matrix. To transfer polymer patterns to QD arrays, two mask materials have been taken under consideration. Firstly, to characterize the profile and distribution of the QDs, a dielectric template mask was utilized and the polymer patterning is transferred on it. After the pattern transfer to the dielectric and subsequent removal of the polymer, single crystal GaAs QDs are selectively grown by MOCVD. SEM images indicate that the QD density is larger than 5×10^10/cm2, comparable to SK growth mode and the size distribution peaks at a 12nm diameter. Finally, to grow QDs and subsequently cover the QDs in situ, an AlxGa1-xAs template mask is being investigated. After the pattern transfer to a 15nm thick AlGaAs template layer using RIE, the native oxide on the patterned AlGaAs surface acts as a selective growth mask for InAs QDs. After deposition of the QDs, capping layers can be grown on QDs without removing the sample from the reactor. We are currently investigating optimal growth conditions for covering the QDs and characterizing the photoluminescence. University of Wisconsin -Madison gratefully acknowledges support from the ARO MURI W911NF-05-1-0262 (Dr. John Prater) and NSF NSEC DMR-0425880.

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