Fabricatable Interconnect and Molecular QCA Circuits

When exploring computing elements made from technologies other than complementary metal-oxide-semiconductor, it is imperative to investigate circuits and systems assuming realistic physical implementation constraints. This paper looks at molecular quantum-dot cellular automata (QCA) devices within this context. With molecular QCA, physical coplanar wire crossings may be very difficult to fabricate in the near to midterm. Here, we consider how this will affect interconnect. We introduce a novel technique to remove wire crossings in a given design in order to facilitate the self-assembly of real circuits - thus, providing meaningful and functional design targets for both physical and computer scientists. The proposed methodology eliminates all wire crossings with minimal logic gate/node duplications. Simulation results based on existing QCA circuits and other benchmarks are presented, and suggest that further investigation is needed.

[1]  P. Barbara,et al.  Contemporary Issues in Electron Transfer Research , 1996 .

[2]  Michael T. Niemier,et al.  Eliminating wire crossings for molecular quantum-dot cellular automata implementation , 2005, ICCAD-2005. IEEE/ACM International Conference on Computer-Aided Design, 2005..

[3]  Robert K. Brayton,et al.  A novel VLSI layout fabric for deep sub-micron applications , 1999, DAC '99.

[4]  C. Lent,et al.  Demonstration of a functional quantum-dot cellular automata cell , 1998 .

[5]  Peter M. Kogge,et al.  Exploring and exploiting wire-level pipelining in emerging technologies , 2001, ISCA 2001.

[6]  Jieying Jiao,et al.  Building blocks for the molecular expression of quantum cellular automata. Isolation and characterization of a covalently bonded square array of two ferrocenium and two ferrocene complexes. , 2003, Journal of the American Chemical Society.

[7]  A Imre,et al.  Majority Logic Gate for Magnetic Quantum-Dot Cellular Automata , 2006, Science.

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Wenchuang Hu,et al.  High-resolution electron beam lithography and DNA nano-patterning for molecular QCA , 2005, IEEE Transactions on Nanotechnology.

[10]  D. F. Wong,et al.  New algorithms for min-cut replication in partitioned circuits , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[11]  Vida Dujmovic,et al.  An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization , 2002, Algorithmica.

[12]  Gary H. Bernstein,et al.  Low temperature development of PMMA for sub-10-nm electron beam lithography , 2003, 2003 Third IEEE Conference on Nanotechnology, 2003. IEEE-NANO 2003..

[13]  Mo Liu Robustness and power dissipation in quantum-dot cellular automata , 2006 .

[14]  X.S. Hu,et al.  Using CAD to Shape Experiments in Molecular QCA , 2006, 2006 IEEE/ACM International Conference on Computer Aided Design.

[15]  Snider,et al.  Digital logic gate using quantum-Dot cellular automata , 1999, Science.

[16]  Cheng-Kok Koh,et al.  Non-crossing OBDDs for mapping to regular circuit structures , 2003, Proceedings 21st International Conference on Computer Design.

[17]  Wen-Jong Fang,et al.  Performance-driven multi-FPGA partitioning using functional clustering and replication , 1998, DAC.

[18]  D. T. Lee,et al.  On crossing minimization problem , 1998, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[19]  E. W. Edwards,et al.  Directed Assembly of Block Copolymer Blends into Nonregular Device-Oriented Structures , 2005, Science.

[20]  Wolfgang Porod,et al.  Quantum-Dot Cellular Automata: Line and Majority Logic Gate , 1999 .

[21]  Cheng-Kok Koh,et al.  Decomposition of BDDs with Application to Physical Mapping of Regular PTL Circuits , 2004 .

[22]  Alexandra Imre,et al.  Experimental study of nanomagnets for magnetic quantum-dot cellular automata (MQCA) logic applications , 2005 .

[23]  John H. Reif,et al.  Stepwise DNA self-assemby of fixed-size nanostructures , 2005 .

[24]  Gary H. Bernstein,et al.  Molecular patterning through high-resolution polymethylmethacrylate masks , 2002 .

[25]  Wolfgang Porod,et al.  Quantum-dot cellular automata , 1999 .

[26]  David A. Ritchie,et al.  Realization of quantum-dot cellular automata using semiconductor quantum dots , 2003 .

[27]  Peter Kogge,et al.  The effects of a new technology on the design, organization, and architectures of computing systems , 2003 .

[28]  M. Lieberman,et al.  Thermodynamic behavior of molecular-scale quantum-dot cellular automata (QCA) wires and logic devices , 2004, IEEE Transactions on Nanotechnology.

[29]  Ken Mai,et al.  The future of wires , 2001, Proc. IEEE.

[30]  Yitzhak Tor,et al.  Ru(II) and Os(II) nucleosides and oligonucleotides: synthesis and properties. , 2002, Journal of the American Chemical Society.

[31]  G.H. Bernstein,et al.  Quantum-dot cellular automata , 2004, Proceedings. 7th International Conference on Solid-State and Integrated Circuits Technology, 2004..

[32]  John P. Hayes,et al.  Unveiling the ISCAS-85 Benchmarks: A Case Study in Reverse Engineering , 1999, IEEE Des. Test Comput..

[33]  Paul W. K. Rothemund,et al.  Design of DNA origami , 2005, ICCAD-2005. IEEE/ACM International Conference on Computer-Aided Design, 2005..

[34]  Andrew B. Kahng,et al.  Quantum-dot cellular automata (QCA) circuit partitioning: problem modeling and solutions , 2004, Proceedings. 41st Design Automation Conference, 2004..

[35]  Milos Hrkic,et al.  An Approach to Placement-Coupled Logic Replication , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[36]  Majid Sarrafzadeh,et al.  Replication for logic bipartitioning , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[37]  E. Winfree,et al.  Algorithmic Self-Assembly of DNA Sierpinski Triangles , 2004, PLoS biology.

[38]  Gang Quan,et al.  A realistic variable voltage scheduling model for real-time applications , 2002, ICCAD 2002.

[39]  Malgorzata Marek-Sadowska,et al.  The crossing distribution problem [IC layout] , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[40]  N. Seeman,et al.  Design and self-assembly of two-dimensional DNA crystals , 1998, Nature.

[41]  Manuel Galán,et al.  Calculation of rate constants from UV-vis spectroscopic data: an application of the Marcus-Hush model , 1996 .

[42]  P. D. Tougaw,et al.  A device architecture for computing with quantum dots , 1997, Proc. IEEE.

[43]  Yasuo Takahashi,et al.  Threshold Voltage of Si Single-Electron Transistor , 2002 .

[44]  Thomas Lengauer,et al.  Combinatorial algorithms for integrated circuit layout , 1990, Applicable theory in computer science.

[45]  John C. Bean,et al.  Growth of quantum fortress structures in Si1−xGex/Si via combinatorial deposition , 2003 .

[46]  Peter Eades,et al.  Drawing Graphs in Two Layers , 1994, Theor. Comput. Sci..

[47]  Malgorzata Marek-Sadowska,et al.  The crossing distribution problem , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[48]  Jerrold R. Griggs,et al.  Interval graphs and maps of DNA. , 1986, Bulletin of mathematical biology.

[49]  C. Lent,et al.  Clocking of molecular quantum-dot cellular automata , 2001 .

[50]  C. Lent,et al.  Power gain and dissipation in quantum-dot cellular automata , 2002 .

[51]  Annegret Liebers,et al.  Journal of Graph Algorithms and Applications Planarizing Graphs — a Survey and Annotated Bibliography , 2022 .

[52]  Martin D. F. Wong,et al.  New algorithms for min-cut replication in partitioned circuits , 1995, ICCAD.

[53]  Yuhui Lu,et al.  Bennett clocking of quantum-dot cellular automata and the limits to binary logic scaling , 2006, Nanotechnology.

[54]  R. Cowburn,et al.  Room temperature magnetic quantum cellular automata , 2000, Science.

[55]  G. Tóth,et al.  Power gain in a quantum-dot cellular automata latch , 2002 .

[56]  Dominik Stoffel,et al.  Cell replication and redundancy elimination during placement for cycle time optimization , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[57]  Marya Lieberman,et al.  A liftoff technique for molecular nanopatterning. , 2003, Journal of nanoscience and nanotechnology.

[58]  V. Metlushko,et al.  Magnetic QCA systems , 2005, Microelectron. J..

[59]  Chung-Kuan Cheng,et al.  A replication cut for two-way partitioning , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[60]  Tsutomu Sasao,et al.  Planar Decision Diagrams for Multiple-Valued Functions , 1996 .

[61]  Derck Schlettwein,et al.  A novel route to molecular self-assembly: self-intermixed monolayer phases. , 2002, Chemphyschem : a European journal of chemical physics and physical chemistry.

[62]  A. Dzurak,et al.  Demonstration of a silicon-based quantum cellular automata cell , 2006 .

[63]  S.-W. Chung,et al.  Direct Patterning of Modified Oligonucleotides on Metals and Insulators by Dip-Pen Nanolithography , 2002, Science.

[64]  C. Lent,et al.  Molecular quantum cellular automata cells. Electric field driven switching of a silicon surface bound array of vertically oriented two-dot molecular quantum cellular automata. , 2003, Journal of the American Chemical Society.

[65]  John Lillis,et al.  Timing optimization of FPGA placements by logic replication , 2003, Proceedings 2003. Design Automation Conference (IEEE Cat. No.03CH37451).

[66]  Charles E. Leiserson,et al.  Retiming synchronous circuitry , 1988, Algorithmica.