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Defect and Temperature Effects on Complex Quantum-Dot Cellular Automata Devices ()

Cummins Engine, Inc., Columbus, USA.

Department of Electrical and Computer Engineering, Valparaiso University, Valparaiso, USA.

Department of Physics and Astronomy, Center for Computational Nanoscience, Ball State University, Muncie, USA.

Z-Terra, Inc., Houston, USA.

The authors present an analysis of the fault tolerant properties and the effects of temperature on an exclusive OR (XOR) gate and a full adder device implemented using quantum-dot cellular automata (QCA) structures. A Hubbard-type Hamiltonian and the Inter-cellular Hartree approximation have been used for modeling, and a uniform random distribution has been implemented for the simulated dot displacements within cells. We have shown characteristic features of all four possible input configurations for the XOR device. The device performance degrades significantly as the magnitude of defects and the temperature increase. Our results show that the fault-tolerant characteristics of an XOR device are highly dependent on the input configurations. The input signal that travels through the wire crossing (also called a crossover) in the central part of the device weakens the signal significantly. The presence of multiple wire crossings in the full adder design has a major impact on the functionality of the device. Even at absolute zero temperature, the effect of the dot displacement defect is very significant. We have observed that the breakdown characteristic is much more pronounced in the full adder than in any other devices under investigation.

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*Journal of Applied Mathematics and Physics*,

**1**, 7-15. doi: 10.4236/jamp.2013.13003.

Conflicts of Interest

The authors declare no conflicts of interest.

[1] | C. S. Lent, P. D. Tougaw and W. Porod, “Bistable Saturation in Coupled Quantum Dots for Quantum Cellular Automata,” Applied Physics Letters, Vol. 62, No. 7, 1993, 714-716. doi:10.1063/1.108848 |

[2] | C. S. Lent, P. D. Tougaw and W. Porod, “Bistable Saturation in Coupled Quantum-Dot Cells,” Journal of Applied Physics, Vol. 74, No. 5, 1993, pp. 3558-3566. doi:10.1063/1.354535 |

[3] | P. D. Tougaw and C. S. Lent, “Logical Devices Implemented Using Quantum Cellular Automata,” Journal of Applied Physics, Vol. 75, No. 3, 1994, pp. 1818-1823. doi:10.1063/1.356375 |

[4] | C. S. Lent and P. D. Tougaw, “Lines of Interacting Quantum-Dot Cells: a Binary Wire,” Journal of Applied Physics, Vol. 64, No. 10, 1993, pp. 6227-6233. doi:10.1063/1.355196 |

[5] | C. S. Lent and P. D. Tougaw, “A Device Architecture for Computing with Quantum Dots,” Proceedings of the IEEE, Vol. 85, No. 4, 1997, pp. 541-557. doi:10.1109/5.573740 |

[6] | C. S. Lent, P. D. Tougaw, W. Porod and G. H. Bernstein, “Quantum Cellular Automata,” Nanotechnology, Vol. 4, No. 1, 1993, pp. 49-57. doi:10.1088/0957-4484/4/1/004 |

[7] | P. D. Tougaw, “Quantum Cellular Automata: Computing with Quantum Dot Molecules,” Ph.D. Dissertation, University of Notre Dame, 1995. |

[8] | E. P. Blair, E. Yost and C. S. Lent, “Power Dissipation in Clocking Wires for Clocked Molecular Quantum-Dot Cellular Automata,” Journal of Computational Electronics, Vol. 9, No. 1, 2009, pp. 49-55. doi:10.1007/s10825-009-0304-0 |

[9] | M. Liu and C. S. Lent, “Power Dissipation in Clocked Quantum-Dot Cellular Automata Circuits,” 63rd Device Research Conference Digest, Santa Barbara, 22-22 June 2005, pp. 123-124. |

[10] | L. Bonci and M. Macucci, “Analysis of Power Dissipation in Clocked Quantum Cellular Automaton Circuits,” Proceedings of the 32nd European Solid-State Circuits Conference, Montreux, 19-21 September 2006, pp. 58-61. |

[11] | F. Rojas, E. Cota and S. E. Ulloa, “Quantum Dynamics, Dissipation, and Asymmetry Effects in Quantum Dot Arrays,” Physical Review B, Vol. 66, No. 23, 2002, Article ID: 235301. doi:10.1103/PhysRevB.66.235305 |

[12] | J. Timler and C. S. Lent, “Power Gain and Dissipation in Quantum-Dot Cellular Automata,” Journal of Applied Physics, Vol. 91, No. 2, 2002, pp. 823-831. doi:10.1063/1.1421217 |

[13] | J. Timler and C. S. Lent, “Maxwell’s Demon and Quantum-Dot Cellular Automata,” Journal of Applied Physics, Vol. 94, No. 2, 2003, pp. 1050-1060. doi:10.1063/1.1581350 |

[14] | E. Cota, F. Rojas and S. E. Ulloa, “Dissipative Dynamics in Quantum Dot Cell Arrays,” Physica Status Solidi B, Vol. 230, No. 2, 2002, pp. 377-383. doi:10.1002/1521-3951(200204)230:2<377::AID-PSSB377>3.0.CO;2-6 |

[15] | F. Rojas, E. Cota and S. E. Ulloa, “Dynamic Behavior of Asymmetric Quantum Dot Cells,” Phyica E (Amsterdam), Vol. 6, No. 1-4, 2000, pp. 428-431. doi:10.1016/S1386-9477(99)00199-X |

[16] | S. E. Frost, “Memory Architecture for Quantom-dot Cellular,” M.S. Thesis, University of Notre Dame, 2005. |

[17] | K. Walus, A. Vetteth, G. A. Jullien and V. S. Dimitrov, “RAM Design Using Quantum-Dot Cellular Automata,” Technical Proceedings of the 2003 Nanotechnology Conference and Trade Show, San Francisco, 23-27 February 2003, pp. 160-163. |

[18] | M. Ottavi, V. Vankamamidi, F. Lombardi, S. Pontarelli and A. Salsano, “Design of a QCA Memory with Parallel Read/Serial Write,” Proceedings of the IEEE Computer Society Annual Symposium on VLSI: New Frontiers in VLSI Design, Tampa, 11-12 May 2005, pp. 292-294. |

[19] | M. Ottavi, V. Vankamamidi, F. Lombardi and S. Pontarelli, “Novel Memory Designs for QCA Implementation,” 5th IEEE Conference on Nanotechnology, Nagoya, 11-15 July 2005, pp. 699-702. |

[20] | M. Ottavi, S. Pontarelli, V. Vankamamidi, A. Salsano and F. Lombardi, “QCA Memory with Parallel Read/Serial Write: Design and Analysis,” IEEE Proceedings on Circuits, Devices and Systems, Vol. 153, No. 3, 2006, pp. 199-206. doi:10.1049/ip-cds:20050094 |

[21] | M. T. Niemier, “Designing Digital Systems in Quantum Cellular Automata,” M. S. Thesis, University of Notre Dame, 2000. |

[22] | M. T. Niemier and P. M. Kogge, “Problems in Designing with QCAs: Layout = Timing,” International Journal of Circuit Theory and Applications, Vol. 29, No. 1, 2001, pp. 49-62. doi:10.1002/1097-007X(200101/02)29:1<49::AID-CTA132>3.0.CO;2-1 |

[23] | L. Bonci, M. Gattobigio, G. Iannaccone and M. Macucci, “Simulation of Time Evolution of Clocked and Nonclocked Quantum Cellular Automaton Circuits,” Journal of Applied Physics, Vol. 92, No. 6, 2002, pp. 3169-3178. doi:10.1063/1.1501747 |

[24] | V. Vankamamidi, M. Ottavi and F. Lombardi, “Clocking and Cell Placement for QCA,” Proceedings of 6th IEEE Conference on Nanotechnology, Cincinnati, 17-20 June 2006, pp. 343-346. |

[25] | S. E. Frost, T. J. Dysart, P. M. Kogge and C. S. Lent, “Carbon Nanotubes for Quantum-Dot Cellular Automata Clocking,” 4th IEEE Conference on Nanotechnology, Munich, 16-19 August 2004, pp. 171-173. |

[26] | C. S. Lent, M. Liu and Y. Lu, “Bennett Clocking of Quantum-Dot Cellular Automata and the Limits to Binary Logic Scaling,” Nanotechnology, Vol. 17, No. 16, 2006, pp. 4240-4251. doi:10.1088/0957-4484/17/16/040 |

[27] | K. Hennessy and C. Lent, “Clocking of Molecular Quantum-dot Cellular Automata,” Journal of Vacuum Science & Technology, Vol. 19, No. 5, 2001, pp. 1752-1755. |

[28] | C. S. Lent and B. Isaksen, “Clocked Molecular Quantum-Dot Cellular Automata,” IEEE Transactions on Electron Devices, Vol. 50, No. 9, 2003, pp. 1890-1896. doi:10.1109/TED.2003.815857 |

[29] | V. Vankamamidi, M. Ottavi and F. Lombardi, “Two-Dimensional Schemes for Clocking/Timing of QCA Circuits,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 27, No. 1, 2008, pp. 34-44. doi:10.1109/TCAD.2007.907020 |

[30] | Y. Lu, M. Liu, and C. S. Lent, “Molecular Quantum-Dot Cellular Automata: From Molecular Structure to Circuit Dynamics,” Journal of Applied Physics, Vol. 102, No. 3, 2007, Article ID: 034311. doi:10.1063/1.2767382 |

[31] | Z. Jin, “Fabrication and Measurement of Molecular Quantum Cellular Automata,” Ph.D. Dissertation, University of Notre Dame, 2006. |

[32] | J. Jiao, “Synthesis, Characterization and Surface Attachment of Square Mixed-valence Complexes as Building Blocks for Molecular Quantum Cellular Automata,” Ph.D. Dissertation, University of Notre Dame, 2004. |

[33] | Q. Hang, “Molecular Liftoff Technology by Electron Beam Lithography for Molecular Electronic Devices,” Ph.D. Dissertation, University of Notre Dame, 2004. |

[34] | C. S. Lent and B. Isaken, “Clocked Molecular Quantum-Dot Cellular Automata,” IEEE Transactions on Electron Devices, Vol. 50, No. 9, 2003, pp. 1890-1896. doi:10.1109/TED.2003.815857 |

[35] | H. Qi, S. Sharma, Z. Li, G. L. Snider, A. O. Orlov, C. S. Lent and T. P. Fehlner, “Molecular Quantum Cellular Automata Cells Electric Field Driven Switching of a Silicon Surface Bound Array of Vertically Oriented Two-Dot Molecular Quantum Cellular Automata,” Journal of the American Chemical Society, Vol. 125, No. 49, 2003, pp. 15250-15259. doi:10.1021/ja0371909 |

[36] | Z. Li and T. P. Fehlner, “Molecular QCA Cells. 2. Characterization of an Unsymmetrical Dinuclear Mixed-Valence Complex Bound to a Au Surface by an Organic Linker,” Inorganic Chemistry, Vol. 42, No. 18, 2003, pp. 5715-5721. doi:10.1021/ic026255q |

[37] | Q. L. Hang, Y. L. Wang, M. Lieberman and G. H. Bernstein, “Molecular Patterning through High-Resolution Polymethylmethacrylate Masks,” Applied Physics Letters, Vol. 80, No. 22, 2002, pp. 4220-4222. doi:10.1063/1.1481784 |

[38] | J. Jiao, G. J. Long, F. Grandjean, A. M. Beatty and T. P. Fehlner, “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,” Journal of the American Chemical Society, Vol. 125, No. 25, 2003, pp. 7522-7523. doi:10.1021/ja035077c |

[39] | C. S. Lent, B. Isaksen and M. Lieberman, “Molecular Quantum-Dot Cellular Automata,” Journal of the American Chemical Society, Vol. 125, No. 4, 2003, pp. 1056-1063. doi:10.1021/ja026856g |

[40] | Y. Lu and C. S. Lent, “A Metric for Characterizing the Bistability of Quantum-Dot Cellular Automata,” Nanotechnology, Vol. 19, No. 15, 2008, p. 155703. doi:10.1088/0957-4484/19/15/155703 |

[41] | K. Hennessy and C. S. Lent, “Clocking of Molecular Quantum-Dot Cellular Automata,” Journal of Vacuum Science & Technology B, Vol. 19, No. 5, 2001, pp. 1752-1755. doi:10.1116/1.1394729 |

[42] | K. K. Yadavalli, A. O. Orlov, J. P. Timler, C. S. Lent and G. L. Snider, “Fanout Gate in Quantum-Dot Cellular Automata,” Nanotechnology, Vol. 18, No. 37, 2007, p. 375401. doi:10.1088/0957-4484/18/37/375401 |

[43] | A. O. Orlov, R. Kummamuru, R. Ramasubramaniam, C. S. Lent, G. H. Bernstein and G. L. Snider, “Clocked Quantum-Dot Cellular Automata Shift Register,” Surface Science, Vol. 532, 2003, pp. 1193-1198. |

[44] | J. Huang, M. Momenzadeh and F. Lombardi, “Defect Tolerance of QCA Tiles,” Proceedings of the Conference on Design, Automation and Test in Europe, Munich, 6-10 March 2006, pp. 774-776. doi:10.1109/DATE.2006.244118 |

[45] | S. Bhanja, M. Ottavi, F. Lombardi and S. Pontarelli, “Novel Designs for Thermally Robust Coplanar Crossing in QCA,” Proceedings of the Conference on Design, Automation and Test in Europe, Munich, 6-10 March 2006, pp. 786-791. doi:10.1109/DATE.2006.244120 |

[46] | M. Momenzadeh, M. Ottavi and F. Lombardi, “Modeling QCA Defects at Molecular-Level in Combinational Circuits,” IEEE International Symposium on Defect and Fault Tolerance in VLSI Systems, Monterey, 3-5 October 2005, pp. 208-216. |

[47] | M. B. Tahoori, J. Huang, M. Momenzadeh and F. Lombardi, “Defects and Fault Characterization in Quantum Cellular Automata,” Proceedings of the Nanotechnology Conference and Trade Show, Vol. 3, 2004, pp. 190-193. |

[48] | M. Liu and C. S. Lent, “Reliability and Defect Tolerance in Metallic Quantum-Dot Cellular Automata,” Journal of Electronic Testing, Vol. 23, No. 2-3, 2007, pp. 211-218. doi:10.1007/s10836-006-0627-8 |

[49] | T. J. Dysart, “Defect Properties and Design Tools for Quantum Dot Cellular Automata,” M.S. Thesis, University of Notre Dame, South Bend, 2005. |

[50] | T. J. Dysart and P. M. Kogge, “Strategy and Prototype Tool for Doing Fault Modeling in a Nano-Technology,” 3rd IEEE Conference on Nanotechnology, San Francisco, 12-14 August 2003, pp. 356-359. |

[51] | J. Han, E. Taylor, J. Gao and J. Fortes, “Faults, Error Bounds and Reliability of Nanoelectronic Circuits,” Proceedings of the 2005 IEEE International Conference on Application-Specific Systems, Architecture Processors, Samos, 23-25 July 2005, pp. 247-253. doi:10.1109/ASAP.2005.36 |

[52] | T. Wei, K. Wu, R. Karri and A. Orailoglu, “Fault Tolerant Quantum Cellular Array (QCA) Design Using Triple Modular Redundancy with Shifted Operands,” Proceedings of the 2005 Asia and South Pacific Design Automation Conference, Shanghai, 18-21 January 2005, pp. 1192-1195. doi:10.1145/1120725.1120938 |

[53] | M. Momenzadeh, J. Huang and F. Lombardi, “Defect Characterization and Tolerance of QCA Sequential Devices and Circuits,” Proceedings of the 20th IEEE International Symposium on Defect and Fault Tolerance in VLSI Systems, Austin, 3-5 October 2005, pp. 199-207. |

[54] | M. Momenzadeh, M. B. Tahoori, J. Huang and F. Lombardi, “Quantum Cellular Automata: New Defects and Faults for New Devices,” Proceedings of the 18th International Parallel and Distributed Processing Symposium, Santa Fe, 26-30 April 2004, pp. 207-214. |

[55] | M. B. Tahoori, M. Momenzadeh, J. Huang and F. Lombardi, “Defects and Faults in Quantum Cellular Automata at Nano Scale,” Proceedings of the 22nd IEEE VLSI Test Symposium, Napa Valley, 25-29 April 2004, pp. 291-296. |

[56] | A Fijany and B. N. Toomarian, “New Design for Quantum Dots Cellular Automata to Obtain Fault Tolerant Logic Gates,” Journal of Nanoparticle Research, Vol. 3, No. 1, 2001, pp. 27-31.doi:10.1023/A:1011415529354 |

[57] | C. G. Smith, “Computation without Current,” Science, Vol. 284, No. 5412, 1999, p. 274. doi:10.1126/science.284.5412.274 |

[58] | M. Governale, M. Macucci, G. Iannaccone, C. Ungarelli, and J. Martorell, “Modeling and Manufacturability Assessment of Bistable Quantum-Dot Cells,” Journal of Applied Physics, Vol. 85, No. 5, 1999, pp. 2962-2971. doi:10.1063/1.369061 |

[59] | J. L. Kanuchok, “The Thermal Effect and Clocking in Quantum-Dot Cellular Automata,” M.S. Thesis, Ball State University, Muncie, 2003. |

[60] | I. Sturzu, J. L. Kanuchok, M. Khatun and P. D. Tougaw, “Thermal Effect in Quantum-Dot Cellular Automata,” Physica E, Vol. 27, No. 1-2, 2005, pp. 188-197. doi:10.1016/j.physe.2004.11.001 |

[61] | I. Sturzu and M. Khatun, “Quantum Calculation of Thermal Effect in Quantum-Dot Cellular Automata,” Complexity, Vol. 10, No. 4, 2005, pp. 73-78. doi:10.1002/cplx.20081 |

[62] | M. K. Hendrichsen, “Thermal Effect and Fault Tolerance in Quantum-Dot Cellular Automata,” M.S. Thesis, Ball State University, Muncie, 2005. |

[63] | T. Barclay, “The Temperature Effect and Defect Study in Quantum-Dot Cellular Automata,” M.S. Thesis, Ball State University, Muncie, 2005. |

[64] | M. Khatun, T. Barclay, I. Sturzu and P. D. Tougaw, “Fault Tolerance Calculations for Clocked Quantum-Dot Cellular Automata Devices,” Journal of Applied Physics, Vol. 98, No. 9, 2005, Article ID: 094904. doi:10.1063/1.2128473 |

[65] | M. Khatun, T. Barclay, I. Sturzu and P. D. Tougaw, “Fault Tolerance Properties in Quantum-Dot Cellular Automata Devices,” Journal of Physics D: Applied Physics, Vol. 39, No. 8, 2006, pp. 1489-1494. doi:10.1088/0022-3727/39/8/006 |

[66] | B. Padgett, G. Anduwan, M. Kuntzman, I. Sturzu and M. Khatun, “Modeling and Simulation of Fault Tolerant Quantum-Dot Cellular Automata Devices,” American Physical Society, Vol. 54, 2009, p. 280. |

[67] | B. D. Padgett, “Modeling and Simulation of Fault Tolerant Properties of Quantum-Dot Cellular Automata Devices,” M.S. Thesis, Ball State University, Muncie, 2010. |

[68] | G. A. Anduwan, B. D. Padgett, M. Kuntzman, M. K. Hendrichsen, I. Sturzu, M. Khatun and P. D. Tougaw, “Fault-Tolerance and Thermal Characteristics of Quantum-Dot Cellular Automata Devices,” Journal of Applied Physics, Vol. 107, No. 11, 2010, p. 114306. doi:10.1063/1.3428453 |

[69] | G. Anduwan, “The Thermal Effect and Fault Tolerance on Nanoscale Devices: The Quantum Dot Cellular Autota,” Doctoral in Education (ED. D) Dissertation, Ball State University, Muncie, 2007. |

[70] | R. K. Kummamuru, A. O. Orlov, R. Ramasubramaniam, C. S. Lent, G. H. Bernstein and G. L. Snider, “Operation of a Quantum-Dot Cellular Automata (QCA) Shift Rester and Analysis of Errors,” IEEE Transactions on Electron Devices, Vol. 50, No. 9, 2003, pp. 1906-1913. doi:10.1109/TED.2003.816522 |

[71] | S. Bhanja, M. Ottavi, F. Lombardi and S. Pontarelli, “QCA Circuits for Robust Coplanar Crossing,” Journal of Electronic Testing, Vol. 23, No. 2-3, 2007, pp. 193-210. doi:10.1007/s10836-006-0551-y |

[72] | W. J. Chung, B. Smith and S. K. Lim, “Node Duplication and Routing Algorithms for Quantum-Dot Cellular Automata Circuits,” IEE Proceedings on Circuits, Devices and Systems, Vol. 153, No. 5, 2006, pp. 497-505. doi:10.1049/ip-cds:20050278 |

[73] | A. Chaudhary, D. Z. Chen, X. S. Hu, K. Whitton, M. Niemier and R. Ravichardran, “Eliminating Wire Crossings for Molecular Quantum-Dot Cellular Automata Implementation,” Proceedings of IEEE/ACM International Conference on Computer-Aided Design, San Jose, 6-10 November 2005, pp. 565-571. |

[74] | B. S. Smith and S. K. Lim, “QCA Channel Routing with Wire Crossing Minimization,” Proceedings of the 15th ACM Great Lakes symposium on VLSI, Chicago, 17-19 April 2005, pp. 217-220. |

[75] | W. J. Chung, B. S. Smith and S. K. Lim, “QCA Physical Design with Crossing Minimization,” Proceedings of the 5th IEEE Conference on Nanotechnology, Nagoya, 11-15 July 2005, pp. 262-265. |

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