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Analysis of Defect Tolerance in Molecular Electronics Using Information-Theoretic Measures

This study explores defect tolerance in molecular electronics using information-theoretic measures. We discuss the challenges of excessive defect rates in crossbar-based molecular integrated systems, propose a novel information processing channel model, and analyze performance limits. The paper evaluates the impact of redundancy on reliability and quantifies the relationship between reliability and defect density. Key findings highlight strategies for achieving reliable operation in the presence of defects, paving the way for future advances in molecular computing.

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Analysis of Defect Tolerance in Molecular Electronics Using Information-Theoretic Measures

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  1. Analysis of Defect Tolerance in Molecular Electronics Using Information-Theoretic Measures Jianwei Dai, Lei Wang, and Faquir JainDepartment of Electrical and Computer EngineeringUniversity of Connecticut

  2. Outline • Computational fabrics beyond CMOS roadmap • Crossbar-based molecular integrated systems • Emerging challenges • Our approach • Molecular electronics as an information processing medium • Information processing channel model • Determining the performance limits via information-theoretic concepts • Evaluation • Conclusion

  3. Pull-up Arrays AND gate Arrays Pull-down Arrays Input Pull-up Arrays Output from AND gate Arrays Output from OR gate Arrays OR gate Arrays Pull-down Arrays Nanowire crossbar structure Molecular Electronics • Nanowire-based crossbar • High density, massive redundancy • Existing systems: nanoPLA, NASICS, and CMOL,etc. • Excessive defect density: defect rate could reach 10-3 ~ 10-1 • Existing solutions • Post-fabrication reconfiguration • Error correcting codes • N-modular redundancy (NMR)

  4. Computational fabrics Information Theoretical Analysis Implementation defects, transient errors, variations Information Transfer Capacity C Research Issues Open problems in molecular electronic computing • What are the performance limits imposed by excessive non-idealities inherent in nano/molecular fabrics? • How can we achieve reliable computing with performance approaching the fundamental limits? Our approach to address these problems

  5. Entropy Example Consider a 2-input AND gate in conventional CMOS  : error probability, e.g.,  = 10-6 Quantifying Reliability via Information-Theoretic Measures • Mutual information • Channel capacity

  6. Defects in molecular electronics Crosspoint stuck-at-open Crosspoint stuck-at-closed Nanowire open Stuck-at-closed J1 J2 J1 J2 A A AB 00 01 10 11 AB 00 01 10 11 Y1Y0 XX XX XX XX J3 Y1Y0 00 00 01 11 J3 B B Y1 Y0 Y1 Y0 Stuck-at-open Nanowire open J1 J2 A A J1 J2 AB 00 01 10 11 AB 00 01 10 11 Y1Y0 X0 X1 X0 X1 J3 Y1Y0 00 10 01 11 J3 B B Y1 Y0 Y1 Y0 Defects in Molecular Electronics

  7. stuck-at-open 0 0 1 1 stuck-at-close = - p 1 p d 0 0 Undetermined nanowire open 1 1 1 Any M out of N rows Crossbar Logic Channel Model Molecular Electronics as An Information Processing Medium • Channel model • Statistical mappings reflect the randomness across different crossbars • Non-symmetric • Scalable to complex systems • Consider a single column with N crosspoints implementing M-input AND (N  M)

  8. Conditional probability of channel mapping under defects: where Determining Performance Limits via Information-Theoretic Concepts • Observation: When mibits in the input Xiare 1, the output Y could be wrong (Xi being mapped to Xe=11…11, thus a 0-to-1 output error) if the number of defect-free crosspoints in this column is no more than mi • From the definition of channel capacity, we can get

  9. Case Studies Case 1: 2-crosspoint column for a 2-input AND gate Case 2: 3-crosspoint column for a 2-input AND gate The reliability of this gate is improved by employing the inherent redundancy in molecular crossbars

  10. Any 2 out of N rows 2-input AND gate Evaluation How much redundancy is needed for a desired level of reliable performance, e.g., matching that of the CMOS technology? • Parameters • Cideal = 1 bit / use • Nr = 0 ~ 4 • Pd = 0.001 ~ 0.1

  11. Quantitative Analysis of Redundancy vs. Reliability Intrinsic relationship between the fundamental limit on reliability (Cu) and inherent redundancy (Nr) in molecular computing systems

  12. Conclusion • Excessive defects in molecular electronics raise a question on how to exploit redundancy effectively and efficiently • An information-theoretic method is developed for analysis of redundancy-based defect tolerance in molecular integrated systems • The proposed method allows quantitative study of the interplay between the fundamental limits on reliability and inherent redundancy in molecular integrated systems • Future work • Exploration of defect-tolerant design techniques approaching the fundamental limits

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