Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Decision trees within a molecular memristor

Abstract

Profuse dendritic-synaptic interconnections among neurons in the neocortex embed intricate logic structures enabling sophisticated decision-making that vastly outperforms any artificial electronic analogues1,2,3. The physical complexity is far beyond existing circuit fabrication technologies: moreover, the network in a brain is dynamically reconfigurable, which provides flexibility and adaptability to changing environments4,5,6. In contrast, state-of-the-art semiconductor logic circuits are based on threshold switches that are hard-wired to perform predefined logic functions. To advance the performance of logic circuits, we are re-imagining fundamental electronic circuit elements by expressing complex logic in nanometre-scale material properties. Here we use voltage-driven conditional logic interconnectivity among five distinct molecular redox states of a metal–organic complex to embed a ‘thicket’ of decision trees (composed of multiple if-then-else conditional statements) having 71 nodes within a single memristor. The resultant current–voltage characteristic of this molecular memristor (a 'memory resistor', a globally passive resistive-switch circuit element that axiomatically complements the set of capacitor, inductor and resistor) exhibits eight recurrent and history-dependent non-volatile switching transitions between two conductance levels in a single sweep cycle. The identity of each molecular redox state was determined with in situ Raman spectroscopy and confirmed by quantum chemical calculations, revealing the electron transport mechanism. Using simple circuits of only these elements, we experimentally demonstrate dynamically reconfigurable, commutative and non-commutative stateful logic in multivariable decision trees that execute in a single time step and can, for example, be applied as local intelligence in edge computing7,8,9.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Circuit element structure and I(V) characteristics.
Fig. 2: In situ spectroscopy.
Fig. 3: Decision thicket within a single molecular film circuit element.
Fig. 4: Realization of multivariable decision trees.

Data availability

The data on which the figures are constructed and from which the conclusions are drawn are available from the corresponding authors upon reasonable request.

References

  1. 1.

    Park, H.-J. & Friston, K. Structural and functional brain networks: from connections to cognition. Science 342, 1238411 (2013).

    Article  Google Scholar 

  2. 2.

    Eliasmith, C. et al. A large-scale model of the functioning brain. Science 338, 1202–1205 (2012).

    CAS  Article  ADS  Google Scholar 

  3. 3.

    Bassett, D. S. & Sporns, O. Network neuroscience. Nat. Neurosci. 20, 353–364 (2017).

    CAS  Article  Google Scholar 

  4. 4.

    Watts, D. J. & Strogatz, S. H. Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998).

    CAS  Article  ADS  Google Scholar 

  5. 5.

    Braun, U. et al. Dynamic reconfiguration of frontal brain networks during executive cognition in humans. Proc. Natl Acad. Sci. USA 112, 11678–11683 (2015).

    CAS  Article  ADS  Google Scholar 

  6. 6.

    Huang, Z., Zhang, J., Wu, J., Mashour, G. A. & Hudetz, A. G. Temporal circuit of macroscale dynamic brain activity supports human consciousness. Sci. Adv. 6, eaaz0087 (2020).

    Article  ADS  Google Scholar 

  7. 7.

    Take it to the edge. Nat. Electron. 2, 1 (2019).

  8. 8.

    Vaughan, O. Working on the edge. Nat. Electron. 2, 2–3 (2019).

    Article  Google Scholar 

  9. 9.

    Topol, E. J. High-performance medicine: the convergence of human and artificial intelligence. Nat. Med. 25, 44–56 (2019).

    CAS  Article  Google Scholar 

  10. 10.

    Shannon, C. A Symbolic Analysis of Relay and Switching Circuits. MS thesis, MIT (1940).

  11. 11.

    Goswami, S. et al. Robust resistive memory devices using solution-processable metal-coordinated azo aromatics. Nat. Mater. 16, 1216–1224 (2017); erratum 17, 103 (2018)0.

    CAS  Article  ADS  Google Scholar 

  12. 12.

    Goswami, S., Thompson, D., Williams, R. S., Goswami, S. & Venkatesan, T. Colossal current and voltage tunability in an organic memristor via electrode engineering. Appl. Mater. Today 19, 100626 (2020).

    Article  Google Scholar 

  13. 13.

    Goswami, S. et al. Charge disproportionate molecular redox for discrete memristive and memcapacitive switching. Nat. Nanotechnol. 15, 380–389 (2020).

    CAS  Article  ADS  Google Scholar 

  14. 14.

    Goswami, S., Goswami, S. & Venkatesan, T. An organic approach to low energy memory and brain inspired electronics. Appl. Phys. Rev. 7, 021303 (2020).

    CAS  Article  ADS  Google Scholar 

  15. 15.

    Goswami, S. et al. Nanometer‐scale uniform conductance switching in molecular memristors. Adv. Mater. 32, 2004370 (2020).

    CAS  Article  Google Scholar 

  16. 16.

    Goswami, S. Resistive Memories Using Metal-Azo Aromatics. Ph.D. thesis, National Univ. Singapore (2018).

  17. 17.

    Baldwin, D. A., Lever, A. B. & Parish, R. V. Complexes of 2,2′-azopyridine with iron(II), cobalt(II), nickel(II), copper(I), and copper(II). Infrared study. Inorg. Chem. 8, 107–115 (1969).

    CAS  Article  Google Scholar 

  18. 18.

    Nagai, K. & Kitagawa, T. Differences in Fe(II)-N epsilon (His-F8) stretching frequencies between deoxyhemoglobins in the two alternative quaternary structures. Proc. Natl Acad. Sci. USA 77, 2033–2037 (1980).

    CAS  Article  ADS  Google Scholar 

  19. 19.

    Benko, B. & Yu, N.-T. Resonance Raman studies of nitric oxide binding to ferric and ferrous hemoproteins: detection of Fe(III)–NO stretching, Fe(III)–N–O bending, and Fe(II)–N–O bending vibrations. Proc. Natl Acad. Sci. USA 80, 7042–7046 (1983).

    CAS  Article  ADS  Google Scholar 

  20. 20.

    Miller, J. S. & Min, K. S. Oxidation leading to reduction: redox‐induced electron transfer (RIET). Angew. Chem. Int. Edn 48, 262–272 (2009).

    CAS  Article  Google Scholar 

  21. 21.

    Sengupta, D. et al. Size-selective Pt siderophores based on redox active azo-aromatic ligands. Chem. Sci. 11, 9226–9236 (2020).

    CAS  Article  Google Scholar 

  22. 22.

    Gass, I. A. et al. Anion dependent redox changes in iron bis-terdentate nitroxide {NNO} chelates. Inorg. Chem. 50, 3052–3064 (2011).

    CAS  Article  Google Scholar 

  23. 23.

    Winkler, C. et al. Understanding the correlation between electronic coupling and energetic stability of molecular crystal polymorphs: the instructive case of quinacridone. Chem. Mater. 31, 7054–7069 (2019).

    CAS  Article  Google Scholar 

  24. 24.

    Baldoni, M., Lorenzoni, A., Pecchia, A. & Mercuri, F. Spatial and orientational dependence of electron transfer parameters in aggregates of iridium-containing host materials for OLEDs: coupling constrained density functional theory with molecular dynamics. Phys. Chem. Chem. Phys. 20, 28393–28399 (2018).

    CAS  Article  Google Scholar 

  25. 25.

    Knuth, D. E. The Art of Computer Programming Vol. 3 (Pearson Education, 1997).

  26. 26.

    Loh, W. Y. Classification and regression trees. Wiley Interdiscip. Rev. Data Min. Knowl. Discov. 1, 14–23 (2011).

    Article  Google Scholar 

  27. 27.

    Altman, N. & Krzywinski, M. Ensemble methods: bagging and random forests. Nat. Methods 14, 933–934 (2017).

    CAS  Article  Google Scholar 

  28. 28.

    Libbrecht, M. W. & Noble, W. S. Machine learning applications in genetics and genomics. Nat. Rev. Genet. 16, 321–332 (2015).

    CAS  Article  Google Scholar 

  29. 29.

    Choi, M. Y. & Ma, C. Making a big impact with small datasets using machine-learning approaches. Lancet Rheumatol. 2, e451–e452 (2020).

    Article  Google Scholar 

  30. 30.

    Rani, P., Sarkar, N. & Liu, C. Maintaining optimal challenge in computer games through real-time physiological feedback. In Foundations of Augmented Cognition (ed. Schmorrow, D. D.) 184 (Taylor & Francis, 2005).

  31. 31.

    Borghetti, J. et al. ‘Memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464, 873–876 (2010).

    CAS  Article  ADS  Google Scholar 

  32. 32.

    Wang, Z. et al. Resistive switching materials for information processing. Nat. Rev. Mater. 5, 173–195 (2020).

    CAS  Article  ADS  Google Scholar 

  33. 33.

    Sebastian, A., Le Gallo, M., Khaddam-Aljameh, R. & Eleftheriou, E. Memory devices and applications for in-memory computing. Nat. Nanotechnol. 15, 529–544 (2020); correction 15, 812 (2020).

    CAS  Article  ADS  Google Scholar 

  34. 34.

    Gidon, A. et al. Dendritic action potentials and computation in human layer 2/3 cortical neurons. Science 367, 83–87 (2020).

    CAS  Article  ADS  Google Scholar 

  35. 35.

    Kim, K. M. & Williams, R. S. A family of stateful memristor gates for complete cascading logic. IEEE Trans. Circuits Syst. I 66, 4348–4355 (2019).

    MathSciNet  Article  Google Scholar 

  36. 36.

    Kim, Y. S. et al. Stateful in‐memory logic system and its practical implementation in a TaOx‐based bipolar‐type memristive crossbar array. Adv. Intell. Syst. 2, 1900156 (2020).

    Article  Google Scholar 

  37. 37.

    Shen, W. et al. Stateful logic operations in one-transistor-one-resistor resistive random access memory array. IEEE Electron Device Lett. 40, 1538–1541 (2019).

    CAS  Article  ADS  Google Scholar 

  38. 38.

    Xu, N. et al. A stateful logic family based on a new logic primitive circuit composed of two antiparallel bipolar memristors. Adv. Intell. Syst. 2, 1900082 (2020).

    Article  Google Scholar 

  39. 39.

    Li, C. et al. Analog content-addressable memories with memristors. Nat. Commun. 11, 1–8 (2020).

    ADS  Google Scholar 

  40. 40.

    Kim, Y. S., Son, M. W. & Kim, K. M. Memristive stateful logic for edge Boolean computers. Adv. Intell. Syst. 3, 2000278 (2021).

    Article  Google Scholar 

  41. 41.

    Du Nguyen, H. A. et al. in Proc. 2015 IEEE/ACM Int. Symp. on Nanoscale Architectures (NANOARCH´ 15) 57–62 (IEEE).

  42. 42.

    Du Nguyen, H. A. et al. On the implementation of computation-in-memory parallel adder. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 25, 2206–2219 (2017).

    Article  Google Scholar 

  43. 43.

    Yu, J., Lebdeh, M. A., Du Nguyen, H. A., Taouil, M. & Hamdioui, S. in Proc. 2020 25th Asia and South Pacific Design Automation Conf. (ASP-DAC) 385–392 (IEEE) (2020).

  44. 44.

    Du Nguyen, H. A. et al. in Proc. 2017 IFIP/IEEE Int. Conf. on Very Large Scale Integration (VLSI-SoC) 1–10 (IEEE) (2017).

Download references

Acknowledgements

This research was supported by the Singapore National Research Foundation (NRF) under the Competitive Research Programs (CRP award no. NRF-CRP15-2015-01). Sreebrata Goswami acknowledges the financial support of SERB, India, through grants SR/S2/JCB-09/2011. R.S.W. acknowledges the X-Grants Program of the President’s Excellence Fund at Texas A&M University. A.A. thanks the Agency for Science, Technology and Research (A*STAR) for its Advanced Manufacturing and Engineering (AME) Individual Research Grant (IRG), A1983c0034. D.T. acknowledges support from Science Foundation Ireland (SFI) under awards 15/CDA/3491 and 12/RC/2275_P2, and supercomputing resources at the SFI/Higher Education Authority Irish Center for High-End Computing (ICHEC). We thank S. Hooda for RBS data, L. Haidong for making the shadow masks, S. Sarkar for helping with the in situ spectroscopic measurement setup, A. Tampèz for tip-induced current and spectroscopic measurements, F. Meyer and S. Demeshko for Mössbauer measurements and D. Deb for inputs regarding the figures. We thank W. Robinett, C. R. Sinha and Q. Xia for their comments and suggestions.

Author information

Affiliations

Authors

Contributions

Sreetosh Goswami devised the project and performed the electrical and spectroscopic measurements. R.S.W. and Sreetosh Goswami designed the experiments and performed data analysis. Sreebrata Goswami introduced the materials and proposed the molecular mechanism. R.P. and S.P.R. performed molecular synthesis and characterization. M.F. provided insights into circuit design. D.T. conceived and performed the electronic structure calculations. Sreetosh Goswami, T.V., D.T., M.F., A.P., A.A., Sreebrata Goswami and R.S.W. discussed and wrote the paper.

Corresponding authors

Correspondence to Sreetosh Goswami or T. Venkatesan or Sreebrata Goswami or R. Stanley Williams.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Matthew Marinella, Ilia Valov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This document contains 9 sections of Supplementary Discussion, with 47 Supplementary Figures and 4 Supplementary Tables providing additional information on circuit element fabrication, material characterisation, electrical, spectroscopic measurements, and data analysis supporting the main text.

Peer Review File

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Goswami, S., Pramanick, R., Patra, A. et al. Decision trees within a molecular memristor. Nature 597, 51–56 (2021). https://doi.org/10.1038/s41586-021-03748-0

Download citation

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing