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STM as a Thermometer

  • Abhay Shastry
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

In Chap.  2 we showed that a measurement of temperature has to be accompanied with a measurement of voltage as well. We discuss here the experimental consequences of the results of Chap.  2. The best spatial resolution so far achieved in thermal imaging of nanoscale conductors is a few nanometers, which is much coarser than routinely achieved for other physical properties. In this chapter, we propose the scanning tunneling thermometer which is capable of mapping sub-angstrom temperature variations in nanoscale conductors. The proposed measurement scheme involves two scanning probe operations to measure the conductance and thermopower, respectively. These two measurements are shown to determine the local temperature with high accuracy in nanoscale conductors where the Wiedemann-Franz law holds quite generally. Our method, if implemented experimentally, would constitute a dramatic improvement of the spatial resolution of scanning thermometry by some two orders of magnitude.

Keywords

Thermometer Potentiometer (also called voltmeter) Engquist–Anderson definition Scanning tunneling microscope Scanning tunneling potentiometer Scanning tunneling thermometer Spatial resolution Wiedemann–Franz law Linear response theory Conductance circuit Thermoelectric circuit Gating Temperature calibration 

References

  1. 1.
    A. Shastry, S. Inui, C.A. Stafford, ArXiv e-prints 1901.09168 (2019)Google Scholar
  2. 2.
    G. Kucsko, P.C. Maurer, N.Y. Yao, M. Kubo, H.J. Noh, P.K. Lo, H. Park, M.D. Lukin, Nature 500(7460), 54 (2013). http://dx.doi.org/10.1038/nature12373. Letter
  3. 3.
    C.Y. Jin, Z. Li, R.S. Williams, K.C. Lee, I. Park, Nano Lett. 11(11), 4818 (2011). https://doi.org/10.1021/nl2026585. http://dx.doi.org/10.1021/nl2026585. PMID: 21967343ADSCrossRefGoogle Scholar
  4. 4.
    M. Mecklenburg, W.A. Hubbard, E.R. White, R. Dhall, S.B. Cronin, S. Aloni, B.C. Regan, Science 347(6222), 629 (2015).  https://doi.org/10.1126/science.aaa2433. http://science.sciencemag.org/content/347/6222/629 ADSCrossRefGoogle Scholar
  5. 5.
    J.S. Reparaz, E. Chavez-Angel, M.R. Wagner, B. Graczykowski, J. Gomis-Bresco, F. Alzina, C.M.S. Torres, Rev. Sci. Instrum. 85(3), 034901 (2014). https://doi.org/10.1063/1.4867166. http://dx.doi.org/10.1063/1.4867166 ADSCrossRefGoogle Scholar
  6. 6.
    P. Neumann, I. Jakobi, F. Dolde, C. Burk, R. Reuter, G. Waldherr, J. Honert, T. Wolf, A. Brunner, J.H. Shim, D. Suter, H. Sumiya, J. Isoya, J. Wrachtrup, Nano Lett. 13(6), 2738 (2013). https://doi.org/10.1021/nl401216y. http://dx.doi.org/10.1021/nl401216y. PMID: 23721106ADSCrossRefGoogle Scholar
  7. 7.
    D. Teyssieux, L. Thiery, B. Cretin, Rev. Sci. Instrum. 78(3), 034902 (2007). https://doi.org/10.1063/1.2714040. http://dx.doi.org/10.1063/1.2714040 ADSCrossRefGoogle Scholar
  8. 8.
    A. Majumdar, Annu. Rev. Mater. Sci. 29, 505 (1999).  https://doi.org/10.1146/annurev.matsci.29.1.505 ADSCrossRefGoogle Scholar
  9. 9.
    K. Kim, W. Jeong, W. Lee, P. Reddy, ACS Nano 6(5), 4248 (2012). https://doi.org/10.1021/nn300774n. http://dx.doi.org/10.1021/nn300774n. PMID: 22530657CrossRefGoogle Scholar
  10. 10.
    W. Jeong, S. Hur, E. Meyhofer, P. Reddy, Nanoscale Microscale Thermophys. Eng. 19(4), 279 (2015). https://doi.org/10.1080/15567265.2015.1109740. http://dx.doi.org/10.1080/15567265.2015.1109740 ADSCrossRefGoogle Scholar
  11. 11.
    F. Menges, P. Mensch, H. Schmid, H. Riel, A. Stemmer, B. Gotsmann, Nat. Commun. 7, 10874 EP (2016). http://dx.doi.org/10.1038/ncomms10874. Article
  12. 12.
  13. 13.
    B.G. Briner, R.M. Feenstra, T.P. Chin, J.M. Woodall, Phys. Rev. B 54, R5283 (1996).  https://doi.org/10.1103/PhysRevB.54.R5283. https://link.aps.org/doi/10.1103/PhysRevB.54.R5283 ADSCrossRefGoogle Scholar
  14. 14.
    G. Ramaswamy, A.K. Raychaudhuri, Appl. Phys. Lett. 75(13), 1982 (1999). https://doi.org/10.1063/1.124892. http://dx.doi.org/10.1063/1.124892 ADSCrossRefGoogle Scholar
  15. 15.
    W. Wang, K. Munakata, M. Rozler, M.R. Beasley, Phys. Rev. Lett. 110(23) (2013).  https://doi.org/10.1103/PhysRevLett.110.236802
  16. 16.
    K.W. Clark, X.G. Zhang, G. Gu, J. Park, G. He, R.M. Feenstra, A.P. Li, Phys. Rev. X 4, 011021 (2014).  https://doi.org/10.1103/PhysRevX.4.011021. http://link.aps.org/doi/10.1103/PhysRevX.4.011021 Google Scholar
  17. 17.
    P. Willke, T. Druga, R.G. Ulbrich, M.A. Schneider, M. Wenderoth, Nat. Commun. 6, 6399 (2015). http://dx.doi.org/10.1038/ncomms7399 ADSCrossRefGoogle Scholar
  18. 18.
    R. Landauer, IBM J. Res. Dev. 1(3), 223 (1957). https://doi.org/10.1147/rd.13.0223 CrossRefGoogle Scholar
  19. 19.
    Y. Dubi, M. Di Ventra, Nano Lett. 9, 97 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    J.P. Bergfield, S.M. Story, R.C. Stafford, C.A. Stafford, ACS Nano 7(5), 4429 (2013). https://doi.org/10.1021/nn401027u CrossRefGoogle Scholar
  21. 21.
    J. Meair, J.P. Bergfield, C.A. Stafford, P. Jacquod, Phys. Rev. B 90, 035407 (2014).  https://doi.org/10.1103/PhysRevB.90.035407. http://link.aps.org/doi/10.1103/PhysRevB.90.035407 ADSCrossRefGoogle Scholar
  22. 22.
    J.P. Bergfield, M.A. Ratner, C.A. Stafford, M. Di Ventra, Phys. Rev. B 91, 125407 (2015).  https://doi.org/10.1103/PhysRevB.91.125407. http://link.aps.org/doi/10.1103/PhysRevB.91.125407 ADSCrossRefGoogle Scholar
  23. 23.
    K. Kim, J. Chung, G. Hwang, O. Kwon, J.S. Lee, ACS Nano 5(11), 8700 (2011). https://doi.org/10.1021/nn2026325. http://dx.doi.org/10.1021/nn2026325. PMID: 21999681CrossRefGoogle Scholar
  24. 24.
    S. Gomès, A. Assy, P.O. Chapuis, Phys. Status Solidi A 212(3), 477 (2015).  https://doi.org/10.1002/pssa.201400360. http://dx.doi.org/10.1002/pssa.201400360 ADSCrossRefGoogle Scholar
  25. 25.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Brooks/Cole - Thomson Learning, Pacific Grove 1976)Google Scholar
  26. 26.
    N. Mosso, U. Drechsler, F. Menges, P. Nirmalraj, S. Karg, H. Riel, B. Gotsmann, Nat Nano 12(5), 430 (2017). Letter. http://dx.doi.org/10.1038/nnano.2016.302
  27. 27.
    L. Cui, W. Jeong, S. Hur, M. Matt, J.C. Klöckner, F. Pauly, P. Nielaba, J.C. Cuevas, E. Meyhofer, P. Reddy, Science 355(6330), 1192 (2017).  https://doi.org/10.1126/science.aam6622. http://science.sciencemag.org/content/355/6330/1192 ADSCrossRefGoogle Scholar
  28. 28.
  29. 29.
  30. 30.
  31. 31.
  32. 32.
  33. 33.
    J.R. Widawsky, P. Darancet, J.B. Neaton, L. Venkataraman, Nano Lett. 12(1), 354 (2012). https://doi.org/10.1021/nl203634m. http://dx.doi.org/10.1021/nl203634m. PMID: 22128800ADSCrossRefGoogle Scholar
  34. 34.
    J.P. Bergfield, C.A. Stafford, Nano Lett. 9, 3072 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    J. Crossno, J.K. Shi, K. Wang, X. Liu, A. Harzheim, A. Lucas, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe, T.A. Ohki, K.C. Fong, Science 351(6277), 1058 (2016).  https://doi.org/10.1126/science.aad0343. http://science.sciencemag.org/content/351/6277/1058 ADSCrossRefGoogle Scholar
  36. 36.
    M. Tsutsui, T. Kawai, M. Taniguchi, Sci. Rep. 2 (2012). Article Number 21. http://dx.doi.org/10.1038/srep00217
  37. 37.
    J.P. Bergfield, J.D. Barr, C.A. Stafford, Beilstein J. Nanotechnol. 3, 40 (2012).  https://doi.org/10.3762/bjnano.3.5 CrossRefGoogle Scholar
  38. 38.
    M. Kiguchi, O. Tal, S. Wohlthat, F. Pauly, M. Krieger, D. Djukic, J.C. Cuevas, J.M. van Ruitenbeek, Phys. Rev. Lett. 101, 046801 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    J.D. Barr, C.A. Stafford, J.P. Bergfield, Phys. Rev. B 86, 115403 (2012).  https://doi.org/10.1103/PhysRevB.86.115403. https://link.aps.org/doi/10.1103/PhysRevB.86.115403 ADSCrossRefGoogle Scholar
  40. 40.
    M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Abhay Shastry
    • 1
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada

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