Thermal conductance of single-molecule junctions

Abstract

Single-molecule junctions have been extensively used to probe properties as diverse as electrical conduction1,2,3, light emission4, thermoelectric energy conversion5,6, quantum interference7,8, heat dissipation9,10 and electronic noise11 at atomic and molecular scales. However, a key quantity of current interest—the thermal conductance of single-molecule junctions—has not yet been directly experimentally determined, owing to the challenge of detecting minute heat currents at the picowatt level. Here we show that picowatt-resolution scanning probes previously developed to study the thermal conductance of single-metal-atom junctions12, when used in conjunction with a time-averaging measurement scheme to increase the signal-to-noise ratio, also allow quantification of the much lower thermal conductance of single-molecule junctions. Our experiments on prototypical Au–alkanedithiol–Au junctions containing two to ten carbon atoms confirm that thermal conductance is to a first approximation independent of molecular length, consistent with detailed ab initio simulations. We anticipate that our approach will enable systematic exploration of thermal transport in many other one-dimensional systems, such as short molecules and polymer chains, for which computational predictions of thermal conductance13,14,15,16 have remained experimentally inaccessible.

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Fig. 1: Experimental set-up and strategy for quantifying heat transport in single-molecule junctions.
Fig. 2: Measurement of electrical and thermal conductance of Au–C6–Au single-molecule junctions.
Fig. 3: Length-dependent electrical and thermal transport in Au–alkanedithiol–Au single-molecule junctions.
Fig. 4: First-principles calculations of the thermal transport through alkanedithiol single-molecule junctions.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.

Code availability

The DFT program used to analyse the electronic structure and vibrational properties is available from www.turbomole.com. The corresponding custom-developed code for the description of phonon transport implements the procedures outlined in ref. 31 and is available from F.P. on reasonable request.

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Acknowledgements

P.R. and E.M. acknowledge funding from the US Office of Naval Research (N00014-16-1-2672, instrumentation), the US Department of Energy (DE-SC0004871, scanning probe microscopy) and the US National Science Foundation (1803983). P.R. and E.M. acknowledge the Lurie Nanofabrication Facility and the Michigan Center for Materials Characterization for facilitating the fabrication and calibration of devices. S.-Y.J. gratefully acknowledges support from a National Research Foundation (NRF) grant funded by the Korean Government (no. 2016R1A5A1012966). J.C.K. and F.P. thank the Collaborative Research Center (SFB) 767 of the German Research Foundation (DFG) for financial support. A large part of the numerical modelling was carried out using the computational resources of the bwHPC programme, namely, the bwUniCluster and the JUSTUS HPC facility.

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Contributions

The work was conceived by P.R. and E.M. The experiments were performed by L.C. The devices were fabricated by S.H. and W.J. The monolayer samples were prepared by Z.A.A. under the guidance of S.-Y.J. The calculations were performed by J.C.K. under the guidance of F.P. The manuscript was written by L.C., F.P., P.R. and E.M. with comments and inputs from all authors.

Corresponding authors

Correspondence to Fabian Pauly or Sung-Yeon Jang or Pramod Reddy or Edgar Meyhofer.

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The authors declare no competing interests.

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Peer review information Nature thanks Victor Manuel Garcia Suarez and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 Fabrication steps for thermal probes.

Step 1, ‘T’-shaped cantilever patterning. Step 2, deposition of Pt for the serpentine heater-thermometer, pads and the tip. Step 3, SiNx layer deposition for front side KOH etching. Step 4, probe cantilever release. Step 5, aligning each probe on the first shadow mask using a thin low-temperature crystal bond layer. Step 6, SiNx sputtering on the serpentine Pt heater-thermometer. Step 7, aligning each probe on the second shadow mask. Step 8, Au sputtering on the tip region. Step 9, detaching the scanning probe from the shadow mask and removing the residual crystal bond by ‘piranha’ cleaning.

Extended Data Fig. 2 Characterization of thermal and electrical properties of the scanning thermal probes.

a, Measured electrical resistance of the Pt heater-thermometer as a function of temperature. b, Measured thermal response of the scanning probe as a function of the heating frequency. c, Calibration of the thermal conductance of the probe (input heating power provided to the Pt heater-thermometer plotted against the temperature rise of the probe). The slope of the dashed fitted line corresponds to the thermal conductance of the probe.

Extended Data Fig. 3 Evaluation of mechanical properties and spatial temperature variation of the scanning thermal probes.

ac, A force of 50 nN was applied either in the normal or the transverse directions of the beams, and the deflection for each case was computed (‘Displacement’, colour key). The stiffness of the probe was calculated to be 14,000 N m−1 (a), 275 N m−1 (b) and 12.5 N m−1 (c), respectively, for the normal and two transverse directions. d, e, Calculated temperature field (colour key at right) of the scanning thermal probe when a 10-µA d.c. current was applied to the embedded serpentine Pt heater-thermometer (d) and a 10-µW heat current was input from the tip (e). The spatial temperature distribution on the island is very uniform (<5% change across locations), supporting the expectation that the distributed Pt heater-thermometer accurately measures the temperature of the suspended region.

Extended Data Fig. 4 Sample electrical and thermal conductance traces for Au–C6–Au molecular junctions.

a, b, Two independent sample recordings. Top and bottom panels show electrical and thermal conductance, respectively. The green- and yellow-shaded regions mark portions of the recordings that capture the rupture of a single-molecule junction to which the time-averaging scheme is applied, while the blue-shaded regions during the earlier portions of the withdrawal cycle represent recordings that contain events involving multi-molecule junctions. A clear last step can be identified in the electrical conductance traces (green-yellow region), indicating the breakdown of a single-molecule junction. As can be seen, there are also additional steps before the last step in the blue-shaded region. The corresponding thermal conductance traces that are shown below each electrical conductance trace do not reveal any thermal conductance steps, owing to the low signal-to-noise ratio. Insets, schematics of single-molecule junctions before and after rupture.

Extended Data Fig. 5 Simulated thermal conductance as a function of electrode displacement for C2, C6 and C10 single-molecule junctions.

The computed thermal conductance data are shown as black dots, coloured regions have the same meaning as in Fig. 4, and snapshots of junction structures are displayed as insets. The initial junction geometries before displacement of the electrodes differ from those used to generate the corresponding plots in Fig. 4, but the procedure employed for stretching the junctions is the same.

Extended Data Fig. 6 Influence of the contact geometry on computed phonon transmission for Au–C10–Au single-molecule junctions.

a, Different junction types that are used to evaluate the effect of contact geometry on the phonon transmission functions. Each terminal sulphur atom in the junction is attached to a single Au tip atom (JT1), to two Au tip atoms (JT2, JT3) or to three Au atoms (JT4). In these geometries, electrodes are oriented along the (111) crystallographic direction (JT1, JT4), the (110) direction (JT2) and the (100) direction (JT3). b, Phonon transmission as a function of energy for the different junction geometries illustrated in a.

Extended Data Fig. 7 Phonon transmission eigenchannels for C2, C6 and C10 junctions.

ac, Displacement patterns associated with the mode shapes of the most transmissive eigenchannel i = 1 for C2, C6 and C10, respectively, evaluated at energies of 13.5 meV, 14 meV and 18 meV. d, Phonon transmission associated with each of the three eigenchannels i = 1, 2, 3 for C2, C6 and C10 molecular junctions. A peak in the transmission of eigenchannel i = 1 is found to occur at energies of around 13.5 meV, 14 meV and 18 meV for C2, C6 and C10 junctions, respectively, and is indicated by the green bars. The displacement patterns of transmission eigenchannel i = 1 in ac have been evaluated at these energies.

Extended Data Table 1 Calculated thermal conductance

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Cui, L., Hur, S., Akbar, Z.A. et al. Thermal conductance of single-molecule junctions. Nature 572, 628–633 (2019). https://doi.org/10.1038/s41586-019-1420-z

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