Moving heat in nanocontacts

Drs. Wilfred T. Tysoe & Nicholas D. Spencer | TLT Cutting Edge August 2014

Nanoscale investigations show how roughness affects thermal transport across interfaces.

 

THE REMOVAL OF HEAT from a sliding interface is an important issue in tribology. Asperity-asperity contact can lead to locally high temperatures that influence additive reactions with surfaces and wear behavior. Surprisingly, though, the way in which heat moves across rough surfaces is remarkably poorly understood. Given that tribological contact occurs between micrometer- or nanometer-scale asperities, these are actually the relevant scales on which to scrutinize heat transfer across an interface.

Contact depends crucially on the applied pressure, but experimentally, theoretically and philosophically, the issue of contact on a very small scale can become problematic, as we have previously discussed in this column (see “Contact Conundrum Conquered?” June 2009 TLT, available digitally at www.stle.org.)

Bernd Gotsmann and Mark Lantz from IBM Research-Zurich in Switzerland have looked at the problem of thermal transmission on the nanoscale by measuring and modeling heat transport between a scanning silicon tip/cantilever with an integrated resistive heater and a very smooth tetrahedral amorphous carbon surface. The experiments were carried out in a vacuum so as to eliminate effects of air conductance. The principal quantity of interest to the researchers was the nanoscale pressure dependence of the thermal transfer.

During most AFM tip-surface experiments, a pressure dependence of the Hertzian tip-surface nominal contact area is observed since the tip end can be thought of as being spherical. This makes it difficult to assess the behavior of the contacts on an atomic level since both pressure and contact area change as load increases. Gotsmann and Lantz used a cunning experimental trick to avoid pressure-dependent, nominal-contact-area variation. By wearing down the probe tip by sliding it for hundreds of meters over the surface, they could form a conformal, flat-punch arrangement. Thus, pressure-dependent experiments could be relied upon to show the actual effect on thermal conductivity of the number of atoms in contact increasing as a function of load.

The experiment involved increasing the load applied to the surface by the cantilever through the surface-conformal, flattened tip, while simultaneously monitoring the temperature of the integrated heater. Since the only dissipation channel that changed with load was the heat transfer across the tip-surface interface, this measurement could yield the interfacial thermal conductance as a function of applied load (see Figure 1).


Figure 1. a, Schematic illustrating the different regimes during measurement of thermal conductivity between flat-punch heated AFM tip and taC-coated surface. Initially they are not in contact (i), and the piezo element driving the cantilever will change the distance between them. When in contact (ii–iv), the displacement is translated into a force due to loading and unloading of the cantilever. b, Measured heater temperature as a function of the piezo-displacement (directions indicated by arrows), as the tip is brought into and out of contact with the surface. c, Thermal resistance of the tip–surface contact, calculated from b. The difference between the thermal resistance with the tip in and out of contact with the surface is due to the tip-surface conductance path. Its pressure dependence is shown by the change of resistance as a function of piezo-displacement. This can be linearly fitted (green line). (Reproduced from B. Gotsmann and M.A. Lantz, Nature Materials, (2013), 12, p. 59, with kind permission)

When contacts are on the nanoscale, the thermal conductivity is quantized since the diameter of a transport channel is less than the transversal thermal coherence length. Using atomistic simulations, the authors could derive the number of nanocontacts between the flattened tip and the surface as a function of load. Assigning a quantum of thermal conductance to each nanocontact, they could then calculate the thermal conductance and its pressure dependence.

Comparing this and alternative conduction and contact theories with the experimental results, they could show that only by taking atomic roughness and quantized transport into account could the data be accurately predicted. No fitting parameters were used, and physical properties were obtained from the literature. The study thus not only provides insights into the mechanisms of conduction between surfaces with nanoscale roughness but also provides support for atomistic contact models.

FOR FURTHER READING:
Gotsmann, B. and Lantz, M.A. (2013), “Quantized thermal transport across contacts of rough surfaces,” Nature Materials, 12, pp. 59-65.


Eddy Tysoe is a Distinguished Professor of Physical Chemistry at the University of Wisconsin-Milwaukee. You can reach him at wtt@uwm.edu.


Nic Spencer is professor of surface science and technology at the ETH Zurich, Switzerland. Both serve as editors-in-chief of STLE-affiliated Tribology Letters journal. You can reach him at nspencer@ethz.ch.