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The Nanoscale Shakes

May 2, 2016

There was much variety in rock music at the start the British Invasion in the 1960s, including a few, unusual, minimalist recordings. One of these was Hippy Hippy Shake, which was a somewhat popular release by The Swinging Blue Jeans in 1964.[1] This song was covered, also by The Beatles on their Live at the BBC album in 1994.

Woodcut, 'Hoola Hoop,' 1962, NARA-558912

The hula hoop, a hip shaking phenomenon of the late 1950s and early 1960s.

An adult-sized hula hoop makes a good length reference, since they are almost exactly a meter in diameter. They became popular in the 1960s when Wham-O marketed a plastic version.

(A 1962 woodcut entitled, "Hoola Hoop," by an unknown artist, from the National Archives and Records Administration, National Archives Identifier, 558912, via Wikimedia Commons.)

Everything in the world suffers from a perpetual shake. While higher temperatures lead to greater movement of atoms, even atoms at absolute zero shake, a consequence of zero-point energy, a strange quantum mechanical effect required by the uncertainty principle. Liquid helium resists freezing until application of pressure because of its zero point energy.

Nanomechanical devices are becoming more common for use as resonators and sensors (see figure). Since nanomechanical resonators can be simply constructed right on a silicon wafer and fabricated to a desired frequency, they're poised to overtake century-old quartz crystal technology for frequency generation. Likewise, nanomechanical cantilevers can be coated with selective compounds to form extremely sensitive biochemical sensors.

nanomechanical devices, resonator, cantilever

Left, a doubly-clamped beam resonator, right, a simple cantilever, each fabricated on a silicon wafer. The length dimension L of these devices is typically of the order of a micrometer (1000 nanometer), or less. Not shown are the connections for actuation, typically electrostatic, and sensing, typically piezoresistive. (Created using Inkscape.)

In devices as small as the ones in the above figure, any little thing can disrupt their normal operation. Aside from the temperature-induced shaking, called thermomechanical noise, there's electronic noise (Nyquist–Johnson noise), noise caused by the adsorption and desorption of gas molecules on the surface, and even noise caused by the motion of lattice defects in the silicon.[2-3]

The thermal noise, which acts as a fundamental limit to the frequency stability of a resonator, is quite apparent for small structures, as shown in the figure. For reference, a quartz resonator crystal has a mass of about a gram.

Thermomechanical limit of resonator noise as a function of mass

Thermomechanical limit of resonator noise as a function of mass.

The Alan deviation is a measure of noise-induced frequency spread, (δf/f).

(Drawn using Inkscape from data in ref. 4.[4]

As the authors of ref. 4 point out, high resonator Q-factor and a little integration aids in thermomechanical noise rejection. They conclude that a very small cantilever could sense the mass of a single proton if it has a Q of about a 1000, and you're willing to integrate the signal over a millisecond.[4]

What can be smaller in mass than a graphene cantilever? A team of physicists and engineers from Cornell University (Ithaca, New York) fabricated a graphene cantilever with a reflective gold patch on its end to facilitate measurement of the tip position with a laser.[5] The affect of the impact of gas molecules is clearly seen in the figure below.

Figure caption

Movement of a 40 μm × 10 μm graphene cantilever caused by Brownian motion.

(Drawn using Inkscape from data in ref. 5.[5]

As I wrote in a previous article (Sound and Heat, August 23, 2011), phonons are the quantized lattice vibrations that carry heat in solids. Electrical engineers and other researchers at ETH Zurich (Zurich, Switzerland) and the Paul Scherrer Institute (Villigen PSI, Switzerland), have examined how phonons interact with electrons in nanoscale materials. They've published their findings in a recent issue of Nature.[6-7]

As their research demonstrates, vibrations at the outermost layers of a nanoparticle greatly affect the properties of the particle. This explains why nanoparticle-based solar cells are not as efficient as expected, since the surface vibrations interact with electrons to reduce the photocurrent.[7] Says ETH professor, Vanessa Wood, an author of the study,
"For some applications, like catalysis, thermoelectrics, or superconductivity, these large vibrations may be good, but for other applications like LEDs or solar cells, these vibrations are undesirable... Now that we have proven that surface vibrations are important, we can systematically design materials to suppress or enhance these vibrations."[7]

Nanocrystal with phonons, © ETH Zurich image by Deniz Bozyigit

Artist's impression of a nanocrystal, showing the interaction of a phonon (q) with an electron wave vector (k).

(© ETH Zurich image by Deniz Bozyigit.)

This research explains one observation involving nanocrystals used in solar cells, that a coating layer improves efficiency. A hard shell of atoms will suppress the surface vibrations.[7]


  1. Swinging Blue Jeans, The Hippy Hippy Shake, YouTube Video by TheVideoJukeBox4, January 11, 2012.
  2. A. N. Cleland and M. L. Roukes, "Noise processes in nanomechanical resonators," J. Appl. Phys., vol. 92, no. 5 (September 1, 2012), pp. 2758-2769, doi: 10.1063/1.1499745. A PDF version of this paper can be found here.
  3. A. N. Cleland, "Thermomechanical noise limits on parametric sensing with nanomechanical resonators," New Journal of Physics,vol. 7 (November 29, 2005), pp. 235-251.
  4. Marc Sansa, Eric Sage, Elizabeth C. Bullard, Marc Gély, Thomas Alava, Eric Colinet, Akshay K. Naik, Luis Guillermo Villanueva, Laurent Duraffourg, Michael L. Roukes, Guillaume Jourdan, Sébastien Hentz, "Frequency fluctuations in silicon nanoresonators," Nature Nanotechnology, February 29, 2016, doi:10.1038/nnano.2016.19. Available also on arXiv.
  5. Melina K. Blees, Arthur W. Barnard, Peter A. Rose, Samantha P. Roberts, Kathryn L. McGill, Pinshane Y. Huang, Alexander R. Ruyack, Joshua W. Kevek, Bryce Kobrin, David A. Muller, and Paul L. McEuen, "Graphene kirigami," Nature, vol. 524, no. 7564 (August 13, 2015, pp. 204-207, doi:10.1038/nature14588.
  6. Deniz Bozyigit, Nuri Yazdani, Maksym Yarema, Olesya Yarema, Weyde Matteo Mario Lin, Sebastian Volk, Kantawong Vuttivorakulchai, Mathieu Luisier, Fanni Juranyi, and Vanessa Wood, "Soft surfaces of nanomaterials enable strong phonon interactions," Nature, Advanced Online Publication (March 9, 2016), doi:10.1038/nature16977.
  7. Atomic Vibrations in Nanomaterials, ETH-Zurich Press Release, March 9, 2016.
  8. Nuri Yazdani, Animation of a vibrating lead sulfide nanocrystal (1.7 MB MP4 File).

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