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Plasma Cushion

September 14, 2015

Love may make the world go 'round, but electrons are what hold it together. Electrons bond atoms together in solids, and matter is affected by electrical forces in many ways. In my graduate research, I was introduced to two unusual ways in which electricity can modify materials. These were electrical discharge machining and electromigration.

HfV2 is an intermetallic compound formed from hafnium and vanadium, and it's interesting because it's a superconductor, and it absorbs hydrogen.[1] It's also an extremely hard material that can't be cut by a hacksaw. The way that we prepared specimens of HfV2 for measurement was to slice them in an electrical discharge machine. Electric current pulses between a razor blade and our alloy in a tank of dielectric liquid made straight cuts at a rate of about a millimeter/hour.

You need more than just smaller transistors to make a smaller integrated circuit. The transistors would be useless without the "wires" that link them together. The "wires" in this case are planar deposits of a conducting metal, and the metal used for these interconnects was originally pure aluminum, since it's easy to deposit. When the cross-sectional area of a current-carrying wire becomes small, the current density, which is the number of electrons moving though the area in a given time, becomes large.

AMD K5 PR150 microprocessor die

There were a modest 4.3 million transistors on this chip in 1997. Advanced CPUs now have 5 billion.

Photo of an AMD K5 PR150 microprocessor die by Pauli Rautakorpi, via Wikimedia Commons.)

Small though they are, moving electrons have momentum, and this flow of electrons tend to bump atoms out of place. This is especially true at grain boundaries, and such movement of material can eventually become so large as to break the electrical connection. Electromigration was first observed about a hundred years ago, and it was discovered to be a problem in integrated circuits in the mid-1960s.

At that time, the interconnects were a few micrometers in dimension; now, they're a few tens of nanometers in dimension, so current densities are up. The effect is mitigated through lower operating voltages and lower currents; and using copper, which is less susceptible to electromigration than aluminum. Also, geometry is a factor, since the current density in a gentle conductor bend is less than that for a right angle bend.

Although it's impossible to model electromigration from first principles, there's a phenomenological model, Black's equation, that allows estimation of the mean-time-to-failure (MTTF) of an integrated circuit arising from electromigration; viz.,

Black's equation for MTTF in electromigration

in which A and n are model parameters, j is the current density, Q is an activation energy, k is the Boltzmann constant, and T is the absolute temperature. This, of course, is a typical Arrhenius law model so useful in many problems, with the values of A, n, and Q determined from experiment. Ideally, n = 2. The model is important, since testing at elevated temperature will predict performance at operating temperature.

Electric fields will affect solids suspended in liquids by the electrorheological effect in which small, non-conducting particles in an insulating fluid will align themselves with the electric field. The alignment arises from the polarizability of the particles, and the polarized particles stick together like magnets. I wrote about this effect in an earlier article (Electrorheology, April 13, 2012)

The electrorheological effect was discovered by Willis M. Wlnslow, who patented some applications in 1947, and published a paper in the Journal of Applied Physics in 1949.[2-3] Winslow was able to attain a reversible shear resistance of several hundred grams per square centimeter. Unfortunately, electric field strengths of the order of a kilovolt per millimeter are required.

Figure 1 of US Patent No. 2,417,850, 'Method and Means for Translating Electrical Impulses into Mechanical Force,' Willis M. Wlnslow, March 25, 1947

Figure 1 of US Patent No. 2,417,850, "Method and Means for Translating Electrical Impulses into Mechanical Force," Willis M. Winslow, March 25, 1947.

(Via Google Patents). [2]

A simple electrorheological material can be made from just cornstarch mixed with vegetable oil. Since electrorheological materials are potentially useful for things such as automotive braking, there's still much ongoing research. A mixture of strontium titanyl oxalate in silicone oil has been shown to give a yield stress of 200 kPa at an applied field of 5 kV/mm.[4]

The electrorheological effect gives us increased friction, but there are ways in which an electric field will reduce friction. One method is to cause migration of a lubricant to a surface. In one experiment, application of an electric field to an acrylamide hydrogel swollen with the ionic surfactant, sodium dodecyl sulfate, caused the surfactant to migrate to one surface, thereby reducing the friction coefficient by about 75%.[5] The effect is reversible, but the friction reduction is from an originally enhanced friction caused by the gel.

Scientists at CEA-LETI (Grenoble, France), the Ecole Polytechnique (Palaiseau, France), and the University Grenoble Alpes (Grenoble, France) have just shown that application of somewhat more than 50 volts between a droplet of weak hydrochloric acid and a metal plate causes the droplet to levitate.

The mechanisms involved are the electrolysis of water, creating hydrogen gas and steam at the liquid-metal interface, and excitation of this gas into a plasma by the applied voltage.[6-7] Electrolysis proceeds, since the droplet is attached to the anode of the electrical circuit, with the metal plate acting as the cathode (see figure).

Droplet schematic diagram

Schematic diagram of a plasma-levitated droplet.

The droplet is a dilute solution of hydrochloric acid. Electrolysis produces oxygen at the anode, and hydrogen at the cathode.

(Illustration by the author using Inkscape.)

This effect was found in experiments designed to investigate a phenomenon in nuclear power plant steam generators called a "boiling crisis." In this phenomenon, bubbles in water merge to form a vapor layer on heat-transfer surfaces, reducing the thermal conductivity at the interface.[7] The team of French scientists decided to study the phenomenon in an experiment using a easy way to generate gas at liquid-metal interface.

Their experiment was designed to produce electrolysis in droplets and to film their behavior at high speed. When a drop touched the metal plate and the applied potential was somewhat above 50 volts, sparks appeared at the bottom of the droplet, it levitated, and a faint blue glow could be seen at the interface between the liquid and metal.[7]

It was first thought that the droplets were just resting on a layer of the generated hydrogen gas, but it was found that the interface was filled with water vapor.[7] The hot water vapor indicated that the levitation was an example of the Leidenfrost effect.[6-7] In the Leidenfrost effect, seen when water droplets dance on a hot pan, a cushion of water vapor levitates a droplet above a hot surface.

It was concluded that the levitation was a thermal phenomenon, caused by heating of the metal surface. Stable levitation was only possible for thin cathode plates that didn't act as heat sinks.[6] While 50 volts is a relatively low voltage, the gap between the liquid and metal is likewise small, so the electric field gradient is large enough to generate a plasma.[7]

Plasma-levitated droplet

Plasma-levitated droplet.

The blue glow of the plasma below the dilute hydrochloric acid solution, generated at somewhat more than 50 volts, is clearly see.

(Photograph: Cedric Poulain, et al / CEA.)

Spectroscopy of the emitted light indicates that some cathodic sputtering occurs, since spectral lines of the metal also appear.[6] Says Cedric Poulain, a physicist at the French Alternative Energies and Atomic Energy Commission, "This method is probably an easy and original way to make a plasma."[7] While the results are quite removed from the original motivation of studying thermal transfer in nuclear reactors, they show how curiosity-driven research can yield interesting results.


  1. P. Duffer, D.M. Gualtieri, and V.U.S. Rao, "Pronounced Isotope Effect in the Superconductivity of HfV2 Containing Hydrogen (Deuterium)," Phys. Rev. Lett., vol. 37, no. 21 (November 22, 1976), pp. 1410-1413.
  2. Willis M. Winslow, "Method and Means for Translating Electrical Impulses into Mechanical Force," US Patent No. 2,417,850, March 25, 1947.
  3. Willis M. Winslow, "Induced fibration of suspensions," Journal of Applied Physics, vol. 20, no. 12 (December 1, 1949), pp. 1137-1140.
  4. Carlos S. Orellana, Jinbo He and Heinrich M. Jaeger, "Electrorheological response of dense strontium titanyl oxalate suspensions," Soft Matter, 2011, vol. 7, no. 18 (2011), pp. 8023-8029.; PDF file available, here.
  5. Hiroshi Matsukawa, Summary of "Friction Control of a Gel by Electric Field in Ionic Surfactant Solution," J. Phys. Soc. Jpn. Online News and Comments, June 10, 2010.
  6. Cedric Poulain, Antoine Dugue, Antoine Durieux, Nader Sadeghi, and Jerome Duplat, "The plasma levitation of droplets," Applied Physics Letters, vol. 107, Document No. 064101 (August 11, 2015), http://dx.doi.org/10.1063/1.4926964. This is an Open Access publication with a PDF file available, here.
  7. Droplets levitate on a cushion of blue light, American Institute of Physics Press Release, August 11, 2015.

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