Dusty Plasmas in the Laboratory, Industry, and Space
Charged microparticles are an annoyance in the
plasmas of fusion energy schemes and semiconductor manufacturing.
But in laboratory plasmas and in space, they can be uniquely informative.
What do the rings of Saturn have in common with industrial reactors
used to manufacture semiconductor microchips? Both are examples
of systems containing charged dust particles whose dynamics are
controlled by electromagnetic and gravitational forces. More specifically,
they are examples of dusty plasmas, defined as partially or fully−ionized
gases that contain micron−size particles of electrically charged
solid material, either dielectric or conducting. Dusty plasmas are
common in astrophysical environments; examples range from the interstellar
medium to cometary tails and planetary ring systems.
The role of dust in cosmic and laboratory plasmas was discussed
early on by Irving Langmuir, Lyman Spitzer, and Hannes Alfvén, three
pioneers of plasma physics in the 20th century.1
In a 1924 speech, Langmuir described the "profound effects" he observed
in an arc discharge when minute droplets of tungsten vapor were
sputtered from the cathode into the plasma. He ascribed the unusual
effects to the attachment of electrons to the droplets, causing
them to become negatively charged and thus move about under the
influence of the electric fields within the discharge. It seems
clear that Langmuir was describing the first laboratory observation
of a dusty plasma.
Spitzer, in 1941, first discussed the processes by which dust particles
in the interstellar medium acquire charge. He pointed out that,
in addition to photoelectric charging by UV radiation, the dust
particles acquire a negative charge due to their immersion in an
ionized gas, even though the system's net charge is zero. The dust
particles become negatively charged simply because their encounters
with the swift electrons are more frequent than with the lumbering
ions. Alfvén, in his 1954 monograph On the Origin of the Solar
System, considered how the coagulation of dust particles in
the solar nebula could have led to planetesimals and subsequently
to comets and planets.
Over the past 20 years, the publication rate on the subject of dusty
plasmas has grown exponentially, spurred by two watershed discoveries.
The first occurred in the early 1980s. Images of Saturn's rings taken
by Voyager 2 revealed certain features in the B ring that were
probably as mysterious to modern planetary scientists as the rings
themselves were to Galileo in 1610. The Voyager images (see
figure 1) revealed a pattern of nearly radial "spokes"
rotating around the outer portion of Saturn's dense B ring.2
As the spacecraft approached the planet, the spokes first appeared
dark against the bright background. But as Voyager 2 withdrew
from the Saturnian system, the spokes appeared brighter than the material
This observation—that the spoke material scatters sunlight more
effectively in the forward direction—indicated that the material
is a fine dust. Perhaps the most interesting aspect of the discovery
of the spokes was that they are not stationary structures. Indeed,
they develop remarkably fast, with new spokes forming in as little
as five minutes. This short dynamical time scale rules out explanations
based solely on gravitational effects, indicating that the dust
particles are affected by electromagnetic fields.
The first proposals that the spokes might consist of charged dust
came from Jay Hill and Asoka Mendis at the University of California,
San Diego, and independently from Christoph Goertz and Greg Morfill
Goertz and Morfill showed that the charged dust particles were electrostatically
levitated about 80 km above the ring plane. They attributed the
charging to bursts of plasma generated in localized regions by micrometeoroids
that sporadically plunge into boulders in the rings.
The insertion of the Cassini spacecraft into orbit around
Saturn as this issue of Physics Today goes to press should provide
the dusty−plasma community with another boost of exciting
results. Cameras aboard Cassini, with higher spatial and
temporal resolution than Voyager's, will give us a much−improved
view of the formation and evolution of the spokes.
The second crucial development in dusty−plasma research,
in the late 1980s, expanded the field across disciplinary boundaries.
Scientists in the semiconductor industry, rather than astrophysicists,
stumbled onto a significant discovery as they searched for the source
of particulate contamination of semiconductor wafers. It had been
widely believed that particle contamination of silicon substrates
occurred mainly during handling of wafers in air. So attention was
focused on improving clean−room standards. Nobody thought
to check whether the contamination might be happening inside the
plasma processing reactors that are used to deposit and etch thin
films on the wafers.
But then Gary Selwyn of IBM made a serendipitous discovery. He was
carrying out a routine measurement with laser−induced fluorescence,
to determine the concentrations of reactive gases in a plasma.4
When Selwyn shined his laser into the plasma, his attempted measurement
of weak optical fluorescence was overwhelmed by scattering of the
incident light. The laser light was illuminating clouds of micron−sized
particles electrically suspended in the plasma above the wafer (see
Selwyn found that particles actually formed and grew in the gas
box 1), aggregating material from gases that were thought to
have been exhausted by the vacuum pump. Then, at the fateful moment
when the plasma−generating RF power was switched off, the
particles fell and contaminated the wafer. Selwyn's discovery revealed
that much of the particle contamination responsible for costly yield
losses was happening not just anywhere in the clean rooms, but inside
the plasma reactors.
Whereas a dusty plasma is something of enduring interest to an
astronomer, it was a vexing problem to be avoided by the semiconductor
manufacturer. Nevertheless, the two communities suddenly found common
ground. Both needed to understand the charging mechanisms and the
forces that transport particles from one place to another in a plasma.
But not all the progress was visible; secretiveness is often the
rule in the semiconductor industry. Successful solutions are often
hidden away as proprietary secrets.
Some solutions are known to involve plasma−chamber designs
that exploit various forces on particles to divert them toward the
vacuum pump. There have also been changes in the method of coupling
RF energy to the plasma. Rather than relying solely on capacitive
coupling, manufacturers now commonly also use inductive coupling
to power a plasma−processing reactor. As a result, the electric
fields are too weak to levitate particles large enough to cause
killer defects on etched wafers.
The discovery by the semiconductor industry that RF−powered
plasmas can levitate dust particles turned out to be a boon for
basic plasma physicists, who study such things as waves and instabilities
in ionized gases. Plasma physicists had heard astronomers talk of
dusty plasmas in space, and they were eager to study them. The laboratory
experimenter, however, has the difficulty that dust particles, unlike
plasma ions and electrons, are so massive that they fall rapidly
to the bottom of the chamber. Experimenters needed a way to fill
a volume of plasma with particles, but gravity seemed sure to thwart
Then came Selwyn's unexpected discovery. Immediately after the
appearance of his 1989 paper, plasma experimenters worldwide realized
how they could levitate particles in an RF−generated plasma.
Soon, other laboratory methods of filling a plasma volume were developed
as well. One can, for example, maintain a dusty plasma by constantly
showering particles in from above.
Dust in fusion plasmas
Much of plasma physics is devoted to developing controlled nuclear
fusion. Igniting a fusion plasma requires heating deuterium and
tritium nuclei to temperatures above 100 million kelvin. At such
high temperatures, however, any solid material is vaporized and
highly ionized. Therefore nobody expected that dust particles could
exist in a fusion plasma, much less that they could be a source
It turns out, however, that a magnetically confined fusion plasma
is in many ways dominated by the conditions at its edges, where
it comes near material surfaces. The outer portions of the plasma
typically have temperatures hundreds of times cooler than its center.
In this more benign edge plasma, solid particles can survive briefly.
Indeed, inspection of the bottoms of magnetic−confinement
fusion devices after periods of operation shows the presence of
fine dust particles.
The particles originate from the solid surfaces exposed to the
plasma. Ion bombardment of the lining material (often graphite)
liberates atoms that are thought to form dust particles and deposit
thin films on other chamber surfaces. As semiconductor engineers
know too well, such films easily flake off, creating dust particles
that fall down. In a fusion energy reactor, the ion bombardment
would be ferocious and long lasting, and the resulting accumulation
of dust could be enormous. That poses safety issues because dust
particles can retain hazardous quantities of radioactive tritium.
Charging the dust
One calculates the charge on an isolated dust particle in a plasma
just as one would calculate the charge on a larger object—for example,
an electric probe in a laboratory plasma or a satellite orbiting
in the ionospheric plasma. In each case, the object is electrically
floating and collects no net current from the plasma. That is,
where Iα represents the possible currents
to the particle. The various contributions come from electron and
ion currents, secondary electron emission, thermionic emission,
and photoelectron emission.6
The individual charging currents depend on Vs,
the electrical potential of the grain relative to the plasma. If
one assumes that the capacitance of a dust grain of radius a
is simply that of a spherical conductor of the same size, one gets
Q = 4πε0aVs
for the charge Q acquired by the particle.
In laboratory dusty plasmas, except under special circumstances,
one only needs to consider contributions from electron and ion currents.
Because the electrons typically move much faster than the positive
ions, an isolated particle immersed in a plasma acquires a negative
Vs and thus repels electrons. That lowers the
electron current and raises the ion current, thus ensuring that
the net current at equilibrium is zero.
The electron and ion currents were first derived by Langmuir and
Harold Mott−Smith for the case of particles at rest in a dilute
Inserting the expressions for those currents in equation 1, one
Vs = −2.51 kT/e
for the surface potential on a particle immersed in a hydrogen
plasma, assuming that the temperature T is the same for the
electrons and the ions.
For a particle of 1−μm radius in a plasma with kT
= 3 eV, equations 2 and 3 predict a charge of −8.4 × 10−16
C. That's about 5000 times the electron charge − e.
This electron excess is large enough that the statistical spread
and temporal fluctuation of charge are quite small in experiments
that use plastic microparticles of uniform size and composition.
Still, the charge−to−mass ratio of a plasma microparticle
is very much smaller than that of an ion.
Astrophysical and space plasmas are typically much less dense than
laboratory plasmas. And they are subjected to much more UV light.
Consequently, the dominant process for charging dust particles in
astrophysical plasmas is often photoelectron emission rather than
the collection of ambient electrons and ions. Photoelectric charging
is apparently responsible for the seemingly bizarre reports of "Moon
clouds" by Apollo astronauts in the 1960s and 70s. The report of
a "weird glow" on the horizon of the Moon turned out to be the reflection
of sunlight from Moon dust particles photoelectrically charged and
electrostatically levitated above the lunar surface.8
Experimenters have devised several methods of measuring dust−particle
charge. For example, they can measure the charge on an individual
grain by letting it fall into a Faraday cup, or they can determine
the depletion of electron density on dust or the speed of plasma
Such methods have verified, among other things, that a particle's
charge scales linearly with its diameter and that the charge is
diminished by the presence of other particles nearby.
In ordinary electron−ion plasmas without dust, the charge
on the ions generally remains fixed, even in plasmas containing
negative ions. But in a dusty plasma, the charge on a particle does
not stay fixed. Because the charge depends on the particle's surface
potential relative to the plasma potential, fluctuations in the
plasma potential brought about, for example, by plasma waves can
cause the dust charge to vary. The charge also varies stochastically,
as individual electrons and ions are absorbed at random times. For
nanometer particles, this effect can actually switch the charge's
sign. Such alternation can enhance the growth rate of particles
by collision or coagulation in the dusty plasmas of semiconductor
manufacturing reactors and prestellar nebulae.
The study of waves and instabilities has always been important
in plasma physics. The addition of dust particles to a plasma generates
many new problems to study.6,9
Theoretically, dust effects have been investigated by extending
the usual two−fluid treatment of plasmas with the addition
of a third component—the dust.
The consequences fall within two categories. First, although dusty
plasmas, like most plasmas, are electrically neutral overall, there
is an important difference. In a dusty plasma, a large fraction
of the negative charge is bound to the particles. This binding is
typically observed by noting the precipitous drop in electron current
when dust is dispersed into a plasma. The depletion of electrons
by absorption on the dust particle affects all kinds of plasma wave
modes. For example, ion acoustic waves—the plasma analog of sound
waves—propagate at higher velocities and experience far less damping
in plasmas containing negatively charged dust particles.
Second, the presence of dust particles, with their large inertia
and small charge−to−mass ratios, gives rise to new,
very low frequency modes (on the order of 1 Hz) that directly involve
the dynamics of the particles. One example is the so−called
dust acoustic wave, in which adjacent dust fluid elements are coupled
by the electric field associated with the wave rather than by collisions,
as they would be in a neutral gas.9
One striking aspect of these dust waves is that they can be imaged
by a video recording of the scattered light. The usual compressions
and rarefactions associated with the acoustic wave appear in figure
3 as bright and dark regions that propagate at the dust acoustic
speed. Because the charge−to−mass ratios of the dust particles
are very small, the wave propagation speed is very slow—only a few
centimeters per second.
Redefining the fourth state
Plasma is often termed "the fourth state of matter" because adding
energy to a solid converts it first to a liquid, then to a gas,
and finally to a plasma. With a dusty plasma, this progression closes
into a circle. It is a plasma that can have the properties of a
liquid or a solid. It forces us to reconsider exactly what is meant
by the term plasma. Defining plasma as a collection of positive
and negative charges that are not atomically bound to one another,
we encounter two possibilities. Most commonly, the charges have
abundant kinetic energy and fly easily past their neighbors, much
like molecules in a gas. That's termed a weakly coupled plasma.
The obverse is the less common strongly coupled plasma, which has
charged particles whose kinetic energy is much less than the electrostatic
potential energy between neighbors. Previously, the best−known
strongly coupled plasmas included the interiors of stars and laser−cooled
ion aggregates. In stellar interiors, the ratio γ of electrostatic
to kinetic energy is large because of high density and small interparticle
spacing. In laser cooling, γ is large because the ion temperature
is so low.
Now we have another way of making a strongly coupled plasma. In
1986, Hiroyuki Ikezi predicted10
that dust particles in plasma could acquire enough charge to produce
a large γ. As soon as Selwyn had discovered a means of levitating
dust particles, experimenters began making dusty plasmas that were
indeed strongly coupled. By their mutual Coulomb repulsion, the
suspended dust particles can organize themselves into spectacular
crystal−like arrays (see box
These arrays are reminiscent of the "Wigner crystals" whose existence
in the electron seas of metals at sufficiently low temperature was
predicted by Eugene Wigner in the 1930s. The hexagonal monolayer
array of 8−μm−diameter plastic microparticles shown
2 is called a Coulomb crystal.
Box 2 also shows an example of the diagnostic techniques that have
been developed not only to image static patterns of dust particles
in a plasma but also to permit a complete mapping of their individual
motions in dynamical situations.12
Nothing like that can be done for the ions of ordinary plasmas,
for which one can only measure statistical distributions. The ability
to image dusty plasmas at the particle level lets researchers study
the melting phase transition, phonons, and other condensed matter
phenomena with unprecedented directness.13
One manifestation of phonons that is uncommon in molecular solids
is the so−called Mach cone, a V−shaped wake created
by a moving supersonic disturbance. In a laboratory dusty plasma,
Mach cones are made by applying force to the particles by means
of laser light. Using a setup like that shown in box 2, one of us
(Goree) and coworkers swept an argon laser beam across a monolayer
suspension of plastic microparticles.12
The laser sweep caused a moving disturbance. The microparticles
were illuminated for imaging by light from a much weaker helium−neon
A Mach cone resulting from the disturbance is shown in figure
4. It's a superposition of acoustic waves, or phonons, whose wavefronts
overlap constructively to concentrate energy in a moving V−shaped
pattern, similar to the wake of a supersonic bullet in air. The cone's
opening angle θ is related to the Mach number M ≡
v/c by sinθ = 1/M, where c and v
are, respectively, the acoustic speed in the medium and the supersonic
speed of the disturbance. The acoustic speed depends on the temperature
of the dust fluid and the charge and mass of the dust particles.
Ove Havnes and coworkers at the Auroral Observatory in Tromso,
Norway have suggested that Mach cones might be found in planetary
rings, produced by big boulders plowing through fields of charged
While the boulders keep pace with the Kepler orbital velocity, they
argue, the Lorentz force of the planet's magnetic field could modify
the orbital motion of the charged dust. A remote search for Mach
cones in Saturn's rings with viewing instruments aboard the Cassini
spacecraft could yield information about the dusty plasma conditions
in regions through which Cassini would not survive direct
The remote imaging is possible because the dust particles scatter
sunlight. As the dust concentration is compressed and then rarefied
in the waves that compose the wakes, it will appear brighter and
then dimmer. Measuring a Mach cone's opening angle would yield information
about dust parameters such as the particle size.
The weightlessness provided by space vehicles in orbital free fall
is ideal for experiments on dusty plasmas. On the ground, experimenters
must contend with gravity. The prospect of a weightless laboratory
environment was so attractive that the first physics experiment
on the International Space Station (ISS), begun in
February 2001, was a dusty−plasma experiment.15
The experiment is a German−Russian collaboration. The plasma
chamber, built in Germany for the space station, has been named the
Nefedov Plasma Crystal Experiment in honor of Anatoli Nefedov, a leader
of the Russian contingent who died in 2001. The apparatus, similar
to the one shown in box
2, is about the size of a microwave oven. A video image of one
of the dust structures (figure
5) shows a variety of features, including a sharply defined void
in the center, a stable crystal−like array below the void, and
fluid vortices along the horizontal axis and outer edges.
In the absence of gravity, one has the opportunity to see both
liquid− and solidlike phenomena as other forces emerge to
affect the dynamics of the dust. Charged dust particles in plasma
are affected by their mutual electrostatic interaction and by interaction
with gas molecules and ions. Thermal gradients produce thermophoretic
forces. Ion drag, which can be the dominant force under weightless
conditions, is thought to have caused the void seen in figure 5
by pushing dust particles out of the center of the plasma chamber's
At an altitude of about 85 km, well below the orbiting ISS,
there's a fascinating example of a naturally occurring dusty plasma:
the so−called noctilucent clouds. These "night−shining"
clouds, seen at high latitudes in the early summer months, are composed
of ice crystals. The clouds form in the polar mesosphere, where
temperatures can get down to 100 K. At this lower reach of the ionosphere,
free electrons can attach to the ice particles (typically 50 nm
across) to form a dusty plasma.
Noctilucent clouds are perhaps related to observations of unexpectedly
strong radar echoes from the polar regions.16
The enormous backscatter cross section observed in the summer mesosphere
came as quite a surprise to radar scientists. Models have been developed
to relate charged dust to localized ionization and electron depletions
that would result in upper−atmosphere inhomogeneities strong
enough to account for the abnormal radar echoes. But there is, as
yet, no consensus. Curiously, there has been an increase in the
observed frequency of the noctilucent clouds over the past 30 years.
The increase may be caused by rocket engine exhaust, which is mostly
water vapor. Water vapor released at very high altitudes tends to
collect near the poles.
Ironically, work on dusty plasmas has been carried out over the
years by groups with entirely opposite motivations. Initially, industrial
scientists and engineers worked feverishly to eliminate dust from
plasma−processing devices. Meanwhile, physicists doing basic
plasma research were devising schemes to get dust into plasmas so
that they could study its effects. As is often the case, researchers
in these varied disciplines barely knew of each other's existence,
rarely talked with each other or attended the same meetings, and
seldom published in the same journals. Eventually, however, they
were brought together by the realization that they were investigating
the same basic phenomena. Nowadays they share in plasma−source
development and diagnostic techniques.
Much progress has also been made in recent years in the theoretical
and numerical analysis of dusty plasmas. Dusty plasmas challenge
modelers for a number of reasons. For example, the dust motion occurs
on a much longer time scale than that of the ions and electrons,
and the dust might have a distribution of particle sizes. The charge
on the particle is not fixed. Futhermore, the dust particles can
be strongly coupled to each other via short−range forces.
That's entirely different from dust−free plasmas, whose constituents
interact through relatively weak, long−range forces.
Nonetheless, so−called particle−in−cell (PIC) methods
are being successfully applied to dusty plasmas. The methods can handle
the inclusion of realistic complications such as ion−dust collisions
and nonspherical particle shapes. Figure
6 shows the result of a PIC calculation, by Martin Lampe and colleagues
at the Naval Research Laboratory in Washington, DC, of the three−dimensional
potential around a negatively charged dust grain immersed in a plasma
with flowing ions.17
Although the upstream potential is typical for a shielded negative
grain, a complex structure downstream shows an electrostatic wakefield
formed by positive ions that are focused into the region immediately
behind the grain. The calculated formation of this positive region
helps explain a pervasive experimental observation in dust crystals—namely,
the tendency for grains to align directly behind one another along
the direction of ion streaming.
The imposing intellectual range of physics issues touched on by
the study of dusty plasmas extends beyond plasma physics to include,
for example, the solid−liquid melting transition and vortex
flows in fluids. And size range of dusty−plasma applications
extends from microgrooves in semiconductor devices to the magisterial
rings of Saturn.
Robert Merlino and John
Goree are professors of physics at the University of Iowa
in Iowa City.
1. I. Langmuir, C. G. Found, A. F. Dittmer, Science
60, 392 (1924); H. Alfvén, On the Origin of the
Solar System, Clarendon Press, Oxford, UK (1954); L. Spitzer
Jr, Physical Processes in the Interstellar Medium, Wiley,
New York (1978).
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M. Horanyi, Annu. Rev.
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6. P. K. Shukla, A. A. Mamun, Introduction to
Dusty Plasma Physics, Institute of Physics, Bristol, UK (2002).
8. See http://www.space.com/scienceastronomy/top_10_weird.
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R. L. Merlino, A. Barkan, C. Thompson, N. D'Angelo, Phys. Plasmas 5,
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A. Piel, A. Melzer, Plasma Phys.
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B. Feuerbacher, D. Möhlmann, Phys. Rev. Lett.
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15. A. Nefedov et al., New J. Phys. 5,
Figure 1. Dynamic spokes in Saturn's B ring,
the wide bright ring just inside the prominent dark Cassini ring.
The square fields at left are successive detailed images of the
same orbiting physical region (yellow square), taken at roughly
10−minute intervals by Voyager 2 in 1981. The observed
pattern of nearly radial "spokes," appearing dark against a bright
background as the spacecraft approaches from the Sun side, changes
quite rapidly. New spokes form in as little as five minutes, which
suggests that the fine dust particles that compose them are affected
by electromagnetic fields. (Courtesy Calvin J. Hamilton.)
Figure 2. Rings of dust particles encircling
silicon wafers in a plasma processing device. In an accidental
1989 discovery, laser light was shone into a plasma used to etch
Si wafers so that the expected weak optical fluorescence would
monitor concentrations of reactive gas. Instead, the fluorescence
was overwhelmed by scattering of the incident light off unanticipated
clouds of micron−sized particles electrically suspended
in the plasma above the wafers.4
Although great pains had been taken to minimize dust contamination
of the clean room, it was discovered that the particles actually
formed and grew in the plasma. When the RF power that generates
the plasma is turned off, the particles fall onto the wafer, contaminating
it. (Inset) An electron−microscope image of a 20−μm−diameter
particle from such a dust cloud. (Adapted from ref.
Figure 3. A dust acoustic wave propagating in
a plasma shows up in a video image of light scattered by dust
clouds in the plasma. The bright bands are compression wavefronts.
Ordinary plasma waves in dustless plasmas cannot be visually imaged
in this way. The wave is essentially a sound wave in the charged
dust component of the plasma. Because the wave propagation involves
the dynamics of the heavy dust particles with small charge−to−mass
ratios, it's very slow (a few centimeters per second) and its
frequency is only on the order of a hertz. By contrast, ion−acoustic
waves in the plasma travel at kilometers per second. (Adapted
from A. Barkan et al., Phys. Plasmas 2, 3563 (1995).)
Figure 4. A Mach cone formed in a laboratory
dusty plasma by suddenly pushing plastic microparticles in a suspended
monolayer toward the left by means of an intense, movable laser
beam in a setup like that depicted in box
2. The disturbed particles are illuminated by another, less
intense laser and imaged with a video camera. False colors indicate
resulting microparticle speeds in different regions of the monolayer.
Red is fastest, blue slowest. The clearly observed Mach cone is
a superposition of supersonic wakes generated by particles moving
faster than the slow acoustic speed of the plasma's dust component,
in which Coulomb repulsion, rather than collision, is the mechanism
of acoustic propagation. The red region is about 2 cm long, and
the displayed field comprises about 104 microparticles.
(Adapted from ref.
Figure 5. A weightless dusty plasma in the Nefedov
Plasma Crystal Experiment aboard the International Space Station,
an RF−powered plasma discharge chamber device similar to
that shown in box
2. The single−frame video image shows that, in the weightless
space station environment, the micron−size dust particles
fill the entire three−dimensional plasma volume except for
a well−defined central void from which dust particles are
expelled by ions retreating from a region of positive plasma potential.
The dust distribution exhibits fluid−like vortices as well
as stable crystal−like domains. (Adapted from ref.
Figure 6. Numerically calculated equipotential
contours near a charged dust grain in a plasma in which the ions
are flowing past the grain from left to right along the z−axis
of cylindrical coordinates.17
The grain's surface potential is negative. The coordinates are
in units of the characteristic Debye shielding length λD
in the plasma. Large negative potential is shown red; large positive
is purple. Near the origin, where the grain is centered, the potential
is large and negative. But it drops off rapidly due to the shielding
by the plasma. A wake forms in the downstream direction, producing
a deep positive well. Thus ions are focused onto the region immediately
downstream of the grain. This wake accounts for the experimental
observation that dust particles tend to align directly behind
each other along the direction of ion streaming. (Courtesy of
Box 1. Unwanted Particles in Silicon Processors
Plasma systems for processing silicon wafers typically ionize a
gas by means of a parallel−plate arrangement powered by a
13.56−MHz RF source. Wafer etching is done in a plasma formed
from a combination of a buffer gas (usually argon) and silane (SiH4
a highly reactive gas. This plasma environment creates unwanted
dust particles. For example, plasma−assisted chemical reactions
lead to the formation of SiO2
particles by accretion
and coagulation of molecular ions. The growth of these particles
from a few nanometers to microns can be monitored by scattered laser
light and electron microscopy. The micrograph at right (adapted
from L. Boufendi, A. Bouchoule, Plasma Source Sci. Tech. 3
262) shows particles roughly 45 nm across.
The particles acquire negative charge by collecting electrons from
the plasma. As the particles grow bigger, their number falls (see
the graph). They eventually settle to the lower "sheath" of the
plasma, levitated at heights where the plasma's quasistatic electric
field balances them against gravity. Because electrons are so much
lighter than ions, the plasma generates quasistatic fields (the
red arrows) near both electrodes. Dust particles of various charge−to−mass
ratios find stable resting places at slightly different heights
above the lower electrode. Eventually, when the RF discharge is
turned off, the particles fall onto the wafer substrate, contaminating
it. A particle larger than half the width of an etched feature on
the wafer can cause a "killer defect." Such defects result in costly
reduction of manufacturing yield.
Box 2. Formation of a Coulomb Crystal
In a number of experiments, one of us (Goree) and coworkers formed
plasmas by applying RF power to the 23−cm−diameter electrode
at the bottom of a parallel−plate plasma chamber like that
shown in box
1. From a "salt shaker" above the electrode, we sprinkled 8−μm−diameter
plastic spheres into the plasma. The particles acquire negative
charge by collecting electrons from the plasma. Thus they become
levitated as a horizontal monolayer several millimeters above the
The suspended microparticles organize themselves by mutual electrostatic
repulsion into a planar triangular Coulomb lattice with hexagonal
The pattern is illuminated by a sheet of helium−neon laser
light and imaged by a video camera. For more dynamical studies,
we can disturb the microparticles with an intense, steerable argon
laser beam (see figure
4 and ref.