Brandon - Doctoral Preliminary Exam

Steven Brandon 31 July 2004

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WRITTEN PRELIMINARY DOCTORAL EXAMINATION FOR STEVEN BRANDON

Dr. Paul L. Dawson - July 21, 2004

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PhD examination for Steve Brandon (7-21-04). You have 10 days to finish

this so you can have plenty of time to think about the solution.

1. Nanotechnology is currently a focus of scientific research. I had an

idea that might be considered nanotechnology. The idea is related to the

generation of nanoscale electrical “sparks” on surfaces to inhibit or kill bacteria. The questions I have related to this idea are:

a. What is the minimum distance (gap) between two points that can

produce an electrical spark? b. What type of particles could be embedded on a surface that when

the whole surface was charged with an electrical impulse would generate sparks?

c. What is the minimum electrical charge needed to generate a spark between our nanoparticle gaps?

2. The big follow-up question is develop a detailed description of how you

would develop and test a 3 x 3 inch surface that when charged with a suggested amount of electricity, would produce numerous sparks across the

whole surface.

Since I know what detail you go into on all of your work this will be the only question I have for you. Also, if we can develop this I would like to include you in an invention disclosure, so we can keep this confidential until we see

if it is feasible.


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Question 1a What is the minimum distance (gap) between two points that can produce an electrical spark?

Sparks

A spark gap consists of an arrangement of two conducting electrodes

separated by a gap filled with some gas (usually air). When a suitable

voltage is supplied, a spark forms, ionizing the gas and drastically reducing its electrical resistance. An electric current then flows until the path of

ionized gas is broken. This happens usually when the voltage drops, but in

some cases when the heated gas rises, stretching out and then breaking the

filament of ionized gas. Usually the action of ionizing the gas is violent and disruptive, often leading to sound (ranging from a snap for a spark plug to

thunder for a lightning discharge), light and heat.1 (See Figure 1, below.)

Figure 1: A spark gap2

Plasma

Refer to Appendix Section A1, Sparks and Lightning, for an entertaining

primer on the physics of sparks and lightning. This article explains that

ionized gas produced by sparks is plasma, the fourth state of matter as distinguished from solids, liquids and gas. Figure 2, below, illustrates this

concept.


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Figure 2: Four states of matter3

Plasmas consist of freely moving charged particles, i.e., electrons and ions.

Formed at high temperatures when electrons are stripped from neutral atoms, plasmas are common in nature. For instance, stars are predominantly plasma. Plasmas are the referred to as "Fourth State of

Matter" because of their unique physical properties, distinct from solids,

liquids and gases. Plasma densities and temperatures vary widely.4 Figure 3, below, illustrates the relationship between lightning (and sparks) and

other forms of plasma.


4

Figure 3: Various kinds of plasma. 5

Destruction of bacteria and other micro-organisms by plasmas has been

reported. Plasma exposure, while being lethal to both Gram-positive and Gram-negative bacterial classes, also produced gross structural damage in

the Gram-negative E. coli while none was observed in the more structurally

robust Gram-positive Bacillus subtilis.6 A one-atmosphere, uniform-glow discharge plasma (OAUGDP), is capable of operating at atmospheric

pressure in air and providing antimicrobially active species at room

temperature. OAUGDP exposures have reduced log numbers of bacteria (Escherichia coli, Staphylococcus aureus, and Pseudomonas aeruginosa),

bacterial endospores (Bacillus subtilis and Bacillus pumilus), and various

yeast and bacterial viruses on a variety of surfaces. These surfaces included

polypropylene, filter paper, paper strips, solid culture media, and glass. Experimental results showed at least a 5 log10 colony forming units (CFU)

reduction in bacteria within a range of 15 to 90 s of exposure.7 A device

using electrostatic charge to remove airborne bacteria from poultry plants is described in Section A8, Zapping Airborne Salmonella and Dust.8 Another

paper presents the results of a study involving plasma arcs submerged in

water.9


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Paschen Curve

The article in Appendix Section A2, Electric Sparks, gives a technical

explanation of the physics of sparks and introduces Paschen’s Law, which

states that the voltage difference across a gap between oppositely charged

electrodes, V, is a function of the product of the gas pressure in the gap, p, and the distance separating the two electrodes, the “spark gap,” d, i.e., V =

f(pd). The article in Section A3, Paschen’s Law, provides formulas relating

breakdown voltage to the gas pressure-spark gap product, pd. These

formulas indicate a roughly linear relationship between breakdown voltage, which must be overcome to initiate a spark discharge, and product pd. See

Figure 4, below.

Figure 4: The Paschen Curve10

The linear range of pd values, for which these formulas are valid, occurs at

pd values greater than about 25 mBar-mm (1.9 torr-cm). At atmospheric

pressure in air, this corresponds to spark gap, d, of about 25 µm. As the pd product is reduced below about 25 mBar-mm, either by reducing pressure or

by reducing the spark gap, the breakdown voltage begins to level off

reaching a minimum near 7.5 mBar-mm (0.57 torr-cm). This corresponds to

a spark gap of about 7 µm in air at atmospheric pressure (at which point the breakdown voltage has fallen to its minimum value in atmospheric pressure

air, 327 V)11. Below this minimum, the voltage required to initiate a spark

increases rapidly.12 (See Section A6, The Paschen Curve, for a more detailed

description of this phenomenon.)


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Most commonly, low pd values have been obtained by reducing gas

pressure. This is the approach employed in a device known as a pseudo-spark switch which is used in high voltage applications. Since, according to

the Paschen Law, breakdown voltage is a function of the product pd, the

phenomenon described above should apply equally well to atmospheric

pressure applications with microscopic spark gaps (d < 25 µm). This means

that, while it is possible to produce sparks in atmospheric pressure air with

microscopic spark gaps, the voltage which must be overcome to initiate the spark may become so large as to become impractical.

However, Wallash and Levit13, who report the results of their study of electrical breakdown behavior for devices with micron and sub-micron gaps

between conductors, came to a different conclusion. They indicate that the

conventional Paschen curve does not adequately describe behavior in these

small spark gaps. Instead they explain that a Modified Paschen Curve should be employed for air at 1 atmosphere pressure and spark gaps smaller than 5 µm. See Figure 5, below.

Figure 5: Paschen curve and Modified Paschen Curve

The modified Paschen curve is explained in more detail in another

reference.14

Wallash and Levit conclude “that breakdown in air at atmospheric pressure can occur well below the Paschen curve minimum of 360V and should be

considered in the processing, handling and operation of devices with micron

and sub-micron gaps.” This paper also presents the following table

describing the relevant physics that dominate over various spark gap scales down to spark gaps below 2 nm, which is well into the scale of organic

macromolecules.


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Figure 6: Spark current mechanism table

From this, I can surmise that there is no practical lower limit to the minimum distance between two points that can produce an electrical spark.

Question 1b What type of particles could be embedded on a surface that when the whole surface was charged with an electrical impulse would generate sparks?

Conductors

A conductor is a substance or body that offers small resistance to the passage of an electric current.15 The article in Section A7, Static Electricity

Sparks and Lightning, gives a good explanation of the necessity for conductors to form sparks. Sparks need conductors, so that the electrons

can freely move about and gather enough charges together to be able to

jump from one material to another. Static electricity is formed and gathered

on the surface of a non-conductor, but it must be then transferred to a

conductor to cause a spark. When a conductor—like a metal rod—is brought

near a charged non-conductor, the free electrons in the conductor will move

to one end or the other of the rod, depending on whether the non-conductor

surface is positive or negative.


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Figure 7: Opposite charges in conductor move toward non-conductor

When the conductor is brought into contact with the non-conductor, the

electrical charges on the surface of the non-conductor are "sucked" into the

conductor. In other words, if negative charges are on the surface of the non-conductor, these electrons will move into the conductor. If positively charged

atoms are on the surface, electrons from the metal or conductor will neutralize those atoms, resulting in an excess of positive charges in the conductor. If another conductor is brought near the first conductor, the

same thing will happen. Since electrons can move so freely in a conductor, many may collect near the surface and actually jump across the air gap as a

spark.16

In science and engineering, conductors are materials that contain movable

charges of electricity. When an electric potential difference is impressed at separate points on a conductor, an electric current appears in accordance

with Ohm's law. While many conductors are metallic, there are many non-metallic conductors as well. Under normal conditions, all materials offer some resistance to flowing charges, which generates heat. The motion of

charges also creates an electromagnetic field around the conductor that exerts a mechanical force on the conductor. Consequently, a conductor of a

given material and volume (length x cross-sectional area) has a limit to the

current it can carry without being destroyed thermally or mechanically. This effect is especially critical in printed circuits, where conductors are relatively

small.17

For these reasons, it is desirable to select a material with a high electrical

conductivity. Table 1, below lists physical properties, including electrical conductivity, of a variety of conductive materials. I have sorted this table in

order of descending electrical conductivity and added the properties of 316L

stainless steel (SS) from another source18 to compare this metal, commonly

used in food processing applications, to the others materials listed in Table

1.


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Table 1: Physical properties of various materials19

Material

Melting

Pt.

Boiling

Pt. Density

Thermal

Conductivity

Electrical

Conductivity

- ºC ºC g/cm³ W/cm-K 106/ohm-cm

silver 962 2212 10.5 4.29 0.63

copper 1083 2567 8.96 4.01 0.596

gold 1064 2807 19.3 3.17 0.452

aluminum 660 2467 2.70 2.37 0.377

magnesium 649 1090 1.74 1.56 0.226

rhodium 1966 3727 12.4 1.5 0.211

iridium 2410 4130 22.5 1.47 0.197

tungsten 3410 5660 19.3 1.74 0.189

molybdenum 2617 4612 10.2 1.38 0.187

cobalt 1495 2870 8.90 1.00 0.172

zinc 420 907 7.14 1.16 0.166

nickel 1453 2732 8.90 0.907 0.143

ruthenium 2310 3900 12.20 1.17 0.137

iron 1535 2750 7.86 0.802 0.0993

platinum 1772 3827 21.4 0.716 0.0966

palladium 1552 3140 12.0 0.718 0.0950

tin 232 2270 7.30 0.666 0.0917

chromium 1857 2672 7.19 0.937 0.0774

tantalum 2996 5425 16.6 0.575 0.0761

niobium 2468 4742 8.55 0.537 0.0693

thorium 1750 4790 11.7 0.540 0.0653

rhenium 3180 5627 21.0 0.479 0.0542

vanadium 1890 3380 5.80 0.307 0.0489

lead 328 1740 11.4 0.353 0.0481

uranium 1132 3818 18.9 0.276 0.0380

hafnium 2227 4602 13.1 0.230 0.0312

zirconium 1852 4377 6.49 0.227 0.0236

titanium 1660 3287 4.50 0.219 0.0234

scandium 1539 2832 3.00 0.158 0.0177

yttrium 1523 3337 4.50 0.172 0.0166

316L SS 1397 7.95 0.134 0.0135

manganese 1244 1962 7.43 0.078 0.00695

graphite 3550 4827 2.62 1.29 0.00061

It is clear that while, 316L SS has the highly desirable property of resistance

to corrosion, which makes it a good choice for food applications, it is not a

particularly good electrical conductor. This means that it would exhibit large voltage loss between the power supply and the spark gap. This lost energy

would be dissipated as heat resulting in high temperature in the metal,

which could damage the structure of the electrode assembly.

It is interesting to note that graphite is reported to have relatively high

thermal conductivity and low electrical conductivity. Actually, the properties

of graphite are highly anisotropic due to its planar crystalline structure, i.e.,

its properties vary greatly depending on whether the property is measured


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parallel to, or normal to the orientation of the crystalline structure. A form

of carbon that is currently of great interest is the carbon nanotube, which has been reported to have very high electrical conductivity along the length

of the tube. However, there is considerable controversy about these

numbers and there is still much development to be done to be able to

assemble the nanotubes into useful, larger-scale structures. Section A9,

Carbon Nanotubes, provides background information.

It is probably wise to consider an electrode material with high conductivity

while retaining the high degree of corrosion resistance required for food

processing applications. The two materials with the highest conductivity listed in Table 1, silver and copper, are both subject to formation of oxides

on their surfaces in food processing environments. Such an oxide layer

would act as an insulator blinding off the surface of the electrode and

inhibiting spark formation. The fourth material in the table, aluminum is resistant to acids, but is quickly attacked by the alkaline cleaning solutions commonly used in food plants. The third material listed in the table, gold,

combines the excellent corrosion resistance with high electrical conductivity, making it an excellent choice for our particle-electrode material. The obvious shortcoming of gold is its high cost. However, depending of the

design of the spark producing apparatus, it is possible that little gold would be required, thereby holding costs to reasonable levels. For these reasons,

my choice for material for the particles could be embedded on the surface of the spark apparatus is gold. Figure 8, below, shows roughly 15-nm gold nanoparticles.

Figure 8: Gold Nanoparticles20

Question 1c What is the minimum electrical charge needed to generate a spark between

our nanoparticle gaps?

According to Wallash and Levit13, for gaps larger than 2 nm but less than

5000 nm, spark discharge is by field emission of electrons from metals. The


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field emission current, I, is described by the Fowler-Nordheim (F-N) equation

,

where E is the electric field, Φ is the work function, and a and b’ are

constants. If current is due to field emission, a plot of 1/E vs. ln(I/E²) -- or

1/V vs. ln(I/V²) -- should yield a straight line with a negative slope that is proportional to the work function of metal. This plot is known as the Fowler-

Nordheim (F-N) plot and can be used to determine whether the current flow

is due to field emitted electrons.

To obtain some realistic values for the work function, and the constants a

and b’, I will use data presented by Wallash and Levit for a 0.9-µm gap device in 1 atmosphere air. See Figure 9, below.

Figure 9: Fowler-Nordheim plot for 0.9-µm gap device near breakdown

The Fowler-Nordheim formula can be re-arranged as follows:

E

b

aeE

I

2

3

'

2 .

Taking the natural logarithm of both sides of this equation yields,


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E

ba

E

I 2

3

2

'lnln

which can, in turn, be rearranged to

aE

bE

Iln

1'ln 2

3

2

A least-squares linear curve fit of 1/E vs. ln(I/E²) data reported by Wallash and Levit in Figure 8, above was found to have a intercept of -24.832, the

constant a = 1.6429 x 10-11. Similarly, since the slope was found to be -0.9117, the term b’Φ3/2 = -0.9117 (µm-Vx10-3). Since the x-axis was plotted

as 1/E (µm-Vx10-3), the slope can be multiplied by 1000 to get b’Φ3/2 = -911.7 (µm-V). Armed with these numbers, I can return to the F-N formula

and solve for I, current.

E

b

aeEI

2

3

2

Substituting the values determined for a and for the term b’Φ3/2 yields,

E

Vm

eEI

7.911

112 106429.1

Since E = V/d and d = 0.9-µm (in this case), E=1.11V (µm-1). So, I =

(1.11V µm-1)2 x (1.6429 x 10-11) x exp[-911.7 (µm-V)/1.11V (µm-1)]. I

used Excel to produce the following table showing calculated current for

voltages from 120 V to 150 V.


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Table 2: Calculated Current

Gap Voltage E E2

a b’Φ3/2

(b’Φ3/2

/E) exp(-) I I

µm V V-µm (V-µm)2

µm-V A nA

0.9 120 133.3 17778 1.6429E-11 -911.7 -6.8378 0.0011 3.1324E-10 0.31

0.9 122 135.6 18375 1.6429E-11 -910.7 -6.7183 0.0012 3.6486E-10 0.36

0.9 124 137.8 18983 1.6429E-11 -909.7 -6.6027 0.0014 4.2311E-10 0.42

0.9 126 140.0 19600 1.6429E-11 -908.7 -6.4907 0.0015 4.8862E-10 0.49

0.9 128 142.2 20227 1.6429E-11 -907.7 -6.3823 0.0017 5.6202E-10 0.56

0.9 130 144.4 20864 1.6429E-11 -906.7 -6.2772 0.0019 6.4397E-10 0.64

0.9 132 146.7 21511 1.6429E-11 -905.7 -6.1752 0.0021 7.3518E-10 0.74

0.9 134 148.9 22168 1.6429E-11 -904.7 -6.0763 0.0023 8.3638E-10 0.84

0.9 136 151.1 22835 1.6429E-11 -903.7 -5.9804 0.0025 9.4831E-10 0.95

0.9 138 153.3 23511 1.6429E-11 -902.7 -5.8872 0.0028 1.0718E-09 1.07

0.9 140 155.6 24198 1.6429E-11 -901.7 -5.7966 0.0030 1.2076E-09 1.21

0.9 142 157.8 24894 1.6429E-11 -900.7 -5.7087 0.0033 1.3566E-09 1.36

0.9 144 160.0 25600 1.6429E-11 -899.7 -5.6231 0.0036 1.5197E-09 1.52

0.9 146 162.2 26316 1.6429E-11 -898.7 -5.5399 0.0039 1.6977E-09 1.70

0.9 148 164.4 27042 1.6429E-11 -897.7 -5.4590 0.0043 1.8916E-09 1.89

0.9 150 166.7 27778 1.6429E-11 -896.7 -5.3802 0.0046 2.1024E-09 2.10

Figure 10, below, is a plot of voltage vs. current from Table 2.

Current vs. Voltage

0.00

0.50

1.00

1.50

2.00

2.50

110 120 130 140 150 160

Voltage, V

Cu

rren

t, n

A

Figure 10: Voltage vs. Current plot based on my calculated current values

This compares favorably with the same data presented by Wallash and Levit (see Figure 11, below).

Figure 11: Voltage vs. Current plot reported by Wallash and Levit


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In their tests, they began with zero volts across the electrodes and then

gradually increased the voltage while monitoring current. They report that the discharge occurred in their test rig with a 0.9-µm gap at 151 V and

about 2.1 nA (nanoamperes) of electrical current.

The precise current required to produce sparks in the device under

consideration would depend on the design details of the device. However, it

is reasonable, based on the discussion above, to expect that the current requirement would be very low.

Question 2 Develop a detailed description of how you would develop and test a 3 x 3

inch surface that when charged with a suggested amount of electricity, would produce numerous sparks across the whole surface.

Development

My approach would be to use gold (for reasons described above) electrodes supported by a non-conducting substrate, such as soda glass. The basic

concept is illustrated in Figure 12, below. Thin layers of gold are arranged in parallel lines alternating between anodic and cathodic electrodes. Electrical

connections are made to each side of the array inducing a voltage difference between the parallel gold bands. These spaces serve as the spark gaps

permitting the formation of transient plasma discharges between conducting

gold bands at numerous locations over the surface of the device.

Figure 12. Conceptual diagram of spark producing device

In the actual device, the parallel bands of gold would be much smaller than

shown in the conceptual illustration in Figure 12, above. The actual device

would have thousands of microscopic, parallel bands of gold with narrow

gaps separating the oppositely charged, alternating bands. The dimension of

the spark gap should be selected to produce sparks of a scale sufficient to be

effective in killing bacterial cells, which typically range from about 0.2 to 2

µm (200 to 2000 nm). For this reason, I believe the optimal spark gap for


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this application would be in the range of 1 µm, rather than the nanometer

scales (1 to 100 nm).

Methods for forming metallic nanoparticle monolayers on glass are described

by Shipway, et al. One method, as shown in Figure 13, below, involves

adsorption of the nanoparticle onto a thin film of polymerized siloxane.

Figure 13. Construction of Au-nanoparticle monolayers on glass21

Another approach, also described by Shipway, et al., is photolithography.

This is illustrated in Figure 14, below.


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Figure 14: Photo-lithographically deposited gold monolayer structures22

Microphotograph C, in Figure 14, above, is particularly interesting, since it shows a structure that is similar to the one I am proposing for the sparking

device. Photolithography, a well established technology, is described in detail in Section A10, Photolithography.23

Testing

A very simple spark gap setup is presented in Section A8, A Simple Spark

Gap Test Rig. The test setup for the proposed spark device should be similar to that used by Wallash and Levit in their study of sub-micron spark gaps as

shown in Figure 15, below.

Figure 15. Experimental setup used by Wallash and Levit.24


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This test rig consists of a Keithley 2400 power source-measurement unit to

supply voltage and measure current to the spark gap device with sufficient sensitivity to measure nano-ampere currents. A Tektronix CT-6 current

probe and a LeCroy 9362 digital oscilloscope were used to measure the

current transient at the point of breakdown. (This may not be useful in a

device in which numerous sparks are planned.) This system was connected

to a computer equipped with LabView software to automate data acquisition.

The test procedure used by Wallash and Levit was to make electrical contact

with the terminals on each side of the spark gap device and then ramp the

voltage from zero volts, in small steps, while measuring the current, until breakdown occurred. The proposed setup would use a similar procedure,

however, rather than stopping with the first spark is observed, the voltage

would be set to a level that produces numerous small sparks.

The effectiveness of the device would be measured by exposing a challenge organism (preferably a non-pathogen, for safety reasons) at a know

concentration to the device and then comparing the reduction in cell counts before and after exposure to a prescribed spark treatment of set voltage and duration. This would be replicated several times at several selected voltage

levels and durations.

The bacterial cell concentration before and after exposure to the device could be measured by filtering a specified volume of the test gas (which

would generally, or always, be air) and then either microscopically examining the filter disk (direct count method) or by transfering the exposed

filter disk to a growth medium and allowing the viable cells to grow into easily observable colonies (plate count method). Such a method is

described in detail by Kelly-Wintenberg, et al.25


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Appendix

Section A1: Sparks and Lightning 26

While attempting to explain sparks and lightning to some friends, I realized that I

didn't have a good gut-level understanding of them myself. As usual, my lack of

understanding was an attractive irritant, like a pimple that one can't help picking at.

And so over many months I kept noticing concepts that could be applied to

explanations of sparks. Here's what I've come up with.

To get a good understanding of sparks, you need to encounter their behavior in

detail. One way to do this would be to magnify a small spark, but sparks happen so

quickly that interesting behavior can't be seen, so in addition to magnifying it, we'd

have to slow it down somehow. Here's a better idea: speed yourself up instead. Imagine that you've been exposed to Tholosian water from 'Old Trek.' This is the

substance which causes you to live many times faster than normal. (TV-show

science fiction trivia experts will recall the appearance of a similar drug on The Wild

Wild West as well!) And then, instead of magnifying a tiny spark, let's go outside

during a storm and look at the behavior of an already-large spark. Except for its size, the strange behavior of lightning is very similar to the behavior of tiny sparks.

So, we're standing outside in the time-frozen world of a raging thunderstorm

viewed from our 1000X perceptual acceleration. The trees and bushes around us

are thrashing frozenly in the stopped wind, and a few torn shingles flying from the

nearby roof hang in the air nearby. Higher up we see a tangled, branching network of dimly glowing wiggly purple lines which look something like a tree root. And like

a root, all the tips of the branches are lengthening. But this can't be lightning, it's

dim and purple, not bright blue-white.

One branch-tip is about a hundred feet up from where we're standing. We can see that the wiggly line isn't moving, it's only growing at its tip. It takes a tortuous,

kinky path as it lengthens, and occasionally a new branch starts growing from the

side of the main one at a spot where there is a particularly sharp bend. Then we

notice something else: everything on the ground is starting to glow. Bits of dim

purple fire are popping into existence on the tops of bushes, the edges of the roof of the nearby house, the tips of the rooftop TV antenna, on the ends of all the tree

branches, and even on the flying pieces of roof shingles. As the exploring finger of

dim purple lightning comes downward, the purple "fire" on all the objects becomes

more and more intense. If you hold your hand in front of you, the tips of all your

fingers spout dim purple fire as well.

Now the dim purple lightning from above is about thirty feet away, and the

downward growth of its tip seems to be speeding up. Then something really

disturbing happens. One of the purple flames coming from your fingers has

suddenly started growing upward as a narrow wiggly violet line! You pull your hand

down, but it's too late, the streamer of purple stays attached and grows upward fast, it's two feet long by now. You notice that this purple streamer from your hand

isn't the only one, there are now jagged purple lines growing upwards from many

places which formerly had the little "St. Elmo's Fire" flames. There's a ten foot


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streamer coming from the tree, another from the bush, and a couple from the roof of the house and the TV antenna. They appear to be moving towards the incoming

lightning strike. There are even several coming from the wind-blown shingles, but

some of these are extending downwards towards the ground while others grow

upwards. The one from you're hand isn't winning, it apparently had a late start,

and the streamers coming from the tree and the shingles are really shooting upwards now ahead of all the others. And the downwards-growing streamer from

the shingles has touched the ground and is spreading out into a small disk of purple

rootlets on the surface of the ground.

Finally the upward-growing streamer from the shingles approaches the lightning streamer coming from above. The two growing branch-tips race together, and just

before they meet they split into several separate branches which all connect. And

NOW it suddenly looks like lightning, because the entire streamer from the shingles

is glowing brighter and brighter. The little disk of purple filaments where it touches

the ground is now several feet across and looks like blazing blue-white tree roots.

The whole thing is far too bright to look at, and it's getting brighter still. And something is happening to you. Your fingers hurt, the muscles in your arm are

tensing by themselves, and you feel yourself blacking out. As you lose

consciousness, you note that the short, dead-end streamer from your hand is still

jutting upwards into the air, glowing bright blue, though nowhere near as brightly

as the streamer from the shingles.

What the heck was all that?! Lightning struck an object hanging in the air?! Well,

sort of, since the shingles somehow launched their own lightning. And how could

lightning be coming from objects on the ground, and from your hand? Why were

you knocked unconscious even though you didn't get struck directly by the main bolt? And isn't lightning supposed to travel at the speed of light? 1000 times

speedup is nothing compared to light speed, so why did we see the lightning as a

bunch of slowly-growing filaments?

There are some mental tricks you can use to understand some of what went on

above. Number one: realize that lightning is not made of electricity. "Lightning is electricity" is a false concept which stands in your way of understanding, and you

need to get rid of it before you can figure out what's going on. The long purple

filaments, which extended through the air, are not electricity; they are actually

made of air. They are nitrogen and oxygen which has been converted into plasma.

Plasma is vaguely like fire, but it is not necessarily hot. When air is converted to plasma, the electrons of the gas atoms are knocked off the atoms and become able

to flow along through the air. Plasma is a conductor, so it's not too wrong to think

of purple plasma filaments as being like wires made of conductive air.

Another mental trick: when you take a conductive object, a metal bar for example, and hold it in a strong electric field, flame-like "St. Elmo's Fire" sprouts from the

ends of the bar. The "fire" is nitrogen/oxygen plasma. And plasma itself IS a

conductive object. So, if an electric field is strong enough, and if a tiny bit of air is

somehow converted into plasma, it's as if your conductive rod has grown little

conductive pieces on its ends. And next, the "sharp" parts of the plasma globs will

themselves sprout extra bits of plasma. And so your metal rod has started "lengthening itself" via fingers of air-plasma. The air can "catch fire" with an


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outbreak of plasma which grows and grows, with more air turning to plasma as the rods of plasma grow more plasma on their tips.

The plasma takes a particular form: long thin twisty rods. This occurs because "St.

Elmo's Fire" always starts on the sharpest part of an object, and the sharpest part

of a rod is the end of the rod. And so a pre- existing rod of plasma will grow more plasma on its tips and lengthen itself. This self-forming plasma conductor is

vaguely like a motorized metal antenna on a car which extends upwards. But the

plasma-antenna can lengthen itself continuously as long as its tip is still in a strong

electrostatic field.

If the twisted plasma rod should make a sharp bend as it grows, the bend can

behave as a sharp point and more plasma fingers can take off from the bend. In

this way a lengthening plasma streamer develops branches as it goes. Growing

plasma doesn't just form twisted rods, it often forms trees, it forms entire

complicated systems of rootlets which advance and spread. Whether it forms trees

or straight unbent paths depends on the shape of the e-field in the space around it. A parallel e-field will allow tree-shapes to grow. A spreading, radial-shaped field

will tend to force one plasma finger to grow faster than all the others, resulting in a

needle-straight spark.

Since plasma is a conductor, what do you think would happen if a piece of air-plasma were to connect itself between two highly-charged objects having opposite

charge? ZAP! The opposite charges would be shorted out. An enormous electric

current would exist for a moment. This is what happens during a lightning strike,

or during the tiniest spark. Long filaments of air-plasma within the clouds extend

and explore downwards towards the ground and upwards into the charged raindrops. A system of fine plasma-rootlets develops which connects most of the

raindrops to the main conductive plasma tree structure. When the conductive

plasma touches the ground, it discharges both the charge on itself and the charge

on the huge number of electrically charged raindrops. The large momentary

electric current makes the dim purple plasma explode with light and sound.

So, what about lightning and the speed of light? Why can we see lightning "strike"

across the clouds, yet light itself moves so fast that we never see moving light

beams? Why can we sometimes see sparks jump from object to object? This is

because the growing motion of lightning and sparks is actually the growth of

plasma filaments. It is not a movement of light. Lightning can "strike" slowly or quickly depending on how fast the plasma filament tips are extending themselves.

In very large Tesla Coil systems, the giant sparks can lengthen VERY slowly, a

human can sometimes outrun them.

In the speed-up story at the top of this page, why were there plasma filaments appearing on the ground and growing upwards? And why did the wind-blown

shingles send plasma filaments both up AND down? This is hard to explain without

going into detail about electric fields and atoms. But here's a similar question:

suppose you squeeze a clod of dirt between your thumb and forefinger until it

cracks. Would you expect the crack to start at your thumb, or at your finger? Or

might it start from a small spot in the dirt and grow outwards in two directions at


21

once? In truth, applying force to the dirtball can cause a crack to start ANYWHERE within the dirt.

Cracks tend to start at defects, and a similar thing is true with lightning and sparks.

An invisible field of electric force, if applied to air, can cause plasma filaments to

burst into existence anywhere in the volume of air where the field exists. When lightning is advancing towards the ground, there is a strong electric field all through

the air around the plasma branch and in the space above the surface of the earth.

This strong field can trigger new plasma filaments to grow anywhere. Of course, its

main effect is to make the main lightning filament lengthen and grow downwards.

But those blowing shingles represented a "defect" in the air, they distort the invisible electrostatic field in the air and strengthened it near the shingles, just as a

bubble in stressed glass can distort the mechanical forces and initiate a crack in the

glass. The electric field, present throughout the air, caused two plasma dendrites

to take off from the shingle and "strike" simultaneously upwards and downwards.

The defect in the air caused the air to "crack" electrically, the crack being made of

3D plasma filaments.

The same thing happens when aircraft fly between oppositely charged parts of a

thunderstorm: the plane acts as a triggering defect in the air, and plasma fingers

launch themselves from two spots on the airplane. Flying a plane near a

thunderstorm is like poking a highly-stressed windowpane with a nail: the cracks start where the nail touches. Yes, that's right, research has shown that aircraft

rarely are struck by lightning, instead the aircraft themselves do the striking, since

the plasma starts on the wingtips and zips outwards, striking the clouds.


22

Section A2: Electric Sparks 27

Electric sparks are a transient form of gaseous conduction. This type of discharge

is difficult to define, and no universally accepted definition exists. It can perhaps

best be thought of as the transition between two more or less stable forms of

gaseous conduction. For example, the transitional breakdown which occurs in the transition from a glow to an arc discharge may be thought of as a spark.

Electric sparks play an important part in many physical effects. Usually these are

harmful and undesirable effects, ranging from the gradual destruction of contacts in

a conventional electrical switch to the large-scale havoc resulting from lightning discharges. Sometimes, however, the spark may be very useful. Examples are its

function in the ignition system of an automobile, its use as an intense short-

duration illumination source in high-speed photography, and its use as a source of

excitation in spectroscopy. In the second case the spark may actually perform the

function of the camera shutter, because its extinction renders the camera

insensitive.

Mechanisms

The spark is probably the must complicated of all forms of gaseous conduction. It

is exceedingly difficult to study, because it is a transient and because there are so

many variables in the system. Some of these variables are the components of the gaseous medium, the gas pressure, the chemical form of the electrodes, the

physical shape of the electrodes, the microscopic physical surface structure, the

surface temperature, the electrode separation, the functional dependence of

potential drop on time, and the presence or absence of external ionizing agents.

One or more of these conditions may change from one spark to the next. Because of the great complexity, it will be impossible to do more than touch on some of the

main features in this article.

The dependence of breakdown, or sparking, potential on pressure p and electrode

separation if is considered first. It was shown, experimentally by F. Paschen and

theoretically by J. S. Townsend, that the sparking potential is a function of the product pd and not of p or d separately (Fig. 1). Further, there is a value of pd for

which the sparking potential is a minimum. Thus, if it is desired to prevent

sparking between two electrodes, the region may be evacuated or raised to a high

pressure. The latter method is used in accelerators of the electrostatic generator

variety. Here the entire apparatus is placed in a pressurized tank.


23

Qualitatively, one of the aspects of a spark is that the entire path between

electrodes is ionized. It is the photon emission from recombination and decay of

excited states which gives rise to the light from the spark. Further, if the spark

leads to a stable conduction state, the cathode must be capable of supplying the needed secondary electrons, and the conduction state produced must permit the

discharge of the inter-electrode capacitance at the very minimum.

In a consideration of the mechanism involved in the spark, the time required for the

breakdown of the gas in a gap is an important element. L. B. Loeb pointed out that

this time is often less than that required for an electron to traverse the gap completely. This implies that there must be some means of ionization present

other than electron impact and that the velocity of propagation of this ionizing

agent or mechanism must be much greater than the electron velocity. It seems

definitely established that this additional method must be photo-ionization. In the

intense electric field which is necessary for the spark, the initial electron will produce a heavy avalanche of cumulative ionization. Light resulting from the decay

processes will produce ionization throughout the gas and electrons at the surfaces

by the photoelectric effect (Fig. 2). The electrons resulting from this will in turn

produce further avalanches through the entire region, so that in a time of the order

of 10-8 sec the entire path becomes conducting. If the pressure is approximately atmospheric, the spark will be confined to a relatively narrow region, so that the

conducting path, while not straight, will be a well-defined line. If the external

circuit can supply the necessary current, the spark will result in an arc discharge.

At lower pressure, the path becomes more diffuse, and the discharge takes on

either a glow or arc characteristic.


24

Figure 2 shows:

A, the electron multiplication of electrons by the cumulative ionization of a single

electron liberated from the cathode by a photon;

B, a secondary electron emitted from the cathode by a positively charged ion;

C, the development and structure of an avalanche, with positively charged ions

behind electrons at the tip;

D, the avalanche crossing the gap and spreading by diffusion; and F, an older avalanche when electrons have disappeared into the anode.

A positive space-charge boss appears on the cathode at F. Ion pairs, outside the

trail, indicate the appearance of photoelectric ion pairs in the gas produced by

photons from the avalanche. E shows a photoelectron from the surface of the cathode produced by the avalanche.

Theory

Mathematically, the theory of Townsend predicts that the current in a self-sustained

discharge of the glow variety will follow Eq. (1),

ax

ax

eI

eII

0

Eq. (1)


25

where I is the current with a given plate separation x, I0 is the current when x approaches zero, and a and γ are constants associated with the Townsend

coefficients. This equation represents the case where the electrode separation is

varied while the ratio of electric field to pressure is held constant. The condition for

a spark is that the denominator approach zero, which may be stated as in Eq. (2).

axe Eq. (2)

Loeb indicated that this criterion must be handled carefully. Townsend's equation

really represents a steady-state situation, and it is here being used to explain a

transient effect. If the processes which are involved are examined more carefully,

it appears that there should be a dependence on I0 as well.

References: 1. J. Beyon, Conduction of Electricity through Gases, 1972.

2. J. D. Cobine, Gaseous Conductors, 1941. 3. L. B. Loeb, Statistical factors in spark discharge mechanisms. Rev. Mod Phys 20:151-

160, 1948. 4. D. Roller and D. H. C. Roller, The Development of the Concept of Electric Charge,

1954.


26

Section A3: Paschen's Law 28

In 1889, F. Paschen published a paper (Wied. Ann., 37, 69) which set out

what has become known as Paschen's Law. The law essentially states that

the breakdown characteristics of a gap are a function, which is (generally

not linear) of the product of the gas pressure and the gap length, usually written as V = f(pd), where p is the pressure and d is the gap distance. In

actuality, the pressure should be replaced by the gas density.

For air, and gaps on the order of a millimeter, the breakdown is roughly a

linear function of the gap length: V = 30pd + 1.35 kV, where d is in

centimeters, and p is in atmospheres.

Much research has been done since then to provide a theoretical basis for the law and to develop a greater understanding of the mechanisms of breakdown. Some of this will be described in the rest of this section, but it

should be realized that there are many, many factors which have an effect on the breakdown of a gap, such as radiation, dust, surface irregularities. Excessive theoretical analysis might help understanding why a gap breaks

down, but won't necessarily provide a more accurate value for the

breakdown voltage in any given situation.

Paschen's Law reflects the Townsend breakdown mechanism in gases, that

is, a cascading of secondary electrons emitted by collisions in the gap. The

significant parameter is pd, the product of the gap distance and the pressure. Typically, the Townsend mechanism, and by extension Paschen's

law, apply at pd products less than 1000 torr cm, or gaps around a centimeter at one atmosphere. Furthermore, some modifications are

necessary for highly electronegative gases because they recombine the secondary electrons very quickly.

In general, an equation for breakdown is derived and suitable parameters

are chosen by fitting to empirical data. Here are three equations:

Breakdown voltage:

VBREAKDOWN = B x p x d / [C + ln(p x d)]

Breakdown field strength:

EBREAKDOWN = B x p / [C + ln(p x d)]

where:

C =ln[A / ln(1 + 1 / gamma)]


27

where: gamma is the (poorly known) secondary ionization coefficient.

For air (data from Bazelyan, p.32):

A = 15 cm-1torr -1

B = 365 Vcm-1 torr-1

and gamma = 10-2

so C = 1.18

Minimum sparking potential for various gases (data from Naidu, p.27):

Gas VS min

(V)

pd at VS

min (torr cm)

Air 327 0.567

Ar 137 0.9

H2 273 1.15

He 156 4.0

CO2 420 0.51

N2 251 0.67

N2O 418 0.50

O2 450 0.7

SO2 457 0.33

H2S 414 0.6

Note that the sparking voltage is affected by the electrode material, with

cathodes of Barium and Magnesium having higher voltages than Aluminum,

for example.

Temperature dependence

Paschen's law, V = f(pd), should really be stated as V = f(Nd) where N is the

density of gas molecules, which is, of course, affected by the temperature as

well as the pressure of the gas (n/V = p/RT). An empirical formula for air,

considering it as an ideal gas, is:

VBREAKDOWN = 24.22 x + 6.08 SQRT(x),

where x = 293 pd / (760 T)

http://home.earthlink.net/~jimlux/hv/hvrefs.htm#Bazelyan

http://home.earthlink.net/~jimlux/hv/hvrefs.htm#Naidu


28

p = pressure in torr (mm Hg),

d = distance in cm, T = Absolute Temperature in Kelvins

VBREAKDOWN in kV

Humidity dependence

In air, increasing humidity increases the breakdown voltage. The effect is

most noticeable in uniform field, and less important in non-uniform gaps

(such as sphere gaps where the gap is a large fraction of the sphere

diameter, or in rod or needle gaps).

Gamma - Townsend's secondary ionization coefficient

Gamma is the net number of secondary electrons produced per incident

positive ion, photon, excited or meta-stable particle. It is a function of gas

pressure and E/p. Electronegative gases (SF6, Freon, oxygen, CO2) re-attach the electrons very quickly, so they have low gammas.

For nitrogen, gamma ranges between 10-3 and 10-2 for E/p of 100 to 700 V

cm-1 torr-1. Insulating gases like SF6 or Freon have gammas of 10-4 or even less.

References:

Naidu, M.S. and Kamaraju, V., High Voltage Engineering, 2nd ed., McGraw Hill, 1995.

Bazelyan, E.M. and Raizer, Yu. P., Spark Discharge, CRC Press, Boca Raton, 1998.


29

Section A4: About common sparks29

Questions about Science and Technology

Alan Wallwork asked: How powerful is a common static electric charge? And can a common charge be measured? (common; as in the type of charge you get when you get out of a car or when you drag your feet across the carpet.)

When you walk across a carpeted floor, friction between your shoes and the carpet causes electrons to be rubbed off the carpet onto your body: your body now has an excess of electrons and as a result has become electrically charged. A split second before you touch a conductor (anything made of metal, like a door knob, will do), the electrons jump across the gap between your fingers and the conductor.

This flow of electricity ionizes (forms charged particles) the air. If the voltage across the gap is great enough, an electric discharge is created. At normal pressure and temperature, that electric discharge is in the form of a spark. (Editor's Note: For a more technical description, refer to Miscellaneous Notes, below.)

Upon formation of the discharge the ionized air produces heat, causing the air to rapidly expand. That expansion of air produces a compression wave, heard as a crackling sound. The heat energy causes the air molecules to emit light and a flash is seen (if you want to see this dramatically illustrated, take off your sweater in a dark closet).

There are all kinds of sparks of course, from lightning to the type created by spark plugs in car engines. To answer the question of what voltage is seen when a "common" spark is formed, we need to look at Paschen's Law.

Paschen's Law states that the voltage at which a spark occurs (known as breakdown voltage) is dependent on the product of air pressure (p) and the separation between the electrodes (d). A graph of Paschen's Law as it applies to air (different gases create sparks differently) is seen below.


30

For a common spark, then, we assume the distance between the two electrodes (your hand and the door knob in this example) is about 1 mm, with one atmosphere of pressure (760 torr, sorry for the ancient units). From the graph, therefore, the voltage of a common spark works out to be around 2000 V.

Miscellaneous Notes

For a more technical explanation of spark formation, refer to the graph of Gaseous Conduction, below, and the following explanation.

As the electrons begin to flow from one electrode to the other, the voltage between the electrodes rises from 0 to V1 and ionization of the air occurs, causing a small current to flow between the electrodes. This stage is known as primary ionization.


31

Between V1 and V2 the current is such that the ions are conveyed to the electrodes as fast as they are produced. At this stage, as the voltage increases, the current remains the same and saturation is said to have been reached.

As the voltage increases beyond V2, the ions created by primary ionization have gained enough energy from the electric field to cause further ionization by collision. This increases the current further. More and more ions are accelerated in this manner, known as secondary ionization.

At V3, breakdown voltage occurs, the current increases indefinitely and the air is no longer able to allow the flow of electrons without electric discharge (or spark formation).

Once the discharge has formed, the current strength drops and remains constant.

If you've ever driven behind a gasoline truck you'll know that they drag a short chain on the ground behind them. This is for safety, because friction between the tires and the road causes the truck to become charged; the chain allows the charge to drain back onto the road. If this wasn't done, formation of a spark might ignite the gasoline vapors.

Lightning is a spark with a length of 150 m to 3 km, a width of 1 cm to 30 cm, a temperature of up to 30,000°C and a lifespan of 0.002 s to 1.6 s.

Townsend Criteria for Formation of a Spark: gamma ead = 1, where d is the gap length, a is the number of electrons produced by a single electron traveling 1 cm in direction of the electric field, and gamma is the secondary ionization coefficient (the number of secondary electrons produced per ionizing collision in the gas).

At a given pressure, the breakdown voltage is a direct linear function of the length of the gap between the electrodes.

When the pressure is low, the electric discharge is in the form of cathode rays. When it's very low, the discharge is in the form of x-rays.

Glossary and Related Terms

Arc Discharge: A luminous electrical gas discharge characterized by very high current. The intense ionization necessary to maintain the large current is provided mainly by the evaporation of the electrodes, which are raised to incandescence by the discharge (the enormous heat produced is utilized in arc-welding).

Breakdown: A sudden electric discharge.

Breakdown Voltage: The voltage at which a sudden electric discharge occurs.

Charge: A property of some elementary particles (e.g., protons and electrons) that causes them to exert forces on one another. Like charges repel and unlike charges attract each other. The charge of an object depends on the relation of the number of the object's protons and electrons. If the object has an excess of electrons, the object is said to have a negative charge. Similarly, if the object has an excess of protons, the object has a positive charge.

Conductor: A substance or body that offers small resistance to the passage of an electric current.

Corona Discharge: A type of electric discharge that results when partial breakdown of the surrounding gas takes place.


32

Current: The rate of flow of electricity, measured in units of amperes. A current of 1 ampere is equivalent to the flow of about 1,000,000,000,000,000,000 electrons per second.

Dielectric: A substance that is capable of sustaining an electrical stress, i.e., an insulator.

Discharge: The removal or reduction of an electric charge of a body. It's also the passage of an electric current or charge through a dielectric, usually accompanied by luminous effects. There are many kinds of discharge, among them spark discharge, glow discharge, arc discharge and corona discharge.

Electric Field: The space surrounding an electric charge within which it is capable of exerting a perceptible force on another electric charge.

Electrode: A device for emitting electric charge carriers, e.g. a wire that leads current into or out of a dielectric.

Electron: An elementary particle carrying a negative charge. They are constituents of all atoms and as free electrons they are primarily responsible for electrical conduction in most substances.

Flashover Voltage: The voltage at which an electric discharge occurs between two electrodes that are separated by an insulator (depends on the wetness of the insulator surface).

Glow Discharge: An electric discharge through a gas, usually at a low pressure, in which the gas becomes luminous. Neon signs utilize glow discharge.

Insulator: A substance that provides very high resistance to the passage of an electric current.

Ionization: The process of forming electrically charged atoms.

Paschen's Law: The breakdown voltage for a discharge between electrodes in gases is a function of the product of pressure and distance.

Potential Difference: The difference between electric field strength at two points.

Spark: A visible discharge of electricity between two places. Preceded by ionization of the path, there is a rapid heating effect of the air through which the spark passes, which creates a sharp crackling noise.

Spark Discharge: Formation of a spark; this type of discharge appears around atmospheric pressure.

Sparking Potential: The lowest voltage at which a spark will be created.

Townsend Criteria: A mathematical formula that illustrates when a spark will be formed.

Volt: The unit of electric potential, defined as the potential difference between two points on a conductor carrying a current of one ampere when the power dissipated is one watt.

Voltage: The potential difference between two specified points in a circuit or device (measured in units of volts).

References and Further Reading

Definitions come from The Penguin Dictionary of Physics, edited by Valerie H. Pitt, published by Penguin Books, Ltd., 1983


33

Section A5: Does an electrical arc spark need air to happen? 30 Date: Fri Jul 25 18:08:37 2003 Posted By: Aaron J. Redd, Post-doc/Fellow, Plasma Physics and Controlled Nuclear Fusion, University of Washington Area of science: Chemistry ID: 1050069563.Ch -------------------------------------------------------------------------------- Message: The short answers: yes, a spark can occur in a vacuum; and, no, the spark isn't really a "fire", but such a spark can start a fire. So it is still a safety hazard. The spark or electrical arc is not a fire, in the sense that it is actually a superheated gas, also known as a plasma. The plasma of the arc does not burn, in the sense that it is sustained by the electrical current traveling through the arc -- just as a wire will heat up when electrical current travels through it, the plasma stays hot because of the current in the arc. In theory, two metal surfaces with a vacuum gap between them can safely hold off an arbitrarily high voltage between them. In the real world, though, there are two important ways for the spark to happen: (1) No vacuum is perfect, so there will be some small amount of gas present. As shown by Paschen in the early 20th century, there is a maximum voltage that can be sustained between two (metal) electrodes, determined by the density of the trace gases in the area and (speaking loosely) the distance between the metal plates. If the voltage is above the so-called Paschen voltage, then there will be an arc between the metal surfaces. Also, the gas doesn't need to be air: helium, neon, hydrogen, carbon dioxide -- any of these will show the same Paschen breakdown. (2) Real surfaces (such as metal surfaces) aren't perfect either, and if the electric field at the surface is too high, then the material will sputter and/or vaporize, creating some gas which can then become an arc plasma. Once the arc is occurring, more material can be sputtered off from the surface, adding more gas to the plasma arc and pitting the metal surface. This is part of the reason why electrical fires are so hard to fight: the spark that causes the fire won't stop until the electrical current stops, so whoever is fighting the fire first has to shut off the current, and then try to put out the fire. As for this pitting on the electrode surfaces, it is quite noticeable -- electrodes tend to look very "beat up" after being exposed to arcs. If your light switches (or any other switches!) generate visible sparks when they are switched on or off, then they need to be replaced immediately. Like I said above, the spark isn't a fire itself, but it can start a fire.


34

Section A6: The Paschen Curve 31

The Paschen curve is a plot of breakdown voltage for gases as a function of the

product of gas pressure and electrode separation. When pressure is given in mBar

(thousandths of an atmosphere) and electrode separation in mm the product is

mBar-mm. For pressure-distance values above about 25 mBar-mm, the breakdown voltage increases with increasing pressure and or separation. For those of us who

have played around with spark gaps, this is not surprising. Below 25 mBar-mm the

curve begins to flatten out and as the pressure-distance product drops below about

7 mBar-mm the breakdown voltage begins to rise very rapidly!

Why does this happen? Gasses become conductive when they are converted into plasma. Plasma, also referred to as the fourth state of matter, is a fluid composed

not of molecules but of positive ions (cations) and electrons. Plasmas are formed

when energy is put into a collection of molecules faster than energy is lost by

radiation when the cations and electrons recombine. Recombination of the cations

and electrons causes energy to be released as light, this is how fluorescent lights

and neon signs work.

In a simple atmospheric pressure spark gap, as the potential difference (voltage)

between the electrodes is increased (or as the distance between the electrodes is

decreased), electrons begin to be emitted by the cathode (negative electrode) and

travel to the anode (positive electrode). As they travel, some of the electrons will

collide with gas molecules, knocking electrons loose and forming cations and more


35

free electrons. Near the electrodes, where the concentration of traveling electrons is highest, a faint glow caused by the recombination of ions and electrons will

become visible. This glow is called a corona discharge and removes energy from

the ionized gas at a high enough rate to prevent the formation of plasma. At

higher voltages (or smaller gaps) the energy put into the molecules by electron

collision exceeds the ability of the corona discharge to dissipate the energy and a plasma is formed. The electric field between the electrodes will then separate the

cations and electrons. The electrons will flow towards the anode, while the cations

will flow towards the cathode. When the cations impact the cathode, they

recombine with electrons from the surface of the cathode, completing the electric

circuit. In an atmospheric pressure spark gap, the flow of cations and electrons tends to be confined to a fairly narrow channel which is called a spark. At the point

on the cathode where the spark connects, a large amount of heat is generated by

the impacting cations, damaging the electrode surface (more current = more

damage). Electrons impacting the anode surface do not cause much damage, since

they are thousands of times lighter than the cations and thus have much less

kinetic energy.

Before we can go further, we need to understand gasses better, particularly how

the rate of collision between gas molecules changes as the pressure changes. The

rate at which molecules collide depends on the concentration of molecules (how

many there are in a given volume) and the average velocity of the molecules. The

temperature of a gas is actually a measure of the average kinetic energy of the molecules which make up the gas. The velocity of the molecules then depends on

temperature and the mass of the individual molecules. The pressure of a gas is the

amount of force the gas exerts against a unit of area. This is a combination of the

kinetic energy of the individual molecules and the total number of molecules in a

unit of volume. (This is the Kinetic Theory of Gasses in a nut shell.) Now, if we consider a sample of gas at constant temperature and volume, it is clear that a

reduction in pressure means that there are fewer molecules and fewer collisions.

Another way to think of this is that the distance a molecule can travel (remember

we have not changed the temperature, so the average velocity of the molecules has

not changed) without colliding with another molecule has increased. This distance

is called the "mean free path". In air at one atmosphere of pressure and a temperature of 0°C (standard temperature and pressure or STP) the mean free

path is 1 X 10-7 meters (or 1 X 10-4 millimeters, 0.1 micrometers, 100 nanometers).

If we go back to the atmospheric pressure spark gap for a moment, we now realize

that one electron, traveling a centimeter or so from the cathode to the anode, will

collide with about 100,000 gas molecules. Whether or not a particular molecule will be ionized depends on how much kinetic energy the electron has when it hits the

molecule. If the energy of the incoming electron is greater than the binding force

of the electrons in the molecule (the "ionization potential") then one or more

electrons can be knocked loose. Unlike the gas molecules, whose kinetic energy

depends on the gas temperature, the kinetic energy of the electrons is determined by the acceleration caused by the electric field between the electrodes and the

distance over which this accelerating force acts. The distance that the electron

"falls" in the electric field (and hence its kinetic energy) is limited by the mean free

path of the gas. Every time the electron collides with a gas molecule, it loses most

of its kinetic energy. If the distance through which the electron accelerates is very


36

small, it will never have enough kinetic energy to ionize the gas molecules. This is why higher pressure requires a greater voltage before a plasma can form. Longer

gaps reduce the electric field strength and consequently reduce the kinetic energy

of the electrons which is why longer gaps require higher voltages to initiate

plasmas.

So what is happening on the "left side of the Paschen curve?” As the pressure drops, the mean free path of the gas increases and the kinetic energy of the

electrons will also increase, meaning that a collision with a gas molecule will be

more likely to result in ionization. Now, remember that the x-axis of the Paschen

curve is not pressure, but the product of pressure and distance. What has

happened is that the distance between the electrodes is now smaller than the mean free path of the gas. The electrons have plenty of kinetic energy, but they are no

longer colliding with any gas molecules, so no ionization occurs.

The author continues by describing pseudo-spark switches, which use a spark gap

in a rarified gas to function as a high-voltage switch. Presumably, since the

determining factor is the product of pressure and spark gap, it is also possible to

reach the “pseudo-spark” range, indicated on the accompanying Paschen curve plot, by reducing the spark gap below the 5 to 50 µm range while maintaining

atmospheric pressure. The shape of the Paschen curve, presented here, means

that employing spark gaps below about 5 µm will require much higher voltage to

produce a spark.


37

Section A7: Static Electricity Sparks and Lightning32

by Ron Kurtus (revised 28 December 2002)

A spark is a stream of electrons jumping across an air gap, heating the air until it glows and

expands. Certain conditions can cause enough static electricity buildup to cause a spark or lightning. A spark often requires both a conductor and non-conductor. Lightning is an

extreme example of a spark.

Conditions for sparks

Sparks do not happen easily. They are violent occurrences that require special conditions.

They need both non-conductors and conductors to occur. The way this happens can get complex. These conditions include walking on a carpet on a very dry day or the rapid

movement of tiny water particles in a summer storm.

In the home

The Triboelectric Series shows that when certain materials are in contact, they can cause a

great increase in electrical charges on the surfaces of those materials. This is typically the case in for sparks that people personally experience.

In the clouds

Normally water inhibits static electricity, but in the case of thunderstorms, there is so much movement of air and water droplets within the clouds that charges collect on the surface of

the droplets. Enormous amount of charges can collect in the clouds, some positive ( + ) and

some negative ( - ).

Sparks require conductors

You know that static electricity collects on the surface of non-conductors. But you seldom—if

ever—see a spark fly from one non-conductor to another. The reason is that sparks need conductors, so that the electrons can freely move about and gather enough charges

together to be able to jump from one material to another.

If you took a charged piece of plastic and put it next to some metal, there would be no spark. The charges are held on the surface of the plastic, so that they won't jump the air

gap

Another good example of this concerns how you can get shocked with a spark. You are a conductor of electricity—although not as good as a piece of metal. The reason you conduct

electricity is because of the salt in your blood and your cells. Now if you notice, you usually see sparks when you start to touch something metal—like a doorknob—or another person or

animal.

So static electricity is formed and gathered on the surface of a non-conductor, but it must be then transferred to a conductor to cause a spark.

http://www.school-for-champions.com/science/static_materials.htm


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Charges move in conductor

When a conductor—like a metal rod—is brought near a charged non-conductor, the free

electrons in the conductor will move to one end or the other of the rod, depending on whether the non-conductor surface is positive or negative.

Opposite charges in conductor move toward non-conductor

When the conductor is brought into contact with the non-conductor, the electrical charges

on the surface of the non-conductor are "sucked" into the conductor. In other words, if negative charges are on the surface of the non-conductor, these electrons will move into the

conductor. If positively charged atoms are on the surface, electrons from the metal or conductor will neutralize those atoms, resulting in an excess of positive charges in the

conductor.

Now, if another conductor is brought near the first conductor, the same thing will happen. Since electrons can move so freely in a conductor, many may collect near the surface and

actually jump across the air gap as a spark.

Anatomy of a spark

Air is a non-conductor of electricity and resists the movement of electrons through it. When the attraction or electrical pressure is great enough between objects with positive ( + ) and

negative ( - ) charges -- or even between a charged object and a neutral one -- some

electrons are able to overcome the resistance and jump the air gap. This electrical pressure is also called potential difference or voltage difference.

Heats up the air

Since air is a non-conductor of electricity, it does not readily let electrons pass through it.

But if the attraction is great enough, some electrons will leave their material and fly to the

other object. While they move through the air, may smash into and bounce off molecules or atoms that are in their way. This heats up the air. (See Heat for an explanation.)

Spark glows white-hot

http://www.school-for-champions.com/science/heat.htm


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Lower resistance

Now, the hotter the air is, the less resistance it gives the electrons. So as the air gets

heated, more and more electrons start jumping over to the other side. This only heats the air even more, until it actually gets white-hot. That is the spark or bolt of lightning that you

see and feel.

Electrons stop jumping

Once enough electrons have made the jump, the attraction is reduced and the flow stops.

The spark quickly cools down and the air stops glowing. It is all over in a fraction of a

second. Since this happens for such a short time, so you may only feel a slight discomfort from the heat of the spark. But if the spark is a bolt of lightning, it can cause an enormous

amount of damage.

Lightning is a real big spark

Lightning works the same way as a little spark, except that it happens on a massive scale.

Some lightning bolts are several miles long. Compare that to the tiny 1/4 inch or 1

centimeter length of the spark that comes off your finger.

Lightning can be quite dramatic

Lightning is created when water drops are churning around in a thunder cloud. They gather

either positive or negative electrical charges, so that soon one cloud may be positive and another cloud may be negative. Or perhaps some object on the earth may have an excess

of opposite charge.

Has high electrical pressure

The electrical pressure builds up, the same way as it does for a spark. Since the distances

are so much greater between the clouds, the electrical pressure must be extremely high for lightning to start. But once it does and a lightning bolt jumps from one cloud to another, it

is a tremendous spectacle.

Most go from cloud to cloud

Most lightning bolts are from cloud to cloud, but sometimes there are no positive charged

clouds nearby, so the negative cloud, sends its electrons to the ground or any object that

may have a slight positive charge.


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Thunder

Air expands when it is heated and contract when it cools. Since the spark happens so fast,

the air expands and contracts very rapidly. When it contracts, the air slaps together, just like when you clap your hands or pop a balloon. The noise you hear from a spark is just a

snap, because it is so small.

On the other hand, the noise of thunder is a tremendous crash, because the size of lightning is so large. The snap of a spark and the crash of thunder are caused by the same effect. The

only difference is in the size of the spark.

In conclusion

Static electricity is caused when friction causes electrical charges to build up on a surface of

a non-conduction material. Its explanation comes from the Atomic Theory of Matter. Static electricity can cause sparks and other problems, but it also is useful in pollution control.

http://www.school-for-champions.com/science/matter.htm


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Section A8: Zapping Airborne Salmonella and Dust 33 Agricultural Research Service scientists have found a way to reduce Salmonella and dust in poultry areas. The technology may sound commonplace, but for many in the poultry industry it's exciting news. The technology uses a negative electrostatic charge to remove dust from the air. Unlike most air cleaners, this device does not require air to move through it for cleaning to occur. Reducing the dust is important, because these particles often give hitchhiking germs a free ride into chicks' lungs and feathers. Bailey W. Mitchell, an agricultural engineer, developed the ionizer system, in cooperation with veterinarian Henry D. Stone. Both researchers work at ARS' Southeast Poultry Research Laboratory in Athens, Georgia. ARS applied for a patent on the technology in July 1998. The first industry trials began in June of 1998, and a commercial product is now available.

Agricultural engineer Bailey Mitchell demonstrates an electrostatic air cleaning system. The hatching cabinet used here is a small version of ones used commercially for hatching chicks.

Early trials in 1994 suggested the process would reduce dust and had the potential to reduce airborne transmission of Newcastle disease virus and other disease organisms such as Salmonella. "When Bailey first started this work, we tested it in a small chick hatcher," says Stone. "He modified it many times. When I saw the consistent reduction in dust particles and bacteria during hatch, I knew it had potential."


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Mitchell says credit is also due to veterinary medical officer Daniel J. King, physiologist R. Jeff Buhr, and microbiologists Peter S. Holt, Richard K. Gast, K.H. Seo, Mark E. Berrang, S. Stan Bailey, and Nelson A. Cox for their collaboration with this research.

Dust Spreads Disease

Keeping hatching cabinets free of pathogens is especially important, because one infected hatching chick can very quickly spread disease organisms to an entire cabinet of 15,000 tiny birds. One reason: The strong air needed to move warmth throughout the cabinet also moves dust. Currently, chemical sprays are the only effective means of reducing airborne disease transmission in hatching cabinets, but they can be expensive and can damage hatching equipment. This electrostatic system would be safer for poultry and other livestock. It would also keep dust levels down better than existing methods and would continually clean the air of pathogens. The Simco Company of Hatfield, Pennsylvania, is one of the world's largest manufacturers of electrostatic equipment. Mitchell says the company provided electrostatic insights, equipment, and instrumentation under a federal-industry cooperative research and development agreement. "It makes sense that reducing the fluff in the hatching cabinet would reduce bacterial contamination at pipping," says Hank Engster, vice president of technical service for Purdue Farms of Salisbury, Maryland. Pipping is when the chick breaks through its shell during hatching. "We are pursuing a test of the technology at one of our complexes on the Delmarva Peninsula," says Engster. Experiments conducted in a small chamber with agar plates exposed to a continuous Salmonella aerosol showed that high levels of charge can, on average, reduce airborne Salmonella levels from over 1,000 per plate to near 0 in what appears to be an instantaneous sterilizing effect.


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The petri dishes below show sterilization effects of negative air ionization on a chamber

aerosolized with Salmonella enteritidis. The left sample is untreated; the right, treated.

The electrostatic technology consistently reduced Salmonella transmission between chicks by 98 percent and reduced Salmonella in air samples by 95 percent in a room with Salmonella-infected egg-laying hens. In other tests, Mitchell built up hatching cabinet dust levels to 40 times above normal. The device reduced airborne particles by 99 percent in 60 seconds. The system was tested on a hatching cabinet with a few infected fertile eggs interspersed among healthy ones. Salmonella counts in the guts of 7-day-old chicks in the cabinet with the device were reduced by a factor of 1,000- to 10,000-fold, when compared to counts in chicks in a hatching cabinet without the device.

Producers May Flock to Air Cleaners

"We are mainly interested in the technology for food safety--but also for improved growth and productivity in our flocks," says Purdue's Engster. "We sent a group down to Athens, Georgia, to assess how well the technology would meet our needs. Bailey showed us a system installed at Seaboard Farms." Seaboard Farms in Athens supplies poultry for many fast-food companies. The company, with four hatcheries, produces over 5 million chicks a week. Installing the ARS ionizer costs about $2,500 per hatching cabinet. Seaboard Farms hopes to install it in all of the cabinets in one hatchery. "We tested the technology at our hatcheries," says Steve Bolden, vice president of live production at Seaboard Farms. "We found it reduced bacteria in three out of five tests and consistently kept dust levels down. We have negotiated with ARS to license the technology."


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In addition, hatchability--the percentage of eggs that produce live chicks--increased as much as 2.7 percent in tests of the system, thanks to reduced pathogens, Mitchell says. "Multiply this seemingly modest increase by the millions of hatching eggs farmers sell and you can see the potential." The technology has also interested turkey producers. Wampler Foods of Harrisonburg, Virginia, the seventh largest U.S. broiler chicken producer and third largest turkey producer, invited Mitchell to demonstrate the technology. Wampler is interested and would like to install units when commercially available, according to Tom Knapp, manager of Wampler's turkey breeding operations. He says the company is also planning on model modifications to better fit their hatching cabinets. "Initial tests in poultry production look promising in terms of improved vitality and health of flocks," says Knapp. "If we can verify reduced levels of bacteria, we think the technology would be a vital component to our overall live production health programs." According to Mitchell, numerous simple ionizer systems have been developed and marketed for air-cleaning applications with little or no research. Although many of these devices had potential in small spaces with light dust loads, they require air to pass through them and are not able to handle the larger space and higher dust levels of a typical hatching cabinet. The supercharged ionizer/dust collection system developed by ARS appears able to do the job. The process is likely to have applications outside agriculture, Mitchell says. In tests, the researcher removed smoke from a 3,300-cubic-foot room with 95-percent efficiency. Many other companies, he adds, are asking to review the technology for environmental and other air-cleaning applications. This research is part of Animal Health, an ARS National Program (#103) described on the World Wide Web at http://www.nps.ars. usda.gov/programs/appvs.htm. Bailey W. Mitchell and Henry D. Stone are with the USDA-ARS Southeast Poultry Research Laboratory, 934 College Station Rd., Athens, GA 30605; phone (706) 546-3443 [Mitchell], (706) 546-3431 [Stone], fax (706) 546-3161, e-mail


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Section A8: A Simple Spark Gap Test Rig

This simple test rig was built by two undergraduate physics students at MIT,

Igor Sylvester and his friend Harry. Their used the following equipment

required to produce sparks: a transformer to convert 120-volt alternating

current (AC) power to direct current (DC); a rectifier to convert direct current to high frequency alternating current; and a capacitor to store

electrical charge until it is discharged by the spark gaps. Their spark gaps

consist of three pairs of nails positioned with the tip of one nail pointed

toward the other nail in each pair leaving a small gap between.

Spark Gap Test Rig Description:

It takes DC current and converts it to high frequency (~200 kHz) AC current. It acts

like a high frequency switch. It's made out of three pairs of nails connected in series. The separations between the nails provide a minimum voltage threshold. When this

threshold is reached (while charging the capacitor) the current "jumps" from one nail to its counterpart and air plasma is formed for a very short period of time. This plasma

lets current flow until the voltage is not high enough to support the plasma (while discharging the capacitor). As a consequence, the plasma is destroyed and the cycle

repeats again, waiting for the voltage to reach the threshold point.34

The spark gap. It takes DC current and transforms it into high frequency AC

current.

The spark gap, capacitor, rectifier and

transformer.

http://web.mit.edu/ias/www/physics/tesla/images/spark_gap.jpg

http://web.mit.edu/ias/www/physics/tesla/images/capacitor_and_transformer.jpg


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Section A9: Carbon Nanotubes Carbon nanotubes, long, thin cylinders of carbon, were discovered in 1991 by

Sumio Iijima.35 These are large macromolecules that are unique for their size,

shape, and remarkable physical properties. They can be thought of as a sheet of

graphite (a hexagonal lattice of carbon) rolled into a cylinder. These intriguing structures have sparked much excitement in the recent years and a large amount

of research has been dedicated to their understanding. Currently, the physical

properties are still being discovered and disputed. What makes it so difficult is that

nanotubes have a very broad range of electronic, thermal, and structural properties

that change depending on the different kinds of nanotube (defined by its diameter,

length, and chirality, or twist). To make things more interesting, besides having a single cylindrical wall (SWNTs), nanotubes can have multiple walls (MWNTs)--

cylinders inside the other cylinders.36 The electrical transport properties of SWNTs

has been recently studied has raised some controversy. The conductance of a tube

is quantized, and a nanotube acts as a ballistic conductor. Nanotubes also have a

constant resistivity, and a tolerance for very high current density.37

An electronic device known as a diode can be formed by joining two nanoscale

carbon tubes with different electronic properties.

Carbon nanotubes are tubular carbon molecules with properties that make them potentially useful in extremely small scale electronic and mechanical applications.

They exhibit unusual strength and unique electrical properties, and are extremely

efficient conductors of heat.

A nanotube has a structure similar to a fullerene, but where a fullerene's carbon atoms form a sphere, a nanotube is cylindrical and each end is capped with half a

fullerene molecule. Their name derives from their size; nanotubes are on the order

of only a few nanometers wide (on the order of one ten-thousandth the width of a

human hair), and their length can be millions of times greater than their width.

Nanotubes are composed entirely of sp² bonds, similar to graphite. Stronger than the sp3 bonds found in diamond, this bonding structure provides them with their

unique strength. Nanotubes naturally align themselves into "ropes" held together

by van der Waals force. Under high pressure, nanotubes can merge together,

trading some sp2 bonds for sp3 bonds, giving great possibility for producing strong,

unlimited-length wires through high-pressure nanotube linking.


47

There are two main categories of nanotubes: single-walled (SWNT) and multi-

walled (MWNT). Additionally, there are a large variety of forms of each of these,

identified by a two-digit sequence. The first digit indicates how many carbon atoms

around the tube is. The second digit determines the offset of where the nanotubes

wrap around to. If the second digit is a zero, the nanotubes are called "armchair". If both digits are the same, the nanotubes are called "zigzag". Otherwise, they are

called "chiral".

The structure of the nanotube, as described above, strongly affects its electrical

conducting properties. For example, (6,0), (6,6), (9,0), and (9,9) nanotubes are all excellent conductors. However, electron holes arise in (7,0), (8,0), (6,2), and (7,5)

nanotubes, making them semiconductors. In theory, nanotubes which conduct can

have an electrical current density more than 1,000 times stronger than metals such

as silver and copper. All nanotubes are expected to be very good thermal

conductors along the tube, but good insulators laterally to the tube.

While it has long been known that carbon fibers can be produced with a carbon arc,

and patents were issued for the process, it was not until 1991 that Sumio Iijima, a

researcher with the NEC Laboratory in Tsukuba, Japan, observed that these fibers

were hollow. This feature of nanotubes is of great interest to physicists because it

permits experiments in one-dimensional quantum physics. Techniques have been developed to produce nanotubes in sizeable quantities, but their cost still prohibits

any large scale use of them.

Fullerenes and carbon nanotubes are not necessarily products of high-tech

laboratories, and are also formed in such mundane places as candle flames. However, these naturally occurring varieties are highly irregular in size and quality,

and attempting to ensure the high degree of uniformity necessary to meet the

needs of research and industry is impossible in such an uncontrolled environment.

Nanotubes can be opened and filled with materials such as biological molecules,

raising the possibility of applications in biotechnology. They can be used to dissipate heat from tiny computer chips.

The strength and flexibility of carbon nanotubes makes them of potential use in

controlling other nanoscale structures, which suggests they will have an important

role in nanotechnology engineering. The highest tensile strength an individual SWNT has been tested to is 63 GPa.

In Earth's upper atmosphere, atomic oxygen erodes the carbon nanotubes, but

other applications rarely need protection of the carbon nanotube surface. Though it

is debatable if nanotube materials can ever be made with a tensile strength approaching that of individual tubes, composites may still yield incredible strengths

potentially sufficient to allow the building of such things as space elevators, artificial

muscles, ultrahigh-speed flywheels, and more. MIT is working on combat jackets

utilizing carbon nanotubes for ultra-strong fibers and for monitoring its wearer's

condition.


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Carbon nanotubes additionally can also be used to produce nano-wires of other chemicals, such as gold or zinc oxide. These nano-wires in turn can be used to cast

nanotubes of other chemicals, such as gallium nitride. These can have very

different properties from CNTs - for example, gallium nitride nanotubes are

hydrophilic, while CNTs are hydrophobic, giving them possible uses in organic

chemistry that CNTs could not be used for.

One use for nanotubes that has already been developed is as extremely fine

electron guns, which could be used as miniature cathode ray tubes in thin high-

brightness low-energy low-weight displays. This type of display would consist of a

group of many tiny CRTs, each providing the electrons to hit the phosphor of one pixel, instead of having one giant CRT whose electrons are aimed using electric and

magnetic fields. These displays are known as Field Emission Displays (FEDs) A

nanotube formed by joining nanotubes of two different diameters end to end can

act as a diode, suggesting the possibility of constructing electronic computer

circuits entirely out of nanotubes. Nanotubes have been shown to be

superconducting at low temperatures.

Current progress

One application for nanotubes that is currently being researched is high tensile

strength fibers. Two methods are currently being tested for the manufacture of

such fibers. A French team has developed a liquid spun system that involves pulling a fiber of nanotubes from a bath which yields a product that is approximately 60%

nanotubes. The other method, which is simpler but produces weaker fibers uses

traditional melt-drawn polymer fiber techniques with nanotubes mixed in the

polymer. After drawing, the fibers can have the polymer burned out of them to

make them purely nanotube or they can be left as they are.

Scientists working at the University of Texas at Dallas produced the current

toughest material known in mid-2003 by spinning fibers of single wall carbon

nanotubes with polyvinyl alcohol. Beating the previous contender, spider silk, by a

factor of four, the fibers require 600J/g to break. In comparison, the bullet-resistant fiber Kevlar is 27-33J/g.

In 2004 Alan Windle's group of scientists at the Cambridge-MIT Institute developed

a way to make carbon nanotube fiber continuously at the speed of several

centimeters per second just as nanotubes are produced. One thread of carbon nanotubes was more than 100 meters long. The resulting fibers are electrically

conductive and as strong as ordinary textile threads.

High purity (80%) nanotubes with metallic properties can be extracted with

electrophoretic techniques. In April of 2001, IBM announced it had developed a

technique for automatically developing pure semiconductor surfaces from nanotubes. On September 19, 2003, NEC Corporation, Japan, announced stable

fabrication technology of carbon nanotube transistors. In June 2004 scientists from

China's Tsinghua University and Louisiana State University demonstrated the use of

nanotubes in incandescent lamps, replacing a tungsten filament in a light bulb with

a carbon nanotube one.


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Nano-mechanical computer storage devices using nanotubes are currently in the prototype stages. Both high speed non-volatile memory which can be used to

replace nearly all solid state memory in computers today, and high density storage

that may replace hard drives, are being developed. Major limiting factors in the

development of nanotubes include their cost and difficulties in orienting the

nanotubes, which tend to tangle because of their length.

As of 2003, nanotubes cost upwards from 20 euro per gram to 1000 euro per gram,

depending on purity, composition (single-wall, double-wall, multi-wall) and other

characteristics.

Carbon nanotubes in electrical circuits

Carbon nanotubes have many properties--from their unique dimensions to an

unusual current conduction mechanism--that make them ideal components of

electrical circuits, and it is exciting to envision, or even to implement, novel

transistors, MEMS devices, interconnects, and other circuit elements.

The major hurdles that must be jumped for carbon nanotubes to find prominent

places in circuits relate to fabrication difficulties. The carbon nanotube production

processes are very different from the traditional IC fabrication process. The IC

fabrication process is somewhat like sculpture--films are deposited onto a wafer

and pattern-etched away. Carbon nanotubes are fundamentally different from films; they are like atomic-level spaghetti (and every bit as sticky).

Today, there is no reliable way to arrange carbon nanotubes into a circuit.

Researchers sometimes resort to manipulating nanotubes one-by-one with the tip

of an atomic force microscope in a painstaking, time-consuming process. Perhaps the best hope is that carbon nanotubes can be grown through a chemical vapor

deposition process from patterned catalyst material on a wafer. Though such a CVD

process has been shown to allow a circuit designer to locate one end of a nanotube,

there is no obvious way to control where the other end goes as the nanotube grows

out of the catalyst.

Even if nanotubes could be precisely positioned, there remains the problem that, to

this date, engineers have been unable to control the types of nanotubes--metallic,

semiconducting, single-walled, multi-walled--produced. This is a problem that

chemical engineers must solve if nanotubes are to find a place in commercial circuits.38


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Section A10: Photolithography 39

Photolithography is a process used in semiconductor device fabrication to transfer a pattern from a photomask (also called reticle) to the surface of a wafer or substrate. It bears a similarity to the conventional lithography used in printing. Lithography involves a combination of etching, chemical deposition, and chemical treatments in repeated steps on an initially flat substrate. A part of a typical silicon lithography procedure would begin by depositing a layer of conductive metal several nanometers thick on the substrate. A layer of photoresist -- a chemical that hardens when exposed to light -- is applied on top of the metal layer. The photoresist is selectively hardened by illuminating it in specific places. For this purpose a transparent plate with patterns printed on it, called a mask, is used together with an illumination source to shine light on specific parts of the photoresist. Then, the photoresist that was not exposed to light and the metal underneath is etched away with a chemical treatment. Finally, the hardened photoresist is etched using a different chemical treatment, and all that remains is a layer of metal in the same shape as the mask. Lithography is used because it affords exact control over the shape and size of the objects it creates, and because it can create patterns over an entire surface simultaneously. Its main disadvantages are that it requires a substrate to start with, it is not very effective at creating shapes that are not flat, and it can require extremely clean operating conditions. In a complex integrated circuit, a wafer will go through the photolithographic area on the order of 20 to 30 times.

Technology

A wafer is introduced onto an automated "wafertrack" system. This track consists of handling robots, bake/cool plates, and coat/develop units. The robots are used to transfer wafers from one module to another. The wafer is initially heated to a temperature sufficient to drive off any moisture that may be present on the wafer surface. Hexa-methyl-disilizane (HMDS) is applied in either liquid or vapor form in order to promote better adhesion of the photo-sensitive polymeric material, called photoresist. Photoresist is dispensed in a liquid form onto the wafer as it undergoes rotation. The speed and acceleration of this rotation are important parameters in determining the resulting thickness of the applied photoresist. The photoresist-coated wafer is then transferred to a hot plate, where a "soft bake" is applied to drive off excess solvent before the wafer is introduced into the exposure system. The desired pattern is then projected onto the wafer in either a machine called a stepper or scanner. The stepper/scanner functions similarly to a slide projector. Light from a mercury arc lamp or excimer laser is focused through a complex system of lenses onto a "mask" (also called a reticle), containing the desired image. The light passes through the mask and is then focused to produce the desired image on the wafer through a reduction lens system. The reduction of the system can vary depending on design, but is typically on the order of 4X-5X in magnitude. When the image is projected onto the wafer, the photoresist material undergoes some wavelength-specific radiation-sensitive chemical reactions, which cause the regions exposed to light to be either more or less acidic. If the exposed regions become more acidic, the material is called a positive photoresist, while if it becomes less susceptible it is a negative photoresist. The resist is then "developed" by exposing it to an alkaline solution that removes either the exposed (positive photoresist) or the unexposed (negative photoresist). This process takes place after the wafer is transferred from the exposure system back to the wafertrack.


51

Developers originally often contained sodium hydroxide (NaOH). However, sodium is considered an extremely undesirable contaminant in MOSFET fabrication because it degrades the insulating properties of gate oxides. Metal-ion-free developers such as tetramethyl ammonium hydroxide (TMAH) are now used. A post-exposure bake is performed before developing, typically to help reduce standing wave phenomena caused by the destructive and constructive interference patterns of the incident light. The develop chemistry is delivered in a similar fashion to how the photoresist was applied. The resulting wafer is then "hardbaked" on a bake plate at high temperature in order to solidify the remaining photoresist, to better serve as a protecting layer in future ion implantation, wet chemical etching, or plasma etching. The ability to project a clear image of a very small feature onto the wafer is limited by the wavelength of the light that is used and the ability of the reduction lens system to capture enough diffraction orders off of the illuminated mask. Current state-of-the-art photolithography tools use Deep Ultraviolet (DUV) light with wavelengths of 248 and 193 nm, which allow minimum feature sizes on the order of 130 to 90 nm. There are indications that 193-nm lithography can be extended to feature sizes below 45-nm using liquid immersion techniques. Also termed immersion lithography, this enables the use of optics with numerical apertures exceeding 1.0. The liquid used is typically ultra-pure, deionised water, which provides for a refractive index above that of the usual air gap between the lens and the wafer surface. This is continually circulated to eliminate thermally-induced distortions. Dopants may be added to the water to give a higher refractive index. Also in development are tools that will use the 157-nm wavelength DUV in a manner similar to current exposure systems. In addition, Extreme Ultraviolet (EUV) radiation lithography systems are currently under development which will use 13-nm wavelengths, approaching the regime of x-rays. Currently, there is uncertainty as to the technology succession in lithography. 157-nm equipment, once targeted to succeed 193 nm at the 65 nm feature size node, has now been pushed back to at least the 45-nm node. This has been due to persistent technical problems with the 157-nm technology and economic considerations that provided strong incentives for the continued use of 193-nm technology. At the 45 nm node and beyond however, 157-nm technology may face competition from both 193-nm technology and EUV lithography. The image for the mask is originated from a computerized data file. This data file is converted to a series of polygons and written onto a square fused quartz substrate covered with a layer of chrome using a photolithographic process. A beam of electrons is used to expose the pattern defined in the data file and travels over the surface of the substrate in either a vector or raster scan manner. Where the photoresist on the mask is exposed, the chrome can be etched away, leaving a clear path for the light in the stepper/scanner systems to travel through. Work is in progress on an optical maskless lithography tool. This uses a digital micro-mirror array to directly manipulate reflected light without the need for an intervening mask. Throughput is inherently low, but the elimination of mask-related production costs - which are rising exponentially with every technology generation - means that such a system would be far more cost-effective for small-scale manufacturing applications.


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