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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 25, NO. 3, SEPTEMBER 2002
Electrical Breakdown in Atmospheric Air Between
Closely Spaced (0.2 m–40 m) Electrical Contacts
Paul G. Slade, Fellow, IEEE, and Erik D. Taylor, Member, IEEE
Abstract—The increasing importance of electrical contacts in
air with micrometer spacing prompted recent experiments on the
electrical breakdown behavior of these gaps. The electrical field
between the contacts used in one of the experiments was analyzed
using finite element analysis to model the electric field. The experimental data on the electrical breakdown voltage could be divided into three regions as a function of the gap spacing. First, at
close gap spacing ( 4 m) both the breakdown voltages as well
as the electrical fields at the cathode were similar to values measured during the breakdown of vacuum gaps of less than 200 m.
Second, at larger gaps ( 6 m) the breakdown voltages followed
Paschen’s curve for the Townsend electron avalanche process in air.
Finally, in between these two regions the breakdown values were
below the expected values for purely vacuum breakdown or purely
Townsend breakdown. The breakdown phenomena have been discussed in terms of field emission of electrons from the cathode and
their effect on initiating the observed breakdown regimes.
Index Terms—Atmospheric pressure, electrical breakdown,
electrical contacts, Paschen’s law, small contact gaps, vacuum
breakdown.
I. INTRODUCTION
T
HIS paper discusses the electric breakdown of closely
spaced contacts (0.2 m to 40 m) in air at atmospheric
pressure. This subject attracted some research effort in the
1950’s [1]–[3], but for the most part has been neglected until
comparatively recently [4], [5]. There are a number of reasons
why discussion of this subject is timely. First, the miniaturization of electrical components is rapidly advancing. This
miniaturization includes higher conductor densities leading to
smaller conductor spacings in connectors, switches, and micro
electro-mechanical systems (MEMS). In these components,
the spacing between electrical conductors is routinely dropping
to the micrometer range. Even a low potential difference
imposed across two such conductors can generate a very high
electric field, possibly leading to an electrical breakdown at
quite low voltages. Second, the automobile industry is actively
changing the electrical system in cars from 14 V to 42 V. It is
commonly believed that if the voltage between two conductors
in atmospheric air is below the Paschen minimum breakdown
voltage in air of 325 V [6], [7], then a breakdown between the
conductors is not possible. However, an electrical breakdown
of the gap between the conductors, leading to an arc, is possible
even at 42 V when the distance between the conductors is a
few micrometers [8]. Third, this subject also can literally come
Manuscript received September 12, 2001; revised November 16, 2001. This
work was recommended for publication by Associate Editor J. W. McBride upon
evaluation of the reviewers’ comments.
The authors are with Eaton Corporation, Cutler-Hammer Products, Horseheads, NY 14845 USA (e-mail: paulgslade@eaton.com).
Digital Object Identifier 10.1109/TCAPT.2002.804615
close to home. A new miniature circuit breaker, called an arc
fault circuit interrupter, has been recently been introduced
for household use [9]. This device detects low-current, arcing
faults on the line, causing the circuit breaker to trip before the
fault can cause severe secondary damage, such as a fire. In the
U.S.A. the usual home circuit is 110 V (rms), so the question
has again risen about how could an arc burn for long enough to
cause damage at these low voltage levels. If the breakdown in
air followed Paschen’s Law, then the low line voltage would be
unable to break down the gap after the arc extinguished at the
first current zero. However, in closely spaced gaps a voltage
of 110 V would be sufficient to cause electrical breakdown,
re-igniting the arc after a current zero. Once an arc has been
initiated, breakdown of a contact gap is not the only means
by which the arc can continue to operate through a number of
current cycles. For example, carbon deposits from dissociated
insulation can permit a conducting path between the arcing
members. An arc carrying a current of a few amperes has a
temperature greater than 5000 K [8], which would be sufficient
to ignite a fire. Finally, increasing interest is being paid to
another potential arcing problem, namely in the hundreds of
kilometers of closely bundled electrical wiring typically used
in commercial and military jet aircraft [10].
In all these cases, the proper design of the electrical system
requires knowledge of the breakdown behavior. Experiments on
contacts in air at micrometer gaps have shown that the contact
gap crucially controls the breakdown voltage. An essential component in eliminating these electrical breakdowns at micrometer
gaps is to quantify the voltage limits and understand the breakdown behavior as a function of contact gap spacing. In this paper
we evaluate recently published electrical breakdown measurements for closely spaced contacts in air at atmospheric pressure
Pa and
Pa. This data is then
and in vacuum between
analyzed in terms of the Townsend electron avalanche theory
and Paschen’s Law for breakdown in air [6]–[8], and in terms of
the vacuum breakdown process involving field emission of electrons from microprojection on the cathode contact [11]–[13].
II. EXPERIMENTAL DATA
The data for electrical breakdown in atmospheric pressure air
comes from two sources [4], [5]. The first set of data was developed by Lee, Chung and Chiou [4]. These researchers made
careful measurements using the contact arrangement shown in
Fig. 1, with contact gaps ranging from 0.2 m to 40 m. The
cathode was a Fe polished needle and the anode was a silver
as a function of condisc. The minimum breakdown voltage
tact gap is shown in Fig. 2. The second data source, also shown
1521-3331/02$17.00 © 2002 IEEE
SLADE AND TAYLOR: ELECTRICAL BREAKDOWN IN ATMOSPHERIC AIR
Fig. 1.
391
The contact structure used in [4]. All dimensions are in millimeters.
Fig. 3.
(1).
Comparison of the data in Fig. 2 with both the Paschen curve in air and
Fig. 2. Electrical breakdown voltage in air as a function of contact gap. Data
points ( ) are from [4], and ( ) are from [5].
4
in Fig. 2, comes from the work of Torres and Dhariwai [5], again
using a very carefully developed contact system. These measurements were taken in a clean room, and three contact materials were tested: Ni, Al and brass. They observed no difference
outside their experimental errors for these materials.
in
Fig. 2 shows that for contact gaps greater than 6 m, the breakis in the range 300–400 V. For contact gaps less
down voltage
is a strong function of the
than 4 m, the breakdown voltage
contact gap . In Fig. 3 we have taken the Paschen Curve in air at
atmospheric pressure [8] and superimposed it on the data given
in Fig. 2. For contact gaps greater than 6 m, the Paschen curve
passes through the breakdown data. For contact gaps less than 4
m, the voltage breakdown points are below the expected values
predicted from the Paschen curve. The data in this region can be
represented as a linear function of the gap spacing
(1)
V m
The two lines are shown in Fig. 3; one is for
and the other is for
V m . This behavior will be
discussed in the following sections.
III. VACUUM BREAKDOWN REGION
The experimental data for the breakdown voltage at small
gaps in air is very similar to the breakdown behavior of contacts
in vacuum. The experimental data for the breakdown voltage
as a function of the contact gap in high vacuum is shown
Fig. 4. Electrical breakdown voltage in vacuum as a function of contact gap.
in Fig. 4. This data is taken from many sources [14]. The data
points shown here are the average values. The contact gap
ranges from 35 m to 200 m and shows a linear dependence
on contact gap
i.e.
(2)
V m
Vm . The value of
Where
for the vacuum breakdown data falls within the range of
in
(1) for the air breakdown data in contact gaps less than 4 m.
These experimental similarities between the breakdown data
in air at very small gaps and breakdown in vacuum for gaps of
less than 200 m suggest that a similar breakdown mechanism
governs both cases. Three other similarities are also present.
First, the electric field at the contact surface for small gaps in
air is comparable in magnitude to those observed in vacuum
breakdown. Second, this electric field is high enough to produce a field emission current from the cathode contact. Finally,
the mean free path of the electrons in air at atmospheric pressure is about 0.5 m. Electrons from the cathode will have very
few collisions before reaching the anode at small contact gaps
m). The presence of air in these small contact gaps will
(
thus have only a small effect on the breakdown process.
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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 25, NO. 3, SEPTEMBER 2002
Fig. 6. Example of a surface profile for a ground and polished mild steel
contact [16].
Fig. 5. Geometrical enhancement factor
Fig. 1 as a function of contact gap.
for the contact structure shown in
TABLE I
GEOMETRICAL ENHANCEMENT FACTOR FOR
CONTACT GAP
THE
TWO RANGES
OF
Even with polished contacts, the microscopic contact surface is
anything but smooth [15], as seen in Fig. 6 [16]. The peaks in
the contact surface result in another field enhancement factor,
, at the surface of a microprojection’s peak. Thus, the total
electric field at the contact’s microsurface is given by
(4)
Putting
then:
(5)
For vacuum breakdown, the critical parameter is the local
electric field at the contact surface. A common method to cal(where is the
culate the electric field is to use the ratio
potential drop impressed across the contact gap ). When the
contact gap is small compared to the radius of curvature at the
tip of a needle contact, or the diameter of broad area contacts, the
peak macroscopic field is very close to this value. There will be
a geometrical effect that produces a higher macroscopic field for
longer contact gaps. For broad area contacts, the peak electric
field is generally on the edge of the contact, and for needle contacts it is generally at the contact tip. If the geometrical enhancement factor for a given gap is then the maximum macroscopic
field, , between the contacts is given by
(3)
The first step in comparing the air breakdown data to the vacuum
theory is to determine . We performed a finite element analas a function
ysis for determining macroscopic electric field
of the contact gap for the arrangement shown in Fig. 1. The data
versus the contact gap for this
in Fig. 5 plots
case. The ratio of the contact gap spacing to the radius of curvature of the needle cathode determines the behavior of the electric
field. When the gap is very much smaller than the needle’s radius of curvature, the needle geometry only has a small effect on
can be used to approximate the electric
the electric field and
field. The peak electric field, however, increases monotonically
as the gap increases. For a contact gap of 40 m (i.e., near to
the needle’s radius of curvature) the value of has the value of
about 1.6. Table I gives the ranges for the geometrical enhancement factor for the contact geometry used in the air breakdown
experiment in [4]. Thus, for a contact gap of 2 m in air, where
is 160 V (Fig. 3) and
is 1.033 (Fig. 5),
Vm when the gap breaks down.
In addition to knowing the macroscopic field, it is also imporat the contact surface.
tant to examine the microscopic field
For polished cathodes, the total enhancement factor
is in the range 100–250 [17]. Calculations of the enhancement
factor generally state the total rather than separately deterand macroscopic
contribumining the microscopic
at breakdown for contact gaps 35
tions. From Fig. 4,
m to 200 m in vacuum is
Vm . Therefore
at breakdown lies between
Vm and
Vm . These field strength values
are comparable to calat breakdown in air for a contact gap of 2 m
culations of
Vm and
Vm ). The Fe cathode
(between
used to generate these experimental data is a carefully prepared
and polished needle. We would therefore expect that for this
at the 2 m
cathode to be closer to 100 than to 250. Thus,
Vm . The breakdown field
gap in air would be closer to
strength for vacuum gaps (35 m–200 m) and contact gaps in
m) are thus very similar.
air (
The enhanced electric field at the cathode contact’s surface
results in the field emission of electrons. The current density
generated by the electric field is give by the Fowler-Nordheim
equation [17], [18]
(6)
is in amp/m , the electric field is in V/m, is the
where
work function of the contact material in eV, and and are di.
mensionless functions of the parameter
In practice, is one and is
(7)
This equation calculates the current density from the metal via
tunneling through the surface potential barrier. A further explanation of the terms of the equation can be found in [19].
comes from a small
Assuming that the emission current
on the contact surface, then the curmicroprojection of area
. Further assuming that the microrent density is
SLADE AND TAYLOR: ELECTRICAL BREAKDOWN IN ATMOSPHERIC AIR
393
Fig. 7. Fowler–Nordheim plot of the prebreakdown field emission current for
Cu contacts spaced 2 mm apart.
Fig. 9. Electrical breakdown process in vacuum for contact gaps less than 500
m and in air for contact gaps less than 4 m.
Fig. 8. Prebreakdown field emission current as a function of the applied
voltage for the data in Fig. 7.
scopic field at the tip of the microprojection
and the total
is given by (3)
gives a value of 248. The electric field in this experiment is
Vm when breakdown occurs. Thus,
only
the electric field for contacts in air spaced at less than 4 m is
certainly sufficient to produce a very high current density at a
cathode microprojection.
The development of space charge in front of the cathode is
often cited as a limiting factor on the current density that can
be extracted from microprojections. Dyke and Trolan [20] observed that the field emission current diverged from the FowlerAm for
Nordheim equation at current densities above
a 1 mm contact gap. This behavior can be attributed to the effects of space charge reducing the electric field at the emitter,
and hence lowering the emission current. Nevertheless, the current density does still increase with increasing electric field and
eventually breakdown is reached. The space charge current limit
can be calculated from the formula [21]
(8)
(11)
then (6) equation can be written as
(9)
meaIf the voltage across the contact gap is varied and
vs.
would give a straight
sured, then a plot of
line with slope :
(10)
from which can be calculated. Fig. 7 shows a typical FowlerNordheim plot for Cu contacts with a 2 mm gap in vacuum [17],
as a function of for the data in Fig. 7.
and Fig. 8 shows
grows exponentially as (and ) increases. In fact, at
(
kV) for this contact structure and gap,
will increase
into the milliampere range. Thus, for a 1.45 times increase in
(and
), from 34.6 kV to 50 kV, the current increases by
. The slope of the line in Fig. 7
four orders of magnitude
is the space charge limited current density, is the
where
bias voltage and is the gap distance. Comparing the ratio of the
current density limit for a typical small gap case in air (
Volt,
m) to that of a macroscopic gap typical of vacuum
kV,
mm) gives
breakdown experiments (
V
kV
m
mm
(12)
Thus, space charge buildup will still affect the emission current,
however, the current limit is higher for smaller gaps because of
the squared dependence on the gap distance. Since breakdown
in the larger gaps occurs via the vacuum breakdown mechanism
despite the effects of space charge, small gaps should be able to
follow the same breakdown process.
For small gaps in air, the space charge effect will only be of
is greater than
Am . This current denconcern once
sity is still too low to heat the cathode macro-projection to a
level that would initiate a breakdown from the production of
field emission electrons alone. One method for overcoming the
394
Fig. 10.
IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 25, NO. 3, SEPTEMBER 2002
Townsend electrical breakdown process in air for contact gaps greater than 6 m.
space charge limitation is to ionize the dense neutral gas desorbed by the current heating [22]. The resulting ions move toward the cathode, thereby reducing the negative space charge
build up and allowing the electric field at the contact surface to
increase. Also, ions falling into the cathode will encounter an
image electron that travels in the projection to recombine with
it. The total current density inside the microprojection thus will
be
(13)
This process is illustrated in Fig. 9 [22].
The background air between the contacts can have only a limited effect on the breakdown process. The mean free path of an
m, so for contact
electron in atmospheric pressure air is
gaps less than 4 m the field emission electrons will only have a
few collisions with gas particles. A voltage drop of 20 to 300 V
across the contact gap gives a reasonable probability of limited
ionization from these few collisions. As the ions drift toward
the cathode, a positive space charge can develop in front of the
to increase. This efcathode microprojection that will allow
fect also helps to compensate for the collisions that may occur
between the electrons and the background gas.
When the in the cathode microprojection reaches values of
to
Am , the explosion emission process
the order of
for vacuum breakdown, as discussed by Juttner [11] (based on
the work by Mesyats [12] and Fursey [13]), can occur for closely
increases (Fig. 9), the temperature
spaced contacts in air. As
of the cathode microprojection increases. In fact, the temperature inside the microprojection increases faster than the surface
as a result of the Nottingham effect [13], [23]. The Nottingham
effect results from the difference in energy between the emitted
electrons and their replacements in the metal lattice from the
external electrical circuit. At a critical temperature, the microprojection will explode and a dense cloud of metal vapor plasma
will form above the cathode surface. This cathode plasma will
expand at
ms [11], crossing a contact gap of 1 m in
s. With closely spaced contacts (
m), the
about
breakdown of the contact gap once the microprojection explodes
is almost instantaneous. Thus, it is reasonable to assume that
the breakdown process for very small contact gaps in air is similar to that described for vacuum breakdown. The breakdown
voltage is a function of the electric field between the contacts,
not a function of the contact gap times the ambient pressure.
Small contact spacing allows low inter-contact voltages to produce breakdowns. In the experiments discussed here, a breakV is observed for a 0.25 m contact
down voltage
gap. Thus, for contact gaps less than 4 m the electrical breakdown follows the sequence expected from experiments on the
breakdown of contact gaps in vacuum. In this process, the current density in the microprojection increases until it explodes,
forming a rapidly expanding plasma ball of metal vapor. When
this plasma reaches the anode, the contact gap breaks down.
IV. PASCHEN BREAKDOWN REGION
Fig. 3 shows that the
as a function of contact gap for
gaps greater than 6 m fits the Paschen Curve for air. The
no longer satisfies the vacuum breakdown curve for gaps
m, where voltages above
V would be required for
the vacuum breakdown processes to occur. For contact gaps
of 6 m or more, field emission electrons from the cathode
will have approximately twice the number of collisions that
would occur for contact gaps of less than 4 m. This produces
more ionizing events, making it reasonable to assume that the
electrical breakdown for longer contact gaps occurs as a result
of Townsend electron avalanche theory [8]. This process is
illustrated in Fig. 10. For a 7 m contact gap with a voltage
drop of 330 V (Fig. 3), and assuming that is 100, then
Vm
Vm
(14)
SLADE AND TAYLOR: ELECTRICAL BREAKDOWN IN ATMOSPHERIC AIR
Inserting this value into the Fowler-Nordheim equation (see (6))
shows that this electric field can generate a field emission electron current in the microampere range. These electrons will interact with the background gas. The growth in current will be
given by [7], [8]
(15)
where is the contact gap, is the first Townsend coefficient,
giving the number of electrons produced per unit distance in
the direction of the electric field and is the second Townsend
coefficient, giving the number of electrons generated by secondary processes per each primary avalanche. Breakdown oc. According to the Paschen curve
curs when
for air, the minimum voltage at which this can occur is about
330 V, as is seen in Fig. 3. Thus, for contact gaps greater than
6 m in air, field emission electrons from microscopic projections at the cathode can still initiate the breakdown process. In
this case, however, the field emission electrons initiate an electron avalanche that leads to a gap breakdown when a voltage
V is impressed across the open contact gap.
V. TRANSITION REGION
For the contact gap in the range 4 m to 6 m, the measured
is less than would be expected from either purely vacuum
breakdown or from Townsend avalanche breakdown. In this region only a partial electron avalanche process would be initiated, because the electrons would only have a limited number
of collisions with the gas before reaching the anode. This partial avalanche would, however, produce more ions, which would
drift toward the cathode microprojection. This enhanced flow
of ions to the cathode projection would result in an increase
(see (13)). Thus, the
in the microprojection current density
cathode microprojection could reach a critical current density at
than for purely vacuum breakdown. In this contact
a lower
gap range, the electron avalanche enhances the vacuum breakdown process.
VI. CONCLUSION
1) For closely spaced contacts in air, Paschen’s Law is only
valid for contact gaps greater than about 6 m.
2) For contact gaps less than about 4 m, the breakdown
, in air is a linear function of the contact gap
voltage,
and is given by:
volts
(16)
is a constant.
is similar in
where is in m and
value to the breakdown voltage expected from contacts
with the same contact gap, but in a vacuum ambient.
3) For contact gaps of less than about 4 m, the electric field
at a micro projection on the cathode contact’s surface can
be high enough to produce a very high current density,
field emission electron beam at the projection. When this
current density exceeds a critical value, the micro projection explodes and a very high-density plasma forms in the
released metal vapor. Electrical breakdown between the
395
contacts is achieved when this plasma reaches the anode
contact. This sequence is very similar to the electrical
breakdown process between open contacts in vacuum (for
contact gaps up to 200 m).
4) For contact gaps greater than about 6 m, the breakdown process follows the classical Townsend electron
avalanche theory. For small gaps, however, field emission
electrons from the cathode contact initiate the electron
avalanche.
5) For contact gaps between 4 m and 6 m, the electrical
breakdown is lower than would be expected from either
Paschen’s Law or from the vacuum breakdown data. We
believe that in this range of contact gap, the electrical
breakdown results from an electron avalanche enhanced
vacuum breakdown.
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Paul G. Slade (M’71–SM’86–F’90) received the
B.S., Ph.D., and Diploma of mathematical physics
degrees from the University of Wales, Swansea,
U.K., and the MBA degree from the University of
Pittsburgh, Pittsburgh.
He has over 30 years experience covering a wide
range of problems associated with switching electric
current. His research has covered electrical contact
and arcing phenomena in air, vacuum, and SF . He
has used this experience to develop new types of circuit breakers and switches. He has authored or co-authored over 70 research papers and has published the book Electrical Contacts,
Principles and Applications. He is presently the Manager of the Vacuum Interrupter Technology Department, Eaton Cutler-Hammer, Horseheads, NY, where
he is responsible for research and development, design, and applications engineering for the vacuum interrupter product.
Dr. Slade is a member of the Institute of Physics (U.K.).
Erik D. Taylor (M’00) received the B.S. degree (with
honors) in applied physics from the California Institute of Technology, Pasadena, in 1993 and the M.S.
and Ph.D. degrees in applied physics from Columbia
University, New York, NY, in 1995 and 2000, respectively.
In 1999, he started working for Eaton
Cutler-Hammer, Horseheads, NY, as a Senior
Scientist/Engineer at their vacuum interrupter factory. His research interests include plasma physics,
vacuum arc physics, electromagnetic field modeling,
vacuum breakdown, magnetic fusion, and plasma-material interactions.