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Solid Tantalum
Capacitor
Dielectric Failure
Mechanism and
Determination of
Failure Rates
by H. W. Holland
KEMET
®
Electronics Corporation
P. O. Box 5928
Greenville, SC 29606
Phone (864) 963-6300
Fax (864) 963-6521
www.kemet.com
F-2695C 4/98
1
DESIGN
To understand the solid tantalum capacitor failure mechanism, some knowledge of
the product design and the manufacturing
process is necessary. The basic raw material is tantalum. In the first manufacturing
step, tantalum is prepared as a fine powder.
The powdered tantalum is fed to molds
where compression produces a coherent
mass, usually in the form of a cylindrical or
rectangular shaped pellet. A tantalum lead
wire is also embedded in the compressed
powder during this operation, the wire
extending axially from the end of the pellet.1
Pressure is controlled so that the pellet
density results in a porous body of high
internal surface area.
The pellets are sintered at high temperature in vacuum furnaces. Sintering vastly
increases cohesion of the tantalum particles
and thus assures high electrical conductivity. The pellets also become mechanically
rugged structures. Just as important is the
purifying effect of the high temperature
vacuum bake. Tantalum is a refractory
metal, and sintering temperatures range
from 1400° to 1900°C. This temperature, in
combination with the low furnace pressure
(usually less than 10-4 torr), vaporizes most
impurity materials, which are then pumped
away in the vacuum system. As will be
shown later, failure of capacitors is directly
influenced by the residual impurities inevitably left behind.
Sintered pellets are anodized in an acidic
bath to form a layer of tantalum pentoxide
(Ta205) on all surfaces reached by the electrolyte. This oxide layer, whose thickness
depends upon the applied voltage, is the
dielectric of the capacitor. The capacitance
value, of course, is inversely proportional to
the dielectric thickness. On the other hand,
higher voltage ratings require thicker dielectric films. The product of capacitance and
anodizing voltage (CV product) is very
nearly constant for a pellet of given surface
1. An alternative procedure welds tantalum wire to a previously-sintered compact pellet. A second sinter is usually
neces-sary to attain the requisite purity.
2
area and is a convenient design parameter.
Anodized pellets are next coated with a
semi-conductor “solid electrolyte” that enters
and fills the pores to contact as much of the
capacitive surface area as possible. The
solid electrolyte is manganese dioxide
(MnO2), formed in situ by pyrolysis of a
manganous nitrate solution into which the
porous pellets are dipped before pyrolysis.
Several cycles of dipping in nitrate solution,
each followed by thermal decomposition of
nitrate to dioxide, are necessary to complete
the solid-electrolyte layer.
The remainder of the manufacturing cycle
is directed at providing an encapsulation
with external lead-wire connections. The
positive, or anode, lead is readily obtained
by welding to the tantalum wire originally
attached to the anode pellet. The cathode
connection begins with application of a
conductive system over the manganese
dioxide. This system is usually composed of
succeeding layers of colloidal graphite,
silver-loaded paint, and for leaded devices,
solder. In the popular hermetically-sealed
designs, the solder anchors the pellet inside
a metal can to which the negative lead wire
is attached. Figure 1 shows this design
schematically. In the surface mount tantalum capacitor, the negative termination is a
lead frame and is attached by a conductive
epoxy.
DEFINITION OF FAILURE
Several criteria could be chosen to define
a failure. The nature of the solid tantalum
capacitor, however, is such that the short
circuit deserves most of the attention. This
type of failure is characterized by a sudden
rise in leakage current, within a few milliseconds, from nanoampere or microampere
magnitude to ampere magnitude in lowimpedance circuits. Failure from an opencircuit condition can be produced through
faulty manufacture, but these parts are
easily detected and scrapped in the plant.
Other definitions of failure would necessarily be centered about changes in leakage
current of relatively small degree or changes
in the other two important parameters,
capacitance and dissipation factor. Leakage
current can be made so small (below 0.01
microampere per rated microcoulomb) that
changes of even 100% become insignificant
in nearly all applications. Similarly, changes
in capacitance and dissipation factor during
normal service life are small enough to
present no real problem to nearly all applications. No circuit designer, however, can
allow for complete short circuit, and this
failure mode properly becomes the focus of
attention in reliability studies.
MECHANISM OF FAILURE
If the tantalum pentoxide layer, which
constitutes the dielectric, were perfectly continuous and of uniform thickness throughout,
leakage current would be several orders of
magnitude lower than that of the best practical capacitors yet made. The leakage currents normally exhibited must flow, not
through the dielectric, but through faults in
the dielectric. These faults occur primarily
because of impurities in the tantalum metal
that have defied efforts at removal. Wherever an impurity is encountered, anodization
cannot produce a continuous Ta205 layer of
uniform thickness. The result is a minute
hole or thin spot in the dielectric layer that
can be filled with the Mn02 solid electrolyte
or with air. Compared with Ta205, either of
these materials will allow relatively heavy
conduction under conditions existing within
the capacitor.
Simple probability indicates that the larger
the capacitive area, the larger the number of
impurity sites to be encountered. If impurities were randomly distributed over the
underlying area of tantalum, the number of
fault sites would be directly proportional to
the size of the anode pellet. However, nearly
all the surface area is reached via pores in
the pellet. Also, it will be recalled that final
purification is accomplished during sintering.
If the pellet’s size is increased (especially by
increasing cross-section) the mean free path
for impurity removal becomes much longer.
Consequently, capacitors with large anodes
present a difficulty in manufacture beyond
that indicated by a simple size relationship.2
There is, in addition, a depthwise distribution
of impurities in any given particle of tantalum
within the pellet. This distribution is also
derived from the purification process, those
impurities near the original surface being
more easily removed during sintering.
Figure 2 represents this situation when
anodizing takes place.3 The layer of tantalum near the original surface has been
reacted electrochemically to form, Ta205. To
form a thicker Ta205 film will obviously
require reaction that penetrates deeper and
encounters higher impurity densities. Thicker dielectric films are necessary for higher
voltage ratings; these ratings consequently
become more difficult to produce.
It has been stated that each impurity site
in the dielectric produces leakage current
when a conductive material is present.
Leakage currents would be many, many
times larger than they are if it were not for a
change in MnO2 structure that takes place
opposite the fault sites. As D.C. voltage is
applied to a newly manufactured capacitor,
high current densities are produced in the
faults. Since the faults are small (in the
Angstrom-unit range), large total currents
are not necessary to produce extremely high
current densities. The high current produces
Joule heating in the MnO2 opposite the fault.
At elevated temperature, MnO2 undergoes
spontaneous reduction to lower oxides. The
lower oxides coincidentally display much
higher electrical resistivities, effectively
reducing the leakage current that originally
produced the heating. The magnitude of this
effect can be deduced by noting that MnO2
has a resistivity of approximately 10 ohmcm, while Mn2O3 has a resistivity of approximately 104 ohm-cm.
If a relatively small fault site is encountered, the mechanism just described may
2. In this discussion it is assumed that manufacturing
variables such as powder particle size, pellet density, and
sintering time and temperature remain fixed. These are
degrees of freedom in design that can be used to alter the
magnitude of the size effect.
3. Figure 2 does not purport to show the exact appearance
of Ta2O5 at fault sites, but illustrates that defects in the
dielectric follow from impurities in the metal substrate.
3
permanently reduce the leakage current
associated with that site to a very low value.
If a large fault site is encountered, the
amount of heat produced may be sufficient
to destroy a yet larger area of dielectric
through crystallization of the normally amorphous oxide. An avalanche condition is then
produced, leading inexorably to a shortcircuited capacitor. Between these extremes
are intermediate conditions producing capacitors with various leakage currents. Some
of these are on the fringe of stability. For
these, a high external circuit impedance
limits the fault current and assists the MnO2
“healing”, whereas a low impedance circuit
produces catastrophic failure. It is thus
important to keep life-test circuit impedance
low to produce worst-case conditions in
reliability studies. Scintillation (or flicker) is a
phenomenon favored by high-impedance
circuits. This term describes a momentary
pulse of current that is shut off by “healing”
action. Low-impedance testing usually
converts scintillation to catastrophic failure.
STATISTICAL STUDIES OF FAILURE
The postulated mechanism of failure may
have a somewhat different beginning to the
same end if it is agreed that impurities
migrate during service, subsequently
causing a dielectric fault. This possibility
should cause no alarm if the chosen mathematical model can allow for such heterogeneity of cause. Indeed, it should be recognized that production lots can probably
never be made such that every capacitor is
precisely identical to every other capacitor;
neither can one lot be made identical to
every other lot. These difficulties should be
overcome if entire lots are tested and the
survival data fitted to a distribution for each
lot.
Behavior of solid tantalum capacitors in
service follows a pattern that is entirely consistent with the failure mechanism described
above. Two service conditions (assuming
constant circuit impedance) are important:
temperature and applied D.C. voltage. At
any given combination of temperature and
voltage, the average leakage current will
4
trend downward during life test. The “healing” effect apparently continues to form
better and better barriers at the fault sites.
Occasionally, there will be a catastrophic
failure when leakage current rises in avalanche fashion. In these instances, a localized failure in the dielectric, resulting from
perturbation of the healing equilibrium, has
apparently taken place. The rate at which
failures occur in any given group of capacitors can be determined by periodic counting of the number failed. Such counts form
the basis for prediction of the probability of
failure during anticipated service life.
Failure rate (usually expressed as percent failed per thousand hours of operation)
of any device can increase, decrease, or
remain constant with respect to time. With
some devices (such as the human being) all
three situations are found: a high infant
mortality, decreasing to a constant rate
caused by random events, and finally a
wear-out period when the rate increases.
Only the first of these periods has been
found applicable to solid tantalum capacitors: that is, the failure rate decreases and
continues to decrease for times at least in
excess of 70,000 hours. Obviously, application of a very large over-stress can cause
immediate failure of all parts, so it is possible to select conditions where failure rate
does not decrease with time. This aspect
will be treated more thoroughly in a discussion of “acceleration.”
The characteristic decreasing failure rate
makes statistical treatment more difficult
than the frequently-assumed constant failure
rate. There is, however, a distribution function, published by Waloddi Weibull, that can
conveniently treat variable failure rates. It is
stated in its useful two-parameter form as:
xβ
F(x) = 1 - exp (- α )
where x = time
β = the "shape parameter"
α = the "scale parameter"
F (x) gives the cumulative fraction of the
group that has failed to time x. The prob-
ability of failure at any particular time x is
given by the first derivative of the cumulative
function:
β β−1
xβ
F' (x) = α x
exp (- α )
The fraction of the group surviving at time x
is one minus the cumulative fraction failed:
xβ
1 - F(x) = exp ( - α )
The instantaneous failure rate is the probability of failure at time x divided by the
fraction of the original group surviving at
time x:
β
F' (x)
β−1
Z(x) = 1-F(x) = α x
To make the easy use of the weibull function, a special graph paper has been constructed, based on the following transformation:
β
1 - F(x) = exp ( - x )
α
β
1
= exp ( - x )
α
1-F(x)
1n
1n 1n
β
1
=x
1-F(x) α
1
= β 1n x-1n α
1-F(x)
The latter equation is the form of a straight
line with slope = β and y-interccept = -1n α.
The grid of Figure 3 has 1n x as the prin1
cipal abscissae and 1n1n
1-F(x)
as the principal ordinate. Auxiliary scales
permit direct plotting of F (x) (cumulative
fraction failed) on the ordinate versus x (time
of failure) on the abscissa.
A straight line is obtained when solid
tantalum capacitors are put on life test and
the cumulative failures plotted versus time
on the Weibull grid. The significance of β
should now be noted. When β = 1, failure
rate is constant; when β>1, failure rate is
increasing; and when β<1, failure rate is
decreasing. Observed slopes of solid
tantalum capacitors are uniformly less than
unity unless stressed well above their temperature-voltage ratings or previously damaged in some way (e.g., by reverse polarization at high voltage). Once the line has
been established, α and β are readily obtained, and the instantaneous failure rate at
any time can be calculated. Extrapolation
will determine the failure rate at some time
in the future, or conversely, the time required before the failure rate falls below some
given value.
ACCELERATION
Solid tantalum capacitors carry rated voltages that are intended to apply at 85°C or
below. Supplemental ratings above 85°C
are made to 125°C, but permissible voltage
is decreased accordingly. This rating
scheme fits the concept described above:
temperature and voltage are the two important and inter-related conditions determining
anticipated life in service. It is well recognized that, at any given temperature below
the maximum 125°C, voltages lower than
rated will lead to improved reliability (i.e,
lower failure rates). Similarly, higher voltages will lead to higher failure rates.
Since failure rate is increased by increased voltage, the failures that would ordinarily be observed over a long period of time
are made to occur within a shorter time span
by application of voltage above rated. Any
aging effects are thus “accelerated”. For
example, application of 1.1 times the rated
voltage might mean that every hour on test
under this condition and at 85°C is equivalent to four hours under the conditions of
rated voltage and 85°C. If very high voltages
are applied, the failure mechanism might
change. There is thus a limit to the degree
of acceleration beyond which consistent
relationship to applied voltage is no longer
obtained.
APPLICATIONS TO DETERMINE
FAILURE RATE
Use of the Weibull distribution as a model
was shown above, and acceleration factors
were described. Combining the two provides
5
a method of determining failure rate of any
given batch of capacitors in reasonable
times. Acceleration factors have been determined by correlating failures occurring under
rated conditions with corresponding failures
occuring in the same lots under conditions
of higher stress. With time accelerated, it is
feasible to place entire lots of capacitors on
life test, observing sufficient failures to determine the Weibull parameters graphically.
With the parameters fixed, the rate at which
failure rate decreases is fixed, and the test
time needed to attain the failure rate goal
can be calculated.
Under this scheme, the failure rate is
determined on an entire lot and not on a
sample. It is also determined quickly enough
to show proof before the lot is shipped. The
scheme recognizes the inherent failure-rate
inequality among various voltage-capacitance ratings (fundamentally the impurity
relationships discussed above) and even
among lots of same rating. It avoids “family”
failure rates that are akin to averages of
apples and pears.
As an example, Figure 3 shows a Weibull
plot for a lot of solid tantalum capacitors
placed on test at 85°C and 52 volts. The
rated voltage of these capacitors was 35, so
the test voltage was 1.48 times rated. Mil-C39003 has established exact acceleration
factors correlating actual time in test at
accelerated voltages to a much longer time
at rated voltage, but for this example, lets
assume that every hour on test is equal to
1,000 hours under rated conditions. This
value is called A, the “acceleration factor.”
From the Weibull plot, -1nα, the intercept
with the principal ordinate, may be read
directly as 6.23, yielding a value for α of
500. The value of β is determined as the
slope of the line:
2.3
β=
6
4.6
= 0.5
Knowing α and β, it is possible to calculate
the instantaneous failure rate, Z(x), at any
time. It is convenient to determine Z(x) at
one hour. The earlier equation,
β
Z(x) = α x
β−1
is now modified by a factor of 105, to convert to the conventional units of percent
failed per thousand hours, and by the acceleration factor, A, to convert to real time:
β
Z(x) = α x
β−1
105
xA
5
5
β
when x = 1, Z(x) = α x 10 = 0.5 x 103 = 0.1%/K hr.
500 10
A
Converting the instantaneous failure rate
equation to logarithmic form simplifies
further calculation:
β
log Z(x) = log α + (β-1) log x
A log-log plot is conveniently constructed
with slope = β-1 and Y-intercept β
α
or the failure rate at one hour. A plot for the
numerical example is given in Figure 4. The
required test time to attain a failure rate goal
can be read directly. The entire lot of capacitors would then remain on test until the
selected goal had been attained.
a
Tantalum
(Ta205)
Solder
Silver
Lap or Butt
Weld
(Third Layer)
Glass to
Metal Seal
a
Solder
Mn02 Coat
(First Layer)
Carbon
(Second Layer)
Tantalum Wire
Metal Can
Lead Wire
Figure 1.
KEMET Solid Tantalum Electrical Capacitor
A
Dots Represent
Impurity Sites
Original Tantalum Section
Figure 2.
B
Anodized to Depth "A"
Anodized to Depth "B"
Effect of Impurities in Anodization of Tantalum
In (Failure Age)
0.0
99.9
99.0
1.0
2.0
3.0
4.0
5.0
6.0
+2.0
+1.0
70.0
-1.0
30.0
20.0
-2.0
10.0
∆ = 4.6
5.0
3.0
2.0
-3.0
100
( 100 - %
Failed )
0.0
50.0
-4.0
1.0
-5.0
∆ = 6.2 - 3.9 = 2.3
0.5
0.3
0.2
In In
Cumulative Percent Failed
90.0
-6.0
0.1
1.0
10
100
1,000
Failure Age - Hours
Figure 3.
Weibull Plot for 35 Volt Capacitor Tested at 52 Volts, 85°C.
0.1
0.01
0.001
1
Figure 4.
10
100
1000
Weibull Parameters Determined from Figure 3. Used
to display Failure Rate versus Test Time.
7
®
KEMET Capacitors
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© KEMET Electronics Corporation 1998
01/16/98