NASA Electronic Parts and Packaging (NEPP) Program
Insulation Resistance and
Leakage Currents in Ceramic
Capacitors with Cracks
Alexander Teverovsky
Parts, Packaging, and Assembly Technologies Office, Code
562 GSFC/ASRC Federal Space and Defense
Alexander.A.Teverovsky@nasa.gov
Introduction
Purpose: Can measurements of insulation resistance (IR) reveal
low-voltage MLCCs with cracks?
Outline:
 Absorption and intrinsic
leakage currents.









Effect of size.
Effect of capacitance.
Effect of voltage.
Effect of temperature.
Effect of cracking.
Absorption capacitance.
Modeling of absorption currents.
IR measured by voltage absorption.
Conclusion.
ESA Sept. 2013
2
Requirements for IR
 IR = VR/I(t), where VR is the rated voltage, and t ≤ 2 min.
 Limits for military MLCCs:
IR > 1011 Ω or 103 MΩ-µF, whichever is less, at +25°C,
IR > 1010 Ω or 102 MΩ-µF, whichever is less, at +125°C.
 Requirements for commercial capacitors are two times less.
 IR is inversely proportional to the value of capacitance and do
not depend on VR and size (thickness of the dielectric)
ρεε 0
εε 0 S
ρH
C=
H
IR =
S
IR =
C
 However, ρ is not constant, and Schottky conduction
increases exponentially with E = V/H.
 A decrease of IRlimit with temperature corresponds to
activation energy of ~0.3 eV, which is much lower than the
values reported for conductivity of ceramic materials.
ESA Sept. 2013
3
Absorption Currents
 Currents decrease with time according to an empirical Curievon Schveindler law:
I (t ) = I 0 × t − n
, where n ~ 1.
 Current relaxation: charges are “absorbed” in the dielectric.
1.E-05
1.E-07
current, A
1.E-09
n = 0.61
n = 0.71
n = 0.76
1.E-10
1.E-11
1.E-12
1.E+0
1.E+2
time, sec
1.E-08
1.E-09
1.E-11
1.E+0
1.E+3
1.E+4
n = 0.75
1.E-07
1.E-10
Mfr.A 0.12uF 50V
Mfr.C 1uF 6.3V
Mfr.N 0.12uF 16V
Mfr.C CDR31 0.018uF 50V
1.E+1
current, A
1.E-06
1.E-08
n = 0.88
1.E+1
2220 Mfr.T 22uF 25V at VR
0805 Mfr.N 0.1uF 50V at VR
0805 Mfr.Pa 3.3uF 6.3V at VR
n = 0.7
1.E+2
time, sec
1.E+3
1.E+4
2220 Mfr.T 22uF 25V at 0V
0805 Mfr.N 0.1uF 50V at 0V
0805 Mfr.Pa 3.3uF 6.3V at 0V
Experimental data for different MLCCs: 0.6 < n < 1.1.
Depolarization, or desorption currents are flowing in the opposite
direction in a short-circuited capacitor.
Depolarization currents have similar value and follow the same
power law.
ESA Sept. 2013
4
Absorption and Intrinsic Leakage
Currents
 Absorption currents, Iabs, and intrinsic leakage currents, Iil,
are reproducible from sample to sample.
 Iabs reduces with time, while Iil remains constant.
1.E-06
1.E-06
1.E-06
6V
12V
20V
n = 0.7
2220 Mfr.A 10uF 50V
n = 0.9
2225 Mfr.B 1uF 50V
1.E-08
1.E-07
9V
15V
n = 0.61
1.E-08
1.E-10
20
200
time, sec
2000
1.E-09
1.E+0
1.E-08
1.E-09
1.E-09
n = 1.3
1825 Mfr.A 0.1uF 100V
1.E+1
1.E+2
1.E+3
time, sec
1.E+4
n = 0.6
1.E-07
current, A
current, A
1.E-07
current, A
0805 Mfr.Pa 3.3uF 6.3V
1206 Mfr.M 22uF 6.3V
Absorption currents in MLCCs
1.E+5
1.E-10
1.E+0
n = 0.69
25.2V
6.3V
12.6V
18.9V
1.E+1
1.E+2
1.E+3
1.E+4
time, sec
 Absorption currents prevail at initial moments of electrification.
 At room temperature and VR intrinsic leakage currents are
relatively small, but might be observed at V>>VR within minutes
of electrification.
ESA Sept. 2013
5
Effect of Size
 Three types of 1 µF 50V capacitors were from the same
manufacturer, but had different case sizes.
 The thickness of the dielectric was 19.4 µm, 8.9 µm, and 4.3 µm for
case sizes 2220, 1206, and 0805, respectively.
1uF 50V MLCCs Mfr.M
 No substantial difference in currents
and IR for the 60-sec measurements.
 The 1000-sec measurements were
~10X less for 2220 parts compared to
2220
0805 capacitors.
1206
0805
 Currents measured after 1000 sec.
have a substantial component related
to the intrinsic leakage currents, while
60-sec currents were due to
current, A
absorption.
99
1000 sec
cumulative probability, %
60 sec
50
10
5
1
1.E-10
1.E-9
1.E-8
1.E-7
 IR does not depend on the case size when absorption currents
prevail.
ESA Sept. 2013
6
Effect of Capacitance
IR, Ohm
 X7R capacitors with EIA case sizes from 0402 to 2225,
voltage rating from 6.3 V to 100 V, and capacitance from 1500
pF to 100 µF.
 Correlation between the values of IR measured by a standard
technique and capacitance for 40 different part types:
IR = 5×109/C, where C is in µF and IR is in Ω.
1.E+13
 The results are in
agreement with the limit
1.E+12
used by manufacturers of
1.E+11
IR = 5E9/C
low-voltage, high-value
1.E+10
IR = 5E8/C
MLCCs: IR = 5×108/C.
1.E+09
 On average, the margin
1.E+08
between the actual IR
1.E+07
0.001
0.01
0.1
1
10
100
values and the limit is ~ 10
capacitance, uF
times.
ESA Sept. 2013
7
Effect of Voltage
 An increase in the applied voltage leads to an increase in the
absorption currents, Iabs ,whereas n remains the same.
 At V > 2VR the current decay levels-off after 1000 seconds,
due to increased Iil.
 Absorption currents increase with voltage linearly.
1206, 10µF, 16V
current, A
1.E-06
n = 0.7
1.5E-07
1.E-07
1.E-08
1.E-09
1.E+0
R = 3.7E8
R = 2.4E8
30V
20V
10V
5V
current at 120 sec, A
1.E-05
n = 0.74
1.0E-07
R = 5.6E8
4.7uF 25V
0.47uF 25V
10uF 16V
22uF 6.3V
5.0E-08
R = 1.5E10
1.E+1
1.E+2
time, sec
1.E+3
1.E+4
0.0E+00
0
20
40
voltage, V
60
80
 Isochronic absorption currents increase with voltage linearly.
 IR does not depend on voltage.
ESA Sept. 2013
8
Effect of Voltage, Cont’d
 Depolarization currents increase linearly to ~ 3VR, and then
saturate with voltage.
Room temperature
 At high voltages, V >~ 3VR, intrinsic
leakage currents prevail.
1.E-04
current, A
1.E-05
0805, 3.3µF, 6.3V
1.E-04
current, A
1.E-05
Mfr.M 1206 22uF 6.3V
Mfr.M 1206 4.7uF 25V
Mfr.M 1206 10uF 16V
Mfr.P 0805 3.3uF 6.3V
1.E-08
1.E-10
1.E-07
1
3
5
7
9
11
13
SQRT(V), V^0.5
1.E-08
n = 0.96
1.E-09
1.E-10
1.E+0
1.E+1
1.E+2
25V
16V dep
50V
25V dep
125C
145C
165C
182C
1.E+3
1.E-05
75V
50V dep
100V
75V dep
 Schottky-like I-V characteristics at
room temperature: ln(I) ~ V0.5.
 A 3/2 power law at 125 °C and higher:
I ~ Vm, m ≈ 1.5.
current,A
16V
6.3V dep
2225, 1µF, 50V at HT
1.E-04
time, sec
ESA Sept. 2013
1.E-07
1.E-09
1.E-06
6.3V
125V
1.E-06
m = 1.42
1.E-06
1.E-07
m = 1.52
1.E-08
1.E-09
1
10
voltage, V
100
9
Effect of Temperature
 Absorption currents at cryogenic and room temperatures
remain the same.
 Temperature increase from 22°C to 165 °C result in a
relatively small (less than 2 times) increase in Iabs.
2220, 100µF, 6.3 V
1.E-07
current, A
current, A
n = 0.89
1.E-07
300K
1.E-09
36K
1.E+1
1.E+2
time, sec
1.E+3
n=0.98
1.E-08
200K
1.E-09
1.E+0
1.E-04
1.E-05
1.E-06
1.E-08
1206 Mfr.M 22uF 6.3V
1825, 0.47µF, 50V
1.E-10
1.E+1
22C
85C
125C
165C
current, A
1.E-05
1.E-06
1.E-07
1.E-08
n=0.91
1.E-09
1.E+1
n = 0.99
1.E+3
1.E+2
1.E+4
time, sec
1.E+2
time, sec
1.E+3
VR_32C
VR_85C
VR_125C
0V_32C
0V_85C
0V_125C
VR_165C
 Absorption currents have weak temperature dependence.
 Intrinsic leakage currents increase with temperature
exponentially.
ESA Sept. 2013
10
Effect of Temperature on Intrinsic DCL
 Temperature dependence of the intrinsic leakage currents
follow Arrhenius law.
 Activation energy, Ea, decreases by 10% to 30% as the
voltage increases from 0.5 V/VR to 5 V/VR.
1206, 22 µF, 6.3V
1.E-03
1uF 50V X7R
1206 X7R MLCCs
1.E-04
1.2
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
0.002
150V
1
1.E-06
0.89eV
1.E-07
10V
1.17eV
1.E-08
5V
10V
20V
30V
Ea, eV
current, A
current, A
Ea = 0.49eV
1.E-05
1.E-09
0.002
0.0022
0.0024
0.0026
0.4
1/T, 1/K
0.003
1/T, 1/K
0.0035
0.8
0.6
0.86eV
Ea = 0.58eV
0.0025
Mfr.M 22uF 6.3V
Mfr.C 4.7uF 25V
Mfr.M 10uF 16V
Mfr.A 0.47uF 25V
1eV
2220 Mfr.A 10V
C2225 Mfr.C 10V
12220 Mfr.M 10V
2220 Mfr.A 150V
C2225 Mfr.C 150V
12220 Mfr.M 150V
0
10
20
30
40
voltage, V
 At rated voltages intrinsic leakage currents, and the
insulation resistance change with temperature exponentially.
 Activation energy is in the range from 0.6 to 1.3 eV and
decreases with voltage.
ESA Sept. 2013
11
Effect of Cracking
 No difference in I-t curves between normal quality parts and
capacitors with cracks.
 For severely damaged parts the difference can be noticeable
after ~ 100 sec.
1.E-06
1210 Mfr.A 0.1uF 50V
1812, 1µF, 50 V
1.E-07
1.E-06
1.E-09
1.E+0
ind. damage SN1
ind. damage SN2
ind. damage SN3
control
1.E+1
1.E+2
time, sec
1.E+3
1.E+4
1.E-08
current, A
1.E-08
current, A
current, A
1.E-07
n = 0.65
1.E-07
n = 0.71
1.E-09
1.E-10
1.E+0
SN1
SN3
ind SN3
1.E+1
1.E+2
time, sec
n = 0.7
1.E-08
1.E-09
SN2
SN4
ind SN4
0805, 3.3µF, 6.3V
virgin
crack
1.E+3
1.E+4
1.E-10
1.E+0
1.E+1
1.E+2
1.E+3
1.E+4
time, sec
 At room temperature, absorption currents, hence IR, are not
sensitive to the presence of cracks.
ESA Sept. 2013
12
Effect of Cracking, Cont’d.
 IR values measured after 120 seconds for 15 types of
virgin and fractured capacitors both, at room and high
temperatures, were closely correlated.
1.E+12
1.E+11
1.E+10
1.E+10
1.E+09
1.E+08
1.E+07
1.E+06
1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12
IR_damaged, Ohm
IR_damaged, Ohm
1.E+11
85C, 125C, 165C
Room temperature
1.E+09
1.E+08
M1206 22uF 6.3V
C1206 4.7uF 25V
M1206 10uF 16V
A1206 0.47uF 25V
V1825 0.47uF 50V
A1825 0.47uF 50V
C1825 0.47uF 50V
A 1825 1uF 50V
P 1825 1uF 50V
1.E+07
1.E+06
IR_initial, Ohm
2225 1uF 50V
2220 1uF 50V
1825 0.1uF 100V
2223 22nF 50V
1206 4.7uF 25V
0805 3.3uF 6.3V
1206 82nF 50V
1206 0.47uF 16V
1210 0.1uF 50V
2220 10uF 50V
1825 1uF 50V
2220 100uF 6.3V
1812 1uF 100V
1210 0.1uF 50V
2220 22uF 25V
1825 0.47uF 50V
1.E+05
1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11
IR_virgin, Ohm
 Fractured parts can pass screening by standard IR measurements.
 High absorption currents at room temperature, and large intrinsic
leakage currents at high temperatures mask the presence of cracks.
ESA Sept. 2013
13
Modeling of Absorption Currents
 Total current through a capacitor with defect:
I (t , T , V , RH ) = I abs (t , V ) + I il (T , V ) + I dl (T , V , RH )
 Dow model for a capacitor with absorption:
V0 V0
V
+
+ ∑ 0 exp − t 
 τi 
Rd Ril
i ri
1.E-06
1.E-07
Ct=1, r=1e8
n = 1.02
Ct=1, 1e10
1.E-08
1.E-09
n = 0.83
Ct=1, r=1e9
Ct=1, r=1e11
sum
current, A
current, A
1.E-07
1.E-06
1.E-06
Absorption currents in 4.7uF 16V MLCC
1.E-08
Ct=1, rt=1e8
Ct=2, rt=1e9
Ct=3, rt=1e10
Ct=4, rt=1e11
sum
1.E-09
1.E-10
1.E-10
1.E-11
1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
time, s
1.E-11
1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
1.E-07
n = 2.02
Ct=1, rt=1e8
Ct=0.33, rt=1e9
Ct=0.1, rt=1e10
current, A
I (t , V ) =
Ct=0.033, rt=1e11
1.E-08
sum
1.E-09
1.E-10
time, s
1.E-11
1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
time, s
 Relaxation of Iabs in a wide range of times can be presented as
a superposition of currents through a few ri - Cti relaxators.
 How large are Cti?
ESA Sept. 2013
14
Absorption Capacitance
 Absorption charge, Qt, increases with voltage linearly.
 The process can be described by a capacitance, Ct, that
is
1000
1000
determined as Ct = Qt/V. Q = I × t − n × dt = I 0 × t1− n
∫
t
1− n
0
1
Absorption charge in X7R and COG
MLCCs
1.E-05
1.5E-03
Mf r.T 47uF 16V X5R
Mf r.T 10uF 50V X7R
charge, C
Mf r.M 100uF 6.3V X5R
9.0E-04
8.E-06
Ct = 13uF
Mf r.C 2.2uF 50V X7R
Ct = 7uF
6.0E-04
10
6.E-06
4.E-06
y = 2.97E-07x
y = 3.14E-09x
Ct = 2.6uF
Ct = 0.6uF
0.E+00
0
0.0E+00
0
20
40
60
80
voltage, V
100
1
0.1
2.E-06
3.0E-04
2225 Mfr.C 1uF 50V X7R
0805 Mfr.P 3.3uF 6.3V X7R
2220 Mfr.C 0.1uF 50V COG
Ct, uF
Ct = 39uF
100
y = 1.06E-07x
Mf r.T 22uF 25V X7R
charge, C
1.2E-03
1
50
100
120
voltage, V
150
200
0.01
0.1
1
10
100
1000
Co, uF
 Qt varies linearly at relatively low voltages and saturates at
V >~ 3VR.
 Absorption capacitance increases with the nominal value of
capacitors; on average, Ct = 0.25×C0.
ESA Sept. 2013
15
Modeling of Insulation Resistance
 Traps with concentration, Nt, are likely located at the metalceramic interface and are filled up at V >~3VR
q × Nt × S
ε × ε0 × S
=α
3 × VR
d
, where α ~0.25. In this case,
1.8×1013 cm-2 < Nt < 6×1013 cm-2.
−1
 1

1
1
 IR = VR/Iabs. At τ = r×Ct > ∆t ~ 100 sec. IR =  + + 
 Rd Ril r 
Ct =
I (t , V ) =
V0 V0
V
+
+ ∑ 0 exp − t 
 τi 
Rd Ril
i ri
 At r < Rd, Ril, and τ > ∆t:
100 × 106 4 × 108
IR = r >
=
0.25 × C0
C0
 The result is in a good agreement with the existing requirements
for IR: IRmax = 5×108/C0
 The absorption model explains IR dependence on capacitance
and is in a reasonable agreement with actual IR values.
ESA Sept. 2013
16
Voltage Absorption in Capacitors
with Cracks
 Measurements of variations of absorption voltages with time
can be used to assess the value of resistance up to 1014 Ω.
2
1825, 0.1µF, 100V
1.E+15
init
voltage, V
1.2
1.E+14
fract. SN1
5E14 Ω
fract. SN2
0.8
2.5E12 Ω
0.4
0
1.E-3
7E10 Ω
1.E-2
1.E-1
1.E+0
time, hr
1.E+1
1.E+2
R_damaged, Ohm
1.6
1.E+13
1.E+12
1.E+11
1.E+10
1.E+09
1.E+08
1E+08 1E+09 1E+10 1E+11 1E+12 1E+13 1E+14 1E+15
R_init, Ohm
 Resistance corresponding to intrinsic leakage currents is in the
range from 5×109 to 1014 Ω.
 Fracturing reduces resistance up to 5 orders of magnitude, but in
many cases still remains within the specified limits.
 Both, test method and requirements need to be revised.
ESA Sept. 2013
17
Conclusion
 Absorption currents prevail during standard measurements of IR at room
temperature. Absorption currents depend on capacitance, have a weak
dependence on temperature, and change linearly with voltage up to 2 - 3 times VR.
 Possible variations of IR for the parts with the same value of capacitance are
likely due to some differences in timing during measurements, rather than to
different quality of the parts.
 Absorption processes in MLCCs can be explained by electron trapping in states
at the metal/ceramic interface, as a result of tunneling. Absorption capacitance
increases with the nominal value of capacitance, and is on average ~25% of C0.
 At relatively low temperatures, intrinsic leakage currents in MLCCs can be
described using the Simmons model. At temperatures above 85°C, I-V
characteristics follow a power law with the exponent close to 1.5. Activation energy
of leakage currents for different types of X7R capacitors is in the range from 0.6 eV
to 1.3 eV.
 Neither room temperature nor high temperature standard IR measurements are
sensitive to the presence of cracks. Development of new, more effective testing
methods to reveal capacitors with structural defects is necessary.
ESA Sept. 2013
18