Electrical Conductivity of Biaxially Oriented Polypropylene
Under High Field at Elevated Temperature
by Janet Ho and Richard Jow
ARL-TR-5720 September 2011
Approved for public release; distribution unlimited.
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Army Research Laboratory Adelphi, MD 20783-1197
ARL-TR-5720 September 2011
Electrical Conductivity of Biaxially Oriented Polypropylene
Under High Field at Elevated Temperature
Janet Ho and Richard Jow
Sensors and Electron Devices Directorate, ARL
Approved for public release; distribution unlimited
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4. TITLE AND SUBTITLE
Electrical Conductivity of Biaxially Oriented Polypropylene Under High Field at
Elevated Temperature
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6. AUTHOR(S)
Janet Ho and Richard Jow
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U.S. Army Research Laboratory
ATTN: RDRL-SED-C
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Adelphi MD 20783-1197
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ARL-TR-5720
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13. SUPPLEMENTARY NOTES
14. ABSTRACT
Although biaxially oriented polypropylene thin films are a common dielectric for many high voltage pulsed power capacitor
applications, the electrical conductivity under high fields at elevated temperatures is mostly unknown. Such knowledge is
valuable for improving the understanding of the origin of the charge species and transport mechanisms at high fields. Results
suggested that conduction is by hopping with the hopping distance increasing from 1.4 nm at 35 °C to 3.2 nm at 100 °C. The
thermal activation energy was determined to be 0.75 eV and field-independent. Such a finding allows the use of an Arrhenius
term and a field-dependent term to describe the field-dependent conductivity up to breakdown.
15. SUBJECT TERMS
Polypropylene, capacitor, electrical conductivity, breakdown, thermal activation energy
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UU
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Janet Ho a. REPORT
Unclassified
b. ABSTRACT
Unclassified
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iii
Contents
List of Figures iv
1. Introduction 1
2. Experimental Details 2
3. Data and Analysis 2
3.1 Conduction Mechanism ...................................................................................................4
3.2 Activation Energy............................................................................................................6
4. Conclusions 8
5. References 9
Distribution List 11
iv
List of Figures
Figure 1. Time dependence of the charging current for 7-m BOPP at 50 °C with various applied fields. .............................................................................................................................3
Figure 2. Charging current as a function of time for 7-m BOPP at 57 MV/m at various temperatures. ..............................................................................................................................3
Figure 3. Electrical conductivity for 7-m BOPP as a function of field at various temperatures. ..............................................................................................................................4
Figure 4. Field dependence of the conduction current density for 7-m BOPP at various temperatures. The solid lines represent the hyperbolic sine curve fitting. ................................5
Figure 5. An Arrhenius plot of electrical conductivity as a function of temperature to compute the activation energy at various electric fields. ...........................................................6
Figure 6. A 3-D representation of equation 2 to the electrical conductivity data as a function of temperature at various fields above 100 MV/m. ...................................................................7
1
1. Introduction
Biaxially oriented polypropylene (BOPP) is the present state-of-the-art capacitor dielectric for
most high voltage, pulsed power applications because of its high breakdown strength
(~600 MV/m at capacitor level), self-clearing capability, and low dissipation factor (~10–4
),
which is independent of frequency. As no dielectric is a perfect insulator, trace electrical
conduction is always present, especially at high electric fields and/or elevated temperatures. At
low electric fields, conduction may arise from ionic impurities like residual catalysts in polymer
resins. At higher fields (>10 MV/m), conduction is generally attributed to electron and hole
mobility, which is promoted by impurity states in the wide bandgap of the insulator. These
impurity states, which are caused by the physical disorder inherent in the amorphous region
(~0.5 eV from the conduction band minimum) and chemical impurities such as carbonyl, vinyl,
and double bonds (0.8 to 3 eV from the valence and conduction band edges), reduce the effective
bandgap to ~1 eV in common polymeric insulators such as polyethylene (1–4).
Although electrical conduction in polypropylene at various temperatures and electric fields has
been studied previously (5–12), the range of fields investigated was below 100 MV/m.
Knowledge of electrical conductivity of capacitor-grade polypropylene thin films at higher
electric fields is technologically important but unavailable, even though in terms of a capacitor,
conduction through the film might be negligible compared to surface leakage across the
unmetallized margin to the end sprayed connection. Nonetheless, such knowledge is valuable
both academically and industrially, as it provides a basis for improved understanding of the
origin of the charge species and transport mechanisms. To this end, the objective of this work is
to study the electrical conductivity of BOPP capacitor film manufactured by the tenter process as
a function of temperature and electric field over the practical range of fields and temperatures
applicable, from which various mechanisms of charge transport were investigated.
Analysis of the conductivity data indicates that the thermal activation energy associated with
conduction is about 0.75 eV and is independent of electric field. Both two- (2-D) and three-
dimensional (3-D) curve fitting to the conductivity data as a function of temperature and electric
field conform to a formula for conductivity that can be expressed as exp( )bE in field and an
Arrhenius term in temperature, i.e., a product of field-dependent and temperature-dependent
terms.
2
2. Experimental Details
Samples cut from rolls of commercially available 7-m capacitor-grade BOPP film were used
as-received. Gold layers of 100 nm thickness were evaporated on both sides of the samples to
ensure good electrical contact with the stainless steel electrodes. The effective electrode area
was about 3 cm2. A guard ring was also evaporated on the low voltage side to minimize
contributions from surface current. Prior to measurement, samples were conditioned for 24 h by
short-circuiting the gold electrodes at about 70 °C, which improved the consistency of the data
(3). The preconditioning method probably removed the electrical memory in the samples.
The apparatus used to measure the conduction current consisted of a ±3-kV DC power supply
(Keithley 247), an electrometer (Keithley 6514), and a set of stainless steel electrodes, which
consist of a guarded measuring electrode and a counter electrode. The current as a function of
time was recorded to a personal computer using the analog output from the electrometer. Prior
to applying an electric field, the sample was equilibrated for about an hour at the test
temperature, which was controlled to ±1 °C. A thermocouple was affixed on the stainless steel
electrode near the sample for monitoring the sample temperature. The charging current was
monitored from 1 s after the application of the electric field until the current reached steady state,
after which the applied field was removed and the sample was allowed to relax overnight. The
same sample was used for the next higher field until the sample broke down. All measurements
were conducted in air.
3. Data and Analysis
Figure 1 shows a typical charging current as a function of time at various fields for 7-m BOPP
at 50 °C. The time for the charging current to reach steady state decreased as the applied field
was increased. This sample broke down at 426 MV/m shortly after the steady-state current was
reached. The time dependence of the charging current at 57 MV/m at various temperatures is
shown in figure 2. Both figures show that the current reached steady state after 104 s, from
which the electrical conductivity was determined. Figure 3 summarizes the electrical
conductivity of BOPP as a function of field at various temperatures. As shown in figure 3, the
electrical conductivity appears to be field-independent below 100 MV/m but increases
substantially at higher fields. The decrease in electrical conductivity with increasing field at
35 °C for fields below 100 MV/m was most likely due to poor signal-to-noise ratio, as indicated
in figure 2.
3
Figure 1. Time dependence of the charging current for 7-m BOPP at 50 °C with various applied fields.
Figure 2. Charging current as a function of time for 7-m BOPP at 57 MV/m at various temperatures.
4
Figure 3. Electrical conductivity for 7-m BOPP as a function of field at various temperatures.
3.1 Conduction Mechanism
The field dependence of the conductivity can be explained by examining the various postulated
conduction mechanisms, such as Poole-Frenkel, Schottky, space charge limited conduction
(SCLC), and hopping conduction. Both the Poole-Frenkel and Schottky mechanisms predict that
ln(J) or ln() E½, where J, , and E are the current density, volume conductivity, and applied
field, respectively, and the slope of the line is related to the dielectric constant of the sample.
Although data from the present work fall approximately on a straight line for such a plot, the
dielectric constants calculated from the slope were 16 and 9 in the case of 50 °C for Poole-
Frenkel and Schottky, respectively, which is too high for polypropylene, the measured dielectric
constant of which is 2.25 from 10 mHz to 1 MHz. Because of the incorrect dielectric constants
calculated from these two mechanisms, both the Poole-Frenkel and Schottky mechanisms are
excluded as the dominant conduction mechanism. SCLC was also examined. The lack of a
“square law” relationship between the current and the applied field suggests that SCLC can be
eliminated. Another plausible mechanism is hopping conduction, in which the current density, J,
is given as
,sinh
2sinhexp2
BEA
Tk
eE
Tk
eWneJ
BB
(1)
where n is the carrier concentration, e is the electric charge of the carriers, is the hopping
distance, is the attempt-to-escape frequency, W is the activation energy in eV, kB is
Boltzmann’s constant, T is the absolute temperature, and E is the applied electric field.
5
Figure 4 shows the curve fit of equation 1 to the conduction current density as a function of
applied field at various temperatures. Equation 1 predicts the observed current quite well, and
therefore, hopping conduction appears to be the dominant mechanism. The hopping distance ,
can be calculated from the fit parameter B. As indicated in figure 4, the hopping distance
increased from 1.4 nm to 3.2 nm as the temperature increased from 35 to 100 °C. The values of
the hopping distance seem rather small compared to the work by Ikezaki et al. (8), which
reported a range of 4.5 to 10 nm at 72 °C depending on the crystallinity. The density of traps
inferred from the hopping distance in our work is 1026
to 1027
m–3
, which seems rather high.
Nonetheless, such values have been reported by Lawson (13) for polyethylene and McCubbin
(14) for octacosane.
Figure 4. Field dependence of the conduction current density for 7-m BOPP at various
temperatures. The solid lines represent the hyperbolic sine curve fitting.
The data at 35 °C are somewhat scattered as a result of the low current density at this
temperature. Therefore, the discussion will be focused on the data for 50 and 100 °C as they
have less scatter and the fits to the data are better. The energy gained from the electric field
between traps is given by =eE. At low electric fields, this energy is below the thermal energy
(0.026, 0.028, and 0.032 eV at 35, 50, and 100 °C, respectively), and the conduction is ohmic.
At fields in the range of 30 MV/m, the energy becomes comparable to the thermal energy, and
the energy gained between traps contributes appreciably to detrapping, as a result of which, the
conductivity becomes field-dependent (15). Based on the computed separation between traps,
the field at which the conductivity becomes nonlinear should be in the range of 35 and 25 MV/m
at 50 and 100 °C, respectively. Examination of figure 3 suggests that the field at which the
conductivity becomes field-dependent is closer to 100 MV/m.
6
When the field is sufficient that the energy gained between traps becomes comparable to the trap
depth, which can be taken as the thermal activation energy of conductivity, charge carriers are no
longer localized by the traps, carrier mobility becomes high, and very rapid high field aging
occurs. The rapid increase in the carrier mobility (conductivity) with the electric field results in
the creation of a space charge limited field when the charge can redistribute as necessary to limit
the field (16, 17).
3.2 Activation Energy
The electrical conductivity measured as a function of temperature at various fields has been
analyzed through 2-D curve fitting to compute the activation energy for different fields as shown
in figure 5. The data indicate that the activation energy at fields from 57 to 300 MV/m is
constant within experimental error, with an average value of 0.75 eV. Similar activation energy
has been reported by Das Gupta et al. (7) and Ikezaki et al. (8).
Figure 5. An Arrhenius plot of electrical conductivity as a function of temperature to
compute the activation energy at various electric fields.
The activation energy can also be computed through a 3-D curve fit to the electrical conductivity
data using an equation of the form
,expexp, bETk
eWaTE
B
(2)
where is the electrical conductivity, a and b are constants, and the remaining symbols are the
same as described in equation 1. Many other functional relationships for the field-dependent
term were examined including exp( )b E , exp( / )b E T , and exp( / )bE T . Exp( )b E and
7
equation 2 provide similar fits to the data. Given that the form exp( )bE also corresponds to the
hopping conduction as shown in figure 4, equation 2 was used to fit to the data above
100 MV/m. As seen in figure 6, the resulting activation energy is 0.75 eV, which is consistent
with the 2-D curve fitting at the various fields (figure 5).
Figure 6. A 3-D representation of equation 2 to the electrical conductivity data
as a function of temperature at various fields above 100 MV/m.
Density functional theory-based computations by Stournara and Ramprasad (18) of the impurity
states in the bandgap of bulk isotactic polypropylene caused by carbonyl and double bonds
indicate that carbonyl causes a “hole trap” about 0.8 eV above the valence band, and double
bonds cause “electron traps” about 0.7 eV below the conduction band, one or both of which may
cause the measured 0.75 eV activation energy. Their work, however, does not provide an
analysis of the spatial distribution of the impurity state wave functions. Such analysis would
give better insight into the likelihood of these states promoting interchain charge transfer, which
is the major impediment to high field conduction in typical polymers, as carrier mobility along
the polymer chain is many orders of magnitude greater than that between polymer backbones
(15).
8
4. Conclusions
Results of electrical conductivity measurement of BOPP suggest that the conduction is through
hopping mechanism with the hopping distance increased from 1.4 nm at 35 °C to 3.2 nm at
100 °C. The thermal activation energy was determined to be 0.75 eV and independent of the
electric field. This finding allows the use of an Arrhenius term together with a field-dependent
term to describe the field-dependent conductivity.
9
5. References
1. Teyssedre, G.; Laurent, C. Charge Transport Modeling in Insulating Polymers: From
Molecular to Macroscopic Scale. IEEE Trans. Dielectr. Electr. Insul. 2005, 12, 857–875.
2. Huzayyin, A.; Boggs, S.; Ramprasad, R. Density Functional Analysis of Chemical
Impurities in Dielectric Polyethylene. Trans. Dielectr. Electr. Insul. 2010, 17, 920–925.
3. Huzayyin, A.; Boggs, S.; Ramprasad, R. Quantum Mechanical Studies of Carbonyl
Impurities in Dielectric Polyehtylene. Trans. Dielectr. Electr. Insul. 2010, 17, 926–930.
4. Huzayyin, A.; Boggs, S.; Ramprasad, R. Density Functional Theory Analysis of the Effect
of Iodine in Polyethylene. Trans. Dielectr. Electr. Insul. 2011, 18, 471–477.
5. Foss, R. A.; Dannhauser, W. Electrical Conductivity of Polypropylene. J. Appl. Poly. Sci.
1963, 7, 1015–1022.
6. Mehendru, P. C.; Pathak, N. L.; Singh, Satbir; Mehendru, P. Electrical Conduction in
Polypropylene Thin Films. Phys. Stat. Sol. (a) 1976, 38, 355–359.
7. Das Gupta, D. K.; Joyner, K. A Study of Absorption Currents in Polypropylene. J. Phys. D:
Appl. Phys. 1976, 9, 2041–2048.
8. Ikezaki, K.; Kaneko, T.; Sakakibara, T. Effect of Crystallinity on Electrical Conduction in
Polypropylene. Jap. J. Appl. Phys. 1981, 20, (3), 609–615.
9. Singh, H. P.; Gupta, D. Conductivity Variation of Polypropylene with Electrode Materials.
Ind. J. Pure & Appl. Phys. 1985, 23, 386–388.
10. Mizutani, T.; Ikeda, S.; Ieda, M. Influence of Chemical Structure on Electrical Conduction
in Insulating Polymers. Jap. J. Appl. Phys. 1985, 24, (9), 1164–1167.
11. Mittal, A.; Jain, V.; Mittal, J. Transient Charging and Discharging Current Studies on
Unstretched and Stretched Polypropylene Films. J. Mat. Sci. Let. 2001, 20, 681–685.
12. Guadagno, L.; Raimondo, M.; Vittoria, V.; Do Bartolomeo, A.; De Vito, B.; Lamberti, P.;
Tucci, V. Dependence of Electrical Properties of Polypropylene Isomers on Morphology
and Chain Conformation. J. Phys. D: Appl. Phys. 2009, 42, 135405.
13. Lawson, W. G. High-field Conduction and Breakdown in Polythene. Brit. J. Appl. Phys.
1965, 16, 1805–1812.
14. McCubbin, W. L. Electronic Processes in Paraffinic Hydrocarbons. Trans. Faraday Soc.
1962, 58, 2307–2315.
10
15. Dissado, L. A.; Fothergill, J. C. Electrical Degradation and Breakdown in Polymers, Peter
Peregrinus Ltd, England, 1992.
16. Hibma, T.; Zeller, H. R. Direct Measurement of Space-charge Injection from a Needle
Electrode into Dielectrics. J. Appl. Phys. 1986, 59, 1614–1620.
17. Boggs, S. A. Very High Field Phenomena in Dielectrics. IEEE Trans. Dielectr. Electr.
Insul. 2005, 12, 929–938.
18. Stournara, M. E.; Ramprasad, R. A First Principles Investigation of Isotactic Polypropylene.
J. Mater. Sci. 2010, 45, 443–447.
11
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