Full text of DOI:10.1051/epjap:2001142

Eur. Phys. J. AP 14, 107–114 (2001)
THE EUROPEAN
PHYSICAL JOURNAL
APPLIED PHYSICS
ꢀ
c EDP Sciences 2001
In situ characterisation of non linear capacitors
1
1
1,a
2
3
L. Laudebat , V. Bley , T. Lebey , H. Schneider , and P. Tounsi
1
´
Laboratoire de G ´e nie Electrique de Toulouse - Universit ´e Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4,
France
2
3
´
´
Laboratoire d’Electrotechnique et d’Electronique Industrielle INP-ENSEIIHT, 2 rue Camichel, 31062 Toulouse Cedex, France
Laboratoire d’Analyse et d’Architecture des Syst `e mes du CNRS, 7 avenue du Colonel Roche, 31077 Toulouse Cedex 4, France
Received: 27 October 2000 / Revised and Accepted: 19 March 2001
Abstract. Multilayers ceramic capacitors (MLCC) presenting non linear behaviours of their C(V ) charac-
teristics may have interesting applications in power electronics. Most of them have already been described.
Nevertheless, the choice of a particular type instead of another one is all the more so difficult since, on one
hand the physical mechanisms able to explain this behaviour is far from being understood. On the other
hand, C(V ) characteristics are in general obtained for low voltage values different from the ones they are
3
going to be involved in. In this paper, direct in situ characterisations of different BaTiO based capacitors
commercially available are achieved. The role of the capacitors’ type (X7R,Z5U), of the temperature and
of the voltage waveform (and more particularly its polarity) is demonstrated. Temperature values up to
◦
2
00 C are measured during normal operations in a RCD dissipative snubber without any alterations of
the C(V ) characteristics. All these results are discussed as regards the main physical properties of the
constitutive materials in order to reach an optimisation of their use through an appropriate dimensioning.
PACS. 77.22.-d Dielectric properties of solids and liquids – 77.80.-e Ferroelectricity and
antiferroelectricity – 77.84.-s Dielectric, piezoelectric, ferroelectric, and antiferroelectric materials
1
Introduction
use is limited due to the limited understanding of the phys-
ical mechanisms driving their non linear behaviours. Even
Multilayer ceramic capacitors (MLCC) are used for long if lot has already been written on such ferroelectric materi-
time in low and medium power applications. This is als [6–10] few is known on the possibility to transfer these
mainly due to their high value of permittivity rather than physical characterisations, mainly developed on material
to their breakdown field. For example, barium titanate samples, to applications involving components.
based multilayer capacitors, classified as type II compo-
For example, most of the electrical characterisations
nents, present a reduced size, leading to a high value of presented in the literature are obtained for low level ac
capacitance per unit of volume. They also present an ex- signal superimposed to a high DC voltage. Such a charac-
cellent ability to withstand stresses for a long period of terisation is far from being representative of PE stresses.
time. Nevertheless, changes in the dielectric constant, with The aim of this paper is to achieve in situ characterisa-
either temperature or applied voltage, have very often lim- tions (i.e. in a system of PE) to compare them to the
ited their use.
ones obtained in the classical approach and derived from
However, they are the objects of a considerable amount these measurements. The comparison of different commer-
of interest over the last few years in power electronics (PE) cially available components is also achieved as regards
applications. As a matter of fact, some circuits of power their characteristics. At last a dimensioning optimisation
electronics need these non-linear behaviours versus the of a snubber using such capacitors is proposed.
applied voltage (resonant inverters, snubbers, ...) [1–3].
It has recently been demonstrated that integrated in
resistance capacitance diode (RCD) dissipative snubber 2 Experimental set up and definitions
switching circuits, they allow, to limit the overvoltages
A. Experimental
during switching, to increase the switching frequency and
to improve the electromagnetic compatibility [4]. Another
In situ characterisations of the capacitors under study are
application consists in introducing them in series reso-
performed using a buck. It behaves as a middle point
nance inverters allowing a simple adjustment of the power
voltage source (magnitude up to 1000 V) and as a cur-
by change of their bias polarisation [5]. Nevertheless, their
rent source (during switching, thanks to a dipole L, R)
a
e-mail: lebey@lget.ups-tlse.fr
(see Fig. 1).

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The European Physical Journal Applied Physics
Fig. 1. Schematic representation of the buck used to perform characterisation.
B. Definitions
For such non linear capacitors, the classical relationship
between current and voltage does not stand anymore and
must be rewritten as:
ꢀ
ꢁ
∂
V
∂C
∂V
∂t
∗
I =
C + V ∂V = C
∂
t
where C is the “magnitude capacitance” defined as Q =
∗
CV and C the “dynamic capacitance” defined as the lo-
(
a)
cal dQ/dV . These definitions are clearly explained in Fig-
ure 4 [11].
During our experiments, the following quantities
dV/dt, i(t)/(dV/dt), Q(t), Q(t)/V ) are measured. They
allow us to derive the values of C and C vs. the applied
voltage and the time of voltage application for the differ-
ent components under study (Fig. 5).
(
∗
3
Results and discussions
A. Experimental results
(
b)
Figure 6 to Figure 8 present the main trends derived from
Fig. 2. The two type of circuits used to study the impact of the measurements performed in the buck for the different
(
a) unipolar and (b) bipolar voltage waveform.
components under study under unipolar voltage after drift
has been stabilised (15 min).
First of all, the maximum of non linearity (dC/dV ) ap-
pears to be dependent on the material nature. The voltage
Since our goal is to characterise ceramic capacitors un- corresponding to this maximum of non linearity will be a
der voltage met in PE applications, two different electrical dimensioning parameter of the snubber. For example, the
configurations are studied. The first one is a classical RCD voltage range may be limited to 0–50 V for Y5V com-
dissipative snubber switching circuit, whereas the second ponents (since its maximum of non linearity (MNL) is in
one is used to study the impact of polarity reversal (as it between 10 to 20 V) whereas X7R samples seem to be
is the case in serial resonant inverters). These two type able to target higher voltage applications (MNL between
of circuits are summarised in Figure 2 whereas Figure 3 30 to 60 V).
∗
presents current waveforms during turn-off switching for
the two previous configurations.
In a second step, it has to be noted that the C be-
haviours are the same than the ones measured under low
level ac signal superimposed to a high DC voltage. Such
a result may appear interesting for at least two reasons:
At last different types of MLCC corresponding to the
EIA (Electronic Industries Association) standard (Z5U,
X7R, Y5V, 2F4) from different manufacturers are used. In
this paper, the results are focused on X7R et Z5U compo-
nents provided by two different manufacturers (A and B).
In a first step, spectrofluorometry X measurements are
performed and their results, summarised in Table 1, de-
scribe the different elements used for their realisation.
– to size the converter before it is built via an off line
characterisation under small signal. Hence the choice of
the appropriate characteristic could be achieved prior
to the converter building. Each application would have
therefore, its own C(V ) characteristic as regards the
applied stresses.

L. Laudebat et al.: In situ characterisation of non linear capacitors
109
Fig. 3. Typical current and voltage waveforms applied to X7R 47 nF components (a) unipolar and (b) bipolar voltage waveform.
∗
Fig. 4. Definition of C and C .
Table 1. Summary of the different elements present in the components under study using spectrofluorometry X measurements.
X7R A
Ba, Ti, Nb
Ag, Pd
X7RB
Ba, Ti, Nb
Ag, Pd
Ag, Pd
Fe Ni
Z5U A
Ba, Ti, Zr
Ag, Pd
Z5U B
Ba, Ti, Zr, Pb
Ni
Dielectric
Electrodes
Ending
Ag, Pd, Zn
Cu
Ag, Pd, Zn, Bi
Cu
Cu
Connections
Encapsulation
Fe Ni
Cerfeuil
Br, Cu
Cerfeuil
BrCu
–
to develop an appropriate maintenance of the system
through on line measurements. As a matter of fact, if
we suppose that the behavior of the component under
stress has been established under small signal charac-
terization, then it allows a better understanding of the
physical mechanisms involved during aging. A transfer
of this knowledge to the real system via the character-
istic changes may be considered as a good indicator of
the component’ aging. Works must however be under-
taken to confirm these assumptions.
However such an observation is true for a static de-
scription because, if the voltage is not removed, and what-
ever the components under study, drifts of these char-
acteristics are observed. The largest drifts are observed
under bipolar applied voltage (Fig. 9). At last, for some
components (mainly Z5U manufacturer B) and whatever

110
The European Physical Journal Applied Physics
Fig. 5. Characteristics measured for each capacitor.
Fig. 7. Dynamic capacitance measured vs. time for X7R com-
ponents.
Fig. 6. Dynamic capacitance measured vs. time for Z5U com-
ponents.
Fig. 8. Drift of maximum non linearity for X7R components.
the polarity of the applied voltage, these drifts lead to the
failure of the capacitors and/or of the IGBT used. These
faults appear briefly after voltage application: around
one is associated to their ferroelectric nature, the observed
drifts could be associated to a temperature increase up to
Tc (the Curie temperature). Then, for higher temperature
values where the ferroelectricity has vanished, the non lin-
ear properties of these components would disappear. In
order to confirm the last assumption, an IR camera, al-
1
0 min under unipolar voltage and 1 min under the bipolar
ones of the same characteristics (Magnitude E = 500 V,
0 − E or (E/2, −E/2), frequency (f = 10 kHz) and duty
cycle R).
(
Taking into account these drifts for the components’ lowing surface thermal measurements, focused on the ca-
choice, our study show that the X7R ones from manufac- pacitor is used. This last one is placed vertically and per-
turer A appear to be the more relevant for these type of pendicular to the substrate where the other components
applications rather than any other material considered in are testing (see Fig. 10). Therefore, there is little or no in-
this study.
teraction between the other components thermal increase
All these results seems to depend on the material na- during switching and the capacitor. X7R samples (capac-
ture and more particularly on their thermal stability (ac- ity 100 nF) are studied for the different following condi-
cording to EIA). The impact of the frequency increase has tions: two frequencies (10 and 20 kHz) for both unipolar
therefore to be studied. For different switching frequencies and bipolar stresses. The current magnitude is 2 A.
(
f = 500 Hz, 1, 10, 15 kHz), a decrease in either the mag-
Figure 11 gives an example of results obtained whereas
nitude and dynamic capacitance is observed whatever the Table 2 and Table 3 summarise the mean temperature
type of components considered. Note that the same trend values measured after drift stabilisation. BaTiO3 ther-
is observed for a fixed frequency during an increase of the mal conductivity and the thickness between electrodes
load current. These results seem to confirm the non negli- (10–20 µm) guarantee an homogeneous temperature af-
gible impact of the temperature on the dynamic behaviour ter some minutes. Note that these values are not extreme
of these components. Since it is often claimed that this last values but statistical ones measured on different samples.

L. Laudebat et al.: In situ characterisation of non linear capacitors
111
Fig. 9. Comparison between unipolar and bipolar mode.
Fig. 10. Description of the physical layout for temperature measurements.
Fig. 11. Example of thermal acquisitions using IR camera for two voltage conditions.

112
The European Physical Journal Applied Physics
Fig. 13. Typical current waveforms applied to capacitor dur-
ing a period.
B. Temperature vs. capacitors
Fig. 12. Changes in the different measured characteristics of Origins of the temperature increase may be either ex-
Z5U components during indirect heating for different temper- trinsic and/or intrinsic to the materials. Intrinsic means
atures.
that it is associated to the material nature. For ferro-
electric materials, two aspects have to be considered: di-
electric losses and hysteresis losses. Nevertheless, for the
frequency and temperature under studies, neither dielec-
tric losses (no dielectric relaxation is observed in this fre-
quency range) nor hysteresis losses (the surface of the hys-
teresis loop is decreasing with frequency) are able to lead
to the observed overheating of the components.
Table 2. Mean values of the measured temperature during
unipolar voltage application for X7R components.
◦
Type
X7R
X7R
Frequency (kHz)
T( C)
140
10
20
200
Extrinsic phenomena are associated to the environ-
ment of the component. Therefore, it is possible to as-
sume that the overheating is due to the type of electrodes
which, despite the low thermal conductivity of the di-
electric (around 2.5 W/m K), could allow the material to
reach the electrode temperatures. This last one is a func-
tion of the square of the current and of the resistivity of
the electrode’s material. Such an approach is able to ex-
plain the difference between Z5U samples A and B (see
Tab. 1) due to the type of the metal used and therefore
to the difference in their resistivities. The resistivity of
Table 3. Mean values of the measured temperature during
bipolar voltage application for X7R components.
◦
Type
X7R
X7R
Frequency (kHz)
T( C)
190
10
20
270
Moreover the capacitor temperature is higher than the one
measured on the other components (IGBT or resistor).
−6
Ni (∼ 6.9 × 10 Ω cm) is higher than the resistivity of
−6
AgPd (∼ 1×10 Ω cm). The current is determined using
Such temperature values are very surprising. They are an approximation presented in Figure 13. It is considered
well above Tc and the material still present a non-linear constant and equal to Ich during ∆t and then varies dur-
1
behaviour! The correlation between ferroelectricity and ing ∆t from I to 0 leading to:
2
2
non linear properties is therefore far from being demon-
strated. Another confirmation of this non univocal rela-
tionship is given through an indirect heating of the com-
ponents. The components are placed in an oven, and short
cables lengths (in order to minimise inductance) link them
to the buck outside. The different electrical measurements
are performed after 30 min at the temperature under
study.
For this study, the switching frequency and the current
values are chosen in order that they do not lead to a tem-
perature rise (I = 0.5 A and f = 500 Hz). An example
of result is given in Figure 12 leading to the conclusions
that these components still present non linear properties
for temperature well above the Curie temperature. Their
use under extreme conditions seems therefore possible.
v
u
u
t
!
Z
Z
∆t1
∆t2
I2
2
ch
Irms =
f
I dt +
I2 −
dt .
∆t2
0
0
For a voltage magnitude of 250 V, a load current of 2 A, a
frequency of 10 kHz, the results are I = 1.2 A and 0.75 A
for X7R components A and B respectively, and 0.5 A and
0
.7 A for Z5U components A and B. At last, it has to
be noted that the current is strongly dependent on the
switching frequency and on the load current value.
However, even if the dependence of the metal resis-
tivity with the temperature is taken into account, this
approach is not sufficient to explain the temperature dif-
◦
ferences (∼ 50 C) induced by the application of unipolar
and bipolar voltage waveforms since the current difference
In the following, we propose and discuss reasons able is for the previous buck characteristics near 0.07 A.
to explain both the increase in temperature and the non
linear properties observed during working.
Other reasons mainly associated to the material itself
have to be derived.

L. Laudebat et al.: In situ characterisation of non linear capacitors
113
(
a)
(b)
Fig. 14. Example of an ideal switching turn off (MOS -a and IGBT -b) allowing the definition of the different parameters.
D. Dimensioning a snubber using non linear capacitance
Taking into account the different previous results a ques-
tion arises: how to dimension a RCD snubber dissipative
circuit using such components?
An example of an ideal switching is given in Figure 14
allowing the definition of the different parameters neces-
sary for the following demonstration. A model of the ca-
pacity associated to this type of switching is given in Fig-
ure 15 [1–3]. Cinit, Cfinal, C50V correspond respectively to
∗
the initial value, the final value (previously named C )
of the capacity and to the maximum of dC/dV (Fig. 8).
Fig. 15. C(V ) ideal profile.
All values are defined after drift stabilisation. When di-
mensioning such a snubber, the goal is to force the volt-
age characteristics to pass through the point (tfi, V0) of
Figure 14a (for MOS transistor turn off switching) cor-
C. Non linear properties
responding to a change in dV/dt slope taking also into
account the changes in the C(V ). This leads to:
As mentioned previously, it is often claimed that the non
Ich
linear properties of barium titanate based ceramic capac-
itors are associated to their ferroelectricity. Our results
seem to indicate the contrary: the working temperature
is far above Tc and the capacitances are still presenting
non linear behaviours. Other reasons, involving intrinsic
dielectric properties have to be considered. Among them,
space charge injection and built up has to be taken into
account. Such an assumption has already been implicitly
made by van Wyk [7]. Different observation are in favour
of it. On one hand, in most of cases the drift observed is
not reversal. The cooling of the samples is unable to re-
store their initial properties. The only way to make disap-
pear the effects of voltage application is to apply bipolar
voltages at very high temperatures. On the other hand,
it = Ich −
× t.
(1)
tfi
Hence current and the voltage on the capacitor plates are:
Ich
ic = tfi × t
(2)
(3)
(4)
Z
tfi
1
Vc =
Ich
tfi
× tdt
C50V
0
Ich × tfi
C50V =
for a MOS.
2
V0
In the particular case of an IGBT commutation
see Fig. 14b):
(
the non linearity depends on the nature of the electrodes for 0 to t1:
(
electronic affinity) and does not seem to depend on the
Ich − Itail
t1
material state (ferroelectric or paraelectric).
it = Ich
−
× t
(5)
(6)
Works must now be undertaken to confirm space
charge existence. Since, if it is responsible of the non between t and t :
1
2
linearity observed, this phenomenon which may be con-
trolled, could give the opportunity to obtain an appropri-
ate C(V ) profile as regards the envisaged applications.
Itail
it = Itail −
× t
t2 − t1

114
The European Physical Journal Applied Physics
Fig. 16. Example of a correct snubber dimensioning.
therefore:
– Using non linear capacitors in snubber circuits de-
creases switching times and stored energies (and there-
fore those dissipated in the resistor) by at least 50% as
compared to linear ones. It has to be noticed however
that despite their quality, ceramic capacitors present
dielectric losses larger than the ones observed in poly-
mer based capacitors. The impact of these losses on
the dynamic performance are not so simple to appre-
ciate. In a first approximation, it may be argued that
from a circuit point of view, they may be considered
as negligible.
ic = Ich − it
(7)
(8)
ꢀ
Z
t1
1
Ich − Itail
t1
Vc =
dt
C50V
0
Z
ꢀ
ꢁ
ꢁ
t2
Itail
+
Ich − Itail +
dt
t2 − t1
t1
Icht2
V0
Itailt2
2V0
Icht1
Itailt1
V0
C50V =
−
−
+
(9)
2V0
Ich × tfi
V0
∼
Works are still in progress in order to determine the
reasons of the non linear behaviour, which seems to be
mainly related to space charge injection and built up, and
to reach an appropriate dimensioning of such components
on the basis of the knowledge of the origin of their non
linear behaviour.
C50V =
for an IGBT or GTO.
(10)
Equation (10) as a first order approximation of equa-
tion (9) allows a correct determination of C50V. This ap-
proximation is all the more true since Itail ꢀ Ich and
t1 ꢀ tfi (Fig. 16). This approach allows a quasi ideal use
of the snubber as may be seem in Figure 16 for an IGBT.
References
4
Conclusions
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2
3
4
5
6
The aim of this paper was to perform in situ measurements
of the characteristics of non linear capacitances using a
buck. We have clearly demonstrated that:
2
7
–
The classical low level ac voltage superimposed to a
high DC voltage characterisation generally performed
is in most of cases sufficient to determine the C-V be-
haviour. By the same way a direct in situ characterisa-
tion may be sufficient for determining the component
ability to be used in its application;
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Sept 1994, p. 101.
–
–
Most of the components studied have a maximum non
linearity for voltage magnitude below 100 V;
Application of bipolar high frequency voltage wave-
forms may lead to the failure of the weakest compo-
nents (Z5U B);
9. E.A. Little, Phys. Rev. 98, 978 (1995).
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–
The working temperature may reach a value up to
man and Hall Ltd, London, 1954), p. 75.
1. G.R. Love, J. Am. Ceram. Soc. 73, 323 (1990).
◦
2
00 C and the non-linear behaviour of the compo-
1
nents is still existing;