Thick Film Piezoresistive Ink: Application To Pressure Sensors
Thick Film Piezoresistive Ink: Application To
Pressure Sensors
M-H Lefort*, V. Djafari**, B. Jouffrey**, Ch. Savary*
*Bourdon Sédème
1, Rue de terre Neuve
Z.A. de Courtaboeuf 1
B. P. 357
F-91959 Les Ulis Cedex
France
Phone: +33-1-69291917
Fax: +33-1-69072208
e-mail: [email protected]
**Ecole Centrale de Paris
Abstract
Using SEM examination and X-ray diffraction analysis, the researchers have established the granular state, crystalline structure and
composition of industrial inks. On the basis of these identifications and bibliographical study, the authors have made a new ink with
oxides of known proportion and grain size. They measured the signals emitted by gauges made with inks produced in the laboratory
and reference inks (industrially produced) grouped in a Wheatstone bridge and subjected to deformation. Satisfactory metrological
results were obtained. The authors have established a model relating the Bridgman coefficients of piezoresistivity, the gauge factor,
and the signal obtained.
Key words:
Piezoresistive Ink, Pressure Sensors, Compositional Measurement, Granular State, and Crystalline Structure.
I. Introduction
Hybrid microelectronics, making use of sintered conductive
and insulating powders, appeared at the same time as semiconductors. In thick film technology, three large industrial families
of piezoresistive inks or pastes have been developed, among which
those based on ruthenium oxide and ruthenate of lead (or Bi)
have gathered considerable momentum. The piezoresistive character of these formulations is more pronounced than that of metals (5 to 10 times greater), and their thermal behavior is often
better than that of semiconductors.
This field, which is of considerable importance in its application, must remain confidential in nature, due to certain work
done in the sectors of both armaments and industrial research.
The literature discussing the properties of thick layer resistances
(thickness deposition of 10 to 40 µm) is relatively sparse. The
metrological performance of current pressure sensors which use
this technology is limited by the effects of temperature as a magnitude of influence. This effect, which is less evident in the case
of semiconductors, nevertheless requires the use of a compensating electronic circuit. The authors objective is to achieve a better
understanding of the observed phenomenon of piezoresistivity
and to control the properties of this type of gauge, used in pressure sensors, in order to improve performance.
The manufacture of these gauges demands a knowledge of
printed inks, their mode of preparation, their composition, and
their physical and chemical behavior. Therefore, it is necessary
to take an interest in the preparation of these inks. The use of
these formulations requires them to be sintered (see Figure 1)
and should possess good electrical and piezoresistive properties.
To this end, the researchers conducted a comparative study of
inks prepared in the laboratory and industrial or commercial inks
(identified as A, B and C). The study focused on the piezoresistive
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properties coupled with the thermal properties of thick film resistances, used in the form of strain gauges grouped together in a
Wheatstone bridge in piezoresistive pressure sensors.
variation in temperature of the conductive resistance, R m , which
is given by the following relation,
R m (T )=R 0m (1 + α m T )
(1)
where αm is the coefficient of thermal resistivity (CTR) of the conductive particles in ppm/K, T is the measured temperature in K,
0
and R m is the resistance of the conductive oxide.
Figure 1. Modification of the deposit on sintering of an
ink.
The researchers’ approach can be broken down into the following aspects;
• the first aspect concerns the preparation of a thick layer ink
from basic constituents (PbO, B2O2, SiO2, RuO2 solvents, etc.);
• the second aspect concerns the role of oxygen, which is
present during industrial sintering operations. Its influence on
the conductive properties of the inks was given particular attention. The latter aspect will be the subject of a future publication.
2.2. Conduction by Tunnel Effect
The conductive particles, separated by a vitreous insulating
layer (Figure 3), accept the passage of a current by tunnel effect
(Figure 2) from one particle to another when the distance, d,
separating them is small enough, of the order ≈ 1 nm. An expression for the variation in temperature of resistance Rt, due to the
tunnel effect, has been proposed by Inokuma4 .
2. Conduction Model
Three mechanisms (Figure 2) are invoked to explain the conduction of piezoresistive inks composed of conductive particles
(conductive oxides) in a vitreous environment (insulating oxides), namely; metallic conduction by direct contact (from B to
C), conduction by tunnel effect (from C to D), and conduction
due to electron hopping (from A to B).
Figure 3. Energy diagram.
2.3. Conduction by Electron Hopping
Electrons can also provide conduction by hopping between
conductive particles, even across a thicker vitreous barrier than
is the case for the tunnel effect, of the order of 10 nm. The doping
which makes this conduction possible may be intentional or fortuitous, but it generally arises from an ionic transfer from the
conductive phase into the vitreous phase.
An expression for conduction by hopping, established by
Pierce6, has been used by several authors. The expression is of
the form,
Figure 2. Transfer of an electron from a particle A to a
particle D.
Rt (T)= R 0
t
(2)
where R 0t = initial resistance, Ua = activation energy, k =
Boltzmann’s constant, d = minimum width of glass separating
two conductive particles, and B = term defining the spatial de2.1. Metallic Conduction
creasing of the wave functions Ψ associated with each particle.
Kusz5 has provided an expression for this activation energy
A conductive particle is in direct contact with another con1
Ua, as a function of the thickness d of the vitreous barrier, and of
ductive particle; in this case, it has been proposed that the variathe mean radius r of the conductive particles. In the case of the
tion of resistance with temperature should be represented as the
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Thick Film Piezoresistive Ink: Application To Pressure Sensors
d
tunnel effect, d << r and Ua a r .
The activation energy, Ua, rapidly tends towards zero as the
radius r of a particle increases.
2
1
æT ö4
Rs (T )=R 0S . 4.ç 0
èT
(3)
• tungsten oxide, WO3, density 7,200 Kg/m3 and micronic grain
size (J. Matthey);
• lead oxide, PbO (litharge), density 9,500 Kg/m3 with mean
grain size ≤ 5 µm (Penarroya);
• silicon oxide, SiO2, density 2,600 Kg/m3 with mean grain size ≤
20 µm (J. Matthey); and
• boron oxide, B2O3 density 2,500 Kg/m3.
0
where R is the initial resistance, and T0 is the Mott hopping
s
coefficient expressed in K7.
2.4. Total Conduction
The total resistance, according to Lieznerski8, is a function of
the statistical coefficients for weight taking account of the respective shares due to metallic conduction and to the tunnel effect or hopping,
R(T) =
(Rt) Zt ⋅(Rm) Zm ⋅(Rs) Zs
(4)
where Zt, Zm, and Zs, are the respective coefficients such that Zm +
Zt + Zs = 1.
Figure 4. Thermal profile of sintering.
3. Experimental Part: Preparation of
Thick Film in a Wheatstone Bridge
“Thick Film” technology consists in screen printing insulating, conductive, or resistive inks on a ceramic substrate (usually
alumina), and then sintering them at high temperature. These
inks are powders incorporated in a liquid containing binders and
organic solvents. For resistive inks, the powders are mixtures of
conductive oxides (types RuO2, (Pb or Bi)2Ru2O7-x at concentrations varying between 5 and 60%) and insulators. When subjected to mechanical strain, they show great variation in their
resistivity. The objective of this work is to find printed inks which
can be used as high-performance piezoresistive pressure sensors.
Therefore, the researchers took an interest in the preparation of
these inks. Their utilization demands that their thermal, electrical, and piezoresistive properties would be good and reproducible.
Having described the procedure for preparing “new inks”, the
authors studied the properties of the most commonly used industrial inks (designated A, B and C) and compared them with those
of the new inks.
3.1. Preparation of the New Inks
To prepare the solvent required for the screen printing operation, the researchers first dissolved ethylcellulose (a binder to
give cohesion to the raw ink) in terpineol (a light solvent), adapting the viscosity of the ink to the screen printing operation to be
performed. The mixture of insulating oxides was then prepared,
and added to the conductive oxides in the mass ratios shown in
Figure 5. Finally, the solvent was added to the mixture of oxides
obtained. The authors carried out screen printing operations with
conductive, resistive, and insulating inks using a semi-automatic
screen printing machine, through screens suited to the viscosity
of the inks and carrying the designs to be reproduced. The researchers adjusted the thickness of the deposits by altering the
settings of the machine. After the screen printing stage, the researchers evaporated the screen printing solvents in a static oven
raised to 150°C, and the deposit, known as a “dry deposit”, was
then reheated in order to perform the sintering operation. This
consists in raising the powders contained in the ink to a high
temperature in order that the grains of conductive and insulating
oxides should bind together and to give them cohesion and
strength. The substances were sintered during the baking operation (sintering in liquid-solid phase) at a temperature lying between 700 and 900°C in the controlled atmosphere of a tunnel
furnace. The sintering temperature depends primarily on the type
of ink (insulating, conductive, or resistive), which necessitates
higher or lower baking temperatures for wetting the conductive
particles with melted oxides, reducing the porosities in the deposit, and increasing the points of local attachment between the
deposit and the ceramic substrate.
The researchers prepared their formulations using known constituents (Figure 4). They consist of the following;
• ruthenium oxide, RuO2, with sub-micronic grain size and
density 7,000 Kg/m3 (Heraeus);
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Figure 5. Summary of manufacture and composition of the
experimental inks tested.
An example of a thermal profile for sintering is shown in
Figure 4. It contains a plateau at 850°C of 11 minutes duration.
The rates for raising and lowering the temperature are set at 28°C,
and 42°C per minute, respectively. This setting is the profile used
to fire conventional inks.
3.2. Change of Phase of Specimen Inks and
Changes in Their Electrical Resistance as a
Function of Sintering Temperature
The industrial inks A, B and C were screen printed on alumina membranes and subjected to progressive sintering temperatures (Pt-Au alloy conductors used, baked at 850°C). They showed
a change of phase on sintering (Table 1). In this Table, the authors show the crystallized constituents obtained by X-ray diffraction.
Table 1. Behavior of piezoresistive inks as a function of
sintering temperature.
A
sintering θ
raw state
600°C
650°C
720°C
825°C
850°C
875°C
900°C
crystallized
phase
Bi2Ru2O6,5
Bi2Ru2O6,5
RuO2
-
B
R in
kΩ
>10MΩ
3±0,5
4,3±0,5
13±1
14,5±1
13,9 ±1
10±0,3
5,6±0,1
crystallized
phase
RuO2
RuO2
Pb2Ru2O6,5
-
Figure 6. Variation of resistances as a fucntion of sintering
termperature: trend of variation.
One can observe that this principal curve is composed of three
essential branches. The branches are as follows,
(a) up to a sintering temperature of 600°C, a descending part
shows a decrease in electrical resistivity. One can attribute this
phenomenon to the evaporation and pyrolysis of the heavy, insulating organic products. As the temperature rises, this film evaporates. On one hand, conductivity by direct contact (percolation)
increases, and on the other, the porosity ratio decreases.
(b) between 600 and 700°C, for ink A, a rising part indicates
an increase in resistivity. In fact, the glass is gradually being
transformed into a more or less viscous liquid and is penetrating
between the grains of conductive oxide aggregates. Thus, the
grains are coated in a film of glass, creating an increase in resistivity. This phenomenon has also been observed by Chiang et
al.9, in an ink composed of 80% glass (65% SiO2, 34% PbO and
1% Al2O3 with grain sizes varying from 3 to 5 µm) and 20% lead
ruthenate (average grain size 34 nm). This phenomenon was not
observed in inks B and C. The authors believe it may be masked
by reductions in porosity and by kinetic differences in the formation of the glass.
C
R in
kΩ
>10MΩ
515±10
300±10
169±5
11,1±1
6,5±1
-
crystallized
phase
RuO2
RuO2
Pb2Ru2O6,5
-
R in
kΩ
>10MΩ
62±1
40±5
12,9±0,5
15±1
-
The general appearance of the resistive variation of the sample
industrial inks as a function of sintering temperature is shown in
Figure 6.
Figure 7. Modification of ink A as a function of sintering
temperature.
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Thick Film Piezoresistive Ink: Application To Pressure Sensors
(c) An horizontal, or slightly falling part, when the temperature
reaches 800°C. Most of the conductive oxide grains are coated in
glass, and conductivity by tunnel effect is becoming the dominant
phenomenon. At the end of this stage, whatever the nature of the
initial conductor, the resistances used present the same order of
magnitude of 10kΩ.
3.3. Characteristics of the New Inks
3.3.1. Analysis by X-Ray Diffraction
The researchers carried out analyses by X-ray diffraction of
our ruthenium oxide RuO2 (Figure 8) and of the baked inks ECP2
and ECP4 (Figures 9a and 9b). On these last two spectra, the
“humps” appearing between 15 and 40° betray the existence of
amorphous glass in the deposits (lead borosilicate).
One can conclude that for ink ECP2, sintering at 850°C has modified the principal conductive phase present in the ink in its raw
state. The authors believe that the lead ruthenate identified may
have appeared during baking by a process of recombination between the oxides of ruthenium and lead, both present in the ink in
its raw state. It is possible to assume the following,
• the proportion by weight of 8.8% RuO2 (ink ECP4 in raw
state) is below the threshold required for chemical reaction with
lead oxide;
• the crystallized phase is present, but in such weak proportions that it cannot be detected by our measuring instrument, as
in the case of the oxide W03. Indeed, this oxide, in proportion by
weight of 1.9% in the raw ink ECP4, also does not appear in the
spectrum of the ink sintered at 850°C either.
Figure 9a and 9b: Spectra of experimental inks obtained
by X-ray diffraction.
Figure 8. Spectrum obtained by X-ray diffrection. Ruthenium
oxide used for the preparation of experimental inks.
The commercial inks A, B and C, screen printed on to membranes of alumina and sintered under the same conditions as the
experimental inks, also undergo a change of the crystallized phase.
In Table 1, the authors showed the crystallized constituents obtained by X-ray diffraction. The authors observed, in the case of
ink A for example, a transformation of the following type (see
Figure 7):
Bi2Ru206,5 ® Ru02 + ...
when approaching 850°C.
One can formulate a hypothesis that we may imagine that, as
in the case of the experimental inks, the phase transformations
observed do not exclude the presence of other phases, and that
after sintering at 850°C, a crystallized phase of the type Pb2Ru2O6,5
or RuO2 may also be present, though in a smaller proportion.
One can note that the phase Al2O3 present in the spectrum of
Figure 8b, originates from the medium on which the ink was
deposited. It is a fact that the composition of raw ink ECP4
includes no alumina.
From Figure 9a, one can observe that the baked ink ECP4
presents a crystallized phase mainly of Ru02, while for ink ECP2,
two main crystallized phases are detected, RuO2 and Pb2Ru2O6,5.
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3.3.2. Scanning Electron Microscopy
The authors have studied the morphology of our inks (Photos
1 and 2) using an SEM equipped with an energy dispersion elemental analyser (Figures 10 and 11) for the elements with atomic
number greater than that of carbon. Photo 1 shows the insulating oxides, presenting grain sizes varying from 5 to 20mm for
PbO and SiO2, while the grain size of the ruthenium oxide is of
the order of 300 nm. Elemental analysis reveals that the light
grey vitrification matrix which is strongly dominant in Photo 2
is composed of the elements Ru, Si, Pb and O. These elements
may be present in the form of oxides of type RuO2, SiO2, PbO or
their compounds, such as lead borosilicate. Indeed, B2O3, which
enters into the initial composition of the ink, possesses a fusion
temperature of 460°C. This consequently makes a very considerable contribution to the vitrification of the ink.
Photo 1. Raw ink ECP3, dried at 150°C.
Figure 10. Grain morphology and elemental analysis of
ink ECP3 before sintering.
Figure 11. Elemental analysis of ink ECP3 after sintering
at 850°C.
3.4. Electrical Properties of the New Inks
3.4.1. Electrical Behavior
Photo 2. Ink ECP3, sintered at 850°C.
The authors measured the electrical properties of the new inks.
The results are shown in Table 2. From inspection of Table 2,
one can make few observations, namely;
(1) Resistance of the inks is a function of their structure and
composition
• As was to be expected, given an identical percentage of glass
and type of conductive oxide (ECP2, ECP3), the resistance increases as the percentage of conductive oxide decreases. This
result is confirmed by a number of authors10,11;
• Given the same proportions of RuO2 and glass (ECP1, ECP2),
the resistance rises as the size of the boron oxide particles decreases (the ratio RECP2/RECP1 is 39). This observation is in agreement with that of Abe and Taketa9. The authors believe that
when the size of the boron oxide particles is large (ink ECP1),
the fusion kinetics are weaker. In other words, when the size of
the boron oxide particles is small (ink ECP2), the fusion kinetics
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Thick Film Piezoresistive Ink: Application To Pressure Sensors
are high. When the quantity of liquid is not so high and viscosity
is greater, the molten glass penetrates less easily between the
conductive particles during sintering. A considerable proportion
of the oxides then provide conductivity by direct contact between
the conductive particles, which has the effect of reducing the
resistivity of the sintered ink (ink ECP1 is an example). This
shows the extent to which particle size affects the tunnel-effect
conductivity of the ink;
• inks ECP3 and ECP4, which contain very similar proportions of conductive oxides, show resistivities which differ by a
factor of 9. Ink ECP4, composed of a mixture of conductive
oxides (RuO2 + WO3) totalling 10.7% weight percent, behaves
differently from ink ECP3, with 9% of RuO2. The presence of a
small proportion of tungsten oxide (18% in the mixture of conductive oxides) considerably reduces the resistance of the baked
ink.
Table 2. Measurements taken on membranes carrying
experimental inks sintered at 850°C (*1).
type
of ink
Resistance
in kOhm
ECP1
R = 0.683
σR = 0.2
-400
mean
imbalance of
the bridge
in mV
d= +1200
σd = 520
R = 26.7
σR = 7.7
-184
d= +1157
σd = 427
-121
d= +235
σd = 775
+387
d= -880
σd = 178
+6
d= +250
σd = 150
ECP2
ECP3
R = 116.2
σR = 41
ECP4
R = 12.52
σR =2.34
encre
industriell
e témoin
R = 11.7
σR = 1
mean CTR
from -10 to +55
°C
in ppm/°C
*1 - R is the mean value of resistances and rR their
standard deviation;
- d is the mean value of imbalances and sd their standard
deviation ;
- the CTR is the mean coefficient of thermal resistivity.
(2) Coefficients of thermal resistivity
• Among the inks having ruthenium oxide as the sole conductive oxide (ECP1, ECP2 and ECP3), the CTR closest to zero is
obtained in ECP3 (-121 ppm/°C), which has the smallest proportion of conductive oxide of type RuO2 in its composition.
The expression for the CTR of a sintered resistance, as given
by Pësic2,3,12, is written as follows,
In this expression, Zm is the statistical weighting coefficient of the
conductive oxide, which varies in accordance with the proportion
of conductive oxides. For RuO2, the thermal coefficient, am, is
positive and equal to +7,000 ppm/K. Taking Pësic’s expression
into account, when the proportion of conductive oxide decreases,
the CTR becomes negative, and the smaller the quantity of conductive oxide, the higher is its absolute value. This accords well
with inks ECP3 and ECP4, but contradicts the results obtained for
inks ECP1 and ECP2.
• the highest CTR value corresponds to the ink containing
WO3; this oxide is thus of little interest for making a pressure
sensor with low thermal variation.
(3) General observation
• the mean imbalances obtained on the Wheatstone bridge are
high, and only ink ECP3 displays a mean imbalance close to that
of the industrial ink, the respective values being +235 and +250
mV;
• the thermal coefficients of these experimental inks are superior to that of the specimen industrial ink.
If reference is made to published results, these results concerning ink ECP1 can be compared with those observed by Abe
and Taketa13, for identical composition as regards RuO2 included
in a lead borosilicate (see Table 3 below).
Table 3. Comparison between ink ECP1 and the ink
prepared by Abe and Taketa.
type of ink
R in Ω
Abe and
Taketa's ink
ECP1
GFL
KL(*)
617
CTR in
ppm/°C
-400
3.3
3.7
400 ≤ R ≤ 683
-400
-
5.0
*See Table 4.
3.4.2. Piezoresistive Behavior
The authors have studied the behavior of the cells under pressure. The results obtained are listed in Table 4. In this Table, the
gauge factor, KL, is deduced (see model § IV) from the output
signa , Ssm, by means of an expression, equation (6), of the form,
Ssm
+ cc
Uε c
K L(deduced ) =
cc + ce
(6)
with: εc - = 327.10-6 ;
Cc - = 0.999 and Ce = 0.266.
Analysis of the values shown in Table 4 leads to the following
results,
1
(a) the inks elaborated all present gauge factors, KL, superior
T0 4
αm
Ea
to those of the metals (from 2 to 4);
CTR =
Zm −
Zt −
Zs
(5)
(b) according to composition, the size of the B2O3 particles
5
1 + α mT
kT 2
and
the nature of the conductive oxide, these gauge factors may
T4
vary by a factor of 2 (scatter of the same order of magnitude is
case of the
industrial
inks);
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Table 4. Measurement results of cells under a pressure of 50
bars-m, average of the results of 10 cells tested, and σ,
standard deviation.
Type
of ink
ECP1
ECP2
Ssm
output signal
at 50 bars
m = 17.4
σ = 0.6
m = 45.8
σ = 3.2
5.0
± 0.2
11.9
± 0.8
m = 36.8
σ = 3.8
m = 27.5
σ = 0.6
m = 60.7
σ = 1.5
9.7
±1
7.4
± 0.2
15.8
± 0.4
ECP3
ECP4
Speci
men
ink
KL
Thermal
Hysteresi
variation (*)
s
in %EM
in µV/V/°C
Lm = 0.9 Hm =1.9
+3
σ = 1.0
σ = 2.3
Lm = 0.14
Hm =
-1.9
0.06
σ = 0.04
σ = 0.025
Lm = 1.8 Hm = 2.2
+5.3
σ = 3.0
σ = 3.3
Lm = 0.5 Hm =0.7
+5.3
σ = 0.2
σ = 0.5
+1.5
Lm = 0.15
Hm =
σ = 0.05
0.05
σ = 0.02
Linearity
in %EM
(c) the highest gauge factor is obtained with ink ECP2 (containing 15% RuO2, with no WO3), but when the scatter of the results is
taken into account (KL = 11.9 ±0.8), ink ECP3, with 9% RuO2, shows
an identical gauge factor (KL = 9.7 ±1). It is inferior to that of the
specimen ink (KL = 15.8), which presents a principal crystallized
phase of ruthenate in its raw state. The fact that inks ECP2 and
ECP3 present practically identical gauge factors shows that, in the
band examined, the proportion of the conductive oxide RuO2 only
has a minor effect on the piezoresistive behaviour of the ink. Canali14
states that, if by taking only the contribution of the tunnel effect to
resistivity, application of a strain to the gauge modifies distance x
(the distance between two adjacent conductive particles in Å),
creating a variation of resistivity of the form,
dρ
ρ
dx
x
=A. Φ.x
(7)
be increased to as much as 11.9 (as for ink ECP2). This result
accords with those of Abe and Taketa13 and with the researchers’
earlier results. In fact, when the size of the boron particles is large,
the fusion kinetics for a given lapse of time are weaker than when
the boron particles are small. The distance of fine vitreous barrier,
which is responsible for the tunnel effect in the conduction of the
inks, is then less, and the gauge factor decreases;
• ink ECP2 distinguished itself very clearly from the other three
types of ink with excellent behavior as regards both linearity and
hysteresis. One may think that it was due to the better preparation
of this ink that it had a more homogeneous structure than the other
experimental inks. Indeed, the authors observed surface defects
with the other inks. The authors believe that these defects may be
present inside the layers and spoil their mechanical behavior, inducing hysteresis and non-linearity, but they did not go in depth
into the influence of these defects on their mechanical properties;
• the addition of tungsten oxide in ink ECP4 (for an identical
proportion and type of glass) caused a significant reduction in
the gauge factor. This signifies that the gauge factor depends
strongly on the nature of the conductive oxide. With ruthenium
oxide, it is possible to obtain a gauge factor superior to that obtained with tungsten oxide;
• the best result was obtained from ink ECP2, made with ruthenium oxide without addition of tungsten oxide (it would have
been useful if tests could have been carried out using an oxide
from the pyrochlore family);
• the gauge factor rises as the size of the glass particles decreases. In the case of B2O3 with small sized particles, the glass,
being formed more rapidly, penetrates better between the conductive particles and reduces conduction by direct contact between particles. Conduction by tunnel effect increases. The effect
of increasing the distance between the conductive grains is then
to increase the effect of piezoresistivity, and thence the gauge
factor;
• the gauge factor also increases when the proportion of conductive oxides decreases.
One can conclude that the good metrological and thermal results obtained with a composition containing 15% RuO2 prove
that pressure cells can be made, but that good homogeneity of the
ink is an essential prerequisite for good thermal properties.
According to the publication, variations in resistivity ρ, for x
varying from 10 to 30 Å and φ from 0.5 to 1 eV, generate gauge
factors lying between 7 and 30, which is in good agreement with
this experiment (from 5 to 12). However, ink ECP2, with 15% conductive oxide, presents a gauge factor superior to that of ink ECP3
with 9% conductive oxide. Considering the different percentages
of glass in inks ECP2 and ECP3, 85 and 91% respectively, it might
be thought that the distance x between 2 conductive particles
4. Circuits and Model Used
might be changed. It was not possible to establish this fact in this
study. In the case of inks ECP2 and ECP3, the variation in the
proportion of glass melted is small (equal to 6%). One can assume
4.1. Construction of the Wheatstone Bridge
that, during baking, this increase in the volume of glass between
the clusters of RuO2 particles was not sufficient, in the case of
The characteristics of the membranes and the test conditions
ECP3, to rise the intergranular distance x to any significant extent.
were as follows,
Furthermore, phenomena such as that of conduction due to per•
membrane used: 96% alumina;
colation between the clusters of conductive oxide particles and
•
external diameter: 34 mm;
stoichiometric modifications for slight variations in sintering con•
thickness e of membrane: 0.80 mm;
ditions may also minimize its effects;
• embedding radius, r = R, to inside of clearance window for
• the lowest gauge factor (5.0) was obtained for ink ECP1, with
external gauges is equal to 9.5 mm;
large particles of B2O3. Reducing the size of these particles, it can
• elasticity modulus E of the alumina is 314 Gpa;
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Thick Film Piezoresistive Ink: Application To Pressure Sensors
• its Poisson’s ratio, n, is equal to 0.23;
• the pressure P applied to the cell was fixed at 20 bars.
is placed a rectangular gauge, perfectly linked to it and subjected
to a strain (for example, by means of pressure). This gauge is
subjected to the principal strain of the substrate εx, εy, εz. These
generate a change of resistance dR/R in this gauge.
Under these conditions, one can obtain the following relation,
dR
=ε x [γ L +1]+ε y [γ T −1]+ε z (γ T − 1)
R
=K L ε x + K T ε y
γL and γT are the Bridgman coefficients to which KL and KT , the
Figure 12. Section through the test cell used, diameter 34mm.
longitudinal and transversal gauge factors of the strain gauges,
are related by equations (8), as follows,
ν
(γ T − 1)
1 ν−ν
(γ T − 1)
KT = γ T − 1 −
1 −ν
K L= γ L +1−
(8)
with ν representing Poisson’s ratio.
4.2.2. Application of This Model to The Case of Thick
Layer Type Gauges
Longitudinal and transversal gauge factors GFL and GFT, different from those which was previously established by the authors,
have been defined by other authors, for a beam of cantilever type,
or for a bar under tension (see Figure 14), under conditions such
that εy = -νεx.
Figure 13. Membrane carrying the gauges (piezoresistive ink)
connected in a Wheatstone bridge.
4.2. The Model
Since the formulae linking coefficients of piezoresistivity
(Bridgman coefficients) and the electrical signals yielded by the
piezoresistive inks had only been very partially established at the
time, the authors were obliged to establish a model describing
their behavior in this respect.
The authors then applied this model to cases of piezoresistive
resistances associated with a circular plate let into a support, corresponding to our own experiments.
4.2.1. The Theoretical Approach - Relations Between
Piezoresistivity and the Gauge Factor
Figure 14. Bar in tension - relations linking K and GF.
The theoretical approach enabled us to link the resistive variaOne can then link these GF coefficients to these K coefficients
tions dR/R of any type of gauge (glued, thin layer or thick layer)
with
expression (9), given as,
to the strain ε which induced them. We employed isotropic linear
elasticity, but applied to a structure of fixed geometry.
Let us consider a substrate (or sensitive element) upon which
The International Journal of Microcircuits and Electronic Packaging, Volume 23, Number2, Second Quarter 2000 (ISSN 1063-1674)
© International Microelectronics And Packaging Society
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Intl. Journal of Microcircuits and Electronic Packaging
ìGFL =K L −ν K T
í
GFT =K T −ν K L
(9)
and, reciprocally, the K coefficients can be deduced from the GF
factors, relation (10),
4
3
2 P R
(
1
)
−
ν
f=
8
E 2 e3
• z, equation for deformation at any point;
GFL + ν GFT
KL=
1 −ν 2
í
GFT + ν GFL
KT =
1 −ν 2
î
ì
z=
(10)
The difference between the gauge factors of an ink on a bar of
alumina (the ceramic usually used as a substrate for thick layer
gauges) in tension is given by R. D. Acqua15; showing that for
hybrid gauges;
GFL - GFT = 2.(1+ν)
ratio, when the behavior of the structure of the embedded, circular
plate (Figure 15) obeys the following equations (16):
• f, deflection at the center of the membrane (r = 0);
(11)
Experimentally, this difference has been measured and finds it to
be of the order of ≈ 2.5.
As Poisson’s ration for alumina, is of the order of 0.23, one can
obtain, equation (10),
KL - KT ≈ 2
and by equation (8),
γL - γT = 0
For thick film gauges (as for glued or thin film gauges), the
Bridgman coefficients are thus equal.
4.2.3. Extension of The Model to The Gauge Factor
of an Embedded, Circular Plate
At fixed pressure, the strain ε = dl/l of an embedded, circular
plate (Figure 14) is a function of the dimensions of this plate and
of the mechanical properties of the material used. The strains εx
and εy in a linear frame of reference becomes εr and εt in the cylindrical frame of reference for variable r.
3
P (R 2 − r 2 ) 2
(1 −ν 2)
16
E
e3
• dr/r, radial or longitudinal strain;
2
2
3
2 P R − 3r
ν
(
1
−
)
dr/r =
8
E e2
• dt/t, tangential strain;
2
2
3
2 P R − 3r
ν
(
1
−
)
dt/t = εt =
.
8
E e2
These relations16 are only valid for slight strains and for a
stress σz = 0 (with σr, radial stress and σt, tangential stress, associated with εr and εt and σz, stress normal to σr and σt. Their limits are
given by W. C. Young and R. J. Roarck17, e < 0.2.R and f < 0.5.e.
According to the analytical relations above, it may be remarked
that, at the center of the membrane (in r = 0), the radial and
tangential strains are equal,
dr/r = dt/t ε c = =
(
)
3P 1 − ν 2 R 2
8Ee 2
(12)
(b) The case of thick film gauges:
Under the effect of strain, and according to the model established
earlier, the electrical resistances situated in r = 0 and r = R will
dR
undergo variations of resistance R such that,
(GFL +GFT )(1 + ν )
ì dR
=ε c (K L + K T )= ε c
R center
1 −ν 2
í dR
(GFL + ν GFT )
=−2ε c K L = −2ε c
1 −ν 2
î R embedding
(13)
Applying equation (12), in the case of gauges made from an
industrial ink, one can deduce the variations dR/R at the center
and at the embedding undergone by the gauges. The maker’s
data19 are:
GFL and GFT with n(alumina) = 0.23
One can deduce, according to equation (10), the following,
KL = 15.9, KT = 13.9 and that:
Figure 15. Strains under pressure of an embedded, circular
membrane.
æ 1−ν ö
(a) The authors first recapitulate the general laws for the deforcL = cT =13,9 çç
+1 = 20.8;
è 1−2ν
mation of an embedded, circular plate:
Let E be the modulus of elasticity of a material and n, its Poisson’s
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Thick Film Piezoresistive Ink: Application To Pressure Sensors
that is to say, for a given ink, the following variations in resistance:
ì dR
=29,8ε c
R center
í dR
=−31,8ε c
î R embedding
(14)
One can then obtain an output. voltage Sa, measured by the Wheatstone bridge, under a central strain, εc, including all the resistive
variations undergone by the gauges:
.
Sa =
ù
U é dR dR
⋅2⋅ê
+
ε
4 ë Rcenter R embedding = 30.8 c U
with U the supply voltage to the bridge.
4.3. Experimental Application
On the basis of the theoretical approach above and in particular expressions (12) and (13), one can exploit the results obtained
under pressure for a given type of cell and different piezoresistive
inks. The initial results will lead us to introduce corrective parameters or, taking into account technological constraints ignored
in the model adopted,
ìæ dR ö measured
=cc ε c (K L + K T )
ç ÷
è R center
í
measured
æ dR ö
=− 2ce ε c K L
ç
î è R embedding
with KL = 15.9 and KT = 13.9 (gauge factors calculated from the
ink manufacturer’s data), one can obtain the shape coefficients,
taking into account the non-circularity of the membrane and the
fact that point geometry is not applicable to our gauges:
Cc = 0.999 and Ce = 0.266.
5. Conclusions
perature of utilization varies;
• at this temperature, the inks are all perfectly sintered and practically free from porosities;
• the baking also modifies the principal crystallized phases;
• the resistivity and piezoresistivity of the inks are a function
of the nature of their component oxides and their respective proportions;
• with glass and conductive oxide identical, resistance apparently increases as the percentage of conductive oxide diminishes;
• at the same proportions of RuO2 and glass, resistance rises
as the size of the boron oxide particles decreases. We attribute
this phenomenon to better wetting of the conductive particles,
which may facilitate conduction by tunnel effect;
• the presence of WO3 in the ink lowers its resistivity, a result
which may be due to low resistivity of this oxide;
• the experimental ink with 15% RuO2 possesses resistive,
piezoresistive and thermal properties close to those of industrial
inks and the properties of these inks could be optimized by improved homogenization of their constituents.
Finally, the researchers have established a model which links
the Bridgman piezoresistive coefficients cL and cT, to the gauge
factors KL and KT, strains ex and ey and their resistive variations.
This model enabled us to compare the gauge factors of industrial
inks.
References
1. H. Baudry, “Détecteurs, Capteurs et Transducteurs Céramiques
Sérigraphiés”, L’ INDUSTRIE CERAMIQUE, No. 855, pp.
834-838, 1990.
2. L. Pësic, “A Review of Thick-Film Glaze Resistors”, Microelectronics Journal, Vol. 19, pp. 71-87, 1988.
3. G. E. Pike, “Electrical Properties and Conduction Mechanism of Ru-based Thick-Film (cermet) Resistors”, Journal of
Applied Physics, Vol. 48, pp. 5152-5156, 1978.
4. T. Inokuma, cité par [9] L. Pësic , Active and Passive Elect.
Components, Vol.12, pp. 155-166, 1987. 5. K. Kusz, cité
par [9] L. Pësic, 5ème conférence ISHM de Pologne, pp. 5665, 1984.
6. J. W. Pierce, cité par [9] L. Pësic, Solid State Technology, pp.
85-93, October 1982.
7. L. Pësic, “A Review of Thick-Film Glaze Resistors”, Microelectronics Journal, Vol. 19, pp. 71-87, 1988.
8. B. W. Licznerski, cité par [9] L. Pësic, Proceedings of ISHM,
Poland Conference, pp. 4-17, 1985.
9. Y. M. CHIANG, L. A. Silvermann, H. French, and R. M.
Cannon, “Thin Glass Film Between Ultrafine Conductor Particles In Thick-Film Resistors”, Journal Of American Ceramic
Society, Vol. 5, No. 77, pp. 1143-1152, 1994.
10. R. F. Geller and E. N. Bunting, Journal Research Nat. Bur.
Standards, Vol. 23, pg. 281, 1939.
11. P. F. Carcia, A. Suna, and W. D. Childers, “Electrical Conduc-
The researchers undertook a systematic study of different industrial inks used in the manufacture of “thick film” sensors.
Through numerous analysis, the authors have confirmed and
demonstrated the following,
• thick film piezoresistive inks are complex compounds, containing metallic oxides, of the type ruthenium oxide RuO2, or of
the types ruthenate of lead or bismuth, incorporated in a matrix of
lead borosilicate glass;
• sintering industrial inks at different temperatures (between
600°C and 900°C) shows that a baking temperature of 850°C is a
good compromise to obtain minimal signal variation when the temThe International Journal of Microcircuits and Electronic Packaging, Volume 23, Number2, Second Quarter 2000 (ISSN 1063-1674)
© International Microelectronics And Packaging Society
201
Intl. Journal of Microcircuits and Electronic Packaging
tion and Strain Sensitivity in RuO2 Thick Film Resistors”, Journal of Applied Physics, Vol. 54, pp. 6002-6008, 1983.
12. L. Pësic, “A Review Of Thick-Film Glaze Resistors”, Microelectronics Journal, Vol. 19, pp. 71-87, 1988.
13. O. Abe and Y. Taketa, “A New Thick Film Strain Sensor”,
ICM Proceedings, pp. 217-221, 1988.
14. C. Canali, D. Malavasi, B. Morten, and M. Prudenziati,
“Piezoresistive Effects in Thick-Film Resistors”, Journal of
Applied Physics, Vol. 51, pp. 3282-3288, 1980.
15. R. D. Acqua, “Thick Film Pressure Sensors: Performance
and Practical Applications”, 3TH European Hybrid Microelectronics Conference, pp. 121-131, 1981.
16. G. Asch, “Les Capteurs en Instrumentation Industrielle”,
Dunod, pp. 378-379, 1983.
17. W. C. Young and R. J. Roarck, “ROARCK’s Formulas of
Stress and Strain” McGraw-Hill, 6 ème édition, pp. 397 et
457, 1976.
The International Journal of Microcircuits and Electronic Packaging, Volume 23, Number2, Second Quarter 2000 (ISSN 1063-1674)
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