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Polymer thick-film technology: A possibility to obtain very low cost pressure sensors?
Sensors and Actuators A, 25-27
(1991) 853-857
853
Polymer Thick-Elm Technology: a Possibility to Obtain Very Low Cost Pressure Sensors? GABOR
HARSANYI
Technical University of Budapest, Department of Electronics Technology, 1521 Budapest (Hungary)
Abstract A new type of pressure sensor has been developed by taking advantage of the piezoresistive effect in polymer thick-film resistors screened and cured on epoxi-glass diaphragms. The device looks promising to satisfy the requirements for low cost, high sensitivity and low thermal drift.The piezoresistive effect in polymer thick-film (PTF) resistors is discussed in comparison with cermet thick films. The possibility of making a highperformance PTF pressure sensor is theoretical supported. Characteristics of the newly developed polymer thick-film sensor are described. In a limited temperature range, the new sensor has parameters that are not worse than those of the cermet thick-film pressure sensor and a much lower cost.
1. Introduction Over the last two decades, the piezoresistive effect in thin metal films and semiconductors has been utilized for strain gauges and related sensor applications. Since the initial observation of piezoresistive behaviour in thick-film resistors, several studies related to strain sensitivity and practical pressure sensor application have been reported [l-4]. Low cost, low sensitivity and moderate zero-point temperature drift are the characteristics of thick-film pressure sensors. The sensitivity is limited partly by the alumina substrate. Carbon-loaded organic polymer thick-film (PTF) resistors can be applied on a wide range of substrates, even on flexible ones. The 0924-4247/91/$3.50
idea naturally arises to make pressure sensors on a polymer basis. The greatest problem is the thermal and long-term drift of the PTF resistors [S]. It can be shown by theoretical analysis that pressure sensors can overcome these problems and we have the possibility of producing highly sensitive polymer sensors with good performance.
2. Theoretical Considerations The sensitivity to strain of a piezoresistive resistor, indicated as the gauge factor (GF), is defined as the ratio between the fractional change in resistance (AR/R) and the strain (E) induced on the resistor by an applied stress: GF = (AR/R)/&
(1)
In film resistors the fractional change in resistor length, the deformation, is inversely proportional to the elasticity modulus and the thickness of the substrate [l-3]: EN l/Es
(2)
The GF of the thick-film resistor can be measured by the so-called cantilever method described elsewhere [ 61. The sensing element of the thick-film pressure sensors generally consists of a circular or square edge-clamped diaphragm on which four thick-film resistors connected in a Wheatstone-bridge configuration are screened and fired (Fig. 1). The strains induced on the diaphragm by a pressure difference on its two faces cause a change in the resistance value of the four resistors. 0 Elsevier Sequoia/Printed in The Netherlands
854
4_
( TCR3 - TCR,)
AT -
2
(TCR, - TCR,)
U
(5)
Fig. 1. Structure and circuit connection of the thickfilm pressure sensor membranes.
where TCR = (AR/AT) (l/R) Provided that they are conveniently positioned and connected, the bridge becomes unbalanced with a voltage output proportional to the load (if R, = R2 = R3 = R4 = R, and R,=R,=O): U, = U(ARIR) = UGFE = UGFKp/Ea
(3)
where the constant K depends only on the geometry of the diaphragm. It is easily seen that in order to maximize the loss of the bridge balance and the voltage output, two resistors must be positioned near to the centre of the diaphragm and another two resistors near to the edges and connected as shown in Fig. 1 [3]. Besides the sensitivity and linearity, the most important parameters of the sensors are the zero-point temperature drift and longterm stability. To estimate these parameters we have to make a theoretical analysis [3-41. If U is the supply voltage and U, is the output voltage, then the output of the bridge shown in Fig. 1. is
u” =
1
+
1 (RJR,)
1 - 1 + (RI/R*)
U
(4)
Let us suppose that the technological target is to obtain a bridge where the maximum difference between the four resistors is within 5%. In this condition the influence of the zerooutput balance-trimming resistors (potentiometer) can be neglected (if their thermal coefficient of resistance (TCR) is not very far from those of the bridge resistors). Expression (4) can be differentiated with respect to temperature:
It becomes obvious that the thermal drift of the bridge depends on the tracking of the temperature coefficients of two adjacent resistors multiplied by a factor which includes the ratio of their resistance values. It is now possible on the basis of the experimental results verified on the tracking of the TCRs of the four resistors of the bridge to compute the worst case by putting into eqn. (5)
(maximum value) and (TCR, - TCR4) = (TCR, - TCR,) = A TCRmx (worst coupling of the TCR values of the four resistors). We obtain (AUJATU)
6 0.5 ATCR,,,
(6)
The thermal drift can be characterized by the parameter (7)
AU,lATGs where U,, is the full-scale output sensor:
of the
(1
u,, = u g
Kp, = usp,
where pN is the nominal pressure value and S the sensitivity. Putting the results of eqns. (6) and (8) into (7), we obtain -=Au, AT&s
Ea ATCR,,, GF
0.5 @N
(9)
855
For the comparison of different sensor types, a special parameter can be defined as a quality factor of the sensor: QT=
GF
(10)
Ea ATCR,,,
A larger quality ratio, at the same geometry and the same nominal pressure value, indicates a sensor with better thermal characteristics. In a similar way we can show for the long-term stability of the zero point that
(11) where &AR/R) means the tracking of the fractional change of the resistance at given conditions. Then the quality factor of the stability is
(12) It can be seen that the thermal and long-term stabilities of the sensor depend not on the TCR value and resistance change themselves, but on their tracking, i.e., on the uniformity of the four resistors only. In Table 1 we can see a comparison between the cermet and polymer thick-film resistors [7, 81. If we can use the same geometry and the substrates mentioned in Table 1, PTF
sensors have about 50 times higher sensitivity than the cermet ones. The quality factors are also much better for the PTF sensors. So the latter can be used for smaller nominal pressure values with as good thermal and stability parameters as the cermet ones. For example, let us suppose that there is a cermet thick-film pressure sensor with the following parameters: PN = lo6 Pa, s = 5 x 10e9 Pa-‘; (AU,/ATUFs) < O.O5%/“C; longterm drift (AU,/U& < 3%. Using the same geometry and the substrates in Table 1, we can produce a PTF sensor with a sensitivity S = 2.5 x lo-’ Pa-‘. If we use this sensor for a nominal pressure value of pN = 2 x 10’ Pa, according to the theoretical results, we obtain (AU,,/ATUFs) 6 0.5%/“C, (AU,/U& < 5%. These parameters can be improved by the use of ‘high reliability’ PTF resistor pastes (see Table 1): (AU,/ATUFs) < 0.2%/“C, (AU,/U& < 0.5%. According to our theoretical results, PTF pressure sensors can be made for lower pressure regions with similar performance to cermet ones. Our theory does not answer the question concerning the thermal and long-term drift of the sensitivity. These parameters depend on the value of the TCGF and on the long-term drift of the GF respectively, and cannot be estimated by the method described above.
TABLE I. Main parameters of cermet and polymer thick-film resistors and the calculated pressure sensor quality factors Cermet thick films
PTF (typical)
High reliability PTF of EMCA [8]
GF
10
Substrate E (N/mm’) a (mm) (substrate thickness) TCR (ppml”C) A TCR,,, (ppm/“C) Stability AR/R(%)
96% alumina 3.3 x lo5 0.6 *50 *5 0.3 (1000 h, 150°C) 0.03 IO 16.8
10 FR4 (glass-epoxy) 2.1 x 104 0.2 +500 *50
10 FR4 (glass-epoxy) 2.1 x lo4 0.2 * 200 *20 0.5% (1000 h, 85 “C) 0.05 120 480
&AR/R) (%) Q,(10-3Km/N)
Q, (W5m/W
:I000 h, 85 “C) 0.5 48 48
856 TABLE 2. Technological parameters of the pressure sensor membranes Properties of the membrane
Substrate material Substrate thickness (mm) Substrate radius (mm) Conductor type Resistor type Drying Curing
Sensor type Cermet
PTF
96% alumina 0.6 25.4 DP9473 Pd-Ag R,,= 10 kR DPl441 15O”C/l5 min 850 “C/IO min
FR4 (epoxy-glass) 0.2 25.4 Tin-coated copper R, ,= 10 kQ Hungarian product 12O”C/l5 min 180 “C/l20 min
3. Experimental Results
4. Concl~ions
In our experiments we used the sensor geometry shown in Fig. 1. The most important technological parameters of the cermet and the PTF sensor types are summarized in Table 2. The diaphragms were attached on screwed metal frames that were fastened in metal cases as shown in Fig. 2. Figure 3 shows typical voltage outputs of the sensors supplied with 10 V. The main technical characteristics of the sensors are summarized in Table 3. The results correspond to our theoretical expectations.
The theoretical analysis has shown that there is a possibility to produce PTF pressure sensors with high sensitivity and good properties even using polymer resistor parts that are not very reliable. In our experiments we have made a comparison between cermet and polymer pressure sensors using the same geometry. We found that according to the theory, the PTF sensors have much higher sensitivity and with a proper choice of nominal pressure
u = 1ov
Membrane Pocking
0
Fig. 2. Mechanical structure of the pressure sensors.
2
L
6
6
10
Fig. 3. Typical characteristics of the cermet and polymer thick-film pressure sensors.
857 TABLE 3. Technical characteristics of the thick-film pressure sensors
Full-scale pressure (Pa) Supply voltage (V) Zero output (mV) Full scale output (F.S.) (mV) Response time (ms) Non-linearity and hysteresis Working temperature (“C) Additional temperature failure Overpressure Long-term drift (1000 h, 85 “C)
Cermet thick film
PTF
10"
2X IO5 10 kO.1 250 <5
10 +0.1
50 <5 < 0.5% F.S. -25-100 < + 0.05% F.S./“C 1.5 times F.S. $0.50~
value they have as good relative thermal characteristics as the cermet ones, with much lower cost.
I F. Forlani, Thick-film sensors for automotive electronics, Proc. 4th European Hybrid Microelectronics Conj, Copenhagen, Denmark, 1983, pp. 165-177. 2 G. Hars&i and S K&i, A piezoresistive thick film pressure sensor, Proc. Int. Spring Seminar Electrotechnology ‘87, Sopozol, Bulgaria, 1987. pp. 86-101. 3 R. Dell’ Acqua, G. Dell’Orto and P. Vicini, Thick-film pressure sensors: performances and practical applications, Proc. 3rd European Hybrid Microelectronics Conf., Avignon, France, 1981, pp. Q-123.
4 G. HarsLnyi and M. Rkczey, Thermal characteristics
of piezoresistive thick film pressure sensors, Acta Polytech. (Prague], 3 (2) (1989) 37-42. 5 G. Castelli and V. Meroni, Screen printed polymeric thick films on epoxy-glass substrates, Proc. 5th European Hybrid Microelectronics Conf., Stress, Italy, 1985, pp. 528-536. 6 S. Chitale et al., High gauge factor thick film resistors for strain gauges, Hybrid Circuit Technol., (May)
(1989) 28-35. 7 Shen-Li Fu, Mong-Song Liang, T. Shiramatsu and Tien-Shu Wu, Electrical characteristics on polymer thick film resistors I-II, IEEE Trans. Components, Hybrids and Manufact. 283-293.
Tech.,
CHMT-4/3
(1981)
8 F. W. Martin, High reliability polymer thick film, So/id State Technol., (Ott) (1982) 173-176.
(1991) 853-857
853
Polymer Thick-Elm Technology: a Possibility to Obtain Very Low Cost Pressure Sensors? GABOR
HARSANYI
Technical University of Budapest, Department of Electronics Technology, 1521 Budapest (Hungary)
Abstract A new type of pressure sensor has been developed by taking advantage of the piezoresistive effect in polymer thick-film resistors screened and cured on epoxi-glass diaphragms. The device looks promising to satisfy the requirements for low cost, high sensitivity and low thermal drift.The piezoresistive effect in polymer thick-film (PTF) resistors is discussed in comparison with cermet thick films. The possibility of making a highperformance PTF pressure sensor is theoretical supported. Characteristics of the newly developed polymer thick-film sensor are described. In a limited temperature range, the new sensor has parameters that are not worse than those of the cermet thick-film pressure sensor and a much lower cost.
1. Introduction Over the last two decades, the piezoresistive effect in thin metal films and semiconductors has been utilized for strain gauges and related sensor applications. Since the initial observation of piezoresistive behaviour in thick-film resistors, several studies related to strain sensitivity and practical pressure sensor application have been reported [l-4]. Low cost, low sensitivity and moderate zero-point temperature drift are the characteristics of thick-film pressure sensors. The sensitivity is limited partly by the alumina substrate. Carbon-loaded organic polymer thick-film (PTF) resistors can be applied on a wide range of substrates, even on flexible ones. The 0924-4247/91/$3.50
idea naturally arises to make pressure sensors on a polymer basis. The greatest problem is the thermal and long-term drift of the PTF resistors [S]. It can be shown by theoretical analysis that pressure sensors can overcome these problems and we have the possibility of producing highly sensitive polymer sensors with good performance.
2. Theoretical Considerations The sensitivity to strain of a piezoresistive resistor, indicated as the gauge factor (GF), is defined as the ratio between the fractional change in resistance (AR/R) and the strain (E) induced on the resistor by an applied stress: GF = (AR/R)/&
(1)
In film resistors the fractional change in resistor length, the deformation, is inversely proportional to the elasticity modulus and the thickness of the substrate [l-3]: EN l/Es
(2)
The GF of the thick-film resistor can be measured by the so-called cantilever method described elsewhere [ 61. The sensing element of the thick-film pressure sensors generally consists of a circular or square edge-clamped diaphragm on which four thick-film resistors connected in a Wheatstone-bridge configuration are screened and fired (Fig. 1). The strains induced on the diaphragm by a pressure difference on its two faces cause a change in the resistance value of the four resistors. 0 Elsevier Sequoia/Printed in The Netherlands
854
4_
( TCR3 - TCR,)
AT -
2
(TCR, - TCR,)
U
(5)
Fig. 1. Structure and circuit connection of the thickfilm pressure sensor membranes.
where TCR = (AR/AT) (l/R) Provided that they are conveniently positioned and connected, the bridge becomes unbalanced with a voltage output proportional to the load (if R, = R2 = R3 = R4 = R, and R,=R,=O): U, = U(ARIR) = UGFE = UGFKp/Ea
(3)
where the constant K depends only on the geometry of the diaphragm. It is easily seen that in order to maximize the loss of the bridge balance and the voltage output, two resistors must be positioned near to the centre of the diaphragm and another two resistors near to the edges and connected as shown in Fig. 1 [3]. Besides the sensitivity and linearity, the most important parameters of the sensors are the zero-point temperature drift and longterm stability. To estimate these parameters we have to make a theoretical analysis [3-41. If U is the supply voltage and U, is the output voltage, then the output of the bridge shown in Fig. 1. is
u” =
1
+
1 (RJR,)
1 - 1 + (RI/R*)
U
(4)
Let us suppose that the technological target is to obtain a bridge where the maximum difference between the four resistors is within 5%. In this condition the influence of the zerooutput balance-trimming resistors (potentiometer) can be neglected (if their thermal coefficient of resistance (TCR) is not very far from those of the bridge resistors). Expression (4) can be differentiated with respect to temperature:
It becomes obvious that the thermal drift of the bridge depends on the tracking of the temperature coefficients of two adjacent resistors multiplied by a factor which includes the ratio of their resistance values. It is now possible on the basis of the experimental results verified on the tracking of the TCRs of the four resistors of the bridge to compute the worst case by putting into eqn. (5)
(maximum value) and (TCR, - TCR4) = (TCR, - TCR,) = A TCRmx (worst coupling of the TCR values of the four resistors). We obtain (AUJATU)
6 0.5 ATCR,,,
(6)
The thermal drift can be characterized by the parameter (7)
AU,lATGs where U,, is the full-scale output sensor:
of the
(1
u,, = u g
Kp, = usp,
where pN is the nominal pressure value and S the sensitivity. Putting the results of eqns. (6) and (8) into (7), we obtain -=Au, AT&s
Ea ATCR,,, GF
0.5 @N
(9)
855
For the comparison of different sensor types, a special parameter can be defined as a quality factor of the sensor: QT=
GF
(10)
Ea ATCR,,,
A larger quality ratio, at the same geometry and the same nominal pressure value, indicates a sensor with better thermal characteristics. In a similar way we can show for the long-term stability of the zero point that
(11) where &AR/R) means the tracking of the fractional change of the resistance at given conditions. Then the quality factor of the stability is
(12) It can be seen that the thermal and long-term stabilities of the sensor depend not on the TCR value and resistance change themselves, but on their tracking, i.e., on the uniformity of the four resistors only. In Table 1 we can see a comparison between the cermet and polymer thick-film resistors [7, 81. If we can use the same geometry and the substrates mentioned in Table 1, PTF
sensors have about 50 times higher sensitivity than the cermet ones. The quality factors are also much better for the PTF sensors. So the latter can be used for smaller nominal pressure values with as good thermal and stability parameters as the cermet ones. For example, let us suppose that there is a cermet thick-film pressure sensor with the following parameters: PN = lo6 Pa, s = 5 x 10e9 Pa-‘; (AU,/ATUFs) < O.O5%/“C; longterm drift (AU,/U& < 3%. Using the same geometry and the substrates in Table 1, we can produce a PTF sensor with a sensitivity S = 2.5 x lo-’ Pa-‘. If we use this sensor for a nominal pressure value of pN = 2 x 10’ Pa, according to the theoretical results, we obtain (AU,,/ATUFs) 6 0.5%/“C, (AU,/U& < 5%. These parameters can be improved by the use of ‘high reliability’ PTF resistor pastes (see Table 1): (AU,/ATUFs) < 0.2%/“C, (AU,/U& < 0.5%. According to our theoretical results, PTF pressure sensors can be made for lower pressure regions with similar performance to cermet ones. Our theory does not answer the question concerning the thermal and long-term drift of the sensitivity. These parameters depend on the value of the TCGF and on the long-term drift of the GF respectively, and cannot be estimated by the method described above.
TABLE I. Main parameters of cermet and polymer thick-film resistors and the calculated pressure sensor quality factors Cermet thick films
PTF (typical)
High reliability PTF of EMCA [8]
GF
10
Substrate E (N/mm’) a (mm) (substrate thickness) TCR (ppml”C) A TCR,,, (ppm/“C) Stability AR/R(%)
96% alumina 3.3 x lo5 0.6 *50 *5 0.3 (1000 h, 150°C) 0.03 IO 16.8
10 FR4 (glass-epoxy) 2.1 x 104 0.2 +500 *50
10 FR4 (glass-epoxy) 2.1 x lo4 0.2 * 200 *20 0.5% (1000 h, 85 “C) 0.05 120 480
&AR/R) (%) Q,(10-3Km/N)
Q, (W5m/W
:I000 h, 85 “C) 0.5 48 48
856 TABLE 2. Technological parameters of the pressure sensor membranes Properties of the membrane
Substrate material Substrate thickness (mm) Substrate radius (mm) Conductor type Resistor type Drying Curing
Sensor type Cermet
PTF
96% alumina 0.6 25.4 DP9473 Pd-Ag R,,= 10 kR DPl441 15O”C/l5 min 850 “C/IO min
FR4 (epoxy-glass) 0.2 25.4 Tin-coated copper R, ,= 10 kQ Hungarian product 12O”C/l5 min 180 “C/l20 min
3. Experimental Results
4. Concl~ions
In our experiments we used the sensor geometry shown in Fig. 1. The most important technological parameters of the cermet and the PTF sensor types are summarized in Table 2. The diaphragms were attached on screwed metal frames that were fastened in metal cases as shown in Fig. 2. Figure 3 shows typical voltage outputs of the sensors supplied with 10 V. The main technical characteristics of the sensors are summarized in Table 3. The results correspond to our theoretical expectations.
The theoretical analysis has shown that there is a possibility to produce PTF pressure sensors with high sensitivity and good properties even using polymer resistor parts that are not very reliable. In our experiments we have made a comparison between cermet and polymer pressure sensors using the same geometry. We found that according to the theory, the PTF sensors have much higher sensitivity and with a proper choice of nominal pressure
u = 1ov
Membrane Pocking
0
Fig. 2. Mechanical structure of the pressure sensors.
2
L
6
6
10
Fig. 3. Typical characteristics of the cermet and polymer thick-film pressure sensors.
857 TABLE 3. Technical characteristics of the thick-film pressure sensors
Full-scale pressure (Pa) Supply voltage (V) Zero output (mV) Full scale output (F.S.) (mV) Response time (ms) Non-linearity and hysteresis Working temperature (“C) Additional temperature failure Overpressure Long-term drift (1000 h, 85 “C)
Cermet thick film
PTF
10"
2X IO5 10 kO.1 250 <5
10 +0.1
50 <5 < 0.5% F.S. -25-100 < + 0.05% F.S./“C 1.5 times F.S. $0.50~
value they have as good relative thermal characteristics as the cermet ones, with much lower cost.
I F. Forlani, Thick-film sensors for automotive electronics, Proc. 4th European Hybrid Microelectronics Conj, Copenhagen, Denmark, 1983, pp. 165-177. 2 G. Hars&i and S K&i, A piezoresistive thick film pressure sensor, Proc. Int. Spring Seminar Electrotechnology ‘87, Sopozol, Bulgaria, 1987. pp. 86-101. 3 R. Dell’ Acqua, G. Dell’Orto and P. Vicini, Thick-film pressure sensors: performances and practical applications, Proc. 3rd European Hybrid Microelectronics Conf., Avignon, France, 1981, pp. Q-123.
4 G. HarsLnyi and M. Rkczey, Thermal characteristics
of piezoresistive thick film pressure sensors, Acta Polytech. (Prague], 3 (2) (1989) 37-42. 5 G. Castelli and V. Meroni, Screen printed polymeric thick films on epoxy-glass substrates, Proc. 5th European Hybrid Microelectronics Conf., Stress, Italy, 1985, pp. 528-536. 6 S. Chitale et al., High gauge factor thick film resistors for strain gauges, Hybrid Circuit Technol., (May)
(1989) 28-35. 7 Shen-Li Fu, Mong-Song Liang, T. Shiramatsu and Tien-Shu Wu, Electrical characteristics on polymer thick film resistors I-II, IEEE Trans. Components, Hybrids and Manufact. 283-293.
Tech.,
CHMT-4/3
(1981)
8 F. W. Martin, High reliability polymer thick film, So/id State Technol., (Ott) (1982) 173-176.