Text-chap6

_______________________________________________6 PYROELECTRIC DEVICES

The pyroelectric effect in certain materials was recognized a long time ago, and such materials were referred as "electric stones." It was observed when such a stone was thrown in the fire, and it started to generate electric charges and caused a "cracking" sound. This is basically due to the temperature dependence of the spontaneous polarization of a polar material.

6.1 PYROELECTRIC MATERIALS (1)

Pyroelectric Effect

Practical applications of the pyroelectric effect in temperature sensors and infrared light detectors have been promoted, enabling some commercial marketing of ferroelectric ceramics. The merits of pyrosensors as compared to semiconducting infrared-sensor materials are summarized as follows: a) wide range of response frequency, b) use at room temperature, c) quick response in comparison with other temperature sensors, d) high quality (optical-grade homogeneity, etc.) materials for the pyrosensors are unnecessary. The principle on which the pyroelectric effect is based concerns the charge generation associated with the spontaneous polarization change with temperature: j = - ∂Ps /∂ t = - (∂Ps /∂T)(∂T/∂ t) = p(∂T/∂ t).

(6.1)

Here p (= |∂ Ps /∂T|) is denoted as the pyroelectric coefficient. The phenomenon is illustrated schematically in Fig. 6.1. Two typical electrode arrangements for pyrosensors are illustrated in Fig. 6.2: (a) face electrodes with the polarization direction parallel to the infrared irradiation, and (b) edge electrodes with the polarization direction perpendicular to the irradiation. The former type has higher efficiency, but requires a sophisticated fabrication process for applying uniform transparent electrodes for the infrared light. 131

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Chapter 6

Heat sensor ! Infrared irradiation

+

+-

+-

-+

+

+

-

-

-

-

Ps -

+

+

+

+

Fig. 6.1 Principle of a pyroelectric sensor: a temperature increase due to the infrared irradiation (such as human body) ---> Spontaneous polarization decrease --> Variation in electric charge (or current).

Ps (a)

Radiation

Ps

(b)

Radiation

A

A a

a

Fig. 6.2 Typical geometric configurations for pyroelectric detectors: (a) face electrodes with the polarization direction parallel to the infrared irradiation, and (b) edge electrodes with the polarization direction perpendicular to the irradiation.

Example Problem 6.1_________________________________________________ When a chopped infrared beam is incident on a pyroelectric material, what is the wave form of the induced pyroelectric current?

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133

Solution When an infrared beam is incident on a pyroelectric material, the temperature of the sample will be increased according to (1 - e- t/ τ). Since the pyroelectric current j is proportional to (∂T/∂t) [see Eq. (6.1)], j ∝ e- t/ τ .

(P6.1.1)

It is evident from this relation that one pulse of infrared (IR) light will provide only one pulse of current. Because the current becomes zero after a certain time, we cannot distinguish whether the IR beam is coming or not. Therefore, to measure the temperature of an IR irradiating object (such as meat in a microwave oven), the infrared beam from the object should be chopped periodically. When the illumination is periodic, a periodic variation in the temperature of a pyroelectric sensor will induce a periodic variation in the pyroelectric current, as illustrated in Fig. 6.3. Since the current is alternating, rectification is necessary to obtain the light intensity (or the object temperature).

Light intensity

Temperature rise

Time

Time Pyroelectric current Time

Fig. 6.3 Pyroelectric response to chopped IR irradiation. ___________________________________________________________________

(2)

Responsivity1)

When the incident power flux is W exp(jωt) (i. e., chopped IR irradiation), the amplitude of the temperature variation is provided by ∆T = ηW A (γ 2A 2 + ω2 K 2) -1/2 ,

(6.2)

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Chapter 6

where η is the transmittance of the incident radiation, A a detecting area, γ a coefficient corresponding to the loss of heat per unit area of the detector to its surroundings due to its increase in temperature, and K = ρ cp Ah , (6.3) where ρ is the density of the pyro-material, cp the specific heat and h is the thickness of the detector [refer to Fig. 6.2(a)]. The current responsivity, ri, is defined by ri = (1/WA) (dq/dt) .

(6.4)

Since the charge generated by a temperature rise ∆T is given as q = p A ∆T ,

(6.5)

using Eq. (6.2), we obtain: ri = ηp ωA (γ 2A 2 + ω2 K 2) -1/2.

(6.6)

Introducing a thermal time constant τD = K / γ A ,

(6.7)

we obtain finally ri = ηp ω γ -1 (1 + ω2 τD 2 )-1/2.

(6.8)

When ωτD >> 1, ri = ηp / ρ cp h. In order to increase ri, neglecting the size or surface effect, the value (p / ρ cp ) should be increased. Figure 6.4 shows an amplifier circuit for measuring a pyroelectric voltage signal. The resistance R is relatively high and is inserted to remove the charge after it is thermally induced on the pyroelectric (CD ). The transistor must have a high impedance (e.g., FET). Vs V0

CD

R

CA

RL V=0

Fig. 6.4 Amplifier for a pyroelectric infrared detector.

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The voltage responsivity for such an amplifier is expressed as: rv = (1/ WA) (dV/dt) = r i |z| (6.9) where z is the impedance of the detector-amplifier combination. Assuming RL<< R, |z| = R (1 + ω2 τE2 )-1/2 (6.10) where τE = R (CD + CA ), and CD and CA are the capacitances of the detector and the amplifier. Therefore, Eq. (6.9) may be written as rv = ηp ω R γ-1 (1 + ω2 τD2 )-1/2 (1 + ω2 τE2 )-1/2 .

(6.11)

At a high frequency (>> 1/ τD , 1/τE), we obtain rv = ηp / ρ cp εA ω ,

(6.12)

assuming that CD > CA . In order to increase rv , neglecting again size or surface effects, the value (p / ρ cp ε) should increase. Note that rv differs from r i by a factor of (1/ ε). The rv decreases with frequency at high frequencies, but that is relatively independent of frequency between 1/τD (0.1 - 10 Hz) and 1/ τE (0.01 Hz).2) Thus, in practice, the irradiation chopping frequency is chosen just between 1/τD and 1/τE.

(3)

Figures of Merit

The pyroelectric sensor is a device for transducing optical/thermal energy to electrical energy, and its efficiency or figure of merit is evaluated in several ways; for example, in terms of p, p/cp or p/(c p ε). Table 6.1 Figures of merit for pyroelectric materials. ___________________________________________________________ Figure of Merit Application ___________________________________________________________ p/cp p/(cp ε) p/(cpαε) p/cp (ε tanδ)1/2

low impedance amplifier high impedance amplifier thermal imaging device (vidicon)

high impedance amplifier when the pyroelectric element is the main noise source ___________________________________________________________ p: pyroelectric coefficient; cp : specific heat; ε: relative permittivity α: thermal diffusivity

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Chapter 6

Table 6.2 Room-temperature properties of various pyroelectric detector materials and some "figures of merit" for their detector operation. ________________________________________________________________ Material p ε'/ ε0 cp p/cp p/(c p ε') p/(c p ε") (nCcm-2K-1)

(Jcm-3K-1) (nAcmW-1) (Vcm-2J-1) (cm3J-1)1/2

________________________________________________________________ TGS 30 50 1.7 17.8 4000 0.149 LiTaO3 19 46 3.19 6.0 1470 0.050 Sr 1/2 Ba1/2Nb 2O 6 60 400 2.34 25.6 720 0.030 PLZT(6/80/20) 76 1000 2.57 29.9 340 0.034 PVDF 3 11 2.4 1.3 1290 0.009 ________________________________________________________________

These are useful figures of merit because the temperature change of the sample is larger for the smaller specific heat (c p ) material under constant heating, and the voltage generated by a certain amount of pyro-charge becomes larger for the smaller dielectric constant (ε) material [refer to the previous section 6.1(2)]. Table 6.1 summarizes several figures of merit. Table 6.2 lists the figures of merit of several pyroelectric materials.3) Example Problem 6.2_________________________________________________ Assuming a second-order phase transition for the Landau free energy: F(P,T) = (1/2)α P 2 + (1/4)β P 4 , α = (T - T 0 )/ε0 C ,

(P6.2.1) (P6.2.2)

calculate the temperature dependence of the figures of merit for a pyroelectric detector: p, p/cp and p/cp ε.

Solution The polarization for zero applied field is obtained from [(T - T 0)/ ε0 C] PS + β PS 3 = 0 . For T < T 0, the minimum of the Landau free energy is obtained at: ______________ PS = √(T 0 - T)/(β ε0 C).

(P6.2.3)

(P6.2.4)

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Since the die lectric constant ε is calculated as: 1/ε = ε0/(∂P/∂E) = ε0(α + 3β P2 ),

(P6.2.5)

we obtain ε = C/[2(T - T0 )] .

(P6.2.6)

(T < T 0)

Concerning the specific heat, modification from the Debye specific heat cp0, ∆cp can be calculated as ∆cp = (?F/?T). Since P S2 = - α/β, F(P,T) = (1/2)α P 2 + (1/4)β P 4 = (1/2)α (- α/β) + (1/4)β (- α/β)2 = - (1/4) α2 /β .

(P6.2.7)

Then, ∆cp = (∂F/ ∂T) = (1/2)(T 0 - T) / β(ε0 C) 2 , and

(P6.2.8)

cp = cp0 + ∆cp = cp0 + (1/2)(T 0 - T) / β(ε0 C) 2.

(P6.2.9)

Fro m the above relations, we can calculate the figures of merit: p = - (∂P S/∂T) = (1/2)(βε0 C) -1/2(T 0 - T)-1/2,

(P6.2.10)

p/cp = (1/2)(βε0 C)-1/2(T0 - T) -1/2 /[c p0 + (1/2)(T 0 - T) / β(ε0 C) 2 ] , (P6.2.11) p/cp ε = β -1/2(ε0 C) -3/2(T 0 - T)1/2 /[c p0 + (1/2)(T 0 - T) / β(ε0 C) 2 ] . (P6.2.12) Refer to Chapter Problem 6.1 for the first-order phase transition. ___________________________________________________________________ Improvement of the characteristics has been attempted by using composites of pyroceramics and polymers.4) In addition to the primary pyroelectric effect, a secondary effect is superimposed. The stress due to the thermal expansion α difference between the ceramic and polymer generates electric charge through the piezoelectric effect. Texas Instruments used a bias voltage on a pyroelectric (Ba,Sr)TiO3 ceramic during detection, and reported a remarkable enhancement of the figure of merit p/cp ε.5) Figure 6.5 shows the figure of merit change with temperature and bias field. Note that the bias field stabilizes the temperature characteristics significantly.

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Chapter 6

p / c pε

Bias = 1 kV/cm

800

2 kV/cm

600

200

3 kV/cm 4 kV/cm

400

100

200 18

p / c pε

300

20

22

Temperature (oC) (a)

24

0

0

5

10

Bias Field (kV/cm) (b)

Fig. 6.5 Figure of merit (p/cp ε) change with temperature (a) and bias field (b) for the Ba 0.67Sr0.33TiO3 -based ceramic. The poling voltage is the same as the biasing voltage. (a) Note that the bias field stabilizes the temperature characteristics significantly. (b) Maximum black body (490o C) response of a 50 µm thick sample of BST at a chopper frequency of 40 Hz.

6.2 TEMPERATURE/INFRARED LIGHT SENSORS

Fig. 6.6 A polymer-based (PVDF) pyroelectric infrared sensor.

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139

Fig. 6.7 Swing-type pyroelectric temperature sensor.

Figure 6.6 shows a typical structure for a polymer pyroelectric infrared sensor. In practical usage, a pyrosensor requires an infrared light (thermal ray) chopper, because the electrical signal can be detected only at the transient stage of light illumination or shut off. An electromagnetic motor is conventionally used as a light-chopper mechanism, but recently a piezoelectric bimorph chopper has been developed by Kuwano et al.,6) which allows for miniaturization of the pyrosensors (Fig. 6.7).

6.3 INFRARED IMAGE SENSORS In Fig. 6.8 the visualization of a thermal-distribution image is exemplified by a pyro-vidicon tube.7) The light emitted from an object is filtered with a germanium lens producing an infrared beam which is focused onto the pyroelectric target through an optical chopper. The temperature distribution of the object is represented on the target as a voltage distribution. This is monitored from the back surface of the target by electron-beam scanning using a conventional TV tube. One of the disadvantages of the pyro-vidicon is the degradation of the image over a long period of usage due to thermal diffusion on the target. Pedder et al. proposed a segmented target design to solve the diffusion problem.8) Figure 6.9 shows the microscopic structure of a D-TGS [deuterated triglycine sulphate, (ND2 CD 2COOD)3 D 2SO 4] target, and Fig. 6.10 is an example of a picture taken in darkness.

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Chapter 6

Fig. 6.8 Structure of a pyro-vidicon tube (a) and its equivalent circuit (b).

Fig. 6.9 Infrared image target with divided fine segments (19 µm width, 16 µm depth, 25 µm pitch).

Pyroelectric Devices

Fig. 6.10 Images taken by a pyro-vidicon on a dark night.

141

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Chapter 6

CHAPTER ESSENTIALS_________________________________ 1.

Merits of pyrosensors compared to other infrared-sensor materials such as semiconductors: a) wide range of response frequency, b) use at room temperature, c) quick response in comparison with other temperature sensors, d) high quality (optical-grade homogeneity, etc.) materials for the pyrosensors is unnecessary.

2.

Figures of merit for pyroelectric materials: ______________________________________________________________

Figure of Merit Application ________________________________________________________ p/cp low impedance amplifier p/(c p ε) p/(c p αε) p/cp (ε tan δ)1/2

high impedance amplifier thermal imaging device (vidicon)

high impedance amplifier when the pyroelectric element is the main noise source ________________________________________________________ p: pyroelectric coefficient; cp : specific heat; ε: relative permittivity; α: thermal diffusivity 3.

Thick film structure is essential for quick responsivity, and a light-chopper mechanism (e.g., piezoelectric bimorphs) is the key to miniaturization. ___________________________________________________________________

CHAPTER PROBLEMS 6.1

Assuming the first-order phase transition for the Landau free energy, calculate the temperature dependence of the figures of merit for a pyroelectric detector: p, p/cp and p/cp ε.

6.2

There is a PLZT (6/80/20) ceramic disk with 1 cm2 in area and 100 µm in thickness electrically poled along the thickness with tranparent electrodes. When the sample is illuminated with a laser light (power: 10 mW/cm2 ) for 0.1 second, calculate the following values: (a) the temperature rise of the sample, (b) the charge generated on the surface transparent electrode, and (c) the open-circuit voltage generated.

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Assume that all the light energy is absorbed by the sample, and that no heat loss nor electric loss is taken into account. Refer to Table 6.2 for the necessary data. Hint Total heat energy: 10 (mW/cm2 ) x 1 (cm2 ) x 0.1 (s) = 1 (mJ) Sample volume v: 1 (cm2) x 0.01 (cm) = 0.01 (cm3) Temperature rise ∆T: 1 (mJ) / [2.57 (J/cm3K) x 0.01 (cm3 )] = 0.039 (K) 6.3

Consider three materials: sharp phase transition, diffuse phase transition and successive phase transition materials (a, b and c in the figure) with the spontaneous polarization vs. temperature relations as illustrated in the following figures. Discuss the merits and demerits of each from a pyrodetector application viewpoint with respect to the following: (1) the magnitude of p, (2) the relative permittivity, (3) temperature stability and (4) aging.

(a) Sharp phase transition

(b) Diffuse phase transition

(c) Successive phase transition

RT

Temperature

REFERENCES 1) 2) 3)

J. M. Herbert: Ferroelectric Transducers and Sensors, p.267, Gordon & Breach, New York (1982). S. G. Porter: Pyroelectricity and Its Use in Infrared Detectors, Plessey Optoelectronics and Microwave Ltd., Towcester, NN12 7JN, UK (1980). M. E. Lines and A. M. Glass: Principles and Applications of Ferroelectrics and Related Materials, Clarendon Press, Oxford (1977).

144 4) 5) 6) 7) 8)

Chapter 6 A. S. Bhalla, R. E. Newnham, L. E. Cross, W. A. Schulze, J. P. Dougherty and W. A. Smith: Ferroelectrics 33, 139 (1981). B. M. Kulwicki, A. Amin, H. R. Beratan and C. M. Hanson: Proc. Int'l Symp. Appl. Ferroelectrics, SC, IEEE, p.1 (1992). K. Shibata, K. Takeuchi, T. Tanaka, S. Yokoo, S. Nakano and Y. Kuwano: Jpn. J. Appl. Phys. 24, Suppl. 24-3, 181 (1985). R. G. F. Taylor and H. A. H. Boot: Contemporary Phys. 14, 55 (1973). D. J. Warner, D. J. Pedder, I. S. Moody and J. Burrage: Ferroelectrics 33, 249 (1981).