#### Read Frequency and Temperature Dependence of Dielectric Constant of Epoxy/BaTiO3 Composite Embedded Capacitor Films (ECFs) for Organic Substrate text version

Frequency and Temperature Dependence of Dielectric Constant of Epoxy/BaTiO3 Composite Embedded Capacitor Films (ECFs) for Organic Substrate

Jin-Gul Hyun, Sangyong Lee, Sung-Dong Cho and Kyung-Wook Paik Department of Materials Science and Engineering Korea Advanced Institute of Science and Technology 373-1, Guseong-dong, Yuseoung-gu, Daejeon, 305-701, Republic of Korea e-mail) [email protected] Phone) +82-42-869-3375 Fax) +82-42-869-3310 Abstract In this study, temperature dependence of capacitance, one of the most important properties of ECFs, was investigated. Temperature dependence of ECFs capacitance was determined by temperature dependence of dielectric constant and thickness, and among these, main factor was dielectric constant of ECFs. Dielectric constant of ECFs is determined by that of epoxy and BaTiO3 powders. Below 130oC, dielectric constant of ECFs increased as temperature increased, and was mainly affected by an epoxy matrix. However, above 130oC, the Curie temperature of BaTiO3, the increase rate of ECFs dielectric constant started decreasing, because BaTiO3 powder undergoes a phase transition from a tetragonal to a cubic structure and its dielectric constant decreases at 130oC. Dielectric constant of BaTiO3 powder was obtained from measured dielectric constants of ECF and applying the Lichtenecker logarithmic rule. Dielectric constants of ECFs at high frequency range (0.1~10GHz) were measured using a cavity resonance method. For both powders, dielectric constants in high frequency range were about 3/4 of the dielectric constants at 1 MHz. This difference is mainly due to the decrease of dielectric constant of epoxy matrix. For BaTiO3 ECFs, there was a dielectric relaxation at 5~9GHz presumably due to the polarization mode change of BaTiO3 powder. Keywords : embedded capacitor, polymer/ceramic composite, barium titanate Introduction Electronic systems are composed of many electronic components such as semiconductors and passive components like resistors (R), inductors (L), and capacitors (C). The passive components become of increasing interest, because the number of passives is steadily growing as the electronics products are progressing toward higher functionality. For example, the ratio of passive to active components in mobile cellular phone is over 20 [1, 2]. Currently these large numbers of passive components are surface-mounted as a discrete format, so they not only occupy large area of substrate but also lower electrical performance and reliability due to longer interconnection length and larger number of solder joints, respectively. To solve these problems, embedded passives technology, which incorporates passive components into multi-layer substrates, has been actively investigated. Among the various embedded passives, embedded capacitors call for special attention, as they are used in relatively large numbers for various functions such as signal de-coupling, switching noise suppression, filtering, and tuning. 0-7803-8906-9/05/$20.00 ©2005 IEEE Thin film capacitors formed by vacuum deposition techniques have an advantage of fairly high capacitance, while at the same time they have draw backs of high processing temperature and higher cost. However, polymer/ceramic composites, which combine processing flexibility of polymers and high dielectric constant of ceramics, are promising materials as embedded capacitor dielectrics, because they use lower-temperature and lowercost processes and have compatibility with flexible organic boards [3, 4]. Most polymer/ceramic capacitor films have been fabricated from a solution spin coating which has a major advantage of thinner films, and hence, higher capacitance. However, the major technical challenges faced in a spin coating method are two fold; first, there is a large waste of materials and second, film thickness control over a large area is not easy, which, in hence, results in non-uniform capacitor properties over a large area. In previous studies, we have introduced embedded capacitor films ECFs for organic substrate applications, and demonstrated that excellent embedded capacitors could be successfully fabricated on PCBs. Characteristics of the ECFs are flexibility, good film formation capability, long shelf life, stability at high temperature and frequency, and uniform thickness and dielectric constant over a large area. In this paper, temperature dependence of capacitance, which one of the most important properties of ECFs, and factors affects ECFs capacitance will be discussed. In addition, dielectric constants of ECFs with various powders contents at high frequency region will be discussed. Experiments A. ECFs Materials & formation process BaTiO3 was chosen as a ceramic powder because it is one of widely-used high dielectric constant powders. In this work, the BaTiO3 powders with various sizes (0.1µm, 0.3µm, and 0.97µm diameter) produced by a hydro-thermal synthesis were used. Phosphate ester was used as a dispersant agent, and 2-Butanone (MEK) and Toluene mixture was used as a solvent [5]. Specially formulated epoxy resin composed of a thermosetting epoxy and thermoplastic resins was used as a polymer matrix which has good flexibility, tackiness of uncured film, good adhesion strength, and high temperature stability after curing [6]. Dicyandiamide (DICY), a latent curing agent, was selected as a curing agent for longer shelf life [7]. BaTiO3 powders, dispersant, solvent, epoxy-resin, and curing agent were mixed, and then ECFs were continuously coated on a releasing film and dried using a comma roll 2005 Electronic Components and Technology Conference

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coater. After drying processes, ECFs were exposed in vacuum at 100oC to remove residual solvents [8]. B. Capacitor fabrication & characterization (1) Temperature dependence of ECFs ECFs were laminated on a PCB on which 18µm thick copper was plated for a bottom electrode. During lamination, temperature was elevated from room temperature at a heating rate of 10oC/min, and kept at 180oC for 20 min under an air pressure of 40~50psi. As a result, ECFs were completely cured during a lamination process. After lamination, 1.0µm thick and 0.126cm2 area copper cap electrodes were deposited on cured ECFs by a sputtering method [8]. a. Capacitance vs. temperature To investigate the relationship between temperature dependence of ECFs capacitance and powder loading, ECFs with 0~40vol% BaTiO3 powder contents were fabricated. At each sample, at 100 kHz frequency with 1oC/min heating rate on a heat block, and an interval of 10oC from 20 to 160oC, capacitance was measured using a LCR meter. The number of samples was 10 for each ECFs with various powder contents. b. ECF thickness vs. temperature For measuring thickness change (tECF) of ECFs, Si/ECF/Si structure samples were fabricated as shown in Fig. 1. Total thickness changes (ttotal) by thermal expansion were measured by the Thermo-mechanical Analyzer (TMA), and then the fraction of thickness changes of Si wafer (tsi)[13] was deducted to obtain tECF.

(2) High frequency measurement Principle of dielectric constant measurement by cavity resonance method was explained in detail in A. Namba's paper [9]. Consider a rectangular cavity resonator that is enclosed by six metal planes and is filled with dielectric material. If the height of the cavity is much less than a wave length, the distribution of electromagnetic fields is uniform in z direction. Therefore, a resonance frequency fmn can be calculated using (2), where m and n are cavitymode numbers, c is the speed of light, r is the dielectric constant (or relative permittivity) of the dielectric material in the cavity, and a and b are the length and width of the resonator, respectively.

f mn =

c

(2) Dimensions of samples evaluated for this study were a (=60mm) × b (=60mm) × h (=0.5mm). Three probing pads, #1, #2 and #4 were located on the samples as shown in Fig. 3. #1 was located at the center of the PCB sample, #2 was located at x=a/4, y=b/4, and #4 was located at x=a/8, y=b/8. At a cavity-mode resonance, reflection coefficient has a dip. The magnitude of resonance depends on the position of the observing point. This can be used to identify cavity-mode numbers. Reflection coefficient S11 was measured in order to calculate the dielectric constant with a HP 8510C network analyzer. This equipment can measure S-parameter from 100MHz to 10GHz. Equation (2) can be rewritten as following.

r

m n + 2a 2b

2

2

r =

t ECF = ttotal - 2 × t si Fig. 2 shows measured values of tSi.

(1)

c2 2 f mn

m 2 n 2 c 2 m 2 + n 2 + = 2 2 2a 2b f mn 4a

(3)

Substituting the resonance frequency fmn and mode numbers m, n into (3), the dielectric constant r was calculated.

a/4 a/2

a/4

4 2

Fig.1 Schematic diagram of Si/ECF/Si structure samples for measuring thickness changes

1

a

0.0003

Thermal exapansion (L/L0)

0.0002

a/2

3 5

0.0001

0.0000

a

-0.0001 20 40 60 80 100 120

o

Fig. 3 PCB size and the probing pads location.

140 160 180

Temperature ( C)

Fig. 2 Temperature vs. thickness changes of a Si wafer

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Results and Discussion A. Temperature dependence of ECF capacitance Generally, capacitance of capacitors can be expressed as

200

A A (4) = 0 k , (k = ) d t 0 ,C is capacitance, k is relative dielectric constant, 0 and are vacuum and dielectric material's permittivity, t and A are the thickness and area of a dielectric material. Based on this equation, relation between temperature dependence of capacitance, dielectric constant, and thickness can be expressed as C =

Capacitance (pF)

150

Epoxy 10vol% 20vol% 30vol% 40vol%

100

50

0

20

40

60

80

100

o

120

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Temperature ( C)

1 dC 1 dk t dt A (5) = + C dT k dT A dT t where 1 dC is defined as temperature coefficient of C dT capacitance (TCC), 1 dk is defined a temperature k dT dependence of dielectric constant (TCK), and t dt A represents dimensional changes during A dT t thermal expansion. Because thermal expansion coefficient of metal electrodes (~10-6/K) is much smaller than polymer composites (~10-4/K) and the dimension of metal electrode increases uniformly as the temperature increases for each sample, it is possible to assume that temperature dependence of electrode area A is negligible. So, temperature dependence of capacitance of ECFs is defined by

when ECF thickness. Therefore, temperature dependence of ECFs capacitance is determined by changes of dielectric constant and thickness of ECFs. Fig. 4(a) and 3(b) show temperature dependence of capacitance and thickness of ECFs. From these values, dielectric constant of ECFs was calculated, and then plotted in Fig. 4(c). As temperature increased, capacitance and dielectric constant of ECFs increased, and the increase rate above glass transition temperature (Tg) of epoxy matrix, about 90oC, was higher than those below Tg. Fig. 5 shows the effect of temperature dependence of dielectric constant and thickness change of ECFs on capacitance of the ECF containing 10vol% BaTiO3 powder. For example, at 150oC, ECFs dielectric constant and thickness increased about 57% and 5% respectively. Consequently, ECFs capacitance increased about 50%. Therefore, the main factor of temperature dependence of capacitance was determined mostly by dielectric constant of ECFs not by thickness increase by thermal expansion. (6) (TCC ) = (TCK ) - ( ECF ) is the thermal expansion coefficient of ECF

(a)

21.4 21.2 Epoxy 10vol% 20vol% 30vol% 40vol%

Thickness (µm)

21.0 20.8 20.6 20.4 20.2 20.0 40

60

80

100

120

o

140

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Temperature ( C)

(b)

40 35 Epoxy 10vol% 20vol% 30vol% 40vol%

Dielectric constant

30 25 20 15 10 5 20

40

60

80

100

o

120

140

160

Temperature ( C)

(c)

Fig.4 Temperature vs. (a) capacitance, (b) thickness, and (c) dielectric constant of ECFs (1) Effect of epoxy matrix Fig. 6 shows relative changes of capacitance, dielectric constant, and thickness of ECFs with various BaTiO3 powder contents. As temperature was elevated up to 130oC, ECFs capacitance and dielectric constant increased with almost the same rate of epoxy matrix. However, above 130oC, increase rates of ECFs capacitance and dielectric constant started decreasing, which is due to the phase transition of BaTiO3 powder at 130oC.[10] This will be discussed in detail at next section.

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70 60 50 Capacitance Dielectric constant Thickness

1.7

Relative dielectric constant

1.6 1.5 1.4 1.3 1.2 1.1 1.0

Changes (%)

40 30 20 10 0 20 40 60 80 100

o

Epoxy 10vol% 20vol% 30vol% 40vol%

120

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160

20

40

60

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100

o

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Temperature ( C)

Temperature ( C)

Fig.5 Effects of temperature dependence of dielectric constant and thickness changes of ECF on capacitance of the ECF containing 10vol% BaTiO3 powder content

(c)

Fig.6 Relative changes of (a) capacitance, (b) thickness, and (c) dielectric constant vs. temperature at various BaTiO3 powder contents Table 1 Epoxy contents vs. thickness changes of ECFs at 160oC Epoxy 10vol% 20vol% 30vol% 40vol% ECFs Vol% of 100 90 80 70 60 Epoxy Thickness 6.0 5.2 4.6 4.0 3.5 change at 160oC (%)

Table 1 shows the relation between total amount of epoxy and thickness changes of ECFs at 160oC. As shown in Figure 5(b) and Table 1, thickness changes ECFs was mostly dependent on total amount of epoxy rather than BaTiO3 powders.

1.7 1.6 Epoxy 10vol% 20vol% 30vol% 40vol%

Relative capacitance

1.5 1.4 1.3 1.2 1.1 1.0 20

Therefore, to improve characteristics of temperature dependence of ECFs capacitance, temperature dependence of epoxy matrix capacitance should be improved.

(2) Effect of BaTiO3 powders As shown in Fig. 6(c), the increase rates of dielectric constant of ECFs started decreasing above 130oC, probably due to the dielectric relaxation of BaTiO3. It is well-known that crystal structure of BaTiO3 changes from a tetragonal to a cubic at the Curie point near 130oC. As a result of the phase transition of BaTiO3 powder, dielectric constant decreases above the Curie point. However, it is not easy to measure dielectric constant of ceramic powders directly. Therefore, indirect method of anticipating the dielectric constants of BaTiO3 powders was adapted. By measuring the dielectric constants of ECFs and the Lichtenecker logarithmic rule, [10, 11] one can calculate the dielectric constant of BaTiO3 powders. In the case of multi-composite materials, general equation is defined by Lichtenecker logarithmic rule defines (7) log = vi log i

i

40

60

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100

o

120

140

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Temperature ( C)

(a)

0.08 0.07 0.06 Epoxy 10% 20% 30% 40%

Relative thickenss

0.05 0.04 0.03 0.02 0.01 0.00 -0.01 20 40

60

80

100

120

o

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Temperature ( C)

(b)

where i is number of components, which consist of the material, vi and i are volume fraction and relative permittivity of component i, respectively. In the case of ECFs, logarithmic rule can be induced as log ECF = vepoxy log epoxy + vBaTiO3 log BaTiO3 (8)

log k ECF = vepoxy log k epoxy + v BaTiO3 log k BaTiO3

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As a function of k BaTiO , 3 (10) k BaTiO3 = 10 Therefore, by measuring dielectric constant of ECFs ( k ECFs ) and pure epoxy ( k epoxy ), dielectric constant of BaTiO3 powders can be calculated. Fig. 7 shows the calculated dielectric constants of BaTiO3 powders using 20vol% BaTiO3 containing ECF. As shown in Fig. 7, dielectric constants of BaTiO3 powders reached the maximum value at 130oC, and then decreased during further heating.

280

1 (log k ECF -vepoxy log kepoxy ) vBaTiO3

32 30 28 26 24 22 20 18 Experiment Calc.

Dielectric constant

0

20

40

60

80

100

o

120

140

160

Temperature ( C)

Dielectric constants of BaTiO3

260

(c)

Fig.8 Measured and calculated values of ECFs with (a) 10vol%, (b) 30vol%, and (c) 40vol% BaTiO3 powders

240

220

200

180 20 40 60 80 100

o

120

140

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Temperature ( C)

Fig.7 Calculated dielectric constants of BaTiO3 powders using 20vol% BaTiO3 containing ECF

10.5 10.0 9.5 Experiment Calc.

Dielectric constant

9.0 8.5 8.0 7.5 7.0 6.5 6.0 0 20 40 60 80 100

o

Above the Curie transition temperature, the ferroelectric form of BaTiO3 has a cubic Perovskite type structure. Below the Curie temperature, the structure of BaTiO3 powder is transferred from a cubic to a tetragonal one. Therefore, dielectric constant of BaTiO3 decreases curing the phase transition. [12] To verify whether the calculation of dielectric constant of BaTiO3 powders was reasonable, calculated values, using data in Fig. 7, were compared with the measured values of other ECFs containing different BaTiO3 powder contents. As shown in Fig. 8, the calculated dielectric constants of ECFs using dielectric constants of BaTiO3 obtained by equation (10) are well fitted to measured dielectric constants of ECFs below 130oC.

B. Measurement of high frequency dielectric constant of ECFs Fig. 9 shows the measured reflection coefficient (S11) at locations #1, #2 and #4 in Fig. 3 for epoxy film without BT powder. Resonance mode numbers (m, n) for each resonance are indicated in the figure, the resonance mode Tmn indicates mode number (m. n). For example, the first resonance mode (1, 1) is TM11 and the second (2, 1) is TM21. For the TM11 mode, the resonance measured at location #1 in the center of the sample was stronger than at location #2 and #3. On the other hand, for the TM21 and TM22 mode, no resonance was observed at location #1. This is because probing position #1 is located at a point where the distribution of Ez is maximum for the TM11 mode and null for the TM21 and TM22 mode. In the same reason, the resonance measured at location #2 was stronger than at location #4 for the TM22, and there was no resonance at location #1 and #2 for the TM41. Comparing the magnitude of the reflection coefficients at location #1, #2 and #4, each resonance mode can be identified.

120

140

160

Temperature ( C)

(a)

22 21 20

Experiment Calc.

Dielectric constant

19 18 17 16 15 14 13 0 20 40 60 80 100

o

120

140

160

Temperature ( C)

(b)

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Table 2 Resonance frequency, mode number, and calculated dielectric constant of 20vol% BT ECF

1.00 (3,3) 0.98

(1/2, 1/2) (3/8, 3/8) (1/4, 1/4)

S11 (dB)

0.96 0.94 (2,1) 0.92 0.90 0.88 0.00E+000 (1,1) (3,1) 2.00E+009 4.00E+009 6.00E+009 8.00E+009 (2,2) (3,2) (4,3) (4,1)(4,2) (5,1) (5,2)

Frequency (Hz)

Fig. 9 Reflection coefficient (S11) measurement result: epoxy film without BT powder

Substituting the measured resonance frequency and the identified mode numbers into (3), relative permittivity of the dielectric material at each frequency is obtained. Table 2 shows values of resonance frequencies and the corresponding values of relative permittivity of 20vol% BT ECF. Relative permittivity calculated in this manner is plotted with frequency as shown in Fig. 10 and Fig. 11. Additional data points of the dielectric constant measured at 1MHz using a LCR meter is shown together in both figures. Fig. 10 shows the dielectric constant changes of the ECFs with 20vol% BaTiO3 powders of 0.1µm (B1), 0.3µm (B3) and 0.97µm (B5) diameter. Dielectric constants are maintained at constant values as frequency increases up to 9GHz. But at 9GHz abrupt change in dielectric constant which is called dielectric relaxation is shown for all the powders amounts. The relaxation is presumably due to changing of polarization mode of BaTiO3 powders with frequency, transferring from dipole polarization to ionic polarization region.

Fig. 10 Dielectric constant changes at various frequencies: BT powders 20vol% ECF

Fig. 11 shows dielectric constant changes of 0~40vol% B5 powder ECFs with frequency. The dielectric constant of the B5 40vol% ECF at 1MHz is 23, but the dielectric constant over 0.5GHz measured using a cavity resonance method is about 17. This dielectric constant reduction is also observed of an epoxy film. The dielectric constant of the epoxy is 4.3 at 1MHz but 3.2 over GHz. Effective dielectric constant of polymer/ceramic composite is proportional to the dielectric constant of polymer matrix. Therefore the dielectric constant reduction of ECFs between 1 MHz~0.5GHz is mainly due to the dielectric constant reduction of epoxy matrix. Above few GHz, dielectric constants abruptly decrease and dielectric relaxation occurs. These relaxation frequencies occur at lower frequency as BT powder loading increases due to more BaTiO3 powder effect in an epoxy matrix.

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Fig. 11 Dielectric constant changes at various frequencies: B5 powder 0~40vol% ECF Conclusions Temperature dependence of ECFs capacitance is determined by temperature changes of dielectric constant and thickness of ECFs. Among these, the main factor determining temperature dependence of the capacitance was not thickness changes but dielectric constants of ECFs. Below the Curie temperature of BaTiO3 powder at 130oC, capacitances and dielectric constants of ECFs increased almost the same rates of epoxy matrix. However, above 130oC, the increase rates of ECFs capacitance and dielectric constant started decreasing, because BaTiO3 powder undergoes a phase transition from a tetragonal to a cubic structure at 130oC. In addition, dielectric constant of BaTiO3 powder was obtained from the dielectric constants of ECFs and applying the Lichtenecker logarithmic rule, because it is difficult to measure dielectric constants of ceramic powders directly. From these results, reasonable dielectric constants of BaTiO3 powders were obtained. As a result, to improve temperature dependence of ECFs capacitane, temperature dependence of epoxy matrix capacitance must be improved. Dielectric constant of ECFs at high frequency range (0.1~10GHz) was measured using a cavity resonance method. Dielectric constants in this frequency ranges were about 3/4 of the dielectric constant at 1 MHz. This difference was presumably due to the decrease of the dielectric constant of epoxy matrix. At 5~9GHz, dielectric relaxation of BT powder was observed due to the change of polarization mode of BT powder. Acknowledgment This work was supported by Center of Electronic Packaging Materials (CEPM) of Korea Science and Engineering Foundation.

References [1] J. Rector, "Economic and Technical Viability of Integral Passives," in Proc. of 48th Electron. Comp. Technol, Conf., pp. 218 (1997) [2] J. Prymark, S. Bhattacharya, and K. W. Paik, "Fundamentals of Pasives: Discrete, Integrated, and Embedded," Chap. 11 in Fundamentals of Microsystems Packaging, ed. by R. R. Tummala, McGraw-Hill Book Company, New York (2001) [3] S. K. Bhattacharya and R. R. Tummala, "Next Generation Integral Passives: Materials, Processes, and Integration of Resistors and Capacitors on PWB substrates," J. Mater. Sci: Materials in Electronics, 11, pp. 253-268 (2000) [4] S. Ogitani, S. A. Bidstrup-Allen, and P.A. Khol, "Factors Influencing the Permittivity of Polymer/Ceramic Composite for Embedded Capacitors," IEEE Trans. on Advanced Packaging, 23, pp. 313-322 (2000) [5] K. Mikeska and W. R. Cannon, "Dispersant for Tape Casting Pure Barium Titanate," in Advances in Ceramics, Vol. 9, Forming of Ceramics, ed. by J. A. Mangels, The American Ceramic Society, pp. 164-183 (1984) [6] S. Asai, U. Saruta, M. Tobita, M. Takano, and Y. Miyashita, "Development of an anisotropic conductive adhesive film (ACAF) from epoxy resins," J. Appl. Polym. Sci., 56, pp. 769-777 (1995) [7] W.G. Potter, "Epoxide Resins," ILIFFE BOOKS, London (1970) [8] Kyung-Wook Paik, Sung-Dong Cho, Joo-Yeon Lee, and Jin-Gul Hyun, "Low Tolerance Epoxy/BaTiO3 Composite Embedded Capacitor Films (ECFs)," in Proc. of the 4th international Symposium on 2002, pp. 341-347 (2002) [9] A. Namba, O. Wada, Y. Toyota, Y. Fukumoto, Z. L. Wang, R. Koga, T. Miyashta, and T. Watanabe, "A simple method for measuring the relative permittivity of printed circuit board materials," IEEE Trans. Electromagn. Compat. , Vol. 43, pp. 515-519 (2001). [10] K. Mazur, "Polymer-Ferroelectric Ceramic Composites," Plast. Eng., vol. 28, 539-610 (1995) [11] C. J. Dias and D. K. Das-Gupta, "Inorganic ceramic/polymer ferroelectric composite electrets," IEEE Trans. Dielectr. Electr. Insul., vol. 3, pp. 706(1996) [12] J.M. Herbert, "Ceramic dielectrics and capacitors," Gordon and Breach Science Publishers, pp. 131-136 (1985) [13] S. Biernacki and M. Scheffler, "The influence of the isotropic composition on the thermal expansion of crystalline Si," J. Phys.: Condens. Matter 6, pp. 8794884, 1994

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