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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5118–5125
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Dielectric behavior of CaCu3Ti4O12 ceramics in the terahertz range

Liang Wu, Furi Ling, Ting Liu, Jinsong Liu, Yebin Xu, and Jianquan Yao  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 5118-5125 (2011)
http://dx.doi.org/10.1364/OE.19.005118


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Abstract

The dielectric properties of 1050 °C/12h sintered CaCu3Ti4O12 (CCTO) ceramics have been investigated by using terahertz time domain spectroscopy in the frequency range of 0.2-1.6 THz at room temperature. When applying an external optical field, an obvious variation of dielectric constant was observed and reached up to 7%. However, the dielectric loss does not change appreciably. From the results, we found the change of refractive index has a linear relationship on scale with the applied light intensity. These findings were attributed to the change of spontaneous polarization in the ceramic caused by the excited free carriers.

© 2011 OSA

1. Introduction

Recently, CaCu3Ti4O12 (CCTO), a complex cubic perovskite material (space group Im3), has drawn the attention of many researchers because of its colossal permittivity and remarkable dielectric properties [1

1. M. A. Subramanian, L. Dong, N. Duan, B. A. Reisner, and A. W. Sleight, “High dielectric constant in ACu3Ti4O12 and ACu3Ti3FeO12 phases,” J. Solid State Chem. 151(2), 323–325 (2000). [CrossRef]

]. The compound shows giant dielectric constant in the order of 105 at room temperature and is weakly temperature dependent between dc and MHz. With decreasing the temperature, a Debye-like relaxation exists in the dielectric constant accompanied with a steplike decrease. The temperature at which the steplike decrease in dielectric constant takes place is found to be strongly depends on the measuring frequency and follows an Arrhenius behavior. High dielectric constant is generally associated with intrinsic ferroelectric or relaxor ferroelectric properties [2

2. Y. Liu, R. L. Withers, and X. Y. Wei, “Structurally frustrated relaxor ferroelectric behavior in CaCu3Ti4O12,” Phys. Rev. B 72(13), 134104 (2005). [CrossRef]

]. From the measurements of high-resolution x-ray, neutron powder diffraction, and Raman phonon, however, no evidence of any structural phase transition has been found in CCTO.

A huge amount of work has been carried out in an attempt to understand the origin of the dielectric properties of CCTO [2

2. Y. Liu, R. L. Withers, and X. Y. Wei, “Structurally frustrated relaxor ferroelectric behavior in CaCu3Ti4O12,” Phys. Rev. B 72(13), 134104 (2005). [CrossRef]

10

10. L. Fang, M. Shen, F. Zheng, Z. Li, and J. Yang, “Dielectric responses and multirelaxation behaviors of pure and doped CaCu3Ti4O12 ceramics,” J. Appl. Phys. 104(6), 064110 (2008). [CrossRef]

]. Both intrinsic [2

2. Y. Liu, R. L. Withers, and X. Y. Wei, “Structurally frustrated relaxor ferroelectric behavior in CaCu3Ti4O12,” Phys. Rev. B 72(13), 134104 (2005). [CrossRef]

5

5. Y. Zhu, J. C. Zheng, L. Wu, A. I. Frenkel, J. Hanson, P. Northrup, and W. Ku, “Nanoscale disorder in CaCu3Ti4O12: a new route to the enhanced dielectric response,” Phys. Rev. Lett. 99(3), 037602 (2007). [CrossRef] [PubMed]

] as well as extrinsic mechanisms have been proposed. With the help of first principles calculation [6

6. L. X. He, J. B. Neaton, M. H. Cohen, D. Vanderbilt, and C. Homes, “First-principles study of the structure and lattice dielectric response of CaCu3Ti4O12,” Phys. Rev. B 65(21), 214112 (2002). [CrossRef]

], it is gradually realized that the giant dielectric constant should originate from extrinsic effects. Among the extrinsic effects, an internal barrier layer capacitance (IBLC) mechanism is widely accepted, which is strongly supported by impedance spectroscopic (IS) results [7

7. D. C. Sinclair, T. B. Adams, F. D. Morrison, and A. R. West, “CaCu3Ti4O12: one-step internal barrier layer capacitor,” Appl. Phys. Lett. 80(12), 2153–2155 (2002). [CrossRef]

,8

8. T. B. Adams, D. C. Sinclair, and A. R. West, “Giant barrier layer capacitance effects in CaCu3Ti4O12 ceramics,” Adv. Mater. (Deerfield Beach Fla.) 14(18), 1321–1323 (2002). [CrossRef]

], as well as by the dependence of measured dielectric properties upon processing conditions and grain size [9

9. A. R. West, T. B. Adams, F. D. Morrison, and D. C. Sinclair, “Novel high capacitance materials: BaTiO3: La and CaCu3Ti4O12,” J. Eur. Ceram. Soc. 24(6), 1439–1448 (2004). [CrossRef]

]. The measurement of impedance spectroscopy also shows that the compound when prepared in air at temperature greater than 1000°C would consist of semiconducting grains and insulating grain boundaries [1

1. M. A. Subramanian, L. Dong, N. Duan, B. A. Reisner, and A. W. Sleight, “High dielectric constant in ACu3Ti4O12 and ACu3Ti3FeO12 phases,” J. Solid State Chem. 151(2), 323–325 (2000). [CrossRef]

,2

2. Y. Liu, R. L. Withers, and X. Y. Wei, “Structurally frustrated relaxor ferroelectric behavior in CaCu3Ti4O12,” Phys. Rev. B 72(13), 134104 (2005). [CrossRef]

]. Fang et al. reported a dielectric relaxation of CCTO at room temperature with an activation energy of 390.3meV, which was attributed to the MW-type relaxation associated with grain boundaries [10

10. L. Fang, M. Shen, F. Zheng, Z. Li, and J. Yang, “Dielectric responses and multirelaxation behaviors of pure and doped CaCu3Ti4O12 ceramics,” J. Appl. Phys. 104(6), 064110 (2008). [CrossRef]

].

In view of the above works, most observations have been carried out at low frequency range (<1MHz). The dielectric properties of CCTO in THz frequency range, however, have rarely been reported. For practical applications, it is necessary for the permittivity to be modulated over as wide a range as possible around room temperature. In this letter, we report the THz spectroscopy of pure CCTO ceramics, as well as the variation of its dielectric properties under an external optical field.

2. Experiment

The polycrystalline CCTO ceramic samples were prepared via a standard solid state reaction by mixing appropriate amount of high purity CaCO3, TiO2, and CuO. The raw materials were thoroughly mixed in an acetone medium and followed by calcinations at 1050 °C for 12h. The X-ray diffraction using Cu Kα radiation showed that the powders were single phase. The polycrystalline powders were then pressed into pellets of 10mm diameter and 1mm thickness. Finally, the samples were sintered in air at 1020 °C for 3h.

We use a terahertz time domain spectroscopy (THz-TDS) [11

11. A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]

] to measure the transmission spectra and dielectric constant of the samples at room temperature, as shown in Fig. 1
Fig. 1 The installation diagram of TDS. A green laser was obliquely incident upon the surface of the sample at an angle of 45° with the polar axis.
. In the THz-TDS system, a model-locked Ti: sapphire femtosecond laser beam (center wavelength of 800 nm, repetition 80 MHz) was divided into two beams via a beam splitter. The pump beam was focused on a GaAs photoconductive antenna in a 20V DC bias for the generation of THz waves, and the detecting beam was focused into a GaAs crystal for the detection of the THz wave by electro-optic sampling (EO sampling). Two polyethylene lenses were used to collimate and focus the emitted THz radiation onto the sample. The transmitted THz wave was collected and focused on the GaAs crystal with two polyethylene lenses. The detectable spectral range was from 0.2 to 1.6 THz (6.6-53 cm−1) with a sensitivity of S/N 1000 in the electric field amplitude. The time resolution for the THz measurement was 66.6 fs, and the spot size was 5mm diameter. In order to get the transmission spectra, the samples were rubbed to 250 μm of thickness and polished before the measurement. An all-solid-state green laser (center wavelength of 532 nm) was employed in the experiment to provide an external optical field. The light was obliquely incident upon the surface of the samples at an angle of 45° with the polar axis, and the spot size was 8mm diameter.

3. Results and discussion

The time domain waveforms were obtained by experiment, as shown in Fig. 2
Fig. 2 (a) Time domain transmission waveform of CCTO ceramics and (b) its time shift under different external optical fields at room temperature.
. The time lag between reference (air) and the sample is around 6 ps, as visible in Fig. 2(a). By applying an external optical field, a time shift could be observed in the time domain. For example, the transmission waveform shifted about 0.25 ps when the light intensity was 750 mW/cm2, compared to that without light excitation, as shown in Fig. 2(b).

Through a Fourier transform, we got the transmission spectra and the intrinsic phase shift of the samples. Figure 3
Fig. 3 Transmission spectra of CCTO ceramics under different external optical fields at room temperature.
shows the transmission spectra of CCTO ceramics under different external optical fields at room temperature. The curve is roughly smooth except a narrow absorption line at 1.1 THz, which is caused by the absorption of vapor. The complex refractive index N*(f) and permittivity ε*(f) were calculated from the THz transmission spectra. Figure 4(a)
Fig. 4 Frequency dependence of (a) real part and (b) imaginary part of complex dielectric constant of CCTO ceramics with different external optical fields at room temperature.
shows the frequency dependence of the real part of dielectric constant ε'(f) and its variation under different external optical fields of CCTO (The oscillation in the low frequency was supposed to be the influence of noises and the absorption of vapor). In the frequency range of 0.6-1.6 THz, CCTO does not show a giant dielectric constant, the magnitude is about 65-75. (This dielectric constant corresponds to a sample thickness of ~210 to 225 microns. The errors are supposed to be induced by the thinning process for the sample). The measured permittivity was found to be tunable by up to 7% via the application of an external optical field, and the dielectric constant nonlinearly decreases with increasing the power of green laser. The measured dielectric constants of CCTO versus light intensity at 0.8 THz and 1.0 THz are shown in Fig. 5
Fig. 5 Light intensity dependence of dielectric constant of CCTO at (a) 0.8 THz and (b) 1.0 THz of CCTO. The data points are our measured values, and the solid lines are the fit by using Eq. (1).
, which fits well with the following empirical expression proposed by Johnson [12

12. K. M. Johnson, “Variation of dielectric constant with voltage in ferroelectrics and its application to parametric devices,” J. Appl. Phys. 33(9), 2826–2831 (1962). [CrossRef]

]:
ε'(I)ε'0=1(1+αε'03I)1/3
(1)
where ε’ 0 and ε’(I) are the dielectric constants under zero optical field and under the applied field, respectively, and α is the anharmonic coefficient. The anharmonic coefficient is assumed to be an order parameter of the anharmonic interactions, and we can fit the profile well using α = 1.198 × 10−6 at 0.8 THz and α = 1.017 × 10−6 at 1.0 THz, respectively. The fitting results using Eq. (1) are shown as solid lines in Fig. 5.

In contrast, Fig. 4(b) demonstrates that the imaginary part of dielectric constant do not show obvious difference, indicating that the dielectric loss do not change appreciably with external optical field. This may be attributed to the fact that two loss mechanisms are responsible for the dielectric loss under external field: a conduction loss tanδR and an intrinsic loss tanδC [12

12. K. M. Johnson, “Variation of dielectric constant with voltage in ferroelectrics and its application to parametric devices,” J. Appl. Phys. 33(9), 2826–2831 (1962). [CrossRef]

,13

13. Y. C. Chen, L. Wu, Y. P. Chou, and Y. T. Tsai, “Curve-fitting of direct-current field dependence of dielectric constant and loss factor of Al2O3-doped barium strontium titanate,” Mater. Sci. Eng. B 76(2), 95–100 (2000). [CrossRef]

]. The intrinsic loss factor was reduced when applying an external optical field, while the conduction loss increased with the optical field strength. Since the influence of the optical field on the loss factor of the specimens is minor, as shown in Fig. 4(b), it indicates that the effect of the intrinsic loss counteracts the effect of conduction effect.

In order to illustrate the microscopic process in CCTO clearly, it is worthwhile to study the variation of its refractive index. Figure 6
Fig. 6 Light intensity dependence of variation of refractive index at (a) 0.8 THz and (b) 1.0 THz of CCTO. The data points are our measured values, and the solid lines are the fit by using Eq. (2).
shows the modulation of refractive index as a function of the applied light intensity and its linear fit. The variation of refractive index |Δn| is found linearly proportional to the intensity of applied light. The results could be described by using a relationship proposed by Johnston and Chen [14

14. W. D. Johnston, “Optical index damage in LiNbO3 and other pyroelectric insulators,” J. Appl. Phys. 41(8), 3279–3285 (1970). [CrossRef]

,15

15. F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40(8), 3389–3396 (1969). [CrossRef]

],
Δn=12(n03γ13ne3γ33)ΔP0εEI
(2)
where no and ne are the refractive index of the ordinary light and extraordinary light, respectively, γij is the linear optoelectronic coefficient, ΔP0 is the variation of the spontaneous polarization, E is the internal space charge field, and I is the applied light intensity. This result indicates that the change of the refractive index dispersion of CCTO may be attributed to the change of spontaneous polarization in the ceramic caused by the excited free carriers.

The micro mechanisms behind the observed effect here are discussed as follows: (1) CCTO ceramics sintered at high temperature are likely to have both Ti3+ and Ti4+ ions, which is confirmed by X-ray photoemission spectroscopy data [16

16. L. Zhang and Z. J. Tang, “Polaron relaxation and variable-range-hopping conductivity in the giant-dielectric-constant material CaCu3Ti4O12,” Phys. Rev. B 70(17), 174306 (2004). [CrossRef]

]. Titanium is a deep centre, and thermal excitations are negligible here. When applying an external optical field, there could be an exchange of electrons between Ti3+ and Ti4+ ions. The Ti-3d electrons in Ti3+ ions can hop to the conduction band, they migrate in a preferred direction and then are captured by the trap level of Ti4+. The dominant charge driving force is supposed to be the photovoltaic effect. Drift and diffusion could also have contribution to the movement of the electrons. The migration process would lead to a redistribution of Ti3+ and Ti4+ ions, which change the macroscopic spontaneous polarization of the samples because the centers of Ti3+ and Ti4+ do not coincide in the unit cell, and the ionic radius of Ti3+ (0.67Å) is larger than that of Ti4+ (0.605Å) [17

17. B. Shri Prakash and K. B. R. Varma, “Ferroelectriclike and pyroelectric behavior of CaCu3Ti4O12 ceramics,” Appl. Phys. Lett. 90(8), 082903 (2007). [CrossRef]

]. Moreover, the oxidation of Cu1+ to Cu2+ ions could have the same effect, which does an additional contribution to the change of the spontaneous polarization, leading to the corresponding variation of refractive index. (2) It should be mentioned that a shielding mechanism could also have a significant contribution to the change of spontaneous polarization. The shielding effect to the spontaneous polarization originates from the intrinsic property of the crystal, which is implemented by the internal electronics and holes. When applying an external optical field, the redistribution of carriers has an additional contribution to the shielding effect, thus change some properties of CCTO such as the domain structure, switching mechanism and coercive field. The space displacement of carriers leads to an internal space charge field, shielding the macroscopic spontaneous polarization of CCTO. The internal field caused the variation of refractive index via a linear electro-optic effect [15

15. F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40(8), 3389–3396 (1969). [CrossRef]

].

In most conditions, however, both direct influence to the spontaneous polarization caused by the oxidation of ions and the shielding effect induced by photo-carriers play the role in the dielectric response of the compounds. Two mechanisms complement with each other, and it is difficult to identify them experimentally.

4. Conclusion

In summary, we have investigated the frequency dependence of dielectric spectra of polycrystalline CaCu3Ti4O12 at room temperature. An obvious variation of refractive index was demonstrated in CCTO with different level of external optical fields. This property originates from the direct influence to spontaneous polarization caused by photo-induced carriers apart from their shielding effect which leads to an internal space charge field. Thus it is presumed that these two mechanisms would complement with each other, resulting in the observed photo-ferroelectric behaviors of CCTO.

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 10974063, the Research Foundation of Wuhan National Laboratory under Grant No. P080008, and the National “973” Project under Grant No. 2007CB310403.

References and links

1.

M. A. Subramanian, L. Dong, N. Duan, B. A. Reisner, and A. W. Sleight, “High dielectric constant in ACu3Ti4O12 and ACu3Ti3FeO12 phases,” J. Solid State Chem. 151(2), 323–325 (2000). [CrossRef]

2.

Y. Liu, R. L. Withers, and X. Y. Wei, “Structurally frustrated relaxor ferroelectric behavior in CaCu3Ti4O12,” Phys. Rev. B 72(13), 134104 (2005). [CrossRef]

3.

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001). [CrossRef] [PubMed]

4.

S. Ke, H. Huang, and H. Fan, “Relaxor behavior in CaCu3Ti4O12 ceramics,” Appl. Phys. Lett. 89(18), 182904 (2006). [CrossRef]

5.

Y. Zhu, J. C. Zheng, L. Wu, A. I. Frenkel, J. Hanson, P. Northrup, and W. Ku, “Nanoscale disorder in CaCu3Ti4O12: a new route to the enhanced dielectric response,” Phys. Rev. Lett. 99(3), 037602 (2007). [CrossRef] [PubMed]

6.

L. X. He, J. B. Neaton, M. H. Cohen, D. Vanderbilt, and C. Homes, “First-principles study of the structure and lattice dielectric response of CaCu3Ti4O12,” Phys. Rev. B 65(21), 214112 (2002). [CrossRef]

7.

D. C. Sinclair, T. B. Adams, F. D. Morrison, and A. R. West, “CaCu3Ti4O12: one-step internal barrier layer capacitor,” Appl. Phys. Lett. 80(12), 2153–2155 (2002). [CrossRef]

8.

T. B. Adams, D. C. Sinclair, and A. R. West, “Giant barrier layer capacitance effects in CaCu3Ti4O12 ceramics,” Adv. Mater. (Deerfield Beach Fla.) 14(18), 1321–1323 (2002). [CrossRef]

9.

A. R. West, T. B. Adams, F. D. Morrison, and D. C. Sinclair, “Novel high capacitance materials: BaTiO3: La and CaCu3Ti4O12,” J. Eur. Ceram. Soc. 24(6), 1439–1448 (2004). [CrossRef]

10.

L. Fang, M. Shen, F. Zheng, Z. Li, and J. Yang, “Dielectric responses and multirelaxation behaviors of pure and doped CaCu3Ti4O12 ceramics,” J. Appl. Phys. 104(6), 064110 (2008). [CrossRef]

11.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]

12.

K. M. Johnson, “Variation of dielectric constant with voltage in ferroelectrics and its application to parametric devices,” J. Appl. Phys. 33(9), 2826–2831 (1962). [CrossRef]

13.

Y. C. Chen, L. Wu, Y. P. Chou, and Y. T. Tsai, “Curve-fitting of direct-current field dependence of dielectric constant and loss factor of Al2O3-doped barium strontium titanate,” Mater. Sci. Eng. B 76(2), 95–100 (2000). [CrossRef]

14.

W. D. Johnston, “Optical index damage in LiNbO3 and other pyroelectric insulators,” J. Appl. Phys. 41(8), 3279–3285 (1970). [CrossRef]

15.

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40(8), 3389–3396 (1969). [CrossRef]

16.

L. Zhang and Z. J. Tang, “Polaron relaxation and variable-range-hopping conductivity in the giant-dielectric-constant material CaCu3Ti4O12,” Phys. Rev. B 70(17), 174306 (2004). [CrossRef]

17.

B. Shri Prakash and K. B. R. Varma, “Ferroelectriclike and pyroelectric behavior of CaCu3Ti4O12 ceramics,” Appl. Phys. Lett. 90(8), 082903 (2007). [CrossRef]

OCIS Codes
(130.0250) Integrated optics : Optoelectronics
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Integrated Optics

History
Original Manuscript: January 19, 2011
Revised Manuscript: February 17, 2011
Manuscript Accepted: February 17, 2011
Published: March 2, 2011

Citation
Liang Wu, Furi Ling, Ting Liu, Jinsong Liu, Yebin Xu, and Jianquan Yao, "Dielectric behavior of CaCu3Ti4O12 ceramics in the terahertz range," Opt. Express 19, 5118-5125 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-5118


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References

  1. M. A. Subramanian, L. Dong, N. Duan, B. A. Reisner, and A. W. Sleight, “High dielectric constant in ACu3Ti4O12 and ACu3Ti3FeO12 phases,” J. Solid State Chem. 151(2), 323–325 (2000). [CrossRef]
  2. Y. Liu, R. L. Withers, and X. Y. Wei, “Structurally frustrated relaxor ferroelectric behavior in CaCu3Ti4O12,” Phys. Rev. B 72(13), 134104 (2005). [CrossRef]
  3. C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001). [CrossRef] [PubMed]
  4. S. Ke, H. Huang, and H. Fan, “Relaxor behavior in CaCu3Ti4O12 ceramics,” Appl. Phys. Lett. 89(18), 182904 (2006). [CrossRef]
  5. Y. Zhu, J. C. Zheng, L. Wu, A. I. Frenkel, J. Hanson, P. Northrup, and W. Ku, “Nanoscale disorder in CaCu3Ti4O12: a new route to the enhanced dielectric response,” Phys. Rev. Lett. 99(3), 037602 (2007). [CrossRef] [PubMed]
  6. L. X. He, J. B. Neaton, M. H. Cohen, D. Vanderbilt, and C. Homes, “First-principles study of the structure and lattice dielectric response of CaCu3Ti4O12,” Phys. Rev. B 65(21), 214112 (2002). [CrossRef]
  7. D. C. Sinclair, T. B. Adams, F. D. Morrison, and A. R. West, “CaCu3Ti4O12: one-step internal barrier layer capacitor,” Appl. Phys. Lett. 80(12), 2153–2155 (2002). [CrossRef]
  8. T. B. Adams, D. C. Sinclair, and A. R. West, “Giant barrier layer capacitance effects in CaCu3Ti4O12 ceramics,” Adv. Mater. (Deerfield Beach Fla.) 14(18), 1321–1323 (2002). [CrossRef]
  9. A. R. West, T. B. Adams, F. D. Morrison, and D. C. Sinclair, “Novel high capacitance materials: BaTiO3: La and CaCu3Ti4O12,” J. Eur. Ceram. Soc. 24(6), 1439–1448 (2004). [CrossRef]
  10. L. Fang, M. Shen, F. Zheng, Z. Li, and J. Yang, “Dielectric responses and multirelaxation behaviors of pure and doped CaCu3Ti4O12 ceramics,” J. Appl. Phys. 104(6), 064110 (2008). [CrossRef]
  11. A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69(16), 2321–2323 (1996). [CrossRef]
  12. K. M. Johnson, “Variation of dielectric constant with voltage in ferroelectrics and its application to parametric devices,” J. Appl. Phys. 33(9), 2826–2831 (1962). [CrossRef]
  13. Y. C. Chen, L. Wu, Y. P. Chou, and Y. T. Tsai, “Curve-fitting of direct-current field dependence of dielectric constant and loss factor of Al2O3-doped barium strontium titanate,” Mater. Sci. Eng. B 76(2), 95–100 (2000). [CrossRef]
  14. W. D. Johnston, “Optical index damage in LiNbO3 and other pyroelectric insulators,” J. Appl. Phys. 41(8), 3279–3285 (1970). [CrossRef]
  15. F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40(8), 3389–3396 (1969). [CrossRef]
  16. L. Zhang and Z. J. Tang, “Polaron relaxation and variable-range-hopping conductivity in the giant-dielectric-constant material CaCu3Ti4O12,” Phys. Rev. B 70(17), 174306 (2004). [CrossRef]
  17. B. Shri Prakash and K. B. R. Varma, “Ferroelectriclike and pyroelectric behavior of CaCu3Ti4O12 ceramics,” Appl. Phys. Lett. 90(8), 082903 (2007). [CrossRef]

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