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Surface potential decay on triglycine sulfate crystal
ARTICLE IN PRESS
Journal of Electrostatics 63 (2005) 1017–1023 www.elsevier.com/locate/elstat
Surface potential decay on triglycine sulfate crystal M. D˛ebska Institute of Experimental Physics, University of Wroc!aw, Pl. M. Borna 9, 50-204 Wroc!aw, Poland Received 4 March 2004; received in revised form 8 July 2004; accepted 22 December 2004 Available online 26 January 2005
Abstract An electrostatic potential decay on the surface of triglycine sulfate crystal (TGS) was measured by the induction probe method. The dependence of the decay rate on relative humidity was found. The values of surface conductivity for TGS crystal under controlled conditions are given for the first time. r 2005 Elsevier B.V. All rights reserved. Keywords: Surface conduction; Charge neutralization; Ferroelectric; TGS crystal
1. Introduction New promising technological applications of ferroelectric thin films have caused increased interest in surface layer ferroelectrics. The surface of a ferroelectric material is unique among the surfaces of solid states; the electric charges caused by spontaneous polarization appear on it [1–4]. These charges can be screened by charges which are attracted from both inside and outside the sample to its surfaces [5]. Partial or complete screening is the most probable state of a ferroelectric surface in air [1,6]. Ferroelectric crystals are a special class of crystals that exhibit a spontaneous polarization over some range of temperature. This polarization can be reversed or Tel.: +48 71 37 59 362; fax: +48 71 32 87 365.
E-mail address: [email protected] (M. D˛ebska). 0304-3886/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2004.12.006
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reoriented by application of an external electric field. The coercive field is the electric field required for switching ferroelectric polarization. One of the most widely studied ferroelectric materials is triglycine sulfate (TGS) crystal [7]. TGS crystal undergoes a typical second-order phase transition at the Curie temperature TC (49 1C). The crystal symmetry is monoclinic. In the ferroelectric phase (below TC), a spontaneous polarization Ps arises. The spontaneous polarization vector is parallel to the crystallographic b-axis and perpendicular to the (0 1 0) cleavage plane. The crystal splits into antiparallel domains (i.e. regions with uniform polarization). TGS crystal belongs to the family of water-soluble ferroelectrics, thus it is hygroscopic in nature. However, the correlation between the humidity and the surface charge screening has not been understood until now. The surface resistance of TGS crystal is strongly dependent on humidity, but quantitative data have not been previously published. In this paper, the decay of the surface potential on TGS crystal and its dependence on the relative humidity is presented. The surface potential decay method was used to determine the surface conductivity of TGS crystal.
2. Experiment The electrostatic potential on TGS (0 1 0) cleavage surface was studied using the induction probe method [8]. The resolution of such a probe is typically 1.5 times the probe diameter [9], and in previously reported experiments was estimated as 45 mm. A block diagram of the experimental setup is shown in Fig. 1. Samples of about 1-mm thickness were prepared by cleaving the TGS crystal at ambient conditions (27 1C and 70% relative humidity). The sample was mounted with conducting silver paste on a grounded metal turntable of diameter 0.09 m. The top surface of the sample was charged over a time period of 20 s by contacting it with a metal foil electrode energized to a potential of 100 V. The applied electric field
Fig. 1. Schematic illustration of an experimental setup for charging and surface potential measurement. (Cpg is the input capacitance of the probe and amplifier, Cps the probe to surface capacitance, and Cs the capacitance of the sample to ground).
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(105 V/m) was greater than coercive field (5 104 V/m) for TGS at this temperature; hence the sample was monodomain. After charging the turntable was rotated at 1 rps under a non-contacting probe. In this way, the magnitude of the potential was monitored across the sample face along a line scan during each revolution of the turntable. The distribution of the surface potential (localized potential profile) was recorded along a line crossing the middle of the charged sample. After these measurements, the probe was calibrated in a separate experiment. The relation between the potential V induced on the probe and the surface potential Vs of the sample is the following [10]: V ¼ V s ð0 S=d 1 C pg Þ; where Cpg is the input capacitance of the probe and amplifier, S the area of the sample directly beneath the probe, and d1 the distance between the probe and the sample surface. The calibration factor S/Cpg was determined by replacing the TGS surface with a metal surface held at a known potential. The experiments were carried out in air at a constant temperature of 27 1C under relative humidities (RH) of 30, 43, 51, 56, 60 and 70%. The temperature and humidity in the testing chamber were kept at desired values by an air conditioner and were measured by thermocouple and hygrometer, respectively. At the beginning of the experiment, the humidity was 70%. The humidity was then reduced at a slow rate (no faster than 0.03%/min.). The sample was kept at constant humidity for 3 h in order to obtain equilibrium; the next measurements were then performed.
3. Results and discussion The potential measured over the entire surface of freshly cleaved TGS sample was equal to zero. This result suggests that since the humidity was high during cleaving, the sample charges induced on the surface were precisely neutralized at once after contact with ambient conditions. Such an effect is in agreement with the results of AFM experiments performed by Balakumar et al. [11]. The (0 1 0) surface reconstructs immediately if the humidity is high during cleavage of the crystal, a result of a strong dissolution of TGS crystal [2]. In order to study, the behavior of surface charges, the sample was charged. It was found that after charging under 60% and higher relative humidity, the surface potential was equal to zero. This result suggests that, for high humidity, the decay of the surface potential was too fast to be recorded in with experimental setup used or, alternatively, the surface charge was not present after charging under such environmental conditions. Under high humidity, the water vapor essentially modifies the crystal’s surface properties [12]. Specifically, the TGS crystal surface is dissolved by the water film. Dissolution of the topmost layers of the crystal occurs immediately after the cleavage of the sample. The surface charge is screened by the conductive liquid film formed on the TGS surface. It is known that after a reduction in humidity, the recrystallization process occurs [11,13]. Therefore, the humidity was reduced and the measurements were continued. The polarity of the surface potential at the point of contact with electrode was the same as the polarity of the electrode potential.
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The potential on the probe is a measure of the surface charge density in a given location. At time t, the charge density in the coordinate point x on the scan line is equal to [9] sðx; tÞ ¼
C pg C s V ðx; tÞ; S C ps
where C pg =S is the factor determined earlier, V(x,t) is the input potential of the probe, and C s ¼ 0 S=d is the capacitance of the sample of thickness d and dielectric permittivity e. The dielectric permittivity of TGS at 27 1C is about 800. Similarly, C ps ¼ 0 S=d 1 is the probe-surface capacitance, and d1 the separation between the probe and the sample surface. The geometric parameters were not changed in the sequence of measurements presented here, hence the ratio C pg C s =SC ps was constant. The surface charge density on the TGS sample was calculated. A surface charge density of the order of 1 104 C/m2 was determined when the surface potential was equal to 100 V. This suggests that the charge density on the surface after electrode charging was about two orders of magnitude lower than the surface charge density resulting from spontaneous polarization (2.8 102 C/m2) of TGS crystal at 27 1C. The P total surface charge measured along the line scan at time t is equal to Q (t) ¼ s(x, t), where summation is performed over all x [14]. The surface charge calculated from the first measurement following charging was used as a reference for subsequent charge normalization. In Fig. 2, the normalized maxima of charge density and total charge along the line scan, plotted against time for 43% and 56% RH, are shown. The decay rates of charge density and total charge are nearly the same under low humidity. The charge density decreases faster than the total charge under higher
Fig. 2. Decay of normalized maximum values of charge densities and total charges.
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humidity. This suggests the presence of lateral migration of surface charges under these conditions. Such motion over the surface was observed by Balakumar et al. [13]. They concluded that the water molecules in the liquid film on the crystal surface play the role of carriers to transport TGS molecules (glycinium and sulfate ions). A method to determine whether the surface potential decay is due to surface conduction over the sample has been described by Crisci et al. [15]. To verify this hypothesis it is necessary to measure the time dependence of the surface potential at a point located just outside the initial distribution of charges. With this objective in mind, charge was deposited only on the central portion of the surface and the time variation of the surface potential at a point located outside the area of contact with the electrode was observed. The potential reached a maximum, then decreased, as shown in Fig. 3. This result confirms the significant contribution of surface conduction to potential decay. Crisci et al. [15] proposed a model for the surface potential decay of an insulating material. They analyzed the decay caused simultaneously by surface and volume ohmic conduction. The expressions of the time constants obtained by them can be used to calculate the surface conductivity if the volume conductivity is known. The predominance of surface conduction over other processes during potential decay allows one to estimate the surface conductivity. Ohmic surface conduction is one of the simplest mechanisms for surface potential decay. Non-ohmic processes (for instance, injection, polarization) often must be taken into account, especially for rather resistive surfaces. However, even for such surfaces this model can be used to obtain the surface conductivity in the first crude approximation. The model permits determination of the surface conductivity from the slope of the decay curve
Fig. 3. Surface potential versus time at a point located 2 mm from the edge of electrode.
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(ln V/V0 versus time) for sufficiently long times. The time constant t of the exponential decay depends on both the volume sv and surface conductivities ss as follows: 1 1 1 ¼ þ ; t t1 t2 where t1 ¼ e/sv, e is the dielectric permittivity of the material, and t2 is related to ss : Assuming that the value of the volume electric conductivity of TGS crystal at 27 1C is on the order of 1013 O1 m1 [16], we can see that the first term in the above equation is negligible in comparison to the second. This suggests the predominance of surface conduction in the surface potential decay process. In such a case, the time constant t2 of the potential decay for a sample of length D, width 2L, and thickness d is given by [15] t2 ¼
4½LD=ðL þ DÞ 2 : p2 dss
The surface conductivity of TGS crystal under various values of humidity was determined by using the results shown in Fig. 4. Table 1 summarizes the time constants obtained from Fig. 4 and the values of surface conductivity calculated by substituting data from the experiment into the above equation. These results are in agreement with the observations obtained from humidity controlled atomic force microscopy [13] and scanning force microscopy systems [12]. Surface topography of TGS crystal in the presence of water is related to the dissolution and recrystallization processes.
Fig. 4. The time dependence of the maximum potential V normalized to the maximum potential V0 of the first potential distribution after charging.
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Table 1 Surface conductivities of TGS crystal obtained under different RH by using time constants from Fig. 4 Relative humidity RH (%)
Time constant t (s)
Surface conductivity ss (O1)
30 43 51 56
7200 1090 440 40
1 104 8 104 20 104 200 104
4. Conclusions Non-contacting surface potential measurement provides a method for investigating the electric properties of ferroelectric crystal. The surface conductivity of TGS crystal was determined under controlled conditions of temperature and humidity. Its value changed from 104 O1 at 30% RH to 200 104 O1 at 56% RH. The rate of surface potential decay was found to be dependent on relative humidity. The charge on the surface was more stable at lower humidity (30% RH) than at higher humidity (56% RH). The experimental results suggest the predominance of surface conduction over other discharge processes under conditions of high relative humidity. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
S. Kalinin, D. Bonnell, Phys. Rev. B 63 (2001) 125411. A. Sawada, R. Abe, Jpn. J. Appl. Phys. 6 (1967) 699. J. Ohgami, Y. Sugawara, S. Morita, E. Nakamura, T. Ozaki, Jpn. J. Appl. Phys. 35 (1996) 2734. J.W. Hong, K.H. Noh, Sang-il. Park, S.I. Kwun, Z.G. Khim, Phys. Rev.B 58 (1998) 5078. S. Kalinin, D. Bonnell, J. Appl. Phys. 87 (2000) 3950. V. Fridkin, Ferroelectric Semiconductors, Consultants Bureau, New York, 1980. M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectric and Related Materials, Clarendon, Oxford, 1977. M. D˛ebska, S. Dacko, Proceedings of the 20th Spring Conference on Ferroelectricity, KTB, MLU Halle-Wittenberg, 1992, p. 119. D.M. Taylor, J. Electrostat. 51–52 (2001) 502. D.K. Das-Gupta, J. Electrostat. 23 (1989) 331. S. Balakumar, H.C. Zeng, Mat. Res. Innovat. 2 (1999) 289. V. Likodimos, M. Labardi, M. Allegrini, N. Garcia, V.V. Osipov, Surf. Sci. 490 (2001) 76. S. Balakumar, H.C. Zeng, J. Mater. Chem. 10 (2000) 651. Y. Hori, J. Electrostat. 48 (2000) 127. A. Crisci, B. Gosse, J.-P. Gosse, V. Ollier-Dureault, Eur. Phys. J. Appl. Phys. 4 (1998) 107. B. Hilczer, M. Michalczyk, Ferroelectrics 22 (1978) 721.
Journal of Electrostatics 63 (2005) 1017–1023 www.elsevier.com/locate/elstat
Surface potential decay on triglycine sulfate crystal M. D˛ebska Institute of Experimental Physics, University of Wroc!aw, Pl. M. Borna 9, 50-204 Wroc!aw, Poland Received 4 March 2004; received in revised form 8 July 2004; accepted 22 December 2004 Available online 26 January 2005
Abstract An electrostatic potential decay on the surface of triglycine sulfate crystal (TGS) was measured by the induction probe method. The dependence of the decay rate on relative humidity was found. The values of surface conductivity for TGS crystal under controlled conditions are given for the first time. r 2005 Elsevier B.V. All rights reserved. Keywords: Surface conduction; Charge neutralization; Ferroelectric; TGS crystal
1. Introduction New promising technological applications of ferroelectric thin films have caused increased interest in surface layer ferroelectrics. The surface of a ferroelectric material is unique among the surfaces of solid states; the electric charges caused by spontaneous polarization appear on it [1–4]. These charges can be screened by charges which are attracted from both inside and outside the sample to its surfaces [5]. Partial or complete screening is the most probable state of a ferroelectric surface in air [1,6]. Ferroelectric crystals are a special class of crystals that exhibit a spontaneous polarization over some range of temperature. This polarization can be reversed or Tel.: +48 71 37 59 362; fax: +48 71 32 87 365.
E-mail address: [email protected] (M. D˛ebska). 0304-3886/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2004.12.006
ARTICLE IN PRESS 1018
M. D˛ebska / Journal of Electrostatics 63 (2005) 1017–1023
reoriented by application of an external electric field. The coercive field is the electric field required for switching ferroelectric polarization. One of the most widely studied ferroelectric materials is triglycine sulfate (TGS) crystal [7]. TGS crystal undergoes a typical second-order phase transition at the Curie temperature TC (49 1C). The crystal symmetry is monoclinic. In the ferroelectric phase (below TC), a spontaneous polarization Ps arises. The spontaneous polarization vector is parallel to the crystallographic b-axis and perpendicular to the (0 1 0) cleavage plane. The crystal splits into antiparallel domains (i.e. regions with uniform polarization). TGS crystal belongs to the family of water-soluble ferroelectrics, thus it is hygroscopic in nature. However, the correlation between the humidity and the surface charge screening has not been understood until now. The surface resistance of TGS crystal is strongly dependent on humidity, but quantitative data have not been previously published. In this paper, the decay of the surface potential on TGS crystal and its dependence on the relative humidity is presented. The surface potential decay method was used to determine the surface conductivity of TGS crystal.
2. Experiment The electrostatic potential on TGS (0 1 0) cleavage surface was studied using the induction probe method [8]. The resolution of such a probe is typically 1.5 times the probe diameter [9], and in previously reported experiments was estimated as 45 mm. A block diagram of the experimental setup is shown in Fig. 1. Samples of about 1-mm thickness were prepared by cleaving the TGS crystal at ambient conditions (27 1C and 70% relative humidity). The sample was mounted with conducting silver paste on a grounded metal turntable of diameter 0.09 m. The top surface of the sample was charged over a time period of 20 s by contacting it with a metal foil electrode energized to a potential of 100 V. The applied electric field
Fig. 1. Schematic illustration of an experimental setup for charging and surface potential measurement. (Cpg is the input capacitance of the probe and amplifier, Cps the probe to surface capacitance, and Cs the capacitance of the sample to ground).
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(105 V/m) was greater than coercive field (5 104 V/m) for TGS at this temperature; hence the sample was monodomain. After charging the turntable was rotated at 1 rps under a non-contacting probe. In this way, the magnitude of the potential was monitored across the sample face along a line scan during each revolution of the turntable. The distribution of the surface potential (localized potential profile) was recorded along a line crossing the middle of the charged sample. After these measurements, the probe was calibrated in a separate experiment. The relation between the potential V induced on the probe and the surface potential Vs of the sample is the following [10]: V ¼ V s ð0 S=d 1 C pg Þ; where Cpg is the input capacitance of the probe and amplifier, S the area of the sample directly beneath the probe, and d1 the distance between the probe and the sample surface. The calibration factor S/Cpg was determined by replacing the TGS surface with a metal surface held at a known potential. The experiments were carried out in air at a constant temperature of 27 1C under relative humidities (RH) of 30, 43, 51, 56, 60 and 70%. The temperature and humidity in the testing chamber were kept at desired values by an air conditioner and were measured by thermocouple and hygrometer, respectively. At the beginning of the experiment, the humidity was 70%. The humidity was then reduced at a slow rate (no faster than 0.03%/min.). The sample was kept at constant humidity for 3 h in order to obtain equilibrium; the next measurements were then performed.
3. Results and discussion The potential measured over the entire surface of freshly cleaved TGS sample was equal to zero. This result suggests that since the humidity was high during cleaving, the sample charges induced on the surface were precisely neutralized at once after contact with ambient conditions. Such an effect is in agreement with the results of AFM experiments performed by Balakumar et al. [11]. The (0 1 0) surface reconstructs immediately if the humidity is high during cleavage of the crystal, a result of a strong dissolution of TGS crystal [2]. In order to study, the behavior of surface charges, the sample was charged. It was found that after charging under 60% and higher relative humidity, the surface potential was equal to zero. This result suggests that, for high humidity, the decay of the surface potential was too fast to be recorded in with experimental setup used or, alternatively, the surface charge was not present after charging under such environmental conditions. Under high humidity, the water vapor essentially modifies the crystal’s surface properties [12]. Specifically, the TGS crystal surface is dissolved by the water film. Dissolution of the topmost layers of the crystal occurs immediately after the cleavage of the sample. The surface charge is screened by the conductive liquid film formed on the TGS surface. It is known that after a reduction in humidity, the recrystallization process occurs [11,13]. Therefore, the humidity was reduced and the measurements were continued. The polarity of the surface potential at the point of contact with electrode was the same as the polarity of the electrode potential.
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The potential on the probe is a measure of the surface charge density in a given location. At time t, the charge density in the coordinate point x on the scan line is equal to [9] sðx; tÞ ¼
C pg C s V ðx; tÞ; S C ps
where C pg =S is the factor determined earlier, V(x,t) is the input potential of the probe, and C s ¼ 0 S=d is the capacitance of the sample of thickness d and dielectric permittivity e. The dielectric permittivity of TGS at 27 1C is about 800. Similarly, C ps ¼ 0 S=d 1 is the probe-surface capacitance, and d1 the separation between the probe and the sample surface. The geometric parameters were not changed in the sequence of measurements presented here, hence the ratio C pg C s =SC ps was constant. The surface charge density on the TGS sample was calculated. A surface charge density of the order of 1 104 C/m2 was determined when the surface potential was equal to 100 V. This suggests that the charge density on the surface after electrode charging was about two orders of magnitude lower than the surface charge density resulting from spontaneous polarization (2.8 102 C/m2) of TGS crystal at 27 1C. The P total surface charge measured along the line scan at time t is equal to Q (t) ¼ s(x, t), where summation is performed over all x [14]. The surface charge calculated from the first measurement following charging was used as a reference for subsequent charge normalization. In Fig. 2, the normalized maxima of charge density and total charge along the line scan, plotted against time for 43% and 56% RH, are shown. The decay rates of charge density and total charge are nearly the same under low humidity. The charge density decreases faster than the total charge under higher
Fig. 2. Decay of normalized maximum values of charge densities and total charges.
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humidity. This suggests the presence of lateral migration of surface charges under these conditions. Such motion over the surface was observed by Balakumar et al. [13]. They concluded that the water molecules in the liquid film on the crystal surface play the role of carriers to transport TGS molecules (glycinium and sulfate ions). A method to determine whether the surface potential decay is due to surface conduction over the sample has been described by Crisci et al. [15]. To verify this hypothesis it is necessary to measure the time dependence of the surface potential at a point located just outside the initial distribution of charges. With this objective in mind, charge was deposited only on the central portion of the surface and the time variation of the surface potential at a point located outside the area of contact with the electrode was observed. The potential reached a maximum, then decreased, as shown in Fig. 3. This result confirms the significant contribution of surface conduction to potential decay. Crisci et al. [15] proposed a model for the surface potential decay of an insulating material. They analyzed the decay caused simultaneously by surface and volume ohmic conduction. The expressions of the time constants obtained by them can be used to calculate the surface conductivity if the volume conductivity is known. The predominance of surface conduction over other processes during potential decay allows one to estimate the surface conductivity. Ohmic surface conduction is one of the simplest mechanisms for surface potential decay. Non-ohmic processes (for instance, injection, polarization) often must be taken into account, especially for rather resistive surfaces. However, even for such surfaces this model can be used to obtain the surface conductivity in the first crude approximation. The model permits determination of the surface conductivity from the slope of the decay curve
Fig. 3. Surface potential versus time at a point located 2 mm from the edge of electrode.
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(ln V/V0 versus time) for sufficiently long times. The time constant t of the exponential decay depends on both the volume sv and surface conductivities ss as follows: 1 1 1 ¼ þ ; t t1 t2 where t1 ¼ e/sv, e is the dielectric permittivity of the material, and t2 is related to ss : Assuming that the value of the volume electric conductivity of TGS crystal at 27 1C is on the order of 1013 O1 m1 [16], we can see that the first term in the above equation is negligible in comparison to the second. This suggests the predominance of surface conduction in the surface potential decay process. In such a case, the time constant t2 of the potential decay for a sample of length D, width 2L, and thickness d is given by [15] t2 ¼
4½LD=ðL þ DÞ 2 : p2 dss
The surface conductivity of TGS crystal under various values of humidity was determined by using the results shown in Fig. 4. Table 1 summarizes the time constants obtained from Fig. 4 and the values of surface conductivity calculated by substituting data from the experiment into the above equation. These results are in agreement with the observations obtained from humidity controlled atomic force microscopy [13] and scanning force microscopy systems [12]. Surface topography of TGS crystal in the presence of water is related to the dissolution and recrystallization processes.
Fig. 4. The time dependence of the maximum potential V normalized to the maximum potential V0 of the first potential distribution after charging.
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Table 1 Surface conductivities of TGS crystal obtained under different RH by using time constants from Fig. 4 Relative humidity RH (%)
Time constant t (s)
Surface conductivity ss (O1)
30 43 51 56
7200 1090 440 40
1 104 8 104 20 104 200 104
4. Conclusions Non-contacting surface potential measurement provides a method for investigating the electric properties of ferroelectric crystal. The surface conductivity of TGS crystal was determined under controlled conditions of temperature and humidity. Its value changed from 104 O1 at 30% RH to 200 104 O1 at 56% RH. The rate of surface potential decay was found to be dependent on relative humidity. The charge on the surface was more stable at lower humidity (30% RH) than at higher humidity (56% RH). The experimental results suggest the predominance of surface conduction over other discharge processes under conditions of high relative humidity. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
S. Kalinin, D. Bonnell, Phys. Rev. B 63 (2001) 125411. A. Sawada, R. Abe, Jpn. J. Appl. Phys. 6 (1967) 699. J. Ohgami, Y. Sugawara, S. Morita, E. Nakamura, T. Ozaki, Jpn. J. Appl. Phys. 35 (1996) 2734. J.W. Hong, K.H. Noh, Sang-il. Park, S.I. Kwun, Z.G. Khim, Phys. Rev.B 58 (1998) 5078. S. Kalinin, D. Bonnell, J. Appl. Phys. 87 (2000) 3950. V. Fridkin, Ferroelectric Semiconductors, Consultants Bureau, New York, 1980. M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectric and Related Materials, Clarendon, Oxford, 1977. M. D˛ebska, S. Dacko, Proceedings of the 20th Spring Conference on Ferroelectricity, KTB, MLU Halle-Wittenberg, 1992, p. 119. D.M. Taylor, J. Electrostat. 51–52 (2001) 502. D.K. Das-Gupta, J. Electrostat. 23 (1989) 331. S. Balakumar, H.C. Zeng, Mat. Res. Innovat. 2 (1999) 289. V. Likodimos, M. Labardi, M. Allegrini, N. Garcia, V.V. Osipov, Surf. Sci. 490 (2001) 76. S. Balakumar, H.C. Zeng, J. Mater. Chem. 10 (2000) 651. Y. Hori, J. Electrostat. 48 (2000) 127. A. Crisci, B. Gosse, J.-P. Gosse, V. Ollier-Dureault, Eur. Phys. J. Appl. Phys. 4 (1998) 107. B. Hilczer, M. Michalczyk, Ferroelectrics 22 (1978) 721.