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Thermal pulse study of the polarization distributions produced in poiyvinylidene fluoride by corona poling at constant current Jose A. Giacometti Institute de FWca e Quimica de . Zio Carlos, Universidade de SZo Paulo, I3560 silo Carlos, Brazil Aim6 S. DeReggi Polymers Division, NationaI Institute of Standards and Technology, Gaithersburg Maryland 20899 (Received 25 November 1992; accepted for publication 26 February 1993) A thermal pulse study of the polarization profiles in samples of 12+m-thick, biaxially oriented polyvinylidene fluoride after corona poling under approximately constant-current conditions, using a modified corona triode in atmospheric air, is reported. An electrical characterization of the corona triode is also reported to show how it may be operated in the constant-current mode. Samples poled without electrode on the corona-exposed surface show polarization distributions sensitive to the corona polarity, with polarization depletion on the corona side of the samples when the corona is positive. Polarization-reversal experiments show switching inhomogeneities with a pronounced dependence on the initial corona polarity. The above observations are consistent with a simple model in which positive charges from the positive corona partially penetrate the sample during poling and cause an inhomogeneous reduction of the poling field. I. INTRODUCTION Several methods are currently used for producing pol- ing electric fields in samples of polarizable materials. In planar samples with metallic electrodes on opposite sur- faces, a known potential difference between the electrodes may be applied by wires connecting the electrodes to the terminals of a high-voltage supply. The potential difference divided by the sample thickness is the nominal applied electric field that in general should be regarded as the spa- tial average of an electric field that depends on position across the thickness. A spatial dependence is expected when space charge is present in the sample during poling as it affects the internal field. Space charge may come from several sources, but in “constant voltage poling” where a steady poling voltage is maintained for the entire poling time, a likely source is charge injection across the metal- polymer interface. The net space-charge buildup by injec- tion is expected to be lower in “hysteresis poling” where a bipolar high-voltage supply is programmed to produce a periodically varying voltage with positive and negative peak amplitudes exceeding the respective positive and neg- ative coercive voltages.’ In “corona poling” no electrode is required on the sample surface exposed to the corona and none is normally used. A bare corona-exposed surface is thought to be a damage-limiting advantage atforded by corona poling in the event of a local dielectric failurem2 Surface charge away from the punch-through region does not readily contribute to the discharge current as it would with a metallized surface (until the discharge current is quenched by evaporation of the metallization in the region surrounding the punch-through point). A bare corona- exposed surface eliminates one metal-polymer interface and hence the charge injection from the metal. However, the corona-exposed surface is bombarded by a variety of particles in the corona and some of these particles may interact with the surface or penetrate it.3 The corona source is usually a voltage-biased metallic point or wire located a fixed distance from a planar elec- trode against which the sample is placed. The sample sur- face in contact with the planar electrode is usually metal- lized to promote ohmic contact. The electric field between the corona source and the planar electrode, a field initially little perturbed by the sample, draws charge from the co- rona to the normally bare surface of the sample. Charge of opposite sign is induced on the counter-electrode. The sur- face charges and space charges in the sample add to the field already in the sample and ultimately become the dom- inant contributions to the poling field. Because charge builds up gradually on the corona-exposed surface, the voltage across the sample during poling (the poling volt- age) is time dependent. In practice this poling voltage buildup cannot be simply measured in the corona diode just described. The corona-poling technique has been extensively studied3-l4 and reviews of the method are given in Refs. 12 and 13. In the laboratory it has become a useful tool for studying ferroelectric polymers.t4 In industry, it has been used for poling electret microphones” and for photocopy- ing machines. l6 In the nonlinear optics community, corona poling is used for poling nonlinear optical materials17-20 without surface electrodes that interfere with light trans- mission. The corona-poling method’ is expected to have obvious advantages in poling future integrated structures consisting of ferroelectrics and semiconductors where the microscale makes constant-voltage poling impractical. In the corona-diode configuration described earlier, the corona point or wire is brought to a fixed known high potential, and the voltage across the sample is allowed to build up to a maximum value without any control. Corona poling under more controlled conditions was first achieved using a corona triode.4 A triode is obtained by interposing a floating or separately voltage-biased grid between the sample and the corona source. With a grid, the charge on the corona-exposed surface has improved uniformity, the 3357 J. Appl. Phys. 74 (5), 1 September 1993 0021-8979/93/74(5)/3357/9/$6.00 @I 1993 American nstitute of Physics 3357 Downloaded 25 Nov 2001 to 140.247.52.54. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp maximum poling voltage is limited to the bias, and the buildup of this voltage may be determined using a vibrating capacitor technique.4 In feedback-controlled versions of the corona triode, poling under constant current becomes possible and has been achieved for several polymers.5-14 The current control is achieved by controlling the corona- tip voltage5-7 or the voltage bias of the grid.7p8 With a nonpolar sample of negligible conduction, the potential of the corona-exposed surface increases linearly at the rate equal to It/C, where I0 and C are the current through the sample (for negligible conduction, this current is the dis- placement current) and the sample capacitance, respec- tively. When the electrical conduction cannot be neglected and the sample polarization is changed by the poling volt- age, the potential buildup rate is smaller than 1,/C. Com- parison of the measured potential buildup to the buildup calculated from theoretical models’2Z’3 thus provides a means of gaining information about both conduction and polarization processes and also allows testing the theoret- ical models. The nature of the sample conduction current during corona poling is basically unknown as well as its relation to the interaction between the excited molecules and ions in the corona and the sample surface exposed to the corona. From prior work3,13 it appears that the surface may selec- tively block, trap, or pass different corona particles so that it seems naive to suppose that ions from the corona simply accumulate on the bare surface of the sample, induce coun- tercharges on the metallized surface, and produce a uni- form poling field. Penetration and transport of carrier spe- cies from the corona to the sample is almost sure to result in a nonuniform poling field and a nonuniform polarization distribution. Thus, it is important to measure the polariza- tion distributions obtained by corona poling samples of different materials in different gases under different con- trolled conditions and to compare these distributions with those obtained with electroded samples using constant- voltage poling or corona poling. In this article we report the first systematic study of the polarization distributions produced in polyvinylidene fluoride (PVDF) by corona poling under controlled con- ditions in atmospheric air. The polarization distributions were studied by the thermal pulse method with a ruby laser providing the thermal pulses.‘l Because the thermal pulses are much shorter than the thermal diffusion times ( lo4 times shorter here), this method is well adapted to probing the near-surface polarization distributions of prime interest here. The influence of various corona variables is analyzed including the corona polarity. We also report a detailed characterization of the corona triode used in our study. This triode arrangement, which has been used previously,” dose not incorporate the feedback control on the current that is a feature of most modern versions of the corona triode577.8 and hence it has been thought until now to be poorly suited to constant-current poling applications. We show here that the triode in fact can be operated under conditions which give a very stable, nearly constant poling current over a wide range of poling currents. 3358 J. Appt. Phys., Vol. 74, No. 5, 1 September 1993 II. SAMPLES The samples used in this work were taken from a roll of 12-pm-thick, biaxially stretched, capacitor-grade PVDF film manufactured by the Kureha Chemical Industry Corn- pany, Ltd.” and supplied without electrodes. These tis have approximately 50% crystallinity with the crystalline parts consisting of nominally equal amounts of a: and fi phases. Aluminum electrodes of 100 nm thickness were applied to the samples by vacuum evaporation through a mask. Each mask-defined electrode pattern consists of a circular main part with a diameter of 1.27 cm and two diametrically opposite tabs extending 3.12 mm outside the circular part for making electrical connections suitable for the thermal pulse measurements. Corona-poled samples re- ceived electrodes on only one surface prior to poling since the conventional practice is to leave the surface to be ex- posed to the corona unmetallized. A few control samples received electrodes on both surfaces prior to corona poling. After poling, the samples with only one electrode each received a matching electrode so that all samples had elec- trodes on both surfaces for the thermal pulse measure- ments. Ill. EXPERIMENT A. Corona trlode The constant-current corona triode has proven to be an excellent tool for the study of conduction phenomena in insulating polymers.5-14 In the typical triode circuit, the charging current is under feedback control and is kept at a desired constant value while the sample surface potential is monitored during the charging process.598 For ferroelectric polymers it was shown that the shape of the potential ver- sus time characteristic, for a given charging current, con- tains information about the development of the remanent polarization and about the coercive field. From this infor- mation, polarization versus field hysteresis loops were obtained.14 The modified corona triode described in this work allows poling samples with approximately constant current. The modified corona triode is shown schematically in Fig. 1. The mechanical components are similar to those of the constant-current corona triode described elsewhereL8 The triode consists of a corona tip, a metallic grid, and a removable sample holder with a guard ring. The corona discharge is produced at the tip which is connected to a reversible voltage suppiy that produces the corona voltage, f V,. A second reversible voltage supply produces a bias voltage f Vg, which is applied to the control grid consist- ing of a tie mesh, metallic screen. The tip is placed in the center of a metallic cylinder which is connected to ground through a 100 Ma resistor. The cylinder draws current from the corona and acquires a potential intermediate be- tween the tip and ground. The function of the biased cyl- inder is to improve the uniformity of deposition of corona ions over the sample as shown previously.7*8 The guard ring is connected to ground and is intended to prevent surface currents from reaching the measuring electrode which has an area A of 5 cm’. An electrometer and an J. A. Giacometti and A. S. DeReggi 3358 Downloaded 25 Nov 2001 to 140.247.52.54. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp I +.k lci c-i77 f7-J INSULATOR q METAL FIG. 1. Schematic diagram of corona triode system; P is the corona tip; V, and Vr are voltage supplies with polarities shown appropriate for producing a positive corona; 1, is the corona current; A is an ammeter measuring current Id; EL is an electrometer measuring current I(t); R is a chart recorder; S is the sample; E is the measuring electrode and G is a guard electrode. Dimensions are in millimeters. ammeter are used for measuring the sample current I(t) and the cylinder current I=i, respectively. The two high voltage supplies are operated with the same polarity. The corona is said to be positive when the tip is positive, as in Fig. 1, and to be negative when the tip is negative, that is, when both supplies in Fig. 1 have their polarity reversed. In the work described herein, positive coronas and negative coronas were used. All corona operations were carried out in an air-conditioned laboratory environment, namely in atmospheric air at a temperature of 23 “C and a relative humidity of 30%-40%. B. Thermal pulse method In order to determine the polarization distributions across the thickness of the PVDF samples, we used the thermal pulse technique.2”23-26 The experimental proce- dure involves applying laser heating pulses, to either one of the two metallized surfaces of a sample, and measuring the corresponding electrical response that is produced while the absorbed heat diffuses one dimensionally from the heated surface to the entire thickness. The mechanism for the response is inhomogeneous thermal expansion. The time scale of the response is set by the diffusion-controlled thermal relaxation time of the sample. The metallic elec- trodes provide both the properties of opacity at the laser wavelength and low thermal mass. Thus, the partial ab- sorption of optical energy and its conversion to thermal energy occur entirely within the electrode. Immediately after the end of the laser pulse, which is of extremely short duration (100 ns) compared to the thermal relaxation time (1 ms), the thermal energy is sharply concentrated within a shallow depth from the incident surface while, at later times, this energy diffuses into the thickness, producing the inhomogeneous thermal deformation responsible for the electrical response. The recorded response is the charge flowing from one electrode to the other in an external cir- cuit which includes a charge amplifier. The external circuit is nominally a short circuit. As a standard procedure two distinct but complemen- tary response signals Q,(t) and QJt) are obtained in sep- arate operations. Q,(t) is obtained by applying the laser pulse to the corona surface denoted by x=0, where x is the coordinate measuring depth from the corona surface. Qd(t) is obtained by applying the laser pulse to the oppo- site surface denoted by x=d. In the results reported here the response transients are presented in pairs. To facilitate comparison of transients, common vertical and horizontal scales are used in Figs. 7-l 1. The procedures for analyzing thermal pulse transients and obtaining quantitative information about charge or po- larization distributions without deconvolution have been discussed previously.“3*25*26 In the case of nonpolar samples, 26 he total charg e in the sample, the electric fields at the two surfaces, and the first moment of the charge distribution may be obtained directly from the initial val- ues of the transients provided that the transients are cali- brated absolutely. In the case of ferroelectric polymer sam- ples, such as those studied here, the relative magnitudes of the polarization at the two surfaces, P(0) and P(d), and of the mean polarization P, may be obtained from the initial and final values of the uncalibrated transients.25 The rele- vant theoretical relations are QoUWQo( w ) =f’(O)/P (1) and QdWQA w > =P(&/P. (2) The numerical procedureZ4 for determining Fourier co- efficients of the pplarization distribution is not needed here because the polarization distributions are either (i) nomi- nally uniform, in which case the Fourier coefficients are small or near zero, apart from the constant (zeroth) term, or (ii) nonuniform with sharp features, in which case the distributions cannot be adequately represented by the lim- ited number of Fourier coefficients that can be determined. The theoretical response of a sample with uniform po- larization receiving a thermal pulse of infinitesimally short duration is a step with a height proportional to the pyro- electric coefficient, a consequence of the fact that, for uni- form polarization, the response any time after the thermal pulse has been absorbed depends on the amount of ab- sorbed thermal energy but not on its distribution.25 Devi- ations of the response from the unit step of amplitude equal to the asymptotic response at long times thus reflect devi- ations of the polarization from the mean value. Changes in the signals at short times, such as the development of ini- tial spikes, that are related to changes in the corona con- ditions, are unambiguously apparent in the signals whereas the corresponding changes in the polarization profiles ob- tained by deconvolution would be subject to uncertainties endemic to summing Fourier series when the number of significant coefficients changes and becomes large. 3359 J. Appl. Phys., Vol. 74, No. 5, 1 September 1993 J. A. Giacometti and A. S. DeReggi 3359 Downloaded 25 Nov 2001 to 140.247.52.54. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp FIG. 2. Schematic diagram of circuit used to determine the current- voltage characteristics, I vs AV= V,- V,. V, is an adjustable voltage supply; other components are as in Fig. 1. IV. RESULTS A. Corona triode characteristics In order to illustrate how the modified corona triode can be operated in an approximately constant current mode, we show in this section its main electrical charac- teristics, including the dependence of the measuring elec- trode current I on the potential drop AV between the grid and the measuring electrode. The measurements shown in this subsection were made in the absence of a sample. In Fig. 1, I depends on Vg which, in the absence of a sample, is also A V. In order to vary A V, as a means of obtaining the characteristic curve, I vs AV, without chang- ing the electrical conditions in the corona circuit, a variable voltage Vb is used to bias the measuring electrode and the guard ring, as shown in Fig. 2. In this modified circuit we have AV= Vg-- Vb, and the corona current and cylinder current are independent of AV. Figures 3 and 4 display the results for I vs AV obtained for two different sets of con- ditions with a positive corona. The characteristics for a negative corona are not shown here because they are sim- ilar to those for the positive corona apart from a reversal of the applied voltages and the resulting currents. 500 V,= 3kV I=.’ 20 pA I AV = Vg - Vb (WI FIG. 3. Corona triode characteristics, Z vs AV for several Z,. Cubes obtained without sample, using V,= + 3 kV. AV- vg- vb (kV) FIG. 4. Z vs A V for two different Vg with Id adjusted to make the curves similar. Curve I obtained with Vs= + 1.5 kV and Zti= +7 PA; curve II obtained with V,= +3 kV and I,= + 12.5 PA. Figure 3 shows I vs A V for several values of rcj. For practical reasons 1, was used to monitor the current in the corona circuit since its value is proportional to the corona current. In those measurements, Vg was +3 kV. The curves illustrate that, as AV increases, I rises at a decreas- ing rate until it becomes almost independent of AV over a wide range of AV. This AV-insensitive range is broader for lower values of Ici than it is for higher values. For example, for Ici= + 10 PA, 1 is nominally flat in the range of 0.6-3 kV. Figure 4 shows the dependence of I on AV when val- ues of Vg of + 1.5 and + 3 kV were used. The range of A V that is available for poling is 0 to Vg, since in general AV<Vg. For these measurements, the values of I,.i were adjusted in order to obtain I= +200 nA when A V= Vg (that is, when V,=O>. Curves I and II are similar in their common range of AV, but the range of curve I is less than that of curve II such that curve I has no extended flat region over which I is independent of AV. In practice, a high value of Vg and a low value of Icj are chosen to make I insensitive to AV during poling. In the following subseq- tion we show that, under such conditions, the setup of Fig. 1 allows one to pole 12-pm-thick PVDF under approxi- mately constant current. B. Constant-current poling The existence of operating conditions that make the electrode current I nearly independent of AV (Fig. 3), for the empty triode, suggests that the corona setup of Fig. 1 could be employed to pole samples with a constant current whenever AV is in the constant current interval. The char- acteristics in Fig. 3 are altered when a sample is inserted in the triode since the potential difference becomes AV(t) = Vg- V,(t), where V,(t) is the time-dependent sample surface poiential. For V,=3 kV and Ici= 10 ,uA, the range of V, where the charging current is approxi- mately constant is O-2.4 kV. Figure 5 shows current versus time curves for PVDF obtained with the modified corona triode for several values of Icj using a positive corona following exposure for a long 3360 J. Appl. Phys., Vol. 74, No. 5, 1 September 1993 J. A. Giacometti and A. S. DeReggi 3360 Downloaded 25 Nov 2001 to 140.247.52.54. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
