corona charging

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 poling electric fields in samples of polarizable materials. In planar samples with metallic electrodes on opposite surfaces, 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 spatial 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 injection 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 negative 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 electrode against which the sample is placed. The sample surface in contact with the planar electrode is usually metallized 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 corona to the normally bare surface of the sample. Charge of opposite sign is induced on the counter-electrode. The surface 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 voltage) 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 Institute of Physics 3357

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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, respectively. When the electrical conduction cannot be neglected and the sample polarization is changed by the poling voltage, the potential buildup rate is smaller than 1,/C. Com- parison of the measured potential buildup to the buildup calculated from theoretical models2Z3 thus provides a means of gaining information about both conduction and polarization processes and also allows testing the theoretical 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 uniform 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 polarization distributions obtained by corona poling samples of different materials in different gases under different controlled 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 conditions 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 received electrodes on only one surface prior to poling since the conventional practice is to leave the surface to be exposed 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 electrodes on both surfaces for the thermal pulse measurements.

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 versus time characteristic, for a given charging current, con- tains information about the development of the remanent polarization and about the coercive field. From this information, 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 consisting 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 between the tip and ground. The function of the biased cylinder 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


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 mill imeters.

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.223-26 The experimental procedure 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 electrodes 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 circuit 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 opposite 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 polarization distributions without deconvolution have been discussed previously.3*25*26 In the case of nonpolar samples, 26 the 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 values of the transients provided that the transients are cali- brated absolutely. In the case of ferroelectric polymer samples, 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) nominally 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 limited number of Fourier coefficients that can be determined.

The theoretical response of a sample with uniform polarization 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 uniform polarization, the response any time after the thermal pulse has been absorbed depends on the amount of absorbed 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 deviations of the polarization from the mean value. Changes in the signals at short times, such as the development of initial spikes, that are related to changes in the corona conditions, are unambiguously apparent in the signals whereas the corresponding changes in the polarization profiles obtained 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


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 characteristics, including the dependence of the measuring electrode 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 conditions with a positive corona. The characteristics for a negative corona are not shown here because they are similar 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 values 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. 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 approximately 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 characteristics 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 approximately 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



POSITIVE CHARGING

p - PVDF

12 pm THICK

5 IO TIME (min)

I5

FIG. 5. Current I as a function of time for several different Ici for 12qm thick sample. The grid voltage was $3 kV. Curves obtained with the corona triode of Fig. 1 (positive corona). Sample was corona poled with a negative corona just prior to polarization reversal. Arrows indicate the time in each curve where current is judged to begin deviating substantially from a constant value.

time to a negative corona. It can be seen that increasing ICi produces a charging current which deviates increasingly from constancy as a function of time in agreement with the empty triode characteristics. For the thermal pulse measurements described in the following subsection, we used lower values of Ici in order to better realize the constant current poling condition.

Figure 6 shows both the sample potential buildup (curve I) obtained with a corona triode with feedback control8 and the current versus time (curve II) obtained with the triode described in this work (in both cases the sample current density J==I/A was approximately 20 nA/cm). Again, the samples were exposed to a negative corona prior to the positive corona measurements. The two curves show that the rising plateau in the potential curve

1- I 2dO

I do

I 6bO

I e&l

I I&

TIME (set)

FIG. 6. Curve I: Surface potential buildup for a 12-pm-thick sample poled with a positive corona and Jo= +20 nA/cm (curve obtained with the corona triode described in Ref. 6). Curve II: Current vs time characteristic for a sample poled using the modified corona triode described in this work. In both measurements samples were corona poled with a negative corona just prior to poling.

3361 J. Appl. Phys., Vol. 74, No. 5, 1 September 1993

(a)

FIG. 7. Thermal pulse transients for PVDF samples after corona poling with corona-exposed surface, using a current density of 40 nA/cm, without electrode and opposite surface with electrode: (a) positive corona; (b) negative corona. Upper transients, thermal pulse applied to corona side; lower transients, thermal pulse applied to opposite side. Vertical scale: charge in arbitrary units; horizontal scale: time, 200 11s per division.

occurs within a time interval during which the current measured from our triode is constant (see Fig. 3). The rising plateau was previously interpreted as a manifestation of poling8p14 on the grounds that the development of dipo- lar charge due to ferroelectric switching partly compen- sates the surface charge delivered by the corona and hence is responsible for the observed decrease in the rate of potential buildup. When switching is complete, the rate of increase of potential again increases. Figure 6 also shows that the rapid decrease in current occurs beyond the rising plateau and hence that poling occurs at constant current.

C. Thermal pulse study

1. Samples with one metallized surface-First poling

Figure 7 shows thermal pulse transients from samples, with one surface left bare and the other aluminized, that were corona poled to saturation using positive or negative coronas with the bare side exposed to the corona. For these samples poling was done using a current density of 40 nA/cm2 and the corona was maintained well past the current drop-off in Fig. 5 (more than 15 min). All transients in Fig. 7 show rounding initially that indicates polarization depletion near the surfaces. This rounding is believed to be due mainly to homopolar charge injection which reduces the poling field near the surfaces. Examination of the upper and lower transients in Fig. 7(a), for positive corona, reveal differences at short times between the two transients that, according to Eqs. ( 1) and (2), indicate an asymmetric polarization distribution with unequal polarization depletions near the two surfaces. The nearly similar transients in Fig. 7 (b), for negative corona, indicate a nominally symmetric and more uniform polarization distribution. Comparing the upper transients of Figs. 7(a) and 7(b) we see evidence for additional polarization depletion near the corona surface when the corona is positive. We conclude that there is more positive charge injection when the corona is positive than there is negative charge injection when the corona is negative.

J. A. Giacometti and A. S. DeReggi 3361


iiiild 60

FIG. 8. Thermal pulse transients for different PVDF samples during polarization reversal using a positive corona and a current density of +20 nA/cm following poling to saturation using a negative corona. Upper transients, thermal pulses applied to corona side; lower trysients, thermal pulse applied to opposite side. Transients (a) initially negative saturation polarization; (b) positive corona for 3 min; (c) same for 4 I miq (d) same for 6 min; (e) same for 7 $ min; (f) same for 9 min; and (g) same to saturation. Scales: same as in Fig. 7.

2. Samples with one metallized surface-Polarization feversa/

The asymmetry in the polarization depletions observed for positive corona is more clearly manifested in the se- quences of transients shown in Figs. 8 and 9. In each sequence all samples of a set were initially poled with a positive or negative corona to saturation using a current density of *40 nA/cm for approximately 15 min. The various samples in the set were then reverse poled by re- versing the corona polarity using a current density of =F 20 nA/cm2 for various time intervals of 3, 4 i, 6, 7$, 9, and 15 min (saturation), in order to characterize the evolution of the polarization distribution during its gradual reversal. Figure 8 is for samples that were initially poled to saturation with a negative corona and then were subjected to a positive corona. Figure 9 is for samples that were initially poled to saturation with a positive corona and then were subjected to a negative corona.

Consider first the sequence starting with the sample initially poIed with a negative corona shown in Fig. 8. The transients in Fig. 8 (a) are similar to those in Fig. 7 (b) and

indicate a nominally symmetric and relatively homogeneous polarization distribution. After a short exposure to the positive corona the partial polarization reversal occurs by nearly homogeneous switching, as indicated by transients 8(b) and 8(c). The transients in 8(d) and 8(e), for samples poled initially with a positive corona, show a strongly asymmetric polarization distribution that suggests that later stages of polarization reversal occur by inhomogeneous switching. The negative initial peak in the other- wise positive response in the upper transient in 8(d) and 8 (e) indicates residual unswitched polarization close to the positive corona surface. A trace of the negative peak is still observable in the upper transient in 8 (f) and 8 (g), show- ing that this residual unreversed polarization persists tena- ciously when the polarization elsewhere has been fully reversed. In contrast to the upper transients, the evolution of the lower transients do not show negative initial peaks.

The transients in IFig. 8 are consistent with the occur- rence of a substantial amount of positive charge injection at the corona-exposed surface when the corona is positive. The homogeneous switching in Figs. S(b) and 8(c) sug-

FIG. 9. Thermal pulse transients for different PVDF samples during polarization reversal using a negative corona and a current density of - 20 nA/cma following poling to saturation using a positive corona. Upper transients, thermal pulses applied to corona side; lower transients, thermal pulse applied to opposite side. Transients (a) initially positive saturation polarization: (b) negative corona for 3 mm; (c) same for 4 $ min; (d) same for 6 min; (e) same for 7 i min; (f) same for 9 mm, and (g) same to saturation. Scales: same as in Fig. 7.



(a)

FIG. 10. Thermal pulse transients for PVDF samples with electrodes on both sides after corona poling, using 40 nA/cm*: (a) positive corona; (b) negative corona. In (a) and (b), upper transients are obtained by applying thermal pulses to comna side, lower transients are obtained by applying thermal pulses to opposite side. Scales: same as in Fig. 7.

gests that the polarization charge impedes positive charge injection until such time as the mean polarization is re- duced to near zero. The penetration depth of the positive injected charge, as estimated from the temporal width (20 ps> of the negative peak in Figs. 8(d) and 8(e) and the diffusion-controlled thermal relaxation time (250 ys), is roughly $ the sample thickness. This follows from the equation S/d= (t/7) 12 where S is the diffusion depth, f is the diffusion time, d the thickness, and T is the diffusion relaxation time. The equation comes from the expression for 7 (Ref. 27) which is r=d/gK, where K is the thermal diffusivity.

Consider next the sequence with initially positive corona shown in Fig. 9. The transients in Fig. 9 are similar to those in Fig. 7, and indicate an initial polarization with more depletion on the corona side than on the opposite side, which is consistent with positive charge injection, as discussed before. The transients in Fig. 9 indicate that reversal of the corona polarity produces a nominally homogeneous reversal of the polarization. These results suggest that there is no corona-related injection when the corona is negative. Furthermore, these results suggest that the positive charge injected when the corona is positive does not remain trapped for a long time in the polymer. If it re- mained trapped indefinitely, the electric field due to this charge would add to the field produced by the negative corona and result in an inhomogeneous reversed poling field, which is not observed.

3. Samples with both surfaces metallized prior to poling

Figure 10 show pairs of thermal pulse transients obtained from samples that were corona poled after aluminum electrodes were deposited on both surfaces. The poling current was +40 nA/cm. Figure IO(a) is for a positive corona poling and Fig., 10(b) for negative corona poling. Upper transients indicate a small polarization depletion near the incident surface which is the corona surface. Lower transients indicate a small polarization excess close to the incident surface, which is now the surface

FIG. 11. Thermal pulse transients for PVDF samples after positive corona poling with corona-exposed surface without electrode for several values of sample current. Upper transients, thermal pulse applied to corona side; lower transients, thermal pulse applied to opposite side. Tran- sients (a) .I,= +18 nA/cm for 20 min; (b) 5,,=+40 nA/cm2 for 15 min; (c) Jo= +60 A/cm for 10 min; and (d) Jo= + 100 nA/cm for 6 min. Scales: same as in Fig. 7.

opposite the corona surface. The deviations from uniformity of the polarization on both surfaces simply change sides when the corona polarity and the polarization are reversed, as shown by the upper and lower transients in Fig. IO (a) which are negative versions of lower and upper transients, respectively, in Fig. lO( b). The observed almost symmetric polarization distribution is similar to that observed in voltage-poled samples as shown by transient pairs not shown here which are virtually identical to those in Fig. i0. From prior work on the measurement of polarization distributions in constant-voltage-poled samples,28 it is reasonable to attribute the inhomogeneity in the polarization distributions shown by Fig. 10 to a variation of the material properties across the thickness of the film that result in an inhomogeneous coercive field. A part of this inhomogeneity in the distributions could also be attributed to poling-field inhomogeneity due to charge injection or ejection. The above results indicate that the inhomogeneous part of the polarization distribution in the doubly metallized samples, regardless of origin, is unrelated to effects of corona poling.

4. Relationship bet ween thermal pulse transients, poling current, and poling time

Figure 11 shows a sequence of thermal pulse transients obtained from samples that were corona poled with the corona surface bare using different current densities from + 18 to + 100 nA/cm2 with the poling times indicated in the figure caption. The poling times were chosen consistently with keeping conditions in the constant current re- gime (refer to Fig. 5). Before being poled with the positive corona the samples were first poled to saturation using a negative corona. These measurements show that the level of polarization achieved and the distribution of polarization are insensitive to the poling current in the current range of 18-100 nA/cm2; Nevertheless, the transient in Fig. 11 (d) does not display the negative peak indicating that the unreversed polarization tends to disappear for higher values of the poling current.

Figure 12 is a plot of the thermal pulse responses at long times proportional to the mean polarizations, taken from Fig. 9, as a function of the charge density Q/A delivered to the sample surface by the corona. Neglecting



FIG. 12. Thermal pulse response as function of the charge density Q/A delivered by the corona to the sample surface. The data were taken from the upper transients of Fig. 9 at the time equal to 1 ms.

charge leakage through the sample, Q/A is estimated as Jot,, where JO is the constant-current density during poling and tc the corona-poling time. The linear relationshipseen in Fig. 12 suggests that Q/A is a measure of the degree of poling. While the linear relationship is consistently observed with a negative corona, it is rather more difficult to observe with a positive corona in normal atmospheric air and the data in Fig. 8, for instance, have a large amount of scatter (plot not shown). A study of the effects of moisture in air3*729 indicates that the effectiveness of corona poling using a positive corona in air depends strongly on the relative humidity and that corona poling is most effective when using dry air. Since during our measurements the laboratory humidity was centrally controlled between lim- its rather than held constant, we believe that the scatter found in the positive corona case could be due to changes in relative humidity.

V. SUMMARY AND CONCLUSIONS

We have developed a variation of the corona-triode circuit that allows corona poling samples under controlled conditions and have determined a range of settings that allow poling 12 pm PVDF under approximately constant- current conditions. We have shown that the ferroelectric remanent polarization can be estimated by Jot,, the prod- uct of the current density and the poling time during which the current has a constant value.

Using the thermal pulse method we have made the first systematic study of the polarization distributions that are obtained in 12+m-thick, biaxially stretched PVDF after corona poling under constant-current conditions, using both positive and negative coronas. We have shown that saturation of the polarization can be attained using poling current densities between 19 and 100 nA/cm2 provided that the current is maintained for the times indicated by the arrows in Fig. 5. At those times the integrated current

densities given approximately by Jot, for low currents is 8 &!/cm. This value is in agreement with the reported saturation polarization for PVDF.30

Corona poling samples metallized on both major surfaces gives polarization distributions that are insensitive to the corona polarity and that are similar to those obtained by constant-voltage poling similar samples using a low- impedance, high-voltage supply. Results from samples with only one surface-metallized and the-other surface exposed to the corona show a marked sensitivity to the corona polarity. When the corona is negative, homogeneous polarization distribution is obtained and there is no sign of charge injection. In contrast, when the corona is positive, anomalous polarization distributions are observed. These distributions indicate that positive charges in the polymer cause polarization depletion. A suspected high-moisture sensitivity of the results suggests that the positive charges could be Hf produced by dissociation of water molecules 3,11,13,29,31,32

Since, in general, the nature of the corona-polymer interaction is likely to depend on the nature of the ions in the corona, the work reported here should be extended to controlled atmospheres different from laboratory air. Work along these lines is planned for the near future.

ACKNOWLEDGMENTS

This work was partially supported by the CNPQ/ RHAE-Brazil program and FAPESP. The authors thank Neri Alves for obtaining the data for curve I in Fig. 6.

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