The unique ability of ferroelectrics to generate high voltage under shock loading is limited by electrical breakdown within the shock-compressed ferroelectric material. Breakdown is a hybrid process of initiation and growth. The possible mechanisms of electrical breakdown in ferroelectric films and bulk ceramics subjected to high-pressure shock loading are discussed and experiments designed to elucidate which mechanisms govern breakdown. Gigapascal shock loading experiments were performed on poled Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3 ferroelectric film specimens in the range of 32–156 μm thickness to determine the dependence of the breakdown field on thickness and on film specimens in the range of 4–16 mm length to determine the dependence of the breakdown field on the duration of shock compression. The resulting breakdown-field vs thickness and breakdown-field vs shock transit time dependencies are consistent with a hybrid electron emission initiation and Joule heating microchannel growth mechanism. Further analysis of data previously obtained on shock-compressed 0.27Pb(In1/2Nb1/2)O3–0.47Pb(Mg1/3Nb2/3)O3–0.26PbTiO3 ferrvoelectric single crystals and Pb(Zr0.65Ti0.35)O3, Pb0.99(Zr0.52Ti0.48)0.99Nb0.01O3, Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3 bulk ceramics is consistent with this dual mechanism. It appears that neither chemical composition nor microstructure (single crystal vs polycrystalline) of the ferroelectric material has a significant effect on the breakdown mechanism in shocked ferroelectrics.

Ferroelectric materials are nonlinear and hysteretic dielectrics that are capable of generating electrical energy through stress driven reorientable ionic polarization.1–8 High-pressure shock loading can initiate domain wall motion and phase transformations in some compositions, resulting in the partial or complete depolarization of the ferroelectric material. This generates a high electric charge density and voltage. This is the foundation for the development of compact, autonomous ferroelectric generators that are capable of producing hundreds of kilovolts and megawatts of power for microsecond intervals of time.1–11 

Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3 (PZT 95/5) ferroelectric ceramics are widely used in these high-power devices because of their ability to be completely depolarized under high-pressure shock loading due to a pressure-induced ferroelectric to antiferroelectric (FE–AFE) phase transition,1–3,9–11 but PZT 95/5 is not the only material that can be used. The results have been reported on investigations of shock-induced depolarization of (Na0.5Bi0.5)TiO3-BiAlO3,4 (Na0.5Bi0.5)TiO3,5 (Ag0.935K0.065)NbO3,6 BiFeO3-based,7 and K0.5Na0.5NbO3 ferroelectric ceramics.8 In addition to ferroelectric ceramics, relaxor ferroelectric 0.27Pb(In1/2Nb1/2)O3–0.47Pb(Mg1/3Nb2/3)O3–0.26PbTiO3 (0.27PIN-PMN-0.26PT) single crystals have been used to produce a high electric charge density and voltage under shock loading and can be utilized in high-power ferroelectric devices.11–16 

Shock-compressed PZT 95/5 ferroelectrics are capable of producing large stress-induced electric charge and kiloampere currents17,18 into a low-impedance load, megawatt power,18–20 and high voltage across a high-impedance load.1,9–11,14,15,21–24 One of the factors limiting high-voltage generation is electrical breakdown within the ferroelectric materials during shock wave transit.1,9–11,14,15,21–24

Electrical breakdown in solids under ambient conditions (atmospheric pressure, room temperature, low humidity) has been studied extensively since the 1940s.25 Several theoretical models have been proposed based on different mechanisms of breakdown in solid dielectrics. The thickness dependence of the breakdown field, Eb(d), is the key experimental dependence on which different theories are tested. The thickness influence on the breakdown phenomena observed for solid dielectrics was introduced by Fronlich26 and was further developed by Seitz,27 Kawamura, and Azuma.28 Good agreement between experimental and theoretical exponential breakdown-field-on-thickness dependence was achieved in the theoretical model developed by Forlani and Minnaja,29,30
E b ( d ) = γ d η ,
(1)
where γ is a material dependent constant, d is the dielectric thickness, and η is the coefficient justified by the mechanism of injection of electrons into a dielectric material and electron–phonon scattering.29,30

The development of electrical breakdown in solid dielectrics can be governed by multiple mechanisms.25 A possible mechanism of the development of breakdown is based on collision ionization induced by a high electric field.29,30 According to a theoretical analysis26,30 and experimental results,31,32 this avalanche mechanism results in the development of breakdown and short-circuiting the electrodes of dielectrics within a few nanoseconds. This mechanism is not consistent with the hundreds of nanoseconds fall times observed in breakdown voltage waveforms of shock-compressed bulk ferroelectric ceramics1,33–38 and relaxor ferroelectric single crystals.14,15

A thermal runway mechanism of electrical breakdown in solid dielectrics was proposed by O'Dwyer.25 In this model, in addition to the breakdown field, there is another important parameter, the delay time of breakdown, tb. The latter parameter is associated with breakdown development. The relationship between the breakdown field and the delay time is given by25 
E b ( t b ) = χ t b 0.5 ,
(2)
where χ is a material dependent constant. According to Eq. (2), a longer delay time corresponds to a lower breakdown field.

Breakdown in shock-compressed ferroelectrics has been under investigation since the 1970s.1,21–24,36–39 Lysne performed studies of breakdown in shock-compressed Pb(Zr0.65Ti0.35)O3 (PZT 65/35) and PZT 95/5 ferroelectric ceramics, and he proposed a phenomenological model for the breakdown in shocked ferroelectrics that takes into account the applied pressure, the ceramic porosity, and the remanent polarization,1,21,38 yet the mechanism of breakdown in shock-compressed ferroelectrics is still not completely understood.

Here, experiments are performed to quantify the dependence of electrical breakdown on the film thickness and shock duration. The results are compared to prior results from the literature and lead to the conclusion that breakdown in shock loaded films is governed by a hybrid mechanism of electron injection initiation and Joule heated microchannel development.

PZT 95/5 films were fabricated by TRS Technologies Inc. PZT 95/5 powder was prepared by mixing stoichiometric amounts of PbO, ZrO2, and TiO2 raw material with 2% Nb2O5 dopants in a water-based slurry. The powder mixture was calcined at a high temperature to form the PZT perovskite phase. The powder was then re-milled and dried. After drying, the powder was mixed with solvents and binders for tape casting using a ball mill. After milling, the slurry was dispensed in a thin layer on a moving steel belt to tape-cast the films. The grain size was 2.4 ± 0.4 μm. The PZT 95/5 films had no substrates. After firing, the film specimens were terminated with fired silver electrodes that covered each film surface completely. Each film specimen was encapsulated with a protective zirconium dioxide ceramic body. Figure 1 shows a cutaway view of the PZT 95/5 film specimen. The output terminals were connected to the external silver electrical contacts by silver loaded epoxy [Fig. 2]. Bulk PZT 95/5 ceramic specimens were fabricated by TRS Technologies Inc. using conventional solid oxide processing (mixing oxide powders, calcining, ball milling, adding a binder, pressing, and sintering). The PZT 95/5 films and bulk ceramic specimens were polarized by the manufacturer to a remanent polarization of Pr = 34 μC/cm2.

FIG. 1.

Cutaway view of the PZT 95/5 ferroelectric film specimen.

FIG. 1.

Cutaway view of the PZT 95/5 ferroelectric film specimen.

Close modal
FIG. 2.

Schematics of the experimental device and the measuring circuit used to investigate the generation of high voltage by ferroelectric films and ceramics subjected to high-pressure shock loading. SW is the shock wave vector.

FIG. 2.

Schematics of the experimental device and the measuring circuit used to investigate the generation of high voltage by ferroelectric films and ceramics subjected to high-pressure shock loading. SW is the shock wave vector.

Close modal

High-pressure experiments were conducted in the facilities of the Energetic Materials Research Laboratory of the Missouri University of Science and Technology in Rolla, Missouri. The loading arrangement utilized a high explosive shock compression scheme.3  Figure 2 shows the schematics of the experimental device and the measuring circuit in the high-voltage mode. In some of the experiments, the Tektronix P6015A high-voltage probe was replaced by a short circuit and a Pearson Electronics 411 current probe to measure the current and determine the charge released in the absence of electrical breakdown.

The experimental device contained two parts, a specially designed detonation material and a ferroelectric specimen encapsulated within a urethane body. The urethane was used as the electrical insulating material and was chosen using shock impedance matching. The diameter of the urethane body was 38 mm, and the length was 75 mm. The distance between the ferroelectric specimen and the top of the urethane body was 20 mm. A high explosive charge of 9 g of desensitized cyclotrimethylene trinitramine (RDX) was initiated by an RP-501 exploding bridge-wire detonator supplied by Teledyne RISI Inc. The orientation of film polarization perpendicular to the shock propagation direction is referred to as the transverse stress mode. The high-voltage probe or current probe and the measuring circuits were placed outside of the blast chamber. High-voltage open circuit experiments and current mode short circuit experiments were conducted on films having thicknesses ranging from 32 to 156 μm.

Additional experiments were conducted with different shock durations. The shock velocity in PZT is 4 mm/μs. To vary the shock wave transit time through the film and, thus, the voltage waveform rise time, the film lengths were increased from 4 to 6, 8, 12, and 16 mm, thereby increasing the time it took for the shock wave to sweep across the entire film. A larger electrode area resulted in a longer charging time because the shock wave front had to travel a longer distance to depolarize a larger fraction of the film and to produce the larger stress-induced charge required for charging the higher-capacitance film to a high enough voltage to initiate breakdown.

The magnitude and distribution of stress in shock-compressed ferroelectric specimens are important parameters that have an effect on the depolarization process. The stress distribution in the ferroelectric films was assessed by performing a numerical simulation of the shock compression using a two-dimensional arbitrary Lagrange/Eulerian second-order accurate hydrodynamics program (CALE).40 The Hugoniot data and mechanical properties of shocked PZT 95/5 and urethane used in the simulation were reported by Furnish et al.,41 Cox et al.,42 Setchell,43 and Marsh.44 The simulations were run in Cartesian coordinates (X, Y, Z), where the Y-axis is the direction of shock wave propagation. The space was divided into “zones” using a rectangular mesh of zones created by planes parallel to the Z-axis and to the X-axis.

Figure 3 shows the CALE graphical results for a 32 μm thick PZT 95/5 film with electrode area of 6.3 × 4.0 mm2 (protective ceramic body size 10 × 8 × 3 mm3). The simulation results indicate that the uniaxial strain associated stress magnitude in the ferroelectric film was on the order of 3 GPa. The shock wave front had almost planar geometry during shock wave transit through the film, while the distribution of pressure behind the shock front is complicated.

The stress applied perpendicular to the polarization vector should stabilize the poled state of the ferroelectric phase. The composition of PZT 95/5 lies very close to the boundary between the ferroelectric and antiferroelectric phases in the PZT phase diagram.45 The results of experimental investigations of shock depolarization of PZT 95/5 ceramics indicate that under transverse shock loading (perpendicular to the polarization vector)1–3,46–48 or longitudinal shock loading (parallel to the polarization vector),49 PZT 95/5 undergoes through the pressure-induced ferroelectric to antiferroelectric (FE-to-AFE) phase transition and becomes completely depolarized under shock pressure exceeding 1.1 GPa. Therefore, under 3 GPa shock compression [Fig. 3], PZT 95/5 films undergo a complete FE-to-AFE phase transition and release electric charge density equal to their remanent polarization.

FIG. 3.

Pressure distribution in a 32 μm thick PZT 95/5 film with electrode area of 6.3 × 4.0 mm2 (protective ceramic body size 10 × 8 × 3 mm3) at (a) 0.125 and (b) 0.5 μs after the shock wave front entered the film. SW is the shock wave vector.

FIG. 3.

Pressure distribution in a 32 μm thick PZT 95/5 film with electrode area of 6.3 × 4.0 mm2 (protective ceramic body size 10 × 8 × 3 mm3) at (a) 0.125 and (b) 0.5 μs after the shock wave front entered the film. SW is the shock wave vector.

Close modal

Open circuit high-voltage experiments were performed with PZT 95/5 films having identical electrode areas 25 mm2 (6.3 × 4.0 mm2) and different thicknesses. The size of ceramic protective bodies for these films was 10 × 8 × 3 mm3. Eight experiments were conducted for each film thickness. The shock wave propagated across the 4 mm length of the PZT 95/5 film, depolarizing the material behind the shock front. The surface charge density that terminated the initial remanent polarization was released by shock-induced depolarization. This charge density remained on the film electrodes, resulting in the generation of a high voltage across the film; i.e., the high-pressure shock loading produced a voltage vs time profile. The parallel capacitance of the cables and other electronics was negligible relative to the capacitance of the shocked specimen.

Figures 4(a) and 4(b) show typical high-voltage waveforms produced by transversely shocked 32 and 128 μm thick PZT 95/5 films. The peak observed voltage was the breakdown voltage, and the peak voltage normalized by the film thickness was the breakdown field.

FIG. 4.

Waveforms of high voltage generated by transversely shock-compressed (a) 32 μm thick and (b) 128 μm thick PZT 95/5 films (film electrode area 25 mm2) in the open circuit mode. Waveforms of stress-induced current and electric charge produced by (c) 32 μm thick and (d) 128 μm thick PZT 95/5 films (film electrode area 25 mm2) in the short circuit mode.

FIG. 4.

Waveforms of high voltage generated by transversely shock-compressed (a) 32 μm thick and (b) 128 μm thick PZT 95/5 films (film electrode area 25 mm2) in the open circuit mode. Waveforms of stress-induced current and electric charge produced by (c) 32 μm thick and (d) 128 μm thick PZT 95/5 films (film electrode area 25 mm2) in the short circuit mode.

Close modal

The voltage produced by a shocked 32 μm thick film [Fig. 4(a)] rose to its maximum of 0.85 kV at 0.54 μs, and then, it subsequently decreased to zero. The voltage rise time of 0.54 μs was almost two times shorter than the shock wave transit time through the 4 mm long film (1.0 μs). The breakdown field for shocked 32 μm thick PZT 95/5 film was Eb = 26.6 kV/mm.

The voltage generated by a shocked 128 μm thick film was a single pulse with the rise time of 0.5 μs [Fig. 3(b)]. The voltage amplitude was Vb = 2.14 kV. For both films, the generation of high voltage was interrupted before the shock front reached the back end of the film.

Films of different thicknesses were subjected to shock depolarization experiments in the short circuit mode. In these experiments, 32 and 128 μm thick PZT 95/5 films identical to those used in the open circuit mode were shock loaded. Figures 4(c) and 4(d) show the waveforms of stress-induced current and stress-induced charge (time integral of the stress-induced current) generated by shock-compressed 32 and 128 μm thick PZT 95/5 films in the short circuit mode. Both current waveforms had a quasi-rectangular shape and practically equal amplitudes. The oscillations in the current waveforms were caused by the interference among the generated current, the capacitance of the ferroelectric film, and the inductance and resistance of the connecting wires that formed an LCR-circuit.

In the short circuit mode, the current pulse duration of 1.0 μs was equal to the shock wave transit time through the films [Figs. 4(c) and 4(d)]. The generation of stress-induced charge started when the shock front entered the film and continued until the moment when the shock front reached the back end of the film. The films released equal amounts of stress-induced charge, 8.3 μC. The corresponding surface charge density of 33 μC/cm2 was approximately equal to the remanent polarization of the films (Pr = 34 μC/cm2); i.e., both films were completely depolarized under transverse shock loading and transferred all stored electric charge into the load circuit.

The breakdown voltage of a shocked 128 μm thick film [2.14 kV in Fig. 4(b)] was significantly higher than that for a 32 μm thick film; however, the breakdown field of the 128 μm thick film, Eb = 16.7 kV/mm, was lower than that for the 32 μm thick film (Eb = 26.6 kV/mm). This difference in the breakdown field of PZT 95/5 films of different thicknesses cannot be explained by the difference in the dynamics of shock-induced charge produced by the films because the experimental results [Figs. 4(c) and 4(d)] indicate that the film thickness did not have a significant impact on the shock-induced current or charge.

Experiments were conducted on films having thicknesses 32, 64, 78, 128, and 156 μm (film electrode area 25 mm2). Figure 5 shows that the voltage amplitude produced by PZT 95/5 films is directly proportional to the film thickness, while the breakdown field is inversely proportional to the film thickness. The experimental data for shock-compressed films in Fig. 5 were fitted to different functions. The best fit was obtained for a power law, Eb(d)  = 62.2d−0.256 (where d is the film thickness).

FIG. 5.

Experimentally obtained breakdown voltage (diamonds) and breakdown field (squares) of transversely shock-compressed PZT 95/5 films (film electrode area 25 mm2) vs film thickness, along with the fitted curves.

FIG. 5.

Experimentally obtained breakdown voltage (diamonds) and breakdown field (squares) of transversely shock-compressed PZT 95/5 films (film electrode area 25 mm2) vs film thickness, along with the fitted curves.

Close modal

Figures 6(a) and 6(b) show the voltage waveforms generated by 64 μm thick PZT 95/5 films with electrode areas of 25 and 50 mm2. One film (electrode area 25 mm2) had a width of 6.3 mm and length of 4 mm. The other film (electrode area 50 mm2) had a width of 6.3 mm and length of 8 mm. The shock wave propagated across the 4 mm side and 8 mm side of these films, respectively. The length of the ceramic protective body for the 8 mm long film was double of that for a 4 mm long film. The experimental results [Figs. 6(a) and 6(b)] indicate that a longer shock wave transit time prior to breakdown results in a lower breakdown voltage and a lower breakdown field for these PZT 95/5 films.

FIG. 6.

Voltage waveforms generated by transversely shock-compressed 64 μm thick PZT 95/5 films with electrode areas (a) 25 mm2 (film length 4 mm) and (b) 50 mm2 (film length 8 mm) in the open circuit mode. (c) Waveforms of stress-induced electric charge produced by 64 μm thick PZT 95/5 films with length 4 (black) and 8 mm (gray) in the short circuit mode.

FIG. 6.

Voltage waveforms generated by transversely shock-compressed 64 μm thick PZT 95/5 films with electrode areas (a) 25 mm2 (film length 4 mm) and (b) 50 mm2 (film length 8 mm) in the open circuit mode. (c) Waveforms of stress-induced electric charge produced by 64 μm thick PZT 95/5 films with length 4 (black) and 8 mm (gray) in the short circuit mode.

Close modal

Figure 6(c) shows the electric charge waveforms generated by similarly shocked 4 and 8 mm long films in the short circuit mode. PZT 95/5 films having identical widths but different lengths (and, thus, different electrode areas) generated practically identical electric charge waveforms for the first microsecond of shock wave transit across the films. The 8 mm long film produced electric charge for 2 μs until the moment when the shock front reached the back end of the film.

Experiments were conducted with 64 μm thick PZT 95/5 films having electrode areas 25, 38, 50, 75, and 100 mm2 (films length of 4, 6, 8, 12, and 16 mm, respectively). Eight experiments were conducted for each film electrode area. Figure 7 shows the experimentally obtained breakdown fields as a function of the shock wave transit time prior to breakdown. The experimental results were fitted in Fig. 7 to a power law [Eq. (2)]. The best fit was for the exponent 0.56 ± 0.05.

FIG. 7.

Experimentally obtained breakdown fields, Eb, as a function of shock transit time prior to breakdown, tb, for transversely shock-compressed 64 μm thick PZT 95/5 films along with the fitted curve.

FIG. 7.

Experimentally obtained breakdown fields, Eb, as a function of shock transit time prior to breakdown, tb, for transversely shock-compressed 64 μm thick PZT 95/5 films along with the fitted curve.

Close modal

Breakdown in solid dielectrics is a complex phenomenon that involves a range of processes. Under ambient conditions, it is understood to involve contributions from several different elementary processes including the injection of electric charge carriers, their movement in the electric field, the resulting heating effects, defect formation within the material, avalanching, and other non-linear phenomena. Electrical breakdown in shock-compressed ferroelectrics involves short-time breakdown in solids under impulse conditions. It is different from D.C. breakdown with long-term degradation under a high electric field. High-pressure shock loading is an additional factor that might have an impact on electrical breakdown.

The results of the analysis of the experimental data [Fig. 5] revealed a similarity of the breakdown-field vs thickness dependence for shock-compressed ferroelectric films to Eq. (1) with an exponent of 0.256 ± 0.021. According to the theoretical model,29,30 an exponent of η = 0.25 in Eq. (1) implies the presence of a tunnel mechanism for the injection of electrons from the negative electrode into a dielectric and in addition, implies strong electron–phonon scattering, while η = 0.3 implies that Schottky barriers dominate the breakdown behavior. Thus, the initiation of breakdown in shocked ferroelectric films is very likely related to a tunneling injection of electrons from the negative electrode and strong electron–phonon scattering associated with an exponent of 0.25.

The observed exponential dependence of the breakdown initiation field on the ferroelectric film thickness [Fig. 5] also holds for data obtained from other materials. Eb(d) for data from the experiments reported here are plotted in Fig. 8 along with breakdown fields previously obtained for shocked 0.27PIN-PMN-0.26PT ferroelectric crystals14,15 and bulk PZT 95/5 and PbZr0.52Ti0.48O3 doped 1% Nb2O5 (PZT 52/48) ferroelectric ceramics37 of different thicknesses.

FIG. 8.

Experimentally obtained breakdown fields for shock-compressed ferroelectric materials vs ferroelectric thickness. PZT 95/5 films (triangles) were investigated in this paper. Raw data for PIN-PMN-PT single crystals (squares) were reported in Refs. 14 and 15. Raw data for bulk PZT 95/5 (diamonds) and PZT 52/48 (circles) ceramic elements were reported in Ref. 37.

FIG. 8.

Experimentally obtained breakdown fields for shock-compressed ferroelectric materials vs ferroelectric thickness. PZT 95/5 films (triangles) were investigated in this paper. Raw data for PIN-PMN-PT single crystals (squares) were reported in Refs. 14 and 15. Raw data for bulk PZT 95/5 (diamonds) and PZT 52/48 (circles) ceramic elements were reported in Ref. 37.

Close modal

The loading arrangement for bulk ferroelectric ceramics37 and ferroelectric single crystals14,15 was similar to that used in these investigations. It utilized a high explosive shock compression scheme. Ferroelectric specimens were encapsulated within urethane bodies and shock loaded perpendicular to the polarization direction. The shock wave front had almost planar geometry, and the shock pressure was in the range of 3 GPa.

In these experiments,14,15,37 the ferroelectric specimen thickness was the only variable parameter. Bulk PZT 95/5 and PZT 52/48 ferroelectric ceramic specimens37 and 0.27PIN-PMN-0.26PT ferroelectric single crystals14,15 were fabricated by TRS Technologies Inc. The grain size of PZT 95/5 and PZT 52/48 bulk ceramics37 was 4 ± 1 μm. The electrodes of PZT 95/5 and PZT 52/48 bulk ceramics specimens were silver. The electrode surfaces were completely covered. The 0.27PIN-PMN-0.26PT ferroelectric single crystal specimens14,15 were single-grain, i.e., single crystals. Vacuum-sputtered Cr/Au films were deposited on the desired surfaces as electrodes, covering the full surface.

The experimental results and fitting curves plotted in Fig. 8 indicate that despite different structures (single crystal vs ceramic), different chemical compositions, and different mechanisms of shock-induced depolarization (domain wall motion or phase transformation), the breakdown-field-on-thickness dependences for shock-compressed PZT 95/5 films, 0.27PIN-PMN-0.26PT single crystals, and bulk PZT 52/48 and PZT 95/5 ceramics can be represented by straight lines with very close slopes, on a log–log scale. Therefore, these breakdown-field-on-thickness dependences can be described by the exponential relationship in Eq. (1) with η = 0.22 ± 0.03.

These results are all consistent with breakdown in shock-compressed ferroelectric films, ferroelectric single crystals, and bulk ferroelectric ceramics being initiated by tunneling electrons from the negative electrode into the shocked ferroelectric material. This initiation mechanism does not change significantly over a wide range of ferroelectric thicknesses or with compositional and structural differences in the materials studied.

The breakdown-field vs thickness dependence was experimentally observed for a variety of solid dielectrics under ambient conditions.25–30,50–52 Based on these results [Fig. 8], one can conclude that this dependence can be extended to shock-compressed ferroelectric films, bulk ferroelectric ceramics, and ferroelectric single crystals.

The current density of the electrons injected into the ferroelectric material due to the tunnel effect is given by the Fowler–Nordheim equation,53,54
j e ( ϕ , E ) = q e 16 π 2 h ( q e E ) 2 ϕ exp [ 4 ( 2 m ) 1 / 2 ϕ 3 / 2 3 h q e E ] ,
(3)
where je is the density of field emission current, E is the microscopic electric field at the negative electrode, ϕ is the electron work function of the electrode material, h is Planck's constant, and qe and m are the charge and the effective mass of the electron, respectively.

According to Eq. (3), E and ϕ are the main parameters that determine the current density of the tunneling electrons and, correspondingly, the probability of breakdown initiation. The microscopic electric field depends on the macroscopic field and field enhancement factors, β, of nanoprotrusions on the negative electrode surface (E = βEb).31,32,55–60 The initiation of electrical breakdown due to the field electron emission from nanoprotrusions limits the reliability of high voltage devices.31,32,55–60 The field enhancement factor of nanoprotrusions on metallic surfaces varies from 30 to 1200.55–60 At macroscopic electric fields on the order of 10 kV/mm [Figs. 5 and 8], the microscopic electric field at the negative electrode of ferroelectric specimen can be in the range of 103–104 kV/mm, providing an intensive field electron emission.

It is possible that reducing the field enhancement through smoothing the negative electrode surface facing the ferroelectric material and using metal with a high ϕ(Pt, Pd, Ir) for the negative electrode61 could suppress the tunnel current density and increase the breakdown field.

The initiation of breakdown is followed by the breakdown development stage, which ends in the short-circuiting of the electrodes of the dielectric. An electron ionization avalanche is one of the mechanisms of the development of breakdown in solid dielectrics.25,29,30 This breakdown development mechanism was observed in a variety of solid dielectrics under high pulsed electric fields under ambient conditions.31,32

In our experiments, breakdown voltage fall times of PZT 95/5 films (which are associated with the final stage of the breakdown development) ranged from 100 to 300 ns [Figs. 4 and 6]. It is longer by two orders of magnitude than the time of the breakdown development due to an electron ionization avalanche.31,32

The dependence of the breakdown field of shocked PZT 95/5 films on the shock transit time observed in this study is one of the characteristics of the breakdown development stage. A longer shock transit time prior to breakdown corresponds to a lower breakdown field of shocked PZT 95/5 films [Fig. 6]. This observation is in an agreement with the report by Lysne,38 who had observed an increase in the breakdown field of shock-compressed bulk PZT 65/35 ferroelectric ceramics with the shortening of the shock transit time prior to breakdown.

The results of the analysis of the breakdown-field dependence on shock duration for PZT 95/5 films [Fig. 7] fit Eq. (2) with an exponent of 0.56 ± 0.05; thus, the results are consistent with a thermal runaway model. If the development of breakdown in shocked ferroelectric films was only based on collision ionization induced by a high electric field, there should have been no observed significant changes for the breakdown field in PZT 95/5 films at different shock wave transit times prior to breakdown. This is because in a collision ionization dominated process, the breakdown field does not depend on the shock transit time prior to breakdown (breakdown delay time) at a given ferroelectric thickness. However, if thermal runaway is a part of the breakdown process in shocked films, the change in shock wave transit time prior to breakdown would result in a change in the breakdown field and breakdown voltage.

In Fig. 9, the breakdown field of PZT 95/5 films as a function of shock wave transit time obtained in this study is plotted on a log–log scale, along with breakdown fields of shocked bulk PZT 95/5 and PZT 52/48 ceramics for different shock transit times prior to breakdown experimentally obtained in Ref. 62.

FIG. 9.

Experimentally obtained breakdown fields, Eb, as a function of shock transit time prior to breakdown, tb, for shock-compressed ferroelectrics. PZT 95/5 films (triangles) were investigated in this paper. Raw data for bulk PZT 95/5 (diamonds) and PZT 52/48 (squares) ceramic elements were reported in Ref. 62.

FIG. 9.

Experimentally obtained breakdown fields, Eb, as a function of shock transit time prior to breakdown, tb, for shock-compressed ferroelectrics. PZT 95/5 films (triangles) were investigated in this paper. Raw data for bulk PZT 95/5 (diamonds) and PZT 52/48 (squares) ceramic elements were reported in Ref. 62.

Close modal

The investigated PZT 95/5 and PZT 52/48 bulk ceramic specimens62 had identical geometry. The breakdown delay time was the only variable parameter in these experiments. The ceramic specimens were fabricated by TRS Technologies Inc. The grain size of PZT 95/5 and PZT 52/48 bulk ceramics62 was 4 ± 1 μm. The loading arrangement utilized a high explosive shock compression scheme similar to that used in these investigations. Ferroelectric specimens were encapsulated within urethane bodies and shock loaded perpendicular to the polarization direction. The shock pressure was in the range of 3 GPa.

The experimental results [Fig. 9] indicate that the breakdown-field vs shock transit time dependences for shocked films and bulk ceramics can be represented by straight lines in log–log coordinates with slopes ranging from 0.47 to 0.56. These breakdown field on transit time dependences can be described by the exponential relationship in Eq. (2) with the exponent 0.52 ± 0.05. These results support the hypothesis that the development of breakdown in shock-compressed ferroelectric films and bulk ceramics is related to thermal runaway.

The shock front enters the ferroelectric specimen and impulsively increases the pressure to gigapascal levels in a thin layer of the ferroelectric material. Shock loading produces a state of uniaxial strain, where there is a compressive strain component in the direction of shock propagation and zero strain components perpendicular to this. Uniaxial strain is present until rarefaction waves enter the specimen (expansion waves coming in from free surfaces or interfaces).63,64 Uniaxial strain produces a state of triaxial compression, with the compressive stress component in the shock wave propagation direction being higher than the compressive stress components perpendicular to the shock propagation direction. The hydrostatic stress is the average of the three principal stress components. Hydrostatic stress drives a volume reduction that is associated with a polar to non-polar phase transformation in PZT 95/5. This fully depolarizes the PZT 95/5.

The rarefaction waves arrive behind the shock front and decompress the material in the directions perpendicular to the shock front propagation. Rarefaction waves are the mechanism by which a material returns to ambient pressure after compression.63,64 The rarefaction wave decreases the pressure over a time interval that increases with the propagation distance, resulting in the cracking and mechanical destruction of a material. The rarefaction behavior depends on several factors, and the resulting stress field anisotropy is complicated.

High-speed photographs of the operation of the shock wave ferroelectric generator65 showed that there was mechanical fragmentation of the region of the ferroelectric element behind the shock wave front due to the rarefaction waves. The macrofragmentation occurred 8 μs after the shock front passed through the region. There were numerous cracks clearly visible in the ferroelectric/urethane interface and ferroelectric element.

Figure 10 shows the CALE results for the compressive stress, Syy, parallel to the direction of shock wave propagation on the axis of a 64 μm thick PZT 95/5 film as a function of time during shock wave transit through the film. The location of this point corresponds to the position of shock front in Fig. 3(a). In Fig. 10, Syy stress stays at its peak on the axis of the ferroelectric film for 70 ns and starts to reduce to zero level due to the rarefaction waves. The simulation results indicate that rarefaction waves decompress the ferroelectric material behind the shock front during nanosecond intervals of time, resulting in the formation of microscopic cracks in the body of the ferroelectric specimen.

FIG. 10.

Compressive stress, Syy, parallel to the direction of shock wave propagation vs time on the axis of a 64 μm thick PZT 95/5 film at 0.5 mm from the front end of the film (where the shock wave entered the film).

FIG. 10.

Compressive stress, Syy, parallel to the direction of shock wave propagation vs time on the axis of a 64 μm thick PZT 95/5 film at 0.5 mm from the front end of the film (where the shock wave entered the film).

Close modal

In the experimental results obtained in this work, the breakdown delay times ranged from 0.5 to 1.1 μs [Fig. 6]. However, cracks observed in the high-speed photographs65 were macroscopic and likely preceded by microscopic cracking of the shocked ferroelectric material not visible in the photographs because of the lack of photographic resolution available. These microscopic cracks could provide conditions for the formation of conductive pathways (conductive channels) within the shocked ferroelectric material.

When the voltage and the corresponding electric field generated by shocked ferroelectric elements rise to a level that provides an intensive field electron emission from the negative electrode, electrons start tunneling into the ferroelectric material and initiate currents in microscopic channels formed in the compressed zone of the ferroelectric element. The experimental results discussed herein for ferroelectric films (this work), bulk ferroelectric ceramics, and relaxor ferroelectric single crystals [Fig. 8] are consistent with the existence of this mechanism of the initiation of breakdown in shock-compressed ferroelectrics.

The development of breakdown is likely related to Joule heating within microscopic channels by flowing current. This breakdown mechanism is associated with an increase in the microchannel temperature and conductance, which leads to the short-circuiting of the electrodes of the ferroelectric element. This thermal mechanism of breakdown development is consistent with both the breakdown field on shock transit time dependence experimentally obtained in this study for shocked ferroelectric films and with experimental results obtained in44 for shock-compressed bulk PZT ceramics [Fig. 9].

The thermal mechanism of the breakdown development in shocked ferroelectrics is also in agreement with the results of recent studies of electric charge and energy losses in shock-compressed bulk PZT 95/5 and PZT 52/48 ceramic elements operating in the high voltage mode.66 The results of these studies indicate that electric currents flowing through microscopic conductive channels formed in the compressed zone of shocked bulk PZT ceramic elements can cause losses of stress-induced electric charge and electric breakdown. The analysis of the experimental data made it possible to obtain the breakdown criterion based on the integral of specific current action,66  j2tb = λ (where j is the density of current flowing in the microscopic channels formed in the compressed zone of the ferroelectric element, λ is the material dependent constant, and tb is the shock transit time prior to the breakdown). It was shown66 that the integral of specific current action does not change significantly for shocked PZT 95/5 and PZT 52/48 ceramics in a wide range of the shock wave transit times from 0.8 to 6.5 μs. This lends strong support to the hypothesis that a thermal mechanism participates in the development of breakdown in shocked ferroelectric materials.

There is a difference between thermal runaway breakdown development in solid dielectrics under ambient conditions and in ferroelectrics under high-pressure shock loading. Under ambient conditions, the microscopic conducive channels are formed in the body of a dielectric due to a high electric field, while in shocked ferroelectrics, microchannels are formed mainly due to a high mechanical stress.

The electrical breakdown of shock-compressed ferroelectric materials was experimentally investigated. Based on the obtained data, breakdown in shocked ferroelectrics can be explained by a hybrid mechanism in which breakdown is initiated by field emission electrons tunneling from the electrodes into the shocked ferroelectric material, and it develops due to the Joule heating of microscopic conductive channels formed in the compressed zone of ferroelectric specimens. The analysis of experimental data obtained in this study, along with results previously obtained for relaxor ferroelectric-based single crystals and bulk ferroelectric ceramics, indicates that the breakdown processes in a variety of shock-compressed ferroelectric materials are consistent with this dual mechanism. This dual mechanism explains the concurrent exponential dependence of the breakdown field on the ferroelectric thickness and the shock transit time prior to breakdown. It appears the chemical compositions and the types of crystalline unit cells of the materials do not have a significant impact on the breakdown mechanism. The magnitude and dynamics of mechanical stress applied to the ferroelectric elements, and the electric field generated by the elements under high-pressure shock loading are the main factors affecting breakdown in shock-compressed ferroelectrics. The thickness dependent breakdown law that was validated experimentally for a variety of solid dielectrics under ambient conditions can be extended to shock-compressed ferroelectric films, bulk ferroelectric ceramics, and ferroelectric single crystals. Different from solid dielectrics under ambient conditions, the formation of microchannels in the body of ferroelectrics is not due to a high electric field but mainly due to rarefaction waves decompressing the shocked ferroelectric material. This could lower the breakdown field of shock loaded ferroelectrics in comparison to dielectrics under ambient conditions. The obtained results are important for the understanding of the breakdown mechanism in shocked ferroelectric materials, the optimization of parameters of high voltage ferroelectric systems, and the prediction of the generated voltage amplitudes.

The authors have no conflicts to disclose.

Sergey I. Shkuratov: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (lead); Writing – original draft (equal); Writing – review & editing (equal). Jason Baird: Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Vladimir G. Antipov: Formal analysis (equal); Investigation (equal); Writing – original draft (equal). Jay B. Chase: Formal analysis (equal); Software (lead); Writing – original draft (equal). Christopher S. Lynch: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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