Ferroelectric crystals for the low-voltage operation of surface dielectric barrier discharges
Michael J Johnson¹, David B. Go¹ , ²*
¹Department of Aerospace and Mechanical Engineering
²Department of Chemical and Biomolecular Engineering
University of Notre Dame, Notre Dame, IN 46556, USA
*Author to whom the correspondence should be addressed, electronic mail: dgo@nd.edu
Supplemental Material
1. Ferroelectric Crystal Switching, Hysteresis, and Poling
A ferroelectric is defined as a material that has a spontaneous polarization that can be switched with an applied electric field. For polarization switching to be possible, ferroelectrics have at least two possible stable directions of polarization. The presence of ferroelectric switching makes the polarization of these materials a function of its history, giving it a unique hysteresis loop. The relationship between the applied electric field and the polarization of a ferroelectric compared to a dielectric is shown in Fig. S1. Ferroelectric switching alters the initial state of the ferroelectric, resulting in two independent curves depending on which direction the polarization originated.
Within a ferroelectric material, different regions can be formed that have different polarizations. A domain is defined as a homogenous region of a ferroelectric in which all unit cells within the domain have the same polarization orientation. Depending on the material, these domains can take many different forms depending on if the unit cells are in a regular geometric lattice or completely amorphous. When first grown, the orientation of each unit cell will align itself to reduce the electric field within the crystal. This process generates many small domains that effectively cancel each other out. The electric field within the crystal at the edges of these domains is very large, especially in single crystal materials. To remove these domains, ferroelectric crystals are usually poled by applying a large electric field to the ferroelectric in order to align the direction of polarization of each unit cell.
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Figure S1. The relationship between the applied electric field and the polarization of a dielectric and a ferroelectric.
2. Properties of Tested Ferroelectric Materials
Table S1. Various parameters for different ferroelectric materials and the relevant reference.
*provided by supplier material coercive field (V/mm) relative permittivity,
 lithium niobate (LiNiO lithium tantalate (LiTaO
3 barium titanate (BTO)
3
)
)
2300
1
1700
2
500
3
30
2
43.5
2
1250
4
PMN PT 250 * 4000 *
PVDF 50000 5
3. Comparison of FBD and DBD Current and Voltage Characteristics
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Figure 2b in the main manuscript shows the voltage distortions and corresponding filament production that occurs with a FBD. To further investigate the switching behavior of the ferroelectric, two Au/Cr electrodes were deposited on the (001) faces of a 0.1 mm thick PMN PT
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sample where one electrode was grounded while the other had a sinusoidal voltage applied to it, as shown in Fig. S2a. It is important to note that no discharge will form in this configuration due to the sample being completely covered by the electrodes. The measured voltage across the
PMN-PT sample is shown in Fig. S2b. At certain points during each half cycle, a large shift in the measured voltage occurs. These shifts occur at roughly the same applied voltage each half cycle, which closely corresponds to the coercive field of PMN-PT. It is believed that these shifts are evidence of ferroelectric switching within the sample. The large spikes in Fig. S2b are similar to what was observed in Fig. 2b in the main manuscript, potentially indicating that the current filaments measured on the adjacent electrode were a direct result of ferroelectric switching within the sample.
Figure S2. (a) The configuration used to measure the behavior of a ferroelectric sample under an applied electric field, and (b) the measured voltage across the sample under the application of a
90 V, 1 kHz sinusoid across a 0.1 mm thick piece of PMN-PT.
At small cycle voltages (500 V), all current filaments in the FBD are accompanied by these voltage distortions which occur roughly once per cycle, as shown in Fig. 2b in the main manuscript. (A filament was defined as a spike in current that has an amplitude three times
3

larger than the noise in the circuit.) However, as the applied voltage increases in Fig. S3a to Fig.
S3b (800 V to 1100 V), multiple of these voltage distortions occur during a single cycle. These multiple distortions are likely due to polarization reversal occurring in different domains further from the driving electrode or from electric field enhancement at the triple point (the point at which the electrode, ferroelectric, and air intersect)
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. Note that at this stronger applied field some of the current filaments do not have corresponding voltage distortions. This behavior is similar in nature to a standard DBD, where numerous discharge filaments form with no voltage distortions as shown in Fig. S3c, suggesting the FBD becomes more DBD-like as the driving voltage increases. This could indicate that a transition occurs between a low-field ferroelectricdriven regime where the discharge is driven through disturbances on the ferroelectric surface due to ferroelectric switching to a high-field regime driven through triple point enhancement, mimicking common DBD mechanisms.
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Figure S3. (a) Current and voltage characteristics as a function of time for a FBD made with a
0.5 mm thick sample of PMN-PT being driven with a 1 kHz sine wave with an amplitude of (a)
800 V, (b) 1100 V. (c) Current and voltage characteristics as a function of time for a DBD made with a 30 µm thick piece of Kapton being driven with a 1 kHz sine wave at an amplitude of 1500
V.
4. Effect of Ferroelectric Thinning on Onset Voltage
By thinning the crystals, the FBD is improved in three ways: by reducing the voltage required to exceed the coercive field, by increasing the capacitance per unit area, which is inversely proportional to the crystal thickness d , and by enhancing the local electric field by
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decreasing the distance between the electrodes. To confirm the impact of thinner crystals on operating voltage, several LiTaO
3 samples where thinned to various different thicknesses and tested in our standard FBD configuration. As expected, the thinner crystals were able to produce discharges at much lower onset voltages than their thicker counterparts as shown in Fig. S4a.
The onset voltage for different LiTaO
3 thicknesses plotted against their respective capacitances is shown in Fig. S4b and follows a similar power-law relationship shown in Fig. 3b of the main manuscript with an exponent of -0.38 as compared to -0.34.
Figure S4. (a) Current measured on the auxiliary electrode as a function of voltage amplitude (at
1 kHz) for different thicknesses of lithium LiTaO
3 where (b) is a plot of the onset voltage against the capacitance per unit area for each corresponding thickness along with a power law curve fit
(solid line).
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