Scaling effects in the alternating-current poling of thin PIN-PMN-PT single crystals

Relaxor-PbTiO₃ (PT) single crystals have been actively studied during the past few decades due to their unprecedented piezoelectric and dielectric properties^1–4 for electromechanical devices, including sonars, diagnostic imaging, nondestructive evaluations, sensors, actuators, and energy harvesting.^5–7 Although relaxor-PT single crystals such as Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃ (PZN-PT) and Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT) show ultrahigh piezoelectricity and electromechanical properties, their low coercive field (E_c) and low depolarization temperature, the so-called rhombohedral–tetragonal phase transition temperature (T_R–T), have limited their use in various applications.⁸ To meet increasing demands on high-power applications wherein heat generation hampers their uses, their low operational temperature should be improved. Being initiated by the investigations of Pb(Mg_1/3Nb_2/3)O₃-Pb(Zr,Ti)O₃ (PMN-PZT) and Pb(In_1/2Nb_1/2)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PIN-PMN-PT), the aforementioned issues are to some extent solved.⁹ Moreover, dopant elements are incorporated into relaxor-PT crystals to further enhance the thermal endurance and mechanical quality factor.⁹ However, even though their thermal stabilities are eventually improved, their piezoelectric and dielectric properties tend to be degraded on the basis of the fact that high depolarization temperature and high electromechanical properties cannot be simultaneously achieved.^5,10 Therefore, it is necessary to further enhance piezoelectric and dielectric properties of these relaxor-PT single crystals with the minimized deterioration in depolarizing temperature.

The solutions to such a trade-off can be divided into two strategies: compositional and non-compositional. Here, the compositional enhancements indicate the modification of compositions or control of a dopant level. Though there has been a milestone on the compositional methods by inducing local structural heterogeneity,^4,11 their vulnerability to external stimuli is still under discussion. On the other hand, non-compositional enhancements are of considerable importance, in that the composition of piezoelectric crystals need not be modified, which is more economically costless. So far, several non-compositional approaches have been studied: (1) nano-electrode patterning and (2) poling. The former enables a non-uniform electric field, resulting in enhanced piezoelectric properties.^12–14 However, nanostructures should be fabricated by implementing lithography, making its feasibility doubtful in mass production. On the other hand, given that poling is indicative of a post-treatment by aligning ferroelectric domains and can be readily conducted, it is a promising candidate in current research directions. To make ferroelectric materials macroscopically piezoelectric, sufficient energy should be induced into ferroelectric materials. Therefore, the commonly used poling method, i.e., conventional direct-current (DC) poling, requires 2–3 times the coercive field for 5–30 min at elevated temperature, which is apparently time-consuming and cost-ineffective. In the meantime, it is worth noting that alternating-current (AC) poling, which was first demonstrated by Yamashita et al.¹⁵ and Yamamoto et al.,¹⁶ is taking center stage because further enhancements in dielectric and piezoelectric properties can be simply achieved by inducing 20–30 cycles of alternating current signals.

Several efforts to optimize the conditions of AC-poling have been actively made in relaxor-PT single crystals with respect to electric field, frequency, cycles, poling temperature, compositions, crystal orientation, vibration modes, and dimension.^17–23 Furthermore, it was reported that the transparency of relaxor-PT single crystals can be improved by AC-poling, which is highly useful for next generation applications.²⁴ Even though AC-poling conditions are well optimized in most cases, AC-poling on single crystals for high-frequency transducers wherein thin crystals are essentially required was not studied yet due to deterioration and inconsistency in their properties after poling.^25,26 Such degradation has been believed to be relevant to surface uniformity or the mechanical damaged layer, which inevitably emanates during sample preparations such as polishing and lapping.²⁷ Nevertheless, how the effects of surface morphology influence the optimization of poling conditions is still doubtful. In this study, AC-poling conditions of PIN-PMN-PT single crystals with respect to crystal thickness were first studied for high-frequency transducers. Here, the thickness of the crystals ranges from 0.06 to 0.16 mm, which were not commonly studied in other AC-poling literatures. A comparative experiment was then conducted to understand how surface morphology including surface roughness uniformity and damaged layer affects the poling effects of piezoelectric single crystals.

(001)-Oriented Pb(In_1/2Nb_1/2)O₃-Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (hereafter shortened as PIN-PMN-PT) single crystals were prepared by two different vendors. Here, the name of the vendors is arbitrarily labeled as vendor 1 and vendor 2 to avoid devaluating a specific vendor. It is well known that we need to pay more attention to directly compare two different types of crystals. Therefore, we carefully selected the crystals to minimize the lack of consistency based on their phase transition temperatures (so-called T_R-T) or Curie temperature (T_c). By comparing their T_c in dielectric permittivity spectra, we tried to avoid significant differences among the vendors (vendor 1: 152.2–159.7 °C and vendor 2: 149.1–155.7 °C) and thicknesses (0.16 mm: 153.4–159.7 °C, 0.1 mm: 149.1–152.8 °C, and below 0.1 mm: 152.2–155.7 °C). These differences tend to diminish in terms of T_c from the loss spectra. The crystals were diced into k_t mode (2 × 2 × t mm³, t = 0.16, 0.145, 0.1, 0.084, and 0.06 mm) with electrodes on the surface. To prevent an electric shortcut or breakdown, DC- and AC-polings were conducted in a silicon oil-bathed sample holder. The DC-poling was performed by applying 10 kV/cm for 300 s, while the AC-poling was carried out by bi-polar triangle signals, which were generated by a function generator (Agilent 33250A, Santa Clara, CA, USA) and amplified by a high-voltage amplifier (Trek, 609B, New York, NY, USA). In this work, the peak-to-peak electric field of 30 kV_pp/cm (8.9 kV_rms/cm) was adopted with different AC-field frequencies. All poling procedures were performed at room temperature (25 °C), and the crystals were annealed at 250 °C for 15 min before all poling processes with shorted top and bottom electrodes.

After each poling process, piezoelectric coefficient (d₃₃) and free dielectric permittivity (ε^T₃₃/ε₀) were measured by using a quasi-static piezo d₃₃ meter (Model ZJ-4B, Chinese Academy of Science, China) and multi-frequency LCR meter (Agilent 4294 A, Santa Clara, CA, USA) at 1 kHz, respectively. The surface roughness indicating the electrode surfaces of single crystals was measured by an atomic force microscopy (Dimension Icon, Bruker, Santa Barbara, CA, USA). The surface uniformity was relatively determined by the range of surface roughness on several different areas. Here, it should be noted that surface roughness is strongly dependent on the conditions of fabrication methods or individual's technical skills. Therefore, the crystals analyzed in the current work cannot represent all crystals manufactured from the vendors. The temperature-dependent dielectric permittivity and loss spectra of differently poled crystals were acquired by an LCR meter in the temperature range of 25–250 °C within a precise temperature controller (LTS420, Linkam, UK).

Figure 1 shows the piezoelectric coefficient and dielectric permittivity of unpoled, DC-poled, and AC-poled PIN-PMN-PT crystals with respect to their thickness and vendor. The solid and dash lines indicate the experimental results from vendor 1 and vendor 2, respectively. Here, the AC cycle number of all experimental data is 20 cycles, given that their properties were fully saturated when the number of cycles is 20 in our experiments. As the properties were enhanced when the frequency of AC electric field increases, the optimum frequencies were determined at their saturated properties. As depicted in the inset of Fig. 1(a), the optimum AC-frequency increases when the thickness is reduced, indicating more energy is required to optimize AC-poling. The reason for such tendency can be attributed to the increasing effects of the depolarization field.^28,29

How properties vary by poling will be described in terms of thickness, i.e., t ≥ 0.1 mm and t <0.1 mm. For t ≥ 0.1 mm, compared with the DC-poled counterparts, the piezoelectric coefficient of the vendor 1 AC-poled samples of t = 0.16 mm and 0.1 mm is 1470 (+16.7%) and 810 (−6.9%), respectively. Additionally, the dielectric permittivity of the vendor 1 AC-poled samples of t = 0.16 mm and 0.1 mm is 5480 (+30.8%) and 3100 (no change), respectively. In the case of vendor 2, the piezoelectric coefficient of the vendor 2 AC-poled samples of t = 0.16 mm, 0.145 mm, and 0.1 mm is enhanced as 1530 (+29.7%), 1490 (+23.1%), and 1130 (+14.1%), respectively. Moreover, the dielectric permittivity of the vendor 2 AC-poled samples of t = 0.16 mm, 0.145 mm, and 0.1 mm is improved as 5410 (+32.6%), 5710 (+38.9%), and 4610 (+32.5%), respectively. Between the two vendors, the discrepancies in the piezoelectric and dielectric properties were obtained after poling.

However, the results become more complicated when t is less than 0.1 mm. Even though the piezoelectric coefficient of the DC-poled samples for both t = 0.084 mm and 0.06 mm increases, their dielectric permittivity rather deteriorates at 10 kV/cm for 300 s. Provided the DC-poling conditions were not fully optimized, it is possible to achieve lower electromechanical properties. Therefore, the optimizations of DC-poling were further conducted with respect to poling time and amplitude of electric field. However, the properties were worse than the initial condition. Although slightly higher or similar properties can be obtained when less poling time or weaker electric field was applied, the current DC-poling condition was adopted for consistency. Nevertheless, AC-poling is still effective for t = 0.084 mm (d₃₃ = 1230 and ε^T₃₃/ε₀ = 5110), while notable differences cannot be measured for t = 0.06 mm (d₃₃ = 690 and ε^T₃₃/ε₀ = 2580), compared with their unpoled counterparts. In terms of practical perspectives, reliability issues including fatigue effects are of considerable importance due to the lifetime of applications. It has been generally accepted that degradations from fatigue effects are attributed to the formation of permanent microcracks, which lower electromechanical responses.³⁰ Therefore, in the case of thin samples, we expect more degradations, considering that the effects of microcracks are likely much larger than thick samples. To verify the hypothesis above, we will investigate the fatigue behaviors of thin AC-poled crystals as one of the future works.

It is generally accepted that surface morphology plays a key role in electric field distribution and ferroelectric domain evolution. As previously shown, a more intensified electric field can be induced from sharp intrusions on surface,³¹ and electric field distribution fluctuates along the interface between a piezoelectric layer and an electrode, resulting in different poling behaviors.¹² Moreover, it is widely known that ferroelectric domain nucleation is likely initiated from defects or edges on interface.³² As a result, surface morphology highly affects domain configurations, which are strongly relevant to piezoelectric and dielectric properties. On the basis of these two facts, comparative experiments were also carried out in order to explore why the discrepancies in properties arise. How surface roughness influences the properties can be deduced from Fig. 1. In this work, surface uniformity relatively defined by the range of surface roughness on several different regions is shown in Table I. Compared with vendor 2 crystals, vendor 1 crystals have a larger deviation in the surface roughness, indicating non-uniformity. The piezoelectric and dielectric properties of vendor 2 0.1 mm crystals are better than that of vendor 1 0.1 mm crystals. Furthermore, AC-poling is not apparently better than DC-poling for the non-uniform vendor 1 0.1 mm. In regard to the difference in the surface uniformity between vendor 1 0.1 mm (non-uniform) and vendor 2 0.1 mm (uniform), it is carefully argued that surface morphology plays a key role in poling effects to some extent. Such effect is also consistent in t < 0.1 mm. Interestingly, vendor 2 0.084 mm crystals show better enhancements after AC-poling, while vendor 1 0.06 mm crystals have worse dielectric permittivity after AC-poling. Even though the surface roughness of vendor 2 0.084 mm crystals is worse than that of vendor 1 0.06 mm crystals, the surface uniformity of vendor 2 0.084 mm crystals is better than that of vendor 1 0.06 mm. At this scale, it can be inferred that surface uniformity is more influential than surface roughness. A reason for the roughness-dependent results can be attributed to non-uniform electric field distribution, which induces different domain structures. In addition, the increasing effect of depolarizing field or damaged layer generated during sample preparations can be one of the factors involved in scaling effects, which also affects domain configurations. Further studies are required to fully verify these hypotheses.

To study how crystal thickness is related to ferroelectric phases and their stability against thermal energy, the temperature-dependent dielectric permittivity and loss spectra of AC-poled crystals were measured with respect to their thicknesses (Fig. 2). Peaks in the spectra imply changes in crystallographic symmetries or ferroelectric order, and different phases are usually evolved as a function of temperature. It is widely known that symmetry-bridging phases (monoclinic phases) play a critical role in high piezoelectricity.^3,11,33 So far, the origin of AC-poling is also believed to be the formation of intermediate phases, which was supported by XRD.¹⁷ However, due to a contradictory issue on the domain size dependence of piezoelectricity, the underlying mechanisms of AC-poling are still under discussion.²⁴ 

To avoid significant differences in the composition of crystals, we tried to measure crystals, which have similar T_c (vendor 2: 149.1–155.7 °C). It is interesting to note that different changes in crystallographic symmetries can be obtained when their thickness is reduced. In the case of 0.16 mm thick samples, there is only one peak at 106.9 °C before its T_c (153.4 °C). However, for 0.145 mm thick AC-poling samples, two peaks begin to be discerned at 104.1 and 107.5 °C before its T_c (149.1 °C), indicating that phase stability against temperature is different from 0.16 mm thick samples. When the thickness is more reduced, their phase transformation behaviors are dissimilar with the thicker samples. There is an additional peak at 121.5 and 125.0 °C in the permittivity spectra of 0.1 and 0.084 mm thick samples, respectively. The origins of these peaks are not clear, but we can carefully argue that the effects of surface morphology or residual stress may affect phase stability against thermal energy. Detail structural analysis is necessarily required to further speculate the current issues.

Considering the phase transformation behaviors above, the effects of surface morphology including a damaged layer are more influential when thickness decreases. This is because of the larger portion of the damaged layer inside thinner single crystals. Furthermore, it is also possible that surface morphology, which is negligible for thick samples, could be influential for thin samples. Such effects can retain or induce some specific phases, making their phase evolution complicated. Or increasing effects of residual stresses or depolarizing field originated from surface morphology could be one of reasons to explain scaling effects. Though mechanisms for how surface morphology affects poling processes are not fully verified in the current work, it was surely shown that several factors are responsible for scaling effects. Further investigations are required to fully understand underlying mechanisms. We hope this work provides a clue for how to minimize inconsistency in the piezoelectric and dielectric properties of thin relaxor-PT single crystals for high-frequency transducers.

In this work, the AC-poling conditions of PIN-PMN-PT single crystals for high-frequency transducers are optimized. The thickness of the crystals used in the current study ranges from 0.06 to 0.16 mm. The required AC-frequency to saturate piezoelectric and dielectric properties increases when the crystal thickness is reduced. For t ≥ 0.1 mm, compared with DC-poled counterparts, AC-poled samples apparently show enhancements in piezoelectric and dielectric properties. However, inconsistency in the poling effect can be obtained for t < 0.1 mm. Moreover, deterioration in dielectric properties can be found in DC-poled samples. Why such phenomena arise can be attributed to the surface morphology of single crystals. The samples with non-uniform surface roughness have worse performance than the samples with uniform surface roughness. Furthermore, changes in crystallographic symmetries are observed with respect to the crystal thickness. The effects of surface morphology including the damaged layer retain or induce specific phases, making its phase transformation sequences complicated. We hope that this work provides a clue for how surface morphology impacts AC-poling effects on relaxor-PT single crystals.

This work was primarily supported by Office of Naval Research (ONR) under Grant No. N00014-21-1-2058. This work was performed in part at Professor Jacob Jones' lab in the Materials Science and Engineering (MSE) Department and the Analytical Instrumentation Facility (AIF) at North Carolina State University, which was supported by the State of North Carolina and the National Science Foundation (Award No. ECCS-1542015). The authors would like to thank Jenny Zeng, Philip Cho, and Jon Mallari who helped with the sample preparations in this work.