Switching 70Pb(Mg_1/3Nb_2/3)O₃-0.30PbTiO₃ single crystal by 3 MHz bipolar field

Abstract

Polarization switching and associated electromechanical property changes at 3.0 MHz were investigated with and without a direct current (dc) bias for [001]_c poled 0.70Pb(Mg_1/3Nb_2/3)O₃-0.30PbTiO₃ single crystal. The results showed that the coercive field under a bipolar pulse at 3.0 MHz is 2.75 times as large as conventional defined E_c (2.58 kV/cm at 0.1 Hz), and a dc bias can further enlarge the driving field. Our results point to an innovative transducer operating mechanism at high frequencies since one could drive the crystal under much larger fields at high frequencies to produce much stronger signals from a small array element for deeper penetration imaging.

The ultrahigh piezoelectric coefficients and electromechanical coupling factors make relaxor-based ferroelectric single crystals such as binary (1-x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PMN-PT) and ternary (1-x-y)Pb(In_1/2Nb_1/2)O₃-yPb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PIN-PMN-PT) single crystals very attractive for high performance transducer applications.^1–4 Among these applications, the most important one is for medical ultrasound imaging transducers, which produced greatly improved ultrasonic images.^1,2,5–8 However, one key issue limits the device performance: the coercive field of PMN-PT single crystals is rather small (∼2.5 kV/cm) compared to the traditional Pb(Zr,Ti)O₃ (PZT) ceramics, which limits the maximum operating voltage of the device to produce a strong enough signal for deep penetration imaging. It is generally believed that the degradation of ferroelectric properties is closely related with the ferroelectric domain reorientations that occur near the coercive field.^1,2,9 Therefore, it is important to investigate the polarization switching behavior in order to improve the performance and reliability of devices made of PMN-PT single crystals.

Many researchers had studied the polarization behavior of ferroelectric single crystals.^1,2,9–14 Since polarization fatigue in a ferroelectric material severely limits its applications, the fatigue behavior of PMN-PT and PIN-PMN-PT crystals poled along various crystallographic directions had been investigated.^10–12 The internal bias of single domain and domain engineered PIN-PMN-PT:Mn single crystals was also investigated by measuring the polarization hysteresis loops.¹³ However, in those works, the applied ac electric fields (E) on the crystals were all in the low frequency range of 0.1–100 Hz. The hysteresis measurement will generate heat if the driving frequency is more than 500 Hz, which will invalid the data obtained since the coercive field becomes much smaller at higher temperatures. To date, the highest frequency used for the hysteresis loop study is limited to 1 kHz. Experimental studies on the polarization switching behavior in high frequency range (>1 MHz) on bulk ferroelectric had not been reported in the literature. On the other hand, many practical devices, such as medical ultrasonic imaging transducers, usually operate in the megahertz range. For example, for abdominal, obstetric, and cardiac imaging applications, the frequency range is usually from 1 MHz to 5 MHz.^1–8 Therefore, it is necessary to investigate the polarization switching behavior of these single crystals in the megahertz frequency range. The situation is very different from ferroelectric random memory application of ferroelectric thin films, in which complete reversal of polarization is needed and there is only 180° polarization reversal involved. Here, so long as a very small volume fraction of polarization is reversed, the transducer will no more be considered functional since it will change the signal processing conditions and degrade the imaging quality.

In this work, we defined a method to quantify such polarization switching behavior of ferroelectric materials under a bipolar high frequency ac electric field. The influence of the polarization switching process on electromechanical properties of PMN-PT single crystal at 3 MHz was quantified using this methodology. Then, we investigated the influence of a dc bias on the polarization switching behavior at 3 MHz by the superposition of a dc bias voltage with a bipolar burst signal. A transducer design strategy at high frequencies is established, which could greatly enlarge the driving range of PMN-PT single crystal transducers to produce larger signals from small transducer array elements to achieve deeper penetration depth imaging.

For medical imaging applications, the ultrasonic transducers are operated in the thickness mode of the piezoelectric element.^1–8 In our work, the [001]_c poled 0.70Pb(Mg_1/3Nb_2/3)O₃–0.30PbTiO₃ (PMN-0.30PT) single crystal (TRS Technologies, USA) was used to conduct the thickness mode tests. The samples were cut and polished into parallelepipeds with the dimensions of 3.20 mm (L) × 3.20 mm (W) × 0.26 mm (T). The sample was sputtered with gold electrodes on the pair of [001]_c surfaces and poled under a 5 kV/cm dc electric field in silicone oil for 20 min. After poling, the sample was immersed in silicone oil to prevent air breakdown during switching experiments at room temperature.

To investigate the influence of the polarization switching behavior of single crystals at high frequencies, an experimental setup was designed as illustrated in Fig. 1(a). A 3 MHz tone-burst signal is generated by a pulse modulator and receiver (MATEC 7700). To avoid unwanted self-heating of the sample in high frequencies, the burst signal with only 1–2 cycles of sine wave is externally triggered by a 4 Hz pulse from a signal generator (WaveTek 81 Pulse/Function Generator) as illustrated in Fig. 1(b). The burst signal of high frequency and low duty cycle is directly applied on the sample and simultaneously monitored by a digital oscilloscope (Tektronix TDS 680 C) by using an attenuator to enlarge the scope range. The positive V_p and negative V_n peak values of the burst signal were adjusted slowly with a small increment in each step. The bipolar electric field was applied on the sample from 0 to 12 kV/cm. In our experiments, the positive electric field (PEF) corresponds to the field along the original polarization direction and the negative electric field (NEF) corresponds to the field against the original polarization direction. Under each given electric field, the burst signal was switched off after 10 s, then the sample was discharged and switched to the port of impedance/gain-phase analyzer (HP 4194A) to measure the impedance spectra. Since the key material parameter is the electromechanical coupling factor for transducer applications,^1–4 the electromechanical coupling factor, k_t, was determined by the series resonant frequency f_s and parallel resonant frequency f_p of the thickness mode¹⁵

$${\mathrm{k}}_{\mathrm{t}}^2=\frac{\pi }{2}\frac{f_s}{f_p}\text{tan}\hspace{0.17em}\frac{\pi }{2}\frac{\Delta f}{f_p},$$ (1)

where $\Delta f=f_{\mathrm{p}}-f_s$. This electromechanical coupling factor k_t is very sensitive to the polarization change. We consider the high frequency coercive field to be the field level at which k_t starts to decrease.

FIG. 1.

Schematic of (a) experimental setup and (b) 3 MHz burst signal triggered by external pulse (burst signal period:T₁ = 333 ns, external trigger period:T₂ = 250 ms, positive peak value: V_p, negative peak value: V_n).

The conventional coercive field E_c was determined from the hysteresis loops of [001]_c poled PMN-0.30PT single crystal samples under a bipolar electric field with the magnitude of 10 kV/cm and frequency of 0.1 Hz. It was found that the remnant polarization P_r is 0.236 C/m² and the coercive field E_c is 2.58 kV/cm.

As shown in Figs. 2(a) and 2(b), the bottom and top electrodes of the sample were connected to the positive and ground port of the pulse generator, respectively. The positive half-period of the burst signal, which is larger than the negative one, corresponds to NEF of the sample since the polarization switching is the result of the action of NEF. For transducer applications, the key material parameter is the electromechanical coupling factor. In addition, the dielectric permittivity is a critical parameter in order to match the electrical impedance of transducer to that of driving electronics. Therefore, after each test, the electromechanical coupling coefficient k_t and dielectric coefficient ${\epsilon }_{33}^{\mathrm{S}}$ were determined by the impedance analyzer as shown in Figs. 2(c) and 2(d).

FIG. 2.

(a) Burst waveform and (b) the applied electric field on the sample; (c) electromechanical coupling factor k_t and (d) dielectric coefficient ${\epsilon }_{33}^{\mathrm{S}}$ of PMN-0.30PT single crystal under a bipolar electric field of different amplitudes.

Polarization reversal of the sample inevitably occurs when the bipolar electric field is increased to a critical level. It was found that the electromechanical coupling coefficient k_t and dielectric coefficient ${\epsilon }_{33}^{\mathrm{S}}$ keep constant values when the NEF was below 7.1 kV/cm, which means that no polarization switching occurred. When the NEF is above 7.1 kV/cm, k_t begins to decrease and ${\epsilon }_{33}^{\mathrm{S}}$ begins to increase slowly, which means that partial depoling started to take place. Due to the short time of the pulse, the polarization reversal only occurred in a very small volume fraction at the beginning, but this decrease of k_t already indicates the critical field level. This polarization switching field (7.1 kV/cm) at 3 MHz is 2.75 times of that of the coercive field E_c (2.58 kV/cm) measured at 0.1 Hz. When the NEF is in the range of 7.7 kV/cm < E < 10 kV/cm, k_t decreases and ${\epsilon }_{33}^{\mathrm{S}}$ increases rapidly. This means that the volume fraction of the reversed polarization increases significantly. Finally, k_t and ${\epsilon }_{33}^{\mathrm{S}}$ reach a stable value when the NEF is above 10 kV/cm, similar to the case of forced vibrations. Consequently, the electromechanical properties of the crystal deteriorated.

This observed phenomenon in the PMN-PT single crystal is related to the dynamics of polarization reversal under a varying bipolar electric field. In general, the polarization switching behavior is induced by domain wall motions and domain re-orientation.^1,2,9 The partial reversal of polarization may be understood as the result of the nucleation and growth processes of reversed domains. The new domain nucleation in the field direction can occur when the applied field is reaching a critical value. The expansion of the reversed domains is a process of new reversed domain nuclei continuously merging into a growing domain. The expansion rate is proportional to the nucleation rate at the domain walls. The partial polarization switching leads to the degradation of dielectric and piezoelectric responses.

Generally, domains in ferroelectric materials can be divided into 180° and non-180° domains. Under an electric field, domains try to align along the applied electric field. Non-180° domain wall motion can affect elastic, dielectric, and piezoelectric properties, whereas 180° domain wall motion only affects the dielectric properties. Both 180° and non-180° domains will reduce the effects of depolarizing electric fields, but only the formation of non-180° domains can minimize the elastic energy.^1,2,9 When the electrical field is <7.1 kV/cm, the crystal responses may be linear, while the dielectric and piezoelectric coefficients are attributed to the intrinsic contribution and reversible domain wall motions. With further increase of the electrical field (7.1 kV/cm < E < 10 kV/cm), the polarization reversal process begins. The switching rate of domains also changes at this stage. More domains switch to the directions inclined to the electric field. There is an increase in dielectric response, being related to more domain wall activities. When the NEF is above 10 kV/cm, k_t and ${\epsilon }_{33}^{\mathrm{S}}$ reach a stable value, which corresponds to the maximum switchable volume fraction of the domains at this frequency and this amplitude under a bipolar pulse. The reason is that domain switching is a time and field dependent nucleation-growth process, so that it depends strongly on the switching frequency.^16–18 At low frequencies, there is sufficient time for domains to align with the external electric field. With the increase of frequency, domain switching becomes harder to complete; we need to increase the field strength to make the switching process faster in order to follow the field change. As a consequence, the “apparent” coercive field E_c increases with the frequency, whereas at very high frequencies, the time is insufficient to complete the domain switching process, even with the increase of the applied electric field.

The polarization switching process of the single crystal at high frequencies is analogous to viscous vibrations. The electrical field force (F_E), elastic restoring force (F_R), and viscous force (F_V) act on the domains simultaneously.^16,19 After the removal of F_E, F_R forces the domains to return to their equilibrium position, while F_V, which is proportional to the domain motion speed, provides a drag to the domain wall motions. At lower frequencies, the field-on time is much more than the domain wall relaxation time, the relatively slower domain wall speed does not provide significant F_V, and more back-switching will occur under a reversed field. Consequently, the coercive field is smaller at low frequencies. With the increase of frequency, the time of F_E “on” becomes shorter, which makes the domain reversal more difficult, so that the “apparent” coercive field (at which the domain switching occurs) increases. In other words, it takes much higher field to cause the back switching of polarization at higher frequencies.

To enhance the reliability of the transducer at high frequencies, the influence of different dc bias on the polarization switching behavior was investigated. In this work, the top and bottom electrodes of the sample were connected to the positive and ground port of the pulse generator, respectively. The combined signal can be regarded as the superposition of a dc bias and a burst signal with the same positive and negative peak values. As shown in Fig. 3(a), the positive peak V_p = 185.9 V of the burst signal equals to the negative peak V_n = 185.9 V without the dc bias. The polarization switching starts when the NEF is about 7.1 kV/cm as shown in Fig. 3(b).

FIG. 3.

(a) Burst waveform applied on the sample without dc bias (V_p = 185.9 V, V_n = 185.9 V); (b) electromechanical coupling factor k_t of PMN-0.30PT single crystal vs. field amplitude.

The situation under a dc bias field is shown in Fig. 4(a). The positive peak V_p = 284.4 V of the burst signal is larger than the negative one V_n = 185.1 V. The burst signal is equivalent to the superposition of a rectangular pulse with the amplitude of 49.7 V and a burst bipolar signal with the effective amplitude of V_p = V_n = 234.8 V. This means that there is a positive dc bias of 49.7 V applied on the sample. From Fig. 4(b), one can see that the polarization switching starts when the NEF is at 7.1 kV/cm; meanwhile, the PEF reached 10.94 kV/cm. This means that the driving voltage V_pp can be increased from 371.8 V (without dc bias) to 469.5 V, with an increase of 97.7 V under the action of the positive dc bias of 49.7 V. This is an important finding because one could utilize a positive dc bias to enlarge the driving range so as to produce stronger ultrasonic signals for deep penetration imaging under a high frequency bipolar electric field.

FIG. 4.

(a) Burst waveform applied on the sample (V_p = 284.4 V, V_n = 185.1 V), which is equivalent to the superposition of a rectangular pulse with an amplitude of 49.7 V and a 3 MHz tone-burst signal with the amplitude of V_p = V_n = 234.8 V; (b) electromechanical coupling factor k_t of PMN-0.30PT single crystal vs. the ac field amplitude. The critical magnitudes of the positive and negative fields reached different levels.

In summary, the influence of the polarization switching process on electromechanical properties of single crystal under high frequency bipolar electric field was experimentally investigated based on a criterion defined in this work. Our results showed that the polarization switching field at 3 MHz is 2.75 times as large as the coercive field E_c (2.58 kV/cm) measured at 0.1 Hz. Most importantly, we showed that the allowable driving field range can be enlarged substantially with the increase of a positive dc bias, which provides a useful guidance on the driving strategy of medical imaging transducers, and to enhance the reliability of high-frequency transducers. With the help of a bias field, a larger driving ac field can be applied, which produces larger signals from a small array element, so that the deep penetration ultrasonic imaging can be achieved. Our experimental results will also provide useful data for more in-depth theoretical analyses on the switching mechanism of single crystal at high frequencies.