Electrocaloric Induced Retarded Ferroelectric Switching

Electrocaloric induced retarded ferroelectric switching

Till Buchacher1,2, Maciej Rokosz1,3, Robert Dorey2,4, Jeremy Allam5 and Andrew Gregory1.

1 National Physical Laboratory, Materials Division, Teddington, TW11 0LW, UK
2 University of Surrey, EPSRC CDT in MiNMaT, Guildford, GU2 7XH, UK
3 Imperial College London, Department of Materials, London, SW7 2AZ, UK
4 University of Surrey, Centre for Engineering Materials, Guildford, GU2 7XH, UK
5 University of Surrey, Advanced Technology Institute, Guildford, GU2 7XH, UK

Ferroelectric switching in bulk materials, at modest electric fields, is a relatively fast process, occurring on time scales of microseconds and less. A secondary retarded switching phenomenon also occurs on time scales of seconds and has previously been attributed to defect induced elevated energy barriers between polarisation states. As ferroelectric switching is a thermally activated process the barrier heights are also affected by temperature which is not constant in ferroelectric materials due to the electrocaloric effect. Here an additional EC induced retardation mechanism is proposed whereby EC induced temperature changes repeatedly temporarily prevent further FE switching during cooling cycles.

The electrocaloric effect recently gained a wave of interest for applications in solid state cooling, following large effects being reported in ferroelectric thin films. [1]–[3] Electrocaloric cooling is a promising alternative to current vapour-compression based refrigeration, combining the potential of major energy savings with unprecedented scalability for applications even in integrated circuits. Research on the effect however is still in its early stages. For the effect to be exploitable in refrigeration, materials need to be optimised towards various key properties such as maximum achievable temperature change and high cycle rates. [4] Such optimisation will require a deeper understanding of the underlying processes that cause the effect. However at present understanding of the electrocaloric effect is still sparse and largely based on thermodynamic approaches that focus on macroscopic and phenomenological treatment of the effect as opposed to mechanistic treatments. [4]–[8] Multiple authors have highlighted the weakness of this explanation and called for a greater understanding of the fundamental theory. [9]–[12] The electrocaloric effect is generally explained in terms of entropy changes in response to changes in the order of the material due to changes in polarisation. [4] In a normal dielectric these changes would be attributed solely to rearrangement of the dipoles. Ferroelectric materials however are known to have strong intrinsic coupling between their electrical, mechanical and thermal properties, so that changes in polarisation have not a single, but various origins and effects. [7], [8] As such one would expect the electrocaloric effect in these materials not to have a single, but multiple contributions. Similarly it has been previously shown that the piezoelectric response of the material contributes significantly to observed temperature changes via the piezocaloric effect. [13]

A major contributor to polarisation changes in ferroelectrics is ferroelectric switching. The theory of ferroelectric switching is well developed at present. Ferroelectric switching is known to be a thermally activated process which depends on factors intrinsic to the material, such as energy barriers between different polarisation states, but it has also an explicit dependence on external factors including the applied electric field and temperature. [14]–[17] An electrocaloric effect caused by ferroelectric switching therefore would create a feedback where the temperature change brought about by the electrocaloric effect affects the rate of ferroelectric switching and vice versa. Similarly the electrocaloric effect has previously been shown to directly affect other properties of ferroelectric materials. [18]

The feedback-coupling between electrocaloric effect and ferroelectric switching raises the question as to whether the electrocaloric effect can modify ferroelectric switching rates to an extent that is observable in the switching behaviour. Ferroelectric switching in a thin film material can occur at pico second [19] time intervals while for bulk material it occurs on nanosecond to microsecond timescales due to the lower breakdown strength of the materials which limits the field that can be applied. Conversely the measurement of the electrocaloric effect relies on thermal propagation within the material which results in a sub-second to second ‘delay’ in the measurement. However a secondary ‘retarded’ ferroelectric switching phenomenon, occurring on time scales similar to those of the electrocaloric effect, has also been observed. [20] This retarded switching has previously been attributed to an inhomogeneous energy barrier landscape in the material arising from defects in the lattice. [20] This is separate from domain wall creep which can be modelled semi-empirically using a (E0/E)µ relationship. [21], [22] Under an applied electric field of 20 kV/cm domain wall creep would be expected to occur at 3 µm/s where the coercive field is 10 kV/cm, µ is 0.6 [22] and the typical energy barrier is 0.5eV. For domains on the order of 500nm in diameter (as found in these materials) this would give a switching time in the range of 150ms which is approximately an order of magnitude faster than the observed retardation time constants and more associated with fast switching. For the case of an energy barrier landscape the size of the energy barriers required to fully account for the observed degree of retardation would need to be double those of normal switching. [16] As ferroelectric switching is known to be a thermally activated process it is possible to offer an alternate hypothesis, which reflects the similarities in time scales, where the origins of these elevated energy barriers are not only intrinsic to the material (e.g. energy barriers) but also a result of temperature fluctuations, and associated changes in switching dynamics, brought about by the electrocaloric effect.

To investigate this possible link between the electrocaloric effect and retarded ferroelectric switching disk shaped samples 10mm in diameter and 0.5mm in thickness of soft commercial lead-zirconate-titanate (PZT) near the morphotropic phase boundary (composition PZT5H), similar to compositions in which retarded switching was observed, were used. [20] All samples were supplied with silver electrodes fired on the two faces. Prior to the experiment the samples were fully poled by cycling the electric field to saturation levels (figure 1b) with maximum electric field of 20 kV/cm. The samples were then placed free standing between two brass needle contacts to avoid excessive heat loss into the electrical connections. One electrode was connected to a high-voltage amplifier and the other to a charge integrator with very long time constant (τ>106s). The high voltage amplifier was used to apply a low-pass filtered step electric field from ground to 20 kV/cm to the sample. The use of a low-pass filter allows the electric field to be applied at a controlled rate and with symmetrical rise and fall times. The experimental apparatus is depicted in figure 1a.

Figure 1: (a) Block diagram of the experimental apparatus. (b) Polarisation-electric field loop of the sample at 1Hz. Indicated is the electric field and polarisation change during the experiment.

Figure 1b shows the polarisation-electric field (PE) loop of the sample recorded during poling, showing the characteristic symmetrical shape of a soft PZT composition. Also indicated is the applied electric field during the experiment. The field was applied in a unipolar manner from 0kV/cm to 20kV/cm and back such that the material was cycled between its remanent polarisation state Pr and saturation polarisation Ps, without significantly altering the remanent polarisation state of the material. Minor hysteretic loops may give rise to a temperature change but this would be positive for both charging and discharging and would result in a gradual change in the mean temperature. This cycle is commonly used to assess the electrocaloric effect and activates predominantly the reversible switching contributions to polarizability while leaving the non-reversible switching contributions unaffected. When applying or removing the electric field the electrical charge and discharge of the sample was recorded using an oscilloscope connected to the charge integrator. Simultaneously the temperature development on the side of the sample was recorded using a high speed infrared camera (InfraTec ImageIR 8320 with a spectral range of 2 to 5.7 µm).

The time-dependent polarisation P(t) of the sample shows two components: a fast component, Pfast, at the rise time of the electric field and a much slower component, Pretarded, accounting for the retarded switching phenomenon. For each of the components there is a statistical variation, about a mean value, of the energy barrier for switching for different regions. The retarded component of switching can be described by a stretched exponential with a stretching exponent β. As such the stretched exponential is a phenomenological description of processes involving a range of timescales that can fit a wide range of phenomena over several orders of magnitude. The stretching exponent takes values between 1 and 0 and where a value of 1 corresponds to a single, defined time constant and small values correspond to a wide distribution of time constants. [23], [24]

For further analysis a least square algorithm was used to fit the recorded electrical behaviour with the equation 1 for the charging transient and equation 2 for the discharging transient.

P(t)=Pfast×1-e-tτfast+Pretarded×1-e-(tτretarded)β
/ Equation 1
P(t)=Pfast×e-tτfast+Pretarded×e-(tτretarded)β / Equation 2

For the case of electrical charging the leakage current (obtained from linear fitting after 500s) was subtracted from the measurement before fitting the equation. The leakage current originates primarily from the current passing across the sample surface [20] and results in a small amount of joule heating that manifest itself as a gradual drift in temperature over timeframes far in excess of the characteristic retarded switching times. Some joule heating may also originate from dielectric losses as a consequence of minor hysteresis loops during cycling. As in the case of DC leakage current such heating would contribute to the long term change in temperature.

Figure 2 shows the electrical response and directly measured electrocaloric effect induced temperature change during charge and discharge of the sample in response to a 20kV/cm step with a driving field rate of 5.7MV/cm.s.

Figure 2: Electric and electrocaloric response of the sample in response to an electrical field being applied (a) or removed (b) at a rate of 5.7MV/cm.s. The electrical response contains a fast contribution corresponding to the RC response as well as a second ‘retarded’ contribution.

A macroscopic temperature change of 80±12mK during rise and -80±12mK during fall of the electric field was observed on the sample. This temperature change is attributed to the electrocaloric effect and its magnitude is in agreement with previous measurements performed on similar compositions [6], [25]. In the electrical response the total amount of polarisation, Ptotal, shows only a minor difference of 0.25μC between charge and discharge that can be attributed to resistive loss. The amount of retarded switching, Pretarded, however shows a significant difference in the two cases.

Table 1: Fitting parameters of the retarded switching
Ptotal [μC] / Pfast[μC] / Τfast [ms] / Pretarded [μC] / τretarded [s] / β
Charge (heating) / 4.87±0.03 / 4.72±0.02 / 20±30 / 0.15±0.03 / 19.2±4.5 / 0.43±0.09
Discharge (cooling) / 4.62±0.03 / 4.10±0.02 / 9±30 / 0.51±0.02 / 8.8±1.1 / 0.40±0.03

During charging, when the electrocaloric effect causes heating, the amount of retardation observed is small (0.15±0.03μC). However during discharge, when the electrocaloric effect causes cooling, the amount of retardation is a lot larger (0.51±0.02 μC). The total amount of retardation is 3% and 11% during charge and discharge, respectively. Reflecting the dynamic nature of heat transfer within the system, temperature gradients may give rise to thermopolarisation effects. [26] However, such effects would be expected to be on the order of 2-3x10-17 C for the samples in this work, which is significantly lower than that observed here.

An alternative explanation could be gained by considering the effects of temperature on ferroelectric switching. A decrease in temperature would make it more difficult for ferroelectric switching to occur and would increase the level of retardation. An increase in temperature would provide more energy to the system and would make switching more easy and would not retard the switching at all, indicating that the retardation noted for the case of charging may be solely intrinsic in nature. This observation indicates that a wholly thermodynamic approach with purely intrinsic distributed energy barriers and overall temperature cannot fully explain the electrocaloric phenomena as it would not differentiate between heating and cooling scenarios. In addition for such a wholly thermodynamic approach, described by Arrhenius behavior, the required activation energies would be unfeasibly large and would not correspond with the observed temperature changes. It is proposed, instead, that much larger temperature changes are observed at a very local scale (sub domain size) and that these temperature changes are sufficient to prevent further switching until the local system has increased in temperature again. This allows both the observed difference between heating and cooling as well as providing sufficiently large changes in activation energy to prevent ferroelectric switching. Like the macroscopic EC effect the proposed large temperature changes are a result of significant entropy changes brought by local ferroelectric switching. Corresponding macroscopic ‘giant’ EC effects are not observed due to the self-terminating nature of the effect.

The time constants for the retarded switching are longer than would be expected (< 1s) if the retarded switching were controlled by thermal diffusion time (d2/α where d=0.5mm is the thickness and α=4×10-7m2/s [27] is the diffusivity). Instead a stop-start type of relaxation type behavior may occur whereby some switching would initially occur thereby preventing further switching due to the local cooling. On warming, controlled by thermal diffusion, further switching would occur only for it to cause a re-freezing of the system. These continued lock-unlock cycles would result a time constant that is longer than that associated with thermal diffusion on its own.

If a correlation does exist between the electrocaloric effect and retarded switching both phenomena should share similar behaviour in response to external driving conditions. The electrocaloric effect is known to scale with temperature, reaching its maximum values in the vicinity of the Curie temperature. [28] The electrocaloric effect is also known to have a strong dependence on the driving electric field rate. [29] While some consider the origin of the driving rate dependence to be due to adiabatic conditions only occurring at switching times less than thermal transit times, Rose et al. postulated a link between this dependence on driving field rate and the occurrence of a large electrocaloric effect via ferroelectric switching. [2]