One-Dimensional Polarization Dynamics in Ferroelectric Polymers

Apr 22, 2019 - For ferroelectric polymers, n is usually considered as an arbitrary fitting parameter, and the reported values are noninteger that vary...
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Letter Cite This: ACS Macro Lett. 2019, 8, 525−529

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One-Dimensional Polarization Dynamics in Ferroelectric Polymers Saleem Anwar†,‡ and Kamal Asadi*,† †

Max-Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany School of Chemical & Materials Engineering, National University of Sciences & Technology, Sector H-12, Islamabad, Pakistan

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‡

ABSTRACT: Despite the realization of ferroelectricity in the δ-phase of poly(vinyleden difluoride) (PVDF) nearly four decades ago, the dynamics of polarization switching has not been studied yet. Here, we unravel the polarization switching mechanism as a onedimensional process that is nucleated by a 90° rotation of a CH2−CF2 repeat unit, forming a kink with reversed dipole along the polymer chain. The kink subsequently propagates in time, yielding full polarization reversal along the chain while preserving TGTG′ chain conformation. We show that the domain wall mobility in δ-phase PVDF is faster than both conventional ferroelectric β-phase PVDF and its copolymers with trifluoroethylene, P(VDF-TrFE). The switching time at infinite electric field for δ-phase PVDF is ten times faster and amounts to 500 ps. Fast switching dynamics combined with the low voltage operation and high thermal stability of polarization make δ-PVDF a suitable candidate for microelectronic applications.

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theory. The switching dynamics is usually described by the model developed by Ishibashi and Takagi,16 the so-called KAI model, which rests on the classical statistical theory of nucleation and unrestricted domain growth, as described by Kolmogorov17 and Avrami.18 The KAI model assumes that polarization switching is stepwise and takes place in four steps: (1) nucleation of a reversed dipole region, (2) growth of the nucleus in the direction of the applied electric field and formation of adomain, (3) transversal growth, and (4) coalescence of the domains with reversed polarization. The KAI model gives the temporal behavior of polarization, ΔP(t), under a constant applied field as ÄÅ nÉ Ñ ÅÅÅ ij t yz ÑÑÑ j z Å ΔP(t )/2Pr = 1 − expÅÅ−jj zz ÑÑÑ ÅÅ j t0 z ÑÑ ÅÇ k { ÑÖ (1)

erroelectric poly(vinyleden difluoride) (PVDF) has been suggested for a myriad of applications in microelectronic devices, ranging from energy generation and storage to memory devices.1,2 PVDF exists in five crystalline phases: α-, β-, δ-, ϒ-, and ε-, of which the α-phase is not ferroelectric, and the β- and δ-phases show stable ferroelectric behavior.3−5 Fabrication of ferroelectric PVDF thin films, as required for microelectronic applications,6−8 is challenging because solution-processed PVDF typically crystallizes in a centrosymmetric nonpolar α-phase, as shown Figure 1a.9 Recently, ferroelectric thin films of δ-PVDF, an overlooked polymorph proposed nearly four decades ago, have been obtained upon electro-forming by applying an electrical pulse larger than 200 MV/m, on a neat α-phase PVDF thin film.8,10 The electric field reorients every second chain in the α-phase crystals, such that the dipole component of the reoriented chain points 180° away from its original position, as shown in Figure 1b. This transformation preserves the TGTG′ conformation but breaks the antipolar arrangement and induces a dipole in the unit cell.11 Therefore, ferroelectric δPVDF has high thermodynamic stability with Curie temperature that is above the melting temperature, which is highly advantageous for applications.8,12 For prediction and optimization of the envisioned ferroelectric devices,13 understanding of dipole switching mechanism and its dynamics is critical.14,15 Despite the attention that ferroelectric δ-PVDF has received for application in microelectronic devices, the mechanism for polarization reversal, polarization dynamics, and the switching mechanism is still unknown. To the best of our knowledge, there is no experimental study on the switching dynamics of δ-PVDF. To understand the mechanism of polarization switching, electrical measurements are usually performed on ferroelectric capacitors, and the recorded polarization transients are analyzed within the framework of nucleation and growth © XXXX American Chemical Society

where n is the Avrami index or dimensionality parameter, and t0 is a characteristic switching time that depends on electric field following Merz Law19 ÅÄÅ E ÑÉÑ t0 = t∞ expÅÅÅÅ act ÑÑÑÑ ÅÅÇ E ÑÑÖ (2) where t∞ is the switching time at infinite electric field and Eact is the activation field. The KAI model has been extensively employed to describe the switching dynamics for a wide range of ferroelectric materials such as single crystals,20,21 epitaxial inorganic thin films,22 as well as polymers.23,24 The Avrami index n determines whether the polarization dynamic is one-, two-, or three-dimensional.16 The dimensionality of the domains therefore should take only integer values; the value is 3 for single crystals and 2 for epitaxial thin films and 1 for Received: March 6, 2019 Accepted: April 15, 2019

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DOI: 10.1021/acsmacrolett.9b00166 ACS Macro Lett. 2019, 8, 525−529

Letter

ACS Macro Letters

ization switching mechanism in δ-PVDF would provide a fundamental understanding of the processes responsible for ferroelectric properties in organic ferroelectrics and is helpful in the design of ferroelectric devices based on organic materials. The α-phase PVDF has a distinct spherulitic structure. The inset of Figure 1c shows the AFM height image a typical αphase PVDF with spherulites of an average area of 5 ± 1 μm2. The films are smooth and clear with rms roughness value well below 20 nm. As-prepared α-PVDF capacitors are not ferroelectric. At low fields, below 200 MV/m, a typical paraelectric (linear dielectric) behavior is observed, as shown in Figure 1c (top). To electrically induce the δ-phase, we increase the electric field stepwise. Increasing the field beyond 200 MV/m induces a hysteretic D−E loop and a remanent polarization, Pr, which then increases with increasing the field strength. Increasing the field beyond 400 MV/m saturates the Pr at 5 μC/cm2 and gives the coercive field of 140 MV/m, both in good agreement with the literature values for δ-PVDF.8,25 Figure 2c (bottom) shows the corresponding switching current Figure 1. Molecular packing of (a) α-PVDF and (b) δ-PVDF viewed along the c-axis. The axes correspond to a = 4.96 Å, b = 9.64 Å, and c = 4.62 Å for both phases. (c) Evolution of D−E hysteresis loops (top) and switching current (bottom) from unpoled α-PVDF films to δPVDF upon electroforming. The inset shows the AFM height topography of a spin-coated α-PVDF thin film. The white scale bar is 10 μm. The height scale bar is from 0 to 160 nm. (d) D−E hysteresis loops (top) and switching current (bottom) of δ-PVDF films. The inset shows the capacitor layout.

stripe-like domains. Furthermore, n should not depend on temperature or the field strength, provided that there is no structural phase transition. For ferroelectric polymers, n is usually considered as an arbitrary fitting parameter, and the reported values are noninteger that vary between 0.5 to 3.5. Moreover, the reported n values show strong field and temperature dependence. A random walk model has been proposed to describe the switching as a far-from-equilibrium dynamics and attributed to the monotonic decrease of the Avrami index with increasing electric field, from n = 2 to 1, to a change in morphology of the domains from circular to highly irregular, entangled chains. Due to the arbitrary choice of the Avrami index n, the dimensionality of the switching mechanism in ferroelectric polymers is still unclear. Here, based on polarization transient measurements over a wide range of electric fields and temperatures, we demonstrate that the switching dynamics in δ-PVDF are one-dimensional, based on which we unravel the polarization switching mechanism for δ-PVDF. We corroborate the dimensionality of the switching process by showing temperature and field independence of the Avrami index n and t∞. We have found that t∞ and domain wall mobility in δ-PVDF are, respectively, shorter and faster than those reported for β-phase PVDF films or even the conventionally used ferroelectric random copolymer poly(vinylidenedifluoride-co-trifluoroethylene, P(VDF-TrFE). We have proposed a switching mechanism that satisfies the experimentally observed dimensionality. The switching involves a 90° rotation of CH2−CF2 repeat units along the polymer chain in δ-phase crystals. The rotation nucleates a reversed dipole along the chain which then propagates in time and yields reversal of the polarization and preserves TGTG′ chain conformation. Unraveling the polar-

Figure 2. (a) Switching transients of δ-PVDF as a function of time at 20 °C at different fields. (b) Switching transients as a function of time at different temperatures at a constant electric field of 220 MV/m. Colored dots show the experimental data, while solid lines are the fits according to the KAI model. (c) Extracted Avrami index n as a function of electric field at different temperatures. The inset shows the remnant polarization Pr as a function of electric field. (d) Extracted switching time, t0, as a function of reciprocal of electric field.

of the capacitor. Structurally, α- and δ-phases have similar crystals8 and spherulitic microstructure as shown in the inset of Figure 1c. Therefore, it is challenging to confirm the formation of the δ-phase using X-ray diffraction. To confirm stable formation of the δ-PVDF, we first depolarize the capacitor with an electric field of decreasing amplitude and then measure a second set of D−E hysteresis and switching current loops. As shown in Figure 1d, opening of the ferroelectric hysteresis loops and switching current peaks appears at much lower fields, showing electroformation of the δ-phase by the first set of field cycles. To pinpoint the dynamics of the polarization transient, we survey the polarization reversal at different temperatures and different electric field strengths. Figure 2a shows a typical 526

DOI: 10.1021/acsmacrolett.9b00166 ACS Macro Lett. 2019, 8, 525−529

Letter

ACS Macro Letters

because δ-phase PVDF is thermodynamically more stable, and therefore the energy barrier to dipole switching is larger. Following the proposal of Miller and Weinreich (M−W), by ignoring the depolarization energy, Eact can be approximated by Eact = cσ2/PskBT, where c is the width of the domain wall which can be approximated by the lattice constant of the unit cell (4.62 Å),8 σ the domain wall energy, Ps the spontaneous polarization, kB the Boltzmann constant, and T temperature. The domain wall energy extracted from the fit in Figure 4b

polarization transient at room temperature for different electric fields starting from 150 MV/m, just above Ec of δ-PVDF, to 240 MV/m. Figure 2b shows temperature dependence of the switching transients at a fixed electric field of 220 MV/m. Pr is temperature independent, for temperature range from −80 °C to +60 °C, and only slightly increases with increasing field strength, as shown in the inset of Figure 2c. The solid lines in Figure 2a,b are the least-squares fit according to the KAI model using eq 1 (note all polarization transients are not shown here). An excellent agreement is obtained. From the fits, we have extracted the dimensionality parameter, n, and its characteristic switching time, t0. For all transient measurements we have obtained n = 1. Figure 2c shows that n is independent of electric field and temperature. From the fits we have also obtained t0, which at 20 °C varies from 2.6 × 10−4 s at 150 MV/m to 2.6 × 10−6 s at 255 MV/m. The t0, at fixed electric field of 220 MV/m, decreased from 1.84 × 10−4 s at −40 °C to 8.7 × 10−6 s at 20 °C. Dependence of t0 on electric field and temperature is clearly shown in Figure 2d, where the values are plotted against the inverse of electric field for the temperature range −80 °C to 60 °C. The field and temperature dependence of t0 follows empirical Merz Law. From the fits in Figure 3d, we

Figure 4. Switching mechanism in δ-PVDF. (a) The chain arrangement viewed along the c-axis with polarization facing up. (b) CH2−CF2 repeat unit along the b-axis with polarization facing up. The red, blue, and gray arrows show the displacement of the F, H, and C atoms, respectively, under the application of electric field leading to dipole flip. (c) δ-PVDF chains along the b-axis with up-polarization (top), followed by initiation of a kink (yellow square) upon application of electric field and subsequent propagation of the kink until full polarization reversal of the chain. (d) The chain arrangement viewed along the c-axis with reversed polarization, pointing down.

Figure 3. (a) Domain velocity of δ-PVDF as a function of reciprocal of electric field measured at room temperature. (b) The extracted activation field of δ-PVDF as a function of reciprocal of temperature. For comparison purposes, the literature values of the domain velocity and activation field for β-PVDF are also plotted.

have obtained t∞ and Eact. The switching time at infinite electric field, t∞, amounts to 500 ps (ps) for all temperatures. Interestingly, the obtained value for t∞ is ten times shorter than those reported for β-phase PVDF and P(VDF-TrFE) copolymers. From the polarization transients we estimate the domain wall velocity at room temperature. Figure 3a shows variation of domain wall velocity, calculated by dividing the lattice constant of 4.62 Å by the switching time, as a function of reciprocal electric field. For comparison, we have also plotted experimental values extracted from the reported switching transient for β-PVDF (data taken from ref 29). Domain wall velocity of δ-PVDF is 1.9 × 10−6 m/s at relatively low electric field, 150 MV/m, and increases exponentially with the applied field reaching 1.9 × 10−4 m/s at 255 MV/m. From the slope ΔV/ΔE in Figure 3a, we calculate a faster domain wall mobility for δ- than for β-PVDF, which amounts to 1.8 × 10−12 and 6.5 × 10−13 m2 V−1 s−1, respectively. The values of Eact (Figure 3b) increase with decreasing temperature ranging from 1.6 GV/m at 60 °C to 2.8 GV/m at −20 °C. For comparison purposes, activation fields for βPVDF are also shown (data extracted from ref 29). The Eact is higher for δ-PVDF as compared to that of β-PVDF for the whole temperature range. Higher activation field is anticipated

amounts to about 40 mJ/m2, which is lower than the value of 58 mJ/m2 obtained for β-PVDF.23,24 We note that the linear fits are force through zero to comply with the M−W approximation for Eact. The proposals for the polarization switching mechanism in δ-PVDF have never been experimentally verified. It has been suggested that polarization switching in δ-PVDF is (I) through 180° physical rotation of the TGTG′ chains around the chain axis,26−28 (II) through initiating of a 180° twist on individual polymer chain and subsequent propagation of the twist along the chains,29 and (III) through 90° rotations about every Gand G′-bonds such that the original TGTG′ is transformed to TG′TG.10,9,30 Rotation by 90° requires initiation of a twist in the angle between T and G (or T and G′) positions in the αphase and then passing through a cis−trans conformation at the midpoint of the transformation. Intermolecular potential energy calculations have shown that scenario (I) is energetically allowed but requires cooperativity.28−30 Therefore, the switching mechanism becomes a cooperative two- or threedimensional event and necessitates high energies. Scenario (II) on the other hand is less energy demanding as it does not 527

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profilometer. Root-mean-square roughness of the films was measured by atomic force microscopy (AFM). Subsequently, the Au top electrode was deposited to finish the capacitors. Due to the quality of the spin-coated PVDF thin films, the evaporated top Au electrodes do not diffuse into the polymer film. Capacitors with PVDF films as thin as 18 nm can be successfully realized.12 The capacitor had a cross-bar pattern with an area of 0.0016 cm2. The displacement loops were recorded using a multiferroic tester (Radiant Technologies). The switching transients were measured using the procedure described in ref 24. First, a negative pulse was applied to the capacitor to set the polarization to −Pr. After shortcircuiting the electrodes for 30 s, a positive square pulse was applied to switch the polarization to +Pr. Then, a second positive square pulse was applied to obtain the nonswitching contributions. The pure displaced charge, or the net switching polarization, was obtained by subtracting the nonswitching component from total polarization.

require cooperativity. In sharp contrast with 180° chain rotation scenarios, rotation by 90° is far less energy demanding but still implies cooperative motion of the polymer chains, rendering the switching mechanism a two- or even threedimensional event. Experimentally, we have determined the values of Avrami index n = 1, indicating that the polarization switching process in δ-PVDF is one-dimensional. Therefore, switching mechanism scenarios (I) and (III) are ruled out. We note in β-PVDF (or equivalently P(VDF-TrFE)) that the chains have all trans conformation, and the polarization switching takes place by a 180° rotation of the repeat units. The value of t∞ obtained for δ-PVDF is 1 order of magnitude shorter than the reported values for both β-PVDF and P(VDF-TrFE). Considering that the TGTG′ chain conformation in δ-PVDF is energetically more stable than the all-trans β-form, for the 180° rotation of TGTG′ repeat units of scenario (III), much longer t∞ for δPVDF in comparison with β-PVDF would be expected, which is in contradiction with the experimental observations suggesting another switching mechanism. We propose an alternative switching mechanism based on 90° rotation of the dipoles. Since polarization reversal is onedimensional, we only consider one PVDF chain, where polarization is pointing upward (Figure 4a), as viewed along the c-axis. The side view of the PVDF chains, along the b-axis, is given in Figure 4c. Polarization reversal proceeds as follows: application of the electric field distorts orientation of a CH2−CF2 repeat unit on the PVDF backbone such that the CF2 and CH2 units rotate 90° with respect to their original position. The movement of the H and F atoms is associated, respectively, with an upward and downward shift in the position of their respective C atom, shown in Figure 4b. Doing so reverses the polarization of the CH2−CF2 repeat unit and does not distort the TGTG′ chain conformation. A kink is then formed on the chain as highlighted in Figure 4c, and a site with reversed polarization is nucleated. The nucleation process is the most energy-intensive step in the switching process and requires high activation field due to the stability of the TGTG′ conformations. Once the nucleus is formed, the kink propagates along the chain until the dipoles along the whole chain are reversed (Figure 4c). We have unambiguously demonstrated one-dimensional polarization switching dynamics for ferroelectric δ-PVDF films over a wide range of temperature and electric fields using the KAI model. The characteristic switching time follows Merz Law, with domain wall mobility that is faster than βPVDF or P(VDF-TrFE). The polarization switching mechanism in δ-PVDF takes place by 90° rotation of fluorine and hydrogen atoms upon application of the electric field, which reverses the dipole of a CH2−CF2 repeat unit. Newly formed conformation propagates along the chain until the polarization is fully reversed.

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AUTHOR INFORMATION

Corresponding Author

*Kamal Asadi: [email protected]. ORCID

Kamal Asadi: 0000-0003-0447-4337 Author Contributions

S.A. performed the experiments. S.A. and K.A. analyzed data and cowrote the manuscript. K.A. designed the experiment and supervised the work. Both authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.A. and K.A. acknowledge the financial support of the Alexander von Humboldt Foundation (Germany) through the Sofja Kovalevskaja Award and the technical support from the Max-Planck Institute for Polymer Research. S.A. thanks the National University of Science and Technology (Pakistan) for the financial support. S.A. and K.A. acknowledge the technical support from the Max-Planck Institute for Polymer Research.

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REFERENCES

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EXPERIMENTAL SECTION

PVDF (180 kg/mol) and dimethylformamide (DMF) (purity ≥99.8%) were purchased from Sigma−Aldrich and Fisher Chemical, respectively. Capacitors were fabricated on thoroughly cleaned glass substrates with a thermally evaporated gold bottom electrode, 50 nm, with 1 nm chromium as an adhesion layer. The PVDF solution in DMF, 5 wt %, was spin coated at elevated substrate temperature of around 100 °C. Solution processing at high substrate temperatures prevents the adverse effects of humidity on the film quality and guarantees high device yield and performance uniformity. The final film thickness was 350 nm measured by a DEKTAK surface 528

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