Ferroelectrics hysteresis

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

The crystals grown in this manner are in the form of clear sheets. The symmetry of the crystals is pseudotetragonal with a cell size of a0 = 3.841 A. and c0 = 32.83 A. Electrodes can be evaporated, or indium amalgam can be applied to the flat surfaces of the crystals, to produce samples for measurements. The d.c. resistance of the crystals is about 1012 fi-cm. They exhibit ferroelectric hysteresis loops up to the Curie temperature of 643°C. 

Figure 1.6 Ferroelectric hysteresis of single domain single crystal (dashed line) and polycrystalline sample (full line)...

The ferroelectric hysteresis originates from the existence of irreversible polarization processes by polarization reversals of a single ferroelectric lattice cell (see Section 1.4.1). However, the exact interplay between this fundamental process, domain walls, defects and the overall appearance of the ferroelectric hysteresis is still not precisely known. The separation of the total polarization into reversible and irreversible contributions might facilitate the understanding of ferroelectric polarization mechanisms. Especially, the irreversible processes would be important for ferroelectric memory devices, since the reversible processes cannot be used to store information. 

Based on these assumptions the measurement of the large signal ferroelectric hysteresis with additional measurements of the small signal capacitance at different bias voltages are interpreted in terms of reversible and irreversible parts of the polarization. As shown for ferroelectric thin films in Figure 1.24, the separation is done by substracting from the total polarization the reversible part, i. e. the integrated C(V)-curve [18]. 

ZnO/ BaTiOs / ZnO Electro-optical effects of BTO, ZnO/BTO, and ZnO/BTO/ZnO heterostructures with fixed/switchable polarization, IV and CV, ferroelectric hysteresis [86-88]... 

A complete review of the reported properties of ferroelectric thin films prepared by CSD is beyond the scope of this chapter. Suffice it to say that fabrication approaches from each of the three CSD categories noted above have been used to prepare high-quality films in a range of thicknesses. The dielectric response and ferroelectric hysteresis behavior have been widely reported and the reader is referred to References 12 and 13 for representative results. Despite space limitations, three aspects of CSD processing and film properties warrant consideration here. These are (i) the ability to prepare oriented films by CSD (ii) typical stress levels within the films and (iii) the general dielectric properties of the thin film materials compared to the corresponding bulk materials. 

For the measurements of the ferroelectric hysteresis of P(VDF-TrFE) via the flatband shift, we used capacitors with oxidised p-type (-lO cm ) silicon substrate (100-235 nm Si02) to prevent large amoimts of leakage current. The copolymer film was prepared as described above. We used films of thickness fiom 100 nm to 1 pm. The structiues were prepared in top electrode geometry , with thermal evaporated aluminium, patterned via a shadow mask. The measiuements of capacitance versus voltage (CV) were carried out with an Agilent 4284A LCR meter at a frequency of 1 MHz with sweep rates fiom... 

The ferroelectric hysteresis of P(VDF-TrFE) is directly investigated by MIS capacitors and OFETs. By using MIS capacitors, a systematic shift of flatband voltage is observed, after applieation of different voltage scan windows. The MIS structures are built up as Al/P(VDF-TrFE)/Si02/Si sandwieh strueture. The dependence of the remanent polarisation on thickness of the eopolymer shows an elevated polarisation voltage for a copolymer film thiekness below 100 nm, obviously due to the above mentioned interface reaction between the eopolymer and aluminium. 

Figure 15.14 (a) Ferroelectric hysteresis loop for a single-crystal, (b) Polycrystalline sample. 

Figure 15.18 Circuit used to measure ferroelectric hysteresis.

Interface polarization Dipole stretching Ferroelectric hysteresis Electric domain wall resonance Electrostriction Kezoelectricity Nuclear magnetic resonance Ferromagnetic resonance Ferrimagnetic resonance... 

Perovskites Structure-Property Relationships 6.33 Ferroelectric Hysteresis Loops... 

Figure 6,9 Ferroelectric hysteresis loops, schematic (a) typical loop indicating P P and Ej (b) single crystal ABO (c) medium-grained ceramic ABO (d) fine-grained ceramic ABO,...

Bharti, V., Kaura, T., Nath, R., (1997) Ferroelectric Hysteresis in Simultaneously Stretched and Corona-Poled PVDF Films, IEEE Transactions on Dielectrics and Electrical Insulation, Vol 4, No. 6, (December 1997) pp. 738-741, ISSN 1070-9878. 

The existence of ferroelectric phase in sufficiently thin antiferroelectric films had been revealed experimentally in several works [64-66]. In Ref. [64], the switchable ferroelectric polarization has been observed in PbZrOs antiferroelectric thin film on Si substrate. It has been revealed, that both in the latter film and in one more antiferroelectric BiNb04 one, the ferroelectric phase appears only if the film thickness is smaller then certain threshold value, which depends on material parameters. For instance, the ferroelectric hysteresis loop has been observed [65] in 100 nm thick PbZrOs/Si Alms, while those thicker than 400-500 nm revealed antiferroelectric behavior. Note, that the other primary ferroic demonstrates the same behavior. Namely, the films of antiferromagnetic BiFeOs on SrTiOs substrate reveal the emergence of ferromagnetism at the thicknesses less than 100 nm [67]. 

Ferroelectric hysteresis loop and remnant polarization appear at temperatures T< Tf(R). This behavior can be called frozen superparaelectric phase. 

Figure 18.11 Ferroelectric hysteresis loops for hard and soft Pbo.5gZro,42Ti03 ceramics modified by various amounts of Nb and Fe dopants (a) on linear scales (b) on semi-logarithmic scale (the first quadrant).

Figure 18.16 Relaxation of the ferroelectric hysteresis loops in hard (doped with 1.0atom% Fe) PZT (58/42) ceramics, (a) For different cooling rates from the paraelectric state (b) The...

Figure 18.17 Comparison of ferroelectric hysteresis loops. Soft (1.0atom% Nb-doped) PZT (58/42) ceramics and hard (1.0atom% Fe-doped) PZT (58/42) ceramics relaxed by ac-field cycling at 125 °C. The measurements are carried out under the same conditions.

Kamlah, M. and Bdhle, U. (2001) Finite element analysis of piezoceramic components taking into account ferroelectric hysteresis behavior. Int. J. Solids Struct., 38, 605-633. 

Smith, R.C, and Horn, C. L. 1999. Domain wall theory for ferroelectric hysteresis. Journal of Intellegent Material Systems and Structures, 10(3)pp. 195-213. 

The FMR field of the Fe304/PZT and Fe304/PMN-PT muitiferroic composites exhibited the characteristic butterfly shape in their FMR field vs. electric field curves as shown in Fig. 7, which coincided with the ferroelectric hysteresis loops of the PZT and PMN-PT respectively and were similar... 

Figure 7. Butterfly curves of resonance fields vs. electric fields and ferroelectric hysteresis loops of muitiferroic composite Fe304/PZT (a) and FesOVPMN-PT (b).

Titanates can also be used as dielectrics in condensers to give relative dielectric constants as high as 4000. For this application, we seek to suppress piezoelectric effects and ferroelectric hysteresis losses. This can best be achieved, according to the ideas above, by producing high density, very fine-grained material with grain sizes < 1 jU. 

Rg.4.5 -1 Ferroelectric hysteresis loop. Ps, spontaneous polarization Pj, remanent polarization Ec, coercive field... 

---