Polarization remanent

Both the Spontaneous polarization PI and the remanent polarization P/ are strong functions of temperature, particularly near the transition temperature T in ferroelectrics (7) ... 

Fig. 5. The dependence of remanent polarization, P, on the melting point, T, in odd nylons (40).

Fig. S3. High quality, biaxially stretched PVDF ferroelectric film can be electrically poled to a remanent polarization of over 9 fxCcm with the Bauer cyclic poling technique. The polarization versus electric field of a typical sample is shown.

From the electrical viewpoint, stress-induced changes in remanent polar-... 

Hysteresis curve of a ferroelectric crystal, v = initial (virginal) curve, Pr = remanent polarization, Ps = spontaneous polarization, Ec = coercive field... 

Pr remanent polarization Ec coercive field. [Reprinted with permission from Ref. 114.]... 

A second type of behavior existing in the PLZT s is the linear (Pockels) effect which is generally found in high coercive field, tetragonal materials (composition 3), This effect is so named because of the linear relationship between An and electric field. The truly linear, nonhysteretic character of this effect has been found to be intrinsic to the material and not due to domain reorientation processes which occur in the quadratic and memory materials. The linear materials possess permanent remanent polarization however, in this case the material is switched to its saturation remanence, and it remains in that state. Optical information is extracted from the ceramic by the action of an electric field which causes linear changes in the birefringence, but in no case is there polarization reversal in the material. 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

A common technique for obtaining macroscopic polar films involves poling by electrical fields. In this case the polarization induced in the sample remains after the removal of the electric field. Figure 21 shows the variation of the polarization of a film of the 55/45 copolymer as a function of an applied electric field [8]. The value of the remanent polarization, Pr, of samples measured in our... 

Fig. 22. Remanent polarization as a function of temperature for various copolymers. The two curves for the 80/20 correspond to two different crystallinities. The (x) symbols correspond to samples with lower crystallinity...

An ideal single crystal shows a P E) behavior as depicted in Figure 1.6. The non-ferroelectric dielectric ionic and electronic polarization contributions are clearly linear, and are suposed by the spontaneous polarization Ps (dashed curve in Figure 1.6). To reverse the polarization an electrical field with an amplitude E > Ec is required. In opposite to single crystals in polydomain ferroelectric ceramics, the remanent polarization Pr is smaller than the spontaneous one Ps due to backswitching even for opposite fields as shown in Figure 1.6. In that case Ps can be estimated by extrapolation of (non-switching) P-values to E — 0. 

A tool to visualize the domains in thin films is the 3-D piezoresponse force microscope (pfm, see also Chapter 12). Figure 1.22 shows an epitaxial pzt thin films grown on a (001) single crystalline SrTiC>3 substrate coated with La0.5Sr0.5CoO3 oxide layer. A detailed analysis point out that a self-polarized polarization mechanism is observed because the out-of-plane polarization in c-domains are preferentially orientated towards the bottom electrode, i. e. a remanent polarization exists without applying an external field. The domain configuration is always of the head-to-tail type. 

To characterize ferroelectric materials usually the dependence of the polarization on the applied voltage is measured by means of a Sawyer-Tower circuit or by recording the current response to a voltage step. The / (V/)-hys(crcsis curve is used to determine the remanent polarization and coercive voltage, respectively coercive field. These two parameters are of critical importance to the design of external circuits of FeRAMs. 

Pr+ positive state of remanent polarization of the dynamically measured hysteresis loop... 

Prrei+ positive state of relaxed remanent polarization, relaxed for one second in the Pr+ state. Equal to the positive state of remanent polarization of the quasi statically measured loop (see Section 3.3.4)... 

Pmax+ — Prrei—) change of polarization when the sample is switched from the negative state of the relaxed remanent polarization into the positive saturation -switching case... 

The third loop establishes the sample into the positive remanent polarization state without sampling data. The fourth loop now starts in the positive relaxed remanent polarization state (Prrei+), turns into the negative saturation (Pmax-), then crosses the polarization axis at zero volts excitation signal in the negative remanent polarization state (Pr ). Afterwards the sample is driven into the positive saturation (Pmax+) and ends up in the positive remanent polarization state (Pr+) when the voltage is zero again. Subsequently, the hysteresis loop is balanced respectively to the values P(+Vmax) and P(-Vmax). From the data of the second loop the parameters Vc-, Pr, Prrei- are determined and from the data of the fourth loop the parameters Vc+, Pr+, Prrei+ The closed hysteresis loop (continuous loop) can be calculated from the second half of the second loop and the second half of the fourth loop. 

Figure 3.17 Typical result of a fatigue measurement in combination with hysteresis measurements is usually depicted as the remanent polarization versus log cycles of the excitation signal.

The failure mechanism within a memory cell is either due to the inability of the programming voltage to switch the ferroelectric material because of an increase of the coercive voltage (write failure) or due to a decrease in the difference of Ps and Pns. This means the two different states of remanent polarization cannot be distinguished by the memory sense amplifier (read failure). This case is shown in Figure 3.19. 

Figure 3.18 Shift of polarization of a sample in the negative state of remanent polarization due to imprint.

Furthermore, the remanent polarization values Pr and Prrei also change due to the shift of the loop. A correlation between voltage shift and polarization change can be given with the static hysteresis loop (see Section 3.3.4). 

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