Ferroelectrics, coercivity

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

The dielectric constant of barium titanate, along [001] is about 200 and along [100] it is 4000 at room temperature.3 The spontaneous polarization at room temperature is 26 X 10-6 C./cm.2, and the value of the coercive field has been found to vary from 500 to 2000 volts/cm. The crystal structure of barium titanate at room temperature can be represented by a tetragonal unit cell with size of a0 = 3.992 A., and c0 = 4.036 A., but the symmetry becomes cubic above 120°C., at which temperature the crystals no longer exhibit ferroelectric properties. 

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. 

Analogous C(V) curves were recorded on pzt bulk ceramics with compositions around the morphotropic phase boundary (mpb). Figure 1.25 displays the relative permittivity as a function of DC-bias for a tetragonal (x = 0.48), a morphotropic (x = 0.52) and a rhombohedral (.x = 0.58) sample. In contrast to thin films additional humps observed in the e E) curves. This could be explained by different coercive fields for 180° and non-180° domains [31]. Their absence in ferroelectric thin films could be taken as evidence for suppressed non-180° domain switching in thin films [30],... 

In such a measurement, the sample is clamped as lightly as possible, and the displacement of the surface in monitored. The amount of sample clamping is important, because the mechanical constraints can impact the ferroelastic response of the sample. That is, in samples where the mechanical coercive stress is low, it is possible to change the domain state of the material by improperly clamping it in the sample fixture. This is especially important in elastically soft piezoelectrics, such as many of the relaxor ferroelectric PbTiC>3 single crystals. 

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. 

Ferroelectric thin films considerably gain in interest within the last couple of years due to their potential application in nonvolatile random-accessmemory devices (FeRAM). Among potential candidates, PbZr. n i, (>> (pzt) is one of the most promising materials because of its large remanent polarization and low coercive field. However, pzt is also well known for its poor fatigue behavior on metal electrodes [1,2] and occurrence of size effects [3-5] which are well due to the ferroelectric/electrode interface properties [1-5]. 

In order to compare calculated and experimentally observed phase portraits it is necessary to know very exactly all the coefficients of the describing nonlinear differential Equation 14.3. Therefore, different methods of determination of the nonlinear coefficient in the Duffing equation have been compared. In the paraelectric phase the value of the nonlinear dielectric coefficient B is determined by measuring the shift of the resonance frequency in dependence on the amplitude of the excitation ( [1], [5]). In the ferroelectric phase three different methods are used in order to determine B. Firstly, the coefficient B is calculated in the framework of the Landau theory from the coefficient of the high temperature phase (e.g. [4]). This means B = const, and B has the same values above and below the phase transition. Secondly, the shift of the resonance frequency of the resonator in the ferroelectric phase as a function of the driving field is used in order to determine the coefficient B. The amplitude of the exciting field is smaller than the coercive field and does not produce polarization reversal during the measurements of the shift of the resonance frequency. In the third method the coefficient B was determined by the values of the spontaneous polarization... 

From the data listed in Table 3, it may be noted that the polarization values of the ceramics are lower than that of the single crystal [7,8] whereas the coercive field is higher. This may be attributed to the existence of the non-ferroelectric layers at the metal-ferroelectric interfaces and grain boundaries. In other way, when the anisotropy of the crystal get stronger, the displacement of ions, which is demanded by polarization inversion, get larger, the coercive field will be stronger. 

Orthorhombic crystals. Very freely sol in water. Has ferroelectric properties Curie point 47". Spontaneous polarization at room temp 2.2 X 10 coul/cm. Coercive field 220 v/cm. 

Amorphous LiNbOs films made by sol-gel processing were subjected to a series of characterizations [57]. It was found that an amorphous LiNbOs film obtained by heating the gel film at 100°C for 2 h showed P-E hysteresis with remnant polarization Pr = 10 pC/cm2 and coercive field Ec= 110 kV/cm. Electron diffraction of such film showed a diffuse ring pattern characteristic of an amorphous nature. These are shown in Fig. 6 in which the scale for E is 147 kV/cm division and that for P is 5.6 pC/cm2 division. Further measurement showed a pyroelectric coefficient of 8 pC/cm2 K at 28°C. Note that for singlecrystal LiNbOa, Pr = 50 pC/cm2 and the pyroelectric coefficient was reported to be 20 pC/cm2 K [1]. Further, a piezoelectric resonance was observed at similar frequency range for both amorphous and crystalline LiNbOa, characteristic of a ferroelectric material [57]. 

In general a ferroelectric perovskite single crystal will be composed of a roughly equal number of domains oriented in all the equivalent directions allowed by the crystal symmetry. The overall polarisation of the crystal will be zero. The application of an electric field will cause a polarisation switch and lead to a classical hysteresis loop in which the important values are P, (the remanent or residual polarisation when the electric field is reduced to zero), and E, (the coercive field, which is the reverse field required to reduce the polarisation to zero). Extrapolation of the high-field portion of the curve to =0 gives the value of the spontaneous polarisation P (Figure 6.9a). 

As stated before, electro-optic properties of PLZT materials are related to their ferroelectric properties [131]. For PLDZT, the reduced coercive field (EJ and the enhanced optical transmittance (7) induced by the Dy substitution have led to improved electro-optic properties. Because the working voltage of a device is mainly dependent on the half-wave voltage of the materials, the lowered yi/2 of materials should be favorable to the improvement in performances of the devices. 

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