Ferroelectric polarisation

In a next step, we study the flatband shift, the polarisation as a function of copolymer film thickness. For the measurements, a relatively thick Si02 buffer layer of 235 nm was used and we reveal a clear thickness dependence of the ferroelectric polarisation [32]. We calculated AiJpvDF s the voltage drop only over the P(VDF-TrFE) layer. For accumulation, negative voltages, the voltage is divided into two parts Ui = 17ipvdf + For depletion, we have to cal-... 

Under radiation damage-free eonditions, we show a clear indication for a surface reaction of P(VDF-TrFE) with A1 electrodes, not only for evaporated aluminium as top electrode, but also, at room temperature, for the aluminium as bottom electrode. In contrast, for PEDOT PSS, the XPS measiuements indicate a layer-by-layer structure of PEDOT PSS/P(VDF-TrFE) without any interface modification. This could be the reason for lower relaxation times, higher switching frequencies and, in consequence, a better field dependenee of the ferroelectric polarisation, if we choose PEDOT PSS as material for the electrode, especially for thin films of the eopolymer. 

The ferroelectric polarisation has been calculated for the tetragonal phase of KNbOs [58] and for HCl [45] in the case of KNbOs, the macroscopic polar-... 

In the layered Ruddlesden-Popper and Dion-Jacobson phases, improper ferroelectricity can also arise in a form termed hybrid improper ferroelectricity. Here, the ferroelectricity arises when two non-polar rotations of BO octahedra combine to produce a polar stmcture. The same effect may well also occur in the Aurivillius phases although this has not yet been proven. The creation of improper ferroelectric polarisation due to magnetic interactions in multiferroic perovskites is described in Section 7.10. 

In the operation of ferroelectric liquid crystal devices, the applied electric field couples directly to the spontaneous polarisation Ps and response times depend on the magnitude E Ps. Depending on the electronic structure (magnitude and direction of the dipole moment as well as position and polarity of the chiral species) and ordering of the molecules P can vary over several orders of magnitude (3 to 1.2 x 10 ), giving response times in the range 1-100 ps. 

PVDF is mainly obtained by radical polymerisation of 1,1-difluoroethylene head to tail is the preferred mode of linking between the monomer units, but according to the polymerisation conditions, head to head or tail to tail links may appear. The inversion percentage, which depends upon the polymerisation temperature (3.5% at 20°C, around 6% at 140°C), can be quantified by F or C NMR spectroscopy [30] or FTIR spectroscopy [31], and affects the crystallinity of the polymer and its physical properties. The latter have been extensively summarised by Lovinger [30]. Upon recrystallisation from the melted state, PVDF features a spherulitic structure with a crystalline phase representing 50% of the whole material [32]. Four different crystalline phases (a, jS, y, S) may be identified, but the a phase is the most common as it is the most stable from a thermodynamic point of view. Its helical structure is composed of two antiparallel chains. The other phases may be obtained, as shown by the conversion diagram (Fig. 7), by applying a mechanical or thermal stress or an electrical polarisation. The / phase owns ferroelectric, piezoelectric and pyroelectric properties. 

Some piezoelectric crystals are electrically polarised in the absence of mechanical stress one example is gem-quality tourmaline crystals. Normally, this effect is unnoticed because the crystal does not act as the source of an electric field. Although there should be a surface charge, this is rapidly neutralised by charged particles from the environment and from the crystal itself. However, the polarisation decreases with increasing temperature and this can be used to reveal the polar nature of the crystal. If tourmaline is heated its polarisation decreases and it loses some of its surface charges. On rapid cooling it has a net polarisation and will attract small electrically charged particles such as ash. Such crystals are known as pyroelectric, and ferroelectric crystals are a special subclass of pyroelectric crystals. 

Pyroelectric detectors depend on the use of a thin slice of ferroelectric material (deuter-ated triglycine sulphate (DTGS), Figure 3.14, is the standard example) - in which the molecules of the organic crystal are naturally aligned with a permanent electric dipole. The thin slab is cut and arranged such that the direction of spontaneous polarisation is normal to the large faces. Typically one surface of the crystal is blackened to enhance thermal absorption, and the entire assembly has very low thermal mass. 

There are certain crystals in which dipoles are spontaneously aligned in a particular direction, even in the absence of electric field. Such substances are called ferroelectric substances and the phenomenon is called ferroelectricty. The direction of polarisation in these substances can be changed by applying electric field. Baruion titanate (BaTi03), sodium potassium tartarate (Rochelle salt), and potassium hydrozen phosphate (KH2I04) are ferroelectric solids. If the alternate dipoles are in opposite directions, then the net dipole moment will be zero and the crystal is called anti-ferroelectric. Lead zirconate (PbZr03) is an anti-ferroelectric solid. 

Polarising Small Domains in Ferroelectric Polymer Films. 192... 

Some keywords for further reading on measurements of electrical properties using the SFM are pulsed-force mode [33, 404, 405], special SFM tips [406-409], lithography assisted by electric potentials [244, 254, 410-426], measurements of polarisation and water droplet manipulation [427-429] or reading and writing of ferroelectric domains and piezoactivity [393, 430-438]. 

In Eq. (20) the three terms are related to the Maxwell stress (first), piezoelectric effect (second) and electrostriction (third). In order to obtain information about ferroelectricity via piezoresponse measurements, we need a link between the spontaneous polarisation and the piezoelectric constant. According to Furukawa and Damjanovic, piezoelectricity in ferroelectrics can be explained as electrostriction biased by the spontaneous polarisation if their paraelectric phase is nonpolar and centrosymmetric [461, 495, 496]. Therefore the d33 constant depends on the spontaneous polarisation P5 ... 

Fig. 51 Schematic macroscopic hysteresis loop of a ferroelectric material. Therein Ec denotes the coercitive field strength, Prei the remanent polarisation and P ei the saturation polarisation...

Spin coated copolymer films show a decrease in remanent polarisation if the film thickness [504, 505] decreases. The application of piezoelectric materials in micro-electro-mechanical systems (MEMS) or sensors makes it often necessary to decrease the lateral dimensions of the elements. Recently, Alexe et al. [506, 507] fabricated freestanding microcells with lateral dimensions down to 100 nm and heights of 110 nm from a ferroelectric PZT by direct... 

PFM is limited by two factors the local dimension of the probe and the sensitivity to the vertical tip movement. The smallest domains polarised in ferroelectric copolymer and subsequently imaged with PFM had diameters of -25 nm [509]. A vertical sensitivity of-1 pm is reasonable and implies that for thin films with low excitation voltages (-1 V) the smallest detectable d33 value is -1 pm/V. 

Calamitic metallomesogens forming a chiral smectic C phase (SmC ) are ferroelectric materials. Due to the low symmetry of this phase when the helix is unwound (C2) the molecular dipoles are aUgned within the layers of the SmC phase, giving rise to ferroelectric order in the layers. Because the SmC phase has a helical structure, there is no net macroscopic dipole moment for the bulk phase. However, it is possible to unwind the helix by application of an external electric field or by surface anchoring in thin cells. Under such conditions, a well-aligned film of the ferroelectric liquid crystal can exhibit a net polarisation, called the spontaneous polarisation (Ps). Ferroelectric liquid crystals are of interest for display applications because the macroscopic polarisation can be switched very fast by an... 

Spontaneous polarisation can also be observed for chiral discotic metallomesogens forming columnar mesophases, when the chiral molecules are tilted with respect to the column axis. The tilt induces a dipole moment within the plane of the molecule. A net macroscopic polarisation can be obtained for rectangular columnar phases with Cz or P2i symmetry. Serrano and Sierra reported on ferroelectric switching in the columnar mesophase for chiral /3-diketonate complexes (Figure 2.52). ... 

As ferroelectric material we use poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)). This copolymer is soluble in non-toxic reagents, for example 2-butanone. The preparation of organic and ferroelectric thin films via spin coating from solution is possible [13]. The polarisation field of P(VDF-TrFE) is relatively high, about 50 MV/m [14]. Here, a downscaling of the P(VDF-TrFE) film thickness into a range below 100 nm is necessary in order to use small bias voltages for polarisation. 

All measurements were started in accumulation and finished there too, after driving the voltage in the investigated range to inversion and back (e.g. -10 V to 10 V and backwards to -10 V we call this a 10 V loop ). Due to the polarisation of the ferroelectric layer, the CV curves show a hysteresis loop [30, 31], which depends on the maximal applied voltage in the CV mode. 

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