*2.4.1.1. The surface layer(s)*

The idea of the existence of a surface layer with suppressed ferroelectric properties imple‐ mented in physical models has demonstrated considerable advantage in explaining asym‐ metric switching and other anomalies in the behavior of ferroelectric materials. In the models, the interface thin layer is considered as *a non-switchable "dead" layer*[48], *a space charge layer*[49], *a low-dielectric constant layer* [50] or *an insulating region* [51] adjacent to the electrode. Pertsev *et al.* [46] have shown that in ultrathin PZT films the nearby-electrode layer does not behave as an insulator, and proposed that a finite electrical conduction exists in this layer. Also, Tagant‐ sev *et al.* [52] have indicated that the anomalous hysteresis behavior displayed by ferroelectric thin film capacitors might be caused by the effect of a conductive non-ferroelectric layer, the so-called "*passive layer*", formed at the interface between the film and electrode. This layer is supposed to behave as a space charge layer (charged positively or negatively), operating as a serial capacitor connected to the film capacitor. A high electric field in the surface layer will cause charge transport across it, resulting in charge separation. The built-in potential devel‐ oped by the trapped and separated charges in the layer due to depletion effects at the ferro‐ electric-electrode contacts would prevent polarization reversal to occur in a symmetrical manner, even though the driving voltage is perfectly symmetrical.[49]

A direct evidence of an oxygen-deficient surface layer in epitaxial (Ba, Sr)TiO3 [50] thin films and Pb(Zr, Ti)O3 nanostructures [53] has been provided using high-resolution transmission electron microscopy. However, the origin of these layers remains yet to be elucidated. Some researchers connected it with *a partial depletion* [54] or *exhaustion* of charge carriers at the Schottky contacts [52], while others related the existence of the surface layer to extrinsic effects such as *structural disordering* [49, 55], *chemical inhomogeneity* (e.g., oxygen deficiency) [41] or *mechanical distortion* [50]. Abe *et al.* [48] have proposed, based on measurement of switching currents in the heteroepitaxial BaTiO3 thin films, that the passive layer is possibly formed by the relaxation of lattice misfit strain developed during film growth. The existence of the interfacial stresses due to elastic interface deformations in thin films has been evidenced by Spaepen [56]. The oxygen-loss related strain gradient at the interfaces of the PZT capacitor was also reported by Wu *et al.* [57]. The role of strain gradients in the asymmetric hysteresis behavior will be discussed in the following section.

### *2.4.2. Mechanical stress effects*

It is well established that internal mechanical stresses and their effects on domain-wall movement are the main cause of the significant difference between the physical properties of ferroelectric thin films and bulk ceramics. Experimental results presented in the literature show that the *residual stresses* developed in the films during fabrication are often larger than hundreds of megapascals and create a considerable clamping effect on domains, thereby hindering polarization switching.[58] The misfit strains arising from the mismatch of the lattice parameters and the coefficients of thermal expansion of the underlying substrate and thin film can lead to the lattice distortion or formation of *misfit dislocations* (Fig. 8), which in turn causes the creation of a lattice strain gradient across the film. This strain gradient may induce a linear polarization response through the *flexoelectric effect*.[59] Tuttle *et al.* [60] have reported that the sign of the film stress at the Curie point controls the orientation of the domain structure, and hence the flexoelectric effect, unlike piezoelectricity, can trigger switchable polarization. Under certain misfit strain-temperature conditions, a strong coupling between the polarization and the stress field of the dislocation can appear, resulting in spatial inhomogeneity of the polarization near the dislocation (Fig. 9).[61] These polarization gradients produce the accumulated interfacial charge, which allows for the development of the internal bias field.

polarization imprint under external bias, as observed by Grossmann *et al.* [38]. The scenario proposed in the interface screening model has consistently and repeatedly been successful in describing, both qualitatively and quantitatively, a wide variety of experimental data on imprint behavior of ferroelectric thin film capacitors, including a logarithmic-type time dependence of imprint [47] and the effects of temperature, illumination and of an externally

The idea of the existence of a surface layer with suppressed ferroelectric properties imple‐ mented in physical models has demonstrated considerable advantage in explaining asym‐ metric switching and other anomalies in the behavior of ferroelectric materials. In the models, the interface thin layer is considered as *a non-switchable "dead" layer*[48], *a space charge layer*[49], *a low-dielectric constant layer* [50] or *an insulating region* [51] adjacent to the electrode. Pertsev *et al.* [46] have shown that in ultrathin PZT films the nearby-electrode layer does not behave as an insulator, and proposed that a finite electrical conduction exists in this layer. Also, Tagant‐ sev *et al.* [52] have indicated that the anomalous hysteresis behavior displayed by ferroelectric thin film capacitors might be caused by the effect of a conductive non-ferroelectric layer, the so-called "*passive layer*", formed at the interface between the film and electrode. This layer is supposed to behave as a space charge layer (charged positively or negatively), operating as a serial capacitor connected to the film capacitor. A high electric field in the surface layer will cause charge transport across it, resulting in charge separation. The built-in potential devel‐ oped by the trapped and separated charges in the layer due to depletion effects at the ferro‐ electric-electrode contacts would prevent polarization reversal to occur in a symmetrical

A direct evidence of an oxygen-deficient surface layer in epitaxial (Ba, Sr)TiO3 [50] thin films and Pb(Zr, Ti)O3 nanostructures [53] has been provided using high-resolution transmission electron microscopy. However, the origin of these layers remains yet to be elucidated. Some researchers connected it with *a partial depletion* [54] or *exhaustion* of charge carriers at the Schottky contacts [52], while others related the existence of the surface layer to extrinsic effects such as *structural disordering* [49, 55], *chemical inhomogeneity* (e.g., oxygen deficiency) [41] or *mechanical distortion* [50]. Abe *et al.* [48] have proposed, based on measurement of switching currents in the heteroepitaxial BaTiO3 thin films, that the passive layer is possibly formed by the relaxation of lattice misfit strain developed during film growth. The existence of the interfacial stresses due to elastic interface deformations in thin films has been evidenced by Spaepen [56]. The oxygen-loss related strain gradient at the interfaces of the PZT capacitor was also reported by Wu *et al.* [57]. The role of strain gradients in the asymmetric hysteresis

It is well established that internal mechanical stresses and their effects on domain-wall movement are the main cause of the significant difference between the physical properties of ferroelectric thin films and bulk ceramics. Experimental results presented in the literature show

manner, even though the driving voltage is perfectly symmetrical.[49]

behavior will be discussed in the following section.

*2.4.2. Mechanical stress effects*

applied bias [36, 38, 42].

220 Ferroelectric Materials – Synthesis and Characterization

*2.4.1.1. The surface layer(s)*

**Figure 8.** High-resolution TEM cross-sectional images of the interfacial layer in the PZT nanostructure (a) and Ba0.7Sr0.3TiO3 thin films (b, c) showing a significant distortion of the ferroelectric lattice around the dislocation cores (labelled by arrow tags). Reproduced with permission from D. Hesse [53] and He *et al*. [50]. Copyright 2005, AIP Pub‐ lishing LLC.

**Figure 9.** Spatial inhomogeneity of the ferroelectric polarization around periodic misfit dislocations due to a strain gra‐ dient in a PbTiO3 film on a LaAlO3 substrate. Reproduced with permission from Alpay *et al*. [61]. Copyright 2004, AIP Publishing LLC.

ak drive voltages

voltage shift an

V

V- and 50 V-pea

F

Fig. 10. (a) The

Stress-induced changes in the local asymmetric switching behavior and piezoelectric proper‐ ties of the sol-gel Pb(Zr0.30Ti0.70)O3 and Mn-doped Pb(Zr0.30Ti0.70)O3 ferroelectric films have been investigated by Koval *et al.*[62] A modified nanoindentation system with a conductive spherical indenter tip was used for the simultaneous application of driving voltage and mechanical loading. It was shown that the switching charge versus applied voltage (Q-V) hysteresis loops shift gradually along the voltage axis with increasing indentation force (100 – 500 mN). The effect of spherical nanoindentation on the asymmetric switching behaviour is shown in Fig. 10a, which compares the Q-V loops obtained at different indentation loads for the Mn-doped PZT (PMZT) film. In addition, a progressive hysteresis gap of the charge – voltage loops is displayed in the figure inset. The parameter of horizontal loop asymmetry *δ* (Fig. 10b) was found to increase almost linearly with the force by an increment of about 0.4-0.5 x10-3 per 100 mN during the application of a sinusoidal signal of 25 V-, 37 V- and 50 V-peak drive voltages and 50 Hz frequency. p p b i w a n V p o i permission from [50]. Copyright Stressproperties of th been investigate indenter tip was was shown that along the voltag nanoindentation V loops obtaine progressive hyst of horizontal loo increment of abo m D. Hesse [53 2005, AIP Publi -induced chang e sol-gel Pb(Zr0 ed by Koval *et a* s used for the sim t the switching c ge axis with inc n on the asymme ed at different in teresis gap of the op asymmetry out 0.4-0.5 x10-3 3] and He *et a* ishing LLC. ges in the local 0.30Ti0.70)O3 and *l.*[62] A modifie multaneous app charge versus ap creasing indenta etric switching b ndentation loads e charge – voltag (Fig. 10b) was 3 per 100 mN du *l*. l asymmetric s Mn-doped Pb(Z ed nanoindentati lication of drivi pplied voltage ( ation force (100 ehaviour is show s for the Mn-do ge loops is displ found to increa uring the applica switching behav Zr0.30Ti0.70)O3 fe ion system with ng voltage and (Q-V) hysteresis 0 – 500 mN). T wn in Fig. 10a, w ped PZT (PMZ ayed in the figur se almost linearl ation of a sinusoi vior and piezoe erroelectric film a conductive sp mechanical load s loops shift gra The effect of sp which compares T) film. In addi re inset. The par rly with the force idal signal of 25 electric ms have pherical ding. It adually pherical the Qition, a rameter e by an V-, 37

s and 50 Hz freq

nd (b) the asymm

quency.

d C doped PZT thin Copyright 2005, n film under na , AIP Publishing anoindentation. R g LLC. Reproduced with h permission fr rom Koval *et al l*. [62]. **Figure 10.** (a) The voltage shift and (b) the asymmetry parameter of the Q-V hysteresis loop of the Mn-doped PZT thin film under nanoindentation. Reproduced with permission from Koval *et al*. [62]. Copyright 2005, AIP Publishing LLC.

metry parameter

of the Q-V hyst

teresis loop of th

he Mn-

T t c c p c *a* n m e r p l These results ar the indentationconcurrent spac controlled by a polarization stat charge trapping *al.* in their early nanoindentation movement of f experimental wo residual stresses position by an ex Stress lifetime of ferro e interpreted in -driven voltage ce charge rearr variation of the te of the film, th at the bottom e y work [63] rep n in the PZT fi ferroelastic dom orks of other re s can change si xternal field. -driven effects electric capacito Ref. 62 by two shift of the Q-V rangement, and internal residua he so-called inter electrode due to ported on an inc ilm capacitors main walls. Th esearchers.[64,65 gnificantly whe in ferroelectric ors can be signifi mechanisms tha V hysteresis loo ii) reduction al stress. The lat rfacial poling, an liberation of de crease of the ef and attributed i his scenario is 5] Pertsev and en a 900 domain thin films indic ficantly affected at may act in par ops: i) defect-d of the clampin ter mechanism r nd potentially m fect-stabilized d ffective piezoele it to the stressconsistent with Emelyanov [66] n wall is shifted cate that reliabi by mechanical f rallel and contrib dipole realignme ng effect on do results in the enh may lead to more domain walls. K ectric coefficien -enhanced irrev h the theoretic ] have shown th d from its equil ility, performan force. Gruverma bute to ent and omains hanced e space Koval *et*  nt upon versible al and hat the librium nce and an *et al.* These results are interpreted in Ref. 62 by two mechanisms that may act in parallel and contribute to the indentation-driven voltage shift of the Q-V hysteresis loops: i) defect-dipole realignment and concurrent space charge rearrangement, and ii) reduction of the clamping effect on domains controlled by a variation of the internal residual stress. The later mechanism results in the enhanced polarization state of the film, the so-called interfacial poling, and potentially may lead to more space charge trapping at the bottom electrode due to liberation of defect-stabilized domain walls. Koval *et al.* in their early work [63] reported on an increase of the effective piezoelectric coefficient upon nanoindentation in the PZT film capacitors and attributed it to the stress-enhanced irreversible movement of ferroelastic domain walls. This scenario is consistent with the theoretical and experimental works of other researchers.[64, 65] Pertsev and Emelyanov [66] have shown that the residual stresses can change significantly when a 900 domain wall is shifted from its equilibrium position by an external field.

c e [67] have repo capacitors. By u either compressi orted on the st using piezorespo ive or tensile str tress-induced p onse force micr ess can change t oling and impr roscopy (PFM) the in-plane pola rinting of (111 they observed t arization compon 1)-oriented PZT that the applica nent of the film T-based ation of via the Stress-driven effects in ferroelectric thin films indicate that reliability, performance and lifetime of ferroelectric capacitors can be significantly affected by mechanical force. Gruverman *et al.*

15

[67] have reported on the stress-induced poling and imprinting of (111)-oriented PZT-based capacitors. By using piezoresponse force microscopy (PFM) they observed that the application of either compressive or tensile stress can change the in-plane polarization component of the film via the flexoelectric effect, and thus produce FeRAM (Ferroelectric Random Access Memory) capacitors in a heavily imprinted state characterized by a strongly shifted hysteresis loop (Fig. 11). Recently, the possibility to write ferroelectric memory bits using pure mechanical force instead of electrical voltage in data storage devices has been proposed by Lu *et al.* [68].

**Figure 11.** Stress-induced polarization reversal and switching characteristics of the (111)-oriented PZT capacitors. (a), (d) and (e) PFM amplitude images; (b), (e) and (h) PFM phase images; (c), (f) and (i) local hysteresis loops measured for as-grown capacitor, after tensile and compressive stress application, respectively. Reproduced with permission from Gruverman *et al*. [67]. Copyright 2003, AIP Publishing LLC.
