*2.4.1. Physical models of imprint and microscopic mechanisms for asymmetrical switching*

In the last two decades, several phenomenological scenarios and microscopic models have been proposed in the literature to explain the asymmetric switching behavior and the related imprint phenomena in ferroelectric thin film capacitors. Among them, two mechanisms seem to be able to consistently describe the polarization imprint and its dynamics: the *defect-dipole alignment model* [37] and the *interface screening model* [38].

### **a. Defect-dipole alignment model**

**2.4. Imprint and biasing effects in ferroelectric thin films**

**Figure 5.** Schematic of the formation of an internal bias after poling.

216 Ferroelectric Materials – Synthesis and Characterization

capacitor.

An internal field developed by charged defects is believed to play an important role in the *imprint phenomenon* in ferroelectric thin films. Imprint generally refers to the preference of a certain polarization state, the so called "hard" state, over the other "ease" state in ferroelectric bi-stable states. The preferential polarization may be induced within the ferroelectric by locking-in a particular domain orientation during electrical, thermal or optical (UV light) treatments.[33] The latter two effects are customarily called *thermal imprint* and *optical imprint*.

The polarization imprint of ferroelectric thin film capacitors, which manifests itself macro‐ scopically by a shift of the polarization hysteresis loop along the electric field axis (Fig. 6), is one of the most serious reliability issues for ferroelectric nonvolatile memories applications. An incomplete polarity reversal of the ferroelectric thin film, which also gives rise to an asymmetry in the remanent polarization and an effective variation of the coercive field, can lead to either "read" or "write" failure of the memory cell.[34] The voltage offset of the imprinted loop is often used as a measure of imprint. The sign of the field offset determines the direction of the preferential polarization in the interior of the ferroelectric thin film

An asymmetric hysteresis behavior has also been reported for as-grown ferroelectric thin films in an initial state, i.e. without heat treatment, ultraviolet radiation or application of an external electric field.[35] However, unlike the preferred polarization generated from capacitor There have been several indications that defects play an essential role in polarization degra‐ dation phenomena in bulk ceramics. To explain the interplay between the voltage shift, defects and polarization, Warren *et al.* [39] proposed the concept of aligning defect dipoles and their involvement in the aging process. By using electron paramagnetic resonance they demon‐ strated that the defect dipoles in BaTiO3 ceramics align along the direction of the spontaneous polarization. The asymmetric distribution of trapped charge and the alignment of defect dipoles near the electrode-ferroelectric interface have been suggested to be responsible for the imprint phenomena in ferroelectric thin film capacitors.[37] The dominating role of defect dipole alignment for producing internal bias field in PZT films was evidenced by the reduction of the thermally induced voltage shifts upon donor doping at the (Zr, Ti) sites. Similar findings on donor (La3+) doping effects have been also reported by Kim *et al.* [40], and the improved imprint behavior of La-doped PZT films was attributed to the reduction of the concentration of defect dipoles induced by the doping. Recently, Folkman *et al.* [41] by monitoring the builtin bias field in epitaxial BiFeO3 thin films have shown that the defect dipole pairs can realign and ultimately disassociate upon electrical cycling. The gradual dissociation of complex oxygen vacancy defects was accounted for a drastic reduction in the built-in bias field and an improvement of imprint characteristics of the films as measured after 104 cycles. u r upon donor dop reported by Kim ing at the (Zr,Ti m *et al.* [40], and i) sites. Similar f d the improved im findings on dono mprint behavior or (La3+) doping of La-doped PZ g effects have bee ZT films was attr en also ributed

> dipoles induced epitaxial BiFeO3

d by the doping. 3 thin films have

 Recently, Folk e shown that the

kman *et*  e defect

#### **b. Bulk and interface screening models** t *a* to the reduction *al.* [41] by moni n of the concentr itoring the builtration of defect -in bias field in e

o

on the electrode

s.

F

Fig. 7. (a) A sk

hysteresis loop i injected from th that is opposite

The co

ketch of ferroele

oncept employe

is thought to be he electrode into to the dipole of

h i t

In contrast to Warren's and Kim's observations [37, 40], the results obtained by Grossmann *et al.* [38] showed only a slight or negligible impact of Nb and Fe addition on the hysteresis and imprint behavior of PZT capacitors. Instead, the experiments with ultraviolet illumination revealed an enhancement of the polarization imprint of the PZT films. It was proposed that the redistribution of electronic species, such as electrons and/or holes, might be the main cause for the imprint phenomena in ferroelectric thin film capacitors, and the defect dipole align‐ ment, if any, is only a secondary imprint mechanism. d o a *(* I s b e dipole pairs can of complex oxyg an improvement *(b) Bulk and int* In contrast to W showed only a behavior of PZ enhancement of n realign and ulti gen vacancy def t of imprint char *terface screenin* Warren's and Kim slight or neglig ZT capacitors. I f the polarization imately disassoc fects was accoun racteristics of the *ng models*  m's observations gible impact of Instead, the exp n imprint of the ciate upon electr nted for a drastic e films as measu [37,40], the resu f Nb and Fe ad periments with PZT films. It w rical cycling. Th c reduction in the ured after 104 cyc ults obtained by ddition on the h ultraviolet illu was proposed tha he gradual disso e built-in bias fie cles. y Grossmann *et a* hysteresis and i umination revea at the redistribu ociation eld and *al.* [38] imprint aled an ution of

Currently, there are two reasonable approaches explaining the imprinted hysteresis loops of ferroelectric capacitors within the general concept of generation, separation and subsequent trapping of electronic charges: the *bulk screening model* [42] and the *interface screening model* [38]. Both models assume the existence of a thin layer at the interface between the electrode and ferroelectric in which the spontaneous polarization is absent or suppressed. However, they differ in modeling the driving force responsible for the charge separation. In the bulk screening model, the driving force is thought to be the *residual depolarizing field* (*Eres*) generated in the interior of the film due to incomplete cancellation of the space and polarization charges by free electronic (screening) charges on the electrodes. e i i f o m w d t i electronic specie in ferroelectric imprint mechani Curren ferroelectric cap of electronic ch models assume which the spont driving force re thought to be t incomplete canc es, such as electr thin film capac ism. ntly, there are tw pacitors within th harges: the *bulk* the existence of taneous polariza sponsible for the the *residual dep* cellation of the s rons and/or hole citors, and the d wo reasonable ap he general conc *screening mode* f a thin layer at t ation is absent o e charge separat *polarizing field* space and polari es, might be the m defect dipole al pproaches explai ept of generatio *el* [42] and the the interface betw or suppressed. H tion. In the bulk *d* (*Eres*) generate ization charges main cause for t lignment, if any ining the imprin on, separation an *interface screen* ween the electro However, they d k screening mod ed in the interio by free electron the imprint phen y, is only a sec nted hysteresis lo nd subsequent tr *ning model* [38] ode and ferroelec differ in modeli del, the driving f or of the film nic (screening) c nomena condary oops of rapping ]. Both ctric in ing the force is due to charges

s p shift of the impr permission from rinted thin film c m Abe *et al*. [48]. capacitor accord . Copyright 2002 ding to the interfa 2, AIP Publishin ace screening m ng LLC. model. Reproduce ed with **Figure 7.** (a) A sketch of ferroelectric thin film capacitor under imprint experiment, and (b) a voltage shift of the im‐ printed thin film capacitor according to the interface screening model. Reproduced with permission from Abe *et al*. [48]. Copyright 2002, AIP Publishing LLC.

ctric thin film c

ed in the interfa

governed by *Eif* o the film. As sh the ferroelectric

m f o might have orig ferroelectric thin of the polarizati ginated from a l n film capacitor on and in the op large electric fie during the accel pposite direction eld *Eif* that deve lerated aging (Fi of the *Eres* field elops within the ig. 7). This field d. A gradual shift e interface layer d points in the di fting of the polar r of the irection rization The concept employed in the interface screening model suggests that the imprint effects might have originated from a large electric field *Eif* that develops within the interface layer of the

ace screening m

imprint experim

ment, and (b) a v

voltage

effects

charges polarity external

hat the imprint

g of electronic c charges have a p eld screens the e

odel suggests th

secutive trapping 7, the injected c uced internal fie

*<sup>f</sup>* due to the cons hown in Figure 7 c, hence, the indu

12

ferroelectric thin film capacitor during the accelerated aging (Fig. 7). This field points in the direction of the polarization and in the opposite direction of the *Eres* field. A gradual shifting of the polarization hysteresis loop is thought to be governed by *Eif* due to the consecutive trapping of electronic charges injected from the electrode into the film. As shown in Figure 7, the injected charges have a polarity that is opposite to the dipole of the ferroelectric, hence, the induced internal field screens the external electric field and a higher applied voltage is required to induce polarization reversal. The experimental observations presented in Ref. 38 indicate that imprint in ferroelectric thin films is governed by the magnitude and orientation of the ferroelectric polarization and the voltage shift follows the direction of the polarization.

of defect dipoles induced by the doping. Recently, Folkman *et al.* [41] by monitoring the builtin bias field in epitaxial BiFeO3 thin films have shown that the defect dipole pairs can realign and ultimately disassociate upon electrical cycling. The gradual dissociation of complex oxygen vacancy defects was accounted for a drastic reduction in the built-in bias field and an

findings on dono mprint behavior dipoles induced epitaxial BiFeO3 ciate upon electr nted for a drastic e films as measu

[37,40], the resu f Nb and Fe ad periments with PZT films. It w es, might be the m defect dipole al

pproaches explai ept of generatio *el* [42] and the the interface betw or suppressed. H tion. In the bulk *d* (*Eres*) generate ization charges

In contrast to Warren's and Kim's observations [37, 40], the results obtained by Grossmann *et al.* [38] showed only a slight or negligible impact of Nb and Fe addition on the hysteresis and imprint behavior of PZT capacitors. Instead, the experiments with ultraviolet illumination revealed an enhancement of the polarization imprint of the PZT films. It was proposed that the redistribution of electronic species, such as electrons and/or holes, might be the main cause for the imprint phenomena in ferroelectric thin film capacitors, and the defect dipole align‐

Currently, there are two reasonable approaches explaining the imprinted hysteresis loops of ferroelectric capacitors within the general concept of generation, separation and subsequent trapping of electronic charges: the *bulk screening model* [42] and the *interface screening model* [38]. Both models assume the existence of a thin layer at the interface between the electrode and ferroelectric in which the spontaneous polarization is absent or suppressed. However, they differ in modeling the driving force responsible for the charge separation. In the bulk screening model, the driving force is thought to be the *residual depolarizing field* (*Eres*) generated in the interior of the film due to incomplete cancellation of the space and polarization charges by free

cycles.

cles.

g effects have bee ZT films was attr Recently, Folk e shown that the he gradual disso e built-in bias fie

en also ributed kman *et*  e defect ociation eld and

*al.* [38] imprint aled an ution of nomena condary

oops of rapping ]. Both ctric in ing the force is due to charges

y Grossmann *et a* hysteresis and i umination revea at the redistribu the imprint phen y, is only a sec

nted hysteresis lo nd subsequent tr *ning model* [38] ode and ferroelec differ in modeli del, the driving f or of the film nic (screening) c

ment, and (b) a v model. Reproduce

voltage ed with

effects r of the irection rization charges polarity external

hat the imprint e interface layer d points in the di fting of the polar g of electronic c charges have a p eld screens the e

cyc

or (La3+) doping of La-doped PZ d by the doping. 3 thin films have rical cycling. Th c reduction in the ured after 104

ults obtained by ddition on the h ultraviolet illu was proposed tha main cause for t lignment, if any

ining the imprin on, separation an *interface screen* ween the electro However, they d k screening mod ed in the interio by free electron

imprint experim ace screening m ng LLC.

odel suggests th elops within the ig. 7). This field d. A gradual shift secutive trapping 7, the injected c uced internal fie

improvement of imprint characteristics of the films as measured after 104

*ng models*  m's observations gible impact of Instead, the exp n imprint of the rons and/or hole citors, and the d

wo reasonable ap he general conc *screening mode* f a thin layer at t ation is absent o e charge separat *polarizing field* space and polari

ctric thin film c capacitor accord . Copyright 2002

ed in the interfa large electric fie during the accel pposite direction governed by *Eif* o the film. As sh the ferroelectric

12

 capacitor under ding to the interfa 2, AIP Publishin

**Figure 7.** (a) A sketch of ferroelectric thin film capacitor under imprint experiment, and (b) a voltage shift of the im‐ printed thin film capacitor according to the interface screening model. Reproduced with permission from Abe *et al*.

The concept employed in the interface screening model suggests that the imprint effects might have originated from a large electric field *Eif* that develops within the interface layer of the

ace screening m eld *Eif* that deve lerated aging (Fi of the *Eres* field *<sup>f</sup>* due to the cons hown in Figure 7 c, hence, the indu

i) sites. Similar f d the improved im ration of defect -in bias field in e imately disassoc fects was accoun racteristics of the

**b. Bulk and interface screening models**

218 Ferroelectric Materials – Synthesis and Characterization

ing at the (Zr,Ti m *et al.* [40], and n of the concentr itoring the builtn realign and ulti gen vacancy def t of imprint char

*terface screenin* Warren's and Kim slight or neglig ZT capacitors. I f the polarization es, such as electr thin film capac

u r t *a* d o a

upon donor dop reported by Kim to the reduction *al.* [41] by moni dipole pairs can of complex oxyg an improvement

*(b) Bulk and int* In contrast to W showed only a behavior of PZ enhancement of electronic specie in ferroelectric imprint mechani

ferroelectric cap of electronic ch models assume which the spont driving force re thought to be t incomplete canc on the electrode

Curren

ism.

s.

*(* I s b e e i i

f o m w d t i o

F s p

Fig. 7. (a) A sk shift of the impr permission from

might have orig ferroelectric thin of the polarizati hysteresis loop i injected from th that is opposite

The co

[48]. Copyright 2002, AIP Publishing LLC.

m f o h i t

ment, if any, is only a secondary imprint mechanism.

electronic (screening) charges on the electrodes.

ketch of ferroele rinted thin film c m Abe *et al*. [48].

oncept employe ginated from a l n film capacitor on and in the op is thought to be he electrode into to the dipole of

ntly, there are tw pacitors within th harges: the *bulk* the existence of taneous polariza sponsible for the the *residual dep* cellation of the s

Within the interfacial screening model, several charge injection mechanisms have been suggested for the imprint phenomena in ferroelectric capacitors, including the *field enhanced thermionic emission* from the electrodes *(Schottky effect)* and *Pool-Frenkel emission* from traps. The Schottky emission current density can be expressed as follows [43]:

$$J\_S = A^\* T^2 \exp\left(\frac{-q\mathcal{D}\_B}{k\_B T}\right) \exp\left(\frac{q\Delta\mathcal{D}\_S}{k\_B T}\right) \tag{5}$$

where *A\** is the effective Richardson constant, *q* is the eletronic charge, *kB* is the Boltzmann constant, *T* is the absolute temperature, and *qϕB* is the Schottky barrier height (i.e., conduction band offset). *Δ*∅*S* denotes the barrier lowering:

$$
\Delta \mathcal{Q}\_S = \sqrt{\frac{qE}{4\pi \epsilon\_r \varepsilon\_0}} \tag{6}
$$

where *E* is the applied electric field, *ε0* is the vacuum permittivity and *ε<sup>r</sup>* is the dynamic dielectric constant of the ferroelectric.

The equation implies that the interfacial-layer charge injection due to thermal emission is exponentially proportional to the barrier lowering, which is dependent on the applied electric field. The standard quantitative expression for the Poole-Frenkel effect is [44]:

$$J \propto E \exp\left(\frac{-q\left(\mathcal{D}\_{\rm B} - \sqrt{qE / \pi \epsilon\_r \epsilon\_0}\right)}{k\_\text{B}T}\right) \tag{7}$$

According to Eq. 7, the displacement of the polarization hysteresis loop along the field axis is expected to be independent of the film thickness, and the voltage offset would increase as the thickness of the sample increases. This effect has been experimentally evidenced in ferroelectric thin film capacitors with variable thickness.[45, 46]

Although the bulk screening model reasonably explains the imprinted hysteresis loops for films illuminated by UV light during poling, it cannot describe an enhancement of the 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 applied bias [36, 38, 42].
