- Email: [email protected]
Polarization modification of PZT thin films by means of electric fields and stress in scanning force microscopy
Surface Science 585 (2005) 144–154 www.elsevier.com/locate/susc
Polarization modification of PZT thin films by means of electric fields and stress in scanning force microscopy K. Franke, M. Weihnacht
*
Leibniz-Institut fu¨r Festko¨rper und Werkstoffforschung Dresden, Postfach 270116, D-01171 Dresden, Germany Received 24 February 2004; accepted for publication 22 March 2005 Available online 23 May 2005
Abstract Polarization switching in scanning force microscopy (SFM) is influenced by both electric fields and stress, whereby the latter can arise inherently from Maxwell stress. We discuss the influence of electric charges and of the polarization asymmetry on the switching behaviour. For single crystallites of PZT(53/47) thin films, the sectors for ferroelectric, ferroelastoelectric and ferroelastic switching are represented in a field-stress map. The influence of stress on the second harmonic of the SFM is also discussed. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Ferroelectricity; Microscopy atomic force; Polarization dielectric; Thin films dielectric
1. Introduction Many efforts have been made throughout the world to develop high-density non-volatile ferroelectric memories (FeRAM). Non-volatile memories would allow to considerably reduce energy consumption with respect to dynamic random access memories and therefore open up new fields of application. Promising storage materials for such memories are PbZrxTi1xO3 (PZT) thin films. * Corresponding author. Tel.: +49 351 4659 330; fax: +49 351 4659 440. E-mail address: [email protected] (M. Weihnacht).
One necessary property of ferroelectric films for high-density FeRAMs is the microscopic perfection of the polarization switching. Considering the small dimensions of the storage elements, the failure of single crystallites within the ferroelectric thin film would already lead to substantial operational deterioration. It was shown that scanning force microscopy (SFM) in piezoresponse mode (PFM) has a great potential to determine microscopic fluctuations of polarization switching [1–3]. In SFM switching experiments, the impact of mechanical stress has to be taken into account as well as the influence of ferroelectric switching. Considerable stress levels may arise simply due to the electrostatic attraction (Maxwell stress)
0039-6028/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.03.064
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
between the tip of the SFM and the sample. The influence of stress in SFM switching was investigated for the first time by Franke et al. [4] and Abplanalp et al. [5]. The stress effects concern the ferroelastoelectric and the ferroelastic polarization switching. In this paper, we determine the magnitude of polarization change in PZT thin films caused by electric fields and stress for the three types of switching mentioned above. The investigated films show a mixture of rhombohedral and tetragonal crystallites. A ferroelectric material with mixed crystallographic symmetry is intentionally used. According to Hwang et al. [6], the polarization of macroscopic samples can be switched by an electric field as close as possible to a direction perpendicular to the sample surface, and by pressure alone as close as possible to the plane of the film. The measurement of the z-component of polarization in both experiments might allow the determination of the absolute (as well as the switchable) amount of polarization and the orientation of the polar axes. In SFM switching, the adequate experiments could offer a new possibility to characterize mixed systems on a microscopic scale. The present paper is thus a first empiric approach in this sense. In PFM, the polarization is derived dividing the piezoresponse value (first harmonic of the PFM signal) by the simultaneously measured second harmonic [7]. As a consequence, the influence of stress on the second harmonic is also investigated in this paper.
145
The first, second and third terms in (1) dominate in ferroelectric, ferroelastic and ferroelastoelectric switching, respectively. The type of switching occurring in a crystallite of a thin film depends not only on electric field and stress, but also on the orientation of the crystalliteÕs polar axes. According to Abplanalp et al. [5], the polarization can even switch antiparallel to the applied electric field, due to the application of stress in cases when in-plane switching (perpendicular to the surface normal) is forbidden for energetic reasons. According to [5], such ferroelastoelectric switching takes place if the third term in Eq. (1) predominates over the first one, i.e. if the stress exceeds a certain threshold. Abplanalp et al. investigated the polarization switching of c-axis oriented tetragonal barium titanate thin films. Here, our purpose is the microscopic study of polarization switching due to electric fields and stress for PZT(53/47) thin films with randomly oriented crystallites.
3. The problem of evaluating the polarization switching
The polarization change due to electric field and stress can be described by the Gibbs free energy G
We measure only the remanent polarization component in the z-direction (surface normal) after having switched off the electric field and stress, and denote it with P. The positive z-direction points away from the sample. The field is generated by applying a voltage Utip between the tip and a grounded electrode at the rear of the sample. The stress is always compressive and directed in the negative z-direction. The polarization in either z-direction (with indices + and , respectively) is described by its extreme value and variable part (Fig. 1).
G ¼ P si Ei esi ri d ij Ei rj 1=2j0 jij Ei Ej
þ Pþ ¼ Pþ max þ DP ;
ð2Þ
P ¼ P min þ DP .
ð3Þ
2. Gibbs free energy
1=2sij ri rj ;
ð1Þ
where the i, j components of the following vectors and tensors are indicated: Ps spontaneous polarization, E electric field, es spontaneous strain, r elastic stress, d piezoelectric tensor, j permittivity, s elastic compliance. For the three types of polarization switching mentioned, different terms of G are minimized.
In our experience, the extreme values P þ max and P min are obtained only when applying an electric field, E = Emax, and zero stress, r = 0. Emax is the electric field strength above which the remanent polarization remains constant. DP+ and DP arise due to the subsequent application of a varying electric field and stress.
146
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
+ Fig. 1. Definition of polarization reversal in SFM switching. P þ max and P min are the extreme values of polarization. DP and DP arise due to electric field–stress application. The mean Pmean of the extreme polarization values often does not correspond to the usually unknown zero-polarization level Pzero. Therefore, the passing of the polarization Pmean does not necessarily indicate a polarization þ reversal (see P þ ¼ P þ max þ DP in (a). A better indication of a polarization reversal is the overlap of the bipolar final polarization states (sign of A in Eq. (6)), i.e. polarization reversal takes place in (b) but not in (a). Additionally, the value of Pzero can be experimentally determined with the aid of the quantity P piezo zero (see Eq. (16)).
In SFM measurements, the problem is often to determine which signal corresponds to the zero level Pzero of the polarization. The reason for this is that the tip force is determined not only by Utip, but also by an usually unknown intrinsic voltage Uint. Electric charges in ferroelectrics may be the source of Uint, as can be verified by calculations with a plate capacitor model [8]. Further sources of Uint may be vacancies, defects, contact potentials, etc. [9,10]. Uint influences the piezoresponse of the PFM. In our experiments (see details on tip preparation in Section 4), the signals of the second harmonic (Sharm2) and of the first harmonic (Sharm1) correspond to the dielectric constant e and to the inverse piezoelectric coefficient plus c1eU, respectively, with c1 as a mainly geometric factor and U the sum of externally applied and intrinsic dc-voltage [7]. To determine the polarization, the inverse piezoelectric coefficient must be divided by e [11]. P¼
S harm1 c1 U int ; S harm2
ð4Þ
where c1 depends on the tip radius and is measured by means of a small Udc variation using c1 = o(Sharm1/Sharm2)/oUdc. In SFM experiments, Uint is usually unknown and an offset remains in the polarization calculation according to Eq. (4),
i.e. the zero level of the polarization is unknown. In the following, we avoid this problem by poling the sample with both Utip-polarities and by using only polarization differences instead of the polarization itself. We define the relative polarization change gdiff as the ratio between the polarization differences when applying an electric field and a stress, and when using optimum poling (Fig. 1): A 1; B A ¼ ðP þ P Þr;E ;
gdiff ¼
B¼
ðP þ max
P min Þr¼0;E¼Emax ;
ð5Þ ð6Þ ð7Þ
where B is the switchable polarization which is always positive. A is positive if the polarization vectors do not overlap after the application of an electric field and a stress (Fig. 1a). Otherwise, A is negative (Fig. 1b) and gdiff becomes smaller than 1. If the polarization values reverse completely, gdiff reaches the value 2. The mean of the polarization extreme values is ðP þ max þ P min Þr¼0;E¼Emax . ð8Þ 2 The difference-based definition of gdiff eliminates the problem of a misinterpretation of the polarization switching.
P mean ¼
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
We now discuss an important example. Abplanalp et al. [5] claim that the polarization during the ferroelastoelectric switching maintains its absolute value but inverts its sign (see Fig. 1b in [5]). However, the bipolar poling curves of Fig. 1c in [5], i.e. under a stress load, do not show any polarization overlap for strong fields. Instead, the poling curves reach the same level, which is obviously the zero polarization level. In [5], the Pmean value was incorrectly defined as Pzero and a polarization reversal was therefore suggested. In any case, the example shows that Pzero can be approximately determined by means of ferroelastoelectric switching. This will be discussed more detailed in Section 5.2.1. Novel pull-off experiments [12] allow the exact determination of the Pzero level. In these experiments, we often find considerable differences between Pzero and Pmean in PZT(53/47) thin films, i.e. P zero 6¼ P mean .
ð9Þ
4. Experimental A in-house constructed SFM is used for measurements. Details of the construction are given in [4]. The SFM is operated in high vacuum to minimize undesired electric sample charging. The cantilever is mounted on a piezoelectric bimorph, in order to apply a stress. The bimorph can be bent by an amount dbim by applying the voltage Ubim. dbim ¼ aU bim .
ð10Þ
The constant a is determined interferometrically. Electrically conductive Si-cantilevers are used with a spring constant k = 2.1 N/m. According to the discussion of Eq. (4), the local permittivity must be known in order to evaluate the polarization. The permittivity can be determined by measuring the second harmonic if the oxide film on the tip is not too thick. We remove the thick oxide by etching the tip with hydrofluoric acid (20%, 10 s). Subsequently, a native oxide of a few nanometers thickness is grown in air to reduce undesired sample charging. During the application of stress, the tip shows unwanted displacements along the surface. We
147
eliminate this shift by correcting the voltages on the x–y stage of the SFM. To vary stress and electric field in SFM independently, the Maxwell stress rMW has to be controlled. rMW originates from the electrostatic attraction between the tip and the sample [4]. As a first approximation, we have rMW ¼ bU 2tip ;
ð11Þ
where b is determined in pull-off measurements [4]. We apply a voltage U off tip to the tip and measure the bimorph voltage U off bim for which the tip pulls off from the sample surface. The cantilever force is then equal to the force induced by Maxwell stress. The value of b is calculated by 2
off b ¼ aU off bim k=½Atip ðU tip Þ ;
ð12Þ
where Atip is the effective tip area and b is measured at a representative tip voltage U off tip 30 V. The value of b depends on the sample permittivity and the tip geometry [8]. Using SEM inspection (Leo 1530, Gemini), the effective tip radius is found to be 40 nm. The bimorph-induced stress rbim at the tip can be roughly described by rbim ¼ aU bim k=Atip c2 U bim .
ð13Þ
An additional correction f(Ubim) is still necessary: when varying Ubim, the cantilever bends and the length of the SFM scanner changes as a response of the SFM control unit. The unwanted variation of the scanner length dsc modifies the stress at the tip and has to be taken into account with f(Ubim) = dsc(Ubim)k/Atip. The total stress rt according to Eqs. (11) and (13) and the expression for f(Ubim) is rt ¼ rMW þ rbim ¼ bU 2tip þ c2 U bim þ f ðU bim Þ.
ð14Þ
In our experiments, the stress and electric field are always varied using the same protocol: the rise and retention times are 3 s and 2 s, respectively, and after having switched off the stress and the electric field, the tip remains for 20 s in its place to collect occasional electrical charging. The extreme polarization values are only reached in correspondence with stress-free poling (rt = 0). We denote the corresponding procedure
148
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
as ‘‘poling with pull-off’’ (PPO) and take the final tip voltage U end tip as argument of PPO, e.g. PPO (30 V). The procedure is the following: starting from zero, Utip is varied and the rising Maxwell stress is simultaneously compensated to about 15% of its uncorrected value by appropriate bimorph bending; after having reached U end tip , we continue to bend the bimorph until the tip pulls off from the sample surface. Thus, the tip is finally completely free of stress. In all of our experiments, at least one PPO (30 V) procedure was carried out before proceeding to any switching. After applying an electric field in combination with a non-zero Maxwell stress, the Maxwell stress or Utip must be switched off in a sufficiently short time. The reason for this is that in switching off Utip, the Maxwell stress ðrMW / U 2tip Þ decreases faster than the electric field (E / Utip). If Utip is decreased slowly, the electric field can refresh the polarization. In our experiments, a decay time of 10 ms is found to be short enough to avoid polarization refreshing. A sol–gel processed PZT(53/47) thin film is used [13]. The film is 2 lm thick, consists of four layers and is deposited on steel. The mean crystallite diameter is 500 nm. The crystallites of the film are randomly oriented and of mixed symmetry. In the virgin state, the film is positively selfpolarized.
picoseconds [14], and the discussed decay time of the Utip-pulses (see Section 4) should be much shorter. However, no polarization refreshing can be observed even for a decay time of 10 ms. This is another indication of the presence of remaining screening charges.
Our SFM experiments are influenced by electric charges. The effects will be shortly discussed.
5.1.2. Tip-induced charges For high values of jUtipj, the sample can be electrically charged by the tip. Experimental indications of this effect can be obtained with the aid of the pull-off voltage U off bim [12]. Tip-induced charges decrease jU off j because they generate bim repulsive forces between tip and sample. Measuring U off bim for bipolar Utip, the symmetry of the charging with respect to Utip can be tested. Simultaneously, non-symmetric U off bim values indicate a difference between Pzero and Pmean. The reason is, according to [12], that the more antipolar dipole charges are present in front of the tip, the stronger the charging effect of the tip on the sample. In other words, for high values of jUtipj, the absolute amount of charging depends monotonously on jPj. Therefore, asymmetric jU off bim j-values indicate an asymmetry of the bipolar jPj values. An example follows. Because the tip must be negative to switch the polarization in the positive off þ z-direction, from jU off follows that bim j < jU bim j þ jP max j > jP min j and finally that Pzero < Pmean. This relation is found for the majority of the investigated PZT-crystallites. Usually, the crystallites have a stronger negative charge than a positive one for jUtipj > 20 V. This dominance of negative charging can be demonstrated furthermore by two typical characteristics of the polarization geometry resulting from different poling experiments.
5.1.1. Screening charges Screening charges strongly influence the polarization switching: (i) In positively self-polarized crystallites, the maximum value of jPj can be reached only after the repeated application of PPO (+30 V) procedures with interruptions of some minutes between each procedure. Apparently, the screening charges must be decreased. (ii) In the absence of screening charges, the fieldinduced polarization switching can occur within
1. When reversing the polarization by means of a negative tip, we get a more widespread distribution (Fig. 2b) than the in case of a positive tip. (Fig. 2a). The explanation for this is that the strong negative charges spread and polarize the surrounding area around the tip. 2. When applying fields that are—contrary to point 1—parallel with the initial polarization (Upar), the diameter of the depolarized area is smaller in the case of a negative Utip value
5. Results 5.1. Influence of electric charges on the switching
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
149
Fig. 2. (a) and (b) Polarization of a PZT crystallite after stress-free polarization switching shows different lateral distributions. Figure dimension: 232 nm. (a) Down-poling by PPO (+30 V). (PPO indicates ‘‘poling with pull-off’’). (b) Up-poling by PPO (30 V). The tip position was situated near the centre of the image. The greyscale varies linearly between the black and the white corresponding to the minimum and maximum, respectively, of the polarization in (a) and (b). (c) Topography of the crystallite. Surface corrugation: 10 nm.
(Fig. 3). The spreading negative charges now prevent the depolarization in the surrounding area around the tip.
5.2. Dependence of polarization switching on stress and field For the discussed three kinds of switching, we experimentally determined the amount gdiff of switching as a function of the electric field and/ or stress. We investigate separately about 50 crystallites of the PZT sample. They are situated along a line of 1 mm length. The polarization is measured directly at the poling position of the tip. The field is characterized by Utip. We denote anti the tip voltages U par tip and U tip when the field is
parallel and antiparallel, respectively, to the initial direction of the polarization. For simplicity, we denote any polarization change, i.e. decrease of jPj, as ‘‘depolarization’’ or ‘‘switching’’ even if the polarization does not change its sign. Fig. 4 shows the gdiff-function of a representative PZT-crystallite in the case of a non-vanishing field. 5.2.1. Ferroelastoelectric switching An area of ferroelastoelectric switching can be seen in the upper half of Fig. 4. Contrary to [5], we do not find a striking stress threshold, rather a continuous change in ferroelastoelectric switching. The typical features are that the onset of switching occurs at 85 MPa, and that the final state is reached above 150 MPa. Remarkably, the
150
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
Fig. 3. Polarization of Fig. 2 after ferroelastoelectric switching. Total pressure rtip at the tip: 127 MPa. Greyscale and tip position as in par Fig. 2. (a) U par tip ¼ þ30 V and (b) U tip ¼ 30 V were applied to the polarization of Fig. 2(a) and (b), respectively. The polarization values at the tip positions are nearly equal (gdiff = 0.9) in the figures. However, the polarization changes compared to Fig. 2 are nonsymmetric: jDP+j/jDPj = 1.65. (c) Topography of the crystallite. Surface corrugation: 10 nm.
extent in the field direction of the area of ferroelastoelectric switching is small. Keeping stress constant, only 10% variation of the tip voltage leads to a noticeable change of gdiff. The stress for maximum switching depends on the second power of the electric field and follows, in our case, exactly the Maxwell stress curve (see Eqs. (11) and (12)). We consider this to be an accidental result of the tip geometry. The crystallites only slightly differ with respect to their individual minimum values of gdiff. We suppose that the strong non-homogeneity of the electric field and pressure near the tip averages the differences which could be expected for different orientations and symmetry of the investigated crystallites. Two further relevant experimental results are the following: (i) the most frequent values of the
gdiff-minimum are near to 1, and the smallest value found is 1.25. We suppose that a stronger polarization change in the opposite direction is prevented by the generation and re-orientation of domains during the application of stress and an electric field. These domains decrease the mean polarization to zero and prevent a further minimization of Gibbs free energy (see Section 2). (ii) In the case of strong ferroelastoelectric switching, jDP+j is usually higher than jDPj. Together with the fact that Pzero is mostly found to be shifted towards P min (see Section 5.1.2), this non-symmetry is a further indication that the ferroelastoelectric switching only proceeds near the zero level of polarization. From this we conclude that Pzero can be approximately determined as
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
151
tion changes are found up to 250 nm away from the tip centre. The corresponding distance for negative Utip is twice the tip radius.
Fig. 4. Relative polarization change gdiff (figure parameters) from Eq. (5) in dependence on compressive stress and electric field, the latter represented by the tip voltage Utip. Evaluation of SFM measurements on a typical crystallite of a PZT(53/47) thin film. The parabola (dashed line) corresponds to the Maxwell stress from Eq. (11). In the upper and lower half of the diagram the field is parallel and antiparallel, respectively, to the initial polarization direction.
P zero P piezo zero ; P piezo zero
þ Pþ max þ DP piezo þ P min þ DP piezo . 2
P piezo zero
ð15Þ ð16Þ
Here is the mean value of the bipolar polarization after strong ferroelastoelectric switching (see Fig. 1b). The DPpiezo values are the corresponding polarization changes. The index ‘‘piezo’’ denotes the dependence of the ferroelastoelectric switching on the piezoelectric coefficient. The given Pzero level enables a better interpretation of SFM polarization switching experiments. Further, we find that the stress which is necessary to reach the gdiff-minimum of the crystallites varies by 30%. After ferroelastoelectric switching, the polarization can be reversed to the initial state in all cases by PPO (+30 V) or PPO (30 V), i.e. the domains are not blocked. Furthermore, in the surrounding area of the tip, a polarization change takes place due to radial pressure. The dimension of this area depends on the Utip polarity because a tip-induced charging (see Section 5.1.2) can take place. In the case of minor charging (positive Utip), very small polariza-
5.2.2. Ferroelectric switching Electric fields that are directed antiparallel to the initial polarization direction (see the lower half of Fig. 4) can in principle switch the polarization to any value between P þ max and P min . The relative polarization change gdiff then varies between 0 and 2. The superposition of stress to the electric field modifies the switching. Now, ferroelastoelectric switching takes place also in the lower half of Fig. 4, symmetrically to the upper half. The final polarization values are the same as if a parallel electric field and stress are applied on the reversed polarization. An example is given. When applying þ U anti tip and stress to P max , we obtain the final polar ization P min þ DP . This is the same polarization that is obtained by applying U par tip and a stress to P . The term A in Eq. (6) maintains its absolute min value but changes in sign. Therefore the relative polarization changes near the parabola in the lower and the upper diagram half gdiff and gdiff, respectively, are related by gdiff ¼ 2 gdiff .
ð17Þ
We define the coercive electric field here as the field that switches the initial polarization to the value P piezo zero . The corresponding tip voltage is 13 V in our PZT film. 5.2.3. Ferroelastic switching We use pure stress (E = 0) in ferroelastic switching and apply the stress to both polarities of the polarization. The necessary stress for the polarization change is found to be much higher than in the case of ferroelastoelectric switching. In SFM we observe the onset of the ferroelastic switching in PZT(53/47) thin films only above 550 MPa (Fig. 5). On the contrary, the ferroelastic switching of compact PZT samples (PZT-4) is reported to start already from 60 MPa [15]. In SFM at comparable pressures, the switched polarization is supposed to be unstable because of the small dimensions of the influenced areas. Increasing the stress in SFM, the switched areas become larger and therefore stable.
152
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
Fig. 5. Relative polarization change gdiff from Eq. (5) as a function of compressive stress for electric field = 0. SFM measurement of a typical crystallite of a PZT(53/47) thin film.
In this regard, we have to correct one result contained in one of our previous publications [4]. For the first time in SFM, a strong depolarization was generated by applying an electric field and a stress. As the stress agreed well with the stress for ferroelastic switching in a compact material, we concluded that ferroelastic switching had been accomplished. Here, we can claim to have carried out ferroelastoelectric switching. When applying pure stress, the crystallites exhibits different polarization effects. Four types of crystallite behaviour can be observed: Type 1: No depolarization (decrease of jPj) occurs even at a pressure of 1.2 GPa. The effect can be explained by assuming that no polar axis exists within the crystallite which is inclined further away from the applied pressure than the actually occupied axis. E.g., for tetragonal crystallites, a (1 1 1) orientation could be present. Type 2: Keeping the tip position constant, both P+ and P are altered in the negative direction due to the stress. Such effects were also observed by Eng [16] in PZT thin films. Subsequently, both Pþ max and P max values (generated by PPO (±30 V) procedures) are smaller than before the application of stress. We conclude that only the intrinsic voltage Uint (Eq. (4)) is changed by the stress. Type 3: Depolarization takes place, but the initial polarization can be re-established by PPO (30 V). This means that the stress-induced domain configuration can easily be changed.
Type 4: Depolarization takes place but the initial polarization cannot be re-established even by application of PPO (45 V). It appears that scarcely moveable domains are created by the stress. The proposed domain-hypothesis for types 3 and 4 cannot be examined by means of SFM, because the domains are too small (domain thickness < 20 nm). Whether the effects depend on the crystallographic symmetry or on other parameters (e.g. on crystalline defects) should be investigated in purely tetragonal and rhombohedral films. For all applied pressure values (61.2 GPa), the amount of ferroelastic switching is small. The smallest gdiff-value reached was 0.45. Generally, the switched areas has large lateral dimensions with diameters up to 400 nm. So far, no clear relation between the ferroelastic and ferroelastoelectric switching of the crystallites has been obtained.
6. The influence of stress on the second harmonic In PFM the polarization is obtained by dividing the first harmonic by the second harmonic according to Eq. (4). If this is not done, the second harmonic can dominate the first harmonic in cases of high values of jUintj, and the first harmonic does not represent the polarization [7]. Therefore, the second harmonic and also its stress dependence is always of interest. In the present PZT film, we find the second harmonic to change in part after the previous stress application. Increasing the stress from zero, we measure in some crystallites a decrease of the second harmonic by 5% at a pressure 6500 MPa, then an increase up to 25% at a pressure P800 MPa. Both percentages are relative to the initial value. The change of the second harmonic inside the crystallites is remarkably stronger than at the grain boundaries. The stress effects appear for both polarization polarities and are reproducible several times in the same crystallite. However, while the stress-induced polarization change is limited to distances up to 200 nm from the tip, the change of the second harmonic is not laterally limited to the surrounding area of the tip. From this we conclude that the observed effects are solely
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
present at the tip, i.e. are artefacts. This can be explained by observing that the value of the second harmonic is determined by the series capacity of the tip and the counter electrode [8]. We assume that the tip is covered by a contaminating layer with low permittivity, probably lead oxide. The capacity of this layer varies due to the stress application and influences the second harmonic. In accordance with this assumption of the presence of a soft lead-oxide layer, the discussed film shows a noticeable abrasion of the surface after SFM scanning. The PZT(53/47) thin film provided by another producer [17] shows no abrasion and the second harmonic is not stress-dependent. Similarly, the grain boundary effects are assumed to be topographic artefacts. These artefacts demonstrate how sensitive the second harmonic is to surface corrugation, as the latter is only 10 nm. However, regardless of the artefacts, the second harmonic strongly influences the PFM piezoresponse in case of high jUintj and has to be measured to correctly determine the polarization.
7. Conclusions In SFM, we measured the polarization change due to the previous application of stress and an electric field on many single crystallites of PZT(53/47) thin films. Three kinds of polarization switching were investigated qualitatively: ferroelastoelectric, ferroelectric and ferroelastic switching. We describe how the influences of different electric charges and of polarity-dependent asymmetries of polarization have to be taken into account and that the knowledge of the polarization zero level is necessary to avoid misinterpretation of the switching. We discuss two possibilities to determine this level experimentally. Contrary to Abplanalp et al. [5], no sharp stress threshold was observed in ferroelastoelectric switching. The optimum stress was found to be proportional to the second power of the electric field. The crystallites varied in the switching behaviour. The typical features were the onset of switching at 85 MPa, the final state being reached above 150 MPa. The ferroelastoelectric switching proceeded only up to
153
about zero polarization. No clear reversal of the polarization sign was detected. In ferroelectric SFM switching without stress compensation, the influence of the Maxwell stress superimposes to the electric field and can cause the same final polarization states as in ferroelastoelectric switching. The necessary pressure in ferroelastic SFM switching of PZT(53/47) thin films was found to be higher by a factor of 9 than in switching of a compact material. We assume that the small dimensions of the switched areas in SFM are the reason for the difference. The stress dependence of the crystallites varied strongly. Four types of crystallites were discussed. The second harmonic of the SFM proved to be in part stress-dependent. We describe the consequences of this effect to the polarization measurement.
Acknowledgments We thank B. Brunner, ISC Wu¨rzburg, and F. Schlenkrich, IKTS Dresden, for providing excellent samples, A. Sotnikov, IFW Dresden, H. Franke, and F. Bosia for helpful discussions. K.F. acknowledges the financial support by the German Federal Research Society (DFG) under Grant No. WE2065/6.
References [1] A. Gruverman, A. Pignolet, K.M. Satyalakshmi, M. Alexe, N.D. Zakharov, D. Hesse, Appl. Phys. Lett. 76 (2000) 106. [2] S.A. Landau, P.A. Weiss, N. Junghans, B.O. Kolbesen, D. Adderton, G. Schindler, W. Hartner, F. Hintermaier, C. Dehm, C. MazureUltrathin SiO2 and High-K Materials for ULSI Gate Dielectrics, vol. 567, Materials Research Society, Warrendale, 1999, p. 567. [3] K. Franke, G. Martin, M. Weihnacht, A.V. Sotnikov, Solid State Commun. 119 (2001) 117. [4] K. Franke, H. Huelz, M. Weihnacht, Surf. Sci. 416 (1998) 59. [5] M. Abplanalp, J. Fousek, P. Gu¨nter, Phys. Rev. Lett. 86 (2001) 5799. [6] S.C. Hwang, C.S. Lynch, R.M. McMeeking, Acta Metall. Mater. 43 (1995) 2073.
154
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
[7] K. Franke, H. Huelz, M. Weihnacht, Surf. Sci. 415 (1998) 178. [8] K. Franke, M. Weihnacht, Ferroelectric Lett. 19 (1995) 25. [9] J.F. Scott, Ferroelectric Memories, Springer-Verlag, Berlin, 2000. [10] X. Lu, F. Schlaphof, Ch. Loppacher, S. Grafstro¨m, L.M. Eng, G. Suchaneck, G. Gerlach, Appl. Phys. Lett. 81 (2002) 3215. [11] M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Clarendon Press, Oxford, 1977 (Chapter 5.7).
[12] K. Franke, L. Eng, Surf. Sci., in preparation. [13] P. Lo¨bmann, S. Seifert, S. Merklein, S. Sporn, J. Sol-Gel Sci. Technol. 13 (1998) 827. [14] J.F. Scott, The physics of ferroelectric ceramic thin films for memory applications, Ferroelectr. Rev. 1 (1998) 1. [15] Q.M. Zhang, J. Zhao, K. Uchino, J. Zheng, J. Mater. Res. 12 (1997) 226. [16] L.M. Eng, private communication. [17] J. Frey, F. Schlenkrich, A. Scho¨necker, Integr. Ferroelectr. 35 (2001) 105.
Polarization modification of PZT thin films by means of electric fields and stress in scanning force microscopy K. Franke, M. Weihnacht
*
Leibniz-Institut fu¨r Festko¨rper und Werkstoffforschung Dresden, Postfach 270116, D-01171 Dresden, Germany Received 24 February 2004; accepted for publication 22 March 2005 Available online 23 May 2005
Abstract Polarization switching in scanning force microscopy (SFM) is influenced by both electric fields and stress, whereby the latter can arise inherently from Maxwell stress. We discuss the influence of electric charges and of the polarization asymmetry on the switching behaviour. For single crystallites of PZT(53/47) thin films, the sectors for ferroelectric, ferroelastoelectric and ferroelastic switching are represented in a field-stress map. The influence of stress on the second harmonic of the SFM is also discussed. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Ferroelectricity; Microscopy atomic force; Polarization dielectric; Thin films dielectric
1. Introduction Many efforts have been made throughout the world to develop high-density non-volatile ferroelectric memories (FeRAM). Non-volatile memories would allow to considerably reduce energy consumption with respect to dynamic random access memories and therefore open up new fields of application. Promising storage materials for such memories are PbZrxTi1xO3 (PZT) thin films. * Corresponding author. Tel.: +49 351 4659 330; fax: +49 351 4659 440. E-mail address: [email protected] (M. Weihnacht).
One necessary property of ferroelectric films for high-density FeRAMs is the microscopic perfection of the polarization switching. Considering the small dimensions of the storage elements, the failure of single crystallites within the ferroelectric thin film would already lead to substantial operational deterioration. It was shown that scanning force microscopy (SFM) in piezoresponse mode (PFM) has a great potential to determine microscopic fluctuations of polarization switching [1–3]. In SFM switching experiments, the impact of mechanical stress has to be taken into account as well as the influence of ferroelectric switching. Considerable stress levels may arise simply due to the electrostatic attraction (Maxwell stress)
0039-6028/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.03.064
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
between the tip of the SFM and the sample. The influence of stress in SFM switching was investigated for the first time by Franke et al. [4] and Abplanalp et al. [5]. The stress effects concern the ferroelastoelectric and the ferroelastic polarization switching. In this paper, we determine the magnitude of polarization change in PZT thin films caused by electric fields and stress for the three types of switching mentioned above. The investigated films show a mixture of rhombohedral and tetragonal crystallites. A ferroelectric material with mixed crystallographic symmetry is intentionally used. According to Hwang et al. [6], the polarization of macroscopic samples can be switched by an electric field as close as possible to a direction perpendicular to the sample surface, and by pressure alone as close as possible to the plane of the film. The measurement of the z-component of polarization in both experiments might allow the determination of the absolute (as well as the switchable) amount of polarization and the orientation of the polar axes. In SFM switching, the adequate experiments could offer a new possibility to characterize mixed systems on a microscopic scale. The present paper is thus a first empiric approach in this sense. In PFM, the polarization is derived dividing the piezoresponse value (first harmonic of the PFM signal) by the simultaneously measured second harmonic [7]. As a consequence, the influence of stress on the second harmonic is also investigated in this paper.
145
The first, second and third terms in (1) dominate in ferroelectric, ferroelastic and ferroelastoelectric switching, respectively. The type of switching occurring in a crystallite of a thin film depends not only on electric field and stress, but also on the orientation of the crystalliteÕs polar axes. According to Abplanalp et al. [5], the polarization can even switch antiparallel to the applied electric field, due to the application of stress in cases when in-plane switching (perpendicular to the surface normal) is forbidden for energetic reasons. According to [5], such ferroelastoelectric switching takes place if the third term in Eq. (1) predominates over the first one, i.e. if the stress exceeds a certain threshold. Abplanalp et al. investigated the polarization switching of c-axis oriented tetragonal barium titanate thin films. Here, our purpose is the microscopic study of polarization switching due to electric fields and stress for PZT(53/47) thin films with randomly oriented crystallites.
3. The problem of evaluating the polarization switching
The polarization change due to electric field and stress can be described by the Gibbs free energy G
We measure only the remanent polarization component in the z-direction (surface normal) after having switched off the electric field and stress, and denote it with P. The positive z-direction points away from the sample. The field is generated by applying a voltage Utip between the tip and a grounded electrode at the rear of the sample. The stress is always compressive and directed in the negative z-direction. The polarization in either z-direction (with indices + and , respectively) is described by its extreme value and variable part (Fig. 1).
G ¼ P si Ei esi ri d ij Ei rj 1=2j0 jij Ei Ej
þ Pþ ¼ Pþ max þ DP ;
ð2Þ
P ¼ P min þ DP .
ð3Þ
2. Gibbs free energy
1=2sij ri rj ;
ð1Þ
where the i, j components of the following vectors and tensors are indicated: Ps spontaneous polarization, E electric field, es spontaneous strain, r elastic stress, d piezoelectric tensor, j permittivity, s elastic compliance. For the three types of polarization switching mentioned, different terms of G are minimized.
In our experience, the extreme values P þ max and P min are obtained only when applying an electric field, E = Emax, and zero stress, r = 0. Emax is the electric field strength above which the remanent polarization remains constant. DP+ and DP arise due to the subsequent application of a varying electric field and stress.
146
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
+ Fig. 1. Definition of polarization reversal in SFM switching. P þ max and P min are the extreme values of polarization. DP and DP arise due to electric field–stress application. The mean Pmean of the extreme polarization values often does not correspond to the usually unknown zero-polarization level Pzero. Therefore, the passing of the polarization Pmean does not necessarily indicate a polarization þ reversal (see P þ ¼ P þ max þ DP in (a). A better indication of a polarization reversal is the overlap of the bipolar final polarization states (sign of A in Eq. (6)), i.e. polarization reversal takes place in (b) but not in (a). Additionally, the value of Pzero can be experimentally determined with the aid of the quantity P piezo zero (see Eq. (16)).
In SFM measurements, the problem is often to determine which signal corresponds to the zero level Pzero of the polarization. The reason for this is that the tip force is determined not only by Utip, but also by an usually unknown intrinsic voltage Uint. Electric charges in ferroelectrics may be the source of Uint, as can be verified by calculations with a plate capacitor model [8]. Further sources of Uint may be vacancies, defects, contact potentials, etc. [9,10]. Uint influences the piezoresponse of the PFM. In our experiments (see details on tip preparation in Section 4), the signals of the second harmonic (Sharm2) and of the first harmonic (Sharm1) correspond to the dielectric constant e and to the inverse piezoelectric coefficient plus c1eU, respectively, with c1 as a mainly geometric factor and U the sum of externally applied and intrinsic dc-voltage [7]. To determine the polarization, the inverse piezoelectric coefficient must be divided by e [11]. P¼
S harm1 c1 U int ; S harm2
ð4Þ
where c1 depends on the tip radius and is measured by means of a small Udc variation using c1 = o(Sharm1/Sharm2)/oUdc. In SFM experiments, Uint is usually unknown and an offset remains in the polarization calculation according to Eq. (4),
i.e. the zero level of the polarization is unknown. In the following, we avoid this problem by poling the sample with both Utip-polarities and by using only polarization differences instead of the polarization itself. We define the relative polarization change gdiff as the ratio between the polarization differences when applying an electric field and a stress, and when using optimum poling (Fig. 1): A 1; B A ¼ ðP þ P Þr;E ;
gdiff ¼
B¼
ðP þ max
P min Þr¼0;E¼Emax ;
ð5Þ ð6Þ ð7Þ
where B is the switchable polarization which is always positive. A is positive if the polarization vectors do not overlap after the application of an electric field and a stress (Fig. 1a). Otherwise, A is negative (Fig. 1b) and gdiff becomes smaller than 1. If the polarization values reverse completely, gdiff reaches the value 2. The mean of the polarization extreme values is ðP þ max þ P min Þr¼0;E¼Emax . ð8Þ 2 The difference-based definition of gdiff eliminates the problem of a misinterpretation of the polarization switching.
P mean ¼
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
We now discuss an important example. Abplanalp et al. [5] claim that the polarization during the ferroelastoelectric switching maintains its absolute value but inverts its sign (see Fig. 1b in [5]). However, the bipolar poling curves of Fig. 1c in [5], i.e. under a stress load, do not show any polarization overlap for strong fields. Instead, the poling curves reach the same level, which is obviously the zero polarization level. In [5], the Pmean value was incorrectly defined as Pzero and a polarization reversal was therefore suggested. In any case, the example shows that Pzero can be approximately determined by means of ferroelastoelectric switching. This will be discussed more detailed in Section 5.2.1. Novel pull-off experiments [12] allow the exact determination of the Pzero level. In these experiments, we often find considerable differences between Pzero and Pmean in PZT(53/47) thin films, i.e. P zero 6¼ P mean .
ð9Þ
4. Experimental A in-house constructed SFM is used for measurements. Details of the construction are given in [4]. The SFM is operated in high vacuum to minimize undesired electric sample charging. The cantilever is mounted on a piezoelectric bimorph, in order to apply a stress. The bimorph can be bent by an amount dbim by applying the voltage Ubim. dbim ¼ aU bim .
ð10Þ
The constant a is determined interferometrically. Electrically conductive Si-cantilevers are used with a spring constant k = 2.1 N/m. According to the discussion of Eq. (4), the local permittivity must be known in order to evaluate the polarization. The permittivity can be determined by measuring the second harmonic if the oxide film on the tip is not too thick. We remove the thick oxide by etching the tip with hydrofluoric acid (20%, 10 s). Subsequently, a native oxide of a few nanometers thickness is grown in air to reduce undesired sample charging. During the application of stress, the tip shows unwanted displacements along the surface. We
147
eliminate this shift by correcting the voltages on the x–y stage of the SFM. To vary stress and electric field in SFM independently, the Maxwell stress rMW has to be controlled. rMW originates from the electrostatic attraction between the tip and the sample [4]. As a first approximation, we have rMW ¼ bU 2tip ;
ð11Þ
where b is determined in pull-off measurements [4]. We apply a voltage U off tip to the tip and measure the bimorph voltage U off bim for which the tip pulls off from the sample surface. The cantilever force is then equal to the force induced by Maxwell stress. The value of b is calculated by 2
off b ¼ aU off bim k=½Atip ðU tip Þ ;
ð12Þ
where Atip is the effective tip area and b is measured at a representative tip voltage U off tip 30 V. The value of b depends on the sample permittivity and the tip geometry [8]. Using SEM inspection (Leo 1530, Gemini), the effective tip radius is found to be 40 nm. The bimorph-induced stress rbim at the tip can be roughly described by rbim ¼ aU bim k=Atip c2 U bim .
ð13Þ
An additional correction f(Ubim) is still necessary: when varying Ubim, the cantilever bends and the length of the SFM scanner changes as a response of the SFM control unit. The unwanted variation of the scanner length dsc modifies the stress at the tip and has to be taken into account with f(Ubim) = dsc(Ubim)k/Atip. The total stress rt according to Eqs. (11) and (13) and the expression for f(Ubim) is rt ¼ rMW þ rbim ¼ bU 2tip þ c2 U bim þ f ðU bim Þ.
ð14Þ
In our experiments, the stress and electric field are always varied using the same protocol: the rise and retention times are 3 s and 2 s, respectively, and after having switched off the stress and the electric field, the tip remains for 20 s in its place to collect occasional electrical charging. The extreme polarization values are only reached in correspondence with stress-free poling (rt = 0). We denote the corresponding procedure
148
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
as ‘‘poling with pull-off’’ (PPO) and take the final tip voltage U end tip as argument of PPO, e.g. PPO (30 V). The procedure is the following: starting from zero, Utip is varied and the rising Maxwell stress is simultaneously compensated to about 15% of its uncorrected value by appropriate bimorph bending; after having reached U end tip , we continue to bend the bimorph until the tip pulls off from the sample surface. Thus, the tip is finally completely free of stress. In all of our experiments, at least one PPO (30 V) procedure was carried out before proceeding to any switching. After applying an electric field in combination with a non-zero Maxwell stress, the Maxwell stress or Utip must be switched off in a sufficiently short time. The reason for this is that in switching off Utip, the Maxwell stress ðrMW / U 2tip Þ decreases faster than the electric field (E / Utip). If Utip is decreased slowly, the electric field can refresh the polarization. In our experiments, a decay time of 10 ms is found to be short enough to avoid polarization refreshing. A sol–gel processed PZT(53/47) thin film is used [13]. The film is 2 lm thick, consists of four layers and is deposited on steel. The mean crystallite diameter is 500 nm. The crystallites of the film are randomly oriented and of mixed symmetry. In the virgin state, the film is positively selfpolarized.
picoseconds [14], and the discussed decay time of the Utip-pulses (see Section 4) should be much shorter. However, no polarization refreshing can be observed even for a decay time of 10 ms. This is another indication of the presence of remaining screening charges.
Our SFM experiments are influenced by electric charges. The effects will be shortly discussed.
5.1.2. Tip-induced charges For high values of jUtipj, the sample can be electrically charged by the tip. Experimental indications of this effect can be obtained with the aid of the pull-off voltage U off bim [12]. Tip-induced charges decrease jU off j because they generate bim repulsive forces between tip and sample. Measuring U off bim for bipolar Utip, the symmetry of the charging with respect to Utip can be tested. Simultaneously, non-symmetric U off bim values indicate a difference between Pzero and Pmean. The reason is, according to [12], that the more antipolar dipole charges are present in front of the tip, the stronger the charging effect of the tip on the sample. In other words, for high values of jUtipj, the absolute amount of charging depends monotonously on jPj. Therefore, asymmetric jU off bim j-values indicate an asymmetry of the bipolar jPj values. An example follows. Because the tip must be negative to switch the polarization in the positive off þ z-direction, from jU off follows that bim j < jU bim j þ jP max j > jP min j and finally that Pzero < Pmean. This relation is found for the majority of the investigated PZT-crystallites. Usually, the crystallites have a stronger negative charge than a positive one for jUtipj > 20 V. This dominance of negative charging can be demonstrated furthermore by two typical characteristics of the polarization geometry resulting from different poling experiments.
5.1.1. Screening charges Screening charges strongly influence the polarization switching: (i) In positively self-polarized crystallites, the maximum value of jPj can be reached only after the repeated application of PPO (+30 V) procedures with interruptions of some minutes between each procedure. Apparently, the screening charges must be decreased. (ii) In the absence of screening charges, the fieldinduced polarization switching can occur within
1. When reversing the polarization by means of a negative tip, we get a more widespread distribution (Fig. 2b) than the in case of a positive tip. (Fig. 2a). The explanation for this is that the strong negative charges spread and polarize the surrounding area around the tip. 2. When applying fields that are—contrary to point 1—parallel with the initial polarization (Upar), the diameter of the depolarized area is smaller in the case of a negative Utip value
5. Results 5.1. Influence of electric charges on the switching
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
149
Fig. 2. (a) and (b) Polarization of a PZT crystallite after stress-free polarization switching shows different lateral distributions. Figure dimension: 232 nm. (a) Down-poling by PPO (+30 V). (PPO indicates ‘‘poling with pull-off’’). (b) Up-poling by PPO (30 V). The tip position was situated near the centre of the image. The greyscale varies linearly between the black and the white corresponding to the minimum and maximum, respectively, of the polarization in (a) and (b). (c) Topography of the crystallite. Surface corrugation: 10 nm.
(Fig. 3). The spreading negative charges now prevent the depolarization in the surrounding area around the tip.
5.2. Dependence of polarization switching on stress and field For the discussed three kinds of switching, we experimentally determined the amount gdiff of switching as a function of the electric field and/ or stress. We investigate separately about 50 crystallites of the PZT sample. They are situated along a line of 1 mm length. The polarization is measured directly at the poling position of the tip. The field is characterized by Utip. We denote anti the tip voltages U par tip and U tip when the field is
parallel and antiparallel, respectively, to the initial direction of the polarization. For simplicity, we denote any polarization change, i.e. decrease of jPj, as ‘‘depolarization’’ or ‘‘switching’’ even if the polarization does not change its sign. Fig. 4 shows the gdiff-function of a representative PZT-crystallite in the case of a non-vanishing field. 5.2.1. Ferroelastoelectric switching An area of ferroelastoelectric switching can be seen in the upper half of Fig. 4. Contrary to [5], we do not find a striking stress threshold, rather a continuous change in ferroelastoelectric switching. The typical features are that the onset of switching occurs at 85 MPa, and that the final state is reached above 150 MPa. Remarkably, the
150
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
Fig. 3. Polarization of Fig. 2 after ferroelastoelectric switching. Total pressure rtip at the tip: 127 MPa. Greyscale and tip position as in par Fig. 2. (a) U par tip ¼ þ30 V and (b) U tip ¼ 30 V were applied to the polarization of Fig. 2(a) and (b), respectively. The polarization values at the tip positions are nearly equal (gdiff = 0.9) in the figures. However, the polarization changes compared to Fig. 2 are nonsymmetric: jDP+j/jDPj = 1.65. (c) Topography of the crystallite. Surface corrugation: 10 nm.
extent in the field direction of the area of ferroelastoelectric switching is small. Keeping stress constant, only 10% variation of the tip voltage leads to a noticeable change of gdiff. The stress for maximum switching depends on the second power of the electric field and follows, in our case, exactly the Maxwell stress curve (see Eqs. (11) and (12)). We consider this to be an accidental result of the tip geometry. The crystallites only slightly differ with respect to their individual minimum values of gdiff. We suppose that the strong non-homogeneity of the electric field and pressure near the tip averages the differences which could be expected for different orientations and symmetry of the investigated crystallites. Two further relevant experimental results are the following: (i) the most frequent values of the
gdiff-minimum are near to 1, and the smallest value found is 1.25. We suppose that a stronger polarization change in the opposite direction is prevented by the generation and re-orientation of domains during the application of stress and an electric field. These domains decrease the mean polarization to zero and prevent a further minimization of Gibbs free energy (see Section 2). (ii) In the case of strong ferroelastoelectric switching, jDP+j is usually higher than jDPj. Together with the fact that Pzero is mostly found to be shifted towards P min (see Section 5.1.2), this non-symmetry is a further indication that the ferroelastoelectric switching only proceeds near the zero level of polarization. From this we conclude that Pzero can be approximately determined as
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
151
tion changes are found up to 250 nm away from the tip centre. The corresponding distance for negative Utip is twice the tip radius.
Fig. 4. Relative polarization change gdiff (figure parameters) from Eq. (5) in dependence on compressive stress and electric field, the latter represented by the tip voltage Utip. Evaluation of SFM measurements on a typical crystallite of a PZT(53/47) thin film. The parabola (dashed line) corresponds to the Maxwell stress from Eq. (11). In the upper and lower half of the diagram the field is parallel and antiparallel, respectively, to the initial polarization direction.
P zero P piezo zero ; P piezo zero
þ Pþ max þ DP piezo þ P min þ DP piezo . 2
P piezo zero
ð15Þ ð16Þ
Here is the mean value of the bipolar polarization after strong ferroelastoelectric switching (see Fig. 1b). The DPpiezo values are the corresponding polarization changes. The index ‘‘piezo’’ denotes the dependence of the ferroelastoelectric switching on the piezoelectric coefficient. The given Pzero level enables a better interpretation of SFM polarization switching experiments. Further, we find that the stress which is necessary to reach the gdiff-minimum of the crystallites varies by 30%. After ferroelastoelectric switching, the polarization can be reversed to the initial state in all cases by PPO (+30 V) or PPO (30 V), i.e. the domains are not blocked. Furthermore, in the surrounding area of the tip, a polarization change takes place due to radial pressure. The dimension of this area depends on the Utip polarity because a tip-induced charging (see Section 5.1.2) can take place. In the case of minor charging (positive Utip), very small polariza-
5.2.2. Ferroelectric switching Electric fields that are directed antiparallel to the initial polarization direction (see the lower half of Fig. 4) can in principle switch the polarization to any value between P þ max and P min . The relative polarization change gdiff then varies between 0 and 2. The superposition of stress to the electric field modifies the switching. Now, ferroelastoelectric switching takes place also in the lower half of Fig. 4, symmetrically to the upper half. The final polarization values are the same as if a parallel electric field and stress are applied on the reversed polarization. An example is given. When applying þ U anti tip and stress to P max , we obtain the final polar ization P min þ DP . This is the same polarization that is obtained by applying U par tip and a stress to P . The term A in Eq. (6) maintains its absolute min value but changes in sign. Therefore the relative polarization changes near the parabola in the lower and the upper diagram half gdiff and gdiff, respectively, are related by gdiff ¼ 2 gdiff .
ð17Þ
We define the coercive electric field here as the field that switches the initial polarization to the value P piezo zero . The corresponding tip voltage is 13 V in our PZT film. 5.2.3. Ferroelastic switching We use pure stress (E = 0) in ferroelastic switching and apply the stress to both polarities of the polarization. The necessary stress for the polarization change is found to be much higher than in the case of ferroelastoelectric switching. In SFM we observe the onset of the ferroelastic switching in PZT(53/47) thin films only above 550 MPa (Fig. 5). On the contrary, the ferroelastic switching of compact PZT samples (PZT-4) is reported to start already from 60 MPa [15]. In SFM at comparable pressures, the switched polarization is supposed to be unstable because of the small dimensions of the influenced areas. Increasing the stress in SFM, the switched areas become larger and therefore stable.
152
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
Fig. 5. Relative polarization change gdiff from Eq. (5) as a function of compressive stress for electric field = 0. SFM measurement of a typical crystallite of a PZT(53/47) thin film.
In this regard, we have to correct one result contained in one of our previous publications [4]. For the first time in SFM, a strong depolarization was generated by applying an electric field and a stress. As the stress agreed well with the stress for ferroelastic switching in a compact material, we concluded that ferroelastic switching had been accomplished. Here, we can claim to have carried out ferroelastoelectric switching. When applying pure stress, the crystallites exhibits different polarization effects. Four types of crystallite behaviour can be observed: Type 1: No depolarization (decrease of jPj) occurs even at a pressure of 1.2 GPa. The effect can be explained by assuming that no polar axis exists within the crystallite which is inclined further away from the applied pressure than the actually occupied axis. E.g., for tetragonal crystallites, a (1 1 1) orientation could be present. Type 2: Keeping the tip position constant, both P+ and P are altered in the negative direction due to the stress. Such effects were also observed by Eng [16] in PZT thin films. Subsequently, both Pþ max and P max values (generated by PPO (±30 V) procedures) are smaller than before the application of stress. We conclude that only the intrinsic voltage Uint (Eq. (4)) is changed by the stress. Type 3: Depolarization takes place, but the initial polarization can be re-established by PPO (30 V). This means that the stress-induced domain configuration can easily be changed.
Type 4: Depolarization takes place but the initial polarization cannot be re-established even by application of PPO (45 V). It appears that scarcely moveable domains are created by the stress. The proposed domain-hypothesis for types 3 and 4 cannot be examined by means of SFM, because the domains are too small (domain thickness < 20 nm). Whether the effects depend on the crystallographic symmetry or on other parameters (e.g. on crystalline defects) should be investigated in purely tetragonal and rhombohedral films. For all applied pressure values (61.2 GPa), the amount of ferroelastic switching is small. The smallest gdiff-value reached was 0.45. Generally, the switched areas has large lateral dimensions with diameters up to 400 nm. So far, no clear relation between the ferroelastic and ferroelastoelectric switching of the crystallites has been obtained.
6. The influence of stress on the second harmonic In PFM the polarization is obtained by dividing the first harmonic by the second harmonic according to Eq. (4). If this is not done, the second harmonic can dominate the first harmonic in cases of high values of jUintj, and the first harmonic does not represent the polarization [7]. Therefore, the second harmonic and also its stress dependence is always of interest. In the present PZT film, we find the second harmonic to change in part after the previous stress application. Increasing the stress from zero, we measure in some crystallites a decrease of the second harmonic by 5% at a pressure 6500 MPa, then an increase up to 25% at a pressure P800 MPa. Both percentages are relative to the initial value. The change of the second harmonic inside the crystallites is remarkably stronger than at the grain boundaries. The stress effects appear for both polarization polarities and are reproducible several times in the same crystallite. However, while the stress-induced polarization change is limited to distances up to 200 nm from the tip, the change of the second harmonic is not laterally limited to the surrounding area of the tip. From this we conclude that the observed effects are solely
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
present at the tip, i.e. are artefacts. This can be explained by observing that the value of the second harmonic is determined by the series capacity of the tip and the counter electrode [8]. We assume that the tip is covered by a contaminating layer with low permittivity, probably lead oxide. The capacity of this layer varies due to the stress application and influences the second harmonic. In accordance with this assumption of the presence of a soft lead-oxide layer, the discussed film shows a noticeable abrasion of the surface after SFM scanning. The PZT(53/47) thin film provided by another producer [17] shows no abrasion and the second harmonic is not stress-dependent. Similarly, the grain boundary effects are assumed to be topographic artefacts. These artefacts demonstrate how sensitive the second harmonic is to surface corrugation, as the latter is only 10 nm. However, regardless of the artefacts, the second harmonic strongly influences the PFM piezoresponse in case of high jUintj and has to be measured to correctly determine the polarization.
7. Conclusions In SFM, we measured the polarization change due to the previous application of stress and an electric field on many single crystallites of PZT(53/47) thin films. Three kinds of polarization switching were investigated qualitatively: ferroelastoelectric, ferroelectric and ferroelastic switching. We describe how the influences of different electric charges and of polarity-dependent asymmetries of polarization have to be taken into account and that the knowledge of the polarization zero level is necessary to avoid misinterpretation of the switching. We discuss two possibilities to determine this level experimentally. Contrary to Abplanalp et al. [5], no sharp stress threshold was observed in ferroelastoelectric switching. The optimum stress was found to be proportional to the second power of the electric field. The crystallites varied in the switching behaviour. The typical features were the onset of switching at 85 MPa, the final state being reached above 150 MPa. The ferroelastoelectric switching proceeded only up to
153
about zero polarization. No clear reversal of the polarization sign was detected. In ferroelectric SFM switching without stress compensation, the influence of the Maxwell stress superimposes to the electric field and can cause the same final polarization states as in ferroelastoelectric switching. The necessary pressure in ferroelastic SFM switching of PZT(53/47) thin films was found to be higher by a factor of 9 than in switching of a compact material. We assume that the small dimensions of the switched areas in SFM are the reason for the difference. The stress dependence of the crystallites varied strongly. Four types of crystallites were discussed. The second harmonic of the SFM proved to be in part stress-dependent. We describe the consequences of this effect to the polarization measurement.
Acknowledgments We thank B. Brunner, ISC Wu¨rzburg, and F. Schlenkrich, IKTS Dresden, for providing excellent samples, A. Sotnikov, IFW Dresden, H. Franke, and F. Bosia for helpful discussions. K.F. acknowledges the financial support by the German Federal Research Society (DFG) under Grant No. WE2065/6.
References [1] A. Gruverman, A. Pignolet, K.M. Satyalakshmi, M. Alexe, N.D. Zakharov, D. Hesse, Appl. Phys. Lett. 76 (2000) 106. [2] S.A. Landau, P.A. Weiss, N. Junghans, B.O. Kolbesen, D. Adderton, G. Schindler, W. Hartner, F. Hintermaier, C. Dehm, C. MazureUltrathin SiO2 and High-K Materials for ULSI Gate Dielectrics, vol. 567, Materials Research Society, Warrendale, 1999, p. 567. [3] K. Franke, G. Martin, M. Weihnacht, A.V. Sotnikov, Solid State Commun. 119 (2001) 117. [4] K. Franke, H. Huelz, M. Weihnacht, Surf. Sci. 416 (1998) 59. [5] M. Abplanalp, J. Fousek, P. Gu¨nter, Phys. Rev. Lett. 86 (2001) 5799. [6] S.C. Hwang, C.S. Lynch, R.M. McMeeking, Acta Metall. Mater. 43 (1995) 2073.
154
K. Franke, M. Weihnacht / Surface Science 585 (2005) 144–154
[7] K. Franke, H. Huelz, M. Weihnacht, Surf. Sci. 415 (1998) 178. [8] K. Franke, M. Weihnacht, Ferroelectric Lett. 19 (1995) 25. [9] J.F. Scott, Ferroelectric Memories, Springer-Verlag, Berlin, 2000. [10] X. Lu, F. Schlaphof, Ch. Loppacher, S. Grafstro¨m, L.M. Eng, G. Suchaneck, G. Gerlach, Appl. Phys. Lett. 81 (2002) 3215. [11] M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Clarendon Press, Oxford, 1977 (Chapter 5.7).
[12] K. Franke, L. Eng, Surf. Sci., in preparation. [13] P. Lo¨bmann, S. Seifert, S. Merklein, S. Sporn, J. Sol-Gel Sci. Technol. 13 (1998) 827. [14] J.F. Scott, The physics of ferroelectric ceramic thin films for memory applications, Ferroelectr. Rev. 1 (1998) 1. [15] Q.M. Zhang, J. Zhao, K. Uchino, J. Zheng, J. Mater. Res. 12 (1997) 226. [16] L.M. Eng, private communication. [17] J. Frey, F. Schlenkrich, A. Scho¨necker, Integr. Ferroelectr. 35 (2001) 105.