University of Groningen

Piezoresponse force microscopy of ferroelectric thin filmsMorelli, Alessio

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* This chapter is based on: A. Morelli, Sriram Venkatesan, B. J. Kooi, G. Palasantzas, J. Th. M. De Hosson, J. Appl. Phys. 105, 064106 (2009)

5

Quantitative

characterization of PTO

samples

In this chapter the functional properties of PTO samples are analyzed with piezoresponse force microscopy in conjunction with transmission electron microscopy. Retention loss analysis, piezoelectric coefficient extrapolation, and hysteresis loops are performed, revealing the nanoscale characteristics of the material.

5.1 Introduction

The quest for miniaturization has given a strong impetus to the nanoscale investigation of the quantitative properties, polarization domain engineering, and domain dynamics in ferroelectric thin films. In particular, over the last decade piezoresponse force microscopy (PFM) has proven a powerful technique for ferroelectric films characterization at a nanoscale level [1]. In view of FeRAM applications, a number of functional properties need to be evaluated at the nanoscale, of which the most important are the piezoelectric coefficient value, coercive voltages, and retention loss.

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Although characterization with PFM has been extensively performed for PbZrxTi(1-x)O3 (PZT) films [2][3], experimental data of nanoscale variations of physical properties of PTO films are still lacking. In fact, reported data on PTO films processed from modified alkoxide solution precursors showed a piezoelectric coefficient value d33§��� SP�9 [4]. Moreover, the d33 hysteresis curves gave evidence of the presence of a weak imprint, i.e. a shift of the hysteresis curve on the voltage axis, leading to a preferential polarization state. Also d33 exhibited nonlinear behavior with increasing amplitude of the applied modulation electric field used in PFM [4]. In addition, for epitaxial grown PTO films on MgO substrates [5] with pulsed laser deposition having also a-domains (which were switching under the influence of external field), d33 values ~20-80 pm/V were reported for film thicknesses of 60-200 nm.

It has to be emphasized that the elastic, dielectric and piezoelectric response of a ferroelectric material are the result of intrinsic and extrinsic contributions. The first is the lattice contribution, corresponding to the response of a monodomain single crystal resulting from the relative displacement of anions and cations in the unit cells. The latter arises mainly from domain walls and defects. The extrinsic contributions are thermally activated processes, disappearing at low temperatures but remaining predominant at room temperature [6][7]. The main extrinsic contribution comes from the movement of the domain walls. The walls move in a potential field influenced by the lattice structure and imperfections [8]. The latter give rise to pinning or clamping domain walls, affecting their nonlinear movement. It implies a dependence of the material properties on field, temperature and frequency [9]. The response of the permittivity and piezoelectric coefficient to an alternating field is characterized by linearity followed by a non-linear behavior beyond a threshold field Eth smaller than the coercive field. The non-linear response at sub-coercive field has an intrinsic and an extrinsic contribution, but the first is comparatively smaller than the latter and as a result the origin of non linearity is considered to be extrinsic [10].

5. Quantitative characterization of PTO samples

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To study nonlinearity in the elastic, dielectric and piezoelectric responses of a ferroelectric material, the Rayleigh law has been utilized [11]. It was formulated to describe the interaction between domain walls and pinning centers in magnetic materials. For permittivity and piezoelectric coefficients the Rayleigh law is expressed as:

acinit Eεαεε += (5.1)

acdinit Edd α+=33 (5.2)

where Eac is the amplitude of the alternating field, dinit and init are the reversible Rayleigh coefficients, and d and the irreversible Rayleigh coefficients. Reversible coefficients are associated with reversible domain walls motion and intrinsic lattice vibrations, while irreversible coefficients are attributed to irreversible domain walls motion. In this regard, the contributions from ferroelectric 180º and ferroelastic non-180º domain walls have to be separated.

It is has been demonstrated [8] that non-linearity in permittivity is determined by both 180º and non-180º domain walls motion under a sub-coercive field. On the other hand the non-linearity on piezoelectric coefficients is determined almost exclusively by non-180º domain walls motion [4][6][9][12][13]. Still, in absence of non-180º domain walls a non linearity in piezoelectric coefficient can be present [14][15]. It is explained by the presence of large scale, nearly reversible domain walls motion, associated with a dynamic poling process. In fact, the application of a modulation voltage higher than a threshold voltage Vth, prompts a poling-depoling process, leading to oscillating 180° domain walls. This results in oscillating piezoelectric response, which increases with increasing modulation voltage amplitude leading to non-linearity in the piezoelectric coefficient response. The resulting non-linearity from 180º domain walls is a minor contribution with respect from the contribution from non-180º domain walls when the latter are present.

In this chapter we will present investigations of the non-linear behavior for single domain PTO films (in absence of a-domains). The study was

90

performed in terms of combined PFM and transmission electron microscopy (TEM) characterization of ferroelectric domain structure and film/substrate interfaces. As a result the quality of the film substrate interface and its impact on the ferroelectric functionality will be explored in detail. In addition, special attention will be paid on retention loss characteristics in combination with any non-linear piezoresponse, and imprint effects.

5.2 Experimental procedure

The specimens under study are PbTiO3 thin films grown by pulsed laser deposition (PLD), on (001) SrTiO3 (STO) substrates, with an intermediate layer of SrRuO3 (SRO) acting as bottom electrode; specifically the sample studied extensively (termed A1) is 130nm PTO/50nm SRO/STO film, while for comparison of nanoscale piezoresponse characteristics another sample (termed A2) 120nm PTO/40nm SRO/STO was used. For the structural characterization of the PTO films a JEOL 2010F TEM was employed, under the same experimental conditions and the same sample preparation as described in §4.2.

The PFM measurements were performed with the AFM setup including the external lock-in amplifier for simultaneous PRphase and PRamplitude acquisition. The measurements were performed with TESP probes, typical applied contact forces were Fc ~ 0.�� 1� –� ���� 1. These forces are sufficiently weak to avoid any significant local depolarization, but sufficiently high to ensure a proper contact to minimize electrostatic contributions to the PFM signal (§2.4.1, §3.1.1).

PRphase images of domains were acquired in scanning mode, with a typical modulation signal frequency of 5kHz and amplitude an Vac=1.5V. The measurement of d33 was performed as described in §2.3.4. Local hysteresis loops were measured as remanent hysteresis (see §2.3.5), with pulsed voltage cycled between -10V and +10V, with tbias=0.2-1s and tsettle=0.1s. The d33 extrapolation following each pulse had Vac ramping between 0.5 and 2.5V (in steps of 0.5V) and an acquisition time of 0.2s.

5. Quantitative characterization of PTO samples

91

5.3 Results and discussion

5.3.1 Retention loss analysis PRphase imaging of the as-deposited films shows a monodomain with

polarization normal to the surface and upward direction (c+ domain). Domains with polarization parallel to the surface (a domains) were not detected by PFM, and if present, they have a lateral size less than the tip radius ∼10-20nm. In addition, TEM measurements confirmed the absence of a domains. Furthermore, domain reversal was performed by applying DC bias voltages 3.5V- 4V. It was applied from the tip at a scanning speed of 1 Hz over a 1[� P2 area in order to obtain a square c domain with reversed polarization (c- domain, Fig. 5.1). Indeed, Fig. 5.1 shows retention loss measurements for more than 750 hours. The figure shows that a latent period is not present, and that the back-switched area can be fitted by formula (4.2) from which the characteristic retention loss time k and d coefficient are obtained.

The PRphase images for calculating the back-switched area were obtained with a Vac low enough not to enhance the retention loss. The fitting gave an exponent d=0.75±0.06 and an effective inversion time k=376±15h. Despite differences, these values are comparable to retention loss times obtained in other studies for PTO films grown on STO (Nb doped) substrates [16]. From the results we can infer that the retention loss occurs by a random walk process since d<1, which is generated by the c+/c- domain wall lateral movement generated by curved domain walls originated by the poling procedure itself (see §4.3). In contrast to the case presented in chapter 4, C-AFM studies did not reveal any leakage currents. The charges accumulated at the curved domain wall cannot be redistributed and the retention loss procedure is thus prompted by this effect.

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Fig. 5.1: PRphase images acquired after polarization reversal: (a) after poling, (b) 345 and (c) 745 h later for sample A1. (d) Plot of area % as a function of time evaluated by PR phase images taken after polarization reversal over a 1 m2 area by poling the tip at 3.5V.

5.3.2 TEM characterization and analysis The samples analyzed by PFM were also imaged using TEM to unravel

any possible disorder at the film substrate interface. Fig. 5.2 shows a cross sectional bright field image for the A1 sample. At room temperature the PTO film has a tetragonal structure with a=b=3.899 Å and c=4.154 Å [17]. SRO is a transition-metal oxide with a metallic conductivity and orthorhombic structure with lattice constants a= 5.567 Å, b= 5.530 Å and c =7.844 Å [18][19], which is often viewed as a tetragonal structure with a= b= 3.93 Å and c = 7.85 Å or a two stacked pseudocubic perovskite unit cell

5. Quantitative characterization of PTO samples

93

with a= 3.93 Å. STO has a cubic structure with lattice constant of 3.905 Å. These crystallographic data indicate the presence of misfit strain at the interfaces. The TEM images show clearly (given the absence of stripes with darker contrast, as in Fig. 5.2) that the PTO film is completely c-axis oriented without any a domain, which was also confirmed using X-Ray Diffraction [20], and it is in agreement with the claim previously from our PFM studies regarding the absence of a domains.

Fig. 5.2: Bright field TEM image of the A1 PTO sample, which shows the presence of defects at the electrode- film interface.

In addition, the PTO/SRO interface shows non-uniformities, with length in the order of 15 to 25nm. The contrast generated by these defects extends up to a few monolayers away from the interface as is observed in the high resolution TEM image of Fig. 5.3. On the other hand, the SRO/STO interface is characterized by a sharp interface, which demonstrates a perfect coherent epitaxial matching. TEM analysis of sample A2 gave similar results. The lack of coherency between PTO and SRO films can be attributed to the existing misfit strain. The in-plane lattice mismatch

94

between SRO and PTO at room temperature is ~0.9% which is larger than the one at the substrate-electrode interface of ~0.6%. However, it is still more likely that the origin of the defects is related to the surface condition of the SRO bottom electrode prior to the PTO-film deposition. Note that with optimal surface conditions it turned out possible to grow a defect-free film [19][20].

Fig. 5.3: High resolution TEM image of A1 showing non-uniformities and defects (highlighted areas) at the electrode/film interface (evidenced by the line in figure).

5.3.3 Piezoelectric coefficient analysis To gain more insight into the influence of interfaces on the PTO film

functionality, we performed detailed PFM studies. Fig. 5.4a shows the Vac dependence of the partial piezoelectric coefficient dp

33=PRamplitude/Vac and of the PRphase (inset) for c+ and c- domain over an area of sample A1. The dp

33 values are relatively constant below a voltage Vth§���9, while they

PTO

SRO

5. Quantitative characterization of PTO samples

95

increase significantly for voltages Vac>Vth. For this reason the actual piezoelectric constant d33 is finally calculated in the range 0.5V to 2.5V from the slope of the PRamplitude vs. Vac plot for higher accuracy giving d33=21.2±0.5pm/V and 25.6±0.4pm/V for c+ and c- domains, respectively. Nonetheless, the piezoelectric coefficient shows a significant variation over different spots of the film surface, in the range d33~10 - 35 pm/V. Moreover, Fig. 5.4b shows the Vac dependence of the dp

33 values, and the PRphase for sample A2 (inset). The piezoresponse over the c- domain gives an initial dp

33 smaller than that for c+ but the nonlinearity is much more pronounced for the c- domain for Vac> Vth. The obtained d33 values (for Vac<Vth) from the linear fit are d33=35.9±0.7 pm/V for the c+, and d33=32.6±0.5 pm/V for c- domains. In addition, these values vary over the film surface in the range d33∼20 - 40 pm/V.

In literature the main source of nonlinearity is supposed to be non-180º domain wall motion. In the PTO films under investigation no a domains were detected, meaning the absence of non-180º domain walls. Therefore, the source of the nonlinearity can be ascribed to 180º ferroelectric domain walls movement occurring via a dynamic poling process [14][15].

For both samples the obtained piezoelectric values are comparable to the ones reported in literature (and obtained by PFM) [5]. Although these values are lower than those obtained with laser interferometry [4], they can become comparable if the reduction given by internal clamping is also taken into account (see §3.1.4 and [21]).

d33 up d33 down Max d33 Min d33

A1 21.2 25.6 35.6 10

A2 35.9 32.6 41 23

Table 5.1: Overview of the piezoelectric coefficients obtained by d33 extrapolation: d33 for c+ and c- domain (d33 up and down) from data shown in Fig. 5.4, and maximum and minimum values measured over the surface. Values expressed in pm/V.

96

Fig. 5.4: Partial dp

33 vs. amplitude of the modulation voltage (a) for sample A1, and (b) for sample A2. The insets show the PRphase vs. amplitude for the modulation voltage. The arrows in (a) indicate qualitatively the position of polarization reversal.

5. Quantitative characterization of PTO samples

97

Moreover, Fig. 5.4a indicates that the response over the c+ domain in sample A1 gives initially a partial dp

33 smaller than that for the c- domain, and in addition a drop occurs for V* §����9. Simultaneously the polarization changes direction since the PRphase increases by about 140º. Such a phenomenon occurred only at determined spots of the film surface, and polarization inversion took place also for c- domains. In fact, the polarization inversion with increasing Vac has already been reported in [22][23]. It was explained by suggesting the presence of hidden 180º domain walls below the film surface, consisting of two layers of opposite polarization. When the Vac generates a strong enough field at the wall position, depinning can occur. Given the in-homogenous field generated in the film by the PFM tip, moving towards the zone where the field is stronger, i.e. towards the tip, the domain of reverse polarization (close to the film /substrate interface) will expand through the whole film thickness. Thus, in Fig. 5.4a where the inversion occurs, the bottom layer is a c- domain, which under increasing Vac, expands until it reaches the top surface of the film.

In ref. [22] inversion occurred only on written domains and the domain wall was generated during the writing operation (polarization reversal), given that the created domain did not reach the bottom of the film. In our case we have both types, i.e., inversion of a written domain and a domain in the as-deposited films. Since the inversion polarization takes place only in some areas and the TEM images (Fig. 5.2 and Fig. 5.3) indicate interface disorder, it is likely that a domain wall is generated by charge trapping caused by the presence of the interface defects. In fact, in the case that the defects are located not exactly at the interface but in its proximity inside the PTO film, trapped charges can give rise to depolarizing fields of opposite direction below and above the domain wall. Therefore, the in-homogeneity due to the presence of interface defects can be a plausible explanation why dp

33 shows different behavior at different areas.

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Fig. 5.5: Diagram of the domain configuration in the film. The as-grown film surface shows a c+ monodomain independent of defects close to the bottom electrode (a). In this case three different volumes are represented from left to right: volume with positive defect charges, volume without defects, and volume with negative defect charges. In (b) the polarization is reverted in the volume with negative charges. As a result two layers of polarization configurations are present within the volume with negative defects. If the surface is scanned with increasing modulation voltage as in (c), the latter triggers polarization back-switching by expansion of the bottom polarization layer.

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The fact that the inversion is recorded for both c+ and c- domains, is interpreted as the result of charges of different sign trapped at defects inside the PTO film. In fact, as schematically represented in Fig. 5.5, the PTO volume between defects and the interface experiences a high permanent electric field. The latter can be strong enough to influence the polarization configuration. Therefore two polarization layers are present in the as- deposited film where the trapped charges are positive (Fig. 5.5a). In a similar manner two layers are created when reversing the polarization over an area below which negative charges are trapped in defects (Fig. 5.5b). As already reported in [22][23], increasing the modulation voltage during reading could de-pin the domain wall resulting in expansion of the domain at the bottom of the film through the whole thickness (Fig. 5.5c). Note that as reported in [22], before inversion the partial dp

33 decreases to zero since at some Vac the responses from the expanding bottom layer and the top layer domains respond equivalently and with opposite phase. However, in our measurements the responses of the c+ and c- domains do not show this behavior. The sudden change in PR without passing through zero could be interpreted as the effect of a strong pinning of the hidden 180º domain walls at defects. When the energy supplied by the modulated field at the wall position is high enough to de-pin the domain walls, the bottom polarization layer would expand very fast through the whole thickness. For this same reason, the detected non-linearity should not be ascribed to these horizontal domain walls, since they are expected to be strongly pinned by the defects at the interface.

5.3.4 Hysteresis loop analysis Finally, piezoresponse hysteresis loops, as shown in Fig. 5.6,

confirmed again the ferroelectric behavior of the films under study, while they showed pronounced imprint. Following the definitions given in §2.3.5, the characterizing properties for the two sample are evaluated by the hysteresis loops. For the measurement in Fig. 6 regarding sample A1 the

100

imprint is Im=-1.13 V, and the coercive bias Vc=3.6V. However, these values vary over the sample surface with Im varying from about ∼-1.7 to +1.5 V, and Vc between ~1.5 and 6 V. In addition, for sample A2 the hysteresis in Fig. 5.6 gave Im=-0.63V, and coercive bias Vc=4.9 V. For this sample, the imprint Im varies in the range ∼-1.6 +0.5 V over the film surface, and Vc between ~3.5 - 4.9 V. The imprint Im is comparable to imprint values of ∼1 V for PTO films in former studies [24]. It can be explained by the different work functions of the bottom SRO electrode and of the Si doped PFM tip acting as top electrode [25][26], and/or by the presence of a depolarizing field caused by charge redistribution due to interface disorder (Fig. 5.2, Fig. 5.3). The obtained parameters from the hysteresis loops indicate that the films have significant ferroelectric properties, however, with significant variation at sub-micron scales.

Fig. 5.6: Piezoelectric hysteresis loop of sample A1 and A2, performed in pulse mode with a pulse time of 0.2 s, a settling time of 0.1 s, an acquisition time of 0.2 s, with a modulation frequency of 5 kHz. The vertical axis is the piezoresponse=d33 cos(PRphase).

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V+ V- Im R+s R-

s R+0 R-

0

A1 2.5 -4.7 -1.1 28.3 -26.9 24.2 -23

A2 4.3 -5.5 -0.6 40.8 -41.3 36.7 -35.6

Table 5.2: Overview of the data obtained by the remanent hysteresis loops of Fig. 5.6, as described in §2.3.5. V+, V- and Im are expressed in Volts, the responses in pm/V.

5.4 Conclusions

The functional properties of PTO samples grown by PLD on SRO electrodes were studied, by means of both TEM and PFM techniques. The TEM images show the presence of defects at the electrode/film interface and confirm the absence of a domains. The presence of defects influences retention, homogeneity of piezoelectric characteristics over the surface, and it could be a competing factor in the polarization inversion under increasing modulation amplitude Vac during PFM measurements of the d33 coefficient. The observed nonlinearity in piezoelectric coefficient dependence by modulation voltage amplitude is explained by 180º domain walls motion due to poling-depoling, since ferroelastic domain walls were not detected in the analyzed PTO films. Retention longer than a month was shown with a loss prompted by c+/c- domain wall movement. The obtained d33 values of 30-40 pm/V were comparable to values reported in literature. Finally, as a reasonable statement concerning the film functionality, we can infer that they possess useful ferroelectric properties despite the nanoscale variation of d33 over the film surface, and the relatively weak imprint found by hysteresis measurements.

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