Nanoscale Investigation of the Ferroelectric Properties of Sol-Gel ( PbZr x Ti 1− x ) O 3 Films

In this paper, nanoscale ferroelectric and piezoelectric properties (e.g. cartography of the piezoelectric coefficient after poling and polarisation direction) of sol-gel PZT thin films are studied using a modified Atomic Force Microscope (AFM). Polarisation patterns are created, and then imaged after more than one year. Hysteresis loops are recorded and it is shown that their shape and related parameters (remanent polarisation and coercitive field) are strongly dependant on the experimental conditions.


INTRODUCTION
The need for the reduction of the size of ferroelectric devices such as Ferroelectric Random Access Memories (FeRAM) or Surface Acoustic Wave (SAW ) devices has made mandatory the development of characterisation techniques capable of providing a nanometric res olution for the spatial repartition of ferroelectric domains and of giving local information about the ferroelectric parameters of the films (coercitive fields, remanent polarisation ... ).The piezoresponse mode of the Atomic Force Microscope (AFM) has already shown its capabilities in supplying reliable information with a sub-micrometric lateral resolution [1] [2] [3].In this paper, we illustrate the piezoresponse mode's contribution in the study of the ferroelectric properties of sol-gel PZT thin films (polarisation direction, coercitive fi elds and remanent polarisation).

2.1
The AFM piezoresponse mode The piezoresponse mode of the AFM is implemented using a modified commercial AFM apparatus (Digital Instrument Nanoscope IIIA) and NT-MDT cobalt coated tips or Nanoprobe Ptlr5 coated tips (force constant '::::'. 1 -lON.m-1).The physical basis of the piezoresponse mode can be found elsewhere [2] [4].Briefly, the piezo electric information is obtained through an AC voltage Yac applied between the tip and the sample while the AFM apparatus is imple mented in the contact mode.The amplitude of the resulting (very weak) piezoelectric vibration, which frequency is the same as Vac, is thought to be proportional to the piezoelectric coefficient d33.It is extracted from the topographic signal using a lock-in amplifier and does not interfere with it, allowing the simultaneous recording of the topographic and piezoelectric image [2].AFM piezoresponse mode allows to record a cartography of the piezoelectric coefficient d33 of the surface, and to modify the polarisation state of the piece of material located under the tip by applying between the tip and the sample a voltage corresponding to an electric fi eld higher than the local coercitive field of the film.Domains with an uniform po larisation and an adjustable shape and size can be created this way.Also, local hysteresis cycles can be recorded by stopping the tip over a given point of the surface and recording the piezoelectric response with respect to a varying electric field.

Preparation of the samples
The sol-gel PZT samples were elaborated by dip-coating on Ti/Pt electrodes and Si substrate.From this elaboration technique, we ex pect piezoelectric thin films with a good purity, low roughness and in teresting piezoelectric and ferroelectric properties [ 5].The cristalline structure of the film has not been determined by X-ray diffraction due to the small size (':::'.5mmx 5mm) and thickness (':::'.100nm) of the sample.However we expect a film orientation along the (001) axis, leading to a polarisation vector perpendicular to the surface of the film [6] [7].The topographic AFM observations (not shown) show a granular morphology, with grains of diameter '::::'.300 nm.Macroscopic hysteresis loops obtained on the samples (using a simple electric Sawyer-Tower setup used at 50 Hz), show a remanent polar- isation Pr � 15µC/cm 2 and a coercitive voltage Ee = 150kV/crn.The film has been uniformely poled by scanning a 5µ x 5µ area with a constant DC voltage of +lOV between the tip and the bottom elec trode, then by scanning a 3µ x 3µ area with a constant DC voltage of -lOV.Finally, the amplitude, phase and lateral piezoresponse image have been recorded.The latter is obtained by recording the lateral vibration amplitude detected in the photodiode signal by the lock-in amplifier, instead of the normal vibration amplitude, and is thought to be related to the vibration of the film in the plane of the surface.
The result of these images can be found in Figure 1.From these images, we can draw the following qualitative conclusions : • The uniformity of the amplitude and phase images in the poled regions suggests an uniform distribution of the piezoelectric coeffi cient d33.The opposite phase between the area poled with -lOV and + lOV indicates that the polarisation has been effectively switched by the applied electric field.Note that with our experimental setup, the phase information is included in the amplitude image, so that the do mains which polarisation is toward the bulk (bright areas, in phase with the reference voltage) appear with a positive amplitude, and the domains which polarisation is toward the surface (dark domains, opposite phase) with a negative amplitude, although the absolute value of the amplitude is comparable for both domains.
• The absence of contrast in the lateral image suggests that the direction of the polarisation is indeed normal to the plane of the surface, with no or little component in the plane of the surface.

Remanent polarisation
In order to position the tip over the same area of the sample at different moments, we have engraved 9 11111-shaped patterns using a Focused Ion Beam (FIB -Gallium source, impact energy : 30 keY).The size of each patterns was about 20µ x 3µ and the depth of each pattern, as measured by AFM '.::::.' 25nm.Left part of Figure  The left part of figure 3 shows exactly the same area as the right part of Figure 2 imaged 80 days after its first polarisation.The pat terns are still easily detectable with a comparable signal to noise ra tio. Figure 3 (middle and right) shows the same polarisation pattern at two different moments separated by 373 days, showing that it has remained identical.However, the signal to noise ratio is lower and some domains have flipped back.This results illustrate the piezore sponse mode's ability to image the antiparallel ferroelectric domains and study their remanent polarisation in terms of spatial repartition after a certain amount of time.Quantitative comparisons are now needed to evaluate the devices' ability to retain information.The bigger white square's size is 10µ x 10µ.

Hysteresis cycles
Information about the very local coercitive fields and remanent polarisations may be needed to understand the fatigue and imprint phenomena in very thin films.Different authors have recorded hys teresis loops using different experimental protocols.Harnagea et al. [3] suggest to wait a least 2 seconds after the application of a volt age pulse in order to avoid any electrostatic interaction between the tip and the bottom electrode.However, using this method, only the rema.nentpiezoelectric coefficients d33 are accessible.Eng [1] applies a voltage ramp and the resulting loops exhibit very different shapes than those from [3].We have tried both methods.In all cases, a AC voltage (1 V, 15.8kHz) was used for piezoelectric measurements.In the first case, a voltage ramp (5mHz) was applied while measuring the piezoresponse.In the second case, a voltage pulse was applied and the piezoresponse was measured immediatly after the end of the pulse.In the last case, the response was measured 3 seconds after the application of the pulse.Results can be seen in Figure 4.
Depending on the experimental conditions, the shape of the loops and the parameters measured from these loops are very different.
The positive and negative remanent d33 and coercitive fields show a variation of more than 100% from one loop to another.However, the loops recorded without the presence of the DC voltage exhibit the same Ee whereas the remanent d33 remain different.This suggests the presence of surface charges when the DC voltage is not switched off before measuring the piezoelectric response as suggested before [3].A more complete study of the dynamic electrostatic interactions between the tip, the surface and the bottom electrode is needed to achieve a complete understanding and quantification of the loops

FtCURE 1 :
Left : Amplitude piezoresponse image after a 3µ x 3µ square polarisation pattern bas been created on the surface.Middle : ph� image showing effective polarisation reversal.Right : lateral piezoresponse image.

2
shows optical images of the resulting patterns.These patterns, easily visible, are used as a guide to position the tip and to create different polarisation patterns using the tip.The precision of the AFM positioning allows to create any polarisation patterns with a high possible lateral resolution.Moreover, a long time after the creation of the polarisation patterns, it has been possible to position the tip exactly at the same place to check whether it had remained at the surface of the film.

FIGURE 2 :
FIGURE 2 : From left to right : L-shaped pattern created by FIB -Closer view of a single pattern -Polarisation patterns realized using the AFM tip.

FIGURE 3 :
FIGURE 3 : Left : the polarisation patterns of F igure 2 are still detectable after 80 days.Size of the image : 40µ x 40µ.Center and right : polarisation pattern i maged at two d i fferent moments separated by more than one year (373 days).The bigger white square's size is 10µ x 10µ.