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Modification and detection of domains on ferroelectric PZT films by scanning force microscopy
s __
_lI!iii
surface science letters Surface Science Letters 302 (1994) L283-L288
ELSEVIER
Surface Science Letters
Modification and detection of domains on ferroelectric by scanning force microscopy
PZT films
K. Franke *, J. Besold, W. Haessler, C. Seegebarth IFW Dresden e. VT,Postfach, D-01 I71 Dresden, Germany
(Received 18 May 1993; accepted for publication 19 October 1993)
Abstract A scanning force microscope @FM) with light fiber sensor was constructed. The SFM operates in the repulsive contact mode. Three pictures have been measured simultaneously: the topography and the 1st and 2nd harmonic. The 1st harmonic can be related to piezoelectricity and polarization. The 2nd harmonic is correlated with electrostriction and permittivity. The conductive tip of the SFM was used to polarize lead zirconate titanate (PZT) films and to image their domain structure on a nanometer scale. In addition, a writing experiment has been performed.
1. Introduction Ferroelectric materials are of widespread interest in science and for technological applications [l]. The correlation between the microstructure of the material and its electrical properties, e.g. coercivity, spontaneous polarization, dielectric and piezoelectric constant, is of fundamental interest for optimizing these properties. Transmission electron microscopy (TEM) [2], scanning electron microscopy 131and some decoration techniques 141 are useful tools for imaging ferroelectric domains. However, these techniques require thinning of samples, may cause beam charging or have low lateral resolution. At present there is a rapid development to use modified scanning force microscopes @FM) for the deter-
* Corresponding
author: Fax: + 49 3.514659 540.
0167-2584/94/$07.00
mination of the parameters mentioned above [5-81. For further details, see Section 3. In this Letter we describe the design of and the first experiments conducted with a SFM with an interferometric optical sensor. The operation mode is similar to the technique used by Guethner [51. Results of polarizing and domain imaging experiments on lead zirconate titanate (PZT) films are given.
2. Force microscope
Fig. 1 shows a schematic of the SFM which we have constructed. A conductive silicon cantilever [9] is mounted near a single mode light fiber. We use a stable HeNe-laser (HNA 18%S> and illuminate the fiber through a semi-transparent mirror. Therefore our equipment is similar to the sensor used by Rugar et al. [lo]. A reference signal for
0 1994 Elsevier Science B.V. All rights reserved
SSDZ 0167-2584(93)E0222-F
and optical sensor
L284
K Franke et al. /Surface
Science Letters 302 (1994) L283-L288
the compensation of changing intensity is not necessary. We use a relatively large gap w between the end of the fiber and the cantilever of about 50 pm and glue the fiber near the cantilever. No mechanical elements which are often unstable, are necessary in our design. The calculated phase noise corresponds to an apparent tip movement of 4 pm, assuming a frequency stability of half of the longitudinal laser mode distance and an unlimited bandwidth. The thermal drift of the cantilever to the fiber is only several nm over a period of hours. Thermal instability of the optical signals may be caused by triple transit light reflections at the beginning (b) of the fiber and at the outer mirror (m) of the laser. We solved this problem by choosing a suitable length of the fiber. By this the undesired wave packets are set between the wave packets reflected from the end (e) of the fiber. Hence they do not interfere. All this results in thermally stable signals at the photodiode.
3. Tip-sample
interactions
In our experiments the tip operates in the so-called contact mode, i.e., it is within the adsorbate layer of the surface and experiences the repulsive force of the sample (see Fig. 1). We applied an AC voltage V, with the frequency w/27 of 1 kHz between the tip and an electrode at the back of the sample to measure ferroelectric properties. An additional DC voltage I$,, is used in series to change the polarization of the sample. The oscillating electrical field between the tip and the electrode affects the sample and the tip in several ways: (a) Generally the thickness t of the sample varies with w due to the piezoelectric effect and with 2w due to electrostriction. The tip follows these oscillations because of its strong coupling to the surface in the contact mode. Guethner considered the w-dependent piezoelectric effect for the interpretation of his SFM experiments [5].
embe
132. Harmonic
Fig. 1. Schematic diagram of the SFM applied for the present experiments. A fiber polarization adjustment is used to maximize the signal of the photodiode. The arrows at the wave packets mark the propagation direction. The lenses for focusing the laser light into the fiber are not drawn.
R Franke et al. /Surface
Science Letters 302 (1994) L283-L288
(b) Dipole charges of the remanent polarization and image charges caused by permittivity also act on the tip and give rise to signal components at w and 2w, respectively. Saurenbach and Terris [6,71 used this o-component for the imaging of charges and domains in the noncontact mode. On the other hand, Guethner [5] operated in the contact mode and neglected this component. (c) Electrostriction and permittivity change also the DC component of the force which influences the tip. The same holds for the force gradient. These DC effects may alter the tip-surface separation d (Fig. 1) and may falsify the measured quantities. A detailed mathematical analysis of all the frequency components of the tip movement and their dependence on the tip-surface distance will be necessary to quantify the different physical parameters. For the contact mode used here we can roughly assume that the 1st hamtonic includes the effects of piezoelectricity and polarization while the 2nd harmonic combines the effects of electrostriction and permittivity. In future experiments we intend to separate these four physical properties by making measurements at different distances between the tip and surface. As the tip-surface separation increases, the effects of the long-range electrical forces increase, whereas the effects of short-range contact forces decrease. Luethi et al. [8] imaged the polarization in the contact and the noncontact mode. using an insulating Si,N, tip. However, this way of imaging of domains in the contact mode is only possible on flat surfaces since the topography signal is superimposed onto the charge signal.
4. Experimental Three pictures were recorded simultaneously from the signal of the photodiode: the topography from the DC component at the output of the servoelectronics and the 1st and 2nd harmonic by a lock-in technique. It is essential to delay the measurement of the harmonics sufficiently after each scan step. We use a variable delay depending on the local slope of the topography signal to
L285
avoid an apparent influence of the topography on the harmonics. The sampling conditions are chosen to give the same results as for a stationary tip at the same position.
5. Results and discussion A ferroelectric PZT film of rhombohedral phase with a thickness of 610 nm was prepared by sputtering at 450°C [ll]. The substrate was oxidized (100) silicon coated with a sputtered Pt electrode. X-ray diffraction reveals randomly orientated PZT crystallites. The TEM image of the cross-section shows a columnar structure of the crystallites. They are predominantely single grains grown from the Pt electrode to the sample surface. The film is characterized by a permittivity of 500, a remanent polarization of 20 &/cm2 and a coercive field of 80 kV/cm. Our SFM experiments show crystallites of about 200 nm in size. The height distribution of the film topography is characterized by a full-width-at-half-maximum of approximately 60 nm. We found a unified polarization on the as deposited PZT film. Subsequently, the tip of the SFM was used to repolarize selected areas of the film by applying I/PO, for a short period. Fig. 2 shows an example of a “writing experiment”. At first the shown area was completely polarized by scanning with a positive tip voltage I/p,,,= 30 V. For this the voltage was applied for 50 ms to each of the 214 points of the scanned area. Then the marked inner square (Fig. 2a) was “written in” by scanning with an opposite tip voltage of - 10 V. Afterwards the image of the 1st harmonic (see Fig. 2a) was obtained with I&,, = 0. Using this value of I/PO,, only half of the scanned area was successfully repolarized. Subsequently, the marked inner square was completely repolarized by scanning with VpO,= - 20 V (Fig. 2b). Not only the repolarized area but also the surrounding areas show a coarse structure. We compare this structure with the simultaneously measured topography (as explained for Fig. 3). We conclude that the coarse structure of the 1st harmonic corresponds with the grain structure. In first-order approximation, whole grains are always polarized.
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K Franke et al. /Surface
Science Letters 302 (1994) L283-L288
across the grain boundary shows a 10% to 90% change of polarization in a distance of 8 nm. Therefore we believe that the resolution in the 1st harmonic picture is better than 10 nm. While the pictures of the 1st harmonic show mostly planar structures, the 2nd harmonic is independent on the polarization distribution and often marks the boundaries of the grains (Fig. 4). We can rule out that this picture is the result of an increased geometric tip-sample capacity at grain boundaries since it is well known that the measured topography cannot show details finer than the tip radius. The measured cross-sections of the topography illustrate the maximum sharn-
Fig. 2. (a) First harmonic picture of a PZT film. The marked square was polarized with the tip voltage V,, = - 10 V. The vertical scale gives the lock-in output. (b) First harmonic picture. The marked square shown in Fig. 2a was polarized with VDO,= - 20 V.The vertical scale gives the lock-in output.
This limits the possible writing density of such films. We assume that the further grain-correlated inhomogeneities of the 1st harmonic are related to the random orientation of the polar axis, since these inhomogeneites are reproduced after writing and erasing. In a second experiment the tip was moved to the position marked by the arrow in Fig. 3a showing the 1st harmonic. At this position only one crystallite. was polarized opposite to the surroundings by applying l&,, = - 30 V. In Fig. 3b the corresponding topography is not toned with its own grey scale but with the grey scale of the 1st harmonic. The region of reversed polarization is clearly limited to a single crystallite. A section
Fig. 3. (a) First harmonic picture of a single polarized lite. The arrow marks the position of the polarizing tip -30 V). The vertical scale gives the lock-in output. (b) raphy of the area shown in Fig. 3a toned with the grey the 1st harmonic.
crystalCl/,,, = Topogscale of
K Franke et al. /Surface
Science Letters 302 (I 994) L283-L288
that the measured 2nd harmonic represents distribution of electrostriction.
L287
the
6. Summary
Fig. 4. (a) Second harmonic picture of a polarized PZT film. The vertical scale gives the lock-in output. (b) Topography of the area shown in Fig. 4a toned with the grey scale of the 2nd harmonic.
ness of the tip and from Fig. 4b we estimate a tip diameter smaller than 20 nm in all directions. In contrast the maximum value of the 2nd harmonic in Fig 4a is reached at a position where the topography is much broader than 20 nm. In a second example there should be a large tip-sample capacity at the grain boundary in the upper right of Fig. 4b. Nevertheless there is a trench in the 2nd harmonic picture. Therefore, we conclude that the 2nd harmonic gives information about permittivity and electrostriction. Since a disturbed perovskite structure is expected at grain boundaries we assume
A modified SFM was constructed to study surface properties of ferroelectric materials. The movement of the tip is detected by an interferometer based on a HeNe-laser. In this way we constructed a thermally stable instrument. An AC voltage is applied between the tip and an electrode at the back of the sample. Pictures at three frequencies are measured simultaneously in the contact mode. The topography is obtained from the DC component. The 1st harmonic picture shows the domain structure. We investigated a ferroelectric PZT film. The tip was used to repolarize selected areas of the surface. The spatial variation of the polarization is correlated to the grain structure of the film. We found also that the grain boundaries are marked by the signal of the 2nd harmonic. The resolution for imaging the domain structure was found to be better than 10 nm. In further experiments we intend to quantify the electrical properties of ferroelectric samples by measuring at different distances from the surface.
Acknowledgements
The authors wish to thank R. Kunze for the design of the electronics, R. Bruchhaus, Siemens Munich, for the PZT samples and their characterization, and G. Martin and M. Weihnacht for many helpful discussions.
References HI Y. Xu, Ferroelectric Materials and their Applications (Elsevier, Amsterdam, 1991). 121 P. Saint-Gregoire, V. Janovec, E. Snoeck, C. Roucau and Z. Zikmund, Ferroelectrics 125 (1992) 209. [3] R. L.e Bihan, Ferroelectrics 97 (1989) 19. [41 J. Hatano, N. Rafii, M.-C. Robert and R. Le Bihan, Ferroelectrics 106 (1990) 39.
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R Franke et al. /Surface
Science Letters 302 (1994) L283-L288
[5] P. Guethner, PhD Thesis, University of Konstanz, Germany (1992). [6] F. Saurenbach and B.D. Terris, IEEE Transactions on Industry Applications 28 (1992) 256. [7] F. Saurenbach and B.D. Terris, Appl. Phys. Lett. 56 (1990) 1703. [8] R. Luethi, H. Haefke, P. Gruetter, H.-J. Guentherodt, L. Szczesniak and K.P. Meyer, Surf. Sci. Lett. 285 (1993) L498.
[9] 0. Walter, Th. Bayer and J. Greschner, Micromachined Silicon Sensors for Scanning Force Microscopy, Proceedings of the STM’90/NANO I Conference, Baltimore, MD, July 23-27,199O. [lo] D. Rugar, H.J. Mamin, R. Erlandsson, J.E. Stern and B.D. Terris, Rev. Sci. Instrum. 59 (1988) 2337. [ll] R. Bruchhaus, H. Huber, D. Pitzer and W. Wersing, Ferroelectrics 127 (1992) 137.
_lI!iii
surface science letters Surface Science Letters 302 (1994) L283-L288
ELSEVIER
Surface Science Letters
Modification and detection of domains on ferroelectric by scanning force microscopy
PZT films
K. Franke *, J. Besold, W. Haessler, C. Seegebarth IFW Dresden e. VT,Postfach, D-01 I71 Dresden, Germany
(Received 18 May 1993; accepted for publication 19 October 1993)
Abstract A scanning force microscope @FM) with light fiber sensor was constructed. The SFM operates in the repulsive contact mode. Three pictures have been measured simultaneously: the topography and the 1st and 2nd harmonic. The 1st harmonic can be related to piezoelectricity and polarization. The 2nd harmonic is correlated with electrostriction and permittivity. The conductive tip of the SFM was used to polarize lead zirconate titanate (PZT) films and to image their domain structure on a nanometer scale. In addition, a writing experiment has been performed.
1. Introduction Ferroelectric materials are of widespread interest in science and for technological applications [l]. The correlation between the microstructure of the material and its electrical properties, e.g. coercivity, spontaneous polarization, dielectric and piezoelectric constant, is of fundamental interest for optimizing these properties. Transmission electron microscopy (TEM) [2], scanning electron microscopy 131and some decoration techniques 141 are useful tools for imaging ferroelectric domains. However, these techniques require thinning of samples, may cause beam charging or have low lateral resolution. At present there is a rapid development to use modified scanning force microscopes @FM) for the deter-
* Corresponding
author: Fax: + 49 3.514659 540.
0167-2584/94/$07.00
mination of the parameters mentioned above [5-81. For further details, see Section 3. In this Letter we describe the design of and the first experiments conducted with a SFM with an interferometric optical sensor. The operation mode is similar to the technique used by Guethner [51. Results of polarizing and domain imaging experiments on lead zirconate titanate (PZT) films are given.
2. Force microscope
Fig. 1 shows a schematic of the SFM which we have constructed. A conductive silicon cantilever [9] is mounted near a single mode light fiber. We use a stable HeNe-laser (HNA 18%S> and illuminate the fiber through a semi-transparent mirror. Therefore our equipment is similar to the sensor used by Rugar et al. [lo]. A reference signal for
0 1994 Elsevier Science B.V. All rights reserved
SSDZ 0167-2584(93)E0222-F
and optical sensor
L284
K Franke et al. /Surface
Science Letters 302 (1994) L283-L288
the compensation of changing intensity is not necessary. We use a relatively large gap w between the end of the fiber and the cantilever of about 50 pm and glue the fiber near the cantilever. No mechanical elements which are often unstable, are necessary in our design. The calculated phase noise corresponds to an apparent tip movement of 4 pm, assuming a frequency stability of half of the longitudinal laser mode distance and an unlimited bandwidth. The thermal drift of the cantilever to the fiber is only several nm over a period of hours. Thermal instability of the optical signals may be caused by triple transit light reflections at the beginning (b) of the fiber and at the outer mirror (m) of the laser. We solved this problem by choosing a suitable length of the fiber. By this the undesired wave packets are set between the wave packets reflected from the end (e) of the fiber. Hence they do not interfere. All this results in thermally stable signals at the photodiode.
3. Tip-sample
interactions
In our experiments the tip operates in the so-called contact mode, i.e., it is within the adsorbate layer of the surface and experiences the repulsive force of the sample (see Fig. 1). We applied an AC voltage V, with the frequency w/27 of 1 kHz between the tip and an electrode at the back of the sample to measure ferroelectric properties. An additional DC voltage I$,, is used in series to change the polarization of the sample. The oscillating electrical field between the tip and the electrode affects the sample and the tip in several ways: (a) Generally the thickness t of the sample varies with w due to the piezoelectric effect and with 2w due to electrostriction. The tip follows these oscillations because of its strong coupling to the surface in the contact mode. Guethner considered the w-dependent piezoelectric effect for the interpretation of his SFM experiments [5].
embe
132. Harmonic
Fig. 1. Schematic diagram of the SFM applied for the present experiments. A fiber polarization adjustment is used to maximize the signal of the photodiode. The arrows at the wave packets mark the propagation direction. The lenses for focusing the laser light into the fiber are not drawn.
R Franke et al. /Surface
Science Letters 302 (1994) L283-L288
(b) Dipole charges of the remanent polarization and image charges caused by permittivity also act on the tip and give rise to signal components at w and 2w, respectively. Saurenbach and Terris [6,71 used this o-component for the imaging of charges and domains in the noncontact mode. On the other hand, Guethner [5] operated in the contact mode and neglected this component. (c) Electrostriction and permittivity change also the DC component of the force which influences the tip. The same holds for the force gradient. These DC effects may alter the tip-surface separation d (Fig. 1) and may falsify the measured quantities. A detailed mathematical analysis of all the frequency components of the tip movement and their dependence on the tip-surface distance will be necessary to quantify the different physical parameters. For the contact mode used here we can roughly assume that the 1st hamtonic includes the effects of piezoelectricity and polarization while the 2nd harmonic combines the effects of electrostriction and permittivity. In future experiments we intend to separate these four physical properties by making measurements at different distances between the tip and surface. As the tip-surface separation increases, the effects of the long-range electrical forces increase, whereas the effects of short-range contact forces decrease. Luethi et al. [8] imaged the polarization in the contact and the noncontact mode. using an insulating Si,N, tip. However, this way of imaging of domains in the contact mode is only possible on flat surfaces since the topography signal is superimposed onto the charge signal.
4. Experimental Three pictures were recorded simultaneously from the signal of the photodiode: the topography from the DC component at the output of the servoelectronics and the 1st and 2nd harmonic by a lock-in technique. It is essential to delay the measurement of the harmonics sufficiently after each scan step. We use a variable delay depending on the local slope of the topography signal to
L285
avoid an apparent influence of the topography on the harmonics. The sampling conditions are chosen to give the same results as for a stationary tip at the same position.
5. Results and discussion A ferroelectric PZT film of rhombohedral phase with a thickness of 610 nm was prepared by sputtering at 450°C [ll]. The substrate was oxidized (100) silicon coated with a sputtered Pt electrode. X-ray diffraction reveals randomly orientated PZT crystallites. The TEM image of the cross-section shows a columnar structure of the crystallites. They are predominantely single grains grown from the Pt electrode to the sample surface. The film is characterized by a permittivity of 500, a remanent polarization of 20 &/cm2 and a coercive field of 80 kV/cm. Our SFM experiments show crystallites of about 200 nm in size. The height distribution of the film topography is characterized by a full-width-at-half-maximum of approximately 60 nm. We found a unified polarization on the as deposited PZT film. Subsequently, the tip of the SFM was used to repolarize selected areas of the film by applying I/PO, for a short period. Fig. 2 shows an example of a “writing experiment”. At first the shown area was completely polarized by scanning with a positive tip voltage I/p,,,= 30 V. For this the voltage was applied for 50 ms to each of the 214 points of the scanned area. Then the marked inner square (Fig. 2a) was “written in” by scanning with an opposite tip voltage of - 10 V. Afterwards the image of the 1st harmonic (see Fig. 2a) was obtained with I&,, = 0. Using this value of I/PO,, only half of the scanned area was successfully repolarized. Subsequently, the marked inner square was completely repolarized by scanning with VpO,= - 20 V (Fig. 2b). Not only the repolarized area but also the surrounding areas show a coarse structure. We compare this structure with the simultaneously measured topography (as explained for Fig. 3). We conclude that the coarse structure of the 1st harmonic corresponds with the grain structure. In first-order approximation, whole grains are always polarized.
L286
K Franke et al. /Surface
Science Letters 302 (1994) L283-L288
across the grain boundary shows a 10% to 90% change of polarization in a distance of 8 nm. Therefore we believe that the resolution in the 1st harmonic picture is better than 10 nm. While the pictures of the 1st harmonic show mostly planar structures, the 2nd harmonic is independent on the polarization distribution and often marks the boundaries of the grains (Fig. 4). We can rule out that this picture is the result of an increased geometric tip-sample capacity at grain boundaries since it is well known that the measured topography cannot show details finer than the tip radius. The measured cross-sections of the topography illustrate the maximum sharn-
Fig. 2. (a) First harmonic picture of a PZT film. The marked square was polarized with the tip voltage V,, = - 10 V. The vertical scale gives the lock-in output. (b) First harmonic picture. The marked square shown in Fig. 2a was polarized with VDO,= - 20 V.The vertical scale gives the lock-in output.
This limits the possible writing density of such films. We assume that the further grain-correlated inhomogeneities of the 1st harmonic are related to the random orientation of the polar axis, since these inhomogeneites are reproduced after writing and erasing. In a second experiment the tip was moved to the position marked by the arrow in Fig. 3a showing the 1st harmonic. At this position only one crystallite. was polarized opposite to the surroundings by applying l&,, = - 30 V. In Fig. 3b the corresponding topography is not toned with its own grey scale but with the grey scale of the 1st harmonic. The region of reversed polarization is clearly limited to a single crystallite. A section
Fig. 3. (a) First harmonic picture of a single polarized lite. The arrow marks the position of the polarizing tip -30 V). The vertical scale gives the lock-in output. (b) raphy of the area shown in Fig. 3a toned with the grey the 1st harmonic.
crystalCl/,,, = Topogscale of
K Franke et al. /Surface
Science Letters 302 (I 994) L283-L288
that the measured 2nd harmonic represents distribution of electrostriction.
L287
the
6. Summary
Fig. 4. (a) Second harmonic picture of a polarized PZT film. The vertical scale gives the lock-in output. (b) Topography of the area shown in Fig. 4a toned with the grey scale of the 2nd harmonic.
ness of the tip and from Fig. 4b we estimate a tip diameter smaller than 20 nm in all directions. In contrast the maximum value of the 2nd harmonic in Fig 4a is reached at a position where the topography is much broader than 20 nm. In a second example there should be a large tip-sample capacity at the grain boundary in the upper right of Fig. 4b. Nevertheless there is a trench in the 2nd harmonic picture. Therefore, we conclude that the 2nd harmonic gives information about permittivity and electrostriction. Since a disturbed perovskite structure is expected at grain boundaries we assume
A modified SFM was constructed to study surface properties of ferroelectric materials. The movement of the tip is detected by an interferometer based on a HeNe-laser. In this way we constructed a thermally stable instrument. An AC voltage is applied between the tip and an electrode at the back of the sample. Pictures at three frequencies are measured simultaneously in the contact mode. The topography is obtained from the DC component. The 1st harmonic picture shows the domain structure. We investigated a ferroelectric PZT film. The tip was used to repolarize selected areas of the surface. The spatial variation of the polarization is correlated to the grain structure of the film. We found also that the grain boundaries are marked by the signal of the 2nd harmonic. The resolution for imaging the domain structure was found to be better than 10 nm. In further experiments we intend to quantify the electrical properties of ferroelectric samples by measuring at different distances from the surface.
Acknowledgements
The authors wish to thank R. Kunze for the design of the electronics, R. Bruchhaus, Siemens Munich, for the PZT samples and their characterization, and G. Martin and M. Weihnacht for many helpful discussions.
References HI Y. Xu, Ferroelectric Materials and their Applications (Elsevier, Amsterdam, 1991). 121 P. Saint-Gregoire, V. Janovec, E. Snoeck, C. Roucau and Z. Zikmund, Ferroelectrics 125 (1992) 209. [3] R. L.e Bihan, Ferroelectrics 97 (1989) 19. [41 J. Hatano, N. Rafii, M.-C. Robert and R. Le Bihan, Ferroelectrics 106 (1990) 39.
L288
R Franke et al. /Surface
Science Letters 302 (1994) L283-L288
[5] P. Guethner, PhD Thesis, University of Konstanz, Germany (1992). [6] F. Saurenbach and B.D. Terris, IEEE Transactions on Industry Applications 28 (1992) 256. [7] F. Saurenbach and B.D. Terris, Appl. Phys. Lett. 56 (1990) 1703. [8] R. Luethi, H. Haefke, P. Gruetter, H.-J. Guentherodt, L. Szczesniak and K.P. Meyer, Surf. Sci. Lett. 285 (1993) L498.
[9] 0. Walter, Th. Bayer and J. Greschner, Micromachined Silicon Sensors for Scanning Force Microscopy, Proceedings of the STM’90/NANO I Conference, Baltimore, MD, July 23-27,199O. [lo] D. Rugar, H.J. Mamin, R. Erlandsson, J.E. Stern and B.D. Terris, Rev. Sci. Instrum. 59 (1988) 2337. [ll] R. Bruchhaus, H. Huber, D. Pitzer and W. Wersing, Ferroelectrics 127 (1992) 137.