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Cantilever vibration control by electrostatic actuation for magnetic force microscopy
Sensors and Actuators A 63 (1997) 125–128
Cantilever vibration control by electrostatic actuation for magnetic force microscopy M.J. Cunningham, D.F.L. Jenkins U, M.A.Hj. Khalid Division of Electrical Engineering, Manchester School of Engineering, University of Manchester, Oxford Road, Manchester, M13 9PL, UK Received 21 January 1997; revised 1 April 1997; accepted 5 April 1997
Abstract Vibration noise reduction has been achieved in non-contact magnetic imaging using magnetic force microscopy by feeding back the inverted noise signal as an electrostatic force between the cantilever and the sample. This simple and low-cost method has been shown to be very effective at improving the imaging performance. q 1997 Elsevier Science S.A. Keywords: Electrostatic actuation; Magnetic force microscopy; Vibration control
1. Introduction Since the introduction of the atomic force microscope (AFM) [1] the instrument has evolved significantly and is now used in a wide variety of surface sciences. The instrument consists of a tiny sharp tip attached to a flexible cantilever, a scanner for positioning the sample and a detection system for measuring the small movements of the cantilever which are produced by the surface forces. By coating the tip with a thin layer of magnetic material, magnetic features can be imaged and studied. This technique is known as magnetic force microscopy (MFM). Electrostatic force has been successfully utilized in microactuators and micro-positioners [2–5]. It has also been successfully applied as active vibration dampers for large structures [6]. In this work the authors investigate the use of the electrostatic force as a means of damping unwanted vibrations in the cantilever of a magnetic force microscope. In MFM, a static electrostatic force is often used to facilitate feedback by applying a d.c. voltage (1–10 V) between the magnetic sample and the cantilever [7]. An electrostatic force is used to produce a net attractive force when the tip experiences attractive and repulsive magnetic forces so as to avoid difficulties with the feedback system. Small cantilevers such as those used in MFM are susceptible to vibrations caused by both acoustic, building-borne and other disturbances. In the development of a high-resoU
Corresponding author. Phone: q44 161 275 4578. Fax: q44 161 275 4527. E-mail: David.Jenkins @man.ac.uk
lution nanometric imaging system, the effect of vibration has to be reduced [8]. Image processing methods can be used, but are largely ineffective until the noise is reduced before imaging. Suppression methods such as elastic damping elements [9] and magnetic levitation [10] have been adopted. In earlier work on developing MFM by the authors [11], a pneumatically isolated actively damped optical table had been used to isolate the magnetic force microscope from external disturbances. This method of isolation is very effective but relatively expensive to implement and since it consists of a large structure, the system portability is reduced. In this work the application of a dynamic electrostatic force to achieve vibration cancellation is investigated.
2. Experimental The experimental arrangement is depicted schematically in Fig. 1. The development of the magnetic force microscope used in this work has been reported elsewhere [11]. It was based on an interferometric method of cantilever deflection detection. The output from the detection system contains a mixture of magnetic information and unwanted signals (noise) due to external disturbances. This output was first of all phase shifted by 1808 and then passed through a simple low-pass filter to generate a feedback signal. The filter will prevent the cancellation of the image information, which has frequencies higher than the vibrational frequencies. The filter output was then summed with a variable d.c. bias voltage to provide the static electrostatic force [12]. Hence, the voltage
0924-4247/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S 0 9 2 4 - 4 2 4 7 ( 9 7 ) 0 1 5 8 6 - 0
Journal: SNA (Sensors and Actuators A)
Article: 1667
126
M.J. Cunningham et al. / Sensors and Actuators A 63 (1997) 125–128
Fig. 1. Block diagram of an electrostatic actuation method for MFM cantilever vibration control.
V applied to the sample was a combination and may be written as VsVd.c.qVa.c.
In this case Vd.c. is around 5 V and V0 is around 1 V, which means that from Eq. (3) the force applied, Fa.c.(v), is considerably greater than Fa.c.(2v). Although Eq. (2) shows that the force is a square-law function of voltage, for a small voltage variation of around 1 V the force variation is approximately linear. This is shown by the experimental plot of the cantilever deflection due to the electrostatic force experienced by the tip as a function of the applied voltage, V, in Fig. 2. This means that for this control system approximately linear behaviour occurs. In order to monitor the dynamic behaviour of the cantilever, the signal from the detector was sampled by an analogueto-digital converter (PC30). The sampled signal could be observed in either the time domain or, by taking its fast Fourier transform (FFT), in the frequency domain. To damp the cantilever vibration, the a.c. signal was applied such that it will produce a force that will cause actuation of the cantilever in the opposite direction to its movement due to noise.
(1)
The cantilever in a magnetic foce microscope has a very fine tip at the end to optimize the spatial resolution. By ignoring the effect of the tip on the electrostatic charge, a simple model of a parallel-plate capacitor can be used for this system. In this case the force, F, between the two plates for a given applied voltage, V, and separation, D, is given by
e0A Fs 2V 2 2D
3. Results To establish the vibration spectra produced by a building, a spectrum analyser was connected to the detection system
(2)
where A is the area and e0 is the permittivity of free space. By representing the voltage as VsVd.c.qV0cosvt then Eq. (2) can be written as
e0A V 02 V 02 2 Fs 2 V d.c. q q2V0Vd.c.cos vtq cos 2vt 2D 2 2
≥
¥
(3)
which can be expressed in a simplified form as FsFstaticqFa.c.(v)qFa.c.(2v)
(4)
Fig. 2. Plot of electrostatic force (N) as a function of d.c. bias voltage (V).
Fig. 3. (a) Frequency spectrum of the noise vibration detected by the magnetic force microscope; (b) frequency spectrum detected with electrostatic feedback damping; (c) frequency spectrum detected with the pneumatically isolated table.
Journal: SNA (Sensors and Actuators A)
Article: 1667
M.J. Cunningham et al. / Sensors and Actuators A 63 (1997) 125–128
127
Fig. 4. (a) Magnetic image obtained without vibration damping; (b) image obtained with electrostatic force active vibration damping; (c) image obtained with the pneumatically isolated table.
output. The spectrum is shown in Fig. 3(a), and it shows that most of the vibration occurs below 100 Hz, the highest amplitude occurring around 50 Hz and 100 Hz. These vibrations may have been excited by machines running at or near mains frequency and by their associated harmonics. The low-pass filter was designed to operate with a y3 dB cut-off frequency at 50 Hz. This is well below the image frequency, which is around 200 Hz, and the cantilever’s resonance frequency at 8 kHz. On applying the electrostatic force feedback and adjusting the tip–sample separation to around 150 nm and the d.c. bias voltage to around q5 V, values for normal operation, the amplifier gain, which controls the a.c. voltage amplitude, was adjusted for optimum noise cancellation. The captured frequency spectrum is shown in Fig. 3(b). It is observed that the noise is much reduced by this method and is comparable with the results obtained when using the pneumatically isolated table, Fig. 3(c). The residual noise is largely electronic noise and can be reduced by careful design of the electronics and tailoring the feedback spectrum. With the above configuration, a magnetic hard-disk sample was imaged. The hard-disk sample was pre-written with bits ‘1’ about 6 mm apart and bit ‘0’ in between. The width of the bit is about 1 mm and the image size is about 34 mm=34 mm. The images of the hard-disk sample without and with electrostatic force feedback are shown in Fig. 4(a) and (b).
There is a considerable reduction in the noise interference in the image (b) and the black stripes representing ‘0’ to ‘1’ transitions and the white stripes representing ‘1’ to ‘0’ transitions can be clearly observed. The images show that active vibration control enables the detailed magnetic information in the image to be observed, whereas such detail is masked by the effect of the vibration in Fig. 4(a). The image obtained when using the pneumatically isolated table (Fig. 4(c)) is similar to that obtained when using active vibration control. Active vibration control is effective provided the vibration spectrum and the signal spectrum do not overlap. This is the case for all but extremely slow scan rates. As the scan rate is progressively increased, such overlap does not occur but eventually the image contrast deteriorates. Such scan rates give rise to signal frequencies well below that of the cantilever resonance.
4. Conclusions Electrostatic actuation is increasingly attractive as mechanical structures become smaller and smaller and is extremely well suited to the control of cantilevers in scanning probe microscopes. The cantilever of an MFM system is extremely susceptible to external disturbances that degrade imaging performance and electrostatic actuation has been successfully
Journal: SNA (Sensors and Actuators A)
Article: 1667
128
M.J. Cunningham et al. / Sensors and Actuators A 63 (1997) 125–128
employed to suppress unwanted cantilever vibrations. The results obtained using this simple, cheap and unobtrusive technique are comparable to those obtained using conventional vibration isolation equipment such as a massive optical table mounted on gas-damped legs.
References [1] G. Binning, C.F. Quate and Ch. Gerber, Atomic force microscope, Phys. Rev. Lett., 56 (1986) 930–933. [2] K. Hoto and K. Hane, Micromachining with a force microscope tip assisted by electrostatic force, Rev. Sci. Instrum., 67 (1996) 587–601. [3] K.E. Peterson, Micromechanical light modulator array fabricated on silicon, Appl. Phys. Lett., 31 (1977) 521–523. [4] T. Go¨ddenhenrich, H. Lemke, U. Hartmann and C. Heiden, Force microscope with capacitance displacement detection, J. Vac. Sci. Technol. A, 1 (1990) 383–387. [5] J.A. van Raalte, A new Schlieren light valve for television projection, Appl. Opt., 9 (1970) 2225–2230. [6] S. Inui, C. Liang and C.A. Rogers, Electrostatic variable friction dampers for active/passive structural vibration control, Proc. 2nd Int. Conf. Intelligent Materials, ICIM 1994, Williamsburg, VA, USA, 5–8 June, 1994, pp. 635–645. [7] D. Rugar, H.J. Mamin, P. Guether, S.E. Lambert, J.E. Lambert, J.E. Stern, I. McFaydec and T. Yogi, Magnetic force microscopy: general principles and application to longitudinal recording media, J. Appl. Phys., 68 (1990) 1169–1183. [8] D. Rugar and P. Gru¨tter, Mechanical parametric amplification and thermomechanical noise squeezing, Phys. Rev. Lett., 67 (1991) 699– 702. [9] D.W. Pohl, Some design criteria in scanning tunneling microscopy, IBM J. Res. Develop., 30 (1986) 417–427. [10] S. Park and C.F. Quate, Scanning tunneling microscope, Rev. Sci. Instrum., 58 (1987) 2010–2017. [11] M.J. Cunningham, S.T. Cheng and W.W. Clegg, A differential interferometer for scanning force microscopy, Meas. Sci. Technol., 5 (1994) 1350–1354. [12] D.F.L. Jenkins, M.J. Cunningham and W.W. Clegg, Sensors and actuators for active vibration control of small cantilevers, Proc. 7th Conf. Sensors and their Applications, Dublin, Ireland, 10–13 Sept., 1995, pp. 401–405.
Biographies Michael Cunningham is chairman of the Electrical Engineering Division of the Manchester School of Engineering, University of Manchester, where he holds the post of senior lecturer. He is honorary editor of the IEE Proceedings ‘Science, Measurement and Technology’ and his research area is instrumentation and measurement. Current interests include the application of sensors and actuators to very small structures for micro-positioning and active vibration-control purposes. This work is investigating the use of bulk, thick- and thin-film piezoelectric material for positioning and vibration control of very small structures and incorporates laser deflection sensing. This work has given rise to the publication of papers on active vibration control using ZnO thin films and sputtered PZT films for moving micromechanical structures with nanometric precision. David Jenkins holds the degrees of B.Sc. (physics), M.Sc. (lasers and their applications) and Ph.D. (photothermal deflection spectroscopy). After completing his Ph.D. research at the Royal Military College of Science, he became a post-doctoral research fellow at Coventry University in 1990, working on magneto-photo-acoustic spectroscopy. Since 1994 he has worked in the Information Storage Group, Division of Electrical Engineering, at University of Manchester, researching into active vibration control of micromechanical structures. Ashhar Khalid holds the degrees of B.Eng. (electrical engineering) from the University of Technology, Malaysia, and M.Sc. (instrument design and application) from the University of Manchester. Since 1982 he has worked as a research engineer at the Government Research Institute in Malaysia. Currently he is completing his Ph.D. thesis in the Electrical Engineering Division, University of Manchester. His research interests include computing, instrumentation and control.
Journal: SNA (Sensors and Actuators A)
Article: 1667
Cantilever vibration control by electrostatic actuation for magnetic force microscopy M.J. Cunningham, D.F.L. Jenkins U, M.A.Hj. Khalid Division of Electrical Engineering, Manchester School of Engineering, University of Manchester, Oxford Road, Manchester, M13 9PL, UK Received 21 January 1997; revised 1 April 1997; accepted 5 April 1997
Abstract Vibration noise reduction has been achieved in non-contact magnetic imaging using magnetic force microscopy by feeding back the inverted noise signal as an electrostatic force between the cantilever and the sample. This simple and low-cost method has been shown to be very effective at improving the imaging performance. q 1997 Elsevier Science S.A. Keywords: Electrostatic actuation; Magnetic force microscopy; Vibration control
1. Introduction Since the introduction of the atomic force microscope (AFM) [1] the instrument has evolved significantly and is now used in a wide variety of surface sciences. The instrument consists of a tiny sharp tip attached to a flexible cantilever, a scanner for positioning the sample and a detection system for measuring the small movements of the cantilever which are produced by the surface forces. By coating the tip with a thin layer of magnetic material, magnetic features can be imaged and studied. This technique is known as magnetic force microscopy (MFM). Electrostatic force has been successfully utilized in microactuators and micro-positioners [2–5]. It has also been successfully applied as active vibration dampers for large structures [6]. In this work the authors investigate the use of the electrostatic force as a means of damping unwanted vibrations in the cantilever of a magnetic force microscope. In MFM, a static electrostatic force is often used to facilitate feedback by applying a d.c. voltage (1–10 V) between the magnetic sample and the cantilever [7]. An electrostatic force is used to produce a net attractive force when the tip experiences attractive and repulsive magnetic forces so as to avoid difficulties with the feedback system. Small cantilevers such as those used in MFM are susceptible to vibrations caused by both acoustic, building-borne and other disturbances. In the development of a high-resoU
Corresponding author. Phone: q44 161 275 4578. Fax: q44 161 275 4527. E-mail: David.Jenkins @man.ac.uk
lution nanometric imaging system, the effect of vibration has to be reduced [8]. Image processing methods can be used, but are largely ineffective until the noise is reduced before imaging. Suppression methods such as elastic damping elements [9] and magnetic levitation [10] have been adopted. In earlier work on developing MFM by the authors [11], a pneumatically isolated actively damped optical table had been used to isolate the magnetic force microscope from external disturbances. This method of isolation is very effective but relatively expensive to implement and since it consists of a large structure, the system portability is reduced. In this work the application of a dynamic electrostatic force to achieve vibration cancellation is investigated.
2. Experimental The experimental arrangement is depicted schematically in Fig. 1. The development of the magnetic force microscope used in this work has been reported elsewhere [11]. It was based on an interferometric method of cantilever deflection detection. The output from the detection system contains a mixture of magnetic information and unwanted signals (noise) due to external disturbances. This output was first of all phase shifted by 1808 and then passed through a simple low-pass filter to generate a feedback signal. The filter will prevent the cancellation of the image information, which has frequencies higher than the vibrational frequencies. The filter output was then summed with a variable d.c. bias voltage to provide the static electrostatic force [12]. Hence, the voltage
0924-4247/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S 0 9 2 4 - 4 2 4 7 ( 9 7 ) 0 1 5 8 6 - 0
Journal: SNA (Sensors and Actuators A)
Article: 1667
126
M.J. Cunningham et al. / Sensors and Actuators A 63 (1997) 125–128
Fig. 1. Block diagram of an electrostatic actuation method for MFM cantilever vibration control.
V applied to the sample was a combination and may be written as VsVd.c.qVa.c.
In this case Vd.c. is around 5 V and V0 is around 1 V, which means that from Eq. (3) the force applied, Fa.c.(v), is considerably greater than Fa.c.(2v). Although Eq. (2) shows that the force is a square-law function of voltage, for a small voltage variation of around 1 V the force variation is approximately linear. This is shown by the experimental plot of the cantilever deflection due to the electrostatic force experienced by the tip as a function of the applied voltage, V, in Fig. 2. This means that for this control system approximately linear behaviour occurs. In order to monitor the dynamic behaviour of the cantilever, the signal from the detector was sampled by an analogueto-digital converter (PC30). The sampled signal could be observed in either the time domain or, by taking its fast Fourier transform (FFT), in the frequency domain. To damp the cantilever vibration, the a.c. signal was applied such that it will produce a force that will cause actuation of the cantilever in the opposite direction to its movement due to noise.
(1)
The cantilever in a magnetic foce microscope has a very fine tip at the end to optimize the spatial resolution. By ignoring the effect of the tip on the electrostatic charge, a simple model of a parallel-plate capacitor can be used for this system. In this case the force, F, between the two plates for a given applied voltage, V, and separation, D, is given by
e0A Fs 2V 2 2D
3. Results To establish the vibration spectra produced by a building, a spectrum analyser was connected to the detection system
(2)
where A is the area and e0 is the permittivity of free space. By representing the voltage as VsVd.c.qV0cosvt then Eq. (2) can be written as
e0A V 02 V 02 2 Fs 2 V d.c. q q2V0Vd.c.cos vtq cos 2vt 2D 2 2
≥
¥
(3)
which can be expressed in a simplified form as FsFstaticqFa.c.(v)qFa.c.(2v)
(4)
Fig. 2. Plot of electrostatic force (N) as a function of d.c. bias voltage (V).
Fig. 3. (a) Frequency spectrum of the noise vibration detected by the magnetic force microscope; (b) frequency spectrum detected with electrostatic feedback damping; (c) frequency spectrum detected with the pneumatically isolated table.
Journal: SNA (Sensors and Actuators A)
Article: 1667
M.J. Cunningham et al. / Sensors and Actuators A 63 (1997) 125–128
127
Fig. 4. (a) Magnetic image obtained without vibration damping; (b) image obtained with electrostatic force active vibration damping; (c) image obtained with the pneumatically isolated table.
output. The spectrum is shown in Fig. 3(a), and it shows that most of the vibration occurs below 100 Hz, the highest amplitude occurring around 50 Hz and 100 Hz. These vibrations may have been excited by machines running at or near mains frequency and by their associated harmonics. The low-pass filter was designed to operate with a y3 dB cut-off frequency at 50 Hz. This is well below the image frequency, which is around 200 Hz, and the cantilever’s resonance frequency at 8 kHz. On applying the electrostatic force feedback and adjusting the tip–sample separation to around 150 nm and the d.c. bias voltage to around q5 V, values for normal operation, the amplifier gain, which controls the a.c. voltage amplitude, was adjusted for optimum noise cancellation. The captured frequency spectrum is shown in Fig. 3(b). It is observed that the noise is much reduced by this method and is comparable with the results obtained when using the pneumatically isolated table, Fig. 3(c). The residual noise is largely electronic noise and can be reduced by careful design of the electronics and tailoring the feedback spectrum. With the above configuration, a magnetic hard-disk sample was imaged. The hard-disk sample was pre-written with bits ‘1’ about 6 mm apart and bit ‘0’ in between. The width of the bit is about 1 mm and the image size is about 34 mm=34 mm. The images of the hard-disk sample without and with electrostatic force feedback are shown in Fig. 4(a) and (b).
There is a considerable reduction in the noise interference in the image (b) and the black stripes representing ‘0’ to ‘1’ transitions and the white stripes representing ‘1’ to ‘0’ transitions can be clearly observed. The images show that active vibration control enables the detailed magnetic information in the image to be observed, whereas such detail is masked by the effect of the vibration in Fig. 4(a). The image obtained when using the pneumatically isolated table (Fig. 4(c)) is similar to that obtained when using active vibration control. Active vibration control is effective provided the vibration spectrum and the signal spectrum do not overlap. This is the case for all but extremely slow scan rates. As the scan rate is progressively increased, such overlap does not occur but eventually the image contrast deteriorates. Such scan rates give rise to signal frequencies well below that of the cantilever resonance.
4. Conclusions Electrostatic actuation is increasingly attractive as mechanical structures become smaller and smaller and is extremely well suited to the control of cantilevers in scanning probe microscopes. The cantilever of an MFM system is extremely susceptible to external disturbances that degrade imaging performance and electrostatic actuation has been successfully
Journal: SNA (Sensors and Actuators A)
Article: 1667
128
M.J. Cunningham et al. / Sensors and Actuators A 63 (1997) 125–128
employed to suppress unwanted cantilever vibrations. The results obtained using this simple, cheap and unobtrusive technique are comparable to those obtained using conventional vibration isolation equipment such as a massive optical table mounted on gas-damped legs.
References [1] G. Binning, C.F. Quate and Ch. Gerber, Atomic force microscope, Phys. Rev. Lett., 56 (1986) 930–933. [2] K. Hoto and K. Hane, Micromachining with a force microscope tip assisted by electrostatic force, Rev. Sci. Instrum., 67 (1996) 587–601. [3] K.E. Peterson, Micromechanical light modulator array fabricated on silicon, Appl. Phys. Lett., 31 (1977) 521–523. [4] T. Go¨ddenhenrich, H. Lemke, U. Hartmann and C. Heiden, Force microscope with capacitance displacement detection, J. Vac. Sci. Technol. A, 1 (1990) 383–387. [5] J.A. van Raalte, A new Schlieren light valve for television projection, Appl. Opt., 9 (1970) 2225–2230. [6] S. Inui, C. Liang and C.A. Rogers, Electrostatic variable friction dampers for active/passive structural vibration control, Proc. 2nd Int. Conf. Intelligent Materials, ICIM 1994, Williamsburg, VA, USA, 5–8 June, 1994, pp. 635–645. [7] D. Rugar, H.J. Mamin, P. Guether, S.E. Lambert, J.E. Lambert, J.E. Stern, I. McFaydec and T. Yogi, Magnetic force microscopy: general principles and application to longitudinal recording media, J. Appl. Phys., 68 (1990) 1169–1183. [8] D. Rugar and P. Gru¨tter, Mechanical parametric amplification and thermomechanical noise squeezing, Phys. Rev. Lett., 67 (1991) 699– 702. [9] D.W. Pohl, Some design criteria in scanning tunneling microscopy, IBM J. Res. Develop., 30 (1986) 417–427. [10] S. Park and C.F. Quate, Scanning tunneling microscope, Rev. Sci. Instrum., 58 (1987) 2010–2017. [11] M.J. Cunningham, S.T. Cheng and W.W. Clegg, A differential interferometer for scanning force microscopy, Meas. Sci. Technol., 5 (1994) 1350–1354. [12] D.F.L. Jenkins, M.J. Cunningham and W.W. Clegg, Sensors and actuators for active vibration control of small cantilevers, Proc. 7th Conf. Sensors and their Applications, Dublin, Ireland, 10–13 Sept., 1995, pp. 401–405.
Biographies Michael Cunningham is chairman of the Electrical Engineering Division of the Manchester School of Engineering, University of Manchester, where he holds the post of senior lecturer. He is honorary editor of the IEE Proceedings ‘Science, Measurement and Technology’ and his research area is instrumentation and measurement. Current interests include the application of sensors and actuators to very small structures for micro-positioning and active vibration-control purposes. This work is investigating the use of bulk, thick- and thin-film piezoelectric material for positioning and vibration control of very small structures and incorporates laser deflection sensing. This work has given rise to the publication of papers on active vibration control using ZnO thin films and sputtered PZT films for moving micromechanical structures with nanometric precision. David Jenkins holds the degrees of B.Sc. (physics), M.Sc. (lasers and their applications) and Ph.D. (photothermal deflection spectroscopy). After completing his Ph.D. research at the Royal Military College of Science, he became a post-doctoral research fellow at Coventry University in 1990, working on magneto-photo-acoustic spectroscopy. Since 1994 he has worked in the Information Storage Group, Division of Electrical Engineering, at University of Manchester, researching into active vibration control of micromechanical structures. Ashhar Khalid holds the degrees of B.Eng. (electrical engineering) from the University of Technology, Malaysia, and M.Sc. (instrument design and application) from the University of Manchester. Since 1982 he has worked as a research engineer at the Government Research Institute in Malaysia. Currently he is completing his Ph.D. thesis in the Electrical Engineering Division, University of Manchester. His research interests include computing, instrumentation and control.
Journal: SNA (Sensors and Actuators A)
Article: 1667