SICE Annual Conference 2008Aug. 20-22, 2008, Univ. of Electro-Communications, Japan

Realization of High-Speed Measurement AM-AFM

Using Surface Topography Learning Observers

Takayuki Shiraishi1 and Hiroshi Fujimoto1

1Department of Electrical and Computer Engineering, Yokohama National University,79-5 Tokiwadai, Hodogaya-ku, Yokohama, 2408501 Japan

(Tel : +81-45-339-4107; Fax : +81-45-338-1157, E-mail:shiraishi@hfl.dnj.ynu.ac.jp, hfuji@ynu.ac.jp)

Abstract: This paper addresses an amplitude modulation dynamic mode atomic force microscope (AM-AFM). AFMis an equipment that can measure nanoscale surface topography of the given sample. It is also known that measurementtime is very long. Therefore, high-speed measurement is required in many industrial applications. In general AFMs, mostcommon approach is only classical feedback control. This paper proposes two feedforward compensation methods bysurface topography learning observer based on surface topography observer. These proposed methods archive high-speedmeasurement in simulation and experimental results.

Keywords: Atomic force microscope, Dynamic mode AFM, Nanoscale servo, Observer

1. INTRODUCTION

AFM is a kind of scanning probe microscopes (STMs)and is known as equipment which can measure nanoscalesurface topography of a sample. AFM detects atomicforce by various methods. Atomic force always existsbetween two atoms of a very close distance. Therefore,unlike STM which cannot measure the insulated sample,AFM does not have the restrictions to sample material.Briefly, AFM can measure any sample materials.

In various samples, AFM is especially used for obser-vation of a biological sample because AFM is measurablenot only in vacuum environment and atmospheric air en-vironment but also in solution environment [1].

Furthermore, AFM is used for the application tonanoscale manipulation [2] and the next-generationmemory [3] in addition to the usage as the measuringequipment. AFM is expected as equipment supportingfuture nanotechnology.

According to [4], problems of AFM are as following,1) Ease of use: An expert operator is required, becauseoperation of AFM is difficult2) Repeatability/calibration: Re-adjustment is required atevery exchange of the cantilever and the sample.3) Measurement speed: Measurement speed of AFM isusually very slow.

In particular, the improvement of 3) is strongly desiredin many industrial applications because low speed mea-surement causes undesirable environmental change in bi-ological sample observation, and low working efficiency.

Most controllers for the high-speed measurement inthe conventional AFM are the feedback control with ana-log implementation. However, many high-speed mea-surement for AFM is reported in recently. For instance,The active dumping method for suppressing the reso-nance peak of Z piezo electric stage [5], feedforwardcompensation using the scanning information of the pre-line [6][7], Q control for maintaining the oscillating am-plitude of the cantilever [8], and repetitive control [9] etc.

Our research group has also proposed some methods

for high-speed AFM. For instance, the surface topogra-phy observer [10] which estimates surface topographybased on observer theory and the single directional typesurface topography learning observer which utilized thepattern of the scanning route in contact mode [12].

In this paper, two new surface topography learning ob-servers are proposed. Simulation and experimental re-sults show that proposal methods reduce the tracking er-ror. Consequently, to reduce the tracking error is equiv-alent to reduce the damage of the sample surface. Ac-cordingly, the proposal method is advantageous to softmaterials such as the biological sample.

From the above background, the purpose of this paperis achievement of the high-speed measurement by controlwithout sacrificing high measurement accuracy.

2. MEASURING METHOD OF AM-AFM

Fig. 4 shows the experimental setup (JEOL JSPM-5200) which is the experimental equipment use in thispaper. The control system is shown in Fig. 5. The plantis the part from control inputu to outputy in Fig. 5. Theremaining part is the control part implemented by DSP(sampling time 0.1 [ms]). As shown in Fig. 5, the con-trol inputu to the Z stage is the special edition convertedso that it could apply from DSP. In addition, the Z stage,the XY scanner, and the element for the cantilever oscil-lation are piezo-electric actuator, and are driven throughthe driver, respectively. Although many measuring meth-ods existed in AFM, the amplitude modulation type dy-namic mode atomic force microscope (AM-AFM) wasused in this paper. The greatest feature of AM-AFM isin periodically contacting the sample surface to the can-tilever tip. Since AM-AFM does not damage the sam-ple and the cantilever easily, as compared with the con-tact mode which always touches the sample surface, itis becoming mainstream measuring mode. The measur-ing principle of general AF-AFM is expressed in orderstep. step1; The sample set on the Z stage. step2; Contin-uous oscillation of the cantilever tip is carried out with

Fig. 4 Experimental setup (JEOL JSPM-5200). Fig. 5 Control system of STLO include STO.

Fig. 1 Simplified mechanical model for AM-AFM.

Fig. 2 Block diagram of plant based on Fig. 1.

own resonance frequency (100kHz order). The piezo-electric actuator for vibration is vibrated with the reso-nance frequency of the cantilever by Direct Digital Syn-thesizer (DDS). step3; The distance between sample andcantilevers is contracted. The oscillating amplitude at thecantilever tip decreases according to atomic force. Then,the amplitude value is determined as the reference value(set point). step4; It irradiates with the laser beam at thetip of the cantilever. A photo diode detects the reflectedlight. step5; If XY scan is runnning, the distance betweensample-cantilevers will change with surface topography,then Amplitude modulation of the vibration of the can-tilever tip will be influent. step6; RMS value conversionof the signal which passed along the band pass filter forAmplitude demodulation is carried out. This is output ofthe control systemy. step7; In order to keep the Outputy to setpoint, the Z stage is controlled (output feedback+ feedback controller). step8; The control inputu to Z

Fig. 3 Atomic force based on LJ potential.

stage driver is given so that surface topography may benegated. Therefore, the control inputu is used as an ob-served value of 3D image. Suppose that aforementionedstep is called the conventional method in this paper.

2.1 The dynamic model of AM-AFMAuthors group proposed a detailed model in which the

vibration piezo-electric element, the cantilever, atomicforce, the sample, and the Z stage [11]. However, thedetailed model is too complicated for analyzing. Fig. 1shows the simplification dynamic model which approxi-mated the piezo-electric elements and the sample with therigid body. Atomic force is expressed with the Lennard-Jones potential shown in Fig. 3. As shown in the fig-ure, repulsive force is dominant in short distance. attrac-tive force is dominant in a long distance. Here, attractiveforce is expressed as negative springka and dumpingba

in Fig. 1. Fig. 2 is the block diagram based on the motionequation of the Fig. 1. Here,m, b, k, x, L, x0 are mass,viscous friction coefficient, spting contrant displacementand natural length ,respectively. About the subscript,pv,pz, c, s, a, r, 0 are the vibratin piezo-electric element,the piezo-electric element of Z stage, the cantilever, thesample, attractive force, repulsive force and initial posi-tion of the cantilever respectively. The saturation func-tions (func1/func2) are based on the natural length of thespringska andkr.

The frequency response of plantP (s) obtained withthe servo analyzer is shown in Fig. 6. Nominal plantPn(s) is fitted for PlantP (s) as draw in the Fig. 6. Thetransfer function of nominal plantPn(s) is described as

Pn(s) =7.703× 1010

s2 + 9111s + 1.328× 109. (1)

Fig. 6 Frequency responces of the plant.

3. MEASUREMENT METODS

3.1 Conventional method and STOIn the experiment, the controller which was done digi-

tal redesigne of the continuous time controller at the sam-pling timeTs was used. Feedback controllerC(s) uses PIcontroller describes as

C(s) = 1.0× 10−3 × s + 1.885× 103

s. (2)

As explained in subsection 2.1, the observed image ofthe surface topography in the conventional method is thecontrol inputu. The transfer function from the surface to-pographyd to the control inputu is equal to the comple-mentary sensitivity functionT (s) of the control system.T (s) is

T (s) = −u

d=

C(s)P (s)1 + C(s)P (s)

. (3)

When the feedback controllerC(s) is the high gain,the control inputu will be converged on surface topog-raphy d at high speed because bandwidth ofT (s) ishighly band region. However, since the feedback con-troller composes the closed loop pole, it is usually re-stricted within the resonance frequency of the plantP (s)from the viewpoint of stability.

On the other hand, in author research group, the sur-face topography observer (STO) which estimates surfacetopography by the disturbance observer was proposed[10]. STO assumes atomic force is the input disturbancewhich is shown in the chain line of Fig. 5. Unlike theusual disturbance observer, the STO does not carry outthe feedback to the control inputu. Briefly, it is used asthe open loop estimator. The estimated surface topogra-phy din which was obtained by STO is

din =(

P (s)Pn(s)

y − u

)Q(s)

= (4(s)(d + u) + d)Q(s). (4)

Where,4(s) is the multiplicative modeling error to thenominal plantPn(s). equation (4) divided byQd is

1Q(s)

× din

d= 4(s)

(1 +

u

d

)+ 1

= (1− T (s))4 (s) + 1. (5)

The sensitivity functionS(s) and the complementarysensitivity functionT (s) have relations ofS(s)+T (s) =1. Equation (5) is multiplied byQ(s)d. The estimatedsurface topographydin is the following equation.

din = (S(s)4 (s) + 1)Q(s) · d (6)

Fig. 7 Scan route of the probe.

Here,Q filter,

Q(s) =(

6.28× 103

s + 6.28× 103

)2

, (7)

is a low pass filter in which designed cut-off frequencywith 1 [kHz]. The transfer function from the actual sur-face topographyd to the estimated surface topographyd is (6). The influence of the modeling error4(s) issuppressed according to the sensitivity functionS(s).Moreover, if relatively small modeling error can be dis-regarded, the estimated surface topographydin will bequickly converged on the actual surface topography d ac-cording to the time constant ofQ filter. The pole place-ment of the STO can be designed without care about thestability of the system, since the pole of STO is unrelatedto the closed loop system. Thus, even if equipment isoperating, poles are relocatable without any hesitation inreal time. However, of course STO does not contributethe closed loop system. Consequently, as speedup of XYscan, the Z piezo-electricity stage cannot follow the sur-face topography of the sample. Briefly, servo stiffness isinsufficient.

Practically, the negative phenomena happen in thehigh-speed scan. In the topography of the convex part,the sample may be hit by cantilever, and damage the sam-ple. On the other hand, exact measurement is impossible,because the sample and the cantilever leave completely inthe concave portion. Feedforward compensation is effec-tive for these problems. The block diagram of the surfacetopography learning observer (STLO) is shown in the al-ternate long and short dash line of Fig. 5 . The output ofthe STLO is described as

u = −dout + C(s)e. (8)

Here,dout is the feed-forward signal generated based ondin.

3.2 Scanning routeFig. 7 shows the scanning route which looked at the

sample from on the Z-axis. In X scans, it scans rightwardfrom the scanning starting position to the scan widthL.In this paper, this route is named the forward scan (FWS).

Next, the same route as FWS is followed and it returnsfrom the right end to the left end. This route is namedthe backward scan (BWS). Here, it is supposed that scan-ning speed FWS and BWS are equal. If the round trip ofFWS/BWS is completed, minute stepping operation willbe carried out in the Y direction. It becomes the field scanif this operation is repeated.

3.3 Single directional type STLO

Single directional type surface topography learningobserver (SD-STLO) was already proposed in contactmode, and has succeeded in large shortening of measure-ment time. First, the surface topographydin obtainedfrom STO at the time of FWS is stored in the stack mem-ory. Next, at the time of BWS, it adds to the control in-put by making into feedforward the value of the memorycalled from the large address. Now, FWS and BWS wereturned up in time. Fig. 8 shows the memory input/output.It can be judged from X scan wave whether the scan isFWS or BWS.

fln shows the learning signal in FWS, subscriptl isequivalent to the line number, andn is equivalent to Xdirectional position. The learning signal in BWS isbln aswell as FWS. The merit of SD-STLO is the high compat-ibility of d and din. Because, the learning signal obtainedby FWS is given as the feedforward signal in the sameposition on the line same at BWS. However, feedforwardoperation is only BWS and it is still the same as the con-ventional method in FWS so that clearly from Fig. 8.

3.4 Pre-line scanning type STLO

The learning signaldin stored in the memory in eachFWS and BWS of the pre-line is used as the feedforwardsignaldout in each FWS and BWS of the next line. More-over, the learning signal is obtained as soon as it outputsthe feedforward signal. Fig. 9 shows the input/output ofthe memory in PLS-STLO.

Following performance improves because FWS andBWS give the feedforward signal. Consequently, thetracking errore which should be suppressed with thefeedback controller decreases. On the other hand, sincethe feedforward signal learned in the Pre-line in PLS-STLO is used unlike SD-STLO, the compatibility ofthe feedforward signal and surface topography cannot beguaranteed. Hence, the feedforward signal is disturbancewhen there is no correlation in the Pre-line and the mea-surement line. However, if the suitable scan field is set,it will be considered that almost all sample surfaces aresmooth. PLS-STLO expects the effective method in prac-tical use.

3.5 Dual directional type STLO

Dual directional type surface topography learning ob-server (DD-STLO) is inherited the advantage of SD-STLO and PLS-STLO. Fig. 10 shows the memory in-put/output of DD-STLO. In BWS, it is the same oper-ation as SD-STLO. Thus, the signal learned in FWS ofthe same line is given as the feedforward signal in BWS.Therefore, the compatibility of DD-STLO of the learn-ing signal and surface topography is high as well as SD-STLO. Next, the signal learned in BWS of the Pre-line isused as the feedforward signal in FWS.

Due to this feedforward, also not only in BWS but inFWS, the distance between the cantilever and the samplecan be kept constant. The problem described in subsec-tion 3.2 is improved and the reliability of STO also im-proves.

Fig. 8 Memory I/O of STLO.

Fig. 9 Memory I/O of PLS-STLO.

Fig. 10 Memory I/O of DD-STLO.

Due to the learning signal does not exist in the FWS ofthe 1st line, each STLO carries out only feedback com-pensation. Furthermore, in PLS-STLO, the BWS of the1st line also carries out only feedback compensation.

4. SIMULATION

Fig. 12 shows the simulation results. In Fig. 12,d, e,u, dout are surface topography, control input and outputof the STLO, respectively. On the same graph,d is drawnwith a dashed line, anddout is drawn as the continuousline. Disturbance is the square wave shown in Fig. 12.The 2nd line is the same height as the 1st line. Heightincreases by the 4th line from the 2nd line. The 5th lineof the last is the same height as the 3rd line. Moreover,disturbance does not vary by FWS and BWS in the sameline. In this simulation, the scan line moves to next-linein every 0.01 second.

In SD-STLO, disturbance can be suppressed only inBWS. However, in FWS, it is the same as the conven-tional method which is only feedback compensation. Thetracking errore is large as disturbance becomes high. InPLS-STLO, the disturbance repressed of the 2nd line towhich the same disturbance as the Pre-line is applied isthe best. Although disturbance is varying after the 2ndline, the information on the Pre-line is utilized for feed-forward, and the tracking errore can be suppressed ratherthan SD-STLO in FWS. However, unlike SD-STLO, thetracking errore remains in BWS. In BWS, DD-STLOshows the good disturbance repressed same with SD-STLO. Moreover, also in FWS, the error can be well sup-pressed by carrying out feedforward compensation based

Fig. 11 Surface topography of the sample (Scanningspeed:2.7µm/s).

on Pre-line information as well as PLS-STLO.

5. EXPERIMENTAL RESULT

The experimental result of the conventional methodand each STLO is compared in this section. A measure-ment sample is a standard sample of the nominal height100 [nm]. In order to obtain a highly precise image, thesurface topography measured by scanning speed 2.7 um/s(4105 sec/image) is shown in Fig. 11.

Fig. 13 and Fig. 14 show 3D image and the trackingerror in scanning speed 16.1 um/s (410 sec/image), re-spectively. Moreover, Fig. 15 and Fig. 16 show 3D imageand the tracking error in scanning speed 53.7 um/s (123sec/image), respectively. Both the conventional methods(a) have the large tracking error at FWS and BWS.

In SD-STLO, although it is the same as the conven-tional method in FWS, the tracking errore is suppressedin BWS, due to feedforward. In PLS-STLO, suppres-sion of the tracking error can be achieved also not onlyin BWS but in FWS, due to feedforward. In DD-STLO,the error can be suppressed to the same level as SD-STLO(BWS) in FWS/BWS. With reference to 3D image of Fig.13, the conventional method and the difference in STLOseem to be little. However, it can be recognized that theerror is decreasing due to the proposal method from Fig.14. It can be confirmed STLO is the measurement whichdoes not damage the sample easily. Moreover, even ifit speeds up the scan, PLS-STLO can suppress the errorwell.

In experimental results, SD-STLO and DD-STLOhave not improved the tracking error repressed such asPLS-STLO. As this cause, it is expected that the correctcorrespondence of FWS and BWS cannot be taken by thehysteresis or creep of XY scanner.

6. CONCLUSION

The conclusion of this paper is shown below.In addition to the SD-STLO which proposed in contact

mode [12], Pre-line scanning type and DD-STLO wereproposed in this paper.

Simulation and experimental results show that pro-posal STLOs are effective for the high-speed measure-ment AFM.

When a Pre-line and a measurement line have correl-ativity, PLS and DD-STLO can suppress a tracking errorcompared with the only feedback control.

DD-STLO could obtain high disturbance suppressedcomparable as PLS-STLO in arbitrary topography bycompensating the nonlinearity of XY scanner is men-tioned.

REFERENCES

[1] Z. Shao, J. Mou, D. M. Czajkowsky, J. Yang, andJ.-Y. Yuan, “Biological atomic force microscopy:what is achieved and what is needed,”Advances inPhysics,vol. 45, no. 1, pp. 1-86, 1996.

[2] M. Sitti, “Atomic force microscope probe basedcontrolled pushing for nanotribological characteri-zation,” IEEE-ASME T. Mech., vol. 9, pp. 343-349,2004.

[3] E. Eleftheriou, T. Antonakopoulos, G. K. Binnig, G.Cherubini, M. Despont, A. Dholakia, U. Durig, M.A. Lantz, H. Pozidis, H. E. Rothuizen, and P. Vet-tiger, “Millipede - a MEMS-based scanningprobedata-storage system,”IEEE Trans. Mag., vol. 39,pp. 938-945, 2003.

[4] D. Y. Abramovitch, S. B. Andersson, L. Y. Pao, andG. Schitter. “A Tutorial on the Mechanisms, Dy-namics, and Control of Atomic Force Microscopes,”Proc. Amer. Ctrl. Conf., pp. 3488-3502, 2007.

[5] N. Kodera, H. Yamashita, and T. Ando, “Activedamping of the scanner for high-speed atomic forcemicroscopy,”Rev. Sci. Instrum., vol. 76, p. 053708,2005.

[6] G. Schitter, A. Stemmer and F. Allgower, “Ro-bust two-degree of-freedom control of an atomicforce microscope,” Asian Journal of Control, 6, 2,pp. 156-163, 2004.

[7] T. Uchihashi, N. Kodera, H. Itoh, H. Yamashitaand T. Ando, “Feed-Forward Compensation forHigh-Speed Atomic Force Microscopy Imaging ofBiomolecules,”JJAP, vol. 45, No. 3B, pp. 1904-1908, 2006.

[8] T. Sulchek, R. Hsieh, J. D. Adams, G. G. Yaralioglu,S. C. Minne, C. F. Quate, J. P. Cleveland, A. Ata-lar, and D. M. Adderton, “Highspeed tapping modeimaging with active Q control for atomic force mi-croscopy,”Applied Physics Letters,vol. 76, p. 1473,2000.

[9] S. Tien, Q. Zou, and S. Devasia, “IterativeControl of Dynamics- Coupling-Caused Errors inPiezoscanners During High-Speed AFM Opera-tion,” IEEE Trans. Ctrl. Sys. Tech., vol. 13, no. 6,pp. 921-931, 2005.

[10] K.Aoki, H.Fujimoto, “Nano Scale Servo Controlof Atomic Force Microscope Based on Surface To-pography Observer,” IIC-06-132, pp1-6, 2006. (inJapanese)

[11] T. shiraishi, H. Fujimoto, “Proposal of Surface To-pography Obserber for Tapping mode AFM,” IIC-07-119, pp. 7-12, 2007. (in Japanese)

[12] T. Ohshima, H. Fujimoto, “Proposal of SurfaceTopography Learnig Obserber for Contact modeAFM,” IIC-07-117, pp. 7-12, 2007. (in Japanese)

(a) SD-STLO (b) PLS-STLO (c) DD-STLOFig. 12 Simulation results.

(a) Conventional (b) SD-STLO (c) PLS-STLO (d) DD-STLOFig. 13 3D-images of sample surface topography (Scanning speed:16.1µm/s).

(a) Conventional (b) SD-STLO (c) PLS-STLO (d) DD-STLOFig. 14 Cross-section views of sample (Scanning speed:16.1µm/s).

(a) Conventional (b) SD-STLO (c) PLS-STLO (d) DD-STLOFig. 15 3D-images of sample surface topography (Scanning speed:53.7µm/s).

(a) Conventional (b) SD-STLO (c) PLS-STLO (d) DD-STLOFig. 16 Cross-section views of sample (Scanning speed:53.7µm/s).

[13] A. Sebastian, M. V. Salapaka, D. J. Chen and J. P.Clevelamd, “Harmonic analysis based of tapping-mode AFM”, Proc. Amer. Ctrl. Conf., pp. 232-236,1999.