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Current Applied Physics 12 (2012) 989e994

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Current Applied Physics

journal homepage: www.elsevier .com/locate/cap

High-speed atomic force microscopy with phase-detection

Donghyeok Lee a,b, Hyunsoo Lee a, N.S. Lee a, K.B. Kim a, Yongho Seo a,b,*

a Faculty of Nanotechnology and Advanced Material Engineering, Sejong University, Seoul 143-747, Republic of KoreabGraphene Research Institute, Sejong University, Seoul 143-747, Republic of Korea

a r t i c l e i n f o

Article history:Received 13 September 2011Received in revised form8 December 2011Accepted 28 December 2011Available online 4 January 2012

Keywords:High-speed scanningPhase-detectionAtomic force microscopeHigh-speed AFMHigh frequency cantilever

* Corresponding author. Graphene Research Instit143-747, Republic of Korea. Fax: þ82 2 3408 3664.

E-mail address: yseo@sejong.ac.kr (Y. Seo).

1567-1739/$ e see front matter � 2012 Elsevier B.V.doi:10.1016/j.cap.2011.12.024

a b s t r a c t

In order to improve the scanning speed of tapping mode AFM, we have studied the phase-detectionmode AFM with a high frequency (1.5 MHz) cantilever. The phase shifts versus tip-sample distancewith different types of samples including polymer, semiconductor, and graphite were measured and theinteraction forces were analyzed. It was found that the phase shift in repulsive region is nearly linear asa function of distance, which can be used for feedback control in general, except that some blunt tipscause reversed polarity of phase shift due to excessive energy dissipation. High-speed image with scanrate of 100 Hz was obtained which were controlled with phase shift as a feedback signal.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Though the atomic forcemicroscopy (AFM) is considered as a veryessential techniquefornano-characterizationandnano-manipulationfields, its slow imaging rate is a critical disadvantage to be utilized inindustrial and multidisciplinary research area. In this context, somegroups have studied on the high-speed AFM including mechanicalfeedback contact-mode AFM (C-AFM) [1e3] and small cantileverbased non-contact (or tapping mode) AFM (NC-AFM) [4e6].

In case of C-AFM, the response time of the cantilever is deter-mined by the mass of the cantilever and force between the tip andsample [7]. On the other hand, the response time of the cantileverfor NC-AFM is complicated depending on whether it is amplitudedetection, phase detection, or frequency detection. In case ofamplitude detection, the amplitude change has delay time s ¼ Q/pf0, where Q is the quality factor and f0 is the resonance frequencyof the cantilever [8]. For the frequency detection mode, generallya phase-locked-loop (PLL) circuit is used to measure the frequencyshift and the bandwidth of the PLL limits the speed of the AFM. Incase of phase-detection mode, however, it is not clear what thebottleneck of the scanning speed is. Theoretically, the responsedelay time of the phase shift is considered as nearly zero, that is, theinstantaneous change occurs in each oscillation cycle [8].

ute, Sejong University, Seoul

All rights reserved.

Amongmany groups who have studied the high-speed NC-AFM,the instrumentation researches on the phase-detection mode wererare. A phase change detection using quartz resonator was re-ported, where the negative phase change �0.1� corresponding toattractive force was detected [9]. This attractive force detectionmeans that the phase shift is muchmore sensitive to the interactionforces than the amplitude. The phase shifts are related withviscosity, elasticity, adhesion, hydrophobicity, and surface charges[10,11]. Uchihashi et al. reported on fast phase imaging NC-AFM,which detected the phase shift with a bandwidth over 1 MHz[11]. They obtained topography and phase image simultaneouslywith imaging rate of 100 ms/frame in pure water. Ando et al. re-ported a high-speed AFM by using phase-modulation mode, wherethe imaging rate was in the range of 500e800 ms/frame [12].

Actually the phase shift is not a monotonic function of theinteraction force between the tip and sample, and it has differentpolarities depending on attractive or repulsive forces. The detailedphase-versus-distance behaviors were studied in theoretically andby using computer simulations [13,14]. Fukuma et al. developed thephase-modulation AFM and demonstrated its high-resolutionperformance using 142 kHz cantilever [15]. But their scanningspeed was at most 469 nm/s, which was typical scanning speedfor conventional AFM. In order to develop the high-speed phase-detection AFM, the phase shifts as a function of the interactionforce with the different types of samples were measured andanalyzed at the high frequency regime (�1 MHz) of the cantileverin this report.

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2. Experimental

The cantilever (ArrowUHF, Nanoworld) with 1.5 MHz resonancefrequency was used, which is 35 mm long and 42 mm wide. Ahomemade RT-AFM setup previously reported by our group [7] wasused for imaging and phase spectroscopy measurements. The mainbody of the RT-AFM was composed of head, PZT tube scanner,optical microscope, and coarse approach mechanism (Picomotor,New focus Inc.) The head consisted of laser diode, lens, mirror, andposition sensitive photodiode (PSPD). For the PSPD the quad-cellssegmented photodiode (OSI optoelectronics, SPOT-4D) was usedfor high-speed signal detection, as it has 3 ns rising time and 5 pFcapacitance. To measure the amplitude and phase simultaneouslywith wide bandwidth, a lock-in amplifier (SR-844, SRS Inc.) withminimum 10 ms time constant was used.

An analog controller was prepared to control z-directionalposition of the tube scanner by using the phase shift signalmeasured by the lock-in amplifier. The controller with 10 ms timeconstant is composed of 6 op-amps (AD713) operating with

Fig. 1. Circuit diagram for PI controller. This controller is composed of 6 op-amps (AD7

proportional-integral control scheme and two polarity switches, asshown in Fig. 1. In other to adapt the polarity change of the phaseshift in case, two switches (in dotted boxes) were inserted. Theswitch 1 is for polarity selection of error signal, and the switch 2 isfor the z-scanner direction selection. For example, if the phasedecreases as the tip approaches, then both of switches should bedown, and vice versa.

3. Result and discussion

One can simply estimate the phase shift polarity from theharmonic approximation, in which the cantilever motion isapproximated as a harmonic oscillator with driven force [8]. Fromthe harmonic approximation, the amplitude always decreasesunder both attractive (positive force gradient) and repulsive(negative force gradient) interactions, when the driving frequencyis set to the resonance frequency (u¼ u0). However, the phase shiftis increased (decreased) in attractive (repulsive) interaction, asshown in Fig. 2 (a, b). In general, the phase 4 is defined from the

13) operating with proportional-integral control scheme and 2 polarity switches.

Fig. 2. Illustrations for the amplitude change (a) and phase shift (b) in attractive andrepulsive interactions. These estimations are based on the harmonic approximation.(c) shows the experimental data for amplitude and phase as functions of the externaldriving frequency.

Fig. 3. (a) Amplitude and (b) Phase versus distance curves measured on HOPG, Si, andpolycarbonate. The amplitude curves show monotonic decreases, and the phase curvesshow slight decreases and sharp increases. Each data curve was shifted 10 nm in x-axis,to avoid overlapping the data points.

Table 1Relative values for maximum slopes of amplitude change and phase change asfunctions of distance.

f0 HOPG Si wafer Polycarbonate

Relative amplitude shift 300 kHz 0.95 � 0.1 0.99 � 0.1 0.99 � 0.11.5 MHz 0.89 � 0.16 0.86 � 0.16 0.85 � 0.14

Relative phase shift 300 kHz 0.97 � 0.1 0.92 � 0.1 0.98 � 0.11.5 MHz 0.90 � 0.16 0.83 � 0.21 0.68 � 0.27

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equation of cantilever motion z ¼ z0 cos(ut�4) when an externalforce F0 cos(ut) is applied, that is, the positive increase of 4 meansthe delay of the cantilever response. The harmonic approximationis valid in limited cases: small oscillation amplitude and constantforce gradient [8]. As a preliminary test, the amplitude and phaseversus frequencies for a cantilever were measured simultaneouslyin our setup, as shown in Fig. 2(c). The resonance frequency andquality factor of this cantilever are estimated to be about 1.27 MHzand 70, respectively.

The phase-distance curve measurements were performed onvarious samples: polycarbonate, Si wafer, highly oriented pyrolyticgraphite (HOPG), with high frequency cantilevers. Fig. 3 show theamplitude (a) and phase (b) versus distance measurement results.While the amplitude curves show monotonic decreases as itapproaches the samples, the phase curves have slight dips(attractive region) and sharp increases (repulsive region), as ex-pected in the harmonic approximation. Note that the phase q in this

data is defined from the cantilever motion z ¼ z0 cos(ut�p/2þq),that is, when q ¼ 0, the cantilever motion is delayed with 90� andpositive value of q means the earlier response than 90�.

The phase shift as a function of distance has not been studied asmuch as the amplitude, theoretically. Particularly, Lee and Jhestudied the phase shift versus distance by calculating numericallyan integral equation for dynamic motion of a cantilever [13].Assuming Lennard-Jones potential with characteristic length l, thephase shift as a function of distance (z/l) shows steep increasefollowing gentle decrease for small oscillation region (A0/l ¼ 0.1), inapproaching process. On the other hand, in case of large oscillationamplitude (A0 z l), a hysteresis behavior is conspicuous inapproaching and retracting cycle. Chen et al. [16] measured the

Fig. 4. Topographic images of polycarbonate surface in a compact disk obtained by amplitude feedback control with different scanning rates. The phase control images show muchdetailed resolution with faster scan rate. The pixel size was 100 � 100, and the scanned area was 1.5 � 1.5 mm2.

D. Lee et al. / Current Applied Physics 12 (2012) 989e994992

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phase shift on mica (stiff) and polystyrene (soft), in which theresonance frequencies were 85 and 300 kHz, corresponding to thecantilever stiffness of 3 and 40 N/m. Referring to their computersimulation results, for 40 N/m cantilever, the phase slope for a stiffsample was higher, while for 3 N/m cantilever, a soft sample causeda deeper attractive dip and the slope was steeper, that is, compli-cated results depending on the stiffness of cantilever werereported.

Overall shapes of phase shift curves measured in our experi-ment are similar to the results of other researcher [13,14,16e18]. Inour experiment, it was quite difficult to obtain consistent quanti-tative data for the sample dependence of the phase shift, becausethe phase shifts were very sensitive to external conditions: tipsharpness, mechanical noise, and laser beam alignment. Particu-larly, in case of the polycarbonate sample, the phase shift polaritywas reversed, (negative slope) occasionally when it was measuredby blunt tips. As the polycarbonate is a polymer material, it isexpected to have relatively strong internal frictional forcecompared with the other samples. The data in Fig. 3(b) seems tohave two different slopes. According to Lee and Jhe [13], when thefree oscillation amplitude A0 is much smaller than the characteristiclength l the data in repulsive region is linear (single slope), while

Fig. 5. Topographic images of HOPG with graphite layer step obtained by (a) amplitude an70 Hz, 90 Hz, and 100 Hz from left-top to right-bottom, respectively. The pixel size was 10

when A0 z l the curve has hysteresis behavior and seems to havetwo different slopes. The steep slope is due to the abrupt jump fromthe attractive region to repulsive region, and the low slope is due tothe monotonic change in repulsive interaction.

In order to acquire more quantitative data, wemeasured 10 datasets with different cantilevers having the same specifications(f0 z 1.5 MHz) where each data set was measured more than 5times at different points and averaged. From the measured ampli-tude and phase versus distance curve, a maximum slope regionwaschosen in repulsive region, and the slopes were estimated by linearregression. As each set of data has a different value due to thedifferent tip and alignment conditions, the values were normalizedso as that the maximum value is set to 1 among the data in one setmeasured by the same cantilever for different samples. The resul-tant data for amplitude and phase are shown in Table 1. From1.5 MHz data in the table, the slope for HOPG was largest and thatfor polycarbonate was smallest. For comparison purpose, the datataken by 300 kHz cantilever are shown together, which show nonoticeable sample dependence within the experimental errorranges. The surface of HOPGwas freshly cleaved and expected to beatomically flat. It is well known that the frictional force on graphitesurface is almost zero, which has been used as a solid lubricant

d (b) phase feedback control with different scanning rates: slow, 10 Hz, 30 Hz, 50 Hz,0 � 100, and the scanned area was 2 � 2 mm2.

D. Lee et al. / Current Applied Physics 12 (2012) 989e994994

material [19]. Therefore, the HOPG surface gives rise to negligibleenergy dissipation.

On the other hand, the polycarbonate which is a kind of polymermaterial is expected to cause larger frictional force. In the repulsiveforce region, the larger amount of energy dissipation is expected,and the cantilever motion is delayed in addition to the influence ofthe repulsive interaction [10,20]. Therefore, phase shift wasdecreased (that is, delayed) as repulsive force is increased, and theslope of phase versus distance curve was lowered. The negativeslope for excessively blunt tip is also, attributed to the extremelyhigh energy dissipation. As a whole, the dips in phase curves cor-responding to the attractive interaction showed similar depthsirrespective of the kind of samples, because the attractive interac-tion rarely involves the energy dissipation. In case of 300 kHzcantilever, the velocity of the motion is much slower, and theenergy dissipation is not expected to be noticeable.

The feasibility study was performed for fast imaging with phasefeedback scheme, in comparisonwith amplitude feedback.With theamplitude feedback scheme, the polycarbonate surface ina commercial compact disk was scanned with the scan rates (lines/sec): slow,10, 20, 30, 40, and50Hz, as shown in Fig. 4(a). Thenumberof pixels was 100 � 100, and scanned area was 1.5 � 1.5 mm2. Thedetailed topographic features in slow image are not visible in 40 or50 Hz image. However, in case of phase feedback images shown inFig. 4(b), fast scan images with scan rate up to 70 Hz show somedetailed features, due to fast response of the phase shift.

For another example, high speed topographic images of HOPGsurface were taken, as shown in Fig. 5. The images in (a) were takenin amplitude feedback scheme and (b) in phase feedback scheme.The number of pixels was 100 � 100, and scanned area was2� 2 mm2. The cantilever vibration amplitudewas about 18 nm andphase set point for feedback control was 10� from the free oscilla-tion phase. While the amplitude-mode images show the back-ground wiggles in fast scanning images, the phase-mode imagesshow almost flat background up to 100 Hz scan rate. Also, a few-layer-graphene step with 2 nm height was clearly resolved inphase-mode up to 100 Hz scan rate. The scan rate of 100 Hzcorresponds to the imaging rate 1 s/frame in the case of 100 � 100pixels. This speed is not better than Uchihashi et al.’s result of 100ms/frame [11], but their images were taken bymeasuring the phaseshifts while the feedback control was done by the amplitude signal.The key point of our work is that the distance control was done byphase shift feedback, which has potential applicability for real-timetapping mode AFM.

4. Conclusion

Phase shifts as a function of distance were measured withdifferent kinds of samples: polymer (polycarbonate), hard (Si), and

frictionless (HOPG) surfaces. The phase curves measured with allsamples showed slight dips and sharp increases as the tipsapproach the samples, which are in agreement with theoreticallycalculated results. Exceptionally, some data showed reversedpolarity (continuous decrease as tip approaches sample), which areattributed to the excessive energy dissipation due to blunt tips. Adistance control was attained successfully, by using the linearincrease of the phase shift. Fast scanning images with scan rateup to 100 Hz were obtained with feedback control of the phaseshift, which showed higher resolutions than those obtained byamplitude mode.

Acknowledgment

This work was supported by Basic Science Research Program(2009-0070725 and 2010-0005393), Priority Research CentersProgram (gs2) (2011-0018395) through NRF funded by MEST, andMinistry of Knowledge Economy Grant (gs3) No. 10033728.

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