APPLIED PHYSICS LETTERS 89, 213112 共2006兲

Fast phase imaging in liquids using a rapid scan atomic force microscope
Takayuki Uchihashia兲 and Toshio Ando
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan and Core
Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Agency(JST), Kawaguchi, Saitama 332-0012, Japan

Hayato Yamashita
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan

共Received 7 May 2006; accepted 4 October 2006; published online 22 November 2006兲
The authors report on fast phase imaging in liquids achieved by fast phase detection in rapid scan
atomic force microscopy. The phase-shift images clearly revealed the compositional heterogeneities
in styrene-butadiene-styrene block copolymer films even at an imaging rate of less than
100 ms/ frame. They found that the contrast variations of the phase images depended on thephase-shift detection timing within a single oscillation cycle. The phase contrast increased as the tip
approached the surface in each oscillation during imaging, while it decreased as the tip withdrew
from the surface. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2387963兴
Amplitude modulation atomic force microscopy
共AFM兲—referred to as tapping-mode AFM—has been established as a standard tool for the nanoscale imaging of thesurfaces of various materials, particularly soft biological andpolymer surfaces.1–3 One of the significant features oftapping-mode AFM is its capability to image compositionalvariations in heterogeneous surfaces in addition to surface
topography by detecting the phase difference between theexciting signal and the cantilever oscillation.3–5 The phaseshift is relevant to several surface properties such as
viscoelasticity,elasticity,adhesion,hydrophobicity/hydrophilicity,4 and surface charges.6 The energy loss of an
oscillating cantilever because of inelastic tip-sample interactions is considered to be the main mechanism of phase
contrast.7,8 On the other hand, efforts to improve the scan
speed of AFM have led to an increase in its imaging rate.9–11
High-speed AFM, particularly that based on tapping mode,
performs more functions than contact-mode AFM. This isbecause it can be used to observe the dynamic processes ofproteins.10,12 Moreover, high-speed tapping-mode AFM canmap dynamic material properties that accompany the structural changes in the sample.
To achieve fast phase imaging, the bandwidth for detecting the phase shift is required to be at least 70 kHz because
in our present system, the feedback bandwidth is approximately 70 kHz. However, the bandwidth of a conventional
lock-in amplifier is limited to dozens of kilohertz. In order toachieve fast phase detection, we have developed a fast phasedetector based on a design by Stark and Guckemberger.13
Figure 1 shows the working principle of fast phase detection.
A two-channel wave form generator produces sinusoidal andsawtooth waves with a synchronized phase. The sinusoidal
wave is used to oscillate the cantilever. The cantilever oscillation signal is fed to a phase detector composed of a highpass filter, variable phase shifter, zero-crossing comparator,
pulse generator, and sample-and-hold 共S/H兲 circuit. A pulse
signal is generated at either the rising or falling edge of theoutput signal of the zero-crossing comparator. The pulse signal serves as a trigger for the S/H circuit. At this triggera兲

Electronic mail: tuchi@kenroku.kanazawa-u.ac.jp

timing, the amplitude voltage of the sawtooth signal is retained by the S/H circuit. In Ref. 13, the usable resonant
frequency of the cantilever is limited to 100 kHz because thesawtooth signal is reset for synchronization with the input
signal. However, the use of the two-channel wave form generator allows us to use a cantilever with a much higher resonant frequency of over 1 MHz. In addition, the variable
phase shifter enables us to vary the timing of the trigger
signal generation within a cantilever oscillation cycle. Thisfunction is important to obtain the maximum phase contrast
because the phase contrast can range from the not observableto the very large depending on the trigger timing as will bedescribed later. By measuring the transient response of theoutput phase signal through a stepwise change in the phaseof the sinusoidal input signal, the time constant ␶ was evaluated to be 0.12 ␮s, and the bandwidth was estimated to be
1.3 MHz, which is sufficiently higher than that of the feedback control of the high-speed AFM. The rms noise of thephase output signal is estimated to be about 3°.14 It is known
that the phase shift at the higher eigenmodes is significantly
different from that at the fundamental frequency.15,16 The fastphase detector does not discriminate the signals with different frequencies. However, the amplitude of the higher eigenmodes is usually less than 10% of the amplitude of the fundamental frequency. Therefore, the influence of the higher
eigenmodes is considered to be negligible.
A block copolymer poly共styrene-butadiene-styrene兲
共SBS兲 was used as a test sample. SBS films are often used
for phase imaging with tapping-mode AFM because the mechanical properties of glassy polystyrene 共PS兲 and rubbery
polybutadiene 共PB兲 differ significantly.3,17 The SBS copoly-FIG. 1. Schematic diagram of the fast phase-detection system for AFM.

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Appl. Phys. Lett. 89, 213112 共2006兲

FIG. 2. 共a兲 Topographic and 共b兲 phase contrast images of a SBS film captured at 84 ms/ frame in pure water. The scan area is 200 nm2 with
100 pixel2. The amplitude set point is 85% of the free amplitude of
13 nmp−p. 共c兲 Topographic image at the amplitude set point is reduced to54%.

mer was prepared with a similar method described in Ref.
18. Before the AFM measurements, the sample was heated at
70 °C for 1 h. We used a home-built high-speed AFM, which
is described in detail elsewhere.10,12,19 The resonant frequency and quality factor of a cantilever in water were
658 kHz and approximately 2, respectively. Their spring
constant was approximately 0.2 N / m.
Figure 2 shows typical 共a兲 topographic and 共b兲 phase
images obtained simultaneously at 84 ms/ frame in pure water. Here, phase detection was set to trigger when the tip
approached the surface. We can obtain clear phase contrast
images even at such a high imaging rate.20 In the phase images, darker regions correspond to an advanced phase withan average shift of approximately 6° relative to the phase ofbrighter regions. To distinguish the compositions, the amplitude set point was reduced while imaging. The higher topographic region shown in Fig. 2共a兲 was suppressed by increasing the loading force, as shown in Fig. 2共c兲. The height wasdecreased by more than 5 nm. Hence, the major compositions in the higher and lower regions in Fig. 2共a兲 were considered to be less stiff PB and stiff PS domains, respectively.
To obtain the optimum phase contrast and an insight into
the phase-shift mechanism, we investigated the dependenceof phase contrasts on trigger timings. Figure 3共a兲 shows thesignal of a cantilever oscillation measured in water. Figures
3共b兲–3共d兲 show typical phase images obtained at varioustrigger timings. At the trigger points on the region indicatedby 共i兲 in Fig. 3共a兲, we observe only a faint phase contrast
关Fig. 3共b兲兴. Since the image contrast of the error signal issimilar to this phase contrast, the faint phase contrast is
mainly due to the amplitude fluctuations. On the other hand,the phase image obtained at the trigger points on region 共ii兲FIG. 4. Phase lags and antilever oscillation amplitudes as a function of therelative tip-surface distance measured on the trigger points in 共a兲 region 共iii兲
and in 共b兲 region 共i兲 shown in Fig. 3共a兲. Solid and dotted curves are obtainedon PS and PB rich domains, respectively.

shows a relative phase advance of approximately 5° in thePB regions 关Fig. 3共c兲兴. Then, at the trigger points on region
共iii兲, we can clearly observe the phase contrast with a relative
phase advance of approximately 10°, in the PB region 关Fig.
3共d兲兴. The phase image obtained at the trigger points on region 共iv兲 showed a similar contrast to that shown in Fig. 3共c兲.
This result implies that the phase shift strongly depends on
the trigger point; in other words, it depends on the directionof the movement of the oscillating tip. The largest phase shift
is observed when the tip approaches the surface. However,when the tip withdraws from the surface, the phase shift
hardly occurs. At the position where the tip velocity is almost
zero, the phase shifts only slightly. Although we used threedifferent cantilevers with resonant frequencies of about
600 kHz, 800 kHz, and 1.2 MHz, similar dependence wasobserved. In addition, the same result was observed, regardless of the scanning speed, free oscillating amplitude, andset-point amplitude.
Figures 4共a兲 and 4共b兲 show the phase lags and oscillation
amplitudes as functions of the relative tip-surface distancerecorded with different trigger timings. The decrease in theoscillation amplitude measured on the PS region is moresignificant than that measured on the PB region because theindentation on the soft PB region is larger than that on thestiff PS region, while the phase difference is only the delay
for both the PS and PB regions. However, the phase lag on
the PS region is larger than that on the PB region in Fig. 4共a兲,
which forms an image contrast in the phase images, as
shown in Figs. 2共b兲 and 3共d兲. On the other hand, the phaselags are almost similar on both the PS and PB regions in Fig.
4共b兲. In other words, the phase delay on the PS region isrecovered at trigger points in region 共i兲.
The phenomenon affecting the AFM phase image iscomplex because the phase difference depends on a numberof instrumental and noninstrumental parameters.3–8,21–24 Instrumental parameters such as the free oscillation amplitude
and the set-point ratio affect the phase image contrast in acomplex manner. It has been reported that a flipped phase
contrast occurs when changing the tapping force level.3,5,24
Such contrast flips generally occur due to the changes in thetip-sample interaction between the net attractive and repulsive force regimes.25,26 However, we did not observe thephase contrast flips. In addition, the amplitude and phasecurves obtained do not show the features of the transition
from the “low-amplitude state” to the “high-amplitudestate”25 as shown in Figs. 4共a兲 and 4共b兲. Therefore, the tipsample interaction is most likely a repulsive interaction 共e.g.,high oscillation amplitude state兲 for both the phase separated

FIG. 3. 共a兲 Cantilever oscillation signal and various trigger regions for phasedetection. The amplitude set point is 63% of the free amplitude of
8.7 nmp−p. The oscillation signal of “0 nm” corresponds to the distance
where the tip is in contact with the surface. The phase contrast images
shown in 共b兲, 共c兲, and 共d兲 are obtained at trigger points within regions 共i兲,共ii兲, and 共iii兲, respectively. The imaging rate is 1.2 s / frame, and the scan
area is 350 nm2 with 200 pixel2.
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Appl. Phys. Lett. 89, 213112 共2006兲

Uchihashi, Ando, and Yamashita

regions under the present imaging conditions, in which thecantilever with a low quality factor is driven at the resonant
frequency.25 Under the repulsive force conditions, the phase
contrast of a PS/PB blend film observed in an ambient condition mainly reflects the mechanical properties.22,26 In thiscase, the phase signal is more delayed on the softer PB region rather than the harder PS region. This can be explainedby the fact that the larger repulsive force on the harder material induces a positive resonant frequency shift, but thedamping constants on both the materials are similar.22,26
Such previous phase contrast does not coincide with ourpresent result. Hence, the phase image contrast in the present
study seems to have not originated from the variations in themechanical properties between the PS and PB regions. Another possibility is the influence of the adhesion forces between the tip and the sample.23,27 Although both PB and PS
are nonpolar materials, PB is more polar than PS because athermal treatment forms some C = O groups or other polargroups such as OH.22 Since the AFM tip used here is composed of hydrophobic amorphous carbon, the adhesion
forces would be larger on the PS region than on the PB
region due to the hydrophobic interaction, which results in alarger phase delay on the PS region. In air, large capillary
forces mask such chemical interactions,23,27 but the mechanical properties are enhanced by a larger quality factor. In reality, we observed the phase contrast originating from themechanical properties even by using the cantilever with ahigh resonant frequency of 2 MHz in air 共data are not shownhere兲.
The trigger timing dependence of the phase contrast
might be explained by the damping of the cantilever oscillation in water that causes significant asymmetry on the sinusoidal oscillation due to damping in water. The phase delays
occur on both the PS and PB regions, while on the harder PS
region, a larger positive frequency shift occurs due to a larger
repulsive force as compared to that on the PB region after thetip contacts the surface. Then, the positive frequency shift
induces the phase advances at the fixed driving frequency. In
liquid environment, the water medium damps the cantilever
oscillation, and hence the phase advances are not kept within
one oscillating cycle.28 In other words, the phase of the oscillating tip advances just after the tip contacts the surface,but such phase advances become smaller with time. However, the phase delay is maintained over the oscillating cycle
because the phase delay is caused by the dissipative adhesion
forces. As a result, when the tip withdraws from the surface,
the phase delay due to energy dissipation cancels the phaseadvance due to the increase in the repulsive force that causesa smaller phase lag on the PS region, as shown in Fig. 4共b兲.
The dependence of the phase contrast on the trigger timing is
not observed in air because the quality factor is relatively
high; therefore, the distortion of the sinusoidal wave form
decreases, and the phase advances on a harder material are
maintained over an oscillating cycle. This would cause theenhancement of the mechanical properties in the phase image contrast under the ambient condition.
In summary, we developed the fast phase detector for
high-speed tapping-mode AFM. It can detect the phase shift
with a bandwidth of over 1 MHz. We succeeded in imaging

both the topography and compositional heterogeneities inSBS films at 84 ms/ frame in pure water. The main source ofthe phase contrast observed in the liquid is not so much themechanical properties but the chemical properties. Furthermore, we found that the phase contrast strongly depends on
the timing when the phase is detected within an oscillating
cycle and is stronger when the tip approaches the surface. A
combination of high-speed AFM and fast phase detection
would enable us to study the dynamic changes in both thesample structures and physicochemical properties in the inliquid tapping mode.
One of the authors 共T.U.兲 was supported by an industrial
technology research grant program in 2004 from NEDO anda Grant in Aid from the Ministry of Education, Culture,Sports, Science, and Technology, Japan.
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