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Mapping of lateral vibration of the tip in atomic force microscopy at the torsional resonance of the cantilever
Ultramicroscopy 91 (2002) 37–48
Mapping of lateral vibration of the tip in atomic force microscopy at the torsional resonance of the cantilever Takayoshi Kawagishi, Atsushi Kato, Yasuo Hoshi, Hideki Kawakatsu* Institute of Industrial Science, University of Tokyo, Komaba 4-6-1, Meguro-ku, 153-8505 Tokyo, Japan Received 14 June 2001; received in revised form 30 December 2001
Abstract Lateral vibration of the tip in atomic force microscopy was mapped at the torsional resonance of the cantilever by attaching a shear piezo element at the base of the cantilever or under the sample. Fixed frequency excitation and selfexcitation of torsional motion were implemented. The lateral vibration utilized as measured by an optical lever was in the order of 10 pm to 3 nm, and its frequency approximately 450 kHz for a contact-mode silicon nitride cantilever. The amplitude and phase of the torsional motion of the cantilever was measured by a lock-in-amplifier or a rectifier and plotted in x and y as the sample was raster scanned. The imaging technique gave contrast between graphite terraces, self-assembled monolayer domains, silicon and silicon dioxide, graphite and mica. Changing contrast was observed as silicon islands oxidized in atmosphere, showing that the imaging technique can detect change in lateral tip mobility due to changes occurring near the surface. Torsional self-excitation showed nanometric features of self-assembled monolayer islands due to different lateral dissipation. Dependence of torsional resonance frequency on excitation amplitude, and contrast change due to driving frequency around resonance were observed. r 2002 Elsevier Science B.V. All rights reserved.
1. Introduction When imaging mica and graphite by contact mode atomic force microscopy (AFM) [1] utilizing an optical lever [2,3] for detection of deflection and torsion, a saw tooth signal is often observed in the torsional signal [4]. This signal arises from the atomic stick-slip behavior of the tip [5]. As the bandwidth of the detector of torsion and deflection was increased to above 1 MHz, superposition of *Corresponding author. Tel.: +81-3-5452-6201; fax: +81-35452-6199. E-mail address: [email protected] (H. Kawakatsu).
the torsional natural frequency vibration of the cantilever became apparent [6]. The amplitude and frequency were found to differ between different samples and sometimes between terraces of graphite separated by atomic steps. We monitored the change in amplitude and phase of this torsional vibration below and above the resonance frequency by fixed frequency excitation. Self-excitation of a rectangular cantilever was also implemented by detecting cantilever torsion and feeding it to a piezo element attached to the base of the cantilever or under the sample. The optical lever detection method utilizing a quadrant photodiode enables simultaneous measurement of both deflection and torsion [2]. However, care is
0304-3991/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 9 1 ( 0 2 ) 0 0 0 8 0 - 3
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needed in the interpretation of the torsion and deflection signals, due to the coupled deformation of the cantilever [7,8]. Lateral position modulation technique was introduced to the STM for differential imaging [9] and tracking control of the STM tip on microscopic features and atomic corrugations [10,11]. Lateral modulation technique was introduced to the AFM in 1991 by Maivald et al. [12] for highlighting edges of a sample. O’Shea applied lateral dithering to the sample at low frequencies for detecting static friction of n-dodecanol [13]. A technique for simultaneous mapping of friction and topography using laser interferometry was introduced by Go¨ddenhenrich et al. [14]. Colchero et al., Ascoli et al., and Yamanaka et al. developed a similar technique with quadrant photodiodes for lessening effect of topography on FFM measurement by lateral dithering [15–18] (lateral modulation AFM, LMAFM, or, dynamic scanning friction microscopy, DSFM). Nakano et al. [19] introduced a technique of characterizing the mechanical properties of a cantilever by oscillating the cantilever in the flexural and torsional directions. The same configuration for exciting the torsional vibration was adopted for this work. Scherer et al. [20] applied lateral position modulation to measure lubrification properties of Z-Dol around 380 kHz. Carpick et al. [21] measured the lateral stiffness of mica. Scherer et al. [22] implemented a lateral force microscope (LFM) by applying up to 2 MHz of lateral position modulation of the sample with fixed frequency excitation (acoustic friction force microscopy, AFFM). The method was effective in lessening scan direction and topography effects on friction or interfacial property measurement. Our work is related to this work, except for the facts that: (i) cantilever torsion was directly excited with a piezo element set at its base, and dithering of the sample was carried out for comparison, (ii) self-excitation of cantilever torsion was implemented for lateral resonance tracking to avoid the problem of contrast change related to selection of driving frequency close to resonance, and (iii) effect of amplitude on the self-excited resonance frequency was measured and discussed. Krotil et al. [23] applied sample dithering at 10 kHz to image
polymers on silicon. The technique is an application of the DSFM [14–18]. Vaccaro et al. [24] discussed image contrast mechanisms of a scanning nearfield optical microscopy (SNOM) shear force control [25] for self-assembled monolayers. Since the probe apex was oscillated in-plane of the sample, the imaging process was closely related to that of lateral tip modulation techniques with tip slip, as presented in this paper. Bernal et al. [26] carried out studies on forces acting between SNOM probes and chemically treated AFM probes. Spychalski-Merle et al. [27] applied the DSFM with lateral modulation frequency close to the flexural natural frequency of the cantilever. Krotil et al. [28] introduced the CODY mode, where low frequency vertical modulation and high frequency lateral modulation of the sample were employed for simultaneous measurement of various properties. Ge et al. [29] measured the glass transition temperature by lateral position modulation of the sample at 1.4 kHz. Related theoretical studies can be found in the literatures [30,31]. In 1994 the ultrasonic atomic force microscopy or ultrasonic force microscopy (UAFM, UFM) was introduced, where the cantilever was oscillated in the deflection direction at higher oscillation modes to measure the local stiffness and damping of the sample. This enabled measurement of stiff samples [32–39]. In 2001, the Q factor mapping technique was introduced to the UAFM [40]. The authors proposed the possibility of Young’s modulus by utilizing torsional resonance, while assuring non-slip of the tip end against the sample. The work presented here differs from the literature on the point that a swinging tip was brought into proximity of the sample, and that the non-slip condition was not assumed. Higher frequency tapping mode and related techniques can be found in the literature [41–43]. Kobayashi et al. [44] introduced the resonance tracking ultrasonic microscope, where the cantilever was oscillated by self-excitation in the deflection direction to implement in-resonance measurement. Non-contact lateral modulation technique for true atomic resolution was pursued separately by Sugawara and Meyer [45]. Other related techniques can be found in the literature [46,47]. Table 1 summarizes scanning probe microscopy with
Table 1 Comparison of various lateral modulation techniques applied to AFM Sample/ cantilever
Lateral excitation Amplitude (nm) Normal force frequency (Hz) (nN)
Cantilever
1
Sample
Gold
5k
20
Si3N4 (0.6 N/m) Modified Nanoscope II
2 3
Sample Sample (buckling)
50–300 o5 Below cantilever A few nm resonance
0–125 —
Si3N4 (0.58 N/m) Lock-in amplifier Lubrication Pyramidal Si3N4 Lock-in amplifier Friction and laser interferometer
4
Sample
n-dodecanol NdFeB film, HOPG, nickel compact disk stamper matrix HOPG
10 k (lateral)
—
—
Si3N4 (0.09 N/m, — deflection resonance: 40 kHz)
10 k — (lateral)+5.6 M (vertical) 16 k 1
—
1.2
Si3N4 (0.09 N/m)
Si wafer (1 0 0) in water
1k
3
0–12
Si3N4 (0.09 N/m) Lock-in amplifier
Magnetic tape
—
o3
0–400
Si (3.2 N/m)
5
Sample
Gold thin film
25
Data acquisition Detected property
Sample
Langmuir— Blodgett film in water or air
—
20
Si3N4 (0.09 N/m) Lock-in amplifier
7
Cantilever
—
—
Si3N4 (0.09 N/m) —
8
Sample
Si3N4 cantilever 0–300 k (resonance) Z-Dol 370–380 k (lubricant)
—
145
Si3N4 (0.6 N/m) Envelope of oscillation
9
—
Cleaved mica
—
A few angstrom
Sample
Metal particle tape
1.59 M (resonance)
—
10
40–40 100
Si3N4 (B0.58 N/m) Si ( )
Lock-in amplifier rms-to-DC converter
Friction
Lateral modulation mode — —
Lateral force modulation mode
Subsurface edge Lateral dislocation ultrasonic force microscopy Static and kinetic friction Kinetic friction Lateral force by friction force modulation curve atomic force microscopy (LM-AFM) Friction and sample deformation Friction by Lateral force friction force modulation curve atomic force microscopy (LM-AFM) Elastic properties — of a cantilever Lubrication Acoustic friction force microscopy (AFFM) Lateral stiffness — of a sample Viscoelasticity Acoustic friction force microscopy
39
6
Edges on gold planes
Name
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
Activation part (sample/ cantilever)
40
Table 1 (continued) Activation part (sample/ cantilever)
Sample/ cantilever
Lateral excitation Amplitude (nm) Normal force frequency (Hz) (nN)
Cantilever
Data acquisition Detected property
Name
(AFFM) oseveral tens of nN
Si3N4 (0.05 N/m) Lock-in amplifier
Dots of CH3 or 9 k (resonance) OH terminated Au substrate in air or water
0–4
—
Optical fiber cantilever
Cantilever
11.6 k Chemically functionalized Si (resonance) cantilever for AFM
4
—
Optical fiber cantilever
14
Sample (buckling)
HOPG in UHV 100 k (resonance) 1–10
—
Si ( )
15
Cantilever (out of plane)+sample (in-plane) Sample
ABC-triblock copolymer
kHz range (out of plane), 150 k (in-plane)
3.25–6.5
—
—
Polymer
1.4 k
3
Typically 25
—
Cantilever/ sample
SiO2 mesa on Si 400–500 k substrate/SAM (resonance)
0.4–4
o20
Sample
Polymer (polyolefine)silicon
12
Cantilever
13
16
17
10 k
Static and Dynamic dynamic friction scanning friction force microscopy (DSFFM) Interferometric Influence of — feedback system wettability on oscillation amplitude damping Laser feedback Influence of — interferometer+ interaction force lock-in amplifier on damping of SNOM tip vibration amplitude Lock-in amplifier Frictional Dynamic damping scanning friction microscopy (DSFM) Lock-in amplifier Adhesive, static, Combined and dynamic dynamic X mode frictional forces (CODY mode)
Lock-in amplifier Glass transition Shear temperatures modulation force (viscoelasticity) microscopy (SMFM) Si3N4 (0.06 N/m) Lock-in Lateral Lateral cantilever amplifier/ABS dissipation by resonance mode amplifier resonance (LCR mode) tracking
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
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lateral modulation techniques. The paper will introduce a new imaging technique for obtaining contrast on graphite terraces, results of fixed and self-excited torsional oscillation, and the dependence of self-excited oscillation amplitude on the natural frequency. 1.1. Instrumental Depicted in Fig. 1 is the block diagram of the apparatus used for the imaging technique. The technique will be referred to as the lateral cantilever resonance (LCR) mode. Related to the excitation technique of lateral or torsional resonance, the LCR mode can be classified into the following. (i) no active excitation, (ii) excitation by a shear piezo at a fixed frequency, in the neighborhood of the torsional resonance of the cantilever when the tip is in proximity or in contact with the sample, and (iii) resonance tracking of LPF
ABS
BPF
Computer LIV/LIA
Frequency Extender
Display
Torsion ∆φ
QPD
LD
Scan
BPF
scanner
Deflection Shear piezo Z piezo controller
Fig. 1. A block diagram depicting the circuit for mapping the lateral vibration amplitude of the tip. Lateral vibration is either actively excited by a shear piezo set at the base of the cantilever or under the sample, or simply by scanning and thermal vibration. In the case of lateral self-excitation, the level of excitation was set to the 100 pm order, as measured as the torsional signal of the quadrant photodiode (QPD). A lock-inamplifier (LIA) and/or a lock-in-voltmeter (LIV) are used to measure the amplitude and phase of the torsional signal of the QPD at the torsional natural frequency of the cantilever. A rectifier was used instead of the LIA for measurement requiring faster response.
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torsional vibration by self-excitation. For fixed frequency excitation, a local oscillator was connected to a shearing piezo element measuring 3 3 1 mm. A similar piezo element was attached under the sample to compare cantilever excitation to sample excitation [22]. The torsional signal of the cantilever was detected by a quadrant photodiode. Torsional signal was fed through a band pass filter, fixed to pass signals around the torsional resonance of the cantilever, which was approximately 450 kHz for a contact mode cantilever. A lock-in-amplifier locked to the reference frequency of the local oscillator was used to detect amplitude and phase. For observation of damping of lateral vibration after every atomic slip, a rectifier and a low pass filter (LPF) were used instead of the lock-in-amplifier since the former had shorter response time. Torsional amplitude and phase were mapped in x and y as the sample was raster scanned. Values of lateral oscillation at the tip end was around 10 pm without active excitation, and typically 0.4 nmp–p and up to 3 nmp–p for fixed frequency and self-excited oscillation. For self-excited oscillation, torsional signal of the optical lever passed through a band pass filter then digitized by saturating the oscillation signal. The digitized signal was phase shifted and fed to the piezo at the base of the cantilever or under the sample. For all experiments, calibration of torsional motion was carried using atomic stick slip signal of mica. As is often pointed out, the calibration is not totally correct since it does not take into account lateral displacement of the contact region, or dynamic slip effects. For all experiments, normal force was controlled with slow feed back by monitoring the deflection of the cantilever. The set value was 20 nN as measured from the point of snap-off.
2. Experimental 2.1. Contrast observed between graphite terraces without active excitation Cleaved graphite was imaged by the LCR mode without active excitation. Fig. 2 shows
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Fig. 2. Contrast seen within an HOPG sample with a step of 2 nm, when using lock-in-voltmeter for amplitude detection. Active excitation was not carried out for this imaging. (a) topography, (b) an example of a lateral vibration amplitude image. The scan size, scan speed, resonance frequency are 1.1 mm2, 5.5 mm/s and 440 kHz.
topographic image and lateral amplitude image for an area of 1.1 mm2. The resonance frequency was 450 kHz. Amplitude was approximately 10 pm. Contrast could be seen between the two terraces separated by a 2 nm step. The brighter region in Fig. 2(b) corresponded to the region where the lateral amplitude of the tip was larger at the torsional natural frequency. The contrast was stable for repeated raster scanning of the sample. Zoom up of the two terraces showed that the crystal orientation of the terraces did not differ between the two. Switch in contrast was sometimes observed as the tip was retracted and reapproached to the same step within the sample. 2.2. Tip swinging and pivoting depending on the excitation frequency To verify the behavior of the tip motion with respect to the excitation frequency, the frequency of the local oscillator in Fig. 1 was swept from offresonance to on-resonance. Fig. 3 shows a typical result. When the cantilever was oscillated at its torsional resonance, the tip swung before and after
Fig. 3. Difference of torsional motion and sample distance. (a) Direct cantilever torsion excitation close to torsional resonance. Torsional motion remains after contact and decreases with increasing normal load. (b) sample activation off-resonance. Torsion increases with increasing normal load. The result indicates that the tip is swinging around the cantilever for (a) and is pivoting about the tip apex for (b).
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contact. Amplitude decreased with increasing normal force. Off-resonance, the cantilever torsion was negligibly small before contact, and increased with increasing normal load. The result showed that close to resonance, swinging motion of the tip continues after contact, and that for the proposed imaging technique, the tip apex is sliding rather than pivoting on the surface. 2.3. Imaging of graphite with and without excitation Depicted in Fig. 4(a) is the torsional signal when the tip was line scanned for a few nm. The upper line is the saw tooth form stick slip signal, the second is the band pass filtered output of the former, leaving the torsional oscillation signal around 450 kHz. The amplitude as calibrated from the lattice spacing was around 10 pm. In this experiment, a rectifier was used instead of the lockin-amplifier for observing damping and excitation of the lateral vibration at every atomic stick-slip. As can be seen from the second line, increase in lateral amplitude was seen at every slip, indicating that slip to the next stick point increased lateral vibration of the tip. Average Q factor of lateral vibration as measured by the envelope of the damped oscillation after every step was 100. Fig. 4(b) shows the torsion signal when the resonance was actively excited by the shear piezo element. The amplitude was set to around 50 pm. Decrease in torsional amplitude was observed at every slip. As shown in Fig. 4(c), when the RF torsional amplitude value was plotted to the xy plane, periodicity reflecting the lattice structure was seen. The dark rings correspond to the region where tip slip occurred. When a larger area of a few micron square was imaged, no difference in contrast was observed between step separated terraces. 2.4. Imaging of silicondioxide mesa on silicon substrate Silicon dioxide mesa were formed on a silicon substrate by masking and etching of the top silicondioxide layer. The height of the mesa was 30 nm. The sample was dipped in dilute HF to
Fig. 4. Comparison of (a) passive and (b) active lateral vibration excitation for graphite. The scanning speeds are (a) 1.1 mm/s, (b) 138 nm/s. 72 mV is applied to a shear piezo in (b) active excitation. The signals are, (1) torsional signal of the QPD showing atomic stick-slip, (2) BPF output of signal (1) at (a) 440 kHz, and (b) 470 kHz, (3) output of the ABS amplifier, where the input is signal (2), (4) output of the LPF, where the input is signal (3), and the cut off frequency (a) 20 kHz, (b) 47 kHz. Note that the vibration amplitude increases after the stepping action for (a) and, decreases for (b). The amplitude is approximately 10 times larger for (b) than (a). The natural frequency at around 450 kHz cannot be resolved at the time scale of the plot, and the sinusoidal signals seen within the plot are subject to digitizing error. Envelopes of signals (1)–(3) do however reflect the actual change in amplitude. (c) Lateral amplitude of the tip plotted against voltages applied to the x and y scanners when the lateral vibration was actively excited. The dark rings correspond to moments when the tip slipped and the vibration amplitude decreased as in (b)-(4).
remove surface oxide on silicon and then immediately imaged by the LCR method with fixed frequency excitation. Fig. 5 shows the topography, FFM image, LCR amplitude image and phase image. With a tip as delivered by the
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formation of a thin oxide layer. An example is shown in Fig. 6. The square seen at the lower left of the images is the silicondioxide mesa.
Fig. 5. Images taken in ambient conditions of silicon with silicondioxide mesa, taken with the active cantilever torsion excitation. (a) topography, (b) FFM image, (c) amplitude image taken with the LIA, (d) phase shift image taken with the LIA. With a tip as supplied by the manufacturer, amplitude was smaller for silicon dioxide than silicon. Features not seen in the topography or FFM images are revealed in the amplitude and phase shift images inside of SiO2. Tip velocity, scan time, scan size, step height are 11.1 mm/s, 926 s, 20 mm2, and 30 nm. On other samples, contrast inverted with a tip functionalized with a self-assembled monolayer.
manufacturer, LCR amplitude was larger on silicon than silicondioxide. This contrast changed when the tip apex was functionalized with a selfassembled monolayer. The LCR technique was compared with the LMAFM. As the surface of the silicon substrate slowly oxidized in air, with the former technique, contrast between the two substrate and the mesa gradually decreased, and after 24 hour, little contrast was observed between the two regions. On the other hand, contrast was still observable by the latter method during and after
Fig. 6. The mapping image of silicondioxide mesa left in ambient condition for a week. The images are (a) topography, (b) FFM, (c) fixed frequency LCR-amplitude, (d) fixed frequency LCR-phase, (e) LM-AFM-amplitude, (f) LMAFM-phase. Except for edge effects, contrast could not be seen in the fixed frequency LCR mode, after the Si substrate was covered with thin oxide layer. However, in LM-AFM image, the contrast corresponding to FFM image could be seen as (e). Excitation frequency of LCR was set slightly below resonance.
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
2.5. Dependence of contrast on excitation frequency around torsional resonance Images obtained in Figs. 5 and 6 were obtained by exciting the cantilever at a frequency slightly below torsional resonance with the tip in contact with the sample. However, contrast is expected to depend on the excitation frequency in relation to the natural frequency, as well as the local Q factor. Fig. 7 was taken on a SAM surface to verify the extent and reproducibility of this effect, and to compare cantilever and sample activation. Roughly speaking, inverse of contrast was seen above and below resonance frequency, and images obtained for two types of modulation methods matched. However, in some regions marked in circles within the figure, different contrast with respect to its surrounding area were seen. This made it difficult to characterize a feature observed within an image.
2.6. Feed-forward excitation of torsion of the cantilever Torsion of the cantilever was excited by driving the piezo attached to the base of the cantilever or under the sample. Torsional signal of the optical lever was band pass filtered and then digitized by saturating the sinusoidal oscillation signal. Digitizing by saturation helped avoid quenching of self-excitation. The digitized output was phase shifted and fed to one of the two excitation piezos. Images are shown in Fig. 8. The images are amplitude images for a fixed excitation amplitude, and corresponds to what may be called dissipation _________________________________________" Fig. 7. Self-assembled monolayer domains imaged in the vicinity of torsional natural frequency. Image size 500 nm2. Imaging time 278 s and tip velocity 924 nm/s. Activation of piezo elements attached to the base of the cantilever and under the sample were adjusted to give the same amplitude of torsional signal of the optical lever. Figures in the middle column correspond to excitation approximately on the resonance peak. Roughly speaking, inversion of contrast was observed between excitation frequencies below and above resonance. Sample activation and probe activation gave more or less the same image, but some regions within the image showed different results.
45
or damping images. For this experiment, cantilever excitation showed higher lateral resolution. Unlike the fixed frequency excitation mode, interpretation of the images was apparently more
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455
Frequency (kHz)
450 445 440 sample excitation cantilever excitation
435 430 425 420 0
0.5
1 1.5 2 Amplitude (nmp-p)
2.5
3
Fig. 9. Dependence of self-excitation torsional resonance frequency on torsional amplitude. At around 2.5 nmp–p, the resonance frequency suddenly decreased to a value corresponding to that of a free standing cantilever. Contrast was lost for cantilever excitation amplitude exceeding the threshold of 2.5 nmp–p.
2.7. Dependence of lateral amplitude on self-excitation frequency Fig. 8. Images of SAM domains taken by lateral resonance self-excitation. Image size 500 nm2. Torsional motion was excited by feeding the torsional signal to the piezo set at the cantilever base or under the sample. For this experiment, probe activation apparently showed higher lateral resolution than the other. A hole in the upper left of the image was 20 nm deep. Islands and strands extending from left to right measure 2 nm in height, and appears as a dark region in the dissipation image.
straightforward; places with less loss showed higher torsional amplitude. This technique may be regarded as a lateral modulation version of the vertical resonance tracking mode [44] and the Q factor mapping mode for vertical oscillations [40]. The sample was Octadecanethiol (ODT, CH3(CH2)17) grown on Au(1 1 1) by immersing the substrate in ethanol with ODT for 24 hour. Protrusions of 2 nm appear as dark regions in the LCR images, which we think are islands and strands of ODT SAM. Self-excited lateral oscillation technique was capable of resolving nanometric features due to difference of lateral damping.
The cantilever was set to oscillate at its torsional resonance by self-excitation, and the natural frequency was measured as a function of lateral tip amplitude. Fig. 9 shows the result for sample and cantilever excitation. Self-excitation was possible from around 0.2 nmp–p. For cantilever excitation, frequency dropped suddenly at around 2.5 nmp–p and stabilized to a frequency within a few 100 Hz of the torsional frequency of a free standing cantilever. As for sample excitation, no drop in frequency was observed. For both cases, lateral amplitude above 3 nmp–p could not be obtained even when the excitation signal of the piezo element was increased.
3. Discussions and comments 3.1. On imaging of graphite When imaging graphite terraces with no active excitation, inverse of contrast was sometimes observed when the tip was reapproached to the
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sample. Due to this experimental result, it is difficult at present to conclude that the imaging technique revealed an intrinsic difference of the graphite terraces. One explanation is that tip switch or attachment of a small monolayer occurred every time the tip crossed the step. When torsional resonance was activated by a shear piezo element, decrease in oscillation amplitude was observed every time the tip made an atomic slip. We attribute the decrease to be caused by the step form disturbance caused by the slip on the harmonic oscillation. Contrast of terraces was not observed with the latter imaging technique. The former technique, although less stable than the latter, was more sensitive in revealing changes occurring at the tip apex.
3.2. On imaging with fixed frequency The lateral cantilever resonance technique with fixed frequency excitation was capable of revealing fine features on the silicon dioxide mesa, which were hardly visible in the topography or FFM images. It was confirmed by changing the excitation frequency that the tip swings about the cantilever or slips on the sample surface when excited close to resonance, and pivots around the contact point when excited off-resonance. From the result, it can be said that the LCRAFM technique has the tip in relative motion to the sample surface. When oxidation of the silicon substrate proceeded, change in contrast was observed in the order of hours. The LMAFM technique gave contrast images of the same sample even when the substrate was covered with a thin film of silicon dioxide. The LCRAFM technique images the lateral mobility of the tip defined by the very surface of the sample, where as, the LMAFM technique measures the mechanical property of a greater depth or volume of the sample in proximity of the tip. As for the difference of exciting the cantilever or the sample, similar images were obtained for both excitation methods, with local contrast difference of certain features, making image interpretation difficult.
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3.3. Lateral self-excitation Lateral self-excitation was implemented for both cantilever and sample excitation. The latter apparently showed better lateral resolution, but contrast was lost as the excitation amplitude increased. In other words, contrast was lost as self-excitation frequency suddenly dropped to the value close to that of a free standing cantilever. For this experiment of ODT on Au(1 1 1), lateral amplitude of around 2.5 nmp–p was the threshold for obtaining reproducible features. As the amplitude and relative velocity of the tip increased, effect of the interfacial layer on the natural frequency decreased. As for sample excitation, no drop in frequency was observed for the amplitude values tested. Acquisition of a frequency to amplitude curve as depicted in Fig. 9 is routinely necessary prior to imaging to obtain a resolved reproducible image.
Acknowledgements The authors thank Professor H. Yamada, Professor K. Yamanaka and Dr. K. Kobayashi for valuable comments and suggestions.
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[11] H. Kawakatsu, Y. Hoshi, H. Kitano, T. Higuchi, J. Vac. Sci. Technol. B 9 (1991) 651. [12] P. Maivald, H.J. Butt, S.A. C. Gould, C.B. Prater, B. Drake, J.A. Gurley, V.B. Elings, P.K. Hansma, Nanotechnology 2 (1991) 103. [13] S.J. O’Shea, M.E. Welland, T. Rayment, Appl. Phys. Lett. 61 (1992) 2240. [14] T. Go¨ddenhenrich, S. Mu¨ller, C. Heiden, Rev. Sci. Instrum. 65 (1994) 2870. [15] C. Ascoli, F. Dinelli, C. Frediani, D. Petracchi, M. Salerno, M. Labardi, M. Allegrini, F. Fuso, J. Vac. Sci. Technol. B 12 (1994) 1642. [16] K. Yamanaka, E. Tomita, Jpn. J. Appl. Phys. 34 (1995) 2879. [17] K. Yamanaka, H. Takano, E. Tomita, M. Fujihira, Jpn. J. Appl. Phys. 35 (1996) 5421. [18] J. Colchero, M. Luna, A.M. Baro, Appl. Phys. Lett. 68 (1996) 2896. [19] S. Nakano, R. Maeda, K. Yamanaka, Jpn. J. Appl. Phys. 36 (1997) 3265. [20] V. Scherer, B. Bhushan, U. Rabe, W. Arnold, IEEE Trans. Magn. 33 (1997) 4077. [21] R.W. Carpick, D.F. Ogletree, M. Salmerlon, Appl. Phys. Lett. 70 (1997) 1548. [22] V. Scherer, W. Arnold, B. Bhushan, Surf. Interface Anal. 27 (1999) 578. [23] H.-U. Krotil, E. Weilandt, Th. Stifter, O. Marti, S. Hild, Surf. Interface Anal. 27 (1999) 341. [24] L. Vaccaro, M.-P. Bernal, F. Marquis-Weible, C. Duschl, Appl. Phys. Lett. 77 (2000) 3110. [25] D.W. Pohl, D. Courjion (Eds.), NATO ASI Series E, 242, Kluwer Academic, Dordrecht, 1993. [26] M.-P. Bernal, F. Marquis-Weible, P.-Y. Boillat, P. Lambelet, Proc. IEEE 88 (2000) 1460. [27] A. Spychalski-Merle, K. Krischker, T. Goeddenhenrich, C. Heiden, Appl. Phys. Lett. 77 (2000) 501. [28] H.-U. Krotil, Th. Stifter, O. Marti, Appl. Phys. Lett. 77 (2000) 3857.
[29] S. Ge, Y. Pu, W. Zhang, M. Rafailovich, J. Solokolov, C. Buenviaje, R. Buckmaster, R. Buckmaster, R.M. Overney, Phys. Rev. Lett. 85 (2000) 2340. [30] S. Hirsekorn, U. Rabe, W. Arnold, Nanotechnology 8 (1997) 57. [31] J.A. Turner, J.S. Wiehn, Nanotechnology 12 (2001) 322. [32] K. Yamanaka, H. Ogiso, Appl. Phys. Lett. 64 (2) (1994) 178. [33] K. Yamanaka, S. Nakano, Jpn. J. Appl. Phys. 35 (1996) 3787. [34] F. Dinelli, S.K. Biswas, G.A.D. Briggs, O.V. Kolosov, Phys. Rev B. 61 (2000) 13995. [35] G.G. Yaralioglu, F.L. Degertekin, K.B. Crozier, C.F. Quate, J. Appl. Phys. 87 (10) (2000) 7491. [36] K. Yamanaka, T. Tsuji, A. Noguchi, T. Koike, T. Mihara, Rev. Sci. Instrum. 71 (6) (2000) 2403. [37] K. Yamanaka, A. Noguchi, T. Tsuji, T. Koike, T. Goto, Surf. Interface Anal. 27 (1999) 600. [38] O. Wright, N. Nishiguchi, Appl. Phys. Lett. 71 (1997) 626. [39] U. Rabe, J. Turner, W. Arnold, Appl. Phys. A 66 (1998) S277. [40] K. Yamanaka, Y. Maruyama, Appl. Phys. Lett. 78 (13) (2001) 1939. [41] N.A. Burnham, O.P. Behrend, F. Oulevey, G. Gremaud, P.-J. Gallo, D. Gourdon, E. Dupas, A.J. Kulik, H.M. Pollock, G.A.D. Briggs, Nanotechnology 8 (1997) 67. [42] R. Garcia, A.S. Paulo, Phys. Rev. 60 (7) (1999) 4961. [43] R.W. Stark, T. Drobek, W.M. Heckl, Appl. Phys. Lett. 74 (22) (1999) 3296. [44] K. Kobayashi, H. Yamada, K. Matsushige, Surf. Interface Anal. 33 (2002) 89. [45] Personal communications. [46] P. Vairac, B. Cretin, Appl. Phys. Lett. 68 (4) (1996) 461. [47] T. Miyatani, M. Horii, A. Rosa, M. Fujihira, Appl. Phys. Lett. 71 (1997) 2632.
Mapping of lateral vibration of the tip in atomic force microscopy at the torsional resonance of the cantilever Takayoshi Kawagishi, Atsushi Kato, Yasuo Hoshi, Hideki Kawakatsu* Institute of Industrial Science, University of Tokyo, Komaba 4-6-1, Meguro-ku, 153-8505 Tokyo, Japan Received 14 June 2001; received in revised form 30 December 2001
Abstract Lateral vibration of the tip in atomic force microscopy was mapped at the torsional resonance of the cantilever by attaching a shear piezo element at the base of the cantilever or under the sample. Fixed frequency excitation and selfexcitation of torsional motion were implemented. The lateral vibration utilized as measured by an optical lever was in the order of 10 pm to 3 nm, and its frequency approximately 450 kHz for a contact-mode silicon nitride cantilever. The amplitude and phase of the torsional motion of the cantilever was measured by a lock-in-amplifier or a rectifier and plotted in x and y as the sample was raster scanned. The imaging technique gave contrast between graphite terraces, self-assembled monolayer domains, silicon and silicon dioxide, graphite and mica. Changing contrast was observed as silicon islands oxidized in atmosphere, showing that the imaging technique can detect change in lateral tip mobility due to changes occurring near the surface. Torsional self-excitation showed nanometric features of self-assembled monolayer islands due to different lateral dissipation. Dependence of torsional resonance frequency on excitation amplitude, and contrast change due to driving frequency around resonance were observed. r 2002 Elsevier Science B.V. All rights reserved.
1. Introduction When imaging mica and graphite by contact mode atomic force microscopy (AFM) [1] utilizing an optical lever [2,3] for detection of deflection and torsion, a saw tooth signal is often observed in the torsional signal [4]. This signal arises from the atomic stick-slip behavior of the tip [5]. As the bandwidth of the detector of torsion and deflection was increased to above 1 MHz, superposition of *Corresponding author. Tel.: +81-3-5452-6201; fax: +81-35452-6199. E-mail address: [email protected] (H. Kawakatsu).
the torsional natural frequency vibration of the cantilever became apparent [6]. The amplitude and frequency were found to differ between different samples and sometimes between terraces of graphite separated by atomic steps. We monitored the change in amplitude and phase of this torsional vibration below and above the resonance frequency by fixed frequency excitation. Self-excitation of a rectangular cantilever was also implemented by detecting cantilever torsion and feeding it to a piezo element attached to the base of the cantilever or under the sample. The optical lever detection method utilizing a quadrant photodiode enables simultaneous measurement of both deflection and torsion [2]. However, care is
0304-3991/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 9 1 ( 0 2 ) 0 0 0 8 0 - 3
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needed in the interpretation of the torsion and deflection signals, due to the coupled deformation of the cantilever [7,8]. Lateral position modulation technique was introduced to the STM for differential imaging [9] and tracking control of the STM tip on microscopic features and atomic corrugations [10,11]. Lateral modulation technique was introduced to the AFM in 1991 by Maivald et al. [12] for highlighting edges of a sample. O’Shea applied lateral dithering to the sample at low frequencies for detecting static friction of n-dodecanol [13]. A technique for simultaneous mapping of friction and topography using laser interferometry was introduced by Go¨ddenhenrich et al. [14]. Colchero et al., Ascoli et al., and Yamanaka et al. developed a similar technique with quadrant photodiodes for lessening effect of topography on FFM measurement by lateral dithering [15–18] (lateral modulation AFM, LMAFM, or, dynamic scanning friction microscopy, DSFM). Nakano et al. [19] introduced a technique of characterizing the mechanical properties of a cantilever by oscillating the cantilever in the flexural and torsional directions. The same configuration for exciting the torsional vibration was adopted for this work. Scherer et al. [20] applied lateral position modulation to measure lubrification properties of Z-Dol around 380 kHz. Carpick et al. [21] measured the lateral stiffness of mica. Scherer et al. [22] implemented a lateral force microscope (LFM) by applying up to 2 MHz of lateral position modulation of the sample with fixed frequency excitation (acoustic friction force microscopy, AFFM). The method was effective in lessening scan direction and topography effects on friction or interfacial property measurement. Our work is related to this work, except for the facts that: (i) cantilever torsion was directly excited with a piezo element set at its base, and dithering of the sample was carried out for comparison, (ii) self-excitation of cantilever torsion was implemented for lateral resonance tracking to avoid the problem of contrast change related to selection of driving frequency close to resonance, and (iii) effect of amplitude on the self-excited resonance frequency was measured and discussed. Krotil et al. [23] applied sample dithering at 10 kHz to image
polymers on silicon. The technique is an application of the DSFM [14–18]. Vaccaro et al. [24] discussed image contrast mechanisms of a scanning nearfield optical microscopy (SNOM) shear force control [25] for self-assembled monolayers. Since the probe apex was oscillated in-plane of the sample, the imaging process was closely related to that of lateral tip modulation techniques with tip slip, as presented in this paper. Bernal et al. [26] carried out studies on forces acting between SNOM probes and chemically treated AFM probes. Spychalski-Merle et al. [27] applied the DSFM with lateral modulation frequency close to the flexural natural frequency of the cantilever. Krotil et al. [28] introduced the CODY mode, where low frequency vertical modulation and high frequency lateral modulation of the sample were employed for simultaneous measurement of various properties. Ge et al. [29] measured the glass transition temperature by lateral position modulation of the sample at 1.4 kHz. Related theoretical studies can be found in the literatures [30,31]. In 1994 the ultrasonic atomic force microscopy or ultrasonic force microscopy (UAFM, UFM) was introduced, where the cantilever was oscillated in the deflection direction at higher oscillation modes to measure the local stiffness and damping of the sample. This enabled measurement of stiff samples [32–39]. In 2001, the Q factor mapping technique was introduced to the UAFM [40]. The authors proposed the possibility of Young’s modulus by utilizing torsional resonance, while assuring non-slip of the tip end against the sample. The work presented here differs from the literature on the point that a swinging tip was brought into proximity of the sample, and that the non-slip condition was not assumed. Higher frequency tapping mode and related techniques can be found in the literature [41–43]. Kobayashi et al. [44] introduced the resonance tracking ultrasonic microscope, where the cantilever was oscillated by self-excitation in the deflection direction to implement in-resonance measurement. Non-contact lateral modulation technique for true atomic resolution was pursued separately by Sugawara and Meyer [45]. Other related techniques can be found in the literature [46,47]. Table 1 summarizes scanning probe microscopy with
Table 1 Comparison of various lateral modulation techniques applied to AFM Sample/ cantilever
Lateral excitation Amplitude (nm) Normal force frequency (Hz) (nN)
Cantilever
1
Sample
Gold
5k
20
Si3N4 (0.6 N/m) Modified Nanoscope II
2 3
Sample Sample (buckling)
50–300 o5 Below cantilever A few nm resonance
0–125 —
Si3N4 (0.58 N/m) Lock-in amplifier Lubrication Pyramidal Si3N4 Lock-in amplifier Friction and laser interferometer
4
Sample
n-dodecanol NdFeB film, HOPG, nickel compact disk stamper matrix HOPG
10 k (lateral)
—
—
Si3N4 (0.09 N/m, — deflection resonance: 40 kHz)
10 k — (lateral)+5.6 M (vertical) 16 k 1
—
1.2
Si3N4 (0.09 N/m)
Si wafer (1 0 0) in water
1k
3
0–12
Si3N4 (0.09 N/m) Lock-in amplifier
Magnetic tape
—
o3
0–400
Si (3.2 N/m)
5
Sample
Gold thin film
25
Data acquisition Detected property
Sample
Langmuir— Blodgett film in water or air
—
20
Si3N4 (0.09 N/m) Lock-in amplifier
7
Cantilever
—
—
Si3N4 (0.09 N/m) —
8
Sample
Si3N4 cantilever 0–300 k (resonance) Z-Dol 370–380 k (lubricant)
—
145
Si3N4 (0.6 N/m) Envelope of oscillation
9
—
Cleaved mica
—
A few angstrom
Sample
Metal particle tape
1.59 M (resonance)
—
10
40–40 100
Si3N4 (B0.58 N/m) Si ( )
Lock-in amplifier rms-to-DC converter
Friction
Lateral modulation mode — —
Lateral force modulation mode
Subsurface edge Lateral dislocation ultrasonic force microscopy Static and kinetic friction Kinetic friction Lateral force by friction force modulation curve atomic force microscopy (LM-AFM) Friction and sample deformation Friction by Lateral force friction force modulation curve atomic force microscopy (LM-AFM) Elastic properties — of a cantilever Lubrication Acoustic friction force microscopy (AFFM) Lateral stiffness — of a sample Viscoelasticity Acoustic friction force microscopy
39
6
Edges on gold planes
Name
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
Activation part (sample/ cantilever)
40
Table 1 (continued) Activation part (sample/ cantilever)
Sample/ cantilever
Lateral excitation Amplitude (nm) Normal force frequency (Hz) (nN)
Cantilever
Data acquisition Detected property
Name
(AFFM) oseveral tens of nN
Si3N4 (0.05 N/m) Lock-in amplifier
Dots of CH3 or 9 k (resonance) OH terminated Au substrate in air or water
0–4
—
Optical fiber cantilever
Cantilever
11.6 k Chemically functionalized Si (resonance) cantilever for AFM
4
—
Optical fiber cantilever
14
Sample (buckling)
HOPG in UHV 100 k (resonance) 1–10
—
Si ( )
15
Cantilever (out of plane)+sample (in-plane) Sample
ABC-triblock copolymer
kHz range (out of plane), 150 k (in-plane)
3.25–6.5
—
—
Polymer
1.4 k
3
Typically 25
—
Cantilever/ sample
SiO2 mesa on Si 400–500 k substrate/SAM (resonance)
0.4–4
o20
Sample
Polymer (polyolefine)silicon
12
Cantilever
13
16
17
10 k
Static and Dynamic dynamic friction scanning friction force microscopy (DSFFM) Interferometric Influence of — feedback system wettability on oscillation amplitude damping Laser feedback Influence of — interferometer+ interaction force lock-in amplifier on damping of SNOM tip vibration amplitude Lock-in amplifier Frictional Dynamic damping scanning friction microscopy (DSFM) Lock-in amplifier Adhesive, static, Combined and dynamic dynamic X mode frictional forces (CODY mode)
Lock-in amplifier Glass transition Shear temperatures modulation force (viscoelasticity) microscopy (SMFM) Si3N4 (0.06 N/m) Lock-in Lateral Lateral cantilever amplifier/ABS dissipation by resonance mode amplifier resonance (LCR mode) tracking
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
—
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T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
lateral modulation techniques. The paper will introduce a new imaging technique for obtaining contrast on graphite terraces, results of fixed and self-excited torsional oscillation, and the dependence of self-excited oscillation amplitude on the natural frequency. 1.1. Instrumental Depicted in Fig. 1 is the block diagram of the apparatus used for the imaging technique. The technique will be referred to as the lateral cantilever resonance (LCR) mode. Related to the excitation technique of lateral or torsional resonance, the LCR mode can be classified into the following. (i) no active excitation, (ii) excitation by a shear piezo at a fixed frequency, in the neighborhood of the torsional resonance of the cantilever when the tip is in proximity or in contact with the sample, and (iii) resonance tracking of LPF
ABS
BPF
Computer LIV/LIA
Frequency Extender
Display
Torsion ∆φ
QPD
LD
Scan
BPF
scanner
Deflection Shear piezo Z piezo controller
Fig. 1. A block diagram depicting the circuit for mapping the lateral vibration amplitude of the tip. Lateral vibration is either actively excited by a shear piezo set at the base of the cantilever or under the sample, or simply by scanning and thermal vibration. In the case of lateral self-excitation, the level of excitation was set to the 100 pm order, as measured as the torsional signal of the quadrant photodiode (QPD). A lock-inamplifier (LIA) and/or a lock-in-voltmeter (LIV) are used to measure the amplitude and phase of the torsional signal of the QPD at the torsional natural frequency of the cantilever. A rectifier was used instead of the LIA for measurement requiring faster response.
41
torsional vibration by self-excitation. For fixed frequency excitation, a local oscillator was connected to a shearing piezo element measuring 3 3 1 mm. A similar piezo element was attached under the sample to compare cantilever excitation to sample excitation [22]. The torsional signal of the cantilever was detected by a quadrant photodiode. Torsional signal was fed through a band pass filter, fixed to pass signals around the torsional resonance of the cantilever, which was approximately 450 kHz for a contact mode cantilever. A lock-in-amplifier locked to the reference frequency of the local oscillator was used to detect amplitude and phase. For observation of damping of lateral vibration after every atomic slip, a rectifier and a low pass filter (LPF) were used instead of the lock-in-amplifier since the former had shorter response time. Torsional amplitude and phase were mapped in x and y as the sample was raster scanned. Values of lateral oscillation at the tip end was around 10 pm without active excitation, and typically 0.4 nmp–p and up to 3 nmp–p for fixed frequency and self-excited oscillation. For self-excited oscillation, torsional signal of the optical lever passed through a band pass filter then digitized by saturating the oscillation signal. The digitized signal was phase shifted and fed to the piezo at the base of the cantilever or under the sample. For all experiments, calibration of torsional motion was carried using atomic stick slip signal of mica. As is often pointed out, the calibration is not totally correct since it does not take into account lateral displacement of the contact region, or dynamic slip effects. For all experiments, normal force was controlled with slow feed back by monitoring the deflection of the cantilever. The set value was 20 nN as measured from the point of snap-off.
2. Experimental 2.1. Contrast observed between graphite terraces without active excitation Cleaved graphite was imaged by the LCR mode without active excitation. Fig. 2 shows
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Fig. 2. Contrast seen within an HOPG sample with a step of 2 nm, when using lock-in-voltmeter for amplitude detection. Active excitation was not carried out for this imaging. (a) topography, (b) an example of a lateral vibration amplitude image. The scan size, scan speed, resonance frequency are 1.1 mm2, 5.5 mm/s and 440 kHz.
topographic image and lateral amplitude image for an area of 1.1 mm2. The resonance frequency was 450 kHz. Amplitude was approximately 10 pm. Contrast could be seen between the two terraces separated by a 2 nm step. The brighter region in Fig. 2(b) corresponded to the region where the lateral amplitude of the tip was larger at the torsional natural frequency. The contrast was stable for repeated raster scanning of the sample. Zoom up of the two terraces showed that the crystal orientation of the terraces did not differ between the two. Switch in contrast was sometimes observed as the tip was retracted and reapproached to the same step within the sample. 2.2. Tip swinging and pivoting depending on the excitation frequency To verify the behavior of the tip motion with respect to the excitation frequency, the frequency of the local oscillator in Fig. 1 was swept from offresonance to on-resonance. Fig. 3 shows a typical result. When the cantilever was oscillated at its torsional resonance, the tip swung before and after
Fig. 3. Difference of torsional motion and sample distance. (a) Direct cantilever torsion excitation close to torsional resonance. Torsional motion remains after contact and decreases with increasing normal load. (b) sample activation off-resonance. Torsion increases with increasing normal load. The result indicates that the tip is swinging around the cantilever for (a) and is pivoting about the tip apex for (b).
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
43
contact. Amplitude decreased with increasing normal force. Off-resonance, the cantilever torsion was negligibly small before contact, and increased with increasing normal load. The result showed that close to resonance, swinging motion of the tip continues after contact, and that for the proposed imaging technique, the tip apex is sliding rather than pivoting on the surface. 2.3. Imaging of graphite with and without excitation Depicted in Fig. 4(a) is the torsional signal when the tip was line scanned for a few nm. The upper line is the saw tooth form stick slip signal, the second is the band pass filtered output of the former, leaving the torsional oscillation signal around 450 kHz. The amplitude as calibrated from the lattice spacing was around 10 pm. In this experiment, a rectifier was used instead of the lockin-amplifier for observing damping and excitation of the lateral vibration at every atomic stick-slip. As can be seen from the second line, increase in lateral amplitude was seen at every slip, indicating that slip to the next stick point increased lateral vibration of the tip. Average Q factor of lateral vibration as measured by the envelope of the damped oscillation after every step was 100. Fig. 4(b) shows the torsion signal when the resonance was actively excited by the shear piezo element. The amplitude was set to around 50 pm. Decrease in torsional amplitude was observed at every slip. As shown in Fig. 4(c), when the RF torsional amplitude value was plotted to the xy plane, periodicity reflecting the lattice structure was seen. The dark rings correspond to the region where tip slip occurred. When a larger area of a few micron square was imaged, no difference in contrast was observed between step separated terraces. 2.4. Imaging of silicondioxide mesa on silicon substrate Silicon dioxide mesa were formed on a silicon substrate by masking and etching of the top silicondioxide layer. The height of the mesa was 30 nm. The sample was dipped in dilute HF to
Fig. 4. Comparison of (a) passive and (b) active lateral vibration excitation for graphite. The scanning speeds are (a) 1.1 mm/s, (b) 138 nm/s. 72 mV is applied to a shear piezo in (b) active excitation. The signals are, (1) torsional signal of the QPD showing atomic stick-slip, (2) BPF output of signal (1) at (a) 440 kHz, and (b) 470 kHz, (3) output of the ABS amplifier, where the input is signal (2), (4) output of the LPF, where the input is signal (3), and the cut off frequency (a) 20 kHz, (b) 47 kHz. Note that the vibration amplitude increases after the stepping action for (a) and, decreases for (b). The amplitude is approximately 10 times larger for (b) than (a). The natural frequency at around 450 kHz cannot be resolved at the time scale of the plot, and the sinusoidal signals seen within the plot are subject to digitizing error. Envelopes of signals (1)–(3) do however reflect the actual change in amplitude. (c) Lateral amplitude of the tip plotted against voltages applied to the x and y scanners when the lateral vibration was actively excited. The dark rings correspond to moments when the tip slipped and the vibration amplitude decreased as in (b)-(4).
remove surface oxide on silicon and then immediately imaged by the LCR method with fixed frequency excitation. Fig. 5 shows the topography, FFM image, LCR amplitude image and phase image. With a tip as delivered by the
44
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
formation of a thin oxide layer. An example is shown in Fig. 6. The square seen at the lower left of the images is the silicondioxide mesa.
Fig. 5. Images taken in ambient conditions of silicon with silicondioxide mesa, taken with the active cantilever torsion excitation. (a) topography, (b) FFM image, (c) amplitude image taken with the LIA, (d) phase shift image taken with the LIA. With a tip as supplied by the manufacturer, amplitude was smaller for silicon dioxide than silicon. Features not seen in the topography or FFM images are revealed in the amplitude and phase shift images inside of SiO2. Tip velocity, scan time, scan size, step height are 11.1 mm/s, 926 s, 20 mm2, and 30 nm. On other samples, contrast inverted with a tip functionalized with a self-assembled monolayer.
manufacturer, LCR amplitude was larger on silicon than silicondioxide. This contrast changed when the tip apex was functionalized with a selfassembled monolayer. The LCR technique was compared with the LMAFM. As the surface of the silicon substrate slowly oxidized in air, with the former technique, contrast between the two substrate and the mesa gradually decreased, and after 24 hour, little contrast was observed between the two regions. On the other hand, contrast was still observable by the latter method during and after
Fig. 6. The mapping image of silicondioxide mesa left in ambient condition for a week. The images are (a) topography, (b) FFM, (c) fixed frequency LCR-amplitude, (d) fixed frequency LCR-phase, (e) LM-AFM-amplitude, (f) LMAFM-phase. Except for edge effects, contrast could not be seen in the fixed frequency LCR mode, after the Si substrate was covered with thin oxide layer. However, in LM-AFM image, the contrast corresponding to FFM image could be seen as (e). Excitation frequency of LCR was set slightly below resonance.
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
2.5. Dependence of contrast on excitation frequency around torsional resonance Images obtained in Figs. 5 and 6 were obtained by exciting the cantilever at a frequency slightly below torsional resonance with the tip in contact with the sample. However, contrast is expected to depend on the excitation frequency in relation to the natural frequency, as well as the local Q factor. Fig. 7 was taken on a SAM surface to verify the extent and reproducibility of this effect, and to compare cantilever and sample activation. Roughly speaking, inverse of contrast was seen above and below resonance frequency, and images obtained for two types of modulation methods matched. However, in some regions marked in circles within the figure, different contrast with respect to its surrounding area were seen. This made it difficult to characterize a feature observed within an image.
2.6. Feed-forward excitation of torsion of the cantilever Torsion of the cantilever was excited by driving the piezo attached to the base of the cantilever or under the sample. Torsional signal of the optical lever was band pass filtered and then digitized by saturating the sinusoidal oscillation signal. Digitizing by saturation helped avoid quenching of self-excitation. The digitized output was phase shifted and fed to one of the two excitation piezos. Images are shown in Fig. 8. The images are amplitude images for a fixed excitation amplitude, and corresponds to what may be called dissipation _________________________________________" Fig. 7. Self-assembled monolayer domains imaged in the vicinity of torsional natural frequency. Image size 500 nm2. Imaging time 278 s and tip velocity 924 nm/s. Activation of piezo elements attached to the base of the cantilever and under the sample were adjusted to give the same amplitude of torsional signal of the optical lever. Figures in the middle column correspond to excitation approximately on the resonance peak. Roughly speaking, inversion of contrast was observed between excitation frequencies below and above resonance. Sample activation and probe activation gave more or less the same image, but some regions within the image showed different results.
45
or damping images. For this experiment, cantilever excitation showed higher lateral resolution. Unlike the fixed frequency excitation mode, interpretation of the images was apparently more
46
T. Kawagishi et al. / Ultramicroscopy 91 (2002) 37–48
455
Frequency (kHz)
450 445 440 sample excitation cantilever excitation
435 430 425 420 0
0.5
1 1.5 2 Amplitude (nmp-p)
2.5
3
Fig. 9. Dependence of self-excitation torsional resonance frequency on torsional amplitude. At around 2.5 nmp–p, the resonance frequency suddenly decreased to a value corresponding to that of a free standing cantilever. Contrast was lost for cantilever excitation amplitude exceeding the threshold of 2.5 nmp–p.
2.7. Dependence of lateral amplitude on self-excitation frequency Fig. 8. Images of SAM domains taken by lateral resonance self-excitation. Image size 500 nm2. Torsional motion was excited by feeding the torsional signal to the piezo set at the cantilever base or under the sample. For this experiment, probe activation apparently showed higher lateral resolution than the other. A hole in the upper left of the image was 20 nm deep. Islands and strands extending from left to right measure 2 nm in height, and appears as a dark region in the dissipation image.
straightforward; places with less loss showed higher torsional amplitude. This technique may be regarded as a lateral modulation version of the vertical resonance tracking mode [44] and the Q factor mapping mode for vertical oscillations [40]. The sample was Octadecanethiol (ODT, CH3(CH2)17) grown on Au(1 1 1) by immersing the substrate in ethanol with ODT for 24 hour. Protrusions of 2 nm appear as dark regions in the LCR images, which we think are islands and strands of ODT SAM. Self-excited lateral oscillation technique was capable of resolving nanometric features due to difference of lateral damping.
The cantilever was set to oscillate at its torsional resonance by self-excitation, and the natural frequency was measured as a function of lateral tip amplitude. Fig. 9 shows the result for sample and cantilever excitation. Self-excitation was possible from around 0.2 nmp–p. For cantilever excitation, frequency dropped suddenly at around 2.5 nmp–p and stabilized to a frequency within a few 100 Hz of the torsional frequency of a free standing cantilever. As for sample excitation, no drop in frequency was observed. For both cases, lateral amplitude above 3 nmp–p could not be obtained even when the excitation signal of the piezo element was increased.
3. Discussions and comments 3.1. On imaging of graphite When imaging graphite terraces with no active excitation, inverse of contrast was sometimes observed when the tip was reapproached to the
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sample. Due to this experimental result, it is difficult at present to conclude that the imaging technique revealed an intrinsic difference of the graphite terraces. One explanation is that tip switch or attachment of a small monolayer occurred every time the tip crossed the step. When torsional resonance was activated by a shear piezo element, decrease in oscillation amplitude was observed every time the tip made an atomic slip. We attribute the decrease to be caused by the step form disturbance caused by the slip on the harmonic oscillation. Contrast of terraces was not observed with the latter imaging technique. The former technique, although less stable than the latter, was more sensitive in revealing changes occurring at the tip apex.
3.2. On imaging with fixed frequency The lateral cantilever resonance technique with fixed frequency excitation was capable of revealing fine features on the silicon dioxide mesa, which were hardly visible in the topography or FFM images. It was confirmed by changing the excitation frequency that the tip swings about the cantilever or slips on the sample surface when excited close to resonance, and pivots around the contact point when excited off-resonance. From the result, it can be said that the LCRAFM technique has the tip in relative motion to the sample surface. When oxidation of the silicon substrate proceeded, change in contrast was observed in the order of hours. The LMAFM technique gave contrast images of the same sample even when the substrate was covered with a thin film of silicon dioxide. The LCRAFM technique images the lateral mobility of the tip defined by the very surface of the sample, where as, the LMAFM technique measures the mechanical property of a greater depth or volume of the sample in proximity of the tip. As for the difference of exciting the cantilever or the sample, similar images were obtained for both excitation methods, with local contrast difference of certain features, making image interpretation difficult.
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3.3. Lateral self-excitation Lateral self-excitation was implemented for both cantilever and sample excitation. The latter apparently showed better lateral resolution, but contrast was lost as the excitation amplitude increased. In other words, contrast was lost as self-excitation frequency suddenly dropped to the value close to that of a free standing cantilever. For this experiment of ODT on Au(1 1 1), lateral amplitude of around 2.5 nmp–p was the threshold for obtaining reproducible features. As the amplitude and relative velocity of the tip increased, effect of the interfacial layer on the natural frequency decreased. As for sample excitation, no drop in frequency was observed for the amplitude values tested. Acquisition of a frequency to amplitude curve as depicted in Fig. 9 is routinely necessary prior to imaging to obtain a resolved reproducible image.
Acknowledgements The authors thank Professor H. Yamada, Professor K. Yamanaka and Dr. K. Kobayashi for valuable comments and suggestions.
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