ARTICLE IN PRESS
Ultramicroscopy 107 (2007) 275–280
www.elsevier.com/locate/ultramic
Cantilever dynamics and quality factor control in AC mode AFM
height measurements
Liwei Chen, Xuechun Yu, Dan Wang
Department of Chemistry and Biochemistry, Ohio University, Athens, OH 45701, USA
Received 18 February 2006; received in revised form 5 June 2006; accepted 16 June 2006
Abstract
We show that inconsistent-imaging dynamics, in which the cantilever oscillates in the attractive regime on substrate background but in
the repulsive regime on sample, leads to artifacts in apparent height in AC mode Atomic force microscopy. Active Q control can be used
to effectively tune the imaging dynamics. Increased effective Q promotes the attractive regime, improves imaging sensitivity, and results
in less invasive imaging of soft biological molecules.
r 2006 Elsevier B.V. All rights reserved.
PACS: 68.37.Ps
Keywords: Atomic force microscopy (AFM)
1. Introduction
Atomic Force Microscopy (AFM) has evolved into an
indispensable tool in topography measurement and the
manipulation of nanometer-scaled features on surfaces
since first invented in 1986 [1]. The introduction of AC
mode operations was one of the most important breakthroughs in the development of the AFM instrumentation
because it greatly reduces the lateral interaction between
the tip and the sample, and thus leads to less invasive and
more versatile AFM operations [2–6]. The quantitative
interpretation of AC mode AFM requires detailed understanding of the cantilever dynamics [7–9]. Garcia et al.
showed that there exist two imaging regimes in AC mode
AFM: the attractive and repulsive regimes [10,11]. In the
attractive regime, the tip oscillates within the attractive
range of the tip–sample interaction, which effectively
reduces the cantilever resonance frequency and results in
a phase lag between the cantilever drive and response
greater than 901. On the other hand, the tip falls into
Corresponding author. Tel: +1 740 517 2852; fax: +1 740 593 0148.
E-mail address: [email protected] (L. Chen).
0304-3991/$ - see front matter r 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ultramic.2006.06.006
intermittent contact with the sample at the bottom of each
oscillation cycle in the repulsive regime. The repulsive
interaction during contact leads to an increased effective
cantilever resonance and a phase lag less than 901.
Using single-walled carbon nanotube (SWNT) probes
with transmission electron microscope (TEM)-characterized diameter as a model system, we recently elucidated
the effect of cantilever dynamics on the tip-induced
broadening in AC mode AFM [12]. The apparent width
of protruding features is broadened only by the diameter of
the SWNT probes when imaged in the repulsive regime,
but the broadening becomes the sum of the probe diameter
and the tip–sample distance at the bottom of oscillation
cycles when imaged in the attractive regime. This draws
our attention to the effects cantilever dynamics may
have on quantitative height measurements in AC mode
AFM.
In this contribution, we show that consistent cantilever
dynamic regimes on the sample feature and the background are necessary to obtain quantitatively accurate
height measurements in AC mode AFM. Active quality
factor (Q) control, which is recently implemented by AFM
manufacturers, provides an experimental control of the
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effective damping. We show that Q-control enables the
adjustment of cantilever dynamics and strongly affects the
height measurement of soft biological molecules such as
individual DNA double helices.
Gold nanoparticles samples were prepared from a gold
colloid solution (Ted Pella, Redding, CA) with diameters
of 571 nm and a concentration of 5 1013 particles/ml.
The stock solution was diluted with distilled water to
2 1011 particles/ml. Onto a piece of freshly cleaved
mica 10 ml of the diluted solution was applied for 5 min
and then the sample was dried under a stream of argon gas.
Double-helix DNA samples were prepared from BstE II
digested Lambda DNA fragments (New England Biolabs,
MA). In all, 10 ml of 0.1 mg/ml DNA solution in 40 mM
Tris–HCl (pH ¼ 8) buffer and 10 mM MgCl2 was applied
to freshly cleaved mica for 5 min and rinsed with distilled
water. Then the sample was dried under a stream of
argon gas.
All AFM images were acquired in AC mode with an
Asylum Research MFP-3D AFM (Santa Barbara, CA)
and Si probes from MikroMasch (Tallinn, Estonia).
Stiff probes (NSC15, 325 KHz resonance) with native
Q factor around 800 in ambient were used for gold
nanoparticle samples and soft probes (NSC18, 75 KHz
resonance) with native Q around 250 were used for
DNA samples. The probes were excited on resonance with
free amplitudes of 10–70 nm and phases of 901. The
imaging amplitude (set point) was chosen between 30%
and 90% of the free amplitude. The amplitude and phase
signals of the cantilever oscillation as a function of
tip–sample separation, which are denoted as force curves
(FCs) hereafter, were recorded for various conditions. The
active Q control is implemented via the fully integrated
module within the Asylum Research AFM. Non-zero Q
gains are used in the probe-tuning process to obtain desired
Q factors.
2. Effects of cantilever dynamics on the apparent height of
gold nanoparticles
It has been observed in experiments and numerical
modeling that the cantilever may oscillate in the attractive
regime or the repulsive regime when approaching surfaces
in AC mode AFM [7,9,10]. We recently studied the effects
of cantilever dynamics on AFM lateral resolution and
demonstrated that sample features are broadened by the
physical size of the AFM probe when imaged in
the repulsive regime but greater than the probes size in
the attractive regime [12]. Since commercial AFM tips are
conically shaped, the tip diameter can be significantly
larger than the sample width when the feature is a few
nanometers tall and wide. The height, rather than the
width, is thus typically used to characterize the size of
samples. Therefore, a natural question to investigate is the
effect of cantilever dynamics on the quantitative height
measurements in the AC mode AFM.
The apparent height of gold nanoparticles depends on
imaging conditions. Fig. 1 shows height and phase images
of the same sample area obtained with different free
cantilever oscillation amplitudes A0. The average height of
ten particles in this area is plotted in Fig. 1(D) when A0 is
varied between 10 and 40 nm and the set point varied
between 80% and 30% of A0. For any fixed A0, the
apparent height is constant when the set point is varied.
The average heights of 4.8, 4.9 and 4.7 nm for free
amplitudes of 40, 30 and 10 nm, respectively, are consistent
with the vendor specification of 5 nm, which is determined
by TEM. Surprisingly, the averaged height becomes 3.5 nm
only when A0 is set to 20 nm. Since the root mean square
noise of height is 0.2 nm in our measurement and the
standard deviation of the height measured among different
particles is 0.4 nm, the reduced apparent height is clearly a
systematic effect due to different A0.
Fig. 1. Height and phase images of Au nanoparticles obtained under different conditions. The free oscillation amplitude and set point of the images are
(A) 30 and 24 nm; (B) 20 and 6 nm; and (C) 10 and 3 nm, respectively. The height and phase scale is the same for three images and shown in (B). The insets
are the zoom-in images of an area at the upper right part of the scan window as shown in (A). Averaged apparent height as a function of free amplitude
and set point is plotted in (D).
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L. Chen et al. / Ultramicroscopy 107 (2007) 275–280
The phase images in Fig. 1 reveal cantilever dynamic
regimes in which these images are acquired. The absolute
value of the phase lag between the cantilever drive and
oscillation is less than 901 on both the gold nanoparticles
and the mica background when A0 is set to 40 and 30 nm
(Fig. 1(A)), which means that the cantilever oscillates in the
repulsive regime in these images. The phase lag signal becomes
greater than 901 when A0 is set to 10 nm (Fig. 1(C)), which
means the cantilever oscillates in the attractive regime on
both gold nanoparticles and the mica background. On the
other hand, the phase lag is less than 901 on gold
nanoparticles but greater than 901 on mica when A0 is set
to 20 nm (Fig. 1B). This indicates that the cantilever
oscillates in the attractive regime on mica but in the
repulsive regime when imaging over gold nanoparticles.
The results indicate that the sample height measured by
AC mode AFM agrees with TEM characterization only
when the cantilever oscillates in the same dynamic regime
on the sample as on the background. We reason this by
considering the z-piezo position of a scan line when the tip
images over a spherical sample. When the tip scans over a
nanoparticle and the mica background in the repulsive
regime, the tip intermittently contacts the sample at the
bottom of each oscillation cycle. Since the oscillation
amplitude is kept constant during the scan, the trace of the
cantilever follows the topography of the sample surface;
therefore, the apparent height, which is the z-piezo
displacement between the particle and the background,
reflects the true size of the nanoparticle (Fig. 2(A)). When
the tip scans in the attractive regime over both the particle
and the background, it is lifted up from the surface. The tip
also follows the surface topography although the tip–
sample distance in the attractive regime may vary slightly
between nanoparticles and the mica background
(Fig. 2(B)). However, the tip does not follow the
topography quantitatively when it oscillates in the attractive regime over the mica background but in the repulsive
regime over nanoparticles. The apparent height is shorter
than the true particle height by the tip–sample distance at
the bottom of oscillation cycles (Fig. 2(C)).
Our results show that there exists a parameter window in
which an AFM probe may stably image over different
sample areas in different dynamic regimes with reversible
transitions in between. The inconsistency of the cantilever
dynamics in this situation leads to inaccurate height
measurements. Specifically, the height difference indicates
Fig. 2. Schematic illustration of cantilever dynamics effects on the
apparent height of a spherical particle on a surface. The imaging regimes
over the substrate and particle are (A) repulsive and repulsive, (B)
attractive and attractive, and (C) attractive and repulsive, respectively.
277
that the tip is about 1 nm above the sample when images in
the attractive regime in our experiments. The 1 nm error in
height becomes significant when the sample height is on the
same order of magnitude. We further predict that this
effect could lead to negative apparent heights for protruding features that are less than 1 nm tall. This is indeed
observed in our experiments and the corresponding images
are displayed in the insets of Fig. 1.
3. Controlling Cantilever dynamics with active Q control
The cantilever oscillation dynamics is determined by the
cantilever geometry, viscous damping, the tip–sample
interaction, and the driving force. Active Q control takes
the cantilever deflection signal, electronically adds a 901
phase shift and then combines it with the drive signal [13].
If both the cantilever trajectory and the drive signal are
perfectly sinusoidal, the Q-control term would be in phase
with the viscous damping and thus effectively tune the Q
G
factor: Q1 ¼ Q1 moQ0 , in which Qeff is the effective quality
eff
factor, Q the native quality factor, GQ the Q gain, m the
point mass of the cantilever, and o0 the resonance
frequency of the cantilever. This technique has raised
much interest [14–19] but has been difficult to implement
until recently commercial AFM vendors such as Asylum
Research and Veeco Instrument started to ship it as
standard or add-on modules. Few experiments have
reported the performance of this technique and its application in imaging remains controversial [15]. Here we systematically investigate the effect of Q control on cantilever
dynamics and its application in quantitative imaging.
Fig. 3 shows the tuning spectra of the stiff probe under
active Q control. The peak amplitude on resonance
increases with increased Q factors (decreased effective
damping) under a constant drive, and vice versa. With the
Asylum Research MFP 3D and their Q control electronics,
we find that the Q gain can be varied between 2.5 and 0.5
for the soft probes, which corresponds to a Q range of
50–860. For the stiff probes, the stable Q gain range is 4.5
to 1.0 and the Q factor ranges from 130 to 2200. Q gains
Fig. 3. Tuning spectra of a stiff probe under active Q control. The driving
amplitude is kept constant.
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outside the stable range lead to greatly distorted resonance.
The correlation between the Q gain and the Q is non-linear.
FCs on mica with different A0 and Q (Fig. 4) display
characteristic discontinuities between the attractive and the
repulsive regimes in both the amplitude and the phase
channels. The FCs have been laterally shifted to a common
onset of tip–sample interaction for comparison. The FCs
with native Q in ambient air (Fig. 4B and E) show
that higher A0 promotes a wider range of the repulsive
regime. The comparison between the two probes indicates
that the soft probe tends to oscillate in the attractive
regime more. Q-controlled FCs (Fig. 4A, C, D, and F) of
the two probes reveal that reduced Q results in a wider
range of the repulsive regime; and increased Q leads to a
wider attractive regime. For any fixed Q, the trend that
higher A0 promotes the repulsive regime holds for both
cantilevers.
The FCs in Fig. 4 indicate that increased Q promotes a
wider range of amplitude set points at which the cantilever
images in the attractive regime and vice versa. This result is
consistent with previous numerical simulations [9]. The
slope of the amplitude curves is directly related with
imaging sensitivity. We notice that for the stiff cantilever,
the slope is close to the theoretical upper limit, 1 nm/nm,
regardless of the Q, A0 and the dynamic regimes. But for
the soft cantilever, the slope is about 0.6 nm/nm with native
Fig. 4. Force calibration curves obtained with the stiff (A–C) and the soft
probes (D–F) on mica.
Q (Fig. 4E). The rather small slope in attractive regime
with native Q does not necessarily mean 40% deformation
of the sample surface during tapping, instead, the
amplitude sensitivity less than 1 nm/nm in the attractive
regime may arise from the reduction in tip–sample distance
at the bottom of oscillation cycles when the surface is
pushed towards the oscillating tip. This distance becomes
a constant of zero in the repulsive regime, where the
amplitude sensitivity approaches 1 nm/nm as seen in
Fig. 4D. When the Q is enhanced and the cantilever
oscillates in the attractive regime, the slope remains about
0.6 nm/nm if A0 is large, but increases to 1 nm/nm if A0 is
30 nm or smaller. Numerical simulation in literature has
predicted that increased Q factor enhances sensitivity when
imaging soft samples [16]. Our results indicate that the
same effect exists for soft cantilevers on samples as hard as
mica.
4. Soft biological molecules imaged in controlled dynamic
regimes
Soft biological molecules such as DNA and protein are
routinely imaged using AC mode AFM [20–25]. Although
the shape of these soft molecules can be reliably
investigated, the quantitative measurement of height and
volume remains a challenge. For example, the apparent
height of DNA double helices has been consistently
reported shorter than the 2 nm diameter in solution.
Moreno-Herrero et al.[26] showed that the discrepancy is
mainly due to a 0.8 nm thick salt layer on mica, in which
DNA molecules are partially or fully embedded.
We imaged individual double-stranded DNA molecules
in both the attractive and the repulsive regimes using active
Q control. The drive amplitude is adjusted to keep A0
constant. The DNA molecule in Fig. 5(A) is imaged under
six different conditions. Consistent with the FC analysis on
mica presented in the previous section, the cantilever
oscillates in the attractive regime under high-Q and high set
point conditions but in the repulsive regime under low-Q
and low-set points. Only one image is presented in the
figure because the height images appear qualitatively the
same. However, the quantitative height of the molecule can
be significantly lower in the repulsive regime than in the
attractive regime. The height profiles of the DNA duplex in
the six images are plotted in Fig. 5(B). The imaging
conditions and the corresponding height and phase
measurements are summarized in Table 1.
Our results show that the same DNA molecule appears
about 3 Å shorter when imaged in the repulsive mode than
in the attractive mode. We believe it is caused by
deformation of the soft DNA molecules under different
tip–sample forces in the two dynamic regimes. This clearly
demonstrates that the tip–sample interaction partially
contributes to the discrepancy between the height of
DNA measured by AFM and that in solution.
The tallest height of 0.52 nm agrees with previously
reported measurements in UHV and ambient conditions
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279
Fig. 5. (A) AFM height image of an individual double-strand DNA molecule. (B) Height profile of the DNA along the length of molecule under different
imaging conditions. The free amplitude A0 is kept at a constant of 37.5 nm.
Table 1
Apparent height of DNA and the phase lag on mica and DNA under
different imaging conditions
Q
120
280
600
Asp/A0
Phase on mica (1)
Phase on DNA (1)
Height (nm)
0.5
45
46
0.19
0.5
50
51
0.22
0.5
68
70
0.25
860
0.7
145
146
0.40
0.4
121
122
0.34
0.7
113
114
0.52
The free oscillation amplitude (A0) is 37.5 nm.
[27]. It is obtained with a set point of 70% of the A0
(37.5 nm) and a Q of 860. This set point falls into a bistable
transition region if the Q had not been enhanced by the
active Q control.
5. Conclusion
We demonstrate that the apparent height of nanoparticles measured in AC mode AFM is strongly affected by
imaging dynamics. There exists a parameter window in
which the AFM tip oscillates in the attractive regime over
the background but in the repulsive regime over protruding
features. The apparent height of the features under these
conditions is reduced by an amount that corresponds to the
tip–sample distance at the bottom of oscillation cycles in
the attractive regime, which is about 1 nm in ambient. We
conclude that consistent dynamic regimes over the sample
and the background are necessities for quantitative AFM
height measurement.
Active Q control adjusts the imaging dynamics by tuning
the effective damping. Enhanced Q factors promote the
attractive regime and suppressed Q factors promote the
repulsive regime. Enhanced Q facilitates AFM imaging by
providing a wider range of the less invasive attractive
regime, in which soft biological molecules such as DNA are
less deformed due to the tip–sample force. Moreover, it
improves imaging sensitivity for soft cantilevers under
regular free amplitudes of 30 nm or less. On the other hand,
it was reported that suppressed Q enables faster scanning
[28,29]. We thus believe that active Q control is a versatile
technique that can be adopted for various purposes.
Acknowledgements
This work is partially funded by the Ohio University
Nano Biotechnology Initiative. DW acknowledges the
support from the Condensed Matter and Surface Sciences
program of Ohio University.
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