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A Unique Self-Sensing, Self-Actuating AFM Probe at Higher Eigenmodes

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Zhichao Wu at Tianjin Polytechnic University
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Tong Guo at Tianjin University
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Ran Tao
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Abstract and Figures

With its unique structure, the Akiyama probe is a type of tuning fork atomic force microscope probe. The long, soft cantilever makes it possible to measure soft samples in tapping mode. In this article, some characteristics of the probe at its second eigenmode are revealed by use of finite element analysis (FEA) and experiments in a standard atmosphere. Although the signal-to-noise ratio in this environment is not good enough, the 2 nm resolution and 0.09 Hz/nm sensitivity prove that the Akiyama probe can be used at its second eigenmode under FM non-contact mode or low amplitude FM tapping mode, which means that it is easy to change the measuring method from normal tapping to small amplitude tapping or non-contact mode with the same probe and equipment.
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Sensors 2015, 15, 28764-28771; doi:10.3390/s151128764
sensors
ISSN 1424-8220
www.mdpi.com/journal/sensors
Article
A Unique Self-Sensing, Self-Actuating AFM Probe at
Higher Eigenmodes
Zhichao Wu, Tong Guo *, Ran Tao, Leihua Liu, Jinping Chen, Xing Fu and Xiaotang Hu
State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University,
Tianjin 300072, China; E-Mails: bertwu@tju.edu.cn (Z.W.); sam1909@163.com (R.T.);
liuleihua@tju.edu.cn (L.L.); chenjinping@tju.edu.cn (J.C.); xingfu@tju.edu.cn (X.F.);
xthu@tju.edu.cn (X.H.)
* Author to whom correspondence should be addressed; E-Mail: guotong@tju.edu.cn;
Tel./Fax: +86-222-7892-691.
Academic Editor: Vittorio M. N. Passaro
Received: 3 October 2015 / Accepted: 9 November 2015 / Published: 13 November 2015
Abstract: With its unique structure, the Akiyama probe is a type of tuning fork atomic
force microscope probe. The long, soft cantilever makes it possible to measure soft
samples in tapping mode. In this article, some characteristics of the probe at its second
eigenmode are revealed by use of finite element analysis (FEA) and experiments in a
standard atmosphere. Although the signal-to-noise ratio in this environment is not good
enough, the 2 nm resolution and 0.09 Hz/nm sensitivity prove that the Akiyama probe can be
used at its second eigenmode under FM non-contact mode or low amplitude FM tapping
mode, which means that it is easy to change the measuring method from normal tapping to
small amplitude tapping or non-contact mode with the same probe and equipment.
Keywords: AFM; quartz tuning fork; higher eigenmode; non-contact; finite element analysis
1. Introduction
Quartz tuning forks are designed for high-precision frequency control and are widely used in clocks,
watches, and digital circuit frequency standards. By taking advantage of their extreme stability in
frequency, their high quality factor, their self-sensing and self-actuating capabilities, and the ease with
which the vibration signal may be obtained with fewer components than the conventional atomic force
OPEN ACCESS
Sensors 2015, 15 28765
microscopy (AFM) probes, and so on, they can be used as force sensors in AFM [1–4]. The tuning fork
AFM probes are typically realized in two forms (Figure 1). The tip of the probe could be a carbon
nanotube, a fiber, a conventional AFM cantilever, or another type of stylus.
Figure 1. Typical tuning fork probe structures.
These probes retain their high quality factor and high prong stiffness which makes them a stable
source for small vibration amplitudes. On the other hand, the high stiffness is a drawback when
measuring soft samples. To couple a soft cantilever to the quartz tuning fork, Bayat et al. designed a
novel probe [5] which has been commercialized by the Nanosensors Corporation (Neuchatel,
Switzerland). As shown in Figure 2, a U-shaped silicon nitride cantilever is combined in a symmetrical
arrangement with a quartz tuning fork. A slant probing tip is at the free end of the cantilever. The two
legs of the cantilever are fixed to the two prongs of the tuning fork respectively. The parameters of the
Akiyama probe are as follows: the resonant frequency is 45–55 kHz; the spring constant is about 5 N/m;
the cantilever’s length, width, thickness are respectively 310 μm, 90 μm, 3.7 μm; and the diameter of
the tip is less than 15 nm. The tip point is vertical, and lies perpendicular to the lateral plane defined by
the tuning fork and cantilever. Under the excitation of the tuning fork, the probe is self-sensing by
converting the deflection of the cantilever to a change in charge.
Figure 2. The appearance and motion of an Akiyama probe.
For the long, soft cantilever, this Akiyama probe cannot be used in non-contact AFM at its first
eigenmode like the conventional tuning fork probe can [6]. As is well known, a cantilever working at
higher eigenmode frequencies can increase the effective stiffness [7,8]. Thus, working at a higher
eigenmode can extend the range of application of the Akiyama probe.
Sensors 2015, 15 28766
2. Finite Element Analysis of the Probe
To account for realistic probe geometries and the electric field distribution, finite element
analysis (FEA) can be a powerful tool. ANSYS was used in this FEA and the parameters [2] are shown
in Table 1.
Table 1. FEA parameters.
Parameters Tuning Fork (Quartz) Cantilever (SiN)
Elastic constant
matrix/GPa
[]
11 12 13 14
11 13 14
33
11 12 14
44
44
00
00
000
()/20
0
ccc c
cc c
c
ANSYS c cc c
c
c


−


=
−





11 12 13
14 33 44
86.74 6.99 11.91
17.91 107.2 57.94
ccc
ccc
===
== =
，，
，，
None
Piezoelectric constant
matrix C/m2
[]
11
11
11
14
14
00
00
000
00
00
00
e
e
ANSYS e e
e
e
−
=
−
−
11 14
0.171 0.0406ee==−，
None
Permittivity F/m 4.43, 4.43, 4.63 (x-, y-, z-directions, respectively)
Young modulus, GPa None 180
Poisson’s ratio None 0.28
Density kg/m3 2290 2300
Length, μm 2690 310
Width, μm 220 90
Thickness, μm 100 3.7
Finite element SOLID226 SOLID95
Figures 3 and 4 are the results of the physical and electric analysis at the first and the second
eigenmodes respectively. As shown in Figure 5, the vibration amplitude of the second eigenmode is
much smaller than that of the first eigenmode, but the electric charge outputs are of the same order of
magnitude, which means that the Akiyama probe can obtain detectable low-level outputs.
1st Eigenmode
2nd Eigenmode
Figure 3. The vibration analysis of the Akiyama probe.
Sensors 2015, 15 28767
Figure 4. The electric field analysis of the Akiyama probe.
(a) (b)
Figure 5. The frequency response curve predicted by FEA. (a) The first eigenmode;
(b) The second eigenmode.
Conventional small-amplitude AFMs often use short, stiff cantilevers to keep the small vibrations
on a low level and ensure that the vibration can be detected. This Akiyama probe, with its long
cantilever, may manifest unique behavior while working as a small-amplitude AFM.
3. Results and Discussion
The Akiyama probe uses an amplification board based on a typical circuit [2] for I-V conversion
and capacitance compensation, as shown in Figure 6 and the influence of the parasitic capacitance is
shown in Figure 7.
Figure 6. Typical circuit diagram for an Akiyama probe amplification board.
Sensors 2015, 15 28768
(a) (b)
Figure 7. The electrical amplitude-frequency response of an Akiyama probe. (a) The first
eigenmode; (b) The second eigenmode.
3.1. Frequency Response of the Probe
The vibration amplitude of the cantilever is measured by laser Doppler vibrometer (LDV). As
shown in Figure 8, the amplitude of the first eigenmode is about 85 nm, the second eigenmode’s
amplitude is about 1.5 nm which is of the same order of magnitude as the conventional small
amplitude AFM. The LDV controller (OFV-3001, Polytec, Waldbronn, Germany) had a velocity decoder
resolution of 0.5 μm/s (RMS), a maximum frequency of 250 kHz, and a measuring range of 5 mm/s/V.
(a) (b)
Figure 8. The vibration amplitude-frequency response of an Akiyama probe. (a) The first
eigenmode; (b) The second eigenmode.
Differing from the FEA prediction, the electrical output from the second eigenmode was only 10%
of that of the first eigenmode, the sensitivity is 0.030 against 0.465 as shown in Figure 9; however, the
signal was still easily obtained with the same amplification as that for the first eigenmode, so the
amplification board can remain the same for different tests. This meant that the same system could
Sensors 2015, 15 28769
accomplish both normal tapping and small-amplitude tapping modes by changing the excitation signal
frequency alone.
(a) (b)
Figure 9. The scale (sensitivity) of the first and second eigenmodes. (a) The first
eigenmode; (b) The second eigenmode.
3.2. The Approach Curve
The tuning fork probes can work in FM non-contact mode [1]. In the test system, a phase-locked
loop (PLL) was used to trace the resonant frequency of the Akiyama probe during its approach to the
sample surface. The PLL (HF2PLL, Zurich Instruments, Zurich, Switzerland) had a frequency
resolution of 0.8 μHz. The approach curve shown in Figure 10 lay in the attraction region within which
non-contact AFM worked.
Figure 10. The approach curve for the second eigenmode in FM mode.
Compared with the 0.8 Hz/nm sensitivity of the first eigenmode in the repulsion region, the
sensitivity of the second eigenmode was about 0.09 Hz/nm; however, under standard atmospheric
conditions, the signal-to-noise ratio was not good enough to obtain a higher resolution.
Sensors 2015, 15 28770
3.3. The Resolution of the Probe
This test used a piezo-stage to raise the sample in steps of 2 nm after the probe touched the surface
with measurements taken at 20 points per step, the measured data and average data of each step are
shown in Figure 11.
Figure 11. The resolution of an Akiyama probe (2 nm increments).
Although the noise was apparent, the 2 nm steps in the average data plot are visible in Figure 11,
which meant that this mode can realize a resolution of 2 nm.
4. Conclusions
For a special structure, an Akiyama probe can be used as an FM-mode, non-contact AFM sensor in
its second eigenmode, although its cantilever is long and soft. According to the results, the second
eigenmode Akiyama probe was similar to the conventional tuning fork AFM probe working under
non-contact mode for which the signal-to-noise ratio is not good enough to obtain a better resolution
under atmospheric conditions. One advantage of the self-sensing, self-actuating AFM probe based on a
tuning fork was the simplicity with which it could be assembled for vacuum AFM to improve the
signal-to-noise ratio. Thus, it was appropriate for the measurement of different samples, such as soft or
movable samples, and for the use of the Akiyama probe in small-amplitude tapping mode or in non-contact
mode, under vacuum, without changing either the probe or the equipment.
Acknowledgments
The authors acknowledge the support of the Tianjin Natural Science Fund (No. 14JCZDJC39400),
the National Key Technology Research and Development MOST Programme (No. 2011BAK15B02),
and the 111 Project fund (B07014).
Sensors 2015, 15 28771
Author Contributions
Zhichao Wu, study design and software design; Tong Guo, literature research and study design;
Ran Tao, hardware design and data acquisition; Leihua Liu, test design and data acquisition;
Jinping Chen, data analysis and manuscript editing; Xing Fu, data analysis and manuscript revision;
Xiaotang Hu, manuscript revision and study concepts.
Conflicts of Interest
The authors declare no conflict of interest.
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Error in dynamic spring constant calibration of atomic force microscope probes due to nonuniform cantilevers
Article
Many common atomic force microscope (AFM) spring constant calibration methods regard the AFM probe as a uniform cantilever, neglecting the tip mass and any nonuniformity in the thickness of the probe along its length. This work quantifies the error in the spring constant estimated by the Sader and thermal calibration methods due to nonuniformity in the thickness of the cantilever and the influence of the mass loading effect of the probe tip. Formulae are presented that can be used to compute the uncertainty in cantilever calibration for an arbitrary thickness nonuniformity, or to correct the calibration methods if the thickness nonuniformity is known. The results show that both methods are quite sensitive to nonuniformity. When the first dynamic mode is used in the calibration, the error in the spring constant estimated by either method is between - 4% and 9% for a cantilever whose thickness increases or decreases linearly by 30% along its length. The errors are several times larger if the second or higher dynamic modes are used. To illustrate the proposed methods, a commercial AFM probe that has significant nonuniformity is considered and the error in calibrating this probe is quantified and discussed. For this particular probe, variations in the thickness of the probe over the last 15% of its length are found to significantly reduce the accuracy of the calibration when the thermal method is used, since that method is sensitive to changes in the shape of the eigenmode of the probe near its free end.
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Calibration of higher eigenmode spring constants of atomic force microscope cantilevers
Article
Standard spring constant calibration methods are compared when applied to higher eigenmodes of cantilevers used in dynamic atomic force microscopy (dAFM). Analysis shows that Sader's original method (Sader et al 1999 Rev. Sci. Instrum. 70 3967-9), which relies on a priori knowledge of the eigenmode shape, is poorly suited for the calibration of higher eigenmodes. On the other hand, the thermal noise method (Hutter and Bechhoefer 1993 Rev. Sci. Instrum. 64 1868-73) does not require knowledge of the eigenmode and remains valid for higher eigenmodes of the dAFM probe. Experimental measurements of thermal vibrations in air for three representative cantilevers are provided to support the theoretical results.
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Dynamic behavior of the tuning fork AFM probe
Article
  • May 2008
  • MICROELECTRON ENG
We recently introduced a new self-actuating and self-sensing atomic force microscope (AFM) probe based on a quartz tuning fork and a micro-fabricated cantilever. This system has two degrees of freedom, associated with its two components. We developed a model for describing how the sample-tip interaction is transduced to the tuning fork. It is based on two coupled spring-mass systems. In a first step, the coupling between the tuning fork and the cantilever was investigated to reveal the influential factors. The analysis of these factors enabled us to deduce their effect on the whole system and to optimize the sensitivity of this novel probe. The theoretical analysis was compared with experimental results and it was found that the model appropriately describes the probe in a qualitative manner while further refinement will be needed for achieving a correct quantitative description.
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  • Jan 2013
  • 1434-1437
  • D G De Oteyza
  • P Gorman
  • Y.-C Chen
  • S Wickenburg
  • A Riss
  • D J Mowbray
  • G Etkin
  • Z Pedramrazi
  • H.-Z Tsai
  • A Rubio
De Oteyza, D.G.; Gorman, P.; Chen, Y.-C.; Wickenburg, S.; Riss, A.; Mowbray, D.J.; Etkin, G.; Pedramrazi, Z.; Tsai, H.-Z.; Rubio, A.; et al. Direct Imaging of Covalent Bond Structure in Single-Molecule Chemical Reactions. Science 2013, 340, 1434-1437.
Study on Development of Self-Sensing AFM Head and Hybrid Measurement System
  • J Zhao
Zhao, J. Study on Development of Self-Sensing AFM Head and Hybrid Measurement System. Ph.D. Thesis, Tianjin University, Tianjin, China, 2011.