Advanced Moiré Methods with High Resolution Scanning Microscopy and
their Application
Huimin Xie1*
Satoshi Kishimoto 2
Yanjie Li1 Bing Pan1 Zhanwei Liu3 Biao Li1** Haixia Shang1
Fulong Dai1
1
FML, Dept of Engineering Mechanics, Tsinghua University Beijing China 100084
2
National Institute for Materials Science, Tsukuba 305-0047, Japan
3
Department of Mechanics, School of Science, Beijing Institute of Technology, Beijing, 100081, China
*Corresponding author. E-mail address: [email protected]
**Host researcher at the FML, Tsinghua university
ABSTRACT
Some novel micro/nano-moiré methods have been developed at the Failure Mechanics Lab in Tsinghua University. This paper
offers an introduction of these new methods, which can be realized under focus ion beam (FIB) system，scanning electron
microscope (SEM), atomic force microscope (AFM), scanning tunneling microscope(STM) as well as laser scanning confocal
microscope (LSCM). These micro/nano-moiré methods are able to provide quantitative analysis to micro/nano-deformation of
the sample. The measurement principles and experimental techniques of these methods are described in detail. Some
applications of these methods are given. The successful experimental results demonstrate the feasibility of these methods and
also verify that these methods can realize high sensitivity displacement measurement with mico/nano-meter spatial resolution,
and their wide applications in micro/nano-mechanics researches are expected.
1.Introduction
In recent years, studies on micro-electron-mechanical systems (MEMS) and nano-electron-mechanical systems (NEMS) have
drawn great attention in many fields. Characterization of the micro-/nano-mechanical properties is of great importance for the
design, fabrication, reliability and packaging of MEMS/NEMS [1-2] since they affect the device performance significantly.
Moreover, to comprehensively understand material properties, it is necessary to study its mechanical property in
micro/nanometer scale.
Traditional moiré methods including geometric moiré method [3-5] and moiré interferometry [6] are effective tools to measure
full-field deformation of the specimen surface. Their displacement measurement sensitivity is decided by the frequency of
reference grating, that is, the higher the frequency is, the higher displacement spatial resolution will be obtained. Since the
grating for geometric moiré method is usually less than 100 lines/mm and for moiré interferometry is usually 1200 lines/mm or
2400 lines/mm, both methods cannot meet micro/nanometer measurement requirement. Fortunately, high resolution
microscopes, such as FIB system, SEM, AFM, STM, as well as LSCM, make it possible to observe the atom or molecule
structure of material surface and offer effective tools for micro/nanometer measurement. By integrating moiré method with the
above mentioned microscopes, some novel moiré methods have been developed at the Failure Mechanics Lab in Tsinghua
University.
In this paper, the measurement principles of these methods are described in detail. Some applications of these methods are
given. The successful experimental results demonstrate the feasibility of these methods and also verify that the methods can
offer a high sensitivity for displacement measurement with mico/nano-meter spatial resolution, and find wide applications in
micro/nano-mechanics researches.
2.Measurement principle of high resolution microscope moiré methods
2.1 Work principle of high resolution microscope
Under high resolution microscopes (FIB system, AFM, SEM, STM and LSCM), images can be formed during scanning
specimen surface point by point.
For FIB system, when focalized ion beam scans on the sample, the secondary ions are emitted from the sample surface. The
electron intensity can be monitored and used to generate an image. The SEM is similar to that of FIB system, the major
difference being the use of an electron beam instead of a gallium ion (Ga+) beam.
For AFM, under contact mode, the cantilever tip scans over the sample surface while monitoring the change in cantilever
deflection with a split photodiode detector. When the tip is close enough to the surface of the specimen, the atomic force
between the cantilever and the surface of the substrate will lead to deflection of the cantilever. This deflection is transformed
into feedback signal. By controlling the force constant, a topographic image corresponding to the surface of the specimen can
be obtained in the CRT.
For STM, when the distance between the scanning probe and specimen surface is less than 1nm, tunnel current will come into
being. Since the distance influence the current value, by controlling the current constant, the sample surface image can be
obtained.
Under LSCM, the laser beam is focalized on the specimen surface and reflected back, but only the light that is reflected from
focus point can be detected and used to form the image of specimen surface.
2
2.2 Measurement principle of high resolution microscope moiré methods
Under the platform of the above microscopes(FIB system, AFM, SEM, STM and LSCM), a high resolution microscopy scanning
moiré method is put forward, the scanning lines of microscopes are considered as reference grating, while the regular array of
the atomic lattice or holographic grating is used as specimen grating. Since the magnification factor and scanning area are
adjustable, the reference grating frequency is adjustable accordingly.
Suppose the spatial frequency of the specimen grating is f s , i.e. the specimen grating pitch is
reference grating
fr
ps .
The frequency of the
can be defined as
fr =
1
N
=
pr L
where N is the number of scanning lines and
L
(1)
is the length of scanning area.
When the specimen grating and the reference grating are parallel to each other and their grating frequencies are matched, the
formed parallel moiré pitch will be given as
pm =
pr p s
p s − pr
(2)
According to Eq. (1) and (2), if the scan area meets the condition
L = ps [ N ± x ]
(3)
moiré fringe with order of x will appear, where “+” means a tensile strain, i.e. the specimen is tensioned, otherwise the strain is
compressive. However, it is obvious that the number of moiré fringe cannot be infinite at a limited scanning size. The results
from the experiment show that moiré patterns are clearly visible only under the condition x<N/2. Therefore, the scanning size is
restricted to a range of 0.5Nps<L<1.5 Nps.
When a cross-line specimen grating is used, the U field and V field moiré fringes can be separately formed by adjusting the
orientation of the scanning line of microscope parallel to the specimen grating lines.
Using the carrier moiré pattern, the real strain components can be calculated by subtracting the initial carrier moiré fringes from
the strain components measured from the deformed moiré fringes. Thus, with the acquired U and V fields before and after
deformation, the desired strain components can be computed using the following equations
3
ε x = ε 1x − ε x0 = ±
ps
p
− (± 0s )
1
S xx
S xx
ε y = ε 1y − ε y0 = ±
ps
p
− (± 0s )
1
S yy
S yy
γ xy = ±
where
S 1yy
S xx0
and
S yy0
S 1xy
ps
ps
ps
ps
+
(
±
)
−
(
±
)
−
(
±
)
1
S xy
S 1yx
S xy0
S yx0
are the spacing between the two adjacent fringes in the initial U field and V field moiré fringes;
are their counterparts after deformation, respectively;
in the direction y and
and
S 1yx
S yx0
(4)
S xy0
S 1xx
and
is the spacing between the two adjacent U field moiré fringes
is the spacing between the two adjacent V field moiré fringes in the direction x before deformation;
are the spacing between the two adjacent U field and V field moiré fringes in the direction y and x after
deformation, respectively.
3. Experimental results of high resolution microscope moiré method
3.1 FIB moiré
The scanning lines of FIB system are used as reference grating and the specimen gratings are directly fabricated on the MEMS
structure surface by FIB milling. The direct writing capability of FIB milling allows nanometer-scale fabrication of specimen grids
on the specific region without requiring of an etch mask and is very suitable for the application to MEMS/NEMS components.
The applicable sample for FIB Moiré method should be conductive materials. For a non-conductive material, a conductive layer
should be deposited before experiment.
The FIB moiré method is applied to measure the creep deformation of a polysilicon MEMS cantilever structure. Using the FIB
milling method, a 140nm pitch grating (parallel type) was fabricated on this cantilever (60 mm long, 10 mm wide, 2 mm thick).
An initial moiré pattern was recorded when the magnification K=2200 and scanning lines N=884; and the result is shown in Fig.
1(a). After 20days, the cantilever was placed back to the FIB system to generated FIB moiré under the same condition. The
moiré pattern with the creep strain plus virtual carrier is shown in Fig. 1(b). With image processing technique and Eq.(4 ), the
creep strain can be obtained.
4
(a) initial moiré image
(b) moiré creeping for 20 days
Figure 1 FIB moiré patterns
3.2 SEM moiré
The scanning lines of SEM are reference grating and specimen grating is directly fabricated on the MEMS structure surface by
FIB milling. The shorter cantilever is 60 micron long with 0.2 micron pitch grating and the longer one is 80 micron long with 0.4
micron pitch grating. SEM moiré was used to measure their residual strain after being etched by HF for 1 hour with a
magnification factor K=500.
(a)before etching
(b)HF etching 1 hour
Figure 2 SEM moiré patterns
3.3 AFM moiré
With a mica sample, AFM nano-moiré is generated by the interference of the atomic lattice of mica and AFM scanning lines.
The mica surface was then irradiated by the Nd-YAG laser (λ = 532 nm, energy 20.6 mJ, duration of illumination 0.43 s). After
illumination, the mica substrate was placed in AFM to measure the residual strain. This nano-moiré pattern is shown as Fig. 3,
which was recorded under the condition of scan line number N = 128, and scanning size is 139.96 nm×139.96nm.
5
Figure 3 AFM moiré pattern
3.4 STM moiré
The scanning lines of STM are used as reference gratings and the lattice of high-orientated pyrolytic graphite (HOPG) is used
as specimen grating. Parallel moiré and rotational moiré patterns are obtained as follows when the scanning lines N=256.
(a) parallel moiré
(b) rotational moiré
Figure 4 STM moiré patterns
3.5 LSCM moiré
In this method, the scanning lines of LSCM are used as reference gratings.
This method was used to measure the residual strain of an Al alloy specimen with width of 8 mm and thickness of 1.22mm.
Before experiment, a holographic grating of 1200 lines/mm was transferred to the specimen surface. Then a load of 120N is
exerted on the specimen and released. Finally the specimen is placed to LSCM sample stage. By adjusting the magnification
6
factor and angle of LSCM, the parallel moiré was obtained as Fig.5. The result illustrates there exists obvious grain sliding as a
result of residual strain.
Figure 5 LSCM moiré pattern
4. Conclusion
(1)The measurement principles and experimental techniques of some novel moiré methods developed at FML in Tsinghua
University are described in detail.
(2)Different microscopes have their own applicability and scanning size, see Table 1. Furthermore, for FIB、SEM and TEM, the
corresponding moiré methods should be implemented under vacuum condition.
Table 1 A comparison of different moiré methods
Moiré
Applicable specimen grating
method
(pitch)
FIB
submicron
AFM
nanometer to micron
SEM
submicron
STM
nanometer to micron
LSCM
submicron to micron
Measurable size
tens of micron to millimeter
tens of nanometer to
hundreds of micron
tens of micron to millimeter
tens of nanometer to
hundreds of micron
micron to millimeter
(3)The sensitivity of displacement measurement in the scanning moiré methods is determined by the pitch or frequency of
reference grating. However, the sensitivity of strain measurement is not only determined by the reference grating pitch but also
by the area measured. For example, provided the length of the measured area is 1mm and 100nm spacing reference grating is
7
used, the minimum strain for generating two fringes in such an area is 100με.　(4)The successful experimental results demonstrate the feasibility of these methods and also verify that these methods can
offer a high sensitivity for displacement measurement with mico/nano-meter spatial resolution, and find wide applications in
micro/nano-mechanics researches.
Acknowledgements
The work is supported by the National Basic Research Program of China through Grant No. 2004CB619304, the National
Natural Science Foundation of China（under grants 10625209, 10472050, 10121202）, the Project from Beijing Natural Sciences
Foundation (3072007) and the Program for New Century Excellent Talents (NCET) in University，Chinese Ministry of Education.
References
[1] Lu T J, Moore D F and Chia M H. Mechanics of micromechanical clips for optical fibres. Journal of
Micromechanics and
Microengineering. 12(2): 168–76, 2002
[2] Moore D. F., Williams J.A. and Hopcroft M.A., et al.. SPIE. 4941: 140–147, 2003,.
[3] Weller R, Shepherd B M. Displacement measurement by mechanical interferometry. Proceedings of the Society for
Experimental Stress Analysis. 6(1): 35–38, 1948
[4] Morse S, Durelli A J, Sciammarella C.A. Geometry of Moiré fringes in strain analysis. J Eng Mech Div, ASCE. 86: 105–126,
1960
[5] Theocaris P S. Moiré fringes in strain analysis. New York: Pergamon Press.1969.
[6] Post D, Han B, Ifjju P. High sensitivity Moiré. Berlin: Springer. 1994.
[7] Kishimoto, Egashira M and Shinya N. Micro-creep deformation measurement by a moiré method using electron beam
lithography and electron beam scan. Opt. Eng. 32: 522–526,1993
[8] Read D T and Dally J W. Electron beam moiré study of fracture of a glass fiber reinforced plastic composite. Trans. ASME.
61: 402–409,1994
[9] Binnig G, Rohrer H, Gerber C and Weibel E. Phys . Rev. Lett ., 49: 57,1982
[10] Hasegawa Y and Avouris P. Science. 258: 1763,1992
[11] Xie Huimin, Li Biao, Geer Robert et al. Focused ion beam Moiré method. Optics and Lasers in Engineering. (40): 163–177,
2003
[12] chen H., Liu D. and Lee A.. Moire in Atomic Force Microscope. Experimental Mechanics. 24(1): 31-32, 2000.
[13] Xie, Huimin; Kishimoto, Satoshi; et al. In-plane deformation measurement using the atomic force microscope moire
method[J]. Nanotechnology. 11(1): 24-29, 2000
[14] Pan Bing, Xie Huimin and Kishimoto Satoshi et al. Experimental study of moiré method in laser scanning confocal
microscopy. Review of Scientific Instruments., 77: 1-4, 2006
8