Jpn. J. Appl. Phys. Vol. 41 (2002) pp. 3974–3977
Part 1, No. 6A, June 2002
#2002 The Japan Society of Applied Physics
Simultaneous Atomic Force Microscope and Quartz Crystal Microbalance Measurements:
Interactions and Displacement Field of a Quartz Crystal Microbalance
J.-M. FRIEDT, K. H. C HOI, L. FRANCIS and A. CAMPITELLI
IMEC, Kapeldreef 75, 3001 Leuven, Belgium
(Received January 22, 2002; accepted for publication February 25, 2002)
We analyze the interaction of two instruments often used in material science analysis, the atomic force microscope (AFM) and
the quartz crystal microbalance (QCM), here combined in a single instrument for simultaneous measurements on a single
sample. We show, using finite element analysis, that the in-plane displacement of a QCM oscillating in liquid with a quality
factor of 2000 is 2 nm. The out-of-plane displacement is about one tenth of the in-plane displacement. This latter effect, due to
the finite size of the electrodes, results in longitudinal acoustic waves launched in the liquid surrounding the QCM. If bounced
against an obstacle, in our case the AFM cantilever holder, these longitudinal waves create standing wave patterns which
cause frequency fluctuations of the resonator when it is moved, and thus decrease the QCM sensitivity.
[DOI: 10.1143/JJAP.41.3974]
KEYWORDS: QCM, displacement, resonance frequency, quality factor, AFM
1.
cut using the formula provided by ref. 7.
Introduction
During the development of a combined quartz crystal
microbalance1) (QCM) — atomic force microscope2) (AFM)
instrument, we faced the challenge of estimating the
displacement of the QCM resonator parallel to the electrode
plane (which defines the lateral resolution of our AFM
imaging) and normal to the electrode plane (which defines
the topography resolution of the AFM scans).
Simultaneous AFM and QCM measurements of a sample
allow the following:
. differents kinds of data to be gathered on different
scales (cm2 scale in the case of the QCM, nm2 scale in
the case of the AFM) and of a very different nature
(mass change/viscosity losses in the case of the QCM,
topography/stiffness in the case of the AFM). These
measurements are performed on a single sample and
thus it is guaranteed that the same conditions are met
during the data gathering, which might not be evident
for successive experiments with various instruments.
. checking of the validity and assumptions in converting
frequency shifts and quality factor (damping) variations
as measured by the QCM to mass changes (using the
Sauerbrey equation).
Although the combination of several measurement
techniques has shown promising progress by obtaining
complementary results,3) simultaneous measurements using
AFM and QCM have not yet been performed to our
knowledge.
We focused on precisely modeling the finite counter
electrode size in order to accurately predict the out-of-plane
displacement which also leads to frequency fluctuations
when an obstacle (AFM cantilever holder) is brought close
to the QCM surface because of the acoustic longitudinal
waves generated in the liquid medium.4)
2.
Simulation Tools
We used the open-source software Modulef,5) latest
release as of September 2001, developed by INRIA (France)
for simulating a cylindrical AT-cut quartz crystal resonator
patterned with finite sized electrodes.
The piezoelectric properties of quartz were defined using
the tabulated values found in ref. 6 and rotated to fit the AT
3.
Static Simulations
Our first approach is to apply a DC voltage between the
electrodes deposited on opposite surfaces of the quartz
resonator. We monitor the spatial distribution of the
displacement field while keeping the position of the sensing
electrode fixed.
We simulate a 14-mm-diameter quartz resonator 400 m
thick, fitted with a 5-mm-diameter massless counter
electrode on which the DC potential (0.5 V, Fig. 2 left) is
applied while the sensing electrode completely covers the
top side of the QCM and is grounded. The total number of
points used for this 3D simulation is 3320, which define
2040 pentaedral finite elements and 1280 hexaedral elements
(Fig. 1). The results of this simulation are as follows:
. the maximum static displacement in the X direction is
1.075 pm, Fig. 3, left,
. the maximum static displacement in the Y direction is
0.126 pm, Fig. 3, right, and
. the maximum static displacement in the Z direction is
0.102 pm, Fig. 2, right.
As expected from an analytical resolution for an infinite
plate, the displacement field is mainly oriented in the X axis
direction (Fig. 1, right).
Inside the volume defined by a vertical cylinder above the
counter electrode, the displacement is mainly parallel to the
X direction, while discrepencies in this behaviour appear on
the frontier of the counter electrode. These results for the X
direction are in close agreement with previous analytical
results presented in refs. 8–10 and they bring new insight to
the Z displacement of the QCM which cannot be analyzed
using an analytical formula which assumes an infinite
electrode surface. The displacement normal to the electrode
plan, about one tenth of the in-plane displacement, is much
larger than previously estimated9) and explains the origin of
the large component of longitudinal waves generated by the
QCM in the surrounding liquid.
4.
Dynamic Simulations
With the intention of achieving conditions closer to the
experimental conditions, a simulation of the dynamic
oscillation of the quartz resonator should be performed in
3974
Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 6A
J.-M. FRIEDT et al.
Z
3975
Z
O
O
Y
X
Y
X
Fig. 1. Final 3D structure after defining the mesh (left), and the displacement field after resolution of the problem (right).
2862
9684
2040
1280
Z
O
X
Y
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
NODES
FACES
PENTAEDRA
HEXAEDRA
4.9750E-04
4.7367E-04
4.4735E-04
4.2102E-04
3.9469E-04
3.6837E-04
3.4204E-04
3.1571E-04
2.8939E-04
2.6306E-04
2.3673E-04
2.1041E-04
1.8408E-04
1.5775E-04
1.3143E-04
1.0510E-04
7.8774E-05
5.2448E-05
2.6121E-05
-2.0539E-07
2862
9684
2040
1280
Z
O
X
Y
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
NODES
FACES
PENTAEDRA
HEXAEDRA
1.0083E-07
9.1142E-08
8.0432E-08
6.9721E-08
5.9011E-08
4.8301E-08
3.7590E-08
2.6880E-08
1.6170E-08
5.4592E-09
-5.2511E-09
-1.5961E-08
-2.6672E-08
-3.7382E-08
-4.8092E-08
-5.8803E-08
-6.9513E-08
-8.0223E-08
-9.0934E-08
-1.0164E-07
Fig. 2. Display of the DC potential (voltage, in kV) distribution (equipotential lines range from 0.5 V to 0:2 mV) and the amplitude of
the out-of-plane (Z) displacement (equidisplacement lines range from 0.1 pm to 0:1 pm).
2862
9684
2040
1280
Z
O
X
Y
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
NODES
FACES
PENTAEDRA
HEXAEDRA
1.0698E-06
1.0177E-06
9.6006E-07
9.0247E-07
8.4488E-07
7.8728E-07
7.2969E-07
6.7210E-07
6.1451E-07
5.5692E-07
4.9932E-07
4.4173E-07
3.8414E-07
3.2655E-07
2.6896E-07
2.1136E-07
1.5377E-07
9.6180E-08
3.8588E-08
-1.9003E-08
2862
9684
2040
1280
Z
O
X
Y
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
NODES
FACES
PENTAEDRA
HEXAEDRA
1.2457E-07
1.1232E-07
9.8787E-08
8.5251E-08
7.1715E-08
5.8179E-08
4.4643E-08
3.1107E-08
1.7571E-08
4.0351E-09
-9.5009E-09
-2.3037E-08
-3.6573E-08
-5.0109E-08
-6.3645E-08
-7.7181E-08
-9.0717E-08
-1.0425E-07
-1.1779E-07
-1.3133E-07
Fig. 3. Display of the amplitude of the displacement in the two in-plane directions (main displacement axes X and Y). Lines of equal
displacement are displayed in m.
order to directly obtain the displacement field enhanced by
the mechanical resonance. This approach presents two major
difficulties:
. in a simulation without damping, the displacement field
for any frequency other than the resonance frequency is
the same as in the DC mode, and the displacement field
is expected to diverge when the resonance frequency is
met.
. when including the damping, the losses that are
dependent on the experimental conditions and the
imaginary part ij (i; j 2 ½1; 6) of the stiffness constants
(i.e., the damping coefficient) are extremely difficult to
estimate. Using the relation7) ij ¼ Cij =ðQij !0 Þ, where
Qij ¼ Q is the quality coefficient (estimated to be equal
to the experimentally observed quality factor Q for all i
and j), !0 the mechanical resonance pulsation and Cij
the real part of the mechanical stiffness constants, leads
to a conclusion similar to enhancing the static
displacement field by a factor Q9) for estimating the
dynamic displacement field.
Hence, we have not focused on obtaining additional
results using dynamic mode simulations which are not
expected to display any new results compared to the static
mode simulation, and we now extend the results obtained
from simulations with a DC electrical field to the dynamic
oscillation by introducing the quality factor Q.
3976
Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 6A
J.-M. F RIEDT et al.
Following these conclusions, we extend the static results
to the dynamic behaviour expected to occur at resonance by
using9) the formula Adynamic ¼ Astatic Q, where Adynamic is
the oscillation amplitude at resonance and Astatic is the
previously computed DC displacement. Since we observe
that our QCMs display quality factors in the 1000 to 3000
range when oscillating in liquid at the resonance frequency
(4.7 MHz), the results are as follows (for Q ¼ 2000):
. the maximum dynamic displacement in the X direction
is 2.1 nm,
. the maximum dynamic displacement in the Y direction
is 0.25 nm, and
. the maximum dynamic displacement in the Z direction
is 0.20 nm.
These results are in agreement, once normalized for the
quality factor, with the measurements obtained by Borovsky
et al. using an STM under vacuum.11)
5.
Experimental QCM Frequency Fluctuations Measurements
We have designed a combined QCM-AFM instrument
(Fig. 4) based on the scanning probe microscope developed
by molecular imaging (Phoenix, USA), with the QCM
probing electronics provided by Q-Sense AB (Göteborg,
photodetector
laser beam
inlet
tubing
glass prism
6.
outlet
tubing
teflon liquid cell
AFM cantilever
Sweden) and laboratory built quartz crystal resonators
designed to oscillate at around 4.7 MHz by coating a 14mm-diameter AT-cut quartz wafer with 50 nm Ti and 50 nm
Au. The output amplitude of the Q-Sense instrument was
measured to be in the 200 mVpp range.
We have experimentally (Fig. 5) observed in the combined QCM-AFM instrument the frequency drift of the
QCM due to the AFM cantilever holder approach, as well as
frequency fluctuations of the quartz crystal resonator during
image scans (1 1 m2 ). We have observed that the first
oscillation mode of the QCM (at 4.7 MHz) is the most
sensitive to these environmental changes, as expected on the
basis of its wider spread over the sensing electrode
surface.12)
Figures 5 and 6 display the influence of the position of the
cantilever holder on the standing wave pattern generated
between the QCM and cantilever holder surfaces, in the first
case during the tip approach and in the second case during a
protein adsorption experiment. The first mode appears to be
much more sensitive to the disturbances due to environmental variations than the higher order modes (the third and
fifth overtones were also measured during this study). As
expected,4) the peaks for the third mode are three times
narrower and closer than the peak displayed for the first
mode (since the wavelength of the standing wave is divided
by 3 when the oscillation frequency is multiplied by 3).
viton O-ring
QCM
Q
Sense QCM parameters measurement setup
Fig. 4. Experimental setup of the combined QCM and AFM instrument,
based on a commercial AFM designed by molecular imaging and a QCM
parameter analysis instrument built by Q-Sense AB (Göteborg, Sweden).
When used in combination with an AFM, the QCM will
not visibly modify the image shape because of its oscillation.
The step range of a typical 1-m-wide, 256 pixel image is
4 nm, smaller than the in-plane oscillation of the quartz
resonator. Similarly, the out-of-plane oscillation will not
affect the resolution of the AFM for typical measurements in
liquid. The main visible interactions are through the longrange longitudinal acoustic waves launched by the QCM
which create standing wave patterns when reflected against
the AFM cantilever holder. However, the tip displacement
and position (tip-electrode distance) feedback then affect the
frequency stability of the QCM and thus its sensitivity.
80
80
approach
60
60
(141 um)
40
f1
40
f
1
100
20
-20
-20
-40
350
400
450
approach
(141 um)
0
f d curve
300
withdraw
(141 um)
20
0
-40
250
Discussion
500
550
-60
600
0
50
100
150
200
time (s)
250
300
350
400
0
50
100
150
200
time (s)
250
300
350
400
time (s)
20
20
15
15
10
f3
3
10
f
f d
curve
look for
resonance freq.
of cantilever
5
5
0
0
-5
-5
-10
250
-10
300
350
400
450
time (s)
500
550
600
-15
Fig. 5. Graphs displaying the effect of longitudinal waves on the frequency stability of the resonator (top graphs show the evolution of
frequency of the first mode, bottom graphs show the evolution of frequency of the third mode). Total displacement during cantilever
approach is 141 m, which is quite close to the theoretical half-wavelength of an acoustic wave propagating in water at 5 MHz
(152 m.4)).
Jpn. J. Appl. Phys. Vol. 41 (2002) Pt. 1, No. 6A
J.-M. FRIEDT et al.
3977
Fig. 6. Sensitivity of the various modes (1, 3 and 5 from left to right) of the QCM to environmental disturbances including hydrostatic
pressure changes when inserting a new sample using the peristatic pump, image scans and protein adsorption (here 2.5 g/ml human
plasma fibrinogen at date 4075 and 15 to 20 g/ml human plasma fibrinogen at date 5530) on the gold-coated grounded electrode. Top
graphs show the frequency variations while bottom graphs display the changes in damping (inverse of the quality factor). The first
mode is obviously the one most affected by environmental disturbances.
7.
Conclusions
We have demonstrated the following using finite element
analysis:
. the in-plane displacement of a resonator oscillating in
liquid with a quality factor in the 1000 to 3000 range is
at maximum in the nm range, typically 1 to 3 nm, when
a 0.5 Vpp sine wave voltage is applied to the resonator,
and
. the out-of-plane displacement of the resonator is about
one tenth of that of the in-plane displacement. Such a
conclusion leads, for a resonator oscillating in liquid
with a quality factor in the 1000 to 3000 range, to an
out-of-plane displacement in the angström range. This
out of plane displacement is a direct reflection of the
finite size of the counter electrode.
The out-of-plane oscillation results in longitudinal waves
being emitted in the liquid, which create standing waves
when they bounce off a planar obstacle parallel to the
electrode located a few microns to a few hundred microns
above the surface (depending on the position of the AFM
cantilever holder during approach and scan). The interaction
of the standing wave pattern and the crystal resonator is the
source of the frequency fluctuations observed during the
approach of the AFM cantilever holder towards the QCM
surface.
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