Device for vibrating cantilever

There is disclosed a device for applying vibrations to a cantilever used in an atomic force microscope. The cantilever has a base portion, and a probe is attached to the front end of the cantilever. The device has a piezoelectric plate subassembly consisting of first and second piezoelectric plates having junction faces cemented together. A piezoelectric plate subassembly support portion supports a part of the second piezoelectric plate. A voltage is applied to the piezoelectric plates so that one of them is stretched vertical to the junction faces and that the other is contracted vertical to the junction faces.

FIELD OF THE INVENTION 
The present invention relates to a device for vibrating a cantilever used 
in a scanning probe microscope such as a noncontact atomic force 
microscope (i.e., attractive-mode atomic force microscope) and, more 
particularly, to a cantilever-vibrating device using piezoelectric plates. 
This kind of cantilever-vibrating device is used to vibrate a cantilever 
at its resonance frequency, the cantilever holding a probe at its front 
end. 
BACKGROUND OF THE INVENTION 
Where the topography of a sample surface is investigated by a scanning 
probe microscope such as a noncontact atomic force microscope (NC-AFM), it 
is necessary to maintain constant the space between the sample surface and 
the probe tip. Therefore, this space must be constantly detected. One 
method of accomplishing this is to utilize changes in the attractive 
atomic force (i.e., force gradient) exerted between the sample surface and 
the probe tip. That is, the attractive force increases as the space 
decreases. 
FIG. 6 illustrates a noncontact atomic force microscope (AFM) This 
microscope has a scanner support portion 01 that supports an XY scanner 02 
moving within the XY plane and a Z scanner 03 moving quite small distances 
along the Z-axis, or up and down. A sample 04 is placed on the top end 
surface of the Z scanner 03. An XY-scanning signal generator 06 and a Z 
scanner drive circuit 07 supply a scanning signal and a driving signal, 
respectively, to the XY scanner 02 and the Z scanner 03, respectively. 
A cantilever 08 made of a resilient material is positioned above the sample 
04. One end of the cantilever 08 is fixed to piezoelectric plates 09 that 
apply vibrations to the cantilever. A probe 012 is mounted to the front 
end of the cantilever 08 such that the tip of the probe 012 faces the 
sample 04. The piezoelectric plates 09 are made of bimorph and act to 
vibrate the cantilever 08. 
Heretofore, some methods have been available to detect the force gradient 
in the noncontact atomic force microscope described above. 
(a) Slope Detection Method 
FIG. 7 illustrates the slope detection method. The cantilever 08 is 
forcedly vibrated at a frequency of .omega..sub.d. The space S (FIG. 6) 
between the probe 012 on the cantilever 08 and the sample 04 varies. The 
resonance frequency of the cantilever 08 changes from .omega..sub.0 to 
.omega..sub.0 '. At this time, the amplitude of the cantilever varies. The 
result is shown in the graph of FIG. 7. Where the space S is reduced while 
the atomic force is exerted between the probe 012 and the sample 04, the 
resonance frequency of the cantilever 08 drops. 
As can be seen from the graph of FIG. 7, where the resonance frequency 
.omega..sub.0 of the cantilever 08 is moved away from the fixed frequency 
.omega..sub.d and reaches .omega..sub.0 ', the amplitude of the cantilever 
08 forcedly vibrated at .omega..sub.d decreases from A.sub.0 to A.sub.0 '. 
Accordingly, the changes in the space S can be detected by detecting the 
increases in the amplitude .DELTA.A. In this way, the slope detection 
method is to detect changes in the space S between the probe 012 and the 
sample 04 by detecting the decreases in the amplitude .DELTA.A. 
(b) FM Detection Method 
In FIG. 6, if the space S between the probe 012 of the cantilever 08 and 
the sample 04 varies, the resonance frequency of the cantilever 08 
changes. That is, where the space S decreases within the range in which an 
atomic force is exerted between the probe 012 and the sample 04, the 
resonance frequency of the cantilever 08 drops. Therefore, changes in the 
space S can be detected by vibrating the cantilever 08 at its resonance 
frequency at all times and detecting variations in the vibration frequency 
of the cantilever 08. In this method, the Q value of the mechanical 
vibration of the cantilever 08 becomes very large in a vacuum. Therefore, 
it is considered that the FM detection method is more appropriate than the 
slope detection method that is generally used under atmospheric pressure. 
In the above-described FM detection method, the cantilever 08 is vibrated 
always at its resonance frequency, and changes in the vibrational 
frequency of the cantilever are detected. Thus, changes in the space S are 
detected. Therefore, the degree of stability of the oscillating system 
containing the cantilever 08 greatly affects the performance of the 
instrument. That is, the ability to supply a stable oscillating signal to 
the cantilever-vibrating device dominates the performance of the 
instrument. The following techniques related to this kind of 
cantilever-vibrating device are known. 
FIG. 8 illustrates a noncontact atomic force microscope (AFM) equipped with 
a cantilever-vibration device making use of the prior art FM detection 
method. It is to be noted that like components, or 01-012, are indicated 
by like reference numerals in both FIGS. 6 and 8. A laser 013 directs 
laser light L onto the cantilever 08. The laser light reflected by the 
cantilever 08 reaches a photodetector 014, which detects the incident 
light. This photodetector 014 consists of two discrete photodiodes. The 
laser light L reflected from the top surface of the cantilever 08 
oscillates across the boundary between the two photodiodes. The difference 
between the output signals from the two discrete photodiodes is a sine 
wave corresponding to the vibrations of the cantilever 08. The oscillation 
frequency of the cantilever 08 is detected from this sine wave. 
The obtained oscillation signal is fed to an amplifier 017 whose gain is 
adjusted by an AGC (automatic gain control) circuit 016. This AGC circuit 
016 controls the gain of the amplifier 017 in such a way that the 
amplitude of the output signal from the photodetector 014 is kept 
constant. The output signal from the amplifier 017 is supplied to a 
band-pass filter 018, which extracts only frequencies close to the 
resonance frequency of the cantilever 08. The phase of the output signal 
from the band-pass filter 018 is adjusted by a phase-adjusting circuit 
019. The output signal from the phase-adjusting circuit 019 is supplied as 
a driving signal to the vibration-applying piezoelectric plates 09. As a 
result, a self-oscillating positive feedback loop is formed. Consequently, 
the cantilever 08 is vibrated at its resonance frequency. 
The output signal from the photodetector 014 is converted into a voltage 
signal by a frequency-to-voltage converter circuit 021. The voltage signal 
Vfv from the converter circuit 021 is sent to a reference voltage 
comparator 022. This comparator 022 produces the difference between the 
voltage signal Vfv and a reference voltage signal VfvO and sends a signal 
to the Z scanner drive circuit 07 via a low-pass filter 023 so that the 
difference (Vfv-VfvO) becomes zero. The reference voltage signal VfvO is a 
voltage corresponding to the preset-space between the probe 012 and the 
sample 04. 
The differential signal extracted via the low-pass filter 023 and a 
scanning signal from the XY scanning signal generator 06 are supplied to 
an image-creating circuit 024, which in turn creates a topographic image 
of the surface of the sample 04. 
The sample 04 is moved toward the probe 012 while the cantilever 08 is 
oscillating with a given amplitude, until an atomic force is exerted 
between the sample 04 and the probe 012. Then, the space is maintained 
constant. The surface of the sample 04 is scanned within the XY plane in 
two dimensions by the XY scanner 02. As the distance between the sample 04 
and the probe 012 decreases, the resonance frequency of the cantilever 08 
decreases by the effect of the atomic force acting on the probe 012. The 
cantilever 08 vibrates at reduced frequencies. As the distance between the 
sample 04 and the probe 012 increases, the cantilever vibrates with 
increasing frequency. At distances where the atomic force can be 
neglected, the vibration frequency is coincident with the resonance 
frequency of the cantilever 08 that is intrinsic to the cantilever. 
For example, if the surface of the sample 04 has a convex portion, and if 
the cantilever 08 vibrates at decreasing frequency as the distance between 
the probe 012 and the sample 04 decreases as a result of the 
two-dimensional scan made by the XY scanner 02, the voltage signal Vfv 
drops, thus increasing the differential signal. The Z scanner 03 
immediately lowers the sample 04 so that the distance to the probe 012 
increases, thus providing feedback control. Therefore, the distance 
between the probe 012 and the sample 04 is held at a given value 
determined by the reference voltage VfvO. Since this control is constantly 
provided, the feedback signal (differential signal) supplied to the Z 
scanner drive circuit 07 corresponds to the topography of the sample 
surface. This feedback signal is accepted as an image signal into the 
image-creating circuit 024 in relation to the two-dimensional scan made by 
the XY scanner 02. An image is displayed according to the accepted image 
signal. In this way, a topographic image of the surface of the sample 04 
owing to the atomic force can be displayed. 
The prior art technique has the following problems. Generally, the bimorph 
forming the vibration-applying piezoelectric plates 09 has a high degree 
of sensitivity. That is, these piezoelectric plates are displaced by large 
amounts when a unit voltage is applied. It is assumed that the cantilever 
08 has a spring constant of approximately 40 N/m and a resonance frequency 
of about 300 kHz. If this cantilever 08 is vibrated at its resonance 
frequency in an ultrahigh vacuum, the amplitude of vibrations at the tip 
of the cantilever 08 is tens of thousands times as large as the amplitude 
of the applied vibrations. Accordingly, if vibrations are applied, using 
piezoelectric plates having a relatively small sensitivity of about 1 
nm/V, and if the amplitude of the vibrations at the tip should be set to 
the order of nanometers, then the voltage applied to the piezoelectric 
plates is approximately 0.1 mV. This feeble voltage must be controlled 
within the oscillator circuit. As a result, the oscillation becomes 
unstable, and variations in the resonance frequency of the body of the 
cantilever due to the atomic force are detected with decreased 
sensitivity. 
SUMMARY OF THE INVENTION 
In view of the foregoing, the present invention has been made. It is an 
object of the present invention to provide a cantilever-vibrating device 
capable of vibrating piezoelectric plates at appropriate amplitudes stably 
by applying a voltage of an alternating magnitude that is easy to control. 
This object is achieved in accordance with the teachings of the invention 
by a device for applying vibrations to a cantilever having a base portion 
and probe at its front end, the device comprising: a piezoelectric plate 
subassembly consisting of a first and a second piezoelectric plates having 
their junction faces cemented together; a piezoelectric plate subassembly 
support member for supporting a part of the piezoelectric plate 
subassembly; and a voltage application means. The base portion of the 
cantilever is held by the second piezoelectric plate. The voltage 
application means applies a voltage to the piezoelectric plate subassembly 
such that alternating one of the first and second piezoelectric plates is 
stretched vertical, i.e. perpendicular, to the junction faces and that the 
other is contracted vertical, i.e. perpendicular, to the junction faces. 
Other objects and features of the invention will appear in the course of 
the description thereof, which follows.

DETAILED DESCRIPTION OF THE INVENTION 
Referring to FIG. 1, there is shown a noncontact atomic force microscope 
comprising a cantilever-vibrating device forming Embodiment 1 of the 
invention. FIG. 2 shows a piezoelectric plate subassembly included in the 
cantilever-vibrating piezoelectric plate subassembly included in the 
cantilever-vibrating device shown in FIG. 1. It is to be noted that like 
components are indicated by like components in FIGS. 1 and 8; however, "0" 
is omitted in FIG. 1 from every reference numeral. 
Referring to FIGS. 1 and 2, a piezoelectric plate subassembly support 
member 26 is mounted integrally with the body of the noncontact atomic 
force microscope and supports a piezoelectric plate subassembly 27 for 
applying vibrations. The piezoelectric plate subassembly 27 consists of 
two piezoelectric plates having different degrees of sensitivity. The 
subassembly 27 has a supported portion 27a in contact with the subassembly 
support member 26. The subassembly 27 further has a cantilever-supporting 
portion 27b on the opposite side of the supported portion 27a. The 
cantilever 8 is held to the cantilever-supporting portion 27b. 
The vibration-applying piezoelectric plate subassembly 27 consists of first 
piezoelectric plate 28 and second piezoelectric plate 29 that have 
junction faces 28a and 29a, respectively, extending parallel to the 
directions of polarization. These junction faces 28a and 29a are cemented 
together. These piezoelectric plates are polarized in opposite directions. 
Electrode surfaces 28b and 28c are formed vertical to the junction face 
28a. Electrode surfaces 29b and 29c are formed vertical to the junction 
face 29a. The electrode surfaces 28b and 29b are connected with the 
phase-adjusting circuit 21, while the electrode surfaces 28c and 29c are 
grounded. The junction faces 28a and 29a are adhesively or otherwise 
cemented together. 
In FIG. 2, the two piezoelectric plates 28 and 29 with different degrees of 
sensitivity are arranged so as to cancel out their displacements, i.e., 
the directions of polarization are opposite to each other. If the 
piezoelectric plates 28 and 29 of different degrees of sensitivity are 
made of lead titanate-based piezoelectric materials M1 and M5 produced by 
Fuji Ceramic Co., Ltd., Japan, so that displacements of these plates 28 
and 29 cancel out, their degrees of sensitivity are 4.3 nm/V and 4.7 nm/V, 
respectively, in d.sub.31 mode. Suppose that each of the piezoelectric 
plates 28 and 29 has a thickness of t and a length of .rho.. If a voltage 
V is applied, the amount of displacement, or sensitivity, of each of the 
piezoelectric plates 28 and 29 is given by 
EQU .DELTA..rho.=d.sub.31 .multidot..rho..multidot.V/t (1) 
where d.sub.31 is the equivalent piezoelectric constant of the d.sub.31 
mode. Assuming that t=.rho., the amount of displacement .DELTA.L of the 
piezoelectric plate subassembly is given by 
EQU .vertline..DELTA.L.vertline.=(4.7-4.3) nm/V=0.4 nm/V (2) 
Accordingly, where the amplitude of the piezoelectric plate subassembly is 
set to a few nanometers (e.g., 1 nm), the absolute value of the applied 
voltage is given by 
EQU 1 (nm)/0.4 (nm/V)=2.5 (V) (3) 
If the shape is so determined that the ratio of the length to the 
thickness, or t/.rho., is equal to 10, then it is necessary to apply a 
voltage of 25 V. It is to be noted that the aforementioned amplifier 17, 
AGC circuit 16, band-pass filter 18, and the phase-adjusting circuit 19 
together constitute a voltage application means. 
The operation of Embodiment 1 constructed as described above is next 
described. In FIG. 2, the vibrating piezoelectric plate subassembly 27 
supporting the cantilever 8 is vibrating at the resonance frequency of the 
cantilever 8. The piezoelectric plates 28 and 29 of the subassembly 27 are 
cemented together such that their directions of polarization are opposite 
to each other. Under this condition, the phase-adjusting circuit 19 
applies a driving voltage to the piezoelectric plates 28 and 29 such that 
the direction of the applied voltage is in the direction of polarization 
of one of the plates 28 and 29 and that the direction of the voltage is 
opposite to the direction of polarization of the other. At this time, if 
the piezoelectric plate 28 contracts, it is stretched vertical to the 
direction of polarization by an amount corresponding to the volume of this 
piezoelectric plate. If the piezoelectric plate 29 to which the voltage is 
applied in a direction opposite to the direction of polarization is 
stretched, the plate 29 contracts vertical to the direction of 
polarization by an amount corresponding to the volume of this plate. In 
consequence, their displacements cancel out. Therefore, if these two 
piezoelectric plates differ in amount of displacement, the 
vibration-applying piezoelectric plate subassembly 27 is displaced only an 
amount equal to the difference between their displacements. Therefore, if 
the driving voltage that is easy to control is applied to the 
piezoelectric plate subassembly 27, the amplitude of the vibration is not 
augmented exorbitantly. Rather, the body of the cantilever 8 vibrates 
stably. 
FIG. 3 is a view similar to FIG. 2, but showing Embodiment 2 of the 
invention. Embodiment 2 is similar to Embodiment 1 except for the 
following points. The piezoelectric plates 28 and 29 are cemented together 
so that they are polarized in the same direction. A voltage is applied to 
the piezoelectric plates 28 and 29 so that the direction of the voltage 
applied to one of the plates 28 and 29 is the same as the direction of 
polarization and that the direction of the voltage applied to the other is 
opposite to the direction of polarization. Embodiment 2 yields the same 
advantages as Embodiment 1 described above. 
FIG. 4 is a view similar to FIG. 2, but showing Embodiment 3 of the 
invention. Embodiment 3 is similar to Embodiment 1 except for the 
following points. The piezoelectric plates 28 and 29 have junction faces 
28a and 29a that are vertical to a common direction of polarization and 
cemented together. The junction faces 28a and 29a have electrodes 
electrically connected with the aforementioned phase-adjusting circuit 19. 
The supported portion 27a and the cantilever-supporting portion 27b have 
electrodes grounded. The phase-adjusting circuit 19 applies a driving 
voltage to the vibration-applying piezoelectric plate subassembly 27 such 
that the direction of the voltage applied to one of the plates 28 and 29 
is the same as the direction of polarization and that direction of the 
voltage applied to the other is opposite to the direction of polarization. 
If one of the piezoelectric plates 28 and 29 is contracted and the other 
is stretched, their displacements cancel out. Therefore, if the 
piezoelectric plates differ in amount of displacement, the piezoelectric 
plate subassembly 27 is displaced by an amount equal to the difference 
between their displacements. Therefore, if the driving voltage having a 
magnitude that can be easily controlled is impressed on the piezoelectric 
plate subassembly 27, the amplitude of the vibration is not augmented 
extremely. Rather, the cantilever 8 vibrates stably. 
FIG. 5 is a view similar to FIG. 2, but showing Embodiment 4 of the 
invention. Embodiment 4 is similar to Embodiment 3 except for the 
following points. The piezoelectric plates 28 and 29 are cemented together 
such that their directions of polarization are opposite to each other. 
Electrodes are formed on the junction faces 28a and 29a of the 
piezoelectric plates 28 and 29. Grounded electrodes are formed on the 
supported face 27a. Electrodes electrically connected with the 
phase-adjusting circuit 19 are formed on the cantilever-supporting face 
27b. A driving voltage is applied between the electrodes formed on the 
supported face 27a and on the cantilever-supporting face 27b. At this 
time, one of the piezoelectric plates 28 and 29 is stretched, while the 
other is contracted. Embodiment 4 produces the same advantages as 
Embodiment 3. 
While the preferred embodiments of the invention have been described in 
detail, it is to be understood that the invention is not limited to those 
embodiments but rather various changes and modifications are possible 
within the scope of the present invention delineated by the claims. For 
instance, the invention can be applied to a cantilever-vibrating device 
for use with a scanning probe microscope other than a noncontact atomic 
force microscope.