U.S. patent application number 16/641540 was filed with the patent office on 2020-08-06 for atomic force microscopy cantilever, system and method.
The applicant listed for this patent is Nederlandse Organisatie voor toegepast-natuurwetenschappelijk onderzoek TNO. Invention is credited to Hamed Sadeghian Marnani, Maarten Hubertus Van Es.
Application Number | 20200249255 16/641540 |
Document ID | / |
Family ID | 1000004825366 |
Filed Date | 2020-08-06 |
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United States Patent
Application |
20200249255 |
Kind Code |
A1 |
Van Es; Maarten Hubertus ;
et al. |
August 6, 2020 |
ATOMIC FORCE MICROSCOPY CANTILEVER, SYSTEM AND METHOD
Abstract
The surface of the atomic force microscopy (AFM) cantilever is
defined by a main cantilever body and an island. The island is
partly separated from the main body by a separating space between
facing edges of the main body and the island. At least one bridge
connects the island to the main body, along a line around which the
island is able to rotate through torsion of the at least one
bridge. The island has a probe tip located on the island at a
position offset from said line and a reflection area. In an AFM a
light source directs light to the reflection area and a light spot
position detector detects a displacement of a hght spot formed from
light reflected by the reflection area, for measuring an effect of
forces exerted on the probe tip.
Inventors: |
Van Es; Maarten Hubertus;
(Voorschoten, NL) ; Sadeghian Marnani; Hamed;
(Nootdorp, NL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Nederlandse Organisatie voor toegepast-natuurwetenschappelijk
onderzoek TNO |
's-Gravenhage |
|
NL |
|
|
Family ID: |
1000004825366 |
Appl. No.: |
16/641540 |
Filed: |
August 23, 2018 |
PCT Filed: |
August 23, 2018 |
PCT NO: |
PCT/NL2018/050551 |
371 Date: |
February 24, 2020 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01Q 20/04 20130101;
G01Q 60/38 20130101; G01Q 70/10 20130101; G01Q 70/14 20130101 |
International
Class: |
G01Q 60/38 20060101
G01Q060/38; G01Q 20/04 20060101 G01Q020/04; G01Q 70/10 20060101
G01Q070/10 |
Foreign Application Data
Date |
Code |
Application Number |
Aug 24, 2017 |
EP |
17187809.3 |
Claims
1. A cantilever for use in an atomic force microscopy (AFM) system,
the cantilever comprising: a main body, the main body forming a
part of a surface of the cantilever; an island, the island forming
a further part of the surface of the cantilever, the island being
partly separated from the main body by a separating space between
facing edges of the main body and the island; at least one bridge
connecting the island to the main body along a line around which
the island is able to rotate through torsion of the at least one
bridge; a reflection area located on the island; and a probe tip
located on the island at a position offset from the line.
2. The cantilever according to claim 1, wherein the at least one
bridge consists of a first bridge and a second bridge, the first
bridge and the second bridge connecting the island to the main body
on opposite sides of the island, wherein the island lies within an
outline of the main body.
3. The cantilever according to claim 1, wherein the main body is
mass balanced with respect to the line.
4. The cantilever according to claim 1, wherein the line extends
along a direction of a longest size of the cantilever.
5. The cantilever according to claim 1, wherein the main body of
the cantilever has an uneven mass distribution m(x) as function of
position x between ends of the cantilever, an average of a product
m(x)*u.sup.2(x) of the mass m(x) and a squared mode shape
u.sup.2(x) as a function of position x along the cantilever divided
by an average of u.sup.2(x) being larger for a contact vibration
mode of order N, with N greater than one, than for a contact
vibration mode of order one.
6. The cantilever according to claim 1, wherein the main body of
the cantilever has an uneven mass distribution m(x) as function of
position x between ends of the cantilever the mass distribution
having a maximum at a belly of a contact vibration mode of order N,
with N greater than one.
7. The cantilever according to claim 1, wherein the main body
comprises: a main portion, a neck portion and a head portion,
wherein the neck portion lies between the main portion and the head
portion, wherein the neck portion has a smaller width than the main
portion and the head portion, wherein the cantilever comprises a
further reflection area located on the head portion, wherein a
difference between a contact resonance frequency of the main body
and a resonance frequency of orientation changes of the head
portion relative to the main portion due to bending of the neck
portion being less than the quality factor of the resonance of said
orientation changes of the head portion times the resonance
frequency of the resonance of the orientation changes of the head
portion.
8. An atomic force microscopy (AFM) system comprising: a cantilever
comprising: a main body, the main body forming a part of a surface
of the cantilever; an island, the island forming a further part of
the surface of the cantilever, the island being partly separated
from the main body by a separating space between facing edges of
the main body and the island; at least one bridge connecting the
island to the main body along a line around which the island is
able to rotate through torsion of the at least one bridge; a
reflection area located on the island; and a probe tip located on
the island at a position offset from the lien around which the
island is able to rotate; a light source positioned to direct a
light to the reflection area; and a light spot position detector
positioned to detect a displacement of a light spot formed from
light reflected by the reflection area, for using said displacement
to measure an effect of forces exerted on the probe tip by a
surface of a sample.
9. The AFM system according to claim 8, further comprising: a
sample platform; a vibration generator coupled to the platform
and/or the cantilever for generating vibration in the sample and/or
the cantilever, a first end of the cantilever being fixed in said
vibration; an actuator for moving the cantilever and the platform
relative to each other, at least in a height direction
perpendicular to the surface of the sample and a scan direction
parallel to the surface of the sample; a control circuit configured
to; control the actuator to move the cantilever and the platform
relative to each other progressively in the scan direction;
activate the vibration generator to generate vibrations of the
sample relative to the cantilever at a frequency of a contact
resonance mode of the cantilever, measure properties of vibration
of the cantilever in the contact resonance mode from a first
component of the displacement during movement of the cantilever and
the platform relative to each other in the scan direction; and
control the actuator to move the cantilever and the platform
relative to each other in the height direction in a feedback loop
in response to a second component of the displacement during
movement in the scan direction.
10. The AFM system according to claim 9, wherein the light spot
position detector is configured to distinguish light spot
displacements in a first dimensional direction and a second
dimensional direction that differs from the first dimensional
direction, wherein the control circuit is configured to derive the
first component of the displacement and the second component of the
displacement from the light spot displacements in the first
dimensional direction and the second dimensional direction,
respectively.
11. The AFM system according to claim 9, wherein the feedback loop
comprises a low pass frequency filter to filter the second
component of the displacement from an output of light spot position
detector.
12. A cantilever for use in an atomic force microscopy (AFM)
system, the cantilever comprising: a main body, having an uneven
mass distribution m(x) as function of position x between ends of
the cantilever, an average of a product m(x)*u.sup.2(x), of the
mass m(x) and a squared mode shape u.sup.2(x) as a function of
position x along the cantilever, divided by an average of
u.sup.2(x) being larger for a contact vibration mode of order N,
with N greater than one, than for a contact vibration mode of order
one; a reflection area located on the cantilever; and a probe tip
on the cantilever at a node of the contact vibration modes.
13. The cantilever according to claim 12, wherein the mass
distribution has a maximum at a belly of the contact vibration mode
of order N.
14. A cantilever comprising a main portion, a neck portion and a
head portion and a probe tip on the main portion, the neck portion
lying between the main portion and the head portion, the neck
portion having a smaller width than the main portion and the head
portion, wherein the cantilever comprises a reflection area located
on the head portion, wherein a difference between a contact
resonance frequency of the main portion and a resonance frequency
of orientation changes of the head portion relative to the main
portion due to bending of the neck portion is less than the quality
factor of the resonance of said orientation changes of the head
portion times the resonance frequency of the resonance of the
orientation changes of the head portion.
15. A method carried out by a cantilever for atomic force
microscopy (AFM), wherein the cantilever comprises: a main body,
the main body forming a part of a surface of the cantilever; an
island, the island forming a further part of the surface of the
cantilever, the island being partly separated from the main body by
a separating space between facing edges of the main body and the
island; at least one bridge connecting the island to the main body
along a line around which the island is able to rotate through
torsion of the at least one bridge; a reflection area located on
the island; and a probe tip located on the island at a position
offset from the line; and wherein the method comprises: generating
vibration of a sample relative to the cantilever at a frequency of
a contact resonance mode of the cantilever; moving the cantilever
and the platform relative to each other, at least in a height
direction perpendicular to the surface of the sample and a scan
direction parallel to the surface of the sample; directing light at
the reflection area and measuring displacement of a light spot due
to light reflected by the reflection area; measuring properties of
vibration of the cantilever in the contact resonance mode from a
first component of the displacement during movement of the
cantilever and the platform relative to each other in the scan
direction; controlling movement of the cantilever and the platform
relative to each other in the height direction in a feedback loop
in response to a second component of the displacement during
movement in the scan direction.
Description
FIELD OF THE INVENTION
[0001] The invention relates to a cantilever for use in an atomic
force microscopy system, to an atomic force microscopy system and
an atomic force microscopy method.
BACKGROUND
[0002] Atomic Force Microscopy (AFM) can be used to form images of
sample surfaces. Moreover, it is known to map structures buried
below the surface using AFM. In an article titled "Detection of
buried reference structures by use of atomic force acoustic
microscopy" by A. Striegler et al. published in Ultramicroscopy 111
(2011) 1405-1416 the possibility of the imaging buried structures
has been shown. Such measurements make use of the effect that
vibration of the surface of buried structures within the sample
will result in sample surface vibration. Vibrations of buried
structures can be excited e.g. due to excitation of vibrations of
the sample surface, which may reach the buried structure as
ultrasound waves.
[0003] AFM is an improvement of Atomic Tunnel Microscopy (ATM). In
ATM movement of the tip perpendicular to the sample surface is
controlled in a feedback loop to maintain a constant electric
current through the tip while the relative position of the sample
and probe tip is scanned in a direction parallel to the surface of
the sample to sense the forces as a function of position on the
sample. AFM more generally measures the effect of forces exerted on
the probe tip in interaction with atoms of the sample. AFM makes
use of a probe tip on a cantilever to sense forces between the
probe tip and atoms on the surface of a sample. In particular,
properties of (near) resonant cantilever vibration may be measured
to sense forces.
[0004] The forces between the probe tip and the sample can be
sensed from their effect on the vibration resonance frequency
and/or quality, the phase and/or amplitude relation between the
cantilever vibration phase/amplitude and ultrasound
phase/amplitude. Different kinds of force interaction between the
probe tip and the sample are possible.
[0005] As is known per se any mechanical object like a cantilever
has a plurality of resonance modes, wherein each resonance mode
corresponds to a resonance frequency and a spatial mode pattern of
vibration amplitude and phase relations. The cantilever is able to
vibrate freely with a sinusoidal time dependence at the resonance
frequency and a spatial pattern with vibration amplitudes in
proportion to the amplitudes of the mode pattern and phase
relations between vibrations at different positions according to
the phase relations of the mode pattern. The amplitude and phase of
any vibration of the cantilever can be represented as a sum of such
mode patterns, each with its own applied amplitude factor and
phase. In periodically driven vibrations, the amplitude factors
become large for the modes of which the resonance frequency are the
same or nearly the same as the excitation frequency. Thus, with
excitation frequencies near the resonance frequency of a mode, the
cantilever vibration substantially corresponds to the mode pattern.
Spatial positions in the mode pattern where the amplitude is zero
are called "nodes" and spatial positions of local maxima of the
amplitude of the mode patterns are called "bellies".
[0006] In "tapping" resonance the probe tip is located at a belly
of the resonance mode, so that the tip and the sample exchange
intense "tap" force peaks in brief, periodic time intervals without
significant interaction outside these time intervals. In contact
resonance, the probe tip is located near a node of the resonance
mode, so that the tip and the sample exchange relevant forces
continuously, not only in brief time intervals and the tip and the
sample substantially stay in the same spatial relation. Tapping
resonance is useful to measure topographic measurements and contact
resonance is more useful to detect sub-surface structure. For both,
the cantilever vibration may be measured using reflection of
(laser) light from the cantilever, in which case AFM is also called
laser force microscopy.
[0007] U.S. Pat. No. 5,646,339 discusses an adaptation of the
cantilever to make it possible to measure the force exerted on the
probe substantially independently in three directions. In order to
do so a cantilever is used that has a plurality of excitation
modes, which differ from each other in that they have at different
resonance frequencies and involve movement in different directions.
Thus forces in different directions can be measured by measuring
response to excitation of vibrations with different frequencies. In
one example, a combination of a transversal vibration mode and a
torsional vibration mode is used. The vibrations are sensed by
heterodyne mixing of laser reflection from a force measurement
point positioned away from the probe tip, that moves in all the
modes.
SUMMARY
[0008] Among others it is an object to provide for an improved
Atomic Force Microscopy (AFM) system and method, which is
particularly suitable for mapping buried structures.
[0009] An AFM cantilever according to claim 1 is provided. The
probe tip of the cantilever is located on an island of the
cantilever that is connected to a main body of the cantilever by at
least one bridge along a line around which the island is able to
rotate through torsion of the at least one bridge. In this way, the
probe tip is located so that different types of cantilever
vibration modes, involving vibration of the main body and torsion
of the island can be excited substantially independently by the
interaction between the probe tip and the sample surface. The
bridge will transmit vibrations of the main body to the island, so
that they affect the orientation of the reflection surface. At the
same time rotation of the reflection surface also results in
orientation changes of the reflection surface, enabling measurement
of both. Such measurements may be performed one at a time or
simultaneously, using e.g. the frequency and/or directions of the
orientation changes to separate the effects of rotation of the
island and vibration of the main body. An AFM system is provided
that comprises such a light source positioned to direct light to
the reflection area and a light spot position detector positioned
to detect a displacement of a light spot formed from light
reflected by the reflection area, for using said displacement to
measure an effect of forces exerted on the probe tip by a surface
of a sample.
[0010] In an embodiment, the AFM system uses a first one of these
modes is used at near the resonance frequency in a contact
resonance mode and simultaneously a second one of these modes at a
low frequency in a feedback loop to control the distance between
the cantilever and the sample surface during a scan of the probe
tip along the sample surface.
[0011] In a embodiment of the cantilever, the island is preferably
mass balanced with respect to the line around which the island is
able to rotate. That is, the center of mass of the island lies in a
plane perpendicular to the top surface of the cantilever that runs
through this line and the parts of islands on opposite sides of
this plane have equal mass. This reduces coupling between rotation
of the island and vibration of the main body. However, an island is
with some mass imbalance of e.g. up to 40% and 60% or up to 25% and
60% of the mass of the island on opposite sides may also be
used.
[0012] The island may be located within an outline of the main
body, as viewed from above the top surface of the cantilever that
is parallel to the sample surface. In an embodiment of the
cantilever, the at least one bridge comprise only a first and
second bridge, the first bridge and the second bridge connecting
the island to the main body on opposite sides of the island, this
island lying within an outline of the main body. This makes it
easier to excite rotation of is island around the line on which the
bridges are located and reduces coupling between the rotation and
vibration of the main body.
[0013] In an embodiment, the main body is mass balanced with
respect to the line around which the island is able to rotate. That
is, the center of mass of the main body lies in a plane
perpendicular to the top surface of the cantilever that runs
through this line. In this way, coupling between vibration modes of
the main body and rotation modes of the islands is minimized.
[0014] In an embodiment of the cantilever, the line around which
the island is able to rotate extends along a direction of longest
size of the cantilever, from the fixed end of the cantilever to its
opposite end, e.g., when the surface of the cantilever has a
rectangular outline, parallel to the longest edge of the
cantilever. As another example, this line may extend perpendicular
to the longest direction. When the line extends along the direction
of longest size of the cantilever, the rotation of the island and
vibrations of the main body result in reflection displacements in
different directions, making it possible to separate their effect
on this basis.
[0015] In an embodiment of the cantilever, the main body of the
cantilever has an uneven mass distribution m(x) as function of
position x between the ends of the cantilever, an average of a
product m(x)*u.sup.2(x) of the mass m(x) and a squared mode shape
u.sup.2(x) as a function of position x along the cantilever divided
by an average of u.sup.2(x) being larger for a contact vibration
mode of order N, with N greater than one, than for a contact
vibration mode of order one. In this way the distance between
different order resonance modes of the main body can be reduced,
which makes it possible to reduce the frequency bandwidth needed to
measure effects of forces on a plurality of resonance modes of the
main body. This may also be used in cantilevers that do not have an
island as claimed in claim 1.
[0016] In an embodiment of the cantilever, the main body of the
cantilever has an uneven mass distribution m(x) as function of
position x between the ends of the cantilever the mass distribution
having a maximum at a belly of a contact vibration mode of order N,
with N greater than one. This is an effective way of reducing the
distance between different order resonance modes of the main body.
This may also be used in cantilevers that do not have an island as
claimed in claim 1.
[0017] In an embodiment of the cantilever the main body comprises a
main portion, a neck portion and a head portion, the neck portion
lying between the main portion and the head portion, the neck
portion having a smaller width than the main portion and the head
portion, the cantilever comprising a further reflection area
located on the head portion, a difference between a contact
resonance frequency of the main body and a resonance frequency of
orientation changes of the head portion relative to the main
portion due to bending of the neck portion being less that the
quality factor of the resonance of said orientation changes of the
head portion times the resonance frequency of the resonance of the
orientation changes of the head portion. This may also be used in
cantilevers that do not have an island as claimed in claim 1: in
that case the further reflection area may be the only reflection
area that is used. When used in combination with the island,
reflection from both the island and the head portion may be
measured. The head portion provides for more sensitive measurements
of vibration of the main body than the main body itself. Vibration
of the head portion will be driven by the main body, and it
provides larger orientation vibration amplitude than the
orientation vibration amplitude of the main body. The size of the
neck portion and/or the mass of the head portion may be adjusted to
tune the resonance frequency of the orientation changes of the head
portion relative to the main portion.
[0018] In an embodiment of the AFM system the AFM system comprises
a sample platform; a vibration generator coupled to the platform
and/or the cantilever for generating vibration in the sample and/or
the cantilever, a first end of the cantilever being fixed in said
vibration; an actuator for moving the cantilever and the platform
relative to each other, at least in a height direction
perpendicular to the surface of the sample and a scan direction
parallel to the surface of the sample; and a control circuit. The
control circuit may be configured, e.g. by means of a control
program of a programmable in the control circuit, to control the
actuator to move the cantilever and the platform relative to each
other progressively in the scan direction; activate the vibration
generator to generate vibrations of the sample relative to the
cantilever at a frequency of a contact resonance mode of the
cantilever; measure properties of vibration of the cantilever in
the contact resonance mode from a first component of the
displacement during movement of the cantilever and the platform
relative to each other in the scan direction, control the actuator
to move the cantilever and the platform relative to each other in
the height direction in a feedback loop in response to a second
component of the displacement during movement in the scan
direction. Thus contact resonance can be measured continuously
during the scan or at least most of the time during the scan.
[0019] In a further embodiment of the AFM system the light spot
position detector is configured to distinguish light spot
displacements in first and second, different two dimensional
directions, the control circuit being configured to derive the
first second component of the displacement from the light spot
displacements in the first and second two dimensional directions.
In this way the measurements of torsion of the island and vibration
of the main body that are transmitted to the island can be at least
partially separated based on the direction of the displacement.
[0020] In an embodiment of the AFM system the feedback loop
comprises a low pass frequency filter to filter the second
component of the displacement from an output of light spot position
detector. This provides for alternative or further of torsion of
the island and vibration of the main body that are transmitted to
the island.
[0021] In use the cantilever may be used by [0022] generating
vibration of a sample relative to the cantilever at a frequency of
a contact resonance mode of the cantilever; [0023] moving the
cantilever and the platform relative to each other, at least in a
height direction perpendicular to the surface of the sample and a
scan direction parallel to the surface of the sample; [0024]
directing light at the reflection area and measuring displacement
of a light spot due to light reflected by the reflection area;
[0025] measuring properties of vibration of the cantilever in the
contact resonance mode from a first component of the displacement
during movement of the cantilever and the platform relative to each
other in the scan direction [0026] controlling movement of the
cantilever and the platform relative to each other in the height
direction in a feedback loop in response to a second component of
the displacement during movement in the scan direction.
BRIEF DESCRIPTION OF THE DRAWING
[0027] These and other objects and advantageous effects will become
apparent of exemplary embodiments with reference to the following
figures.
[0028] FIG. 1 shows an AFM system
[0029] FIG. 2, 2a-c show an AFM cantilevers for contact resonance
mode measurement
[0030] FIG. 3 shows a control circuit
[0031] FIG. 4, 4a show an AFM cantilevers for contact resonance
mode measurement
[0032] FIG. 4b shows mode patterns
[0033] FIG. 5 shows an AFM cantilevers for contact resonance mode
measurement
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0034] FIG. 1 shows an AFM system (components not to scale)
comprising a cantilever 10, a light source 12, a light position
detector 14, an actuator 16, an ultrasound transducer 17 and a
control circuit 18. Cantilever has a fixed end connected to a
cantilever support 102. A probe tip 100 is located on cantilever 10
at a distance from the fixed end. A sample 19, which does not form
part of the AFM system per se, is shown to illustrate the operation
of the AFM system. In the illustrated embodiment, sample 19 is
located between ultrasound transducer 17 and cantilever 10, on a
sample platform 190 of the AFM system. A surface of sample 19 faces
cantilever 10. Probe tip 100 is directed from cantilever 10 towards
the surface of sample 19.
[0035] Actuator 16 is configured to move sample 19 and cantilever
10 relative to each other in directions transverse and parallel to
the surface of sample 19, so that probe tip 100 may be moved
parallel and transverse to the surface of sample 19 due to the
effect of actuator 16. For the sake of illustration an x and z
direction are indicated that are parallel and perpendicular to the
surface of sample 19. By way of example, an actuator 16 for
translating cantilever 10 in three directions relative to a base of
the AFM system is shown, with sample 19 fixed on the base. But
alternatively an actuator may be used that is configured to move a
sample platform for sample 19 or both the sample platform and
cantilever 10 relative to the base to realized movement in one or
more of the directions. Actuator 16 may comprise a plurality of
bodies of piezoelectric material coupled between the base of the
AFM system and cantilever 10 and/or the sample platform. Control
circuit 18 may be configured to apply voltages to these bodies of
piezoelectric material to cause motion. Alternatively, another type
of actuator may be used, such as a magnetic field driven actuator
or an actuator that is driven by electric forces without piezo
material.
[0036] Ultrasound transducer 17 may similarly comprise one or more
bodies of piezo electric material. Alternatively, other forms of
excitation may be used, such as photothermic excitation. In the
illustrated example ultrasound transducer 17 is used to excite
vibrations that travel to the probe tip through the sample, but
alternatively a transducer at a different location may be used to
excite at the same surface as where the probe tip is located, for
example via the probe tip or elsewhere on the surface.
[0037] Light source 12, which is preferably a laser light source,
is directed to transmit a light beam to a reflection area on
cantilever 10 and light position detector 14 is placed to receive
the light beam after reflection from the reflection area. The
entire upper surface of cantilever 10 may be reflective, or a part
of the upper surface that is equal to or larger than the reflection
area may be reflective. The reflection area is a part of this
surface that receives light from light source 12. A coating layer
or area of e.g. aluminum or gold may be provided at the upper
surface of cantilever 10 to provide for improved reflection. The
reflected light forms a light spot on light position detector 14.
Light position detector 14 may comprise four photodiodes, located
in respective quadrants. Alternatively another light spot position
detector may be used, such as an image sensor, or a pair of
adjacent photodiodes. Control circuit 18 has an input coupled to an
output of light position detector 14 and outputs coupled to control
inputs of actuator 16. FIG. 2 shows an exemplary cantilever
geometry that allows for vibration in different directions by the
main body of the cantilever and of an island 24 respectively. This
embodiment may be called a cantilever-in-cantilever geometry. In
this geometry, cantilever 10 has a rectangular outline, with a
fixed end 20 and a free end 22 on opposite sides of the rectangular
outline. Preferably fixed end 20 and a free end 22 are the shortest
edges of the rectangular outline. In FIG. 2, x and y directions are
indicated along the direction between fixed end 20 and free end 22
and perpendicular to that direction respectively. Fixed end 20 is
connected to the base of the AFM system, e.g. via the actuator (not
shown). Free end 22 is permanently connected to the base only
through cantilever 10 and fixed end 20.
[0038] Within the rectangular outline, cantilever 10 comprises an
island 24, in the form of an interior rectangle, that is connected
to a main body of cantilever 10 only at two connecting bridges
26a,b on two opposite edges of interior rectangle 24 along a
separation between the island and the main body, midway along these
opposite edges. As used herein, an island is a part of the
cantilever that, seen in top view, is connected to the main body of
the cantilever only via one or more connecting bridges that
interrupt the separation between the island and the main body of
the cantilever. In the illustrated embodiment, connecting bridges
26a,b extend only over part of the opposite edges, e.g. over less
than one fifth or one tenth of the opposite edges. The remainder of
the circumference of interior rectangle 24 is separate from the
main body of cantilever 10. Connecting bridges 26a,b may be an
integral part of the body of cantilever 10. The cantilever may be
formed from a body of material and cutting (e.g. laser cutting) or
etching through the body along the circumference of interior
rectangle 24, except at bridges 26a,b.
[0039] As illustrated, connecting bridges 26a,b are preferably
located on the central line (in the x-direction) midway the longest
edges of the rectangular outline of cantilever 10. The longest
direction of interior rectangle 24 may be perpendicular to this
central line, i.e. along the y-direction. Island 24 may be located
near free end 22, or more generally not closer to fixed end 20 than
to free end 22. A probe tip at a probe tip position 28 and a
reflection area 29 are provided on island 24 on the surfaces of
island 24 that face the sample and face away from the sample
respectively. As noted the upper surface of the island may be
intrinsically reflective or a reflective surface layer may be
added. The reflection area should be large enough to provide for
orientation dependent reflection of light from the light source,
e.g. with a direction dependent intensity that peaks in a peak
direction dependent on the orientation of the reflection surface.
The center of the probe tip position 28 is offset in the xy plane
from the line connecting bridges 26a,b (offset in the y-direction).
In the illustrated embodiment, probe tip position 28 and the
position of reflection area 29 are offset in the xy plane on
opposite sides of the line connecting bridges 26a,b. Alternatively,
reflection area 29 may be located on this line, or the probe tip
position 28 and the position of reflection area 29 may be offset in
the xy plane on the same side of that line.
[0040] The cantilever geometry with an interior rectangle connected
by bridges supports different vibration modes, which substantially
correspond to bending of the cantilever as a whole, and rotation of
island 24 around the line connecting bridges 26a,b due to torsion
of connecting bridges 26a,b respectively. In the mode that
substantially corresponds to bending of the cantilever as a whole
there is little or no rotation of island 24 and vice versa the same
applies to the mode that substantially corresponds to rotation of
island 24. Therefore, the resonance frequencies of these modes can
be adapted substantially independently, so that both are within
measurement range.
[0041] Preferably, the mass (volume) of the island 24 is much
smaller than that of the main body of the cantilever (e.g. less
than one fourth or one tenth), so that the main body has a
substantial mass involved in vibration of the cantilever. To ensure
that the resonance frequencies are far apart, bridges 26a, b that
are narrower than the cantilever, so that the stiffness that acts
against independent vibration of island 24 is small. Simultaneous
movement in more than one mode is provided for, by asymmetry of the
position of the position 28 probe tip with respect to the central
symmetry line (in the x-direction) of the main body of the
cantilever. In operation, control circuit 18 controls actuator 16
to scan (preferably translate) the relative position of sample 19
and cantilever 10 in one or two directions (x and/or y direction)
parallel to the surface of sample 19. During the scan, light source
12 directs a light beam at reflection area 29 on cantilever 10.
Reflection area 29 reflects the light beam to light position
detector 14, where it forms a light spot at a position that depends
on an orientation of reflection area 29.
[0042] In the illustrated embodiment, the two described modes
result in orientation changes of reflection area 29 around two
axes, which in turn result in light spot position changes in two
directions at light spot detector 14. Spot detector 14 detects
these position changes. For example, when a four quadrant light
detector 14 is used, relative changes of the resulting light
intensities detected by four quadrant light detector 14 are
indicative of changes of the position of the light spot and hence
the orientation of reflection area 29. Changes of the orientation
of reflection area 29 can be the result of bending of the main body
of cantilever 10 (rotation of reflection area 29 around the
y-direction as a result of bending of cantilever 10 in the x-z
plane,) and of rotation of island 24 relative to main body of
cantilever 10 (rotation of reflection area 29 around the x-axis in
a result of rotation the y-z plane,). Control circuit 18 is
configured to derive signals representing these two rotations, from
the light intensities that are detected by four quadrant light
detector 14.
[0043] In the illustrated embodiment control circuit 18 controls
ultrasound transducer 17 to excite ultrasound waves at the bottom
of sample 19. The ultrasound waves travel through sample 19. At
probe tip 100, vibrations of cantilever 10 are excited due to
effects of the ultrasound waves on the sample. In one embodiment
ultrasound transducer 17 is used to excite ultrasound waves at a
plurality of frequencies in the sample. Non-linear mixing effects,
e.g. between the sample and the probe tip, are used to produce
surface vibrations at a difference frequency. These surface
vibrations result in vibrations of cantilever 10. In turn, the
vibrations of cantilever (e.g. bending in the x-z plane) causes
periodic rotation of reflecting area 29, which causes periodic
deflection of light from light source 12 and periodic changes of
the output signals from light position detector 14. During the
scan, ultrasound transducer 17 is used to generate vibrations at a
frequency or frequencies that result in vibrations of cantilever 10
at or near a contact mode resonance frequency of cantilever 10.
[0044] As is known per se, contact resonance corresponds to a
resonance mode of cantilever 10 that has a node near the position
of probe tip 100. In the contact mode resonance, the surface
orientation of cantilever 10 at the node varies periodically. The
resonance frequencies of such cantilever modes may be computed
analytically or numerically using the Euler-Bernoulli equations of
cantilever vibration. Alternatively, one or more of such
frequencies may be determined experimentally.
[0045] In a contact resonance mode, probe tip 100 and sample 19
exchange relevant forces continuously. These forces are affected by
elastic and inelastic responses of the sample, including responses
due sub-surface structures near the surface. These responses in
turn affect resonance properties, such as the resonance frequency
and/or quality. This makes contact mode resonance suitable for
detecting and analyzing such sub-surface structures. Control
circuit 18 derives measurements of properties of the contact
resonance from these periodic changes. This is known per se. For
example, control circuit 18 may determine the amplitude and/or
phase of the periodic changes, and/or the resonance frequency
and/or quality. The latter two may be determined for example by
sweeping the excitation frequency and measuring amplitude and/or
phase of periodic changes during the sweep. Control circuit 18 is
configured to determine the resonance properties using a first
component of light spot position changes, which corresponds to
movements that are part of the contact resonance. For example, when
the mode that substantially corresponds to bending of the
cantilever as a whole is excited at or near the contact resonance
frequency, rotation of reflecting area 29 around the y-axis may be
measured for this purpose, by measuring in light spot movement in
the x direction (the longest direction of cantilever 10).
[0046] Control circuit 18 is configured to control the height of
cantilever above the surface of sample 19 in a feedback loop during
the scan, to keep the rotation of reflecting area 29 around the
other axis on average constant during the scan. Changes of this
rotation are due scanning motion rather than contact resonance
excitation. In the example wherein the mode that substantially
corresponds to bending of the cantilever as a whole is excited at
or near the contact resonance frequency, the rotation of island 24
around the x-axis relative to main body of cantilever 10 may be
kept on average constant during the scan. For this purpose, control
circuit 18 is preferably also configured to apply low pass
filtering to the signal that represents the rotation component of
reflecting area 29 that is perpendicular to rotation due to the
contact resonance, and to use the low pass filtered signal to
control the input signal of actuator 16 that controls the height of
cantilever 10. The low pass filter bandwidth is selected to ensure
suppression of frequency components at frequencies corresponding to
contact mode resonance frequencies.
[0047] Preferably, control circuit 18 is configured to measure the
rotation in response to contact resonance mode excitation
simultaneously with controlling the height of cantilever above the
surface of sample 19 in the feedback loop, or alternately using
measurements of rotation response and for control so that the
control of the height remains effective during measurement of the
rotation in response to this excitation. In theory, the feedback
control can be interrupted briefly during time intervals that are
so short that the height cannot vary significantly in these
intervals, but preferably it is continuous during the contact mode
resonance measurements.
[0048] Although a specific cantilever geometry with an island in
the form of an interior rectangle connected by bridges has been
shown, it should be appreciated that other geometries could be
used. For example, the island may have another shape in the
interior of the cantilever, such as an ellipse, or a polygon such
as a regular hexagon or a bow-tie and/or one of connecting bridges
26a,b may be omitted.
[0049] FIG. 2a-c show other examples of other layouts. In FIG. 2a,b
the position 28 probe tip and the position of the reflection area
29 are on a first part of the cantilever that is connected to the
remainder of the cantilever via a single bridge 26a, and this first
part is exterior to the remaining part, rather than surrounded by
the remaining part. In FIG. 2c, an internal island is shown that
rotates around a line in the y direction, by torsion of bridges
26a,b that extend in the y direction on opposite sides of the
symmetry line of the main body 20. Instead of rectangles other
shapes may be used for the first part or the bridge. It should be
noted that FIGS. 2, 2a-c do not show limitative examples. Other
layouts may be used.
[0050] Preferably, the probe tip is located offset from an axis of
rotation of the island around the bridge or bridges. This
facilitates excitation of rotation of this axis by the probe tip.
More preferably, the surface shape of the island is mirror
symmetric about a symmetry line on which the bridge or bridges are
located, or at least that the mass of the island is balanced with
respect to the axis of rotation, i.e. that the center of mass of
the island lies substantially on the axis of rotation. This reduces
coupling between the rotation of the island and vibration of the
main body of the cantilever. Preferably, the mass of main body is
balanced with respect to the axis of rotation of the island, e.g.
the bridge or bridges may lie on a line about which the main body
of the cantilever is mirror symmetric. This reduces coupling
between the rotation of the island and vibration of the main body
of the cantilever.
[0051] The reflection area is preferably located on the island, so
that the orientation of the reflection area will vary both with
vibration of the island and vibration of the main body of the
cantilever. The reflection area may be located over the rotation
axis of the island. When the surface of the main body of the
cantilever is mirror symmetric and the bridge or bridges are
located on the mirror symmetry line of the surface of the main
body, the orientation changes due to rotational vibrations of the
island and vibration of the main body modes are substantially
perpendicular, so that both can be measured substantially
independently of each other, from perpendicular motion components
of light spot movement.
[0052] However, although substantially perpendicular motions make
measurements easier, they are not indispensable. Low pass filtering
may be used to suppress the effect of contact resonance movement on
the feed back loop and/or the direction of the light spot movement
component used for the feedback may be set along a direction along
which the contact resonance movement has no effect. In other
embodiments a plurality of reflections areas may be used to measure
different displacement components. A first reflections area may be
located on the island and a second reflections area may be located
elsewhere. Displacements of separate light spots may be
measured.
[0053] The cantilever geometries of FIGS. 2, 2a, 2b and similar
geometries make it possible to optimize individual parts of the
geometry largely independently for feed back and contact resonance.
Preferably the part of the geometry whose motion is used for the
feed back is made less stiff than the part used for the contact
resonance. For example, when the rectangle in rectangle geometry is
used, the optical effect of rotation of the island around the axis
through bridges 26a,b may be used for the feed back. In this case,
narrow bridges 26a,b could be used to reduce stiffness of this
rotation and the remainder of the cantilever can be made to have a
higher stiffness for use in contact resonance measurements to
measure sub-surface structures. Similar optimizations may be used
in similar embodiments such as the embodiments of FIGS. 2a, b. The
cantilever geometries of FIGS. 2, 2a, 2b and similar geometries
also make it possible to maximize the separation between the motion
direction due to feedback and resonance.
[0054] FIG. 3 shows an exemplary embodiment of control circuit 18,
comprising a scan signal generator 30, a filter 32, a differential
amplifier 33, an oscillator 34 and a detector 36. Scan signal
generator 30 may comprise an oscillator with an x and/or y control
output coupled to an output or outputs 30a of control circuit for
connection to x and/or y movement control inputs of the
actuator.
[0055] An input of filter 32 is coupled to an input 32a of control
circuit for connection to a first output of the light spot position
detector, for a signal indicating spot displacement in a first
direction by the light spot position detector. Differential
amplifier 33 has first and second inputs coupled to an output of
filter 32 and a reference input. Differential amplifier 33 has a z
control output coupled to outputs 33a of control circuit for
connection to a z movement control input of the actuator.
[0056] Oscillator 34 is configured to oscillate at a frequency at
or near a resonance frequency of a contact vibration mode of the
cantilever. Oscillator 34 has an output coupled to an output 34a of
control circuit for connection to the ultrasound transducer. An
input of detector 36 is coupled to an input 32a of control circuit
for connection to a second output of the light spot position
detector, for a signal indicating spot displacement in a second
direction by the light spot position detector. Detector 36 may be a
synchronous detector, with an input for a reference signal or
signals from oscillator 34 at the frequency at or near a resonance
frequency of a contact vibration mode of the cantilever. In other
embodiments, oscillator 34 may be replaced by a pair of oscillators
configured to oscillate at frequencies spaced by that
frequency.
[0057] Although FIG. 3 shows the embodiment in terms of components
that may be realized as distinct circuits, control circuit 18 may
comprise a programmable computer and a memory wherein a computer
program is stored to configure the computer to implement part or
all of the different components of the embodiment of FIG. 3
digitally. In addition to the illustrated components, the computer
program may provide for pre-processing of the signals from the
light spot position detector and post-processing to the detected
vibration properties and for storing measurements in correspondence
with different scan positions of the generated x and/or y scan.
Alternatively, or in addition control circuit 18 may comprise
hardware components to implement part of all of the components.
[0058] Contact mode resonance for detecting and/or analyzing
effects of sub-surface structures usually provide only for
measurements in a limited stiffness variation range, because the
resonance frequency has an S-shape dependence on stiffness. To
provide for more ranges, or a larger range, with a single
cantilever it is desirable to be able to measure contact resonance
changes of a plurality of contact resonance modes. However, it is
undesirable to do so in a way that increases stiffness too much, as
this increases the risk of damage to the substrate surface. FIG. 4
illustrates a cantilever 40 design for increasing the number of
contact resonance modes that can be used for the measurements.
[0059] FIG. 4 shows a side view of another embodiment of a
cantilever 40 with a probe tip 400. Herein the thickness of
cantilever 40 varies unevenly as a function op position from the
fixed end 42 to the location of probe tip 400 (along the
x-direction). The variation of thickness is shown as an embodiment
of an uneven distribution of mass of cantilever 40 as a function op
position from the fixed end 42 to the location of probe tip 400.
Other embodiments of uneven mass distribution include variation of
the width of cantilever 40 (in the y direction, cf. FIG. 4a) and a
combination of variation of width and thickness. A maximum 44, or
maxima, of the mass distribution is or are located at the position
of a belly or bellies of a contact resonance mode of order N>1
that has node at probe tip 400 and a further node between probe tip
400 and fixed end 42. As shown, in FIG. 4, a single rise in the
height of the top surface in a belly may be used. Alternatively
rises at a plurality of bellies may be used, and/or lowered bottom
surface. Similarly, the width of cantilever 40 may be increased in
multiple bellies on both sides of cantilever 40 as shown in FIG.
4a, or in a single belly and/or or one side. Embodiments like FIG.
4, 4a and their variations may be used in combination with
embodiments like those of FIGS. 2, 2a, 2b, or on their own.
[0060] FIG. 4b illustrates mode patterns of orders N=1 and N=2 as a
function of x-positions with on the cantilever: the z displacement
at different x-positions is the product u(x)*f(t) of a mode
amplitude u(x) the mode pattern with a periodic time dependent
function f(t). The x-scale is in FIG. 4b is the same as in FIG. 4.
As is known per se, nodes 48 of a vibration mode are positions
along cantilever 40 at which the z-position does not change as a
result of vibration according to the vibration mode, i.e. where
u(x)=0 and bellies 46 are positions where the amplitude |u(x)| of
the z-position change is maximal. The number N of bellies 46 will
be referred to as the order N of the vibration mode.
[0061] The resonance frequency of the modes generally increases
with increasing order N. In practice, vibration in vibration modes
with resonance frequencies above that of a critical order Nc are
not detectable in an AFM. Often Nc=1 for contact resonances, so
that only the lowest order vibration contact resonance is
detectable. A typical maximum detectable resonance frequency in AFM
is 5 MHz.
[0062] Per se, addition of mass to a cantilever has the effect that
it reduces the resonance frequencies of its vibration modes. This
makes it possible to raise the critical order, e.g. to Nc=2.
However, the addition of mass also increases the stiffness of
cantilever 40, which increases the risk of damage to the substrate
or cantilever 40, and counteracts the effect on the resonance
frequency. The uneven mass distribution as a function of x position
with a maximum at a belly 46 of the contact vibration mode of order
N=2 makes it possible to improve the ratio between the reduction of
the resonance frequency and the increase of the stiffness for the
mode of order N=2. Thus, for example, the uneven distribution makes
it possible to accomplish the same reduction in resonance frequency
for the contact resonance more of order N=2 with less increase in
stiffness and hence less risk of damage. In this way contact
resonance modes of more others can be made detectable, e.g. up to
N=2, or even up to N=3 or N=4. With more resonance modes effects
deeper below the sample surface become detectable.
[0063] It should be appreciated that this ratio of the effect on
frequency and stiffness is maximal when the maximum or maxima of
the mass distribution are concentrated at the belly or bellies. But
such an optimum is not necessary to obtain at least some effect. An
effective unevenness suffices. Similarly, for a given mass spread,
it is optimal but not necessary locate the maximum or maxima of the
mass distribution at the position of the belly or bellies.
[0064] The effective unevenness can be quantified in terms of a
correlation coefficient C between the square of the mode amplitude
factor for a cantilever with evenly distributed mass and the actual
uneven mass. Such a correlation coefficient corresponds to
<m(x)*u.sup.2(x)>/<u.sup.2(x), i.e. the average, taken
over positions x along the length of the cantilever of the product
m(x)*u.sup.2(x) of the mass m(x) and the squared mode shape factor
u.sup.2(x) as a function of position x along the cantilever,
divided by the average of u.sup.2(x). The average kinetic energy of
mode motion is proportional to this correlation coefficient. When
the unevenness increases the ratio C(N.sub.h)/C(N.sub.l) of the
correlation coefficients of modes N.sub.h and N.sub.l (e.g.
N.sub.h=2 and N.sub.l=1) the ratio f(N.sub.h)/f(N.sub.l) of their
resonance frequencies decreases. Preferably, a mass distribution is
used that at least increase the ratio C(N.sub.h=2)/C(N.sub.l=1) for
the second and first mode. This can be realized by increasing the
mass around the bellies of the higher order mode Nh, e.g. by using
a mass distribution that has a maximum at the belly of the higher
order mode N.sub.h, preferably for N.sub.h=2 The embodiment with
the uneven mass increase of FIG. 4 may be combined with the
embodiment of FIG. 2 and its use to regulate the height during the
scan while contact mode resonance properties are measured.
Alternatively, the embodiment with the uneven mass increase may be
used separately from the embodiment of FIG. 2. The advantage of
using a combination of the embodiments of FIGS. 2 and 4 is that
more modes can be measured in parallel with use of the feedback
loop.
[0065] FIG. 5 shows a top view (in the xy plane) of another
embodiment of a cantilever 50 wherein the probe tip and the
reflecting surface lie in different parts of the cantilever that
have different motion properties. Cantilever 50 has a main portion
52, a neck portion 54 and head portion 56. In this embodiment neck
portion 54 lies between head portion 56 and main portion 52. A
plurality of neck portion 54 may be used in parallel between head
portion 56 and main portion 52. A cantilever 50 with a main portion
52 and a neck portion 54 would have two underlying types of
vibration: vibration of main portion 52 and vibration of head
portion 56, if the resonance frequencies of these vibrations would
not be close to each other.
[0066] The position of probe tip 500 lies in main portion 52,
between neck portion 54 and the fixed end 51 of cantilever 50. In
neck portion 54 the width of cantilever 50 is smaller than in head
portion 56 and main portion 52 that contains fixed end 53 and probe
tip 500. A reflection area 58 is provided on head portion 56.
[0067] The purpose of the smaller width in neck portion 54 is to
make the orientation changes of reflection area 58 as a result of
vibration of main portion 52 in contact resonance modes larger than
the orientation changes elsewhere on cantilever 50. This improves
detectability of vibration. Instead of the bridge-connected island
formed by head portion 56 other geometries may be used such as an
island connected by more than one bridge, an island within the main
portion of the cantilever and/or an island along the side of the
cantilever.
[0068] The orientation changes of the head portion due to bending
of neck portion 54 are mechanically similar to vibration of the
mass of head portion 56 under influence of a spring force provided
by neck portion 54, with a resonance frequency that is proportional
to the square root of the stiffness of neck portion 54 divided by
the mass of head portion 56. The width, thickness and/or the length
of neck portion 54 may be adjusted to change the stiffness of neck
portion 54 in order to tune the resonance frequency. Similarly, the
mass of head portion 56 may be changed to tune the resonance,
keeping the mass much smaller than that of main portion 52 (e.g.
less than 10% of the mass of main portion 52).
[0069] Preferably a difference between a contact resonance
frequency of main portion 52 and a resonance frequency of
orientation changes of head portion 56 relative to main portion 52
due to bending of neck portion 54 is less that the quality factor
of the resonance of said orientation changes of head portion 56
times the resonance frequency of the resonance of the orientation
changes of head portion 56 and preferably less than half that
product. As is known per se the quality factor characterizes a
resonator's bandwidth relative to its center frequency. The
resonance frequencies can be adjusted to be close to one another by
adjusting the mass and/or stiffness of head portion 56 and/or neck
portion 54 relative to those of main portion 52. Adding mass and
reducing stiffness reduces the resonance frequency and vice versa.
Suitable values may be determined experimentally or by
simulation.
[0070] As a result head portion 56 provides for more sensitive
measurements of vibration of main portion 52 than main portion 52
itself. Vibration of head portion 56 will be driven by the main
portion 52, and it provides larger orientation vibration amplitude
of head portion 56 than the orientation vibration amplitude of main
portion 52.
[0071] In contrast to the embodiments of FIG. 2, 2a, 2b, the head
portion 56 and main portion 52 and neck portion 54 are configured
so that resonance frequencies of resonance of the two underlying
types of vibration are selected to lie so close to one another that
this result in a mode pattern that strongly couples the vibration
mode patterns of underlying types of vibration of the head portion
and the main portion that would occur in the case of disparate
resonances frequencies of the head portion and the main
portion.
[0072] The embodiment with the neck portion of FIG. 5 may be
combined with the embodiment of FIGS. 2 and/or 3 and their use to
regulate the height and/or reduce the resonance frequency of the
higher order mode(s). In an embodiment the cantilever may have a
first and second reflecting surface, lying on a first and second
island part of the cantilever respectively, that are each connected
to the remainder of cantilever by one or more bridges. The probe
tip may lie on the first island, which may be configured as in FIG.
2 for example, and the second island may be configured as shown in
FIG. 5. In another or further embodiment, a further island with the
reflections surface may be connected to the island with the probe
tip. In an embodiment the cantilever may have an uneven mass
distribution as in the embodiment of FIG. 4 and an island with a
reflecting surface like head portion 56. Alternatively, the
embodiment with the neck portion of FIG. 5 may be used separately
from the embodiment of FIGS. 2 and/or 4. The advantage of using a
combination of the embodiments of FIGS. 5 and 2 or 4 is that larger
amplitude changes in light spot position are made possible in
combination with at least one of the modes.
* * * * *