Friction force microscope
View Patent ↗Provided is a friction force microscope that can measure a friction force by a cantilever in a quantitative manner. The friction force microscope includes a friction force calculating mechanism that calculates an effective probe height and a torsional spring constant of the cantilever from bending sensitivity determined from displacement information in a bending direction of the cantilever and torsional sensitivity determined from displacement information in a torsional direction of the cantilever, respectively, so as to use the calculated values for calculating the friction force.
1. A friction force microscope, comprising:
a cantilever including a probe at a free end portion thereof;
an X-Y drive mechanism for moving the probe on a sample surface opposed to the probe in an X-Y plane parallel to the sample surface;
a Z drive mechanism for moving the probe in a Z direction perpendicular to the sample surface;
displacement detection means for detecting displacement information of the cantilever in a bending direction and displacement information of the cantilever in a torsional direction; and
a controller configured to calculate a probe height h from a center of cantilever torsion to the tip of the probe and a torsional spring constant K t based on bending sensitivity determined from the displacement information of the cantilever in the bending direction and torsional sensitivity determined from the displacement information of the cantilever in the torsional direction, and calculate a friction force between the sample and the probe based on the calculated probe height h and torsional spring constant K t .
2. A friction force microscope according to claim 1 , wherein the controller is configured to calculate the probe height h according to the following equation:
h
=
(
L
-
d
)
·
S
DIF
S
FFM
·
G
FFM
G
DIF
where L denotes a length of a lever portion of the cantilever, d denotes a length parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe, S DIF denotes a ratio between a displacement signal and a displacement amount in the bending direction of the cantilever in the Z direction, G DIF denotes a displacement signal amplification factor in the bending direction of the cantilever in the Z direction, S FFM denotes a ratio between a displacement signal and a displacement amount in the torsional direction of the cantilever in an X-Y direction, and G FFM denotes a displacement signal amplification factor in the bending direction of the cantilever in the X-Y direction.
3. A friction force microscope according to claim 2 , wherein the controller is configured to calculate the torsional spring constant K t according to the following equation:
K
t
=
8
3
·
w
4
h
2
·
f
t
3
·
(
L
-
d
)
2
·
ρ
3
G
where L denotes a length of a lever portion of the cantilever, d denotes a length parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe, w denotes a width of the cantilever, f t denotes a resonance frequency of the cantilever in a torsional mode, ρ denotes a density of the cantilever based on a material of the cantilever, and G denotes a modulus of transverse elasticity based on the material of the cantilever.
4. A friction force microscope according to claim 1 , further comprising cantilever vibrating means for vibrating the cantilever in the Z direction, and wherein
the controller is configured to determine a resonance frequency f t in the torsional direction from frequency characteristics in the bending direction, which are obtained from a vibrating state acquired when the cantilever is swept in a predetermined frequency range close to a resonance frequency in the bending direction, and frequency characteristics in the torsional direction, which are obtained together with the frequency characteristics in the bending direction.
5. A friction force microscope according to claim 1 , wherein the controller is configured to measure a length L of a lever portion of the cantilever, a length d parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe and a width w of the cantilever based on one of an optical image or an electron image.
6. A friction force microscope according to claim 1 , wherein the controller is configured to calculate the torsional spring constant K t by the following equation:
K
t
=
8
3
·
w
4
h
2
·
f
t
3
·
(
L
-
d
)
2
·
ρ
3
G
where L denotes a length of a lever portion of the cantilever, d denotes a length parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe, w denotes a width of the cantilever, f t denotes a resonance frequency of the cantilever in a torsional mode, ρ denotes a density of the cantilever based on a material of the cantilever, and G denotes a modulus of transverse elasticity based on the material of the cantilever.
7. A method of determining a friction force using a friction force microscope which comprises a cantilever including a probe at a free end portion thereof; an X-Y drive mechanism for moving the probe on a sample surface opposed to the probe in an X-Y plane parallel to the sample surface; and a Z drive mechanism for moving the probe in a Z direction perpendicular to the sample surface, the method comprising:
detecting displacement information of the cantilever in a bending direction and displacement information of the cantilever in a torsional direction;
calculating parameters necessary for calculating a friction force between the sample and the probe from a torsional displacement signal based on the displacement information of the cantilever in the torsional direction, the parameters comprising a probe height h from a center of cantilever torsion to the tip of the probe and a torsional spring constant K t obtained based on the cantilever torsion, based on bending sensitivity determined from the displacement information of the cantilever in the bending direction and torsional sensitivity determined from the displacement information of the cantilever in the torsional direction, and
determining the friction force based on the calculated probe height h and torsional spring constant K t .
8. A method of determining a friction force using a friction force microscope according to claim 7 , wherein the probe height h is determined by the following equation:
h
=
(
L
-
d
)
·
S
DIF
S
FFM
·
G
FFM
G
DIF
where L denotes a length of a lever portion of the cantilever, d denotes a length parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe, S DIF denotes a ratio between a displacement signal and a displacement amount in the bending direction of the cantilever in the Z direction, G DIF denotes a displacement signal amplification factor in the bending direction of the cantilever in the Z direction, S FFM denotes a ratio between a displacement signal and a displacement amount in the torsional direction of the cantilever in an X-Y direction, and G FFM denotes a displacement signal amplification factor in the bending direction of the cantilever in the X-Y direction.
9. A method of determining a friction force using a friction force microscope according to claim 8 , wherein the torsional spring constant K t is determined by the following equation:
K
t
=
8
3
·
w
4
h
2
·
f
t
3
·
(
L
-
d
)
2
·
ρ
3
G
where L denotes a length of a lever portion of the cantilever, d denotes a length parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe, w denotes a width of the cantilever, f t denotes a resonance frequency of the cantilever in a torsional mode, ρ denotes a density of the cantilever based on a material of the cantilever, and G denotes a modulus of transverse elasticity based on the material of the cantilever.
10. A method of determining a friction force using a friction force microscope according to claim 7 , further comprising determining a resonance frequency f t in the torsional direction from frequency characteristics in the bending direction, which are obtained from a vibrating state acquired when the cantilever is swept in a predetermined frequency range close to a resonance frequency in the bending direction, and frequency characteristics in the torsional direction, which are obtained together with the frequency characteristics in the bending direction.
11. A method of determining a friction force using a friction force microscope according to claim 7 , wherein the measuring of a length L of a lever portion of the cantilever, a length d parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe and a width w of the cantilever is performed based on one of an optical image or an electron image.
12. A method of determining a friction force using a friction force microscope according to claim 7 , wherein the torsional spring constant K t is determined by the following equation:
K
t
=
8
3
·
w
4
h
2
·
f
t
3
·
(
L
-
d
)
2
·
ρ
3
G
where L denotes a length of a lever portion of the cantilever, d denotes a length parallel to the lever portion from an end portion of the cantilever on the probe side to a tip position of the probe, w denotes a width of the cantilever, f t denotes a resonance frequency of the cantilever in a torsional mode, ρ denotes a density of the cantilever based on a material of the cantilever, and G denotes a modulus of transverse elasticity based on the material of the cantilever.