Method of determining a spring constant of a cantilever and scanning probe microscope using the method
View Patent ↗In a cantilever which is used in a scanning probe microscope or the like and has a trapezoidal cross-sectional shape formed through anisotropic etching in a silicon process, a cantilever spring constant is determined without measuring a thickness directly. A cantilever thickness is determined based on upper base and lower base lengths of the trapezoidal cross-sectional shape and geometric regularity of a surface generated by the anisotropic etching. Then, the cantilever spring constant is determined based on the cantilever thickness, a cantilever length, and a Young's modulus.
1. A method of manufacturing a cantilever for use in a scanning probe microscope, the method comprising:
anisotropically etching out the cantilever from monocrystal silicon to have cross-sections along a length of the cantilever in a form of an isosceles trapezoid, the cross-sections including a first flat surface corresponding to a lower base of the isosceles triangle, the first flat surface extensive along a (100) crystal plane of the monocrystal silicon, the cross-sections further including a second flat surface which is substantially parallel to the first flat surface and which corresponds to an upper base of the isosceles triangle, the cross-sections further including oblique side surfaces joining the first flat surface and the second flat surface, the oblique side surfaces extensive along a (111) crystal plane of the monocrystal silicon:
measuring widths of upper and lower bases of the trapezoid and a length of the cantilever; and
calculating the spring constant from Young's modulus (E), a secondary moment (I) of the cross-section of the cantilever, and the measured length (L) of the cantilever, wherein calculating the spring constant comprises calculating the secondary moment (I) from the measured widths of the upper and lower bases of the trapezoid, and an internal angle of the trapezoid defined by the predetermined crystal planes.
2. The method according to claim 1 , further comprising:
calculating an altitude of the trapezoid from the measured widths of the upper and lower bases of the trapezoid and the internal angle,
wherein the calculating the secondary moment (I) comprises using the measured widths of the upper and lower bases of the trapezoid to calculate the secondary moment (I).
3. The method according to claim 1 , wherein the first flat surface is configured for connection to a silicon substrate as a pedestal in a cantilevered state and wherein the second flat surface is configured to be mounted with a probe for use in the scanning probe microscope.
4. The method according to claim 1 , wherein measuring widths of upper and lower bases of the trapezoid and a length of the cantilever comprises:
illuminating a base surface of the cantilever vertically in an altitude direction of the trapezoid in an optical microscope;
visually discerning the vertically illuminated base surface from the obliquely illuminated leg surface, including discerning outer edges of the vertically illuminated base surface and inner edges of the obliquely illuminated leg surface;
determining a length of the lower base as an interval between the outer edges of the vertically illuminated base surface; and
determining a length of the upper base as an interval between the inner edges of the obliquely illuminated leg surface.
5. A scanning probe microscope comprising a cantilever anisotropically etched out from monocrystal silicon, the cantilever having cross-sections along a length of the cantilever in a form of an isosceles trapezoid, the cross-sections including a first flat surface corresponding to a lower base of the isosceles triangle, the first flat surface extensive along a (100) crystal plane of the monocrystal silicon, the cross-sections further including a second flat surface which is substantially parallel to the first flat surface and which corresponds to an upper base of the isosceles triangle, the cross-sections further including oblique side surfaces joining the first flat surface and the second flat surface, the oblique side surfaces extensive along a (111) crystal plane of the monocrystal silicon, and the cantilever being sized to have a spring constant calculable from Young's modulus (E), a secondary moment (I) of the cross-section of the cantilever, and a length (L) of the cantilever, wherein the secondary moment (I) is calculable from widths of the upper and lower bases of the trapezoid, and an internal angle of the trapezoid defined by the predetermined crystal planes.
6. The scanning probe microscope according to claim 5 , wherein the cantilever is given a spring constant calculated from the secondary moment (I) which in turn is calculable from an altitude of the trapezoid, which is geometrically calculated from the widths of the upper and lower bases of the trapezoid and the internal angle.
7. The scanning probe microscope according to claim 5 , wherein the predetermined crystal planes extend in a (100) direction and a (111) direction, respectively.