METHODS FOR DESIGNING AND PROCESSING A MICROCANTILEVER-BASED PROBE WITH AN IRREGULAR CROSS SECTION APPLIED IN AN ULTRA-LOW FRICTION COEFFICIENT MEASUREMENT AT A NANOSCALE SINGLE-POINT CONTACT

Abstract

A method for designing and processing a microcantilever-based probe with an irregular cross section applied in the ultra-low friction coefficient measurement at a nanoscale single-point contact includes: first, establishing a universal theoretical model of the friction coefficient measurement; then, combined with the structural features of the microcantilever-based probe with the irregular cross section, establishing a specific theoretical model of the friction coefficient measurement suitable for the microcantilever-based probe with the irregular cross section; and based on above, combined with constraint conditions such as the friction coefficient resolution, the loadable maximum positive pressure or the measurable minimum friction force, and the atomic force microscope characteristics, etc., designing the microcantilever-based probe with the irregular cross section meeting the measurement requirements.

Claims

1. A method for designing a microcantilever-based probe with an irregular cross section applied in an ultra-low friction coefficient measurement at a nanoscale single-point contact, wherein an axis of a microcantilever-based probe with the irregular cross section is a straight line, and a uniform cross section is provided along a direction of the axis; the uniform cross section is the irregular cross section composed of a plurality of rectangles having an equal wall thickness; the method for designing the probe comprises the following steps: step (1): establishing a universal theoretical model of a friction coefficient measurement using the microcantilever-based probe, wherein a friction force and a positive pressure are respectively measured by a torsion and a bending of the microcantilever-based probe according to a measurement principle of an atomic force microscope, namely,
F.sub.L=K.sub.TInvOLS.sub.LU.sub.L (1),
F.sub.N=K.sub.NInvOLS.sub.NU.sub.N (2), wherein F.sub.L and F.sub.N refer to the friction force and the positive pressure, respectively; K.sub.T and K.sub.N refer to a torsional elastic coefficient and a normal elastic coefficient of the microcantilever-based probe, respectively; InvOLS.sub.L and InvOLS.sub.N refer to a reciprocal of a lateral optical lever sensitivity and a reciprocal of a normal optical lever sensitivity, respectively; U.sub.L and U.sub.N refer to a lateral output voltage and a normal output voltage of a photodetector; and the universal theoretical model of the friction coefficient measurement using the microcantilever-based probe is then established, as shown in the following equation: $\begin{array}{cc}=\frac{F_L}{F_N}=\frac{K_T{\mathrm{InvOLS}}_L{U}_L}{K_N{\mathrm{InvOLS}}_N{U}_N},& \left(3\right)\end{array}$ wherein is the friction coefficient; step (2): establishing a specific theoretical model of the friction coefficient measurement using the microcantilever-based probe with the irregular cross section, wherein according to a measurement principle of an optical path system, the reciprocal of the lateral optical lever sensitivity InvOLS.sub.L and the reciprocal of the normal optical lever sensitivity InvOLS.sub.N are expressed as follows: $\begin{array}{cc}{\mathrm{InvOLS}}_L=\frac{H/{}_L}{4.Math.{\mathrm{dU}}_{\mathrm{sum}}/{}_{\mathrm{sum}}},& \left(4\right)\\ {\mathrm{InvOLS}}_N=\frac{\mathrm{Hl}/{}_N}{6.Math.{\mathrm{dU}}_{\mathrm{sum}}/{}_{\mathrm{sum}}},& \left(5\right)\end{array}$ wherein H is a length of a photosensitive surface of the photodetector; d is a length of an optical path; l is a length of the micro-cantilever; U.sub.sum is a total voltage generated by a laser in four quadrants of the photodetector; and .sub.sum, .sub.L, and .sub.N respectively refer to magnification times of a total output current, a lateral output current, and a normal output current of the photodetector subjected to a current/voltage converter, with a unit of V/A; based on an elastic mechanics and material mechanics theory of thin plates, the torsional elastic coefficient K.sub.T of the microcantilever-based probe with the irregular cross section is expressed as follows: $\begin{array}{cc}{K}_T=\frac{F_L}{{}_{\mathrm{tip}}}=\frac{G{I}_t}{\left(h_{\mathrm{tip}}+e_1\right)l},& \left(6\right)\end{array}$ wherein .sub.tip is a torsion angle of the microcantilever-based probe with the irregular cross section under an action of the friction force F.sub.L; G is a shear modulus of a material of the micro-cantilever; I.sub.t is a torsional inertia moment of the irregular cross section, h.sub.tip is a tip height, e.sub.1 is a distance from a centroid of the irregular cross section to a bottom side; the normal elastic coefficient K.sub.N of the microcantilever-based probe with the irregular cross section is expressed as follows: $\begin{array}{cc}{K}_N=\frac{F_N}{{}_{\mathrm{tip}}}=\frac{3.Math.E{I}_{x_C}}{l^3},& \left(7\right)\end{array}$ wherein .sub.tip is a deflection of the microcantilever-based probe with the irregular cross section under an action of the positive pressure F.sub.N; E is an elastic modulus of the material of the micro-cantilever; I.sub.xC is an inertia moment of the irregular cross section to a neutral axis x.sub.C; the equations (4)-(7) are put into the universal theoretical model (3) established in the step (1) to calculate and obtain the specific theoretical model for measuring the friction coefficient of the microcantilever-based probe with the irregular cross section, as shown in the following equation: $\begin{array}{cc}=\frac{Gl}{2.Math.E\left(h_{\mathrm{tip}}+e_1\right)}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N},& \left(8\right)\end{array}$ wherein I.sub.L is the lateral output current of the photodetector, and I.sub.L=U.sub.L/.sub.L; I.sub.N is the normal output current of the photodetector, and I.sub.N=U.sub.N/.sub.N; and step (3): designing the microcantilever-based probe with the irregular cross section meeting measurement requirements for an ultra-low friction coefficient, wherein according to the step (2), assuming that is a friction coefficient resolution .sub.min, and F.sub.N is a loadable maximum positive pressure F.sub.Nmax, or F.sub.L is a measurable minimum friction force F.sub.Lmin; combined with constraint conditions of the friction coefficient resolution .sub.min, the loadable maximum positive pressure F.sub.Nmax or the measurable minimum friction force F.sub.Lmin, characteristics of the atomic force microscope, the equations (1)-(8) are considered to calculate and designed dimensions of the microcantilever-based probe with the irregular cross section to meet the measurement requirements; the designed dimensions comprise the length l of the micro-cantilever, a width w.sub.i of an i-th sub-rectangle constituting the irregular cross section, and a wall thickness t.

2. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 1, wherein the micro-cantilever with the irregular cross section comprises a first beam for reflecting laser and a second beam fixedly connected to the first beam for supporting and fixing.

3. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 2, wherein a shape of the irregular cross section is selected from the group consisting of a hollow rectangular shape, an I shape, an H shape, an inverted T shape, and a U shape; the irregular cross section comprises a horizontal side constituting the first beam and a vertical side constituting the second beam; at least one horizontal side and at least one vertical side are provided; and the horizontal side and the vertical side are rectangles with an equal wall thickness.

4. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 1, wherein in the step (2), when h.sub.tip is ten times greater than e.sub.1, the specific theoretical model is simplified as follows: $\begin{array}{cc}=\frac{Gl}{2.Math.E{h}_{\mathrm{tip}}}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N}.& \left(9\right)\end{array}$

5. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 4, wherein the step (3) comprises the following sub-steps: step (3a) based on a set friction coefficient resolution .sub.min, calculating and obtaining a quantitative relationship 1 of the length l of the micro-cantilever with the irregular cross section, the torsional inertia moment I.sub.t, and the inertia moment I.sub.xC to the neutral axis x.sub.C according to the equation (8) or (9); step (3b) based on the loadable maximum positive pressure F.sub.Nmax or the measurable minimum friction force F.sub.Lmin, calculating and obtaining a quantitative relationship 2 of the length l of the micro-cantilever with the irregular cross section, the torsional inertia moment I.sub.t, or/and the inertia moment I.sub.xC to the neutral axis x.sub.C according to according to the equations (1)-(7); step (3c) obtaining a relationship between the torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis xc and the width w.sub.i of the i-th sub-rectangle constituting the irregular cross section, the wall thickness t according to structural parameters of the micro-cantilever with the irregular cross section; putting the relationship into the quantitative relationship 1 and the quantitative relationship 2 of I, I.sub.t and I.sub.xC obtained in the step (3a) and the step (3b) respectively to obtain a quantitative relationship 1 and a quantitative relationship 2 of l, w.sub.i and t, the width w.sub.i of the i-th sub-rectangle comprises a width w.sub.R of the first beam for reflecting the laser and a width w.sub.H of the second beam for supporting and fixing; step (3d) calculating and obtaining value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle, and the wall thickness t; and step (3e) setting at least two parameters of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th segment rectangle, and the wall thickness t according to the value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle and the wall thickness t; and calculating and obtaining remaining unknown parameter of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle, and the wall thickness t to obtain the designed dimensions of the microcantilever-based probe with the irregular cross section according to the quantitative relationship 1 and/or the quantitative relationship 2.

6. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 5, wherein in the step (3), the designed dimensions of the microcantilever-based probe with the irregular cross section are put into a finite element simulation model to determine whether key indexes of a friction coefficient measurement meet the measurement requirements or not, the key indexes comprise the friction coefficient resolution, the loadable maximum positive pressure or the measurable minimum friction force, a maximum stress, and a resonance frequency; if the key indexes meet the measurement requirements, the designed dimensions of the microcantilever-based probe with the irregular cross section are determined; if the key indexes do not meet the measurement requirements, the material or/and a reflective surface coating of the micro-cantilever with the irregular cross section are changed, and then go back to the step (3); or the atomic force microscope is changed, and then go back to the step (3) until the key indexes of the friction coefficient measurement meet the measurement requirements.

7. A method for processing the microcantilever-based probe with the irregular cross section designed by the method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 1, comprising the following steps: obtaining the designed dimensions of the microcantilever-based probe with the irregular cross section; processing to obtain the micro-cantilever with the irregular cross section; and installing a tip at an end of the micro-cantilever.

8. The method for processing the microcantilever-based probe with the irregular cross section according to claim 7, wherein a commercial probe having dimensions similar to the designed dimensions of the microcantilever-based probe with the irregular cross section is taken as a processing object; and the microcantilever-based probe with the irregular cross section is processed by a focused ion beam technique.

9. The method for processing the microcantilever-based probe with the irregular cross section according to claim 8, wherein the focused ion beam technique comprises at least one selected from the group consisting of a focused ion beam milling, a focused ion beam deposition and a focused ion beam etching.

10. The method for processing the microcantilever-based probe with the irregular cross section according to claim 9, wherein the method comprises the following steps, step (1): processing a first beam for reflecting laser and a second beam for supporting and fixing by the focused ion beam milling; step (2): attaching the second beam for supporting and fixing obtained from the milling to the first beam for reflecting laser by the focused ion beam deposition; and step (3): bonding the tip to the end of the micro-cantilever after processing to complete fabrication of the probe;

11. The method for processing the microcantilever-based probe with the irregular cross section according to claim 9, wherein the method comprises the following steps, step (1): obtaining the micro-cantilever with the irregular cross section having the designed dimensions by the focused ion beam etching; and step (2): bonding the tip to the end of the micro-cantilever after processing to complete the fabrication of the probe.

12. The method for processing the microcantilever-based probe with the irregular cross section according to claim 7, wherein a material of the tip is at least one selected from the group consisting of silicon, silicon nitride, silicon dioxide, diamond, diamond-like material, aluminum oxide, zirconium dioxide, titanium dioxide, cerium oxide, graphite, gold and graphene, molybdenum disulfide, and hexagonal boron nitride.

13. The method for processing the microcantilever-based probe with the irregular cross section according to claim 7, wherein the microcantilever-based probe with the irregular cross section is applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact under a superlubricity state of a sample.

14. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 2, wherein in the step (2), when h.sub.tip is ten times greater than e.sub.1, the specific theoretical model is simplified as follows: $\begin{array}{cc}=\frac{Gl}{2.Math.E{h}_{\mathrm{tip}}}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N}.& \left(9\right)\end{array}$

15. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 3, wherein in the step (2), when h.sub.tip is ten times greater than e.sub.1, the specific theoretical model is simplified as follows: $\begin{array}{cc}=\frac{Gl}{2.Math.E{h}_{\mathrm{tip}}}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N}.& \left(9\right)\end{array}$

16. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 14, wherein the step (3) comprises the following sub-steps: step (3a) based on a set friction coefficient resolution .sub.min, calculating and obtaining a quantitative relationship 1 of the length l of the micro-cantilever with the irregular cross section, the torsional inertia moment I.sub.t, and the inertia moment I.sub.xC to the neutral axis xc according to the equation (8) or (9); step (3b) based on the loadable maximum positive pressure F.sub.Nmax or the measurable minimum friction force F.sub.Lmin, calculating and obtaining a quantitative relationship 2 of the length l of the micro-cantilever with the irregular cross section, the torsional inertia moment I.sub.t, or/and the inertia moment I.sub.xC to the neutral axis x.sub.C according to according to the equations (1)-(7); step (3c) obtaining a relationship between the torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis xc and the width w.sub.i of the i-th sub-rectangle constituting the irregular cross section, the wall thickness t according to structural parameters of the micro-cantilever with the irregular cross section; putting the relationship into the quantitative relationship 1 and the quantitative relationship 2 of I, I.sub.t and I.sub.xC obtained in the step (3a) and the step (3b) respectively to obtain a quantitative relationship 1 and a quantitative relationship 2 of l, w.sub.i and t, the width w.sub.i of the i-th sub-rectangle comprises a width w.sub.R of the first beam for reflecting the laser and a width w.sub.H of the second beam for supporting and fixing; step (3d) calculating and obtaining value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle, and the wall thickness t; and step (3e) setting at least two parameters of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th segment rectangle, and the wall thickness t according to the value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle and the wall thickness t; and calculating and obtaining remaining unknown parameter of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle, and the wall thickness t to obtain the designed dimensions of the microcantilever-based probe with the irregular cross section according to the quantitative relationship 1 and/or the quantitative relationship 2.

17. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 15, wherein the step (3) comprises the following sub-steps: step (3a) based on a set friction coefficient resolution .sub.min calculating and obtaining a quantitative relationship 1 of the length l of the micro-cantilever with the irregular cross section, the torsional inertia moment I.sub.t, and the inertia moment I.sub.xC to the neutral axis x.sub.C according to the equation (8) or (9); step (3b) based on the loadable maximum positive pressure F.sub.Nmax or the measurable minimum friction force F.sub.Lmin, calculating and obtaining a quantitative relationship 2 of the length l of the micro-cantilever with the irregular cross section, the torsional inertia moment I.sub.t, or/and the inertia moment I.sub.xC to the neutral axis x.sub.C according to according to the equations (1)-(7); step (3c) obtaining a relationship between the torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis x.sub.C and the width w.sub.i of the i-th sub-rectangle constituting the irregular cross section, the wall thickness t according to structural parameters of the micro-cantilever with the irregular cross section; putting the relationship into the quantitative relationship 1 and the quantitative relationship 2 of l, I.sub.t and I.sub.xC obtained in the step (3a) and the step (3b) respectively to obtain a quantitative relationship 1 and a quantitative relationship 2 of l, w.sub.i and t, the width w.sub.i of the i-th sub-rectangle comprises a width w.sub.R of the first beam for reflecting the laser and a width w.sub.H of the second beam for supporting and fixing; step (3d) calculating and obtaining value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle, and the wall thickness t; and step (3e) setting at least two parameters of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th segment rectangle, and the wall thickness t according to the value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle and the wall thickness t; and calculating and obtaining remaining unknown parameter of the length l of the micro-cantilever with the irregular cross section, the width w.sub.i of the i-th sub-rectangle, and the wall thickness t to obtain the designed dimensions of the microcantilever-based probe with the irregular cross section according to the quantitative relationship 1 and/or the quantitative relationship 2.

18. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 16, wherein in the step (3), the designed dimensions of the microcantilever-based probe with the irregular cross section are put into a finite element simulation model to determine whether key indexes of a friction coefficient measurement meet the measurement requirements or not, the key indexes comprise the friction coefficient resolution, the loadable maximum positive pressure or the measurable minimum friction force, a maximum stress, and a resonance frequency; if the key indexes meet the measurement requirements, the designed dimensions of the microcantilever-based probe with the irregular cross section are determined; if the key indexes do not meet the measurement requirements, the material or/and a reflective surface coating of the micro-cantilever with the irregular cross section are changed, and then go back to the step (3); or the atomic force microscope is changed, and then go back to the step (3) until the key indexes of the friction coefficient measurement meet the measurement requirements.

19. The method for designing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact according to claim 17, wherein in the step (3), the designed dimensions of the microcantilever-based probe with the irregular cross section are put into a finite element simulation model to determine whether key indexes of a friction coefficient measurement meet the measurement requirements or not, the key indexes comprise the friction coefficient resolution, the loadable maximum positive pressure or the measurable minimum friction force, a maximum stress, and a resonance frequency; if the key indexes meet the measurement requirements, the designed dimensions of the microcantilever-based probe with the irregular cross section are determined; if the key indexes do not meet the measurement requirements, the material or/and a reflective surface coating of the micro-cantilever with the irregular cross section are changed, and then go back to the step (3); or the atomic force microscope is changed, and then go back to the step (3) until the key indexes of the friction coefficient measurement meet the measurement requirements.

20. The method for processing the microcantilever-based probe with the irregular cross section according to claim 7, wherein the micro-cantilever with the irregular cross section comprises a first beam for reflecting laser and a second beam fixedly connected to the first beam for supporting and fixing.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to clarify the embodiments of the present invention or the technical solutions in the prior art, the drawings required in the description of the embodiments or the prior art will be briefly described hereinafter. Obviously, the drawings described below merely show a part of the embodiments of the present invention. Those of ordinary skill in the art can derive other embodiments and drawings thereof according to the embodiments shown in these drawings without creative efforts.

[0046] FIG. 1 is a flow chart showing a method for designing a microcantilever-based probe with an irregular cross section applied in an ultra-low friction coefficient measurement at a nanoscale single-point contact provided by an embodiment.

[0047] FIG. 2 is a schematic diagram showing the friction coefficient measurement using the microcantilever-based probe provided by the embodiment.

[0048] FIG. 3 is a schematic diagram showing the structural parameters of a cross section with a hollow rectangular shape (a), an I shape (b), an H shape (c), an inverted T shape (d), and a U shape (e) provided by the embodiment, wherein 1 is a horizontal side and 2 is a vertical side.

[0049] FIG. 4 shows a finite element simulation result of a microcantilever-based probe with a U-shaped cross section provided by an embodiment, wherein (a) is a stress distribution diagram at a cross section with the maximum stress when 25 N positive pressure is loaded (the safety factor is 10); (b) is a finite element simulation result of the normal elastic coefficient when 0-5 N positive pressure is loaded; (c) is a finite element simulation results of the torsional elastic coefficient when 2.5 N positive pressure and 0-0.25 N friction force are loaded.

[0050] FIG. 5 shows a finite element simulation result of a microcantilever-based probe with a U-shaped cross section provided by an embodiment, wherein (a) is a stress distribution diagram at a cross section with the maximum stress when 250 N positive pressure is loaded (the safety factor is 10); (b) is a finite element simulation result of the normal elastic coefficient when 0-50 N positive pressure is loaded; (c) is a finite element simulation results of the torsional elastic coefficient when 25 N positive pressure and 0-0.25 N friction force are loaded.

[0051] FIG. 6 is a schematic diagram showing a focused ion beam milling/deposition process of a microcantilever-based probe with a U-shaped cross section provided by the embodiment, wherein (a) shows a processing of a second beam for supporting and fixing; (b) shows that deposition the beam after milling is attached on the first beam for reflecting the laser; (c) shows a schematic diagram after the tip is bonded.

[0052] FIG. 7 is a schematic diagram showing a focused ion beam etching process of a microcantilever-based probe with a U-shaped cross section provided by the embodiment, wherein (a) shows an original cantilever; (b) shows a U-shaped cantilever obtained by etching; (c) shows a schematic diagram after the tip is bonded.

[0053] FIG. 8 shows a comparison between the original cantilever (a) and the micro-cantilever (b) with a U-shaped cross section obtained by focused ion beam etching provided by the embodiment.

[0054] FIG. 9 shows a lateral output voltage U.sub.trace (solid line) and U.sub.retrace (dashed line) of a photodetector corresponding to a roundtrip path of a probe under different positive pressures by using an MFP-3D atomic force microscope provided by the embodiment, wherein U.sub.L=(U.sub.trace-U.sub.retrace)/2, (a) corresponds to U.sub.L=0.006 mV, and (b) corresponds to U.sub.L=0.019 mV.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] The technical solutions of the various embodiments of the present invention are clearly and completely described hereinafter with reference to the drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention instead of all. Any other embodiment obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts should be considered as falling within the scope of the present invention.

Embodiment 1

[0056] According to a microcantilever-based probe with the irregular cross section designed in the present embodiment, the micro-cantilever with the irregular cross section mainly includes two parts, namely, a first beam for reflecting laser and a second beam fixedly connected to the first beam for supporting and fixing. The axis line of the micro-cantilever with the irregular cross section is a straight line. A uniform cross section is provided along the direction of the axis line. In order to facilitate the laser reflection and improve the processability of the probe, the cross section is an irregular cross section composed of a plurality of elongate rectangles having an equal wall thickness. In the present embodiment, the cross sections with five shapes are taken as the design basis, and the five shapes include a hollow rectangular shape, an I shape, an H shape, an inverted T shape, and a U shape. The method for designing the microcantilever-based probe with the irregular cross section is specifically described. However, the above-mentioned five shapes are not intended to limit the microcantilever-based probe with the irregular cross section of the present invention in any aspect. It is easy to see that these irregular cross sections each include a horizontal side 1 constituting the first beam and a vertical side 2 constituting the second beam. At least one horizontal side and at least one vertical side are provided. The horizontal side and the vertical side are elongate rectangles with an equal thickness, and have a width of w.sub.i (i=R,H) and a wall thickness of t.

[0057] In the present embodiment, the microcantilever-based probe with the irregular cross section is designed based on the following requirements of the ultra-low friction coefficient measurement: 1) the ultra-low friction coefficient measurement with the resolution in the magnitude that is equal to or less than 10.sup.6 should be realized; 2) the loadable maximum positive pressure is equal to or around 2.5 N; 3) the material of the micro-cantilever is silicon nitride; 4) the tip has a height of 23 m, and the material of the tip is graphene-coated silica microsphere; 5) the experimental platform is MFP-3D atomic force microscope.

[0058] The characteristics of the MFP-3D atomic force microscope in the present embodiment are listed below. 1) The size of the laser spot is micron-scaled, and in order to make the laser spots totally fall within the reflective surface, the width w.sub.R (i.e., the width of the horizontal side of the irregular cross section) of the first beam for reflecting the laser that constitutes the micro-cantilever of the to-be-designed probe should be not less than 20 m, and the length l of the micro-cantilever of the to-be-designed probe should be not less than 50 m. 2) The wall thickness t (i.e., the wall thickness of the horizontal side and the vertical side of the irregular cross section) of the silicon nitride micro-cantilever usually ranges 0.2 m-0.6 m. 3) After measuring, the fitting relationship of the reciprocal of the normal optical lever sensitivity InvOLS.sub.N in the optical path system and the length l of the micro-cantilever, the total voltage U.sub.sum generated by the laser in the four quadrants of the photodetector is InvOLS.sub.N(nm/V)=0.00274l/U.sub.sum+24.7, and the fitting relationship of the reciprocal of the lateral optical lever sensitivity InvOLS.sub.L and U.sub.sum is InvOLS.sub.L (rad/V)=0.0697/U.sub.sum+0.00879 (4.5 V<U.sub.sum<5.8 V). 4) The voltage resolution U.sub.Lmin of the photodetector is 0.01 mV (besides, the reference J. Li, C. Zhang, P Cheng, X Chen, W Wang and J. Luo, Langmuir, 32, 5593 (2016) shows that U.sub.Lmin of MFP-3D atomic force microscopy is 0.002 mV, which is not adopted by the present invention), and the maximum value U.sub.Nmax of the voltage measurement range is 20 V. 5) the ratio I.sub.Lmin/I.sub.Nmax of the current resolution I.sub.Lmin and the current measurement range I.sub.Nmax of the photodetector is 710.sup.6.

[0059] As shown in FIG. 1, the present embodiment provides a method for designing a microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact, which includes the following steps.

[0060] Step (1): a universal theoretical model of a friction coefficient measurement using the microcantilever-based probe is established.

[0061] The friction force and positive pressure are respectively measured by a torsion and a bending of the microcantilever-based probe according to a measurement principle of an atomic force microscope, as shown in FIG. 2, namely,

F.sub.L=K.sub.TInvOLS.sub.LU.sub.L (1)

F.sub.N=K.sub.NInvOLS.sub.NU.sub.N (2)

[0062] where F.sub.L and F.sub.N refer to friction force and positive pressure, respectively; K.sub.T and K.sub.N refer to a torsional elastic coefficient and a normal elastic coefficient of the microcantilever-based probe, respectively; InvOLS.sub.L and InvOLS.sub.N refer to a reciprocal of a lateral optical lever sensitivity and a reciprocal of a normal optical lever sensitivity, respectively; U.sub.L and U.sub.N refer to a lateral output voltage and a normal output voltage of a photodetector, respectively.

[0063] After that, the universal theoretical model of the friction coefficient measurement using the microcantilever-based probe is established, as shown in the following equation:

[00007]$\begin{array}{cc}=\frac{F_L}{F_N}=\frac{K_T{\mathrm{InvOLS}}_L{U}_L}{K_N{\mathrm{InvOLS}}_N{U}_N}& \left(3\right)\end{array}$

[0064] where is the friction coefficient.

[0065] Step (2): A specific theoretical model of the friction coefficient measurement using the microcantilever-based probe with the irregular cross section is established.

[0066] According to a measurement principle of an optical path system, the reciprocal of the lateral optical lever sensitivity InvOLS.sub.L and the reciprocal of the normal optical lever sensitivity InvOLS.sub.N are expressed as follows:

[00008]$\begin{array}{cc}{\mathrm{InvOLS}}_L=\frac{H.Math.\text{/}.Math.{}_L}{4.Math.{\mathrm{dU}}_{\mathrm{sum}}.Math.\text{/}.Math.{}_{\mathrm{sum}}}& \left(4\right)\\ {\mathrm{InvOLS}}_N=\frac{\mathrm{Hl}.Math.\text{/}.Math.{}_N}{6.Math.{\mathrm{dU}}_{\mathrm{sum}}.Math.\text{/}.Math.{}_{\mathrm{sum}}}& \left(5\right)\end{array}$

[0067] where H is a length of a photosensitive surface of the photodetector; d is a length of an optical path; l is a length of a micro-cantilever; U.sub.sum is a total voltage generated by the laser in four quadrants of the photodetector; and .sub.sum, .sub.L, and .sub.N refer to magnification times of a total output current, a lateral output current and a normal output current of the photodetector after subjected to a current/voltage converter, with a unit of V/A.

[0068] Based on elastic mechanics and material mechanics theory of thin plates, the torsional elastic coefficient K.sub.T of the microcantilever-based probe with the irregular cross section is expressed as follows:

[00009]$\begin{array}{cc}{K}_T=\frac{F_L}{{}_{\mathrm{tip}}}=\frac{G{I}_t}{\left(h_{\mathrm{tip}}+e_1\right)l}& \left(6\right)\end{array}$

[0069] where .sub.tip is a torsion angle of the microcantilever-based probe with the irregular cross section under an action of friction force F.sub.L; G is a shear modulus of the micro-cantilever material; I.sub.t is a torsional inertia moment of the irregular cross section, h.sub.tip is a tip height, e.sub.1 is a distance from a centroid of the irregular cross section to a bottom side.

[0070] The normal elastic coefficient K.sub.N of the microcantilever-based probe with the irregular cross section is expressed as follows:

[00010]$\begin{array}{cc}{K}_N=\frac{F_N}{{}_{\mathrm{tip}}}=\frac{3.Math.E{I}_{x_C}}{l^3}& \left(7\right)\end{array}$

[0071] where .sub.tip is a deflection of the microcantilever-based probe with the irregular cross section under the action of the positive pressure F.sub.N; E is an elastic modulus of the micro-cantilever material; since the micro-cantilever material may be anisotropic (such as silicon), a conventional formula G=E/2(1+) ( is Poisson's ratio) is not always true; I.sub.xC is an inertia moment of the irregular cross section to a neutral axis x.sub.C (an intersection line of a neutral layer and the cross section, which passes through the centroid of the cross section).

[0072] The equations (4)-(7) are put into the universal theoretical model (3) established in step (1) to calculate and obtain the specific theoretical model of the friction coefficient measurement using the microcantilever-based probe with the irregular cross section, as shown in the following equation:

[00011]$\begin{array}{cc}=\frac{Gl}{2.Math.E\left(h_{\mathrm{tip}}+e_1\right)}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N}& \left(8\right)\end{array}$

[0073] where I.sub.L is a lateral output current of the photodetector, and I.sub.L=U.sub.L/.sub.L; I.sub.N is a normal output current of the photodetector, and I.sub.N=U.sub.N/.sub.N.

[0074] In the present embodiment, when h.sub.tip is ten times greater than e.sub.1, the specific theoretical model is simplified as follows:

[00012]$\begin{array}{cc}=\frac{Gl}{2.Math.E{h}_{\mathrm{tip}}}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N}.& \left(9\right)\end{array}$

[0075] Step (3): the microcantilever-based probe with the irregular cross section meeting the requirements for the ultra-low friction coefficient measurement is designed.

[0076] According to step (2), assuming that a friction coefficient resolution .sub.min, and F.sub.N is a loadable maximum positive pressure F.sub.Nmax, or F.sub.L is a measurable minimum friction force F.sub.Lmin, combined with constraint conditions such as the friction coefficient resolution .sub.min, the loadable maximum positive pressure F.sub.Nmax or the measurable minimum friction force F.sub.Lmin, and the atomic force microscope characteristics etc., the equations (1)-(9) are considered with structural features of the irregular cross section to calculate and design the dimensions of the microcantilever-based probe with the irregular cross section that meets the measurement requirements. The dimensions include a length l, a width w.sub.i of an i-th sub-rectangle, a wall thickness t, etc. Also, a finite element simulation is used for check and verification.

[0077] In the present embodiment, the specific processes of designing the microcantilever-based probe with the irregular cross section that meet the requirements for the ultra-low friction coefficient measurement at the nanoscale single-point contact are as follows.

[0078] a) The friction coefficient resolution .sub.min10.sup.6 is set in the present embodiment, that is,

[00013]$\begin{array}{cc}{}_{\min }={\left(\frac{F_L}{F_N}\right)}_{\min }={\left(\frac{Gl}{2.Math.E{h}_{\mathrm{tip}}}\frac{I_t}{I_{x_C}}\frac{I_L}{I_N}\right)}_{\min }=\frac{Gl}{2.Math.E{h}_{\mathrm{tip}}}\frac{I_t}{I_{x_C}}\frac{I_{L.Math..Math.\min }}{I_{N.Math..Math.\max }}{10}^{-6}& \left(10\right)\end{array}$

[0079] where I.sub.Lmin and I.sub.Nmax refer to the current resolution and the current measurement range of the photodetector, respectively; G of silicon nitride is 61 GPa; E of silicon nitride is 156 GPa; a tip height h.sub.tip is 23 m, and I.sub.Lmin/I.sub.Nmax is 710.sup.6. The above parameters are put into the equation (10) to calculate the quantitative relationship 1 of l, I.sub.t and I.sub.xC, that is

[00014]$\begin{array}{cc}l\frac{I_t}{I_{x_C}}16.8& \left(11\right)\end{array}$

[0080] where the unit of length is m.

[0081] b) The loadable maximum positive pressure F.sub.Nmax is set to be equal to or around 2.5 N in the present embodiment, that is

F.sub.Nmax=(K.sub.NInvOLS.sub.NU.sub.N).sub.max=K.sub.NInvOLS.sub.NU.sub.Nmax2.5 (12)

[0082] where U.sub.Nmax is the voltage measurement range of the photodetector. As previously mentioned, in the present embodiment, the voltage measurement range U.sub.Nmax of the photodetector of the MFP-3D atomic force microscope is 20 V; the fitting relationship of the reciprocal of the normal optical lever sensitivity InvOLS.sub.N and the length l of the micro cantilever, the total voltage U.sub.sum generated by the laser in the four quadrants of the photodetector is expressed as follows:

InvOLS.sub.N (nm/V)=0.00274l/U.sub.sum+24.7 (13) .

[0083] In the present embodiment, the reflective surface coating of the micro-cantilever with the irregular cross section is made of gold, and the total voltage U.sub.sum generated by the laser reflected to the four quadrants of the photodetector by the gold coating is about 5 V, so putting U.sub.sum=5V into equation (13) to calculate and obtain the following equation:

InvOLS.sub.N (nm/V)=0.000548l+24.7 (14)

[0084] The equations (7) and (14) are put into the equation (12) to calculate and obtain the quantitative relationship 2 between l and I.sub.xC, that is,

[00015]$\begin{array}{cc}\frac{0.000548l+0.0247}{l^3}{I}_{x_C}2.67{10}^{-7}& \left(15\right)\end{array}$

[0085] where the unit of length is m.

[0086] c) I.sub.t is the torsional inertia moment of the irregular cross section, and is related to the structural parameters of the cross section including the width w.sub.R of the first beam for reflecting the laser (i.e., the width of the horizontal side of the irregular cross section), the width w.sub.H of the second beam for supporting and fixing (i.e., the width of the vertical side of the irregular cross section), and the wall thickness t. I.sub.xC is the inertia moment of the irregular cross section to the neutral axis x.sub.C, and is related to the structural parameters of the cross section including w.sub.R, w.sub.H and t. According to the structural parameters of the irregular cross section, the relationships between I.sub.t, I.sub.xC and w.sub.R, w.sub.H and t are obtained, respectively.

[0087] As shown in FIG. 3, the hollow rectangular shaped cross section consists of two symmetrically disposed horizontal sides and two vertical sides fixedly connected to two ends of the two horizontal sides. The torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis x.sub.C, and the distance e.sub.1 from the centroid to the bottom side are respectively expressed as follows:

[00016]$\begin{array}{cc}{I}_t=\frac{2.Math.{\left(w_R+t\right)}^2{\left(w_H-t\right)}^{2}t}{w_R+w_H}& \left(16\right)\\ I_{x_C}=\frac{\left(w_R+2.Math.t\right)w_H^3-w_R{\left(w_H-2.Math.t\right)}^3}{12}& \left(17\right)\\ e_1=\frac{w_H}{2}.& \left(18\right)\end{array}$

[0088] As shown in FIG. 3, the I-shaped cross section consists of two symmetrically disposed horizontal sides and one vertical side fixedly connected to the middle portion of the two horizontal sides. The torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis x.sub.C, and the distance e.sub.1 from the centroid to the bottom side are expressed as follows:

[00017]$\begin{array}{cc}{I}_t=\frac{\left(2.Math.w_R+w_H\right)t^3}{3}& \left(19\right)\\ I_{x_C}=\frac{w_R{\left(w_H+2.Math.t\right)}^3-\left(w_R-t\right)w_H^3}{12}& \left(20\right)\\ e_1=\frac{w_H}{2}+t.& \left(21\right)\end{array}$

[0089] As shown in FIG. 3, the H-shaped cross section consists of two symmetrically disposed vertical sides and one horizontal side fixedly connected to the middle portion of the two vertical sides. The torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis x.sub.C, and the distance e.sub.1 from the centroid to the bottom side are expressed as follows:

[00018]$\begin{array}{cc}{I}_t=\frac{\left(w_R+2.Math.w_H\right)t^3}{3}& \left(22\right)\\ I_{x_C}=\frac{2.Math.t{w}_H^3+w_R{t}^3}{12}& \left(23\right)\\ e_1=\frac{t}{2}.& \left(24\right)\end{array}$

[0090] As shown in FIG. 3, the inverted T-shaped cross section consists of one horizontal side and one vertical side fixedly connected to the middle portion of the horizontal side, and the vertical side is located above the horizontal side. The torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis x.sub.C, and the distance e.sub.1 from the centroid to the bottom side are expressed as follows:

[00019]$\begin{array}{cc}{I}_t=\frac{\left(w_R+w_H\right)t^3}{3}& \left(25\right)\\ I_{x_C}=\frac{w_R{e}_1^3-\left(w_R-t\right){\left(e_1-t\right)}^3+t{\left(w_H+t-e_1\right)}^3}{3}& \left(26\right)\\ e_1=\frac{t{\left(w_H+t\right)}^2+\left(w_R-t\right)t^2}{2\left[t\left(w_H+t\right)+\left(w_R-t\right)t\right]}.& \left(27\right)\end{array}$

[0091] As shown in FIG. 3, the U-shaped cross section consists of two symmetrically disposed vertical sides and one horizontal side fixedly connected to the lower ends of the two vertical sides. The torsional inertia moment I.sub.t, the inertia moment I.sub.xC to the neutral axis x.sub.C, and the distance e.sub.1 from the centroid to the bottom side are expressed as follows:

[00020]$\begin{array}{cc}{I}_t=\frac{\left(w_R+2.Math.w_H\right)t^3}{3}& \left(28\right)\\ I_{x_C}=\frac{w_R{e}_1^3-\left(w_R-2.Math.t\right){\left(e_1-t\right)}^3+2.Math.t{\left(w_H+t-e_1\right)}^3}{3}& \left(29\right)\\ e_1=\frac{2.Math.t{\left(w_H+t\right)}^2+\left(w_R-2.Math.t\right)t^2}{2\left[2.Math.t\left(w_H+t\right)+\left(w_R-2.Math.t\right)t\right]}& \left(30\right)\end{array}$

[0092] The equations (16)-(30) are put into the quantitative relationship 1 (i.e. equation (11)) and the quantitative relationship 2 (i.e. equation (15)) to calculate and obtain the quantitative relationship 1 and the quantitative relationship 2 of the length l of the micro-cantilever with a hollow rectangular shaped cross section, an I-shaped cross section, an H-shaped cross section, an inverted T-shaped cross section, or a U-shaped cross section, the width w.sub.R of the first beam for reflecting the laser, the width w.sub.H of the second beam for supporting and fixing, and the wall thickness t.

[0093] d) According to the constraint conditions such as characteristics of the atomic force microscope and the processability of the probe, the value ranges of the length l of the micro-cantilever with the irregular cross section, the width w.sub.R of the first beam for reflecting the laser, and the wall thickness t are determined.

[0094] According to the MFP-3D atomic force microscope characteristics described above, the width w.sub.R of the first beam for reflecting the laser (i.e., the width of the horizontal side of the irregular cross section) that constitutes the micro-cantilever of the to-be-designed probe should be not less than 20 m, the length l of the micro-cantilever of the to-be-designed probe should be not less than 50 m, and the wall thickness t (i.e., the wall thickness of the horizontal side and the vertical side of the irregular cross section) of the silicon nitride micro-cantilever usually ranges 0.2 m-0.6 m.

[0095] e) According to the equation (9), it can be deduced that the friction coefficient resolution .sub.min of the microcantilever-based probe with the irregular cross section is directly proportional to the length l of the micro-cantilever. In order to as much as possible set aside a margin for designing the dimensions of the cross-section, the length l of the micro-cantilever should be as short as possible. In the present embodiment, combined with the value range of the length l of the micro-cantilever determined in step d), the length l of the micro-cantilever is set as a minimum value of 50 m. Furthermore, in order to facilitate processing, the width w.sub.R of the first beam for reflecting laser in the present embodiment is consistent with the width of a commercial probe. The commercial silicon nitride probe available now has a width of 35 m, so that the first beam for reflecting laser is designed to have a width of 35 m. The set length l of the micro-cantilever and the width w.sub.R of the first beam for reflecting the laser are put into the quantitative relationship 1 and/or the quantitative relationship 2 to calculate and obtain the quantitative relationship between the width w.sub.H of the second beam for support fixation and the wall thickness t. According to the value range of the wall thickness t of the micro-cantilever determined in step d), for the convenience of processing, the wall thickness t is determined to be 0.2 m. According to the quantitative relationship between w.sub.H and t, a value of the width w.sub.H the second beam for supporting and fixing is calculated and obtained.

[0096] Since the design process involves the round-off of the significant figures, a re-substitution and a calculation are performed. The theoretical calculation results of the hollow rectangular cross section, the I-shaped cross section, the H-shaped cross section, the inverted T-shaped cross section and U-shaped cross section are shown in Table 1.

TABLE-US-00001 TABLE 1 The theoretical calculation results and the finite element simulation results of the micro-cantilever probe with the irregular cross section (Note: the safety factor is 10 during stress analysis, that is, the loaded positive pressure is 10 times than the set positive pressure F.sub.nset) Cross F.sub.nset Calculation l w.sub.R w.sub.H t h.sub.tip K.sub.N K.sub.T .sub.max f F.sub.nmax F.sub.Lmin section (N) Material results (m) (m) (m) (m) (m) (N/m) (N/rad) (GPa) (kHz) (N) (pN) .sub.min Hollow 2.5 silicon theoretical 50 35 0.6 0.2 23 2.30 117 x x 2.39 26.5 1 10.sup.5 reatangular nitride calculation finite element 2.22 125 1.11 324 2.31 28.5 1 10.sup.5 simulation 25 theoretical 1.5 22.7 1179 x x 23.7 268 1 10.sup.5 calculation finite element 21.6 1183 3.35 922 22.5 269 1 10.sup.5 simulation I-shaped 2.5 theoretical 0.2 2.270 9.80 x x 2.37 2.23 9 10.sup.7 calculation finite element 2.170 9.82 1.45 319 2.26 2.23 1 10.sup.6 simulation 25 theoretical 1.2 26.0 9.73 x x 27.1 2.21 8 10.sup.8 calculation finite element 23.9 9.76 4.51 1039 24.9 2.21 9 10.sup.8 simulation H-shaped 2.5 theoretical 2.7 2.54 5.69 x x 2.65 1.29 5 10.sup.7 calculation finite element 2.54 5.65 2.49 462 2.64 1.28 5 10.sup.7 simulation 25 theoretical 5.8 24.4 6.56 x x 25.5 1.49 6 10.sup.8 calculation finite element 24.2 6.52 5.55 1324 25.3 1.48 6 10.sup.8 simulation Inverted 2.5 theoretical 2 2.30 5.20 x x 2.40 1.18 5 10.sup.7 T-shaped calculation finite element 2.26 5.20 4.15 452 2.36 1.18 5 10.sup.7 simulation 25 theoretical 4.6 23.7 5.51 x x 24.7 1.25 5 10.sup.8 calculation finite element 22.6 5.52 8.73 1342 23.5 1.25 5 10.sup.8 simulation U-shaped 2.5 theoretical 1.6 2.38 5.36 x x 2.48 1.22 5 10.sup.7 calculation finite element 2.33 5.36 3.20 450 2.42 1.22 5 10.sup.7 simulation 25 theoretical 3.7 23.8 5.88 x x 24.8 1.34 5 10.sup.8 calculation finite element 22.6 5.88 6.80 1321 23.5 1.34 6 10.sup.8 simulation

[0097] Furthermore, the obtained designed dimensions of the microcantilever-based probe with the irregular cross section are put into the finite element simulation model, and the finite element software NX Nastran is used to simulate to obtain the friction coefficient resolution, the loadable maximum positive pressure or the measurable minimum friction force, the maximum stress, the resonance frequency, and finite element simulation results, as shown in Table 1 and FIG. 4. It can be seen that the I-shaped cross section, the H-shaped cross section, the inverted T-shaped cross section, and the U-shaped cross section all entirely meet the set requirements, except for the hollow rectangular cross section. For the hollow rectangular cross section, a method of changing the atomic force microscope may be used to ensure proper optical path system, photodetector and the associated current/voltage converter thereof, so that the key indexes of measuring the friction coefficient meet the set requirements. Since the I shaped cross section, H-shaped cross section, inverted T-shaped cross section, and U-shaped cross section in the embodiment all entirely meet the set requirements, the process of optimizing the hollow rectangular cross section does not need to be described in detail.

Embodiment 2

[0098] In the present embodiment, the microcantilever-based probe with the irregular cross section is designed based on the following requirements of the ultra-low friction coefficient measurement: 1) the ultra-low friction coefficient measurement with an resolution in the magnitude that is equal to or less than 10 should be realized; 2) the loadable maximum positive pressure is equal to or around 25 N; 3) the material of the micro-cantilever is silicon nitride; 4) the tip height is 23 m, and the material of the tip is graphene-coated silica microsphere; 5) the experimental platform is MFP-3D atomic force microscope.

[0099] In the present embodiment, the steps of designing the microcantilever-based probe with the irregular cross section are consistent with the steps of Embodiment 1, and the results of theoretical calculations and the finite element simulation are shown in Table 1 and FIG. 5. It can be seen that the I-shaped cross section, the H-shaped cross section, the inverted T-shaped cross section, and the U-shaped cross section all entirely meet the set requirements, except for the hollow rectangular cross section. For the hollow rectangular cross section, a method of changing the atomic force microscope may be used to ensure proper optical path system, photodetector and the associated current/voltage converter thereof, so that the key indexes of measuring the friction coefficient meet the set requirements. Since the I shaped cross section, H-shaped cross section, inverted T-shaped cross section, and U-shaped cross section in the embodiment all entirely meet the set requirements, the process of optimizing the hollow rectangular cross section does not need to be described in detail.

[0100] In conclusion, the feasibility and the accuracy of the method for designing the microcantilever-based probe with the irregular cross section are verified by Embodiment 1 and Embodiment 2 in both aspects of theoretical calculation and the finite element simulation.

Embodiment 3

[0101] The present embodiment provides a method for processing the microcantilever-based probe with the irregular cross section by the focused ion beam milling/deposition, which meets the requirements for the ultra-low friction coefficient measurement at the nanoscale single-point contact. In consideration of the probe processing convenience, taking a microcantilever-based probe with the U-shaped cross section as an example, two commercial silicon nitride microcantilever-based probes HYDRA2R-50NG-TL (without tips, produced by Applied NanoStructures, USA) having dimensions similar to the designed dimensions of the U-shaped cross section were selected as the processing object. As shown in FIG. 6, first, two second beams for supporting and fixing are milled from one of the two HYDRA2R-5ONG-TL commercial probes by means of the focused ion beam milling. Then, the two second beams for supporting and fixing obtained by milling is attached to another uncut HYDRA2R-50NG-TL commercial probe (i.e., the first beam for reflecting the laser) by means of the focused ion beam deposition. Finally, the tip is bonded to the end of the micro-cantilever through the AB Glue (or UV light curable glue etc.) on the MFP-3D atomic force microscope to complete the fabrication of the probe.

Embodiment 4

[0102] The present embodiment provides a method for processing the microcantilever-based probe with the irregular cross section by the focused ion beam etching, which meets the requirements for the ultra-low friction coefficient measurement at the nanoscale single-point contact. In consideration of the probe processing convenience, taking a microcantilever-based probe with the U-shaped cross section as an example, a commercial silicon microcantilever-based probe FCL (without tip, produced by Applied NanoStructures, USA) having dimensions similar to the designed dimensions of a U-shaped cross section was selected as the processing object. As shown in FIG. 7, first, according to the calculation results, the area to be processed and the corresponding path of processing are determined. Then, a groove having the designed dimensions is etched and processed on the commercial probe by means of the focused ion beam etching technique to complete the processing of the micro-cantilever with a U-shaped cross section. Finally, the tip is bonded to the end of the micro-cantilever through the AB Glue (or UV light curable glue etc.) on the MFP-3D atomic force microscope to complete the fabrication of the probe.

[0103] As previously mentioned, the G of silicon is 50 GPa, the E of silicon is 169 GPa, the G of silicon nitride is 61 GPa, and the E of silicon nitride is 156 GPa. Thus, the G and E of silicon and silicon nitride are basically the same. The same designed dimension may be obtained through processing the silicon nitride micro-cantilever by means of the focused ion beam milling/deposition technique in Embodiment 3, as well as through processing the silicon micro-cantilever by means of the focused ion beam etching technique in the present embodiment.

Embodiment 5

[0104] As shown in FIG. 8, the present embodiment provides a micro-cantilever with a U-shaped cross-section having the designed dimensions obtained by processing with the focused ion beam etching technique in Embodiment 4. Then, a silica ball having a diameter of 23 m is bonded to the end of the micro-cantilever with the U-shaped cross section by the glue to complete the fabrication of the probe. After that, the normal and torsional parameters are obtained by calibration. Specifically, the reciprocal of the normal optical lever sensitivity InvOLS.sub.N obtained by calibrating with the force curve on the silicon wafer is 145 nm/V. The normal elastic coefficient K.sub.N obtained by calibrating with the thermal noise method is 17 N/m. The torsional coefficient K.sub.TInvOLS.sub.L obtained by calibrating with the wedge method is 1.2 N/V. The voltage resolution U.sub.Lmin of the photodetector of the MFP-3D atomic force microscope is about 0.01 mV (as shown in FIG. 9 , when F.sub.N=53.9 nN, it is difficult to distinguish the lateral output voltages U.sub.trace (solid line) and U.sub.retrace (dashed line) of the photodetector corresponding to the roundtrip path of the probe, in this case, U.sub.L=0.006 mV; and when F.sub.N=113.9 nN, it is easy to distinguish the lateral output voltages U.sub.trace (solid line) and U.sub.retrace (dashed line) of the photodetector corresponding to the roundtrip path of the probe, in this case, U.sub.L=0.019 mV, thus, in the present embodiment, it is believed that U.sub.Lmin is between 0.006 mV and 0.019 mV, rounded to 0.01 mV). The voltage measurement range U.sub.Nmax of the photodetector of the MFP-3D atomic force microscope is 20 V. As shown in equation (31) below:

[00021]$\begin{array}{cc}{}_{\min }=\frac{K_T{\mathrm{InvOLS}}_L{U}_{\mathrm{Lmin}}}{K_N{\mathrm{InvOLS}}_N{U}_{\mathrm{Nmax}}}.& \left(31\right)\end{array}$

[0105] The parameters obtained from the calibration are put into the equation (31) and calculated to obtain the result that the friction coefficient resolution .sub.min is 210.sup.7. The result is put into the equation (12) to calculate and obtain the result that the loadable maximum positive pressure F.sub.Nmax is 49 N, which fully meet the measurement requirements in Embodiment 1 and Embodiment 2.

[0106] Thus, the irregular-shaped microcantilever-based probe fabricated according to the design and processing method proposed by the present invention can be applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact in the superlubricity state of the sample.

[0107] The present invention provides a method for designing and processing the microcantilever-based probe with the irregular cross section applied in the ultra-low friction coefficient measurement at the nanoscale single-point contact, which greatly improves the resolution for the friction coefficient measurement, realizes the ultra-low friction coefficient measurement with the resolution in the magnitude that is equal to or less than 10.sup.6, ensures the authenticity and reliability of the quantitative analysis in the superlubricity process, and provides an important measurement means for the establishment of the superlubricity theory and the application of the superlubricity technology in important fields such as the aerospace field, the advanced manufacturing field and the energy field in China.