A design method for microcantilever beams for TEM measurement mechanics

Abstract

This invention discloses a design method for a microcantilever beam used in TEM (Transient Mechanical Analysis) for measuring mechanics, comprising the following steps: In TEM, the normal and horizontal displacements of the microcantilever beam are observed to be at the nanometer level. The experiment requires measuring the normal and horizontal forces with nanonewton-level precision. The normal elastic coefficient and the total horizontal elastic coefficient of the microcantilever beam are calculated according to Hooke's Law. Then, the length, width, thickness, and tip height of the microcantilever beam are calculated. This invention avoids the complexity and uncertainty of mechanical measurements of microcantilever beams in AFM (Automatic Mechanical Analysis) by directly measuring the tip displacement to calculate the normal and horizontal forces, thus achieving stability. By directly observing the horizontal bending and tip torsion of the microcantilever under TEM, it avoids the problem of low horizontal force measurement accuracy due to a large width-to-thickness ratio caused by the inability to observe the horizontal bending of the microcantilever in AFM. A cantilever beam with a small width-to-thickness ratio is designed to achieve high-precision measurement of normal and horizontal forces of 1 nN.

Description

Technical Field

[0001] This invention relates to a microcantilever beam design method, specifically a microcantilever beam design method for TEM measurement mechanics. Background Technology

[0002] In recent years, with the development of micro-nano manufacturing technology and the semiconductor industry, the scale of micro-nano structures / devices has been continuously shrinking. Therefore, the characterization and measurement of materials at the nanoscale have gradually gained attention. AFM, with its flexibility and non-destructive nature, has become an important tool for measuring the mechanics of nanomaterials. The working principle of its measurement mechanics is as follows: A laser beam is irradiated at the end of a micro cantilever beam with a needle tip. When there is an interaction force between the needle tip and the sample, it will cause the cantilever beam tip to deflect or its oscillation signal to change (such as amplitude, frequency, or phase). This causes the beam reflected back to the photodetector from the cantilever beam to deflect. The amount of deflection is fed back to the detection system, and a force-distance curve is plotted according to Hooke's law, thereby performing mechanical measurement.

[0003] However, there are problems with using microcantilever beams for mechanical measurements in AFM: First, the sensitivity of the detector and the changes in the feedback parameters ultimately determine the performance of the tip's normal and torsional motion, making accurate and intuitive mechanical measurements impossible; second, the laser beam needs to be directed at the end of the microcantilever beam to feed back the tip's offset to the detection system. During this process, only the normal bending of the microcantilever beam and the tip's torsion can be detected, but the horizontal bending (in-plane deformation) of the microcantilever cannot be observed. Figure 1 As shown. Therefore, AFM microcantilever beams generally have a large width-to-thickness ratio to prevent horizontal bending of the microcantilever, resulting in a large horizontal spring constant and significantly reducing the measurement accuracy of the horizontal force (the measurement accuracy can only reach 10). 2 (nN level). Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of the existing technology, the purpose of this invention is to provide a design method for microcantilever beams used for TEM measurement mechanics that can accurately and effectively measure quantitatively.

[0005] Technical solution: The present invention provides a design method for a microcantilever beam used in TEM measurement mechanics, comprising the following steps:

[0006] Step 1: The normal and horizontal displacements of the microcantilever beam were observed in the TEM at the nanometer level. The experiment required measuring the normal and horizontal forces with nanonewton-level precision. The normal elastic coefficient and the total horizontal elastic coefficient of the microcantilever beam were calculated according to Hooke's law.

[0007] Step 2: Calculate the length, width, thickness, and tip height of the micro-cantilever beam using the following formulas.

[0008]

[0009] In the formula, k N Let k be the normal elastic modulus of the microcantilever beam. L′ Let be the total horizontal elastic modulus of the microcantilever beam, E be the Young's modulus of the microcantilever beam, G be the shear modulus of the microcantilever beam, w be the width of the microcantilever beam, t be the thickness of the microcantilever beam, l be the length of the microcantilever beam, and k be the horizontal elastic modulus of the microcantilever beam. L Let k be the elastic modulus of the microcantilever beam under horizontal bending. T denoted as the torsional elastic coefficient of the microcantilever beam tip, and h as the height of the microcantilever beam tip.

[0010] Furthermore, in step one, Hooke's Law states that...

[0011] F N =k N ×Δy

[0012] F L =k L′ ×Δx

[0013] In the formula, F N For normal force, F L Δy is the horizontal force, Δy is the normal displacement, and Δx is the horizontal displacement.

[0014] Furthermore, in step one, a needle tip is provided at one end of the microcantilever beam, and the needle tip contacts the surface of the target material.

[0015] Preferably, the microcantilever beam is a single-crystal gold microcantilever beam. The calculated normal elastic modulus of the microcantilever beam is 3 N / m, and the total horizontal elastic modulus of the microcantilever beam is 2 N / m.

[0016] Furthermore, in step two, G is the shear modulus of the microcantilever beam, which is 25 GPa.

[0017] Furthermore, in step two, E is the Young's modulus of the microcantilever beam, which is 70 GPa.

[0018] Furthermore, in step two, the length of the microcantilever beam is calculated to be 60 μm, the width to be 2 μm, the thickness to be 2 μm, and the tip height to be 7 μm.

[0019] Furthermore, after the microcantilever beam dimensions are designed, the flat surface of the fracture end of the single-crystal gold wire is processed using a focused ion beam. The diameter of the single-crystal gold wire is 0.2–0.3 mm, and its purity is above 99.9 wt.%.

[0020] Design Principle: TEM, a characterization technique with extremely high atomic-level resolution and ultrafast spatiotemporal resolution, is frequently used to study the microstructure of nanomaterials. Therefore, combining a microcantilever beam from AFM with TEM not only allows for mechanical measurements of nanomaterials but also characterizes changes in their atomic structure morphology. Since the normal and horizontal movement of the microcantilever beam tip can be directly observed in TEM, without the need for laser beam irradiation and feedback detection, the complexity and uncertainty of the environment encountered in mechanical measurements of microcantilever beams in AFM can be directly addressed, thus ensuring the stability of microcantilever beam mechanical measurements. Furthermore, TEM provides real-time and direct observation of the horizontal bending (in-plane deformation) and tip torsion of the microcantilever beam, overcoming the problem of large width-to-thickness ratios in AFM where horizontal bending cannot be observed. This results in a smaller width-to-thickness ratio for the microcantilever beam under TEM, improving the accuracy of horizontal force measurements and achieving high-precision normal and horizontal force measurements of 1 nN, providing more accurate and effective quantitative measurements for various mechanical tests.

[0021] Beneficial effects: Compared with the prior art, the present invention has the following significant features:

[0022] 1. By directly measuring the needle tip displacement, the normal force and horizontal force on the target material can be intuitively calculated. The method is direct and convenient, avoiding the environmental complexity and uncertainty of mechanical measurement of micro cantilever beams in AFM, thereby achieving the stability of mechanical measurement of micro cantilever beams.

[0023] 2. By directly observing the horizontal bending and tip torsion of the microcantilever through TEM, microcantilever beams with a small width-to-thickness ratio can be designed for TEM measurement of mechanical processes. This improves the problem of low accuracy in horizontal force measurement caused by the large width-to-thickness ratio of traditional AFM microcantilever beams, thus enabling high-precision measurement of normal and horizontal forces of 1nN in TEM, providing more accurate and effective quantitative measurement for various mechanical tests. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the mechanical measurement method for micro cantilever beams under AFM (Automatic Mechanical Measurement).

[0025] Figure 2 This is a schematic diagram of the microcantilever beam mechanical measurement method under TEM according to the present invention;

[0026] Figure 3 These are SEM images of the micro cantilever beam of the present invention, wherein (a) is a top view and (b) is a side view;

[0027] Figure 4 This is a real-time data graph of the normal and horizontal forces measured by the gold microcantilever under TEM according to the present invention. Detailed Implementation

[0028] The microcantilever beam used for TEM measurement of mechanics has a needle tip perpendicular to it at the top and is fixed at the bottom. The needle tip of the microcantilever beam is aligned with the target material and perpendicular to the electron beam. The target material is connected to a displacement control mechanism. The needle tip of the microcantilever beam and the target material are placed under a transmission electron microscope (TEM) to observe the changes in their normal and lateral displacements. The changes in normal and lateral displacements are obtained by acquiring TEM images in real time.

[0029] A design method for microcantilever beams used in TEM measurement mechanics includes the following steps:

[0030] (1) Based on experimental requirements, single-crystal gold was selected as the material for the microcantilever beam. In TEM, the normal and horizontal displacements (Δy and Δx) of the single-crystal gold microcantilever beam were directly observed to be at the nanometer level. However, the experiment required the measurement of mechanical properties with nanonewton-level precision (i.e., nanometer-level Fmax). N and F L Therefore, based on the actual experimental requirements and the following formula:

[0031] F N =k N ×Δy (i)

[0032] F L =k L′ ×Δx (ii)

[0033] k was calculated N and k L′ The values ​​are 3 N / m and 2 N / m, respectively.

[0034] In the formula, F N For normal force, F L It is a horizontal force.

[0035] (2) Then, given that the Young's modulus E and shear modulus G of gold are 70 GPa and 25 GPa respectively, according to the following formula:

[0036]

[0037] The designed micro cantilever beam has a length l of 60μm, a width w of 2μm, a thickness t of 2μm, and a tip height h of 7μm.

[0038] In the formula, k N Let k be the normal elastic modulus of the microcantilever beam. L′ Let be the total horizontal elastic modulus of the microcantilever beam, E be the Young's modulus of the microcantilever beam, G be the shear modulus of the microcantilever beam, w be the width of the microcantilever beam, t be the thickness of the microcantilever beam, l be the length of the microcantilever beam, and k be the horizontal elastic modulus of the microcantilever beam. L Let k be the elastic modulus of the microcantilever beam under horizontal bending. Tdenoted as the torsional elastic coefficient of the microcantilever beam tip, and h as the height of the microcantilever beam tip.

[0039] Next, based on the designed dimensions of the gold microcantilever beam, the fracture surface of the single-crystal gold wire (0.25 mm, 99.9 wt.% purity) was processed using a focused ion beam (Dualbeam Helios 5CX), thereby achieving nano-Newton-level mechanical measurements of the single-crystal gold micro-protrusion. Due to some processing errors, the final processing result is as follows... Figure 3 As shown, the length l is 58.58 μm, the width w is 2.88 μm, the thickness t is 2.39 μm, and the tip height h is 7.34 μm.

[0040] The designed and fabricated gold micro cantilever beam was applied to TEM for the coordinated measurement of normal and horizontal forces, such as... Figure 4 As shown, they can all achieve high precision at the nanonewton level, 1nN accuracy, thus enabling precise and effective mechanical measurements.

Claims

1. A design method for a microcantilever beam used in TEM measurement mechanics, characterized in that, Includes the following steps: Step 1: Based on the experimental requirements, single-crystal gold metal was selected as the material for the microcantilever beam. The normal and horizontal displacements of the microcantilever beam were observed to be at the nanometer level in the TEM. The experiment required the measurement of the normal and horizontal forces with nanonewton-level precision. The normal elastic coefficient and the total horizontal elastic coefficient of the microcantilever beam were calculated according to Hooke's law. Step 2: Calculate the length, width, thickness, and tip height of the micro-cantilever beam using the following formulas. In the formula, k N Let be the normal elastic modulus of the microcantilever beam. The horizontal total elastic modulus of the microcantilever beam is... E The Young's modulus of the microcantilever beam. G The shear modulus of the microcantilever beam. w The width of the micro-cantilever beam. t The thickness of the micro-cantilever beam. l The length of the micro-cantilever beam. k L Let be the elastic modulus of the micro-cantilever beam under horizontal bending. k T The torsional elastic coefficient of the microcantilever beam tip. h The height of the needle tip of the microcantilever beam.

2. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: In step one, Hooke's Law is: In the formula, F N For normal force, F L For horizontal force, △ y For normal displacement, Δ x This represents horizontal displacement.

3. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: In step one, a needle tip is provided at one end of the microcantilever beam, and the needle tip is in contact with the surface of the target material.

4. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: In step one, the normal elastic coefficient of the microcantilever beam is calculated to be 3 N / m, and the total horizontal elastic coefficient of the microcantilever beam is 2 N / m.

5. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: In step two, G is the shear modulus of the microcantilever beam, which is 25 GPa.

6. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: In step two, E is the Young's modulus of the microcantilever beam, which is 70 GPa.

7. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: In step two, the length of the microcantilever beam is calculated to be 60 µm, the width to be 2 µm, the thickness to be 2 µm, and the tip height to be 7 µm.

8. The design method of a microcantilever beam for TEM measurement mechanics according to claim 1, characterized in that: After the dimensions of the microcantilever beam are designed, the flat surface of the fracture of the single crystal gold wire is processed by focused ion beam.

9. The design method of a microcantilever beam for TEM measurement mechanics according to claim 8, characterized in that: The single-crystal gold wire has a diameter of 0.2~0.3 mm and a purity of 99.9 wt.% or higher.

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