Scanning probe microscopy and methods

Abstract

To provide a technique for improving the accuracy of calculating the elastic modulus of a sample. [Solution] The control unit of a scanning probe microscope, which has a displacement detector for detecting the displacement of the probe, generates a first force curve, which is the measurement result of the probe's displacement due to a change in the distance between the probe and the sample, using the detection output of the displacement detector for the sample. The control unit also generates a second force curve by excluding the region in the first force curve where the distance from the inflection point is shorter than the region in the first force curve. The control unit then calculates the elastic modulus of the sample based on the second force curve and a theoretical formula.

Description

Technical Field

[0001] The present invention relates to calculating the elastic modulus of a sample using a SPM (Scanning Probe Microscope).

Background Art

[0002] The SPM has a cantilever, and a probe is provided at the tip of the cantilever. The SPM acquires information on the sample surface by bringing the probe close to the sample, and generates an observation image based on this information. Japanese Patent Application Laid-Open No. 2022-013401 (Patent Document 1) mentions calculating the elastic modulus of a sample using a SPM.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] The elastic modulus is an index related to the hardness of a sample. In the conventional technology, as the elastic modulus of a sample, a value deviating from the value assumed from the actual hardness of the sample may be calculated.

[0005] The present invention has been conceived in view of such circumstances, and its object is to provide a technique for improving the accuracy of calculating the elastic modulus of a sample.

Means for Solving the Problems

[0006] A scanning probe microscope according to a certain aspect of this disclosure comprises a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a movement mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe relative to the base, and a control unit for controlling the movement mechanism. The control unit uses the detection output of the displacement detector to generate a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample. In the first force curve, a first region is identified, which starts from the jump-in portion and corresponds to a range shorter than the jump-in portion. In the jump-in portion, the probe begins to receive an attractive force from the sample as the distance decreases. The control unit identifies a basic region in the first region, which is the region from the first inflection point closest to the jump-in portion among the one or more inflection points in the first region to the jump-in portion, and an excluded region, which is the region other than the basic region. By excluding the excluded region from the first force curve, a second force curve is generated, and the elastic modulus of the sample is calculated based on the second force curve and a theoretical formula. It is structured in this way.

[0007] A scanning probe microscope according to a certain aspect of this disclosure comprises a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a movement mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe relative to the base, and a control unit for controlling the movement mechanism. The control unit is configured to generate a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample, by utilizing the detection output of the displacement detector, generate a second force curve by excluding the region where the distance is shorter than the inflection point in the first force curve, and calculate the elastic modulus of the sample based on the second force curve and a theoretical formula.

[0008] A method according to a certain aspect of the present disclosure is a method for calculating the elastic modulus of a sample using a scanning probe microscope, the scanning probe microscope comprising: a sample stage on which the sample is placed; a cantilever with a fixed base and a probe at its tip; a movement mechanism for relatively changing the positional relationship between the sample stage and the base; a displacement detector for detecting the displacement of the probe relative to the base; and a control unit for controlling the movement mechanism, the method comprising the steps of: generating a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample, using the detection output of the displacement detector; and excluding from the first force curve regions where the distance is shorter than the inflection point. The method comprises the steps of generating a second force curve and calculating the elastic modulus of the sample based on the second force curve and a theoretical formula, wherein the step of generating the second force curve includes identifying a first region in the first force curve that corresponds to a range starting from the jump-in portion and being shorter in distance than the jump-in portion, where the probe begins to receive an attractive force from the sample as the distance decreases, and the step of generating the second force curve further includes identifying the inflection point in the first region that is closest to the jump-in portion among one or more inflection points in the first region.

[0009] A method according to a certain aspect of the present disclosure is a method for calculating the elastic modulus of a sample using a scanning probe microscope, the scanning probe microscope including a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a moving mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe relative to the base, and a control unit for controlling the moving mechanism, comprising the steps of: generating a first force curve, which is the result of measuring the displacement due to a change in the distance between the probe and the sample, using the detection output of the displacement detector; generating a second force curve by excluding from the first force curve a region that is shorter than the inflection point; and calculating the elastic modulus of the sample based on the second force curve and a theoretical formula. [Effects of the Invention]

[0010] In accordance with certain aspects of this disclosure, a technique is provided for improving the accuracy of calculating the elastic modulus of a sample. [Brief explanation of the drawing]

[0011] [Figure 1] This diagram schematically shows the configuration of the SPM100 according to the embodiment. [Figure 2] This figure shows an example of the hardware configuration of the information processing device 20. [Figure 3] This diagram schematically illustrates the dynamical model based on the JKR (Johnson, Kendall, Roberts) method. [Figure 4] This figure shows an example of a force curve obtained by measurement when adhesion is present on the sample. [Figure 5] This figure shows an example of a load-displacement curve. [Figure 6] This diagram schematically represents the state of the probe 3 on the cantilever 2 and the sample at the equilibrium point and the point of maximum adhesion. [Figure 7] This figure shows an example of a force curve obtained by measurement unaffected by adhesion. [Figure 8] This represents the contact theory model in the Hertz method. [Figure 9] This figure shows the load-displacement curve obtained by redrawing the force curve in Figure 7. [Figure 10] This diagram schematically illustrates the dynamical model on which the Sneddon method is based. [Figure 11] This figure shows an example of a force curve obtained by measurement unaffected by adhesion. [Figure 12] This represents the contact theory model in the Sneddon method. [Figure 13] This figure shows the load-displacement curve obtained by redrawing the force curve in Figure 11. [Figure 14] This figure shows an example of a force curve generated according to the measurement results of the sample. [Figure 15] This figure shows a concrete example of a force curve. [Figure 16] It is a figure showing the force curve of FIG. 15 together with an annex. [Figure 17] It is a figure for explaining the correction of the force curve of FIG. 15. [Figure 18] It is a figure showing a specific example of a force curve. [Figure 19] It is a figure showing the force curve of FIG. 18 together with an annex. [Figure 20] It is a figure showing the force curve after correction. [Figure 21] It is a flowchart of the process performed by the information processing apparatus 20 for calculating the elastic modulus. [Embodiments for Carrying Out the Invention]

[0012] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are denoted by the same reference numerals and their description will not be repeated.

[0013] [Configuration of Scanning Probe Microscope] FIG. 1 is a diagram schematically showing the configuration of the SPM100 according to the embodiment. The SPM100 is an atomic force microscope (AFM: Atomic Force Microscope) that observes the sample S by using the interatomic force (attractive force or repulsive force) acting between the probe and the surface of the sample S.

[0014] Referring to FIG. 1, the SPM100 includes an observation device 80, an information processing device 20, a display device 26, and an input device 28. The observation device 80 includes an optical system 1, a cantilever 2, a scanner 10, a sample stage 12, a drive unit 16, an arithmetic unit 17, and a control unit 18.

[0015] The scanner 10 is a moving device for changing the relative positional relationship between the sample S and the probe 3. The sample S is held on a sample stage 12 placed on the scanner 10. The scanner 10 has an XY scanner that scans the sample S in two mutually orthogonal axes, X and Y, and a Z scanner that finely moves the sample S in the Z axis direction. The XY scanner and the Z scanner are made up of piezoelectric elements that deform according to the voltage applied from the drive unit 16, and according to the voltage applied to the piezoelectric elements, the scanner 10 scans in three dimensions (X axis direction, Y axis direction, Z axis direction). This makes it possible to change the relative positional relationship between the sample S placed on the scanner 10 and the probe 3 in three dimensions.

[0016] The cantilever 2 has a surface facing the sample S and a back surface opposite to the surface. One end of the cantilever 2 is supported by a holder 4. The cantilever 2 has a probe 3 on the surface of its free end, the tip. The probe 3 is positioned facing the sample S. The probe 3 moves along the surface of the sample S, and the cantilever 2 is displaced by the interatomic force acting between the probe 3 and the sample S.

[0017] An optical system 1 is provided above the cantilever 2 for detecting the displacement of the cantilever 2 in the Z-axis direction. When observing the sample S, the optical system 1 irradiates the back surface of the cantilever 2 with laser light and detects the laser light reflected from the back surface of the cantilever 2. The optical system 1 includes a laser light source 6, a beam splitter 5, a mirror 7, and a photodetector 8.

[0018] The laser light source 6 has a laser oscillator that emits laser light. The photodetector 8 has a four-segment photodiode that detects the incident laser light. The laser light LA ​​emitted from the laser light source 6 is reflected by the beam splitter 5 and irradiates the back surface of the cantilever 2.

[0019] The cantilever 2 is made of silicon or silicon nitride, and can reflect laser light irradiated from the optical system 1 on its back surface. The laser light reflected from the back surface of the cantilever 2 is further reflected by the mirror 7 and incident on the photodetector 8. By detecting the laser light with the photodetector 8, the displacement of the cantilever 2 can be detected.

[0020] Specifically, the photodetector 8 has multiple (usually two) light-receiving surfaces divided in the direction of displacement of the cantilever 2 (Z-axis direction). Alternatively, the photodetector 8 has four light-receiving surfaces divided in the Z-axis direction and the Y-axis direction. When the cantilever 2 is displaced, the ratio of the amount of light irradiated onto these multiple light-receiving surfaces changes. The photodetector 8 outputs a detection signal to the calculation unit 17 corresponding to the amount of light received by these multiple light-receiving surfaces. Upon receiving the detection signal, the calculation unit 17 calculates the amount of displacement of the cantilever 2 based on the detection signal. The calculation unit 17 controls the position of the sample S in the Z direction so that the interatomic force between the probe 3 and the surface of the sample S remains constant. The calculation unit 17 calculates a voltage value that displaces the scanner 10 in the Z-axis direction based on the amount of displacement of the cantilever 2 and outputs it to the scanner 10.

[0021] Furthermore, the calculation unit 17 outputs a detection signal to the control unit 18. The control unit 18 generates a control signal based on the detection signal and outputs the control signal to the information processing device 20.

[0022] The information processing device 20 is communicatively connected to the control unit 18, the display device 26, and the input device 28. The information processing device 20 generates image data (profile data) based on control signals from the control unit 18.

[0023] The information processing device 20 displays the observed image on the display device 26 based on the generated image data. The observed image is an image showing the surface of the sample S. The information processing device 20 also controls the drive unit 16 via the control unit 18 to drive the scanner 10 in a three-dimensional direction.

[0024] The input device 28 receives user input. The input device 28 outputs a signal to the information processing device 20 according to the user's operation. The information processing device 20 outputs this signal to the control unit 18. The control unit 18 performs control on the observation device 80 based on this signal. The input device 28 may be a touch panel provided on the display device 26, or it may be a dedicated operation button, a mouse, or a keyboard or other physical operation key.

[0025] [Hardware configuration of information processing equipment] Figure 2 shows an example of the hardware configuration of the information processing device 20. The information processing device 20 has as its main components a CPU (Central Processing Unit) 160, a ROM (Read Only Memory) 162, a RAM (Random Access Memory) 164, an HDD (Hard Disk Drive) 166, a communication I / F (Interface) 168, a display I / F 170, and an input I / F 172. Each component is interconnected by a data bus.

[0026] Communication I / F 168 is an interface for communicating with the observation device 80. Display I / F 170 is an interface for communicating with the display device 26. Input I / F 170 is an interface for communicating with the input device 28.

[0027] ROM162 stores the program executed by CPU160. RAM164 can temporarily store data generated by the execution of the program on CPU160, as well as data input via communication I / F168. RAM164 can function as temporary data memory used as a working area. HDD166 is a non-volatile storage device. Alternatively, semiconductor storage devices such as flash memory may be used instead of HDD166.

[0028] Furthermore, the program stored in ROM 162 may be stored on a storage medium and distributed as a program product. Alternatively, the program may be provided by an information provider as a program product that can be downloaded via the so-called Internet. The information processing device 20 reads the program provided on the storage medium or via the Internet. The information processing device 20 stores the read program in a predetermined storage area (for example, ROM 162). The CPU 160 executes the above-described display process by executing the stored program.

[0029] The storage medium is not limited to DVD-ROM (Digital Versatile Disk Read Only Memory), CD-ROM (compact disc read-only memory), FD (Flexible Disk), or hard disk, but may also be a medium that permanently stores programs, such as magnetic tape, cassette tape, optical discs (MO (Magnetic Optical Disc) / MD (Mini Disc) / DVD (Digital Versatile Disc)), optical cards, mask ROM, EPROM (Electronically Programmable Read-Only Memory), EEPROM (Electronically Erasable Programmable Read-Only Memory), or semiconductor memory such as flash ROM. The recording medium is a non-temporary medium from which a computer can read programs and other data. At least one of ROM 162, RAM 164, and HDD 166 corresponds to the "memory" in this disclosure. In other words, the memory stores information used by the information processing device.

[0030] [Calculation of the elastic modulus of the sample] In the SPM100, when calculating the elastic modulus of a sample, the information processing apparatus 20 uses a force curve. At this time, the information processing apparatus 20 performs force curve measurement. Force curve measurement means changing the distance between the sample and the cantilever 2 by sweeping the cantilever 2 in the vertical direction (Z direction) near the sample, and measuring the force acting on the cantilever 2 during this period. The relationship between the distance between the proximal end of the cantilever and the sample and the force acting on the cantilever 2 obtained by force curve measurement is obtained. The graph representing this relationship is called a "force curve".

[0031] For calculating the elastic modulus, theoretical formulas are used. Hereinafter, as a specific example, three types of theoretical formulas will be described.

[0032] <Theoretical formula according to the JKR method> ≪Model overview≫ The JKR method is based on a mechanical model that assumes a spherical shape for the indenter, a planar shape for the sample, and three points: the indenter tip and the sample surface are in spherical contact. For the following explanations, for example, the following three references can be cited. ·Experimental Physical Science Series 6 "Scanning Probe Microscopy", co-authored by Shigekawa, Yoshimura, and Kawazu, Kyoritsu Shuppan, ISBN: 9784320033818) ·Ken NAKAJIMA, Hao LIU, Makiko ITO, So FUJINAMI, J.Vac.Soc.Jpn., 2013, 56, 258 ·Sae NAGAI, So FUJINAMI, Ken NAKAJIMA, Toshio NISHI (Nihon Reoroji Gakkaishi, 2008, 36, 99) Figure 3 is a diagram schematically showing the mechanical model based on the JKR method. In this mechanical model, as shown in Figure 3, the tip of the indenter 200 and the surface of the sample 201 are in spherical contact. When in spherical contact, there is a relationship of "R>δ" between the radius of curvature R of the tip of the indenter 200 and the sample deformation amount δ. In this model, the adhesion of the sample is considered.

[0033] ≪Applicable force curve≫ Figure 4 shows an example of a force curve obtained by measurement when adhesion is present on the sample. In Figure 4, the horizontal axis shows the distance between the base end of the cantilever 2 and the sample as the "Z position". On the vertical axis, the displacement of the cantilever 2 ("cantilever displacement") is shown as an index corresponding to the force acting on the cantilever 2. The displacement of the cantilever 2 represents the displacement of the probe 3 due to the force acting on the cantilever 2.

[0034] In the force curve shown in Figure 4, during the approach phase, data is added in the direction that decreases the Z position value over time (to the right in Figure 4). During the release phase, data is added in the direction that increases the Z position value over time (to the left in Figure 4).

[0035] During the approach process, a jump-in occurs where the cantilever displacement changes abruptly near the sample surface. Even after the jump-in, the sample is brought closer to the cantilever (for example, the Z scanner is driven to decrease the Z position value). As a result, the cantilever displacement value changes from negative (probe 3 is bent toward the sample due to attractive force) to positive (probe 3 is aligned with the opposite side of the sample due to repulsive force), beyond the equilibrium point.

[0036] During the release process, even if the distance between the proximal end of cantilever 2 and the sample increases beyond the point where jump-in occurs (even if the Z position value increases beyond the point where jump-in occurs), cantilever 2 continues to be subjected to adhesive force. Then, immediately after receiving the maximum adhesive force, a jump-out is observed in which the cantilever displacement changes rapidly.

[0037] The equilibrium point represents the point where the elastic force acting on cantilever 2 (probe 3) and the adhesion force due to the sample are balanced, resulting in a net force of zero. The maximum adhesion point represents the point in the Z-axis direction where the force acting on the cantilever during the release process is maximized due to the adhesion of the sample.

[0038] The JKR method is applied to a force curve that reflects the adhesion of the sample, as described above (i.e., a force curve in which the cantilever displacement changes curvilinearly with respect to changes in the Z position).

[0039] The force curve shown in Figure 4 represents the case when the sample is soft. On the other hand, when the sample is sufficiently hard, the cantilever displacement changes linearly with respect to the change in Z position, as shown by the dotted line in Figure 4. That is, the amount of deformation of the sample (the difference between the solid line and the dotted line at each Z position) becomes very small. In the JKR method, the amount of deformation of the sample is used to calculate the elastic modulus. Therefore, when the amount of deformation of the sample is very small, the JKR method cannot be applied to calculate the elastic modulus.

[0040] In Figure 4, dZ represents the piezoelectric Z displacement (scanner control amount from jump-in to the end of the push-in). d△ represents the cantilever displacement value corresponding to the piezoelectric Z displacement. The following relationship, shown in equation (1), holds between the sample deformation amount dδ corresponding to the piezoelectric Z displacement, the piezoelectric Z displacement amount dZ, and the cantilever displacement value d△.

[0041]

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[0042] ≪Points to note during measurement≫ To obtain a force curve used in conjunction with a theoretical formula according to the JKR method for detecting the modulus of elasticity, the following points must be considered.

[0043] • To ensure spherical contact between the probe tip and the sample surface, the amount of probe insertion should be less than the radius of curvature of the probe tip.

[0044] • Use a cantilever with an appropriate spring constant. (If the cantilever's spring constant is too high, the amount of pressure applied to a soft sample during the approach may become excessive. Conversely, if the spring constant is too low, sufficient pressure may not be applied to a hard sample during the approach.) ≪Analysis method≫ In order to calculate the modulus of elasticity from the obtained force curve, it is necessary to rewrite the force curve into a load-displacement curve (F-δ curve) that represents the relationship between the force F applied to the cantilever and the deformation amount δ of the sample, thereby generating a theoretical F-δ curve, and then to fit the theoretical F-δ curve to the measured F-δ curve by overlaying it.

[0045] Figure 5 shows an example of a load-displacement curve. In the curve in Figure 5, the horizontal axis represents the amount of sample deformation in the force curve in Figure 4. In one implementation example, the displacement of probe 3 (the cantilever displacement value in Figure 4) is used as the amount of sample deformation. The vertical axis represents the force acting on cantilever 2. The force acting on cantilever 2 is calculated as the product of the deflection of cantilever 2 and the spring constant. In Figure 5, as in Figure 4, the curve when the sample is soft is shown as a solid line, and the curve when the sample is sufficiently hard is shown as a dashed line.

[0046] In the JKR method, the relationship between F and δ is expressed by equations (2) and (3) below, through the contact circle radius a between the tip of probe 3 and the sample surface. w represents the adhesion energy, R represents the radius of curvature of probe 3, and K represents the elastic modulus of the sample.

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[0049] Equations (2) and (3) are very complicated. Therefore, even if we obtain a theoretical F-δ curve by eliminating a from equations (2) and (3) and rewriting them into a relationship between only F and δ, it is difficult to fit this theoretical F-δ curve onto the load-displacement curve in Figure 5 by superimposing it.

[0050] Therefore, the elastic modulus is calculated using the equilibrium point and the point of maximum adhesion shown in Figure 5. This method is also called the "two-point method."

[0051] Figure 6 schematically shows the state of the probe 3 on the cantilever 2 and the sample at the equilibrium point and the point of maximum adhesion. For the force F acting on the cantilever, the amount of sample deformation δ, and the contact circle radius a between the tip of the probe 3 and the sample surface, the values ​​at the equilibrium point are denoted with the subscript "0", and the values ​​at the point of maximum adhesion are denoted with the subscript "1".

[0052] In Figure 4, dZ represents the scanner control amount from jump-in to the end of the push-in. On the other hand, in Figure 6, dZ represents the difference between the Z position value at the equilibrium point and the Z position value at the maximum adhesion point.

[0053] The following describes the procedure for determining F and δ at both points and then calculating the modulus of elasticity. First, let's consider the point of maximum adhesion. At the point of maximum adhesion, the probe 3 and the sample surface are in a state just before separation. Therefore, the contact circle radius a0 is minimized. Consequently, the value inside the square root in equation (2) becomes 0, as shown in equation (4) below.

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[0055] Solving equation (4), F1 is expressed by equation (5).

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[0057] By substituting equation (5) into equation (2), we obtain equation (6).

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[0059] By substituting equation (6) into equation (3), we obtain equation (7).

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[0061] Next, let's consider the equilibrium point. At the equilibrium point, F0 = 0. By substituting F0 = 0 into equation (2), we obtain equation (8).

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[0063] By substituting equation (8) into equation (3), we obtain equation (9).

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[0065] By using equations (7) and (9), equation (10) can be obtained.

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[0067] By rearranging equation (10), we obtain equation (11).

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[0069] The elastic modulus E of the sample is given by equation (12), where ν is the Poisson's ratio of the sample.

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[0071] By substituting equation (11) into equation (12), equation (13) is obtained.

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[0073] According to equation (13), the elastic modulus E of the sample can be calculated using the Poisson's ratio ν of the sample, the force F1 applied to the cantilever at the maximum adhesion point, the sample deformation amount δ0 at the equilibrium point, and the sample deformation amount δ1 at the maximum adhesion point. In this sense, equation (13) constitutes an example of a theoretical formula for calculating the elastic modulus.

[0074] <Theoretical formula according to Hertz method> ≪Model overview≫ The Hertz method is based on a mechanical model that assumes a spherical shape for the indenter, a planar shape for the sample, and that the indenter tip and the sample surface are in spherical contact. For the following explanations, for example, the following three references can be cited. ·Experimental Physics Science Series 6 "Scanning Probe Microscope", co-authored by Shigekawa, Yoshimura, and Kawazu, Kyoritsu Shuppan, ISBN: 9784320033818 ·Ken NAKAJIMA, Hao LIU, Makiko ITO, So FUJINAMI, J. Vac. Soc. Jpn., 2013, 56, 258 ·Textbook of Manufacturing - Practical Material Mechanics (Nikkei Manufacturing Series - Textbook of Manufacturing), Chapter 24, written by Toshiyuki Sawa, Nikkei BP, ISBN: 9784822218997 The mechanical model based on the Hertz method is schematically shown in Figure 3, similar to the mechanical model based on the JKR method. However, in the mechanical model based on the Hertz method, the adhesion of the sample is not considered.

[0075] ≪Applicable force curve≫ Figure 7 shows an example of a force curve obtained by measurement unaffected by adhesion. For example, if the force curve measurement is performed in a liquid, jump-in and jump-out do not occur, and therefore the Hertz method may be applied to the force curve. In the graph of Figure 7, the horizontal axis (probe-sample distance) represents the Z position, and the vertical axis represents the cantilever displacement.

[0076] In Figure 7, the solid line represents the force curve when the sample is soft, and the dotted line represents the force curve when the sample is sufficiently hard. In the force curve shown in Figure 7, no jump-in is observed in the cantilever displacement near the sample surface during the approach process. Since the Hertz method does not consider adhesive force, it can be applied to calculating the modulus of elasticity using a force curve that shows a rise without jump-in.

[0077] In the example shown in Figure 7, the relationship shown in equation (1) above holds between the sample deformation dδ corresponding to the piezoelectric Z displacement, the piezoelectric Z displacement dZ, and the cantilever displacement value dΔ.

[0078] ≪Points to note during measurement≫ To obtain a force curve (a force curve without jump-ins) to be used with the theoretical formula according to the Hertz method for detecting the modulus of elasticity, the following points must be considered.

[0079] • To ensure spherical contact between the probe tip and the sample surface, the amount of indentation of probe 3 should be smaller than the radius of curvature of the probe tip 3.

[0080] • To suppress jump-in, a cantilever with a large spring constant is used. • To minimize jump-in measurements, the measurement will be taken underwater.

[0081] ≪Analysis method≫ Figure 8 shows the contact theory model in the Hertz method. Figure 8 shows the contact between object 211 and object 212. R1 represents the radius of curvature of object 211, and R2 represents the radius of curvature of object 212. E1 represents the elastic modulus of object 211, and E2 represents the elastic modulus of object 212. ν1 represents the Poisson's ratio of object 211, and ν2 represents the Poisson's ratio of object 212.

[0082] According to Hertz's contact theory, when two spheres come into contact under a force F, equation (14) is given for the sample deformation δ. * This represents the combined elastic modulus of object 211 and object 212.

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[0084] Also, the composite modulus E * When the modulo elasticity E1, E2 and Poisson's ratios ν1, ν2 are used, it can be expressed as shown in equation (15).

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[0086] In actual measurements, R2 is much larger than R1. Therefore, under the assumption that R2 → ∞ (plane approximation), equation (15) is transformed into equation (16).

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[0088] Furthermore, assuming that the elastic modulus of cantilever 2 is very large compared to the elastic modulus of the sample, equation (15) can be transformed into equation (17).

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[0090] Substituting equation (17) into equation (16), we derive equation (18) as the relationship between F and δ.

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[0092] To calculate the modulus of elasticity from the force curve obtained during measurement, it is necessary to rewrite the force curve as a load-displacement curve (F-δ curve) that represents the relationship between the force F applied to the cantilever 2 and the deformation amount δ of the sample, and then fit it with the theoretical F-δ curve of the model to be applied.

[0093] Figure 9 shows the load-displacement curve obtained by redrawing the force curve in Figure 7. In Figure 9, the horizontal axis represents the amount of deformation of the sample in the force curve of Figure 7, and the vertical axis represents the force acting on the cantilever, calculated as the product of the cantilever deflection and the spring constant.

[0094] According to the load-displacement curve shown in Figure 9, the force F acting on the cantilever 2 can be approximated to be proportional to the 3 / 2 power of the sample deformation δ, as shown in equation (19).

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[0096] By taking the logarithm of both sides of equation (19), we obtain equation (20). Note that the base of equation (20) can be arbitrary, but for example it can be "10".

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[0098] Equation (20) has the form of a linear function, that is, the form of Y = aX + b. Therefore, by applying the least squares method to Equation (20) obtained according to the measurement results, it is possible to calculate the regression line. The theoretically slope of the regression line is the coefficient of Log 10 of δ, that is, 3 / 2. And as shown in Equation (21), using the intercept b of the regression line, the elastic modulus E2 of the object 212 is derived.

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[0100] When the object 211 is the cantilever 2 and the object 212 is the sample, the elastic modulus of the sample is derived as the elastic modulus E2.

[0101] <Theoretical formula according to Sneddon method> ≪Model overview≫ The Sneddon method is based on a mechanical model that assumes a conical shape for the indenter, a planar shape for the sample, and that the indenter tip and the sample surface are in conical contact. For the following explanations, for example, the following literature can be referred to. · Textbook of Manufacturing _ Practical · Mechanics of Materials (Nikkei Manufacturing Books _ Textbook of Manufacturing), Chapter 24, written by Toshiyuki Sawada, Nikkei BP, ISBN: 9784822218997 Figure 10 is a diagram schematically showing the mechanical model based on the Sneddon method. As shown in Figure 10, in the mechanical model of the Sneddon method, the shape of the indenter 221 contacting the sample 222 is conical. In Figure 10, R represents the radius of curvature of the indenter 221, and δ represents the sample deformation amount. The relationship of R > δ holds between R and δ. In the mechanical model based on the Sneddon method, the adhesion of the sample is not considered.

[0102] ≪Applicable force curve≫ Figure 11 shows an example of a force curve obtained by measurement unaffected by adhesion. In the graph in Figure 7, the horizontal axis (probe-sample distance) represents the Z position, and the vertical axis represents the cantilever displacement.

[0103] In Figure 11, the solid line represents the force curve when the sample is soft, and the dotted line represents the force curve when the sample is sufficiently hard. In the force curve shown in Figure 11, no jump-in is observed in the cantilever displacement near the sample surface during the approach process. Since the Sneddon method does not consider adhesive force, it can be applied to calculating the modulus of elasticity using a force curve that shows a rise without jump-in.

[0104] In the example shown in Figure 11, the relationship shown in equation (1) above holds between the sample deformation dδ corresponding to the piezoelectric Z displacement, the piezoelectric Z displacement dZ, and the cantilever displacement value dΔ.

[0105] ≪Points to note during measurement≫ To obtain a force curve (a force curve without jump-ins) to be used with a theoretical formula following the Sneddon method for detecting the modulus of elasticity, the following points must be considered.

[0106] - The amount of indentation of probe 3 should be smaller than the radius of curvature of the probe tip 3 so that the probe tip and the sample surface make conical contact.

[0107] • To suppress jump-in, a cantilever with a large spring constant is used. • To minimize jump-in measurements, the measurement will be taken underwater.

[0108] ≪Analysis method≫ Figure 12 shows the contact theory model in the Sneddon method. Figure 12 shows the contact between the indenter 221 and the sample 222. R1 represents the radius of curvature of the indenter 221, and R2 represents the radius of curvature of the sample 222. E1 represents the modulus of elasticity of the indenter 221, and E2 represents the modulus of elasticity of the sample 222. ν1 represents the Poisson's ratio of the indenter 221, and ν2 represents the Poisson's ratio of the sample 222.

[0109] According to Sneddon's contact theory, when two spheres come into contact under a force F, equation (22) is given for the amount of sample deformation δ. * α represents the combined elastic modulus of the indenter 221 and the sample 222. α represents the half-vertex angle of the indenter 221.

[0110]

number

[0111] Also, the composite modulus E * This can be expressed as shown in equation (23) when the modulo elasticity E1, E2 and Poisson's ratios ν1, ν2 are used.

[0112]

number

[0113] Assuming that the elastic modulus of cantilever 2 is very large compared to the elastic modulus of the sample, equation (23) can be transformed into equation (24).

[0114]

number

[0115] Substituting equation (24) into equation (22), we derive equation (25) as the relationship between F and δ.

[0116]

number

[0117] To calculate the modulus of elasticity from the force curve obtained during measurement, it is necessary to rewrite the force curve as a load-displacement curve (F-δ curve) that represents the relationship between the force F applied to the cantilever 2 and the deformation amount δ of the sample, and then fit it with the theoretical F-δ curve of the model to be applied.

[0118] FIG. 13 is a diagram showing a load-displacement curve obtained by redrawing the force curve of FIG. 11. In FIG. 13, the horizontal axis represents the sample deformation amount in the force curve of FIG. 11, and the vertical axis represents the force applied to the cantilever calculated as the product of the deflection amount of the cantilever and the spring constant.

[0119] According to the load-displacement curve shown in FIG. 13, as shown in equation (26), the force F applied to the cantilever 2 can be approximated to be proportional to the square of the sample deformation amount δ.

[0120] [Number]

[0121] By taking the logarithm of both sides of equation (26), equation (27) is obtained. In equation (27), the base is arbitrary, for example, it can be "10".

[0122] [Number]

[0123] Equation (27) has the form of a linear function, that is, the form of Y = aX + b. Therefore, by applying the least squares method to equation (27) obtained according to the measurement results, it is possible to calculate the regression line. The theoretical slope of the regression line is the coefficient of Log 10 δ in equation (27), that is, 2. And as shown in equation (28), the elastic modulus E2 of the sample 222 is derived using the intercept b of the regression line.

[0124] [Number]

[0125] [Correction of force curve] [Correction of force curve used in the theoretical formula according to the JKR method] Figure 14 shows an example of a force curve generated according to the measurement results of a sample. In the example in Figure 14, the sample is placed on a substrate. In Figure 14, the dashed line represents the sensitivity line obtained from the force curve of the substrate alone. The slope of the sensitivity line is the sensitivity S of the cantilever. Sensitivity S is a coefficient used when the deflection amount of the cantilever 2 is converted from voltage value (V) to distance (nm). The sensitivity line is set to have a slope equal to sensitivity S and pass through the minimum value of the cantilever displacement during jump-in (point A), and is superimposed on Figure 14.

[0126] In the example shown in Figure 14, the force curve is used to determine δ0 (sample deformation at the equilibrium point) and δ1 (sample deformation at the point of maximum adhesion) that are applied to the theoretical formula above. More specifically, δ0 is determined as the difference between the sensitivity line and the force curve at the equilibrium point. δ1 is determined as the difference between the force curve and the sensitivity line at the point of maximum adhesion.

[0127] If the sample set on the substrate is sufficiently thick (e.g., several tens of micrometers or more), the influence of the substrate on the force curve can be ignored. However, if the sample is a thin film, the force curve is affected by the hardness of the substrate. If the elastic modulus is calculated using a force curve affected by the hardness of the substrate, the elastic modulus may deviate from the value expected from the sample's inherent hardness. More specifically, this effect is unlikely to appear in the indentation after the equilibrium point during the approach process, but it is expected to appear between the jump-in and the equilibrium point.

[0128] Therefore, in this embodiment, the force curve may be corrected to reduce the influence of the substrate.

[0129] Figure 15 shows a specific example of a force curve. Figure 15 shows a plot consisting of triangular markers acquired during the approach phase and a plot consisting of circular markers acquired during the release phase. During the approach phase, markers are added from left to right in Figure 15 as time progresses. During the release phase, markers are added from right to left in Figure 15 as time progresses. Line L1 represents the baseline identified in the force curve in Figure 15.

[0130] In the example in Figure 15, point P11 represents the point of maximum adhesion. Point P12 represents the equilibrium point. The equilibrium point is identified as the intersection of the plot and the baseline during the approach process (or release process).

[0131] However, in the force curve shown in Figure 15, the curvature of the curve formed by the plots is not constant between point P11 and point P12, during both the approach and release phases.

[0132] Figure 16 shows the force curve from Figure 15, along with annotations. As shown in Figure 16, the curvature of the force curve changes at point P13 between points P11 and P12. More specifically, in the example in Figure 16, the portion of the force curve from point P11 to point P13 is a curve, while the portion from point P13 to point P12 is a straight line. In Figure 16, point P14 represents the minimum value of the cantilever displacement during the jump-in.

[0133] In this embodiment, the information processing device 20 corrects the force curve. In correcting the force curve, the information processing device 20 first identifies the minimum value of the cantilever displacement during the jump-in.

[0134] The information processing device 20 then searches for an inflection point in the region where the probe-sample distance is longer than the minimum value (right side in Figures 15 and 16). The search for an inflection point may be performed in the portion of the force curve obtained during the approach process or in the portion obtained during the release process.

[0135] The information processing device 20 then identifies the inflection point closest to the local minimum from the one or more inflection points obtained as a result of the search. In the example in Figure 16, point P13 is identified as the inflection point closest to the local minimum.

[0136] The information processing device 20 then corrects the force curve by removing the portion corresponding to the region where the probe-sample distance is longer than the inflection point identified above (the right side in Figures 15 and 16).

[0137] Figure 17 is a diagram illustrating the correction of the force curve in Figure 15. In the force curve shown in Figure 17, the portion to the right of point P13 has been removed compared to the force curve shown in Figure 15.

[0138] The information processing device 20 extrapolates the data from point P14 to point P13 in the force curve shown in Figure 17 using a straight line or curve. In Figure 17, the line obtained by extrapolation is shown as line L2.

[0139] Then, the intersection point of the straight line or curve (line L2) obtained by the above extrapolation and the baseline (line L1) is identified as the equilibrium point. In Figure 17, the equilibrium point identified using the corrected baseline is shown as point P15.

[0140] The information processing device 20 generates a force curve of the sample in order to calculate the elastic modulus of the sample, and uses the force curve to identify δ0 (amount of sample deformation at the equilibrium point) and δ1 (amount of sample deformation at the maximum adhesion point). The information processing device 20 also identifies the force acting on the cantilever at the maximum adhesion point as F1. Furthermore, the information processing device 20 obtains the Poisson's ratio ν of the sample. The Poisson's ratio ν of the sample is input from the user, for example, via the input device 28. The information processing device 20 then calculates the elastic modulus of the sample by applying these values ​​to the theoretical formula shown as equation (13).

[0141] When δ0 and δ1, derived from the force curve shown in Figure 15, were used, the modulus of elasticity was 1299.1 kPa. On the other hand, when δ0 and δ1, derived from the force curve (corrected force curve) shown in Figure 17, were used, the modulus of elasticity was 469.7 kPa. In other words, the value of the final determined modulus of elasticity changed when the corrected force curve was used.

[0142] In this embodiment, the force curve shown in Figure 15 constitutes an example of a first force curve, which is a measurement result. The force curve shown in Figure 17 constitutes an example of a second force curve, which is generated by deleting data from a given region from the first force curve.

[0143] Furthermore, in this embodiment, point P11 and the portion to the right of point P11 in the force curve shown in Figure 15 constitute an example of the first region (a region that starts from the jump-in portion and corresponds to a range in which the distance between the probe and the distance is shorter than that of the jump-in portion). The jump-in portion refers to the portion in the force curve in which the value of the cantilever displacement changes abruptly due to the jump-in.

[0144] In this embodiment, for the force curve shown in FIG. 15, a search for an inflection point is performed on the portion to the right of point P11, and thereby, in the portion to the right of point P11, point P13 is specified as the inflection point. By point P13, the portion to the right of point P11 is divided into a portion from point P11 to point P13 and a portion from point P13 to point P12.

[0145] The portion from point P11 to point P13 constitutes an example of a basic region (a region connected to the jump-in portion). The portion from point P13 to point P12 constitutes an example of an exclusion region (a region with a lower curvature than the basic region).

[0146] In the force curve shown in FIG. 15, it is assumed that the portion from point P11 to point P13 mainly reflects the influence of the sample physical properties, and the portion from point P13 to point P12 mainly reflects the influence of the substrate physical properties. More specifically, it is assumed that the substrate is harder than the sample, and thus, in the approach process, after the jump-in, when the probe-sample distance becomes sufficiently short, the cantilever displacement is assumed to increase linearly. The reason is that when the sample is soft, before the probe-sample distance becomes sufficiently short, the sample deforms before the value of the cantilever displacement changes in response to the pushing-in of the cantilever 2. On the other hand, when the probe-sample distance becomes sufficiently short and the amount of sample deformation corresponding to the pushing-in of the cantilever 2 is completed, the value of the cantilever displacement changes in response to the pushing-in of the cantilever 2. And it is assumed that the change in the value of the cantilever displacement after the amount of sample deformation corresponding to the pushing-in of the cantilever 2 is completed appears as the above-mentioned linear increase.

[0147] Therefore, the information processing device 20 may divide the portion to the right of point P11 into a curved portion and a linear portion, and specify the linear portion as the exclusion region. And the information processing device 20 may specify the portion closer to point P for the above-mentioned linear increase.

[0148] <Correction of the force curve used in the theoretical formulas according to the Hertz method and the Sneddon method> Figure 18 shows a specific example of a force curve. Figure 18 shows plots acquired during the approach process. During the approach process, data is added over time from right to left in Figure 18 (i.e., in the direction where the probe-sample distance value decreases).

[0149] Figure 19 shows the force curve from Figure 18, along with annotations. As shown in Figure 19, the curvature of the force curve changes at point P21. More specifically, in the example in Figure 19, the portion of the force curve to the right of point P21 is a curve, while the portion to the left of point P21 is a straight line.

[0150] In the force curve shown in Figure 19, the portion to the right of point P21 is assumed to mainly reflect the influence of the sample's physical properties, while the portion to the left of point P21 is assumed to mainly reflect the influence of the substrate's physical properties. The reason for this is that, when the sample is soft, before the probe-sample distance becomes sufficiently short, the sample deforms in response to the indentation of cantilever 2 before the cantilever displacement value changes. On the other hand, once the probe-sample distance becomes sufficiently short and the sample deformation is complete to correspond to the indentation of cantilever 2, the cantilever displacement value changes in response to the indentation of cantilever 2. It is assumed that the change in the cantilever displacement value after the sample deformation is complete to correspond to the indentation of cantilever 2 appears as the linear increase described above.

[0151] Therefore, the information processing device 20 identifies an inflection point in the force curve and corrects the force curve so as to remove the portion where the probe-sample distance is shorter than the identified inflection point. Figure 20 shows the corrected force curve. In the example described with reference to Figures 18 to 20, the force curve shown in Figure 18 or Figure 19 constitutes an example of a first force curve. Furthermore, the force curve shown in Figure 20, that is, the force curve generated by correcting the force curve shown in Figure 18 or Figure 19, constitutes an example of a second force curve.

[0152] The information processing device 20 uses the corrected force curve to calculate the elastic modulus of the sample. More specifically, in the case of the Hertz method, the information processing device 20 redraws the corrected force curve as a load-displacement curve (Figure 9) and obtains a relationship between the force F acting on the cantilever 2 and the sample deformation δ as shown in equation (19). Then, the information processing device 20 uses equation (19) to determine the value of the intercept in equation (20). Then, as explained with reference to equation (21), the information processing device 20 uses the obtained intercept value to calculate the elastic modulus of the sample.

[0153] In the Sneddon method, the information processing device 20 redraws the corrected force curve as a load-displacement curve (Figure 13) and obtains a relationship between the force F applied to the cantilever 2 and the sample deformation δ, as shown in equation (26). The information processing device 20 then uses equation (26) to determine the value of the intercept in equation (27). The information processing device 20 then uses the obtained intercept value to calculate the elastic modulus of the sample, as explained with reference to equation (28).

[0154] [Process Flow] Figure 21 is a flowchart of the process performed by the information processing device 20 for calculating the elastic modulus. The process in Figure 21 is initiated, for example, when the calculation of the elastic modulus is instructed in an application program executed by the information processing device 20. In one implementation example, the process in Figure 21 is performed after the measurement for force curve generation has been completed for the sample for which the elastic modulus is to be calculated. The contents of the above process will be explained with reference to Figure 21.

[0155] In step S10, the information processing device 20 reads the specification of the theoretical formula to be used. More specifically, the user inputs the specification of the theoretical formula to be used (a theoretical formula according to the JKR method, Hertz method, Sneddon method, or other method) to the information processing device 20 (or the application program running on it). The information processing device 20 reads the input specification. That is, the information processing device 20 is configured to calculate the modulus of elasticity using each of several theoretical formulas, and in step S10, it selects the theoretical formula to be used to calculate the modulus of elasticity from among these several theoretical formulas.

[0156] In step S12, the information processing device 20 generates a first force curve based on the results obtained in the above measurement.

[0157] In step S14, the information processing device 20 generates a second force curve by deleting a portion of the first force curve as described above.

[0158] In step S16, the information processing device 20 calculates the elastic modulus of the sample using the second force curve and the theoretical formula specified by the designation read in step S10.

[0159] In step S18, the information processing device 20 outputs the modulus of elasticity calculated in step S16, and terminates the process shown in Figure 21. The output of the modulus of elasticity is achieved, for example, by displaying it on the display device 26.

[0160] In the processes described above, when theoretical formulas according to the JKR method, Hertz method, or Sneddon method are used, an inflection point (point P13 in Figure 16 for the JKR method; point P21 in Figure 19 for the Hertz or Sneddon method) is required in the generation of the second force curve in step S14. In one implementation example, the JKR method is selected for soft samples such as polymer materials and biomaterials, while the Hertz method may be selected when the sample is a harder material and / or when no jump-in is observed during liquid measurement.

[0161] In the above process, the inflection point may be identified by the information processing device 20 or by the user. If the inflection point is identified by the user, the user inputs the inflection point to the information processing device 20 (or the application program running on it). At this time, the information processing device 20 may display the first force curve on the display device 26. The user may input a given point on the displayed first force curve as an inflection point to the information processing device 20 by touching that point.

[0162] In step S10, when reading the specified theoretical formula, the information processing device 20 may accept input of information regarding the hardness of the sample (type of sample, hardness of the sample, etc.). The information processing device 20 may store a database that associates information regarding the hardness of the sample with the type of theoretical formula to be used. The information processing device 20 may treat the type of theoretical formula corresponding to the input "information regarding hardness" as the specified "theoretical formula to be used".

[0163] The information processing device 20 may further calculate the modulus of elasticity using the first force curve and the theoretical formula specified by the designation read in step S10, as a comparison, and output it together with the second force curve and the modulus of elasticity calculated using the above theoretical formula as a comparison value.

[0164] [Pattern] Those skilled in the art will understand that the above-described exemplary embodiments are specific examples of the following embodiments.

[0165] (Section 1) A scanning probe microscope according to one embodiment comprises a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a movement mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe relative to the base, and a control unit for controlling the movement mechanism, wherein the control unit generates a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample, and in the first force curve, starting from the jump-in portion and in a range where the distance is shorter than the jump-in portion The control unit may be configured to identify a first region corresponding to the enclosure, and in the jump-in portion, the probe begins to receive an attractive force from the sample as the distance decreases, and in the first region, identify a basic region which is the region from the first inflection point closest to the jump-in portion among the one or more inflection points in the first region to the jump-in portion, and an excluded region which is the region other than the basic region, generate a second force curve by excluding the excluded region from the first force curve, and calculate the elastic modulus of the sample based on the second force curve and a theoretical formula.

[0166] (Section 2) In the scanning probe microscope described in Section 1, the control unit may be configured to identify one or more inflection points in the first region and to identify the first inflection point from the one or more inflection points.

[0167] (Clause 3) In the scanning probe microscope described in paragraph 1 or 2, the control unit may be configured to identify a region with zero curvature as the exclusion region.

[0168] (Clause 4) A scanning probe microscope according to one embodiment comprises a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a movement mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe relative to the base, and a control unit for controlling the movement mechanism, wherein the control unit is configured to generate a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample, by utilizing the detection output of the displacement detector, generate a second force curve by excluding from the first force curve the region where the distance is shorter than the inflection point in the first force curve, and calculate the elastic modulus of the sample based on the second force curve and a theoretical formula.

[0169] (Clause 5) In a scanning probe microscope as described in any one of paragraphs 1 to 4, the control unit may be configured to receive a designation regarding the type of theoretical formula and to select the theoretical formula from two or more types of theoretical formulas in accordance with the designation.

[0170] (Clause 6) In the scanning probe microscope described in any one of paragraphs 1 to 5, the control unit may be configured to receive a specification regarding the hardness of a sample and to select a theoretical formula from two or more types of theoretical formulas according to the specification.

[0171] (Clause 7) In the scanning probe microscope described in any one of Clauses 1 to 6, the control unit may further be configured to calculate a comparative value of the elastic modulus of the sample based on the first force curve and the theoretical formula.

[0172] (Clause 8) A method according to one embodiment is a method for calculating the elastic modulus of a sample using a scanning probe microscope, the scanning probe microscope including a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a moving mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe with respect to the base, and a control unit for controlling the moving mechanism, the method comprising the steps of generating a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample, using the detection output of the displacement detector, and excluding from the first force curve a region in which the distance is shorter than the inflection point The method comprises the steps of generating a second force curve and calculating the elastic modulus of the sample based on the second force curve and a theoretical formula, wherein the step of generating the second force curve includes identifying a first region in the first force curve that corresponds to a range starting from a jump-in portion and having a shorter distance than the jump-in portion, where the probe begins to receive an attractive force from the sample as the distance decreases, and the step of generating the second force curve may further include identifying the inflection point in the first region, which is the inflection point among one or more inflection points in the first region that is closest to the jump-in portion.

[0173] (Clause 9) A method according to one embodiment is a method for calculating the elastic modulus of a sample using a scanning probe microscope, wherein the scanning probe microscope includes a sample stage on which a sample is placed, a cantilever with a fixed base and a probe at its tip, a moving mechanism for relatively changing the positional relationship between the sample stage and the base, a displacement detector for detecting the displacement of the probe with respect to the base, and a control unit for controlling the moving mechanism, and the method may include the steps of: generating a first force curve, which is the measurement result of the displacement due to a change in the distance between the probe and the sample, using the detection output of the displacement detector; generating a second force curve by excluding from the first force curve a region in which the distance from the inflection point is shorter; and calculating the elastic modulus of the sample based on the second force curve and a theoretical formula.

[0174] The embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The scope of this disclosure is indicated by the claims rather than by the description of the embodiments above, and all modifications within the meaning and scope equivalent to the claims are intended to be included. Furthermore, each technology in the embodiments is intended to be practiced individually or, as far as possible, in combination with other technologies in the embodiments. [Explanation of Symbols]

[0175] 1 Optical system, 2 Cantilever, 3 Probe, 4 Holder, 5 Beam splitter, 6 Laser light source, 7 Mirror, 8 Photodetector, 10 Scanner, 12 Sample stage, 16 Drive unit, 17 Calculation unit, 18 Control unit, 20 Information processing unit, 26 Display device, 28 Input device, 80 Observation device, 100 SPM, 162 ROM, 164 RAM, 200, 221 Indenter, 201, 222, S Sample, 211, 212 Object.

Claims

1. A sample stage on which the sample is placed, A cantilever with a fixed base and a probe at its tip, A movement mechanism that changes the relative positions of the sample stage and the base end, A displacement detector for detecting the displacement of the probe relative to the base end, The system comprises a control unit for controlling the aforementioned moving mechanism, The control unit, Using the detection output of the displacement detector, a first force curve is generated, which is the measurement result of the displacement due to the change in distance between the probe and the sample. In the first force curve, a first region is identified that corresponds to a range starting from the jump-in portion and having a distance shorter than the jump-in portion. In the jump-in portion, as the distance decreases, the probe begins to receive an attractive force from the sample. The control unit, In the first region, a basic region is identified, which is the region from the first inflection point closest to the jump-in portion among the one or more inflection points in the first region to the jump-in portion, and an excluded region is the region other than the basic region. By excluding the exclusion region from the first force curve, a second force curve is generated. The elastic modulus of the sample is calculated based on the second force curve and the theoretical formula. A scanning probe microscope configured as follows.

2. The scanning probe microscope according to claim 1, wherein the control unit is configured to identify one or more inflection points in the first region and to identify a first inflection point from the one or more inflection points.

3. The scanning probe microscope according to claim 1 or 2, wherein the control unit is configured to identify a region with zero curvature as the exclusion region.

4. A sample stage on which the sample is placed, A cantilever with a fixed base and a probe at its tip, A movement mechanism that changes the relative positions of the sample stage and the base end, A displacement detector for detecting the displacement of the probe relative to the base end, The system comprises a control unit for controlling the aforementioned moving mechanism, The control unit, Using the detection output of the displacement detector, a first force curve is generated, which is the measurement result of the displacement due to the change in distance between the probe and the sample. A second force curve is generated by excluding the region where the distance is shorter than the inflection point in the first force curve from the first force curve. The elastic modulus of the sample is calculated based on the second force curve and the theoretical formula. A scanning probe microscope configured as follows.

5. The control unit, We accept specifications regarding the type of theoretical formula. A scanning probe microscope according to claim 1 or 4, configured to select a theoretical formula from two or more types of theoretical formulas in accordance with the above designation.

6. The control unit, We accept specifications regarding the hardness of the sample. A scanning probe microscope according to claim 1 or 4, configured to select a theoretical formula from two or more types of theoretical formulas in accordance with the above designation.

7. The scanning probe microscope according to claim 1 or 4, wherein the control unit is further configured to calculate a comparative value of the elastic modulus of the sample based on the first force curve and the theoretical formula.

8. A method for calculating the elastic modulus of a sample using a scanning probe microscope, The scanning probe microscope described above is A sample stage on which the sample is placed, A cantilever with a fixed base and a probe at its tip, A movement mechanism that changes the relative positions of the sample stage and the base end, A displacement detector for detecting the displacement of the probe relative to the base end, Includes a control unit for controlling the aforementioned moving mechanism, The steps include: generating a first force curve, which is the measurement result of the displacement due to the change in distance between the probe and the sample, using the detection output of the displacement detector; The steps include generating a second force curve by excluding the region where the distance from the inflection point is shorter from the first force curve, The procedure includes the step of calculating the elastic modulus of the sample based on the second force curve and the theoretical formula, The step of generating the second force curve is: The first force curve includes identifying a first region that starts from the jump-in portion and corresponds to a range where the distance is shorter than the jump-in portion, In the jump-in portion, as the distance decreases, the probe begins to receive an attractive force from the sample. The step of generating the second force curve is: A method further comprising identifying the inflection point in the first region that is closest to the jump-in portion among one or more inflection points in the first region.

9. A method for calculating the elastic modulus of a sample using a scanning probe microscope, The scanning probe microscope described above is A sample stage on which the sample is placed, A cantilever with a fixed base and a probe at its tip, A movement mechanism that changes the relative positions of the sample stage and the base end, A displacement detector for detecting the displacement of the probe relative to the base end, Includes a control unit for controlling the aforementioned moving mechanism, The steps include: generating a first force curve, which is the measurement result of the displacement due to the change in distance between the probe and the sample, using the detection output of the displacement detector; The steps include generating a second force curve by excluding the region where the distance from the inflection point is shorter from the first force curve, A method comprising the step of calculating the elastic modulus of the sample based on the second force curve and the theoretical formula.

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