JP2018173310A - Measurement accuracy evaluation method, elastic modulus measurement method, program, and scanning type probe microscope system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for evaluating validity of a measured elastic modulus quantitatively and quickly.SOLUTION: Provided is a method for evaluating accuracy of measurement by force mapping mode measurement of a scanning type probe microscope, comprising: a step S41 of acquiring force curve measurement data at a plurality of measurement points on a surface of a measurement object by force mapping mode measurement using the scanning type probe microscope; a step S42 of calculating, for each measurement point, a measured load displacement curve from the force curve measurement data; a step S43 of calculating an elastic modulus per measurement point from the measured load displacement curve using a theoretical formula; a step S44 of calculating, for each measurement point, a theoretical load displacement curve by substituting the elastic modulus and a measurement parameter in force mapping measurement for the theoretical formula; a step S45 of calculating, for each measurement point, a degree of disagreement between the measured load displacement curve and the theoretical load displacement curve, the degree of disagreement being represented by a dimensionless number.SELECTED DRAWING: Figure 8

Description

  The present invention relates to a technique for measuring elastic modulus using a scanning probe microscope, and in particular, to evaluate the measurement accuracy of force curve mapping measurement using an atomic force microscope (AFM), and to improve and simplify the accuracy. It relates to the technology to be realized.

  One of the microscopes for observing microscopic local areas is a cantilever with a very small protruding needle (probe) at the tip as a probe. There is a scanning probe microscope (SPM) in which a surface state such as a three-dimensional shape such as unevenness is magnified and observed by scanning in a tracing manner. The SPM can measure and examine the undulation state of the sample surface and its surface properties through changes in the cantilever due to the interaction between the probe tip and the sample surface.

  There are three types of SPM measurement methods: contact mode measurement (contact mode measurement), dynamic mode measurement (tapping mode measurement), and force curve measurement (force-distance curve measurement). In general, dynamic mode measurement and force curve measurement are widely used.

  The dynamic mode measurement can detect not only the surface shape of a substance but also information related to its viscoelasticity and visualize it as a phase (difference) image, and thus is very useful in surface observation and physical property evaluation of a soft material. However, the obtained phase image is qualitative data, and has a drawback that comparison between images and samples is difficult.

  On the other hand, the force curve measurement is suitable for measuring the elasticity of the sample surface, and the elastic modulus can be obtained as a quantitative physical property value of the sample surface. Among the soft materials, there is active research on the elastic modulus measurement of rubber materials in particular. In the study of contact mechanics describing the elastic contact phenomenon between the cantilever and the sample, Hertz contact mechanics model, DMT theory, JKR Various theories such as theory have been proposed. For example, by using the JKR theory, a force curve mapping measurement method has been already reported that allows two-dimensional force curve measurement within a field of view of several micrometers square to examine the elastic modulus distribution (elastic modulus mapping image). (Patent Document 1 and Non-Patent Document 1).

  However, it is not easy to actually perform this force curve mapping measurement and obtain a reliable elastic modulus mapping image. For example, when the force curve mapping measurement performed in Non-Patent Document 1 is given, actually measured data at 128 × 128 = 16384 measurement points is obtained for one force curve mapping measurement. When the elastic modulus at each measurement point is calculated from each of these actual measurement data by the JKR theoretical formula and the theoretical data (JKR curve) is obtained from the elastic modulus, the measurement point where the actual measurement data and the theoretical data are in good agreement, There are points that do not match very much.

  On the other hand, in Non-Patent Document 2, the cause of the discrepancy between the measured data and the theoretical data is assumed to be energy dissipation due to viscoelasticity, and an image obtained by calculating and mapping the energy dissipation amount at all measurement points is obtained. It is disclosed in Fig 2. (g). In Non-Patent Document 2, it is described that the Young's modulus (elastic modulus) derived from the JKR theory is unreliable at measurement points where the difference between the actual measurement data and the theoretical data is large.

  Therefore, in order to obtain a reliable elastic modulus, the degree of inconsistency between the theoretical data obtained from the above-mentioned various theories and the measured data is confirmed, and the accuracy of the elastic modulus obtained by theoretical calculation is evaluated (validity Evaluation) is essential. However, as in Non-Patent Document 2, when the deviation between the measured data and the theoretical data is determined by the energy dissipation amount due to viscoelasticity, the energy dissipation amount due to viscoelasticity is a quantity having a unit, so the range of values is Indeterminate and strongly dependent on the measurement object and measurement parameters. For this reason, it is not possible to determine a quantitative measure of how much the actually measured data matches the theoretical calculation data, and whether the obtained elastic modulus can be regarded as appropriate.

  In addition, when there are many measurement points where the actual measurement data and the theoretical calculation data do not match, the measured elastic modulus mapping image cannot be said to be valid, so it is necessary to reset appropriate measurement parameters. Since the validity evaluation itself is a difficult task as described above, the resetting of the measurement parameters is also extremely difficult. Therefore, in order to search for an effective measurement parameter, it is necessary to quantitatively and quickly evaluate the validity of the measured elastic modulus.

JP, 2006-105054, A

Ken Nakajima et al., J. Vac. Soc. Jpn., Vol. 7, 2013, 258-266 Fujinami, et al., “Viscoelastic analysis of elastomer blends by atomic force microscope force measurement”, Polymers, Vol. 69, No. 7, 2012, pp.435-442

  The present invention solves the above-mentioned problems in force curve mapping measurement using a scanning probe microscope system, particularly an atomic force microscope, and quantitatively and rapidly evaluates the validity of the measured elastic modulus. It is an object to provide a method.

  The present inventors have found that the validity of the elastic modulus can be quantitatively and rapidly evaluated by using an index represented by a dimensionless number as the degree of inconsistency between the measured data and the theoretical data. The present invention was completed through repeated studies.

The invention encompasses, for example, the subject matter described in the following sections.
Item 1.
An evaluation method of measurement accuracy by force mapping mode measurement of a scanning probe microscope,
A force curve acquisition step of acquiring force curve measurement data at a plurality of measurement points on the surface of the measurement object by force mapping mode measurement using the scanning probe microscope;
Actual measurement data calculation step for calculating an actual load displacement curve from the force curve measurement data for each measurement point;
An elastic modulus calculation step of calculating an elastic modulus for each of the measurement points using a theoretical formula from the measured load displacement curve;
A theoretical data calculation step for calculating a theoretical load displacement curve for each measurement point by substituting the measurement parameters in the elastic modulus and the force mapping mode measurement into the theoretical formula;
A mismatch degree calculating step for calculating a mismatch degree between the measured load displacement curve and the theoretical load displacement curve for each measurement point;
Have
The evaluation method, wherein the inconsistency is expressed by a dimensionless number.
Item 2.
The evaluation method according to Item 1, wherein the degree of inconsistency is represented by an R-factor determined by the following Expression 7 or 8.
d _data : a load at a certain deformation amount of the measurement object in the actual load displacement curve or a deformation amount of the measurement object at a certain load d _calc : a deformation amount of the measurement object in the theoretical load displacement curve 2. Load or deformation amount term of the measurement object at a certain load
The theoretical formula is a theoretical formula based on the JKR theory,
Item 3. The evaluation method according to Item 1 or 2, wherein the degree of inconsistency is represented by an R-factor determined by the following Equation 1.
δ _data : deformation amount of the measurement object at a certain load in the actually measured load displacement curve δ _calc : deformation amount of the measurement object at a certain load in the theoretical load displacement curve
The theoretical formula is a theoretical formula based on Hertz's contact dynamic model or DMT theory,
Item 3. The evaluation method according to Item 1 or 2, wherein the degree of inconsistency is represented by an R-factor determined by the following Equation 5.
F _data : Load at a certain deformation amount of the measurement object in the measured load displacement curve F _calc : Load term at a certain deformation amount of the measurement object in the theoretical load displacement curve 5.
A mapping image for generating a mapping image in which an area corresponding to each measurement point is displayed in such a manner that a region corresponding to each measurement point can be visually discriminated from the size of the measurement point. Item 5. The evaluation method according to any one of Items 1 to 4, further comprising a generation step.
Item 6.
Item 6. The evaluation method according to any one of Items 1 to 5, wherein the scanning probe microscope is an atomic force microscope.
Item 7.
Item 7. The evaluation method according to any one of Items 1 to 6, wherein the measurement object is a soft material, a metal, a ceramic, or a composite thereof.
Item 8.
A method for measuring the elastic modulus of the surface of an object to be measured by force mapping mode measurement of a scanning probe microscope,
A preliminary measurement step in which the scanning probe microscope measures force curves at a plurality of measurement points on the surface of the measurement object based on one or more measurement parameters of the scanning probe microscope;
Force curve measurement data that is measurement data of the force curve measured in the preliminary measurement step is acquired, an actual load displacement curve is calculated for each measurement point from the force curve measurement data, and a theoretical value is calculated from the actual load displacement curve. Calculate the elastic modulus for each measurement point using an equation, and calculate the theoretical load displacement curve for each measurement point by substituting the measurement parameters in the elastic modulus and the force mapping mode measurement into the theoretical formula, A measurement accuracy evaluation step for calculating a degree of inconsistency represented by a dimensionless number between the measured load displacement curve and the theoretical load displacement curve for each measurement point;
An effective measurement parameter determining step for determining an effective measurement parameter from the one or more measurement parameters based on the inconsistency calculated in the measurement accuracy evaluation step;
Based on the effective measurement parameters, the main measurement step of measuring the elastic modulus of the surface of the measurement object at more measurement points than the measurement points in the preliminary measurement step;
A measuring method.
Item 9.
Item 9. The measurement method according to Item 8, wherein the degree of inconsistency is represented by an R-factor determined by the following Equation 7 or Equation 8.
d _data : a load at a certain deformation amount of the measurement object in the actual load displacement curve or a deformation amount of the measurement object at a certain load d _calc : a deformation amount of the measurement object in the theoretical load displacement curve 9. Load or deformation amount term of the measurement object at a certain load
The theoretical formula is a theoretical formula based on the JKR theory,
Item 10. The measurement method according to Item 8 or 9, wherein the degree of inconsistency is represented by an R-factor determined by the following Equation 1.
δ _data : deformation amount of the measurement object at a certain load in the measured load displacement curve δ _calc : deformation amount of the measurement object at a certain load in the theoretical load displacement curve
The theoretical formula is a theoretical formula based on Hertz's contact dynamic model or DMT theory,
Item 10. The measurement method according to Item 8 or 9, wherein the degree of inconsistency is represented by an R-factor determined by the following Equation 5.
F _data : Load at a certain deformation amount of the measurement object in the measured load displacement curve F _calc : Load term at a certain deformation amount of the measurement object in the theoretical load displacement curve 12.
Item 12. The measurement method according to any one of Items 8 to 11, wherein, in the effective measurement parameter determination step, a measurement parameter in which an average of the mismatches at all measurement points is equal to or less than a predetermined reference value is determined as an effective measurement parameter.
Item 13.
Item 13. The measuring method according to any one of Items 8 to 12, wherein the scanning probe microscope is an atomic force microscope.
Item 14.
Item 14. A program for causing a computer to execute each step according to any one of Items 1 to 13.
Item 15.
Item 14. A scanning probe microscope system equipped with a program for causing a computer to execute each step according to any one of Items 1 to 13.
Item 16.
Item 14. An atomic force microscope system equipped with a program for causing a computer to execute the steps according to any one of Items 1 to 13.

  According to the present invention, the validity of the elastic modulus can be quantitatively and rapidly evaluated. Also, it becomes easy to search for effective measurement parameters for measuring the elastic modulus.

It is a block diagram showing a schematic structure of an elastic modulus measuring system concerning one embodiment of the present invention. It is an example of the graph which shows the force curve in a certain measurement point. It is an example of the graph which shows the actual measurement load displacement curve and theoretical load displacement curve in a certain measurement point. It is an example of the elastic modulus image in the elastic modulus measurement using JKR theory. FIG. 5 is an example of a mapping image that visually represents the distribution of R-factor sizes in the elastic modulus image shown in FIG. 4. FIG. It is a flowchart which shows each step of the measuring method of the elasticity modulus which concerns on one Embodiment of this invention. (A)-(c) is an example of the mapping image obtained in preliminary measurement, respectively. It is a flowchart which shows each step of the evaluation method of the measurement precision which concerns on one Embodiment of this invention. It is an example of the elasticity-modulus image in the elasticity-modulus measurement using the Hertz contact dynamics model. 10 is an example of a mapping image that visually represents the distribution of R-factor sizes in the elastic modulus image shown in FIG. 9. 11 is a graph showing an actual load displacement curve and a theoretical load displacement curve in a block having the smallest R-factor in the mapping image shown in FIG. It is a modification of the mapping image which expressed the size distribution of R-factor visually. It is an example of the image which superimposed the mapping image and the elasticity modulus image. (A) And (b) is an example of an elasticity-modulus image and a mapping image. It is a flowchart which shows each step of the measuring method of the elasticity modulus which concerns on the modification of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, this invention is not limited to the following embodiment.

(Device configuration)
FIG. 1 is a block diagram showing a schematic configuration of an elastic modulus measurement system (scanning probe microscope system, atomic force microscope system) according to an embodiment of the present invention. This elastic modulus measurement system measures the elastic modulus of the surface of a sample S that is an object to be measured, and includes an atomic force microscope (AFM) 1 and an arithmetic device 2. The sample S is a rubber material, for example, and is set at a predetermined position of the AFM 1. In the present invention, the measurement object is not limited to the rubber material, and any substance other than the rubber material can be the measurement object.

  The AFM 1 is a scanning probe microscope that magnifies and observes the surface state (three-dimensional information such as irregularities) while scanning the surface of a substance using a minute probe (probe) having a sharp tip. This is a microscope using atomic force. In the present embodiment, the AFM 1 measures the amount of deflection of the cantilever and the relative distance to the sample S while changing the distance between the sample S and the probe provided in the cantilever (force curve measurement). The amount of deflection of the cantilever can be measured by optical means, and the relative distance between the sample S and the cantilever can be measured by a piezo element. In this case, the relative distance between the sample S and the cantilever is expressed as a displacement amount of the piezo element. Relative distance between sample S and cantilever In this embodiment, the force curve measurement is performed at multiple points so that the surface of the sample S is scanned two-dimensionally on the nanometer to micrometer order (force mapping mode measurement). ). Thereby, for example, a force curve showing the relationship between the amount of deflection of the cantilever and the relative distance to the sample S as shown in FIG. In FIG. 2, the solid line is a force curve when the cantilever is approaching the sample S, and the broken line is a force curve when the cantilever is moving away from the sample S. The force curve measurement data is transmitted to the arithmetic device 2 connected to the AFM 1.

  The computing device 2 computes the elastic modulus of the surface of the sample S based on the force curve measurement data received from the AFM 1, and is constituted by a general-purpose personal computer, for example. The arithmetic device 2 includes a CPU (not shown), a memory (not shown), an auxiliary storage device 3 and the like as a hardware configuration, and the CPU reads various programs into the memory and executes them to execute various operations. Execute the process. Further, a display device (not shown) such as a liquid crystal display and an input device (not shown) such as a keyboard or a touch panel are connected to the arithmetic device 2.

  As shown in FIG. 1, the arithmetic device 2 includes a measurement instruction unit 4, a measurement parameter setting unit 5, an accuracy evaluation unit 6, and an effective measurement parameter determination unit 7 as functional blocks. These functional blocks are realized by the CPU of the arithmetic device 2 executing the program according to the present embodiment, whereby the arithmetic device 2 can measure the measurement accuracy and the elastic modulus measurement according to the present invention described later. Execute the method. The program according to the present embodiment may be recorded on a non-transitory computer-readable recording medium such as a CD-ROM. By causing the arithmetic device 2 to read the recording medium, the program is stored in the auxiliary storage device 3. Stored in Alternatively, the arithmetic device 2 may be connected to a communication network such as the Internet, and the program code of the program may be downloaded via the communication network.

  The measurement instruction unit 4 transmits an instruction signal for performing force mapping mode measurement on the sample S to the AFM 1 in accordance with a user instruction operation or the like via the input device. In response to this, the AFM 1 measures the deflection amount of the cantilever at a plurality of measurement points on the surface of the sample S, the displacement amount and displacement range of the piezo element with respect to the sample S, and generates force curve measurement data at each measurement point.

  The measurement parameter setting unit 5 sets measurement parameters for the AFM 1 to perform force mapping mode measurement. Examples of the measurement parameters include the speed of the cantilever with respect to the sample S, the end position of the cantilever, the measurement range and the measurement density (number of measurement points) on the surface of the sample S, and the like. The measurement parameter may be set by an operation through a user input device, or may be automatically set by a function such as an effective measurement parameter determination unit 7 described later. Each time the measurement instruction unit 4 instructs the AFM 1 to perform force mapping mode measurement, the measurement parameter setting unit 5 stores the measurement parameters in the force mapping mode measurement in the auxiliary storage device 3. The stored measurement parameter is recorded as a measurement history H.

  The accuracy evaluation unit 6 is a functional block for executing a measurement accuracy evaluation method according to the present invention, which will be described later. Based on force curve data from the AFM 1, measurement of the elastic modulus at the measurement point on the surface of the sample S and It has a function to evaluate the measurement accuracy of elastic modulus. In order to realize this function, the accuracy evaluation unit 6 includes a force curve acquisition unit 61, an actual measurement data calculation unit 62, an elastic modulus calculation unit 63, a theoretical data calculation unit 64, a mismatch degree calculation unit 65, and a mapping image generation unit 66. doing.

  The force curve acquisition unit 61 has a function of communicating with the AFM 1 and acquiring force curve measurement data from the AFM 1.

  The actual measurement data calculation unit 62 has a function of calculating an actual load displacement curve (measurement data) based on the actual measurement from the force curve measurement data acquired by the force curve acquisition unit 61 for each measurement point. The actually measured load displacement curve is a curve showing the relationship between the load applied to the cantilever and the deformation amount of the sample S, and is shown by a solid line in FIG. 3, for example.

  The elastic modulus calculation unit 63 has a function of calculating the elastic modulus of the sample S for each measurement point from the actual load displacement curve calculated by the actual measurement data calculation unit 62. In this embodiment, the elastic modulus is calculated by a theoretical formula based on the JKR theory. FIG. 4 is an example of an elastic modulus image showing the elastic modulus when the measurement point is 32 × 32 = 1024. In this elastic modulus image, each block (area) corresponds to the position of the measurement point, blocks with a large elastic modulus (hard) are displayed in red, and blocks with a small elastic modulus (soft) are displayed in blue.

  The theoretical data calculation unit 64 substitutes the elastic modulus calculated by the elastic modulus calculation unit 63 and the measurement parameter (displacement range of the piezo element) in the force mapping mode measurement into the theoretical formula, thereby calculating the theoretical load displacement curve (theoretical data). ) For each measurement point. The theoretical load displacement curve is a curve showing the relationship between the load applied to the cantilever and the amount of deformation of the sample S, calculated using the elastic modulus and adhesion energy calculated from the measured data. For example, the broken line in FIG. Indicated by

The mismatch degree calculation unit 65 has a function of calculating the degree of mismatch between the actual load displacement curve calculated by the actual data calculation unit 62 and the theoretical load displacement curve calculated by the theoretical data calculation unit 64 for each measurement point. In the present embodiment, the degree of inconsistency is represented by an R-factor obtained by the following formula 1.
δ _data : deformation amount of sample S at a certain load in the measured load displacement curve δ _calc : deformation amount of sample S at a certain load in the theoretical load displacement curve

  R-factor is a dimensionless number having a value greater than or equal to 0. The smaller the mismatch degree, the closer to 0, and the larger the mismatch degree, the larger the value. Therefore, R-factor is suitable as an index for intuitively understanding the degree of mismatch. In addition, since the calculation of R-factor is easy, in this embodiment, R-factor is used as an index that quantitatively indicates the degree of mismatch. The mismatch degree calculation unit 65 calculates an R-factor indicating the degree of mismatch for all measurement points.

  The mapping image generation unit 66 generates a mapping image that visually represents the distribution of the size of the R-factor based on the R-factor of all the measurement points calculated by the mismatch degree calculation unit 65. FIG. 5 shows an example of a mapping image when the measurement point is 32 × 32 = 1024. In this mapping image, each block (area) corresponds to the position of the measurement point, and is displayed with a density and color corresponding to the size of the R-factor of the measurement point. Specifically, each block is displayed lighter as the R-factor is smaller, and darker as the R-factor is larger.

  The mapping image data is transmitted to a display device (not shown), and the mapping image is displayed on the display device. The user can intuitively grasp whether the elastic modulus calculated by the elastic modulus calculation unit 63 is appropriate as a whole based on the mapping image. Therefore, it becomes easy to determine whether or not the measurement parameter for obtaining the elastic modulus is appropriate.

  Note that the display form of each block of the mapping image is not particularly limited as long as it is displayed in a form in which the size of the R-factor can be visually discriminated. For example, a mode in which the size of the R-factor is displayed only in shades of gray, a mode in which the size of the R-factor is displayed in a dense pattern such as hatching, or a warmer color is displayed as the R-factor is larger. In addition, there is a mode in which the smaller the R-factor, the lower the color is displayed.

Further, in the present embodiment, when the calculation of the R-factor at all the measurement points is completed, the mismatch degree calculation unit 65 calculates the average value R-factor _ave. Is calculated.
i: horizontal coordinate j: vertical coordinate N: total number of measurement points

The mismatch degree calculation unit 65 calculates the calculated R-factor _ave. Is associated with the measurement parameter and recorded in the measurement history H.

In this embodiment, as will be described later, force mapping mode measurement is performed once or a plurality of times while changing measurement parameters with a relatively small number of measurement points (for example, 16 × 16 = 256). Each time the force mapping mode measurement is performed, the measurement parameter in the force mapping mode measurement and the R-factor _ave. Are sequentially stored in the measurement history H.

The effective measurement parameter determination unit 7 _reads the R-factor _ave. Is less than or equal to a reference value (for example, 0.60), and if it is less than or equal to the reference value, it is evaluated that the accuracy of the calculated elastic modulus is acceptable, and the R-factor _{ave .} Is determined as an effective measurement parameter. The effective measurement parameter determination unit 7 _receives the R-factor _ave. The timing for determining whether or not is less than or equal to the reference value may be every time force mapping mode measurement is performed, or after a predetermined number of times of force mapping mode measurement.

  When an effective measurement parameter is determined by the effective measurement parameter determination unit 7, the measurement parameter setting unit 5 increases the number of measurement points (increases the measurement density), and sets a setting value other than the number of measurement points as a set value in the effective measurement parameter Reset the measurement parameters to be the same as. The measurement instruction unit 4 instructs the AFM 1 to perform force mapping mode measurement based on the reset measurement parameter. Thereafter, the force curve measurement data acquired by the AFM 1 is transmitted to the computing device 2, and the elastic modulus is calculated by the force curve acquisition unit 61, the actual measurement data calculation unit 62 and the elastic modulus calculation unit 63.

(Elastic modulus measurement method and measurement accuracy evaluation method)
Hereinafter, an embodiment of an elastic modulus measurement method and measurement accuracy evaluation method according to the present invention will be described. Since the measurement accuracy evaluation method is used in some steps in the elastic modulus measurement method, the overall flow of the elastic modulus measurement method will be described first.

(Measuring method)
FIG. 6 is a flowchart showing each step of the elastic modulus measurement method according to the present embodiment. In this measurement method, first, in step S1, the user sets the sample S, which is the measurement object, at a predetermined position of the AFM 1. Subsequently, in step S2, the measurement parameter setting unit 5 sets measurement parameters in the force mapping mode measurement. The measurement parameter may be set by an operation via a user's input device, or may be automatically selected from a plurality of measurement parameters prepared in advance. In the measurement parameter in step S2, the number of measurement points is preferably set to be relatively small. In this embodiment, for example, 16 × 16 = 256 points. The order of steps S1 and S2 is not particularly limited.

  Subsequently, in step S3 (preliminary measurement step), preliminary measurement is performed based on the set measurement parameters. Specifically, the measurement instruction unit 4 transmits an instruction signal including a measurement parameter to the AFM 1, and in response to this, the AFM 1 performs a force mapping mode measurement on the sample S and measures a force curve at each measurement point. To do. Force curve measurement data (force curve measurement data) is transmitted from the AFM 1 to the computing device 2.

Subsequently, in step S4 (measurement accuracy evaluation step), the measurement accuracy is evaluated. This measurement accuracy evaluation is performed by the measurement accuracy evaluation method according to the present embodiment. As will be described later, as an index of measurement accuracy, the average value R-factor _ave. Are recorded in the measurement history H in association with the measurement parameters set in step S2. The specific contents of step S4 will be described later with reference to FIG.

Subsequently, the effective measurement parameter determination unit 7 determines an effective measurement parameter based on the degree of mismatch calculated in step S4. In the present embodiment, first, in step S5, the effective measurement parameter determination unit 7 determines that the R-factor _ave. Is determined to be less than or equal to the reference value. The reference value is appropriately set according to the type of sample S, the application, the allowable measurement time, the calculation capability of the calculation device 2, and the like. In this embodiment, it is preferably 0.60 (60%), for example. 0.10 (10%) is more preferable.

R-factor _ave. Is equal to or less than the reference value (YES in step S5), the process proceeds to step S6. On the other hand, R-factor _ave. Is larger than the reference value (NO in step S5), the process returns to step S2. Then, the measurement parameters excluding the number of measurement points are changed (step S2), the preliminary measurement is performed again (step S3), and the measurement accuracy is evaluated (step S4). R-factor _ave. These steps S2 to 4 are repeated until it is determined that is less than or equal to the reference value (YES in step S5).

In addition, the average value R-factor _{ave. Of} R-factor obtained from the first preliminary measurement _. If S is less than or equal to the reference value, steps S2 to S4 are not repeated, and as a result, preliminary measurement is performed based on only one measurement parameter. On the other hand, when steps S2 to S4 are repeated, preliminary measurement is performed based on a plurality of measurement parameters.

Subsequently, in step S6, the effective measurement parameter determination unit 7 determines that the measurement accuracy of the elastic modulus is acceptable, and from the one or more measurement parameters used in the preliminary measurement up to that point, the effective measurement parameter determination unit 7 R-factor _ave. Is determined as an effective measurement parameter.

FIGS. 7A to 7C are examples of mapping images obtained in the first to third preliminary measurements, respectively. The measurement parameters in the first to third preliminary measurements are as shown in Tables 1 to 3.

In this example, the average value R-factor _{ave. Of} R-factor obtained in the first and second preliminary measurements _. Is larger than the reference value, and the average value R-factor _{ave. Of} R-factor obtained in the third preliminary measurement _. Is below the reference value. In that case, the measurement parameter in the third preliminary measurement becomes the effective measurement parameter.

  Subsequently, in step S7, the measurement parameter setting unit 5 increases the number of measurement points (increases the measurement density), and resets the measurement parameters so that parameters other than the number of measurement points are the same as the effective measurement parameters. . The number of measurement points after the resetting is not particularly limited as long as it is larger than the number of measurement points in the preliminary measurement in step S3. For example, 64 × 64 = 4096 points.

  Subsequently, in step S8 (main measurement step), the main measurement is performed at more measurement points than the measurement points in step S3 based on the reset measurement parameters. Specifically, the measurement instruction unit 4 transmits an instruction signal including the reset measurement parameter to the AFM 1, and in response thereto, the AFM 1 performs force mapping mode measurement on the sample S, and performs measurement at each measurement point. Force curve data is generated and transmitted to the computing device 2. Then, the elastic modulus at each measurement point is calculated by the force curve acquisition unit 61, the actual measurement data calculation unit 62, and the elastic modulus calculation unit 63. Thereby, a high-resolution elastic modulus image can be obtained efficiently.

  As described above, in the elastic modulus measurement method according to this embodiment, preliminary measurement is performed while changing measurement parameters until it is determined that the measurement accuracy is acceptable with a relatively small number of measurement points (low resolution). Based on the measurement parameters determined to be acceptable accuracy, the main measurement is performed with a relatively large number of measurement points (high resolution). Thereby, reliable elastic modulus data can be obtained efficiently and quickly.

Even if steps S2 to S4 are repeated for all measurement parameters, R-factor _ave. Is not determined to be equal to or less than the reference value (NO in step S5), the measurement of the elastic modulus is terminated without determining the effective measurement parameter.

(Evaluation method)
Next, a measurement accuracy evaluation method according to this embodiment will be described. The measurement accuracy evaluation method according to the present embodiment is used in step S4 described above.

  FIG. 8 is a flowchart showing each step of the measurement accuracy evaluation method according to the present embodiment. In this evaluation method, the force curve acquisition unit acquires the force curve data measured by the AFM 1 in the preliminary measurement (step S3) shown in FIG. 6 (step S41, force curve acquisition step).

  Subsequently, in step S42 (actual data calculation step), the actual data calculation unit 62 calculates actual load displacement curves (actual data) based on the actual measurement from the force curve measurement data acquired by the force curve acquisition unit 61 for each measurement point. To do.

  Subsequently, in step S43 (elastic modulus calculation step), the elastic modulus calculator 63 calculates the elastic modulus of the sample S for each measurement point from the actual load displacement curve calculated by the actual data calculator 62. The elastic modulus calculation unit 63 may generate an elastic modulus image as shown in FIG.

  Subsequently, in step S44 (theoretical data calculation step), the theoretical data calculation unit 64 substitutes the elastic modulus calculated by the elastic modulus calculation unit 63 and the measurement parameter in the force mapping mode measurement into the theoretical formula. A load displacement curve (theoretical data) is calculated for each measurement point.

  Subsequently, in step S45 (mismatch degree calculation step), the mismatch degree calculation unit 65 determines the degree of mismatch between the actual load displacement curve calculated by the actual data calculation unit 62 and the theoretical load displacement curve calculated by the theoretical data calculation unit 64. Calculate for each measurement point. In the present embodiment, the R-factor obtained by the above equation 1 is used as the degree of mismatch.

Subsequently, in step S46, the mismatch degree calculation unit 65 determines that the average value R-factor _ave. And calculated R-factor _ave. Is associated with the measurement parameter and recorded in the measurement history H. In the present embodiment, the measurement history H is stored in the auxiliary storage device 3. However, the storage in the auxiliary storage device 3 is not essential, and the measurement history H may be stored in a working memory.

  Subsequently, in step S47 (mapping image generation step), the mapping image generation unit 66 visually determines the distribution of the size of the R-factor based on the R-factors of all the measurement points calculated by the mismatch degree calculation unit 65. The mapping image expressed in (5) is generated. This step S47 may be performed before step S46 or may be omitted.

As described above, the average value R-factor _{ave. Of} R-factor at each measurement point corresponding to one measurement parameter _. Is recorded and the evaluation of measurement accuracy is completed. Thereafter, the process proceeds to step S5 illustrated in FIG. 6, and R-factor _ave. Is determined as an effective measurement parameter (step S6), and based on the effective measurement parameter, the main measurement is performed with a larger number of measurement points than the preliminary measurement (step S8).

  As described above, in this embodiment, the measurement accuracy is evaluated by using the R-factor as an index of the degree of mismatch. Since R-factor is a dimensionless number, it does not depend on the type of sample S or measurement conditions. Therefore, the reference value for evaluating the validity of the elastic modulus can be set to a constant value, and the evaluation can be performed quantitatively and quickly. Accordingly, it becomes easy to search for effective measurement parameters for measuring the elastic modulus, and high-resolution elastic modulus data can be obtained with high reliability and accuracy.

  Note that the measurement accuracy in the main measurement may be evaluated after the main measurement step (step S8 shown in FIG. 6). Specifically, R-factor indicating the degree of inconsistency between the actual measurement data and the theoretical data obtained in this measurement is calculated for each measurement point, and whether the measurement accuracy is appropriate based on the calculated R-factor May be confirmed.

(Modification)
Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the spirit of the present invention.

For example, in the above embodiment, an index represented by R-factor is used as the degree of mismatch between the actually measured load displacement curve and the theoretical load displacement curve calculated by the mismatch degree calculation unit 65 in step S45 shown in FIG. Any index representing an error other than the R-factor can be used as an index indicating the degree of mismatch. As such an index, for example, a residual square value defined by the following Equation 3 can be cited.
δ _data : deformation amount of sample S at a certain load in the measured load displacement curve δ _calc : deformation amount of sample S at a certain load in the theoretical load displacement curve

However, in order to easily evaluate the validity of the elastic modulus, it is preferable that the degree of inconsistency be an index represented by a dimensionless number such as R-factor. As an index represented by a dimensionless number, for example, a value obtained by the following expression 4 may be used.
δ _data : deformation amount of sample S at a certain load in the measured load displacement curve δ _calc : deformation amount of sample S at a certain load in the theoretical load displacement curve

  If theoretical data and measured data are aligned, the residual square value can be used as a definition / calculation index for any theory. However, since it is a value having a unit, it is considered difficult to use it as a reference value. However, any error index may be used as long as it is an index indicating an error that is versatile and has no practical problem.

  In addition, by using an index represented by a dimensionless number, the evaluation method according to the present invention is applied not only to elastic modulus measurement using the JKR theory but also to elastic modulus measurement using other elastic contact phenomenon model equations. it can. For example, when the sample S is a metal, ceramic, or soft material (in solution), a theoretical formula based on the Hertz contact dynamic model can be used. When the sample S is a material having an elastic modulus of several GPa or more, DMT It can also be used for theoretical formulas other than JKR theory, such as theory.

When evaluating the validity of the elastic modulus measurement using the Hertz contact dynamic model or the theoretical formula based on the DMT theory, the dimensionless number index indicating the degree of inconsistency between the actual load displacement curve and the theoretical load displacement curve is as follows: It is represented by Formula 5 or Formula 6.
F _data : Load at a certain deformation amount of the sample S in the actually measured load displacement curve F _calc : Load at a certain deformation amount of the sample S in the theoretical load displacement curve
F _data : Load at a certain deformation amount of the sample S in the actually measured load displacement curve F _calc : Load at a certain deformation amount of the sample S in the theoretical load displacement curve

  FIG. 9 is an example of an elastic modulus image in the elastic modulus measurement using the Hertz contact mechanics model, and FIG. 10 visually represents the distribution of the size of R-factor in the elastic modulus image shown in FIG. It is a mapping image. In this example, as the sample S, Yodoflon PTFE (F4) having a thickness of 2 mm manufactured by Yodogawa Hutec Co., Ltd. was used. Further, FIG. 11 shows an actually measured load displacement curve and a theoretical load displacement curve in a block having the smallest R-factor (R-factor = 0.00294) in the mapping image shown in FIG.

  In addition, when R-factor is used as the degree of inconsistency, it is 0 when there is no degree of inconsistency, which is easy to calculate, in addition to the advantage that it can be applied to elastic modulus measurement using a theoretical formula other than the JKR theory. The R-factor is most preferably used because there are advantages that the degree of inconsistency can be understood intuitively and it is easy to determine a reference value for determination.

As examples in the present invention, examples of analysis based on JKR theory, Hertz contact mechanics model and DMT theory are given. However, R-factor is an index that can be defined and calculated as long as there is a combination of measured data and theoretical data. For example, the present invention can be applied to analysis using an MD theory, an MYD theory, or an unknown theory that will be newly proposed in the future. Therefore, the generalized R-factor and the residual square value are expressed by the following Expression 7, Expression 8, and Expression 9.
d _data : a load at a certain deformation amount of the measurement object in the actual load displacement curve or a deformation amount of the measurement object at a certain load d _calc : a deformation amount of the measurement object in the theoretical load displacement curve Load or deformation amount of the measurement object at a certain load

  Note that the amount of energy dissipation due to viscoelasticity described in Non-Patent Document 2 is an amount that can be applied when using the JKR theory, and was calculated using, for example, a theoretical formula based on the Hertz contact dynamic model, DMT theory, or the like. It cannot be applied to the evaluation of elastic modulus.

  In the above embodiment, as shown in FIG. 5, the R-factor mapping image has a configuration in which the density and color of each block change in proportion to the size of the R-factor. The display mode of -factor is not limited to this. For example, blocks having an R-factor less than or equal to a predetermined value change density and / or color in proportion to the size of the R-factor, and blocks having an R-factor greater than a predetermined value are all the same color and / or the same. It may be an aspect of displaying by density. Specifically, in the mapping image shown in FIG. 12, all blocks having an R-factor greater than 0.01 are displayed in black. Even in such a display mode, the user can intuitively grasp whether the measured elastic modulus is appropriate as a whole based on the mapping image.

Further, in the elastic modulus measurement method according to the above embodiment, in order to determine an effective measurement parameter based on a plurality of inconsistencies obtained in the preliminary measurement, as shown in step S5 shown in FIG. Average value R-factor _ave. However, the present invention is not limited to this. If the number of measurement points in each preliminary measurement is the same, the average value R-factor _ave. Instead, the total value of R-factor at all measurement points is calculated, and the effective measurement parameter is determined based on whether the total value is a reference value (for example, 0.60 × number of measurement points) or less. May be.

  In step S47 shown in FIG. 8, a mapping image is generated, or instead of generating a mapping image, an image in which the mapping image and the elastic modulus image are superimposed may be generated. For example, each block generates an image having an area displayed in a color (or light and shade) indicating an elastic modulus, and an area surrounding the area and displayed in a color (or light and dark) indicating an R-factor. Also good. Thereby, the distribution of elastic modulus and the distribution of R-factor can be confirmed with one image.

  An example of an image in which the mapping image and the elastic modulus image are superimposed is shown in FIG. The image shown in FIG. 13 is obtained by superimposing the elastic modulus image shown in FIG. 14A and the mapping image shown in FIG. 13 and 14 show only a part of a 16 × 16 square image.

In addition, instead of generating a mapping image, or instead of generating a mapping image, the average value of R-factor R-factor _ave. May be displayed in the vicinity of the corresponding elastic modulus image. Also by this, the user can easily determine whether the elastic modulus calculated by the elastic modulus calculator 63 is appropriate as a whole.

  The elastic modulus measurement method according to the above embodiment is a method suitable for quickly searching for effective measurement parameters. FIG. 15 shows a method for obtaining highly accurate elastic modulus data.

FIG. 15 is a flowchart showing each step of the elastic modulus measurement method according to the modification of the present invention. The measurement method according to this modification is obtained by replacing step S5 shown in FIG. 6 with step S5 ′. Specifically, in the measurement method according to the present modification, a plurality of measurement parameters are prepared in advance, preliminary measurement and evaluation of measurement accuracy are performed for all the measurement parameters, and R-factor _ave. Is recorded in the measurement history H in association with each measurement parameter. Thereafter, in step S <b _> 6, the effective measurement parameter determination unit 7 determines that the R-factor _ave. The lowest R-factor _ave. Is determined as an effective measurement parameter.

  Note that the plurality of measurement parameters to be prepared may be arbitrarily set by the user, or may be all measurement parameters that can be measured by the AFM 1. The greater the number of measurement parameters for performing the preliminary measurement, the longer the measurement time, but the higher the possibility of obtaining more accurate elastic modulus data. In particular, by performing preliminary measurement and evaluation of measurement accuracy for all measurement parameters that can be measured by the AFM 1, it is possible to search for an optimum measurement parameter among all measurement parameters.

  The present invention is particularly suitable for force curve mapping measurement using an atomic force microscope. However, the present invention is not limited to this, and scanning of a scanning tunnel microscope, an environmental control scanning probe microscope, a spin-polarized scanning tunneling microscope, etc. The present invention can also be applied to elastic modulus measurement using a scanning probe microscope.

1 Atomic force microscope (AFM)
2 Computing device (computer)
3 Auxiliary storage device 4 Measurement instruction unit 5 Measurement parameter setting unit 6 Accuracy evaluation unit 7 Effective measurement parameter determination unit 61 Force curve acquisition unit 62 Actual data calculation unit 63 Elastic modulus calculation unit 64 Theoretical data calculation unit 65 Inconsistency degree calculation unit 66 Mapping Image generation unit H Measurement history S Sample (object to be measured)
S3 Preliminary measurement step S4 Measurement accuracy evaluation step S41 Force curve acquisition step S42 Actual data calculation step S43 Elastic modulus calculation step S44 Theoretical data calculation step S45 Inconsistency calculation step S47 Mapping image generation step S6 Effective measurement parameter determination step S8 Main measurement step

Claims (16)

An evaluation method of measurement accuracy by force mapping mode measurement of a scanning probe microscope,
A force curve acquisition step of acquiring force curve measurement data at a plurality of measurement points on the surface of the measurement object by force mapping mode measurement using the scanning probe microscope;
Actual measurement data calculation step for calculating an actual load displacement curve from the force curve measurement data for each measurement point;
An elastic modulus calculation step of calculating an elastic modulus for each of the measurement points using a theoretical formula from the measured load displacement curve;
A theoretical data calculation step for calculating a theoretical load displacement curve for each measurement point by substituting the measurement parameters in the elastic modulus and the force mapping mode measurement into the theoretical formula;
A mismatch degree calculating step for calculating a mismatch degree between the measured load displacement curve and the theoretical load displacement curve for each measurement point;
Have
The evaluation method, wherein the inconsistency is expressed by a dimensionless number. The evaluation method according to claim 1, wherein the degree of inconsistency is represented by an R-factor obtained by the following formula 7 or formula 8.


d _data : a load at a certain deformation amount of the measurement object in the actual load displacement curve or a deformation amount of the measurement object at a certain load d _calc : a deformation amount of the measurement object in the theoretical load displacement curve Load or deformation amount of the measurement object at a certain load The theoretical formula is a theoretical formula based on the JKR theory,
The evaluation method according to claim 1, wherein the degree of inconsistency is represented by an R-factor determined by the following formula 1.
δ _data : deformation amount of the measurement object at a certain load in the actually measured load displacement curve δ _calc : deformation amount of the measurement object at a certain load in the theoretical load displacement curve The theoretical formula is a theoretical formula based on Hertz's contact dynamic model or DMT theory,
The evaluation method according to claim 1, wherein the degree of inconsistency is represented by an R-factor obtained by the following formula 5.
F _data : Load at a certain deformation amount of the measurement object in the measured load displacement curve F _calc : Load at a certain deformation amount of the measurement object in the theoretical load displacement curve   A mapping image for generating a mapping image in which an area corresponding to each measurement point is displayed in such a manner that a region corresponding to each measurement point can be visually discriminated from the size of the measurement point. The evaluation method according to claim 1, further comprising a generation step.   The evaluation method according to claim 1, wherein the scanning probe microscope is an atomic force microscope.   The evaluation method according to claim 1, wherein the measurement object is a soft material, a metal, a ceramic, or a composite thereof. A method for measuring the elastic modulus of the surface of an object to be measured by force mapping mode measurement of a scanning probe microscope,
A preliminary measurement step in which the scanning probe microscope measures force curves at a plurality of measurement points on the surface of the measurement object based on one or more measurement parameters of the scanning probe microscope;
Force curve measurement data that is measurement data of the force curve measured in the preliminary measurement step is acquired, an actual load displacement curve is calculated for each measurement point from the force curve measurement data, and a theoretical value is calculated from the actual load displacement curve. Calculate the elastic modulus for each measurement point using an equation, and calculate the theoretical load displacement curve for each measurement point by substituting the measurement parameters in the elastic modulus and the force mapping mode measurement into the theoretical formula, A measurement accuracy evaluation step for calculating a degree of inconsistency represented by a dimensionless number between the measured load displacement curve and the theoretical load displacement curve for each measurement point;
An effective measurement parameter determining step for determining an effective measurement parameter from the one or more measurement parameters based on the inconsistency calculated in the measurement accuracy evaluation step;
Based on the effective measurement parameters, the main measurement step of measuring the elastic modulus of the surface of the measurement object at more measurement points than the measurement points in the preliminary measurement step;
A measuring method. The measurement method according to claim 8, wherein the degree of inconsistency is represented by an R-factor determined by the following formula 7 or formula 8.


d _data : a load at a certain deformation amount of the measurement object in the actual load displacement curve or a deformation amount of the measurement object at a certain load d _calc : a deformation amount of the measurement object in the theoretical load displacement curve Load or deformation amount of the measurement object at a certain load The theoretical formula is a theoretical formula based on the JKR theory,
The measurement method according to claim 8 or 9, wherein the degree of inconsistency is represented by an R-factor determined by the following formula 1.
δ _data : deformation amount of the measurement object at a certain load in the actually measured load displacement curve δ _calc : deformation amount of the measurement object at a certain load in the theoretical load displacement curve The theoretical formula is a theoretical formula based on Hertz's contact dynamic model or DMT theory,
The measurement method according to claim 8 or 9, wherein the degree of inconsistency is represented by an R-factor obtained by the following formula 5.
F _data : Load at a certain deformation amount of the measurement object in the measured load displacement curve F _calc : Load at a certain deformation amount of the measurement object in the theoretical load displacement curve   The measurement method according to claim 8, wherein in the effective measurement parameter determination step, a measurement parameter in which an average of the inconsistencies at all measurement points is equal to or less than a predetermined reference value is determined as an effective measurement parameter.   The measurement method according to claim 8, wherein the scanning probe microscope is an atomic force microscope.   The program for making a computer perform each step in any one of Claims 1-13.   A scanning probe microscope system equipped with a program for causing a computer to execute each step according to claim 1.   An atomic force microscope system equipped with a program for causing a computer to execute each step according to claim 1.