Electrical resistance measuring device and electrical resistance measuring method

Abstract

A plate-shaped sample is sandwiched between an electrode indenter A and an electrode indenter B, and a current Iind is passed between the electrode indenter A and the electrode indenter B. In this state, an i-th probe A and an i-th probe B are used to measure a potential difference Vprobe (i, x (i)) in the thickness direction at a position where the distance from the outer surfaces of the electrode indenter A and the electrode indenter B is x (i). The relationship between x (i) and Vprobe (i, x (i)) is fitted using a function, and the real potential difference Vreal generated in the thickness direction of the plate-shaped sample is estimated using the fitted function. Further, an estimated value Rest of electrical resistance in the thickness direction of the plate-shaped sample and / or an estimated value ρest of resistivity are calculated using Vreal and Iind.

Description

Electrical Resistance Measuring Device and Method for Measuring Electrical Resistance

[0001] The present invention relates to an electrical resistance measuring device and a method for measuring electrical resistance. More specifically, the present invention relates to an electrical resistance measuring device capable of accurately calculating the electrical resistance and / or resistivity in the thickness direction of a thin plate-like sample, and a method for measuring electrical resistance using the same.

[0002] As methods for measuring the electrical resistance of a material, a two-terminal method, a four-terminal method, a four-probe method, a van der Pauw method, etc. are known. The two-terminal method is a method of measuring electrical resistance by connecting terminals to both ends of the object to be measured. The two-terminal method is used for measurements in cases where the electrical resistance of the object to be measured is relatively high or in applications where the accuracy requirement is low. In the two-terminal method, since the influence of contact resistance and lead wire resistance at the terminal contacts is included in the measured value, when the electrical resistance of the object to be measured is equal to or less than these, the electrical resistance cannot be accurately measured.

[0003] The four-terminal method is a method of measuring electrical resistance by connecting two current terminals and two voltage terminals to the object to be measured. In the four-terminal method, the influence of contact resistance and lead wire resistance at the terminal contacts, which was a problem in the two-terminal method, is eliminated, so an accurate voltage drop can be measured between the voltage terminals, and the electrical resistance of the object to be measured can be measured with high accuracy.

[0004] The four-probe method is a method derived from the four-terminal method. It is a method of contacting two probe-like current terminals and two probe-like voltage terminals with the surface of a plate-like object to be measured, measuring the current and voltage between each probe, and calculating the electrical resistance (sheet resistance). The van der Pauw method is a method of providing terminals at four corners of an object to be measured with an arbitrary shape and a constant thickness, and calculating the resistance from the relationship between the current and voltage between the individual terminals (see Non-Patent Document 1). Furthermore, an electrode resistance measurement system related to the four-probe method is also commercially available (see Non-Patent Document 2). This electrode resistance measurement system is an extension of the four-probe method, and the difference from the four-probe method is that a large number of probes for voltage measurement are used.

[0005] As described above, several methods for measuring low electrical resistance have been known conventionally. The four-probe method, the van der Peau method, and the electrode resistance measurement system, all of which are methods for measuring the electrical resistance of sheet materials, involve passing current in the in-plane direction of the object being measured. Therefore, all of these methods measure the in-plane electrical resistance of sheet materials. However, there have been no conventional examples of devices proposed that can accurately measure the electrical resistance in the thickness direction of thin sheet materials.

[0006] van der Pauw, LJ (1958). "A method of merasuring specific resistivity and Hall effect of discs of arbitrary shape." Philips Research Reports. 13: 1-9. Nobuhisa Handa, "Electrode Resistance Measurement System RM2610," HIOKI Technical Report, Vol. 41 (2020).

[0007] The problem that the present invention aims to solve is to provide an electrical resistance measuring device capable of accurately measuring the electrical resistance and / or resistivity in the thickness direction of a thin, plate-like sample. Another problem that the present invention aims to solve is to provide a method for measuring electrical resistance and / or resistivity using such an electrical resistance measuring device.

[0008] To solve the above problems, the electrical resistance measuring device according to the present invention comprises: an electrode indenter A and an electrode indenter B for clamping a plate-shaped sample in the thickness direction; a pressurizing device for pressing the electrode indenter A and / or the electrode indenter B onto the plate-shaped sample; an i-th probe A (1 ≤ i ≤ n, n ≥ 1) positioned adjacent to the electrode indenter A; a moving device for moving the i-th probe A in the thickness direction of the plate-shaped sample, or in the thickness direction and in the in-plane direction of the plate-shaped sample; a potential difference measuring device for measuring the potential difference Vprobe(i,x(i)) between the i-th probe A and the electrode indenter B at an arbitrary position where the distance from the outer surface of the electrode indenter A is x(i); a current applying device for applying a DC current or AC current to the plate-shaped sample via the electrode indenter A and the electrode indenter B; an ammeter for measuring the current value Iind flowing between the electrode indenter A and the electrode indenter B; and a calculation device for estimating the electrical resistance and / or resistivity in the thickness direction of the plate-shaped sample. The calculation device includes a Vreal estimation device that estimates the true potential difference Vreal generated in the thickness direction of the plate-shaped sample based on x(i) and Vprobe(i,x(i)), and a resistance calculation device that calculates an estimated value Rest of the electrical resistance in the thickness direction of the plate-shaped sample and / or an estimated value ρest of the resistivity in the thickness direction of the plate-shaped sample based on Vreal and Iind.

[0009] The electrical resistance measuring device further comprises an i-th probe B (1 ≤ i ≤ n, n ≥ 1) positioned adjacent to the electrode indenter B and facing the i-probe A, the moving device further comprises a device for moving the i-probe A and the i-probe B in the thickness direction, or in the thickness direction and the in-plane direction, while maintaining the state in which the i-probe A and the i-probe B are facing each other, and the potential difference measuring device preferably comprises a device for measuring at least one selected from the group consisting of (a) the potential difference between the i-probe A and the electrode indenter B, (b) the potential difference between the i-probe B and the electrode indenter A, and (c) the potential difference between the i-probe A and the i-probe B as the Vprobe(i, x(i)).

[0010] The method for measuring electrical resistance according to the present invention comprises the step of calculating the electrical resistance in the thickness direction of a plate-shaped sample and / or the resistivity in the thickness direction of the plate-shaped sample using an electrical resistance measuring device according to the present invention.

[0011] When a plate-shaped sample is clamped between electrode indenters A and B, and a current is passed between electrode indenters A and B, an electric field spreads around electrode indenters A and B. As a result, a potential difference is generated even outside electrode indenters A and B. Furthermore, the potential difference generated outside electrode indenters A and B decreases as the distance x(i) from the outer surface of electrode indenters A and B increases. Moreover, the curve of change in the potential difference has a shape close to a sigmoid curve.

[0012] Therefore, by approximating the relationship between the distance x(i) from the outer surface of electrode indenters A and B and the potential difference Vprobe(i,x(i)) at that position with a sigmoid curve, the electrical resistance and / or resistivity in the thickness direction of the plate-like sample can be estimated. The estimated electrical resistance value Rest obtained using the method according to the present invention does not include the contact resistance Rcont_A between the plate-like sample and electrode indenter A, and / or the contact resistance Rcont_B between the plate-like sample and electrode indenter B. Therefore, using the method according to the present invention, the electrical resistance and / or resistivity in the thickness direction of the plate-like sample can be accurately calculated.

[0013] This is a schematic diagram of the electrical resistance measuring device according to the present invention. Figure 2(A) shows the relationship between the distance from the outer surface of the electrode indenter and the measured potential difference. Figure 2(B) shows the relationship between the distance from the outer surface of the electrode indenter and the measured potential difference approximated by a sigmoid curve. This is a flowchart of the electrical resistance measurement method according to the present invention.

[0014] Figure 4(A) is a circuit diagram of the two-terminal method. Figure 4(B) is a circuit diagram of the four-terminal method. Figure 5(A) is a schematic diagram of the electrical resistance measurement method using the four-terminal method. Figure 5(B) is a schematic diagram of the electrical resistance measurement method using the four-probe method. These are a bird's-eye view and a front view of the CAE model used in the simulation. This figure shows the relationship between the distance from the outer surface of the electrode indenter and the voltage.

[0015] [Configuration 1] The configuration comprises: an electrode indenter A and an electrode indenter B for clamping a plate-shaped sample in the thickness direction; a pressurizing device for pressing the electrode indenter A and / or the electrode indenter B against the plate-shaped sample; an i-th probe A (1 ≤ i ≤ n, n ≥ 1) positioned adjacent to the electrode indenter A; a moving device for moving the i-th probe A in the thickness direction of the plate-shaped sample, or in the thickness direction and in the in-plane direction of the plate-shaped sample; a potential difference measuring device for measuring the potential difference Vprobe(i,x(i)) between the i-th probe A and the electrode indenter B at an arbitrary position where the distance from the outer surface of the electrode indenter A is x(i); a current applying device for applying a DC current or AC current to the plate-shaped sample via the electrode indenter A and the electrode indenter B; an ammeter for measuring the current value Iind flowing between the electrode indenter A and the electrode indenter B; and a calculation device for estimating the electrical resistance and / or resistivity in the thickness direction of the plate-shaped sample, wherein the calculation device An electrical resistance measuring device comprising: a Vreal estimation device that estimates the true potential difference Vreal generated in the thickness direction of the plate-shaped sample based on x(i) and Vprobe(i,x(i)); and a resistance calculation device that calculates an estimated value Rest of the electrical resistance in the thickness direction of the plate-shaped sample and / or an estimated value ρest of the resistivity in the thickness direction of the plate-shaped sample based on Vreal and Iind.

[0016] [Configuration 2] The electrical resistance measuring device according to Configuration 1, wherein the calculation device further comprises a contact resistance calculation device A for calculating the contact resistance Rcont_A between the plate-shaped sample and the electrode indenter A, the contact resistance calculation device A for calculating the apparent electrical resistance Rapp by dividing the apparent potential difference Vapp between the electrode indenter A and the electrode indenter B by Iind, the device for calculating Rest which includes the contact resistance Rcont_B between the plate-shaped sample and the electrode indenter B based on x(i) and Vprobe(i,x(i)), and the device for calculating Rcont_A by subtracting Rest from Rapp.

[0017] [Configuration 3] An electrical resistance measuring device according to Configuration 1 or 2, further comprising an i-th probe B (1 ≤ i ≤ n, n ≥ 1) positioned adjacent to the electrode indenter B and facing the i-probe A, wherein the moving device further comprises a device for moving the i-probe A and the i-probe B in the thickness direction, or in the thickness direction and the in-plane direction, while maintaining the state in which the i-probe A and the i-probe B are facing each other, and the potential difference measuring device comprises a device for measuring at least one selected from the group consisting of (a) the potential difference between the i-probe A and the electrode indenter B, (b) the potential difference between the i-probe B and the electrode indenter A, and (c) the potential difference between the i-probe A and the i-probe B, as Vprobe(i,x(i)).

[0018] [Configuration 4] The electrical resistance measuring device according to Configuration 3, wherein the calculation device further comprises a contact resistance calculation device B for calculating the contact resistance Rcont_B between the plate-shaped sample and the electrode indenter B, the contact resistance calculation device B for calculating the apparent electrical resistance Rapp by dividing the apparent potential difference Vapp between the electrode indenter A and the electrode indenter B by Iind, the device for calculating Rest which includes the contact resistance Rcont_A between the plate-shaped sample and the electrode indenter A based on x(i) and Vprobe(i,x(i)), and the device for calculating Rcont_B by subtracting Rest from Rapp.

[0019] [Configuration 5] An electrical resistance measuring device according to any one of Configurations 1 to 4, comprising a plurality of i-probes A, wherein the plurality of i-probes A are spaced apart on a straight line passing through the centroid of the electrode indenter A, and x(i) is greater than zero and less than or equal to rA. However, "rA" means the distance between the centroid of the electrode indenter A and the intersection point of the straight line passing through the outer circumference of the electrode indenter A and the centroid.

[0020] [Configuration 6] An electrical resistance measuring device according to any one of Configurations 1 to 5, wherein the moving device is capable of moving the i probe A in the in-plane direction along a straight line passing through the center of gravity of the electrode indenter A, and within the range where x(i) is greater than zero and less than or equal to rA. However, "rA" means the distance between the center of gravity of the electrode indenter A and the intersection point of the straight line passing through the outer circumference of the electrode indenter A and the center of gravity.

[0021] [Configuration 7] The electrical resistance measuring device according to any one of Configurations 1 to 6, wherein the Vreal estimation device is equipped with a device that estimates Vreal using at least one selected from the group consisting of the logistic function, sigmoid function, hyperbolic tangent function (tanh), inverse probit function, Gompertz function, arctangent function (arctan), and Gutermann function.

[0022] [Configuration 8] An electrical resistance measuring device according to any one of Configurations 1 to 7, further comprising a support device for supporting the plate-shaped sample.

[0023] [Configuration 9] A method for measuring electrical resistance, comprising the step of calculating the electrical resistance in the thickness direction of a plate-shaped sample and / or the resistivity in the thickness direction of the plate-shaped sample using an electrical resistance measuring device described in any one of Configurations 1 to 8.

[0024] [1. Electrical Resistance Measuring Device] Figure 1 shows a schematic diagram of an electrical resistance measuring device according to the present invention. In Figure 1, the electrical resistance measuring device 10 includes an electrode indenter A14, an electrode indenter B16, a pressurizing device 18, first to fourth probes A22, 22..., first to fourth probes B24, 24..., moving devices 26a, 26b, a potential difference measuring device 30, a current application device 42, an ammeter 44, a support device 50, and a calculation device 60.

[0025] [1.1. Electrode indenter A, electrode indenter B] Electrode indenter A14 and electrode indenter B16 are for clamping the plate-shaped sample 12 in the thickness direction. The material of electrode indenter A14 and electrode indenter B16 is not particularly limited, as long as it is a material that has rigidity that allows a predetermined pressure to be applied to the plate-shaped sample 12 and conductivity that allows a predetermined current to be applied to the plate-shaped sample 12.

[0026] The cross-sectional shape, cross-sectional area, and height of electrode indenters A14 and B16 are not particularly limited, as long as they allow for accurate measurement of the electrical resistance in the thickness direction of the plate-shaped sample 12. To accurately measure the electrical resistance in the thickness direction of the plate-shaped sample 12, it is preferable that the cross-sectional shape and cross-sectional area of ​​electrode indenter A14 are the same as those of electrode indenter B16. Furthermore, it is preferable that electrode indenters A14 and B16 are positioned so that their centers coincide.

[0027] [1.2. Pressurizing device] The pressurizing device 18 is a device for pressing the electrode indenter A14 and / or electrode indenter B16 onto the plate-shaped sample 12. The pressurizing device 18 may be any of the following: (A) capable of pressing only the electrode indenter A14 onto the plate-shaped sample 12, (B) capable of pressing only the electrode indenter B16 onto the plate-shaped sample 12, or (C) capable of pressing both the electrode indenter A14 and the electrode indenter B16 onto the plate-shaped sample 12. In the example shown in Figure 1, the electrode indenter B16 is fixed on the table 20, and the pressurizing device 18 is configured to be capable of pressing only the electrode indenter A14 onto the plate-shaped sample 12.

[0028] [1.3. Probe iA, Probe iB] [1.3.1. Probe material and shape] The first to fourth probes A22, 22... and the first to fourth probes 24, 24... (hereinafter also simply referred to as "probes") are used to acquire data necessary to calculate the true potential difference Vreal generated in the thickness direction of the plate-shaped sample 12 when an electric current is applied to the plate-shaped sample 12. The material and shape of the probes are not particularly limited, as long as they enable the acquisition of such data.

[0029] In Figure 1, the probe positioned above the plate-shaped sample 12 is labeled "probe A22," and the probe positioned below the plate-shaped sample 12 is labeled "probe B24." This distinction is for convenience only. In the following explanation, the probe positioned above the plate-shaped sample 12 will be referred to as "probe A22," but the same effect can be obtained even if the probe positioned below the plate-shaped sample 12 is also referred to as "probe A22."

[0030] [1.3.2. Number of Probes] In Figure 1, the first to fourth probes A22, 22... are positioned adjacent to the electrode indenter A14. The first to fourth probes B24, 24... are positioned adjacent to the electrode indenter B16 and opposite to the first to fourth probes A22, 22... "Opposite to each other" means that, when viewed from the thickness direction of the plate-shaped sample 12, the projection plane of the tip of the i-th probe A22 and the projection plane of the tip of the i-th probe B24 overlap in whole or in part.

[0031] In Figure 1, a total of four sets of probes are shown, but this is merely an example, and the number of probes is not particularly limited. The number (i) of the i-th probe A22 may be one or two or more. Similarly, the number (i) of the i-th probe B24 may be one or two or more.

[0032] Furthermore, the electrical resistance measuring device 10 does not necessarily need to be equipped with both the i-probe A22 and the i-probe B24; it may be equipped with only one of them. In order to more accurately measure the electrical resistance in the thickness direction of the plate-shaped sample 12, it is preferable that the electrical resistance measuring device 10 be equipped with both the i-probe A22 and the i-probe B24. This is because, when both the i-probe A22 and the i-probe B24 are equipped, it becomes possible to calculate the electrical resistance of the plate-shaped sample 12 after excluding both the contact resistance between the plate-shaped sample 12 and the electrode indenter A14, and the contact resistance between the plate-shaped sample 12 and the electrode indenter B16.

[0033] [1.3.3. Probe Spacing] When the electrical resistance measuring device 10 is equipped with multiple probes, the spacing between adjacent probes is not particularly limited. That is, the spacing between each probe may be the same, or it may differ depending on the location. As will be described later, the gradient of change in the probe measurement value becomes smaller as the distance x(i) from the outer surface of the electrode indenter A14 or electrode indenter B16 increases. For this reason, it is preferable to narrow the spacing between probes as the probe position gets closer to the electrode indenter A14 or electrode indenter B16.

[0034] [1.3.4. Probe Installation Range] When the electrical resistance measuring device 10 is equipped with multiple probes, the installation range of the probes is not particularly limited, and the optimal position can be selected according to the purpose.

[0035] Here, let "x(i)" be the distance from the outer surface of the electrode indenter A14 to the potential difference measurement position (the installation position of the i-th probe A22). Also, when a straight line is drawn passing through the centroid of the electrode indenter A14, let "rA" be the distance between the centroid of the electrode indenter A14 and the intersection point of the straight line passing through the outer circumference of the electrode indenter A and the centroid. If the cross-sectional shape of the electrode indenter A14 is a circle, rA corresponds to the radius of the circle. In this case, it is preferable that the multiple i-th probes A22, 22... are installed spaced apart on a straight line passing through the centroid of the electrode indenter A14, and within the range where x(i) is greater than zero and less than or equal to rA. Installing the multiple i-th probes A22, 22... within this range improves the accuracy of estimating the electrical resistance in the thickness direction of the plate-shaped sample 12.

[0036] The same applies to the i-th probe B24. Specifically, let "x(i)" be the distance from the outer surface of the electrode indenter B16 to the potential difference measurement position (the installation position of the i-th probe B24). Also, when a straight line is drawn passing through the centroid of the electrode indenter B16, let "rB" be the distance between the centroid of the electrode indenter B14 and the intersection point of the straight line passing through the outer circumference of the electrode indenter B16 and its centroid. If the cross-sectional shape of the electrode indenter B16 is a circle, rB corresponds to the radius of the circle. In this case, it is preferable that the multiple i-th probes B24, 24... are installed spaced apart on a straight line passing through the centroid of the electrode indenter B16, and within the range where x(i) is greater than zero and less than or equal to rB.

[0037] [1.4. Moving Device] Moving device 26a is a device for moving the i-probes A22, 22... in the thickness direction of the plate-shaped sample 12, or in the thickness direction and in the in-plane direction of the plate-shaped sample 12. Moving device 26b is a device for moving the i-probes B24, 24... in the thickness direction, or in the thickness direction and in the in-plane direction, while maintaining the i-probes A22, 22... and i-probes B24, 24... facing each other. Note that if the electrical resistance measuring device 10 is not equipped with i-probes B24, 24..., moving device 26b can be omitted.

[0038] If the electrical resistance measuring device 10 is equipped with a relatively large number of probes, the moving devices 26a and 26b only need to have the function of moving the probes in the thickness direction of the plate-shaped sample 12. The "function of moving in the thickness direction" refers to the function of bringing the tip of the probe into contact with the surface of the plate-shaped sample 12, and the function of detaching the probe from the surface of the plate-shaped sample 12.

[0039] On the other hand, if the electrical resistance measuring device 10 has a relatively small number of probes, it is preferable that the moving devices 26a and 26b have the function of moving the probes not only in the thickness direction of the plate-shaped sample 12 but also in the in-plane direction. If the moving devices 26a and 26b have the function of moving in the in-plane direction, even if the number of probes is small, the potential difference can be measured at multiple positions with different x(i). As a result, the electrical resistance in the thickness direction of the plate-shaped sample 12 can be estimated more accurately.

[0040] When the moving device 26a is equipped with a device capable of moving the i-th probes A22, 22... in the in-plane direction of the plate-shaped sample 12, it is preferable that the device can move the i-th probes A22, 22... in the in-plane direction on a straight line passing through the center of gravity of the electrode holder A14 and within the range where x(i) is zero or more and rA or less.

[0041] Similarly, when the moving device 26b is equipped with a device capable of moving the i-th probes B24, 24... in the in-plane direction of the plate-shaped sample 12, it is preferable that the device can move the i-th probes B24, 24... in the in-plane direction on a straight line passing through the center of gravity of the electrode holder B16 and within the range where x(i) is zero or more and rB or less.

[0042] [1.5. Potential difference measuring device] The "potential difference measuring device 30" refers to a device for measuring the potential difference Vprove(i, x(i)) generated in the plate-shaped sample 12 at an arbitrary position where the distance from the outer surface of the electrode holder A14 or the electrode holder B16 is x(i) when a direct current or an alternating current is applied to the plate-shaped sample 12.

[0043] Specifically, when the electrical resistance measuring device 10 includes only the i-th probes A22, 22..., the "potential difference measuring device 30" refers to a device for measuring the potential difference Vprobe(i, x(i)) between the i-th probe A22 and the electrode holder B16 at an arbitrary position where the distance from the outer surface of the electrode holder A14 is x(i).

[0044] When the electrical resistance measuring device 10 includes the i-th probes A22, 22... and the i-th probes B24, 24..., the "potential difference measuring device 30" refers to a device for measuring at least one selected from the group consisting of (a) the potential difference between the i-th probe A22 and the electrode holder B16, (b) the potential difference between the i-th probe B24 and the electrode holder A14, and (c) the potential difference between the i-th probe A22 and the i-th probe B24 as Vprobe(i, x(i)).

[0045] When Vprobe(i, x(i)) is the potential difference between the i-th probe A22 and the electrode element B16, this Vprobe(i, x(i)) includes the potential difference caused by the contact resistance Rcont_B between the plate-like sample 12 and the electrode element B16, but does not include the potential difference caused by the contact resistance Rcont_A between the plate-like sample 12 and the electrode element A14. Conversely, when Vprobe(i, x(i)) is the potential difference between the i-th probe B24 and the electrode element A14, this Vprobe(i, x(i)) includes the potential difference caused by Rcont_A, but does not include the potential difference caused by Rcont_B. Further, when Vprobe(i, x(i)) is the potential difference between the i-th probe A22 and the i-th probe B24, this Vprobe(i, x(i)) does not include both the potential difference caused by Rcont_A and the potential difference caused by Rcont_B.

[0046] The potential difference measuring device 30 is not particularly limited as long as it can measure such Vprobe(i, x(i)). In the example shown in FIG. 1, the potential difference measuring device 30 includes: a potential difference detector 32 for measuring Vprobe(i, x(i)); a changeover switch 34a for connecting any one of the first to fourth probes A22, 22,... to the potential difference detector 32; an open / close switch 36a for directly connecting the electrode element A14 to the potential difference detector 32; a changeover switch 34b for connecting any one of the first to fourth probes B24, 24,... to the potential difference detector 32; and an open / close switch 36b for directly connecting the electrode element B16 to the potential difference detector 32.

[0047] For example, (a) opening the open / close switch 36a; (b) connecting any one of the i-th probes A22 to the potential difference detector 32 by the changeover switch 34a; (c) opening all of the changeover switches 34b; and (d) closing the open / close switch 36b, the potential difference Vprobe(i, x(i)) between any one of the i-th probes A22 and the electrode element B16 can be measured.

[0048] On the other hand, if (a) the on / off switch 36a is closed, (b) all the changeover switches 34a are opened, (c) one of the i-th probes B24 is connected to the potentiometer 32 using the changeover switch 34b, and (d) the on / off switch 36b is opened, the potentiometer Vprobe(i,x(i)) between one of the i-th probes B24 and the electrode indenter A14 can be measured.

[0049] Furthermore, by (a) opening the on / off switch 36a, (b) using the changeover switch 34a to connect one of the i-probes A22 to the potentiometer 32, (c) using the changeover switch 34b to connect the i-probe B24 opposite to the i-probe A22 connected to the potentiometer 32 to the potentiometer 32, and (d) opening the on / off switch 36b, the potential difference Vprobe(i,x(i)) between the opposing i-probes A22 and B24 can be measured.

[0050] The type of potentiometer 32 is not particularly limited, as long as it is capable of measuring Vprobe(i,x(i)). For example, if the current applied to the plate-shaped sample 12 is a DC current, a voltmeter is preferred as the potentiometer 32. On the other hand, if the current applied to the plate-shaped sample 12 is an AC current, an impedance analyzer or the voltage detection unit of an LCR meter is preferred as the potentiometer 32.

[0051] [1.6. Current Application Device] The current application device 42 is a device for applying a direct current or alternating current to a plate-shaped sample 12 via electrode indenters A14 and B16. One end of the current application device 42 is connected to electrode indenter A14, and the other end is connected to electrode indenter B16.

[0052] [1.7. Ammeter] The ammeter 44 is a device for measuring the current value Iind flowing between the electrode indenter A14 and the electrode indenter B16. The installation position of the ammeter 44 is not particularly limited, as long as it is possible to measure Iind. In Figure 1, the ammeter 44 is connected between the current application device 42 and the electrode indenter A14.

[0053] [1.8. Support Device] The support device 50 is a device for supporting the plate-shaped sample 12. In the example shown in Figure 1, the support device 50 includes a pair of insulating plates 52a and 52b having openings. When measuring the electrical resistance of the plate-shaped sample 12, the plate-shaped sample 12 is sandwiched between the insulating plates 52a and 52b, and the electrode indenter A14, electrode indenter B16, i-probe A22, and i-probe B24 are brought into contact with the plate-shaped sample 12 through the openings. Note that if the plate-shaped sample 12 has sufficient rigidity to stand on its own, the support device 50 can be omitted.

[0054] [1.9. Calculation Unit] The calculation unit 60 is a device for estimating the electrical resistance in the thickness direction of the plate-shaped sample 12. In Figure 1, the calculation unit 60 includes a setting unit 62 for inputting various settings, a control and measurement unit 64 that controls each part and measures current and voltage using the input setting values, a calculation unit 66 that performs various calculations using the measured data, and an output unit 68 that outputs the calculation results.

[0055] In the present invention, the calculation device 60 includes, in addition to various devices for controlling the general operation of the electrical resistance measuring device 10, a Vreal estimation device that estimates the true potential difference Vreal generated in the thickness direction of the plate-shaped sample 12 based on x(i) and Vprobe(i,x(i)), and a resistance calculation device that calculates an estimated value Rest of the electrical resistance in the thickness direction of the plate-shaped sample 12 and / or an estimated value ρest of the resistivity in the thickness direction of the plate-shaped sample 12 based on Vreal and Iind.

[0056] The calculation device 60 may further include: (A) a contact resistance calculation device A for calculating the contact resistance Rcont_A between the plate-shaped sample 12 and the electrode indenter A14, and / or (B) a contact resistance calculation device B for calculating the contact resistance Rcont_B between the plate-shaped sample 12 and the electrode indenter B16.

[0057] [1.9.1. Vreal Estimation Device] The "Vreal estimation device" is a device that estimates the true potential difference Vreal generated in the thickness direction of a plate-shaped sample 12 based on x(i) and Vprobe(i,x(i)). When the plate-shaped sample 12 is sandwiched between electrode indenters A14 and B16, and current is injected into the plate-shaped sample 12 via electrode indenters A14 and B16, an electric field spreads around electrode indenters A14 and B16. Therefore, a potential difference is generated in the thickness direction of the plate-shaped sample 12 even at a distance x(i) from the outer surface of electrode indenter A14 or electrode indenter B16.

[0058] Figure 2(A) shows the relationship between the distance from the outer surface of the electrode indenter and the measured potential difference. As shown in Figure 2(A), the potential difference Vprobe(i,x(i)) generated in the thickness direction of the plate-shaped sample 12 decreases exponentially as x(i) increases. On the other hand, within the region of the plate-shaped sample 12 sandwiched between electrode indenter A14 and electrode indenter B16, it is estimated that the potential difference Vprobe(i,x(i)) increases exponentially as x(i) decreases.

[0059] Therefore, Vprobe(i,x(i)) can be approximated using a function that draws a sigmoid curve, i.e., a sigma-type function. Figure 2(B) shows the relationship between the distance from the outer surface of the electrode indenter and the measured potential difference approximated by a sigmoid curve. As shown in Figure 2(B), when the potential difference measured outside the electrode indenter A14 and electrode indenter B16 is approximated by a sigma-type function, the true potential difference Vreal generated in the center of the electrode indenter A14 and electrode indenter B16 can be estimated using the obtained sigma-type function.

[0060] Examples of sigma-type functions include the logistic function, sigmoid function, hyperbolic tangent function (tanh), inverse probit function, Gompertz function, arctangent function (arctan), and Gutermann function. In this invention, Vreal may be estimated using one of these functions, or two or more may be used.

[0061] [1.9.2. Resistance Calculation Device] A "resistance calculation device" refers to a device that calculates the estimated electrical resistance Rest in the thickness direction of a plate-shaped sample 12, and / or the estimated resistivity ρest in the thickness direction of a plate-shaped sample 12, based on Vreal and Iind. The structure of the resistance calculation device is not particularly limited, as long as it performs the above function. Rest is obtained by dividing Vreal by Iind. ρest can be calculated based on Vreal, Iind, the cross-sectional areas of electrode indenters A14 and B16, and the thickness of the plate-shaped sample 12.

[0062] [1.9.3. Contact Resistance Calculation Device A] "Contact Resistance Calculation Device A" refers to a device that calculates the contact resistance Rcont_A between a plate-shaped sample 12 and an electrode indenter A14. More specifically, "Contact Resistance Calculation Device A" refers to a device that calculates the apparent electrical resistance Rapp by dividing the apparent potential difference Vapp between electrode indenter A14 and electrode indenter B16 by Iind, calculates Rest which includes the contact resistance Rcont_B between the plate-shaped sample 12 and electrode indenter B16 based on x(i) and Vprobe(i,x(i)), and calculates Rcont_A by subtracting Rest from Rapp.

[0063] By opening both the changeover switches 34a and 34b and closing the on / off switches 36a and 36b, the apparent potential difference Vapp between electrode indenter A14 and electrode indenter B16 can be measured. Dividing this Vapp by Iind allows the apparent resistance Rapp between electrode indenter A14 and electrode indenter B16 to be calculated. This Rapp includes the potential difference due to the contact resistance Rcont_A between electrode indenter A14 and plate-shaped sample 12, and the potential difference due to the contact resistance Rcont_B between electrode indenter B16 and plate-shaped sample 12.

[0064] On the other hand, by connecting one end of the potentiometer 32 to the i-th probe A22 and the other end of the potentiometer 32 to the electrode indenter B16, and performing the measurement of Vprobe(i,x(i)) and approximating the measured value with a sigmoid curve using the procedure described above, it is possible to calculate the estimated electrical resistance Rest in the thickness direction of the plate-shaped sample 12. This Rest does not include Rcont_A. Therefore, Rcont_A can be calculated by subtracting Rest from Rapp. The structure of the contact resistance calculation device A is not particularly limited as long as it performs the above functions.

[0065] [1.9.4. Contact Resistance Calculation Device B] "Contact Resistance Calculation Device B" refers to a device that calculates the contact resistance Rcont_B between a plate-shaped sample 12 and an electrode indenter B16. More specifically, "Contact Resistance Calculation Device B" refers to a device that calculates the electrical resistance Rapp by dividing the apparent potential difference Vapp between electrode indenter A14 and electrode indenter B16 by Iind, calculates Rest which includes the contact resistance Rcont_A between the plate-shaped sample 12 and electrode indenter A14 based on x(i) and Vprobe(i,x(i)), and calculates Rcont_B by subtracting Rest from Rapp.

[0066] By connecting one end of the potentiometer 32 to the electrode indenter A14 and the other end of the potentiometer 32 to the i-th probe B24, and performing the measurement of Vprobe(i,x(i)) and approximating the measured value with a sigmoid curve using the procedure described above, the estimated electrical resistance Rest in the thickness direction of the plate-shaped sample 12 can be calculated. This Rest does not include Rcont_B. Therefore, Rcont_B can be calculated by subtracting Rest from Rapp. The structure of the contact resistance calculation device B is not particularly limited as long as it performs the above function.

[0067] [2. Method for Measuring Electrical Resistance] The method for measuring electrical resistance according to the present invention comprises the step of calculating the electrical resistance in the thickness direction of a plate-shaped sample and / or the resistivity in the thickness direction of a plate-shaped sample using an electrical resistance measuring device according to the present invention.

[0068] [2.1. Measurement Target] In the method according to the present invention, the measurement target is a plate-shaped sample. The thickness of the plate-shaped sample is not particularly limited. Using the method according to the present invention, the electrical resistance in the thickness direction can be estimated even for plate-shaped samples with a thickness of 5 mm or less, 3 mm or less, or 1 mm or less.

[0069] In the present invention, the material of the plate-shaped sample is not particularly limited. Examples of materials for the plate-shaped sample include: (a) a single material (especially a single material with anisotropic properties), (b) a composite material in which particles are dispersed in a matrix, and (c) a laminate of multiple layers with different properties.

[0070] For example, in the case of a composite material in which low-resistance fibrous particles are dispersed within a high-resistance matrix, the electrical resistance in the thickness direction is often different from the electrical resistance in the in-plane direction. This is also true for laminated materials in which high-resistance layers and low-resistance layers are stacked. In this case, conventional methods can measure the electrical resistance in the in-plane direction, but it is difficult to measure the electrical resistance in the thickness direction. Here, "high resistance" refers to its relative magnitude to low resistance, meaning a resistance low enough to require measurement using the four-terminal method. In contrast, using the method according to the present invention, the electrical resistance in the thickness direction can be accurately estimated even when the electrical resistance of a plate-shaped sample exhibits anisotropy.

[0071] [2.2. Flowchart] Figure 3 shows a flowchart of the method for measuring electrical resistance according to the present invention. First, in step 1 (hereinafter also referred to as "S1"), a plate-shaped sample 12 is sandwiched between electrode indenters A14 and B16. Next, a predetermined load is applied to the plate-shaped sample 12 using a pressurizing device 18. In this state, a current Iind is injected into the plate-shaped sample 12 using a current application device 42.

[0072] Next, in S2, the i-th probe A22 and / or the i-th probe B24 are brought into contact with the plate-shaped sample 12, and the potential difference V(i) between the upper and lower surfaces of the plate-shaped sample 12 is measured at one or more locations. See Figure 2(A). In this invention, since the change in V(i) is approximated by a sigmoid curve, the measurement can be performed at just one location. However, in order to improve the estimation accuracy, it is preferable to measure the potential difference at multiple locations. On the other hand, measuring V(i) over a wider range than necessary does not make a difference in effect and is not practical. Therefore, it is preferable to perform the measurement within the range where x(i) is greater than zero and less than or equal to rA.

[0073] Next, in S3, the relationship between the distance x(i) from the outer surface of electrode indenters A14 and B16 and the potential difference V(i) is measured. See Figure 2(A). More specifically, the measurement position x(i) of V(i) and the measured V(i) are associated, and these are stored in memory as the potential difference distribution Vprobe(i,x(i)). Next, in S4, the potential difference distribution Vprobe(i,x(i)) is fitted with a sigma function. See Figure 2(B). Then, using the sigma function obtained by fitting, the potential difference Vreal at the center of electrode indenters A14 and B16 is estimated. Furthermore, in S5, the resistance value Rest in the thickness direction is calculated from the estimated potential difference Vreal and the known current Iind. Alternatively, since the cross-sectional areas of electrode indenters A14 and B16, and the thickness of the plate-shaped sample are known, the resistivity in the thickness direction of the plate-shaped sample 12 can be calculated using these values.

[0074] [3. Function] [3.1. Conventional Electrical Resistance Measurement Methods] Common electrical resistance measuring devices include resistance meters and digital multimeters. Methods for measuring electrical resistance using these devices can be broadly classified into two types: the two-terminal method and the four-terminal method.

[0075] Of these, the two-terminal method is the simplest and most commonly used method. Figure 4(A) shows a circuit diagram of the two-terminal method. The dotted lines in the figure represent the internal circuitry of a digital multimeter or resistance meter. "HI" represents the high of the differential input, and "LO" represents the low of the differential input. "R" is the object under test, and each wire is connected to the object under test. Each wire has its own inherent resistance Rlead. For simplicity, the contact resistance generated at the point of contact between the object under test and the wire is also included in Rlead. Therefore, the circuit has Rlead1 and Rlead2.

[0076] The measuring device outputs a known current Itest and measures the voltage Vm between the HI input and the LO input. Applying Ohm's law to the measurement, the following equation (1) is obtained: R + Rlead1 + Rlead2 = Vm / Itest …(1) When R is sufficiently large compared to Rlead1 and Rlead2, equation (1) can be approximated as equation (2): R = Vm / Itest …(2)

[0077] However, when the electrical resistance of the object being measured is low, the resistance of the conductor and the contact resistance cannot be ignored, and equation (2) no longer holds true. To measure the electrical resistance of a low-resistance object, it is necessary to remove the voltage drop caused by the conductor and contact resistance and measure only the resistance component related to the object being measured. This process can be achieved by using the four-terminal method.

[0078] The four-terminal method uses four terminals to measure low electrical resistance. Specifically, the four terminals used for measurement are divided into two sets of lines. Current is passed through the object under test using one set of lines, and the potential difference is measured using the other set of lines. During measurement, the circuit is separated into one that supplies current to the object under test and another that measures the voltage drop across the object under test. In the voltage measurement circuit, the internal resistance of the voltmeter is high, so almost no current flows. Therefore, the effects of voltage drop due to wire resistance and contact resistance can be eliminated.

[0079] Figure 4(B) shows the circuit diagram for the four-terminal method. One pair of current lines and one pair of voltage sensing lines are arranged in parallel, and four wires are connected to R (the object under test). Similar to the two-terminal method, the current lines generate a voltage drop across R along the HI and LO wires. The second pair of wires is separated from the current lines and forms a direct voltage loop to measure the voltage drop across R. The second pair of voltage sensing wires are HI sense and LO sense.

[0080] Since the resistance of a voltmeter is generally very high (>10 MΩ), the resistance of the conductor and contact resistance have little effect on the voltage measurement. Therefore, Rlead1 to Rlead4 can be ignored and are independent of the current source Itest. Thus, the following equation (3) is obtained: VR ≈ Vm …(3) Here, VR is the voltage across the device under test, and the voltmeter measures the voltage as Vm. Since the current flowing through the device under test is Itest, the resistance R can be found by the following equation (4): R = Vm / Itest …(4)

[0081] [3.2. Problems with Conventional Methods] Figure 5(A) shows a schematic diagram of a method for measuring electrical resistance using the four-terminal method. As shown in Figure 5(A), the four-terminal method allows for the measurement of electrical resistance in the in-plane direction of a plate-shaped sample. Furthermore, if the plate-shaped sample is thick, the four-terminal method can also be used to measure the electrical resistance in the thickness direction of the plate-shaped sample. However, as the thickness of the plate-shaped sample decreases, it becomes difficult to provide voltage terminal pairs in the thickness direction of the plate-shaped sample. On the other hand, when measuring electrical resistance in the thickness direction, if voltage measurement terminals are formed on the input / output surfaces of the current, contact resistance occurs, affecting the voltage drop of the object being measured. Therefore, it is practically difficult to measure the electrical resistance in the thickness direction of thin plate-shaped samples using the four-terminal method.

[0082] Figure 5(B) shows a schematic diagram of the electrical resistance measurement method using the four-probe method. In the four-probe method, the resistivity of the object being measured is calculated by multiplying the measured sheet resistance by its thickness. Using this method, the electrical resistance in the thickness direction for any area can be obtained. The van der Poël method and commercially available electrode resistance measurement systems work similarly and provide electrical resistance in the thickness direction. However, these methods all have in common that a current is passed in the in-plane direction of the object being measured during measurement, which is equivalent to measuring the resistance in the in-plane direction of the object being measured. Therefore, if the object being measured is an isotropic material, there is no problem in considering the electrical resistance in the in-plane direction as the electrical resistance in the thickness direction. However, the resistivity of real materials is not always isotropic.

[0083] Non-isotropic materials include, for example, materials in which low-resistance fibrous particles are dispersed within a matrix with higher resistance. In this case, the connectivity of the low-resistance fibrous particles may differ between the in-plane direction and the thickness direction of the plate material. Furthermore, even in laminates of multiple types of materials with different resistivity, the electrical resistance may differ between the in-plane direction and the thickness direction. Moreover, even in the case of a single material, if the crystal structure has anisotropy, the electrical resistance may differ between the in-plane direction and the thickness direction. Therefore, conventional methods for measuring electrical resistance cannot accurately measure the electrical resistance in the thickness direction of a thin plate-like sample.

[0084] [3.3. Method for Measuring Electrical Resistance According to the Present Invention] In contrast, in the present invention, a plate-shaped sample is sandwiched between electrode indenters A and B, and a current is injected between electrode indenters A and B. Since the current injected from one side of the plate-shaped sample flows toward the other side of the plate-shaped sample, the current is also conducted into the interior of the plate-shaped sample. If the surface of the plate-shaped sample is larger than the current injection surface of electrode indenters A and B, the current will spread throughout the entire plate-shaped sample. That is, an electric field is generated outside the outer surfaces of electrode indenters A and B, so a potential difference is generated outside electrode indenters A and B as well.

[0085] In this invention, the voltage distribution around electrode indenters A and B is measured by utilizing the electric field spreading around them, and the voltage drop between electrode indenters A and B is estimated using the voltage distribution. It is possible to place probes outside electrode indenters A and B, and the voltage between the probes at that point can ignore contact resistance. Therefore, by measuring the potential difference at multiple locations outside electrode indenters A and B, the potential difference between electrode indenter A and electrode indenter B can be estimated. Sigma-type functions such as the sigmoid function or hyperbolic tangent function can be used to estimate the potential difference. Alternatively, the Laplace equation or Poisson equation may be used for estimation.

[0086] [1. Test Method] The effectiveness of the present invention was verified using an isotropic graphite plate as a sample. Specifically, it was verified whether the same results could be obtained using an existing measurement method and the measurement method of the present invention. Since the sample used was an isotropic material, there should be no difference in the results due to differences in measurement methods. The resistivity of the sample was measured in advance using the four-probe method. As a result, the resistivity was 1.3 mΩcm. The resistivity obtained from the electrical resistance value obtained by the method of the present invention was verified using computer-aided engineering (CAE) to see if it was the same as the result of the four-probe method. Femtet®, a registered trademark of Murata Software, Inc., was used for the calculations.

[0087] Figure 6 shows the bird's-eye view and front view of the CAE model used in the simulation. The dimensions of the plate-shaped sample were: width: 20 mm, depth: 10 mm, thickness: 1 mm. The diameter of the electrode indenter placed in the center of the plate-shaped sample was 5 mm. The resistivity of the plate-shaped sample was set to 1.3 mΩcm based on measured results. The resistivity of the electrode indenter was 10 -4 The resistance was set to mΩcm. A current of 0.1A was injected from the upper surface of electrode indenter A, which was placed above the plate-shaped sample, and the lower surface of electrode indenter B, which was placed below the plate-shaped sample, was used as ground.

[0088] In reality, contact resistance occurs at the contact surface between the electrode indenter and the plate-shaped sample. Therefore, a resistive component was introduced at the interface between the plate-shaped sample and the electrode indenter, and this was defined as the contact resistance. The actual contact resistance depends on the applied pressure, but for simplicity in this calculation, a fixed value of 0.1Ω was given for both the top and bottom. When current flows, a voltage drop occurs due to the contact resistance. However, since the plate-shaped sample and the resistive component are connected in series with respect to the input current, the current flowing in from the current source is conducted directly through the plate-shaped sample.

[0089] When the x-coordinate of the outer surface of the electrode indenter is set to x=0, the potential difference between probes outside the electrode indenter (x>0) can be measured. Therefore, the potential difference in the thickness direction of a plate-like sample was calculated by CAE at multiple positions outside the electrode indenter along a radial line from the center of the electrode indenter. The calculated potential difference obtained as a simulation was treated as a measured value, and this value was fitted with a function. Using the obtained function, the potential difference in the central part of the electrode indenter (x=-2.5), which cannot be directly measured, was estimated. The sigmoid function represented by the following equation (6) was used as the function: f(x)=1 / [1+exp(-ax)] …(6) where a>0.

[0090] The sigmoid function is a function that converts any input value into a numerical value in the range of 0.0 to 1.0 and outputs it. The sigmoid function has the coordinate (0, 0.5) as its base point (inflection point), is point-symmetric, and its graph is a sigma-shaped curve. Fitting was performed using the function (logistic function) represented by the following equation (7), where the potential difference of the plate-shaped sample is the output value A. The output at x = -2.5 represents the potential difference in the thickness direction of the plate-shaped sample. f(x) = A / [1 + exp(-ax)] ... (7) where a > 0.

[0091] [2. Results] Figure 7 shows the relationship between the position from the outer surface of the electrode indenter and the voltage. The potential difference was almost zero at positions far from the outer surface of the electrode indenter, but increased as the distance to the center of the electrode indenter increased. The resistivity of the plate-shaped sample was calculated using the estimated potential difference A at the center of the electrode indenter, the input current value (0.1 A), the plate thickness of the plate-shaped sample (1 mm), and the electrode area of ​​the electrode indenter (diameter: 5 mm). The results are shown in Table 1. Measured values ​​are also shown in Table 1. The resistivity calculated using the method according to the present invention was in good agreement with the measured values.

[0092]

[0093] As described above, it was confirmed that the potential difference in the thickness direction of a thin plate-like sample can be estimated by measuring the potential difference distribution outside the electrode indenter. In reality, it has also been confirmed that a potential difference is generated in the thickness direction of a plate-like sample outside the electrode indenter. Furthermore, although the above example showed an example in which an isotropic graphite plate with a thickness of 1 mm was clamped with an electrode indenter with a diameter of 5 mm, the material and size of the plate-like sample and electrode indenter to which the present invention applies are not limited to the above example.

[0094] Although embodiments of the present invention have been described in detail above, the present invention is not limited in any way to the above embodiments, and various modifications are possible without departing from the spirit of the present invention.

[0095] The electrical resistance measuring device according to the present invention can be used as a device for measuring the electrical resistance and / or resistivity in the thickness direction of a thin plate-shaped sample.

Claims

1. The apparatus comprises electrode indenters A and B for clamping a plate-shaped sample in the thickness direction; a pressurizing device for pressing electrode indenters A and / or electrode indenter B onto the plate-shaped sample; an i-th probe A (1 ≤ i ≤ n, n ≥ 1) positioned adjacent to electrode indenter A; a moving device for moving the i-th probe A in the thickness direction of the plate-shaped sample, or in the thickness direction and in the in-plane direction of the plate-shaped sample; a potential difference measuring device for measuring the potential difference Vprobe(i,x(i)) between the i-th probe A and electrode indenter B at an arbitrary position where the distance from the outer surface of electrode indenter A is x(i); a current applying device for applying a DC current or AC current to the plate-shaped sample via electrode indenters A and electrode indenter B; an ammeter for measuring the current value Iind flowing between electrode indenter A and electrode indenter B; and a calculation device for estimating the electrical resistance and / or resistivity in the thickness direction of the plate-shaped sample, wherein the calculation device An electrical resistance measuring device comprising: a Vreal estimation device that estimates the true potential difference Vreal generated in the thickness direction of the plate-shaped sample based on x(i) and Vprobe(i,x(i)); and a resistance calculation device that calculates an estimated value Rest of the electrical resistance in the thickness direction of the plate-shaped sample and / or an estimated value ρest of the resistivity in the thickness direction of the plate-shaped sample based on Vreal and Iind.

2. The electrical resistance measuring device according to claim 1, further comprising a arithmetic device, the arithmetic device, the arithmetic device, the arithmetic device, the arithmetic device, the arithmetic device, the arithmetic device, the arithmetic device, the arithmetic device, further comprising a contact resistance calculating device A for calculating the contact resistance Rcont_A between the plate-shaped sample and the electrode indenter A, the arithmetic device 3. The electrical resistance measuring device according to claim 1, further comprising an i-th probe B (1 ≤ i ≤ n, n ≥ 1) positioned adjacent to the electrode indenter B and facing the i-th probe A, wherein the moving device further comprises a device for moving the i-th probe A and the i-th probe B in the thickness direction, or in the thickness direction and the in-plane direction, while maintaining the state in which the i-th probe A and the i-th probe B are facing each other, and the potential difference measuring device comprises a device for measuring at least one selected from the group consisting of (a) the potential difference between the i-th probe A and the electrode indenter B, (b) the potential difference between the i-th probe B and the electrode indenter A, and (c) the potential difference between the i-th probe A and the i-th probe B, as Vprobe(i,x(i)).

4. The electrical resistance measuring device according to claim 3, further comprising a arithmetic device, the arithmetic device, which further comprises a contact resistance calculation device B for calculating the contact resistance Rcont_B between the plate-shaped sample and the electrode indenter B, wherein the contact resistance calculation device B comprises a device for calculating the apparent electrical resistance Rapp by dividing the apparent potential difference Vapp between the electrode indenter A and the electrode indenter B by Iind, calculating Rest which includes the contact resistance Rcont_A between the plate-shaped sample and the electrode indenter A based on x(i) and Vprobe(i,x(i)), and calculating Rcont_B by subtracting Rest from Rapp.

5. An electrical resistance measuring device according to claim 1, comprising a plurality of i-probes A, wherein the plurality of i-probes A are spaced apart on a straight line passing through the centroid of the electrode indenter A, and x(i) is greater than zero and less than or equal to rA. However, "rA" means the distance between the centroid of the electrode indenter A and the intersection point of the straight line passing through the outer circumference of the electrode indenter A and the centroid.

6. The electrical resistance measuring apparatus according to claim 1, comprising a device capable of moving the i probe A in the in-plane direction along a straight line passing through the center of gravity of the electrode indenter A, and within the range where x(i) is greater than zero and less than or equal to rA. However, "rA" means the distance between the center of gravity of the electrode indenter A and the intersection point of the straight line passing through the outer circumference of the electrode indenter A and the center of gravity.

7. The electrical resistance measuring device according to claim 1, wherein the Vreal estimation device is equipped with a device that estimates Vreal using at least one selected from the group consisting of the logistic function, sigmoid function, hyperbolic tangent function (tanh), inverse probit function, Gompertz function, arctangent function (arctan), and Gutermann function.

8. The electrical resistance measuring device according to claim 1, further comprising a support device for supporting the plate-shaped sample.

9. A method for measuring electrical resistance, comprising the step of calculating the electrical resistance in the thickness direction of a plate-shaped sample and / or the resistivity in the thickness direction of the plate-shaped sample using an electrical resistance measuring device according to any one of claims 1 to 8.

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