Testing method for sheet resistance and contact resistance of connecting point of sheet material

Abstract

A testing method for the sheet resistance and contact resistance of connecting point of a sheet material, comprising: mounting at least four small electrodes on the surface of the sheet material; measuring the resistance between the electrodes; and calculating the sheet resistance and electrode contact resistance of the sheet material on the basis of a theoretical model from the resistance measured between the electrodes and the distances between the electrodes. As a main feature, the testing method is a convenient nondestructive testing method for the sheet resistance and electrode contact resistance of the sheet material, and has no strict requirement on the distribution of electrodes.

Claims

1. A testing method for a sheet resistance and an electrode contact resistance of a sheet material, comprising: mounting at least four electrodes, including a first electrode and a second electrode, on a surface of the sheet material; measuring resistances between the at least four electrodes; and calculating the sheet resistance and the electrode contact resistance of the sheet material on the basis of the following equation from the resistances measured between the at least four electrodes and distances between the at least four electrodes, $R_{\mathrm{ABm}}=\frac{R_{.}}{}\ln \left(L_{\mathrm{AB}}\right)+\left[\frac{R_{.}}{2}\ln \left(\frac{1}{r_A}\right)+R_{\mathrm{IA}}\right]+\left[\frac{R_{.}}{2}\ln \left(\frac{1}{r_B}\right)+R_{\mathrm{IB}}\right]=\frac{R_{.}}{}\ln \left(L_{\mathrm{AB}}\right)+R_{\mathrm{CA}}+R_{\mathrm{CB}}$ wherein, R.sub.ABm is a resistance between the first electrode and the second electrode, R.sub. is the sheet resistance of the sheet material, r.sub.A and r.sub.B are radii of the first electrode and the second electrode respectively, L.sub.AB is a distance between the first electrode and the second electrode, R.sub.1A is an interface contact resistance between the first electrode and the sheet material, R.sub.1B is an interface contact resistance between the second electrode and the sheet material, R.sub.CA is a total contact resistance between the first electrode and the sheet material, and R.sub.CB is a total contact resistance between the second electrode and the sheet material.

2. The testing method according to claim 1, wherein the sheet material is a conductive material, including metal material, alloy material, semiconductor material, coating, or film material.

3. The testing method according to claim 1, wherein the sheet material includes monolayer material or multilayer material, and the sheet material is stand-alone or supported by a non-conductive substrate.

4. The testing method according to claim 1, wherein the first electrode and the second electrode are connection means between the sheet material and a circuit, and the first electrode and the second electrode are connected to the sheet material by pressure-contact, gluing, soldering, or electric welding of the surface of the sheet material.

5. The testing method according to claim 1, wherein a thickness of the sheet material is uniform; and wherein the thickness of the sheet material is much less than diameters of the first electrode and the second electrode.

6. The testing method according to claim 1, wherein the distance between the first electrode and the second electrode is much greater than diameters of the first electrode and the second electrode.

7. The testing method according to claim 1, wherein planar dimensions of the sheet material are much greater than the distance between the first electrode and the second electrode; and wherein the planar dimensions are a length, a width, or a diameter of the sheet material.

8. The testing method according to claim 1, wherein the distance between the first electrode or the second electrode and an edge of the sheet material is much greater than the distance between the first electrode and the second electrode.

9. The testing method according to claim 1, wherein the sheet resistance and the electrode contact resistance of the sheet material are calculated from the resistances measured between the at least four electrodes and the distances between the at least four electrodes using a minimum-variance method according to a theoretical model.

10. The testing method according to claim 1, wherein the sheet resistance of the sheet material is calculated from the resistances measured between the at least four electrodes and the distances between the at least four electrodes using a least-squares linear fitting method according to a theoretical model.

11. The testing method according to claim 1, wherein the resistance between the first electrode and the second electrode is calculated using a mirror image method for a rectangular sheet material, or using a conformal mapping method for a circular sheet material, when a planar size of the sheet material is small.

12. The testing method according to claim 5, wherein the thickness of the sheet material has an unevenness of less than 1%.

13. The testing method according to claim 5, wherein the thickness of the sheet material is less than 1/10 of a smallest diameter of the at least four electrodes.

14. The testing method according to claim 6, wherein a minimum distance between the at least four electrodes is greater than 5 times a maximum diameter of the at least four electrodes.

15. The testing method according to claim 7, wherein the planar dimensions of the sheet material are greater than 10 times a maximum distance between the at least four electrodes.

16. The testing method according to claim 8, wherein the distance between the first electrode or the second electrode and the edge of the sheet material is greater than 5 times a maximum distance between the electrodes.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic view of a method for measuring the sheet resistance of a sheet material with two circular electrodes.

(2) FIG. 2 is a schematic view of a method for measuring the sheet resistance and the electrode contact resistance of a sheet material with four small electrodes.

(3) FIG. 3 is an illustrative diagram of calculating the sheet resistance of a sheet material by a least-squares linear fitting method. L.sub.a and L.sub.b are the distances between the electrodes of two electrode pairs, respectively, and R.sub.at+bt is the sum of the measured resistances between the electrodes of the two electrode pairs. The subscripts a and b represent different pairs of electrodes. The three simulated measurement points (asterisk-shaped) are obtained from the following simulated measurement conditions: four small electrodes are mounted on the surface of the sheet material; and the electrodes are located at the four corners of a rectangle with a length of 3 and a width of 2; wherein the distances between the electrodes are respectively L.sub.12=3, L.sub.13={square root over (13)}, L.sub.14=2, L.sub.23=2, L.sub.24={square root over (13)}, and L.sub.34=3.

(4) The simulated contact resistances of the electrode surfaces are R.sub.c1=1, R.sub.c2=0.5, R.sub.c3=0.7, and R.sub.c4=0.3. Any unit can be used in the distance measurement, and the same measurement unit is required to be used in each distance measurement. The unit of the calculated sheet resistance is same as the measurement unit of the resistance measured between the electrodes. FIGS. 4-6 contain the related equations used in the present application.

(5) Reference numbers:

(6) 1Sheet material; 2Electrode A; 3Electrode B; 4Electrode leads; 12First electrode; 13Second electrode; 14Third electrode; 15Fourth electrode; 16Electrode leads.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(7) The present invention will be further described below with reference to the accompanying drawings and the following embodiments. It should be understood that the accompanying drawings and the following embodiments are only used for describing the present invention rather than limiting the present invention.

(8) FIG. 1 is a schematic view of a method for measuring the sheet resistance of a sheet material with two circular electrodes. Wherein the radii of electrode A (i.e., the electrode 2 on the left in FIG. 1) and electrode B (i.e., the electrode 3 on the right in FIG. 1) are r.sub.A and r.sub.B, respectively, and the distance between the centers of the two electrodes is L.sub.AB. FIG. 2 is a schematic view of a method for measuring the sheet resistance and the electrode contact resistance of a sheet material with four small electrodes. FIG. 3 demonstrates the sheet resistance calculation of a sheet material by a least-squares linear fitting method. L.sub.a and L.sub.b are the distances between the electrodes of two electrode pairs, respectively, and R.sub.at+bt is the sum of the measured resistances between the electrodes of the two electrode pairs. The subscripts a and b represent different pairs of electrodes.

(9) In view of the issues in the prior art, the present application provides a testing method for the sheet resistance and the contact resistance of a connecting point of a sheet material: mounting at least four electrodes on the surface of the sheet material; measuring the resistances between the electrodes; and calculating the sheet resistance and the electrode contact resistance of the sheet material, on the basis of a theoretical model, from the resistances measured between the electrodes and the distances between the electrodes.

(10) The testing method for sheet resistance and electrode contact resistance of sheet material in the present application is a non-destructive testing method in which the electrodes for measurement can be dispersedly distributed, and the influence from other electrodes on the potential field generated by the electrodes for measurement can be reduced, compared with the standard collinear four-probe array method currently used.

(11) In the present application, the electrode refers to the connection means between the sheet material and a circuit, including pressure-contact, gluing, soldering, electric welding, and other connection modes between the sheet material and the electric conductor.

(12) In the present application, it is required that the thickness of the sheet material be much smaller than the diameter of the electrodes; therefore, in the present application, it is considered that the potential and current in the sheet material generated by the electrodes are uniform in the depth direction, and thus the theoretical analysis thereof can be treated mathematically as a two-dimensional problem. The planar dimensions of the sheet material are much greater than the distances between the electrodes, and the distance between each electrode and the edge of the material is much greater than the distances between the electrodes. Therefore, the potential and current at the edge of the material is very small and the edge reflection effect can be neglected. It is required in the present application that the conductivity of the electrode material be much greater than the conductivity of the sheet material, and thus the potential within the electrodes can be considered to be uniform (see FIG. 1).

(13) The study found that the resistance R.sub.AB in the sheet material between the two electrodes can be calculated according to equation (1) in FIG. 4.

(14) Herein, r.sub.A and r.sub.B are the radii of electrode A and electrode B respectively, L.sub.AB is the distance between the centers of the two electrodes, and R.sub.=/t is the sheet resistance of the sheet material, wherein and t are the resistivity and the thickness of the sheet material, respectively (see FIG. 1). =3.1416 is the constant of pi.

(15) In the case of small electrodes, r.sub.AL.sub.AB, and r.sub.BL.sub.AB, thus equation (1) can be approximately expressed as equation (2) in FIG. 4.

(16) Equation (2) shows that in the case of small electrodes, the resistance in the sheet material between the two electrodes consists of three parts, the first part being related to the sheet resistance (R.sub.) of the sheet material and the distance (L.sub.AB) between the electrodes, and other parts being related to the sheet resistance of the sheet material and the radii (r.sub.A and r.sub.B) of the electrodes.

(17) In many cases, the position of the small electrode and its effective contact area with the sheet material are difficult to be precisely controlled during the preparation of the sample to be tested. In addition, the interface resistance at the contact position between the small electrode and the sheet material cannot be neglected, thus equation (2) cannot apply directly to the measurement of the sheet resistance of the sheet material. The resistance between the two electrodes in the actual measurement can be expressed as equation (3) in FIG. 4.

(18) Herein, R.sub.IA and R.sub.IB are respectively the interface contact resistances between the two electrodes and the sheet material, and R.sub.CA and R.sub.CB are the total contact resistances of the two electrodes and the sheet material, respectively.

(19) For a particular measurement system, equation (3) shows that the resistance between the electrodes consists of three parts: the first part is related to the sheet resistance of the sheet material and the distance between the electrodes, and the other two parts are related to the sheet resistance of the sheet material, the radii of the electrodes, and the contact resistance of the electrode/sheet material interface.

(20) In the present application, four or more electrodes are mounted on the surface of the sheet material, from which a number of electrode pair combinations can be made. For example, four electrodes may form up to six different pairs of electrodes, and five electrodes can make up to ten different pairs of electrodes. In the measurement system shown in FIG. 2, six independent resistance measurements can be made between the four electrodes. The resistance between the electrode pairs can be described as equations (4)-(9) in FIG. 4.

(21) Herein, subscripts 1, 2, 3, and 4 represent different electrodes, respectively. In the experiment, the distance between the electrodes can be measured, so there are five unknowns in the above equations, i.e., R.sub.C1, R.sub.C2, R.sub.C3, R.sub.C4, and R.sub..

(22) By comparing the resistances measured between the electrodes and the theoretical model, the above five unknowns can be calculated using the least-squares method of minimum variance. For the measurement system shown in FIG. 2, the variance between the experimental measurements and the theoretical model can be described as equation (10) in FIG. 4.

(23) Herein, R.sub.12t, R.sub.13t, R.sub.14t, R.sub.23t, R.sub.24t, and R.sub.34t are the six resistances measured between the electrodes, respectively, and subscripts 1, 2, 3, and 4 represent the different electrodes, respectively.

(24) The partial derivatives of x.sup.2 with respect to R.sub.C1, R.sub.C2, R.sub.C3, R.sub.C4, and R.sub., are found and set to zero, to give equations (11)-(15) in FIG. 5.

(25) From the above equations, R.sub.C1, R.sub.C2, R.sub.C3, R.sub.C4, and R.sub., can be calculated separately, thus the electrode contact resistance and the sheet resistance of the sheet material can be determined. If the radius of the contact area between the electrode and the sheet material is known, the interface contact resistance between the electrode and the sheet material can be further determined by equation (3).

(26) The sheet resistance of the sheet material can also be determined by a simpler and faster linear fitting method. Equations (4)-(9) are rearranged to obtain equations (16)-(18) in FIG. 5.

(27) The six resistances R.sub.12t, R.sub.13t, R.sub.14t, R.sub.23t, R.sub.24t, and R.sub.34t measured between the electrodes are compared with the theoretical model (equations (16)-(18)), then the sheet resistance of the sheet material R.sub., and the sum of the electrode contact resistances R.sub.C1+R.sub.C2+R.sub.C3+R.sub.C4 can be determined by selecting any two equations to compare with the resistances measured between the electrodes, and thus the measurement error resulting from the electrode contact resistance can be eliminated. For example, see equations (19) and (20) in FIG. 6.

(28) In addition, three points (ln(L.sub.12L.sub.34), R.sub.12t+34t), ln(L.sub.13L.sub.24), R.sub.13t+24t), and (ln(L.sub.14L.sub.23), R.sub.14+23t) are plotted in Cartesian coordinates and linearly fitted to a straight line as shown in FIG. 3. According to equations (16)-(18), the slope of this line is R.sub./ and the intercept of the line in the Y-axis is R.sub.C1+R.sub.C2+R.sub.C3+R.sub.C4 . Therefore, the sheet resistance of the sheet material can be determined from the slope of the fitted straight line, eliminating the measurement error caused by the electrode contact resistance.

(29) The method for measuring the sheet resistance and the electrode contact resistance of a sheet material with multiple electrodes as described in this application is also applicable to the case of non-circular contact points since the newly invented method utilizes the far-field approximation of the electric field generated by the small electrode. In the resistance measurement of the electrode pair, one electrode is in the far field of the potential field generated by the other electrode, and the potential field generated by a small, non-circular electrode may be approximately equivalent to the potential field generated by a small, circular electrode.

(30) The method for measuring the sheet resistance and the electrode contact resistance of a sheet material with multiple electrodes as described in this application is also applicable in the case of more than four electrodes. The measuring principle and procedure are similar to those of the four electrodes described above. In the measuring system with n electrodes, up to n(n1)/2 different electrode pairs can be made so that n(n1)/2 independent resistance measurements between electrodes can be performed.

(31) The method for measuring the sheet resistance and the electrode contact resistance of a sheet material with multiple electrodes as described in this application is, in some cases, applicable to a sheet material with a small planar size, in which the resistance between the electrodes can be calculated by using a mirror image method (for example, for rectangular sheet materials), a conformal mapping method (such as for circular sheet materials), or other mathematical transformation methods.

(32) The invention can be embodied in many forms without departing from the essential nature of the application, and the embodiments of the application are intended to be illustrative and not restrictive. The scope of the invention is defined by the claims rather than the specifications, and all modifications which fall within the scope of the claims, or equivalents of the scope of the invention, are to be included in the claims.