CN116930798A - Method and system for measuring sheet resistance of contact type battery piece - Google Patents
Method and system for measuring sheet resistance of contact type battery piece Download PDFInfo
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Abstract
The invention discloses a method and a system for measuring sheet resistance of a contact type battery piece, which belong to the technical field of sheet resistance measurement, and the method comprises the following steps: selecting four contact points A, B, C, D at the edge of the to-be-detected battery piece, wherein the included angle between the connecting line between the first contact point A and the third contact point C and the connecting line between the second contact point B and the fourth contact point D is between 85 degrees and 95 degrees; probes are connected to the four contact points A, B, C, D, respectively; passing a current between the adjacent first contact point A and the second contact point BI AB Measuring the distance between the third contact point C and the fourth contact point DVoltage value of (2)V CD Calculate a first resistanceR 1 The method comprises the steps of carrying out a first treatment on the surface of the S104: passing a current between the adjacent first contact point A and the fourth contact point DI AD Measuring the voltage value between the second contact point B and the third contact point CV BC Calculate the second resistanceR 2 The method comprises the steps of carrying out a first treatment on the surface of the According to the first resistanceR 1 And the second resistorR 2 And calculating the sheet resistance of the battery piece to be measured.
Description
Technical Field
The invention belongs to the technical field of sheet resistance measurement, and particularly relates to a method and a system for measuring sheet resistance of a contact type battery piece.
Background
The rapid development of science and technology has prompted mass production of integrated circuits, and has also led to a continual reduction in chip size. The battery piece is a substrate material of a chip in the integrated circuit, and the battery piece is required to have good micro-area characteristics while the diameter of the battery piece is required to be continuously reduced, so that the battery piece has very important significance for measuring the micro-area resistance of the battery piece in order to meet the performance requirement of the integrated circuit.
The most common test method for the resistance of the battery piece is a four-probe method, the basic principle of the four-probe method is mature, the operation mode is simple, and compared with other resistance measurement modes, the method has unique advantages.
However, in the conventional four-probe method, probes are required to be positioned on the same straight line surface, and the pitches between the probes are required to be equal, and as the diameters of the battery pieces are continuously reduced, it is difficult to accurately set four probes at equal pitches on the same straight line surface, thereby causing a decrease in measurement efficiency. Meanwhile, the conventional four-probe method is also susceptible to the effects of edges and thickness, and the probe is easily shifted in position when being in contact with the battery plate, thereby causing the reduction of measurement accuracy.
Disclosure of Invention
In order to solve the technical problems that the traditional four-probe method is difficult to accurately arrange four probes with equal intervals on the same straight line surface along with the continuous reduction of the diameter of a battery piece, so that the measurement efficiency is reduced, the influence of uneven current distribution caused by edge and thickness effects is easy to occur, the position of the probe is easy to deviate when the probe is contacted with the battery piece, and the measurement precision is reduced.
First aspect
The invention provides a sheet resistance measuring method of a contact type battery piece, which comprises the following steps:
s101: selecting four contact points A, B, C, D at the edge of the to-be-detected battery piece, wherein the included angle between the connecting line between the first contact point A and the third contact point C and the connecting line between the second contact point B and the fourth contact point D is between 85 degrees and 95 degrees;
s102: probes are connected to the four contact points A, B, C, D, respectively;
s103: passing a current between the adjacent first contact point A and the second contact point BI AB Measuring the voltage value between the third contact point C and the fourth contact point DV CD Calculate a first resistanceR 1 ：
；
S104: passing a current between the adjacent first contact point A and the fourth contact point DI AD Measuring the voltage value between the second contact point B and the third contact point CV BC Calculate the second resistanceR 2 ：
；
S105: according to the first resistanceR 1 And the second resistorR 2 Calculating the sheet resistance of the battery piece to be measured:
wherein ,R s represents the sheet resistance of the battery piece to be tested,representing the correction factor.
Second aspect
The invention provides a contact type battery sheet resistance measuring system which is used for executing a contact type battery sheet resistance measuring method in a first aspect.
Compared with the prior art, the invention has at least the following beneficial technical effects:
(1) In the invention, the four-probe method is improved, four probes are not required to be arranged on the same straight line surface at equal intervals, the position requirement of the four probes is changed into that the connecting line between two probes is basically perpendicular to the connecting line between the other two probes, even if a small error exists in the position during real arrangement, the measurement is not affected by the included angle between 85 degrees and 95 degrees, and when the diameter of a battery piece is smaller, the arrangement difficulty of the probes is reduced, and the sheet resistance measurement efficiency is improved.
(2) According to the invention, a correction coefficient is introduced when the sheet resistance is calculated, so that the influence of uneven current distribution caused by edge and thickness effects is reduced, the influence that the position of the probe is easily deviated when the probe is contacted with a battery piece is reduced, and the sheet resistance measurement accuracy is improved.
Drawings
The above features, technical features, advantages and implementation of the present invention will be further described in the following description of preferred embodiments with reference to the accompanying drawings in a clear and easily understood manner.
Fig. 1 is a schematic flow chart of a sheet resistance measurement method for a contact battery sheet.
Fig. 2 is a schematic diagram of a probe arrangement provided by the present invention.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will explain the specific embodiments of the present invention with reference to the accompanying drawings. It is evident that the drawings in the following description are only examples of the invention, from which other drawings and other embodiments can be obtained by a person skilled in the art without inventive effort.
For simplicity of the drawing, only the parts relevant to the invention are schematically shown in each drawing, and they do not represent the actual structure thereof as a product. Additionally, in order to simplify the drawing for ease of understanding, components having the same structure or function in some of the drawings are shown schematically with only one of them, or only one of them is labeled. Herein, "a" means not only "only this one" but also "more than one" case.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
In this context, it should be noted that the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected, unless otherwise explicitly stated and defined. Either mechanically or electrically. Can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In addition, in the description of the present invention, the terms "first," "second," and the like are used merely to distinguish between descriptions and are not to be construed as indicating or implying relative importance.
Example 1
In one embodiment, referring to fig. 1 of the specification, a schematic flow chart of a sheet resistance measurement method of a contact battery sheet provided by the invention is shown.
The invention provides a sheet resistance measuring method of a contact type battery piece, which comprises the following steps:
s101: four contact points A, B, C, D are selected at the edges of the battery piece to be tested.
Referring to fig. 2 of the drawings, there is shown a schematic diagram of a probe arrangement according to the present invention.
Wherein the included angle between the connecting line between the first contact point A and the third contact point C and the connecting line between the second contact point B and the fourth contact point D is between 85 DEG and 95 deg.
It should be noted that, the included angle between the connection line between the first contact point a and the third contact point C and the connection line between the second contact point B and the fourth contact point D is between 85 ° and 95 °, specifically, the connection line between the first contact point a and the third contact point C and the connection line between the second contact point B and the fourth contact point D remain as vertical as possible.
This is because a magnetic field is generated around when a current flows through the battery cells. If the current lines and the measurement lines are oriented in similar directions, the magnetic field of the current may interfere with the measurement of the voltage of the measurement lines, thereby affecting measurement accuracy, while maintaining the lines as perpendicular as possible reduces the likelihood of such interference.
Further, if the angle between the lines is not vertical, the resistance path will change with the change in angle, which may lead to errors in the resistance measurement, and maintaining the vertical line between the contact points as much as possible minimizes this change, improving the stability of the measurement.
Compared with the traditional four-probe method, the sheet resistance measurement mode provided by the invention does not need to arrange four probes on the same straight line surface at equal intervals, the position requirement of the four probes is changed into that the connecting line between two probes is basically perpendicular to the connecting line between the other two probes, even if a small error exists in the position during real arrangement, the measurement is not influenced by the included angle between 85 degrees and 95 degrees, and when the diameter of a battery piece is smaller, the arrangement difficulty of the probes is reduced, and the sheet resistance measurement efficiency is improved.
S102: probes are connected to the four contact points A, B, C, D, respectively.
S103: passing a current between adjacent first and second contact points A and BI AB Measuring the voltage value between the third contact point C and the fourth contact point DV CD Calculate a first resistanceR 1 ：
。
S104: passing a current between adjacent first and fourth contact points A and DI AD Measuring the voltage value between the second contact point B and the third contact point CV BC Calculate the second resistanceR 2 ：
。
It should be noted that by measuring the voltage and current between two adjacent sets of contacts separately, it is ensured that the current path and voltage measurement line are fixed during each set of measurements and do not change with the current and voltage changes during the overall measurement. Such a stable resistive path helps to improve the stability and repeatability of the measurement.
S105: according to the first resistanceR 1 And a second resistorR 2 Calculating the sheet resistance of the battery piece to be measured:
wherein ,R s the sheet resistance of the battery piece to be tested is represented,representing the correction factor.
In the present invention, if the current and voltage of the entire battery cell are directly measured, there may be a large variation in the distribution of the current and voltage due to factors such as the size and material uniformity of the battery cell. The first resistor and the second resistor are calculated by measuring local current and voltage, and then the sheet resistance is calculated according to the first resistor and the second resistor, so that the changes can be limited in a small range, and the error of a measurement result is reduced.
Furthermore, a correction coefficient is introduced when the sheet resistance is calculated, so that the influence of uneven current distribution caused by edge and thickness effects is reduced, the influence that the position of the probe is easily deviated when the probe is contacted with a battery piece is reduced, and the sheet resistance measurement accuracy is improved.
In one possible embodiment, the coefficients are modified in order to reduce the effects of edge and thickness effects induced current maldistributionThe calculation mode of (a) is as follows:
wherein ,tthe integral variable is represented by a value of the integral variable,rthe range of the values is as follows。
By mathematical modeling of current distribution non-uniformity and over integration rangeAnd (5) calculating a correction coefficient. The correction factor can be varied according to the ratio of the different resistivities>And sample geometry, the resistivity of the sample can be estimated more accurately by applying a correction factor to the resistance measurements.
In the invention, the introduction of the correction coefficient can correct errors caused by non-uniformity of current distribution, especially under the condition of higher resistance or complex material structure. By correction, the difference between the measurement result and the actual value can be reduced, thereby improving the accuracy of measurement.
Compared with the prior art, the invention has at least the following beneficial technical effects:
(1) In the invention, the four-probe method is improved, four probes are not required to be arranged on the same straight line surface at equal intervals, the position requirement of the four probes is changed into that the connecting line between two probes is basically perpendicular to the connecting line between the other two probes, even if a small error exists in the position during real arrangement, the measurement is not affected by the included angle between 85 degrees and 95 degrees, and when the diameter of a battery piece is smaller, the arrangement difficulty of the probes is reduced, and the sheet resistance measurement efficiency is improved.
(2) According to the invention, a correction coefficient is introduced when the sheet resistance is calculated, so that the influence of uneven current distribution caused by edge and thickness effects is reduced, the influence that the position of the probe is easily deviated when the probe is contacted with a battery piece is reduced, and the sheet resistance measurement accuracy is improved.
Further, in the contact measurement method, since the probe needs to be in contact with the battery piece to be measured, contact resistance may be generated during contact, and sheet resistance measurement errors near the probe may be caused. Furthermore, the current and voltage distribution in the boundary region may be different from that in the internal region due to the influence of boundary effects, which may lead to measurement errors. Therefore, the edge area of the battery piece to be measured, on which the probe is placed, is only corrected by the correction coefficient, so that the requirement of measurement accuracy is difficult to meet, and further correction is needed.
In one possible embodiment, the method for measuring sheet resistance of a contact battery further includes:
s106: and correcting the sheet resistance of the edge area of the battery piece to be tested by a boundary element method.
The boundary element method (Boundary Element Method, BEM) is a numerical analysis method for solving the numerical solution of the partial differential equation problem.
It should be noted that, the finite element method is also a calculation method for solving the voltage and resistance distribution, but the boundary element method adopted by the present invention has significant advantages compared with the finite element method, which will be described in detail later.
In the invention, the boundary and interface conditions of the material can be effectively modeled by the boundary element method. In sheet resistance measurements, the current and voltage distribution of the boundary region may be affected by geometry and material contact. The boundary element method can accurately evaluate the influence of contact resistance and boundary effect, and accurately measure the voltage and current distribution of the edge area, thereby providing accurate current distribution information. And thus accurately corrects for boundary effects.
In one possible implementation, S106 specifically includes:
s1061: and calculating the voltage distribution of the edge area of the battery piece to be measured by a boundary element method.
In one possible embodiment, S1061 specifically includes:
S1061A: dividing the boundary of the edge area of the battery piece to be tested intonAnd selecting the midpoint of each boundary unit as a node, wherein the integral equation for the node can be discretized as follows:
wherein ,representing boundary element->Node on->Representing node->Voltage value of>Representing boundary cellsThe node on the upper side of the node,nrepresenting the number of nodes to be connected,u j representing boundary element->Voltage distribution of>Represents the normal derivative of the current density function, +.>Representing node->The boundary element where the boundary element is located,q j representing boundary element->Is used for the normal derivative distribution of (c),representing a voltage function.
It should be noted that, by dividing the edge area of the battery piece to be measured into boundary units and selecting the midpoint of each boundary unit as a node, the originally complex integral equation can be simplified into a matrix form. This reduces the computational complexity and increases the computational efficiency, especially for large-scale problems.
S1061B: order theThe integral equation for a node can be reduced to:
S1061C: order theWhen->When (I)>Under the rest condition->The integral equation for the node is further reduced to:
in matrix form, the formula can be:
wherein ,H、Gthe matrix of coefficients is represented and,Ucolumn vectors representing the voltage function values of the boundary cell nodes,Qcolumn vectors representing the current density function normal vector values.
It should be noted that, by converting the integral equation into a matrix form, the voltage value of the node and the normal derivative value of the current density function may be stored in the matrix, thereby reducing the memory consumption. This is particularly important for large scale problems, as the original integral equation may require the storage of a large number of intermediate variables and calculations. Matrix form integral equations are generally easier to numerically calculate and solve.
In one possible embodiment, the coefficient matrixHThe calculation mode of each element is as follows:
wherein ,H ii representing coefficient matrixHMiddle (f)iLine 1iThe value of the column element is taken,H ij representing coefficient matrixHMiddle (f)iLine 1jThe value of the column element is taken,r ij representing nodesTo node->Is used for the distance of (a),h ij representing node->To boundary element->Is arranged in the vertical distance of (a),l i representing boundary element->Is a length of (c).
Coefficient matrixGThe calculation mode of each element is as follows:
。
wherein ,G ii representing coefficient matrixGMiddle (f)iLine 1iThe value of the column element is taken,H ij representing coefficient matrixGMiddle (f)iLine 1jThe column element takes a value.
S1061D: for matrix equationSolving to obtain the voltage distribution of the edge area of the battery piece to be testedu。
It should be noted that, the stability and accuracy advantage of the numerical calculation can be utilized by adopting the matrix form, so as to improve the numerical stability of the whole solving process.
When solving the edge region of the battery piece to be measured, the boundary element method only needs to discretize the boundary, and does not need to mesh the whole region. In contrast, the finite element method requires meshing of the entire region, which may result in a larger number of meshes in the case of an edge ring region, increasing computational complexity and storage requirements. Therefore, the use of the boundary element method has advantages of reducing the computational complexity and reducing the memory requirements compared to the finite element method when solving the internal voltage distribution of the edge ring region.
According to the invention, the voltage distribution of the edge area of the battery piece to be measured is calculated by the boundary element method, so that the problems can be effectively simplified, the calculation efficiency is improved, the memory consumption is reduced, and meanwhile, the numerical stability is ensured, thereby obtaining an accurate voltage distribution result. This is important for the accuracy and reliability of the sheet resistance measurement of the contact battery.
Further, the edge area of the battery piece to be measured is divided into boundary units, the voltage distribution of the edge ring area is solved after the matrix form is adopted for discretization of the integral equation, the memory consumption is reduced, the numerical stability is improved, and the flexibility and the expandability are improved, so that the method has important advantages and application values in resistivity measurement.
S1062: and constructing a resistivity calculation objective function according to the voltage distribution of the edge area of the battery piece to be measured and the measured voltage values at the four contact points.
In one possible embodiment, S1062 specifically includes:
the resistivity calculation objective function is constructed by the following formula:
wherein the edge regions of the battery pieces to be tested are sharedMThe number of units in a single cell,ρrepresentation ofMThe vector of the distribution of the resistivity is maintained,ρthe elements of (a) correspond to the resistivity of the individual cells,V(ρ) Indicating a resistivity distribution asρThe boundary voltage value at the time of the time,Urepresenting the measured voltage value at the contact point,representing the modular operation of the matrix.
It should be noted that, the objective function is used to evaluate the resistivity distribution of the edge region of the battery piece to be measured asρBoundary voltage value at timeV(ρ) And the measured boundary voltage valueUDifferences between them. By evaluating the resistivity distribution of the edge region of the battery piece to be measured asρBoundary voltage value at timeV(ρ) And the measured boundary voltage valueUThe difference between the two is used for measuring the internal resistivity distribution of the battery piece to be measuredρIs accurate. Thus, the optimization objective is to find a resistivity distributionρSo that the objective functionAnd the minimum value is that the calculated boundary voltage value is closest to the actual measured value, so that the resistivity distribution which is most consistent with the actual measured value is obtained.
In the invention, the construction of the resistivity calculation objective function is an effective mathematical modeling method, and by optimizing the objective function, more accurate resistivity distribution can be obtained, the measurement accuracy is improved, and the non-invasive measurement of the internal resistivity of the battery piece is realized.
Further, the inventor finds that in the research process, in the solution of the resistivity of the edge area of the battery piece to be tested, the pathogenicity exists, the output (solution) is very sensitive to the tiny change of the input (data or parameters), and even if the input data has slight disturbance, the output result can generate great change. In a pathological problem, a minute error of input data may cause a huge error of an output result, so that the solution of the problem becomes unstable and unreliable. In order to improve the pathogenicity of the resistivity solution of the edge area of the battery piece to be tested, a regularization method is innovatively introduced in the construction process of the objective function,
in one possible embodiment, S1062 specifically includes:
by introducing regularization parameters, a resistivity calculation objective function is constructed:
wherein, the battery piece to be measured is shared in the interiorMThe number of units in a single cell,ρrepresentation ofMThe vector of the distribution of the resistivity is maintained,ρthe elements in (a) correspond to the resistivity values of the individual cells,V(ρ) Indicating a resistivity distribution asρThe boundary voltage value at the time of the time,Urepresenting the value of the measured boundary voltage,modulo arithmetic representing matrix,/->The regularization factor is represented as a function of the regularization factor,Lthe regularization matrix is represented as a representation,ρ 0 representing the initial resistivity value.
The regularization matrix in the regularization parametersLTypically for constraining the smoothness of the solution. In resistivity calculations, the resistivity distribution typically has some smoothness in space. Through regularization parameters, the solution can be made smoother in space, avoiding excessive oscillation or unreasonable local variation.
In the invention, the regularization parameters can introduce some additional constraint conditions, such as smoothness, sparsity and the like, into the objective function, so that the space of the solution is limited, and the instability of the problem is reduced. The degree of constraint can be adjusted by controlling the regularization parameters, and the relation between data fitting and model constraint is balanced, so that the solution is more stable and reliable, and the pathological problem is improved.
S1063: and determining the resistivity distribution of the edge area of the battery piece to be measured by taking the extremum of the calculated target function of the solved resistivity as a target.
In one possible embodiment, the solution is toCalculating the resistivity of the edge region of the to-be-measured battery piece of the objective function for the resistivity, S1063 specifically includes:
S1063A: calculating an objective function for resistivityThe derivative is obtained, and the derivative value is 0, and then:
wherein ,representing the Jacobian matrix, which can be expressed as +.>。
S1063B: to derivativesThe taylor expansion is performed, and only linear terms of the taylor expansion are reserved, and then the following steps are:
wherein ,represent the firstkResistivity distribution for the multiple iterations.
S1063C: obtaining the first according to the Taylor expansion resultkIncrement in multiple iterations：
wherein ,represent the firstkJacobian matrix of the next iteration, +.>Indicating a resistivity distribution of +.>Boundary voltage value at that time.
S1063D: judgment of the firstkIn each iteration, whether the convergence condition is satisfied:
wherein ,ethe value of the error is indicated and,Urepresenting the value of the measured boundary voltage,representing the two norms of the matrix,εrepresenting a preset error value.
Wherein, a person skilled in the art can set the preset error value according to the actual situationεThe size of (3) is not limited in the present invention.
It should be noted that, the determination of the convergence condition is introduced, that is, whether the convergence condition is satisfied is determined by comparing the error between the current voltage distribution and the measurement boundary voltage value. Thus, the error can be controlled, the iteration process is ensured to be carried out within the error allowable range, and infinite loop and excessive iteration are prevented.
Specifically, by introducing a preset error valueεThe convergence condition can be flexibly adjusted in the iterative process. When the error value reaches a preset range, i.e. the convergence condition is satisfied, the iteration may be terminated and the final resistivity distribution may be output. Thus, the preset error value can be adjusted according to specific problems and data conditions, so that the iteration process is better controlled.
S1063E: when meeting the requirementsEnding the iteration when the convergence condition is met, and outputting the firstkResistivity profile for multiple iterations. When the convergence condition is not satisfied, the ∈>And continuing the next iteration until the convergence condition is met.
It should be noted that, by means of iterative solution, the optimal solution may be approximated gradually. In each iteration, the direction of optimization of the current resistivity distribution can be found by calculating the derivative and increment of the objective function so that the objective function gradually decreases. Therefore, the convergence speed can be increased, and especially under the conditions of complex objective function and high nonlinearity degree, the optimal solution can be approached more quickly through iterative gradual optimization.
According to the invention, the efficiency and stability of the resistivity solution of the edge area of the battery piece to be measured can be improved by introducing an iterative solution mode, so that more accurate resistivity distribution is ensured.
Further, in one possible embodiment, the solution is toCalculating the resistivity of the edge region of the battery piece to be measured of the objective function for the resistivity, S1063 specifically includes substeps S10631 to S10633:
s10631: deriving an objective function of the resistivity calculation and performing Taylor expansion to obtain the firstkIncrement in multiple iterations：
wherein ,represent the firstkResistivity profile of the next iteration,/->Represent the firstkThe jacobian matrix of the next iteration,indicating a resistivity distribution of +.>The boundary voltage value at the time of the time,Urepresents the measured boundary voltage value,/->The regularization factor is represented as a function of the regularization factor,Lthe regularization matrix is represented as a representation,ρ 0 representing the initial resistivity value, +.>Representing the matrix transpose.
It should be noted that, first, the objective function of the resistivity calculation is derived, and the Taylor expansion is used to obtain the firstkThe resistivity distribution increases with each iteration. Introducing regularization parametersλAnd regularization matrixLThe purpose of regularization is to prevent morbidity when solving the resistivity of the edge region of the battery sheet under test, i.e. to make the condition number of the problem too large or to cause instability of the solution. The regularization term plays a role in controlling the change amplitude of the resistivity distribution in the objective function, so that the iterative solution is more stable.
Selecting，IRepresenting an identity matrix>Increment->Can be simplified into:
s10632: judgment of the firstkIn each iteration, whether the convergence condition is satisfied:
wherein ,ethe value of the error is indicated and,Urepresenting the value of the measured boundary voltage,representing the two norms of the matrix,εrepresenting a preset error value.
S10633: ending the iteration when the convergence condition is satisfied, and outputting the firstkResistivity profile for multiple iterations. When the convergence condition is not satisfied, the ∈>And continuing the next iteration until the convergence condition is met.
In the invention, by solving the objective function after regularization parameters are introduced, some additional constraint conditions such as smoothness, sparsity and the like can be introduced into the objective function, so that the space of the solution is limited, the instability of the problem is reduced, and the pathological problem is improved. By introducing an iterative solution mode, the optimal solution can be better approximated by gradually adjusting parameters and optimizing the solution, the success rate and the accuracy of the solution are improved, and the efficiency and the stability of the resistivity solution of the edge area of the battery piece to be measured are improved.
S1064: and determining the sheet resistance distribution of the edge area of the battery piece to be tested according to the resistivity distribution of the edge area of the battery piece to be tested.
In one possible implementation, S1064 is specifically:
according to the following formula, calculating the square resistance distribution of the edge area of the battery piece to be measured:
wherein ,ρthe resistivity is represented by a value of the electrical resistivity,R s the square resistance is represented by the square resistance,wand the thickness of the battery piece to be measured is shown.
In the invention, the boundary and interface conditions of the material can be effectively modeled by the boundary element method. In sheet resistance measurements, the current and voltage distribution of the boundary region may be affected by geometry and material contact. The boundary element method can accurately evaluate the influence of contact resistance and boundary effect, and accurately measure the voltage and current distribution of the edge area, thereby providing accurate current distribution information. And thus accurately corrects for boundary effects.
Example 2
In one embodiment, the invention provides a system for measuring sheet resistance of a contact battery, which is used for executing the method for measuring sheet resistance of a contact battery in embodiment 1.
The step and effect of the method for measuring sheet resistance of a contact battery in the above embodiment 1 can be achieved by the system for measuring sheet resistance of a contact battery provided by the invention, and in order to avoid repetition, the invention is not repeated.
Compared with the prior art, the invention has at least the following beneficial technical effects:
(1) In the invention, the four-probe method is improved, four probes are not required to be arranged on the same straight line surface at equal intervals, the position requirement of the four probes is changed into that the connecting line between two probes is basically perpendicular to the connecting line between the other two probes, even if a small error exists in the position during real arrangement, the measurement is not affected by the included angle between 85 degrees and 95 degrees, and when the diameter of a battery piece is smaller, the arrangement difficulty of the probes is reduced, and the sheet resistance measurement efficiency is improved.
(2) According to the invention, a correction coefficient is introduced when the sheet resistance is calculated, so that the influence of uneven current distribution caused by edge and thickness effects is reduced, the influence that the position of the probe is easily deviated when the probe is contacted with a battery piece is reduced, and the sheet resistance measurement accuracy is improved.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The foregoing examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (9)
1. The method for measuring the sheet resistance of the contact type battery piece is characterized by comprising the following steps of:
s101: selecting four contact points A, B, C, D at the edge of the to-be-detected battery piece, wherein the included angle between the connecting line between the first contact point A and the third contact point C and the connecting line between the second contact point B and the fourth contact point D is between 85 degrees and 95 degrees;
s102: probes are connected to the four contact points A, B, C, D, respectively;
s103: passing a current between the adjacent first contact point A and the second contact point BI AB Measuring the voltage value between the third contact point C and the fourth contact point DV CD Calculate a first resistanceR 1 ：
；
S104: passing a current between the adjacent first contact point A and the fourth contact point DI AD Measuring the voltage value between the second contact point B and the third contact point CV BC Calculate the second resistanceR 2 ：
；
S105: according to the describedFirst resistorR 1 And the second resistorR 2 Calculating the sheet resistance of the battery piece to be measured:
wherein ,R s represents the sheet resistance of the battery piece to be tested,representing the correction coefficient;
wherein the correction coefficientThe calculation mode of (a) is as follows:
wherein ,tthe integral variable is represented by a value of the integral variable,rthe range of the values is as follows。
2. The method for measuring sheet resistance of a contact battery according to claim 1, further comprising:
s106: and correcting the sheet resistance of the edge area of the battery piece to be detected by a boundary element method.
3. The method for measuring sheet resistance of a contact battery according to claim 2, wherein the step S106 specifically includes:
s1061: calculating the voltage distribution of the edge area of the battery piece to be tested by a boundary element method;
s1062: constructing a resistivity calculation objective function according to the voltage distribution of the edge area of the battery piece to be measured and the measured voltage values of the four contact points;
s1063: determining the resistivity distribution of the edge area of the battery piece to be detected by taking the extremum of the resistivity calculation objective function as a target;
s1064: and determining the sheet resistance distribution of the edge area of the battery piece to be tested according to the resistivity distribution of the edge area of the battery piece to be tested.
4. The method for measuring sheet resistance of a contact battery according to claim 3, wherein the step S1061 specifically includes:
S1061A: dividing the boundary of the edge area of the battery piece to be tested intonAnd selecting the midpoint of each boundary unit as a node, wherein the integral equation for the node can be discretized as follows:
wherein ,representing boundary element->Node on->Representing node->Voltage value of>Representing boundary element->The node on the upper side of the node,nrepresenting the number of nodes to be connected,u j representing boundary element->Voltage distribution of>Represents the normal derivative of the current density function, +.>Representing node->The boundary element where the boundary element is located,q j representing boundary element->Is used for the normal derivative distribution of (c),representing a voltage function;
S1061B: order theThe integral equation for a node can be reduced to:
S1061C: order theWhen->When (I)>Under the rest condition->The integral equation for the node is further reduced to:
in matrix form, the formula can be:
wherein ,H、Gthe matrix of coefficients is represented and,Ucolumn vectors representing the voltage function values of the boundary cell nodes,Qcolumn vectors representing current density function method guideline values;
S1061D: for matrix equationSolving to obtain the voltage distribution of the edge area of the battery piece to be testedu。
5. The method for measuring sheet resistance of a contact battery according to claim 4, wherein the coefficient matrixHThe calculation mode of each element is as follows:
wherein ,H ii representing coefficient matrixHMiddle (f)iLine 1iThe value of the column element is taken,H ij representing coefficient matrixHMiddle (f)iLine 1jThe value of the column element is taken,r ij representing nodesTo node->Is used for the distance of (a),h ij representing node->To boundary sheetYuan->Is arranged in the vertical distance of (a),l i representing boundary element->Is a length of (2);
the coefficient matrixGThe calculation mode of each element is as follows:
；
wherein ,G ii representing coefficient matrixGMiddle (f)iLine 1iThe value of the column element is taken,H ij representing coefficient matrixGMiddle (f)iLine 1jThe column element takes a value.
6. The method for measuring sheet resistance of a contact battery according to claim 5, wherein the step S1062 specifically includes:
the resistivity calculation objective function is constructed by the following formula:
wherein the edge regions of the battery pieces to be tested are sharedMThe number of units in a single cell,ρrepresentation ofMThe vector of the distribution of the resistivity is maintained,ρthe elements of (a) correspond to the resistivity of the individual cells,V(ρ) Indicating a resistivity distribution asρThe boundary voltage value at the time of the time,Urepresenting the measured voltage value at the contact point,representing the modular operation of the matrix.
7. The method for measuring sheet resistance of a contact battery according to claim 6, wherein the step S1063 specifically includes:
S1063A: calculating an objective function for the resistivityThe derivative is obtained, and the derivative value is 0, and then:
wherein ,representing the Jacobian matrix, which can be expressed as +.>；
S1063B: to derivativesThe taylor expansion is performed, and only linear terms of the taylor expansion are reserved, and then the following steps are:
wherein ,represent the firstkResistivity distribution for the second iteration;
S1063C: obtaining the first according to the Taylor expansion resultkIncrement in multiple iterations：
wherein ,represent the firstkJacobian matrix of the next iteration, +.>Indicating a resistivity distribution of +.>Boundary voltage values at the time;
S1063D: judgment of the firstkIn each iteration, whether the convergence condition is satisfied:
wherein ,ethe value of the error is indicated and,Urepresenting the value of the measured boundary voltage,representing the two norms of the matrix,εrepresenting a preset error value;
S1063E: ending the iteration when the convergence condition is satisfied, and outputting the firstkResistivity profile for multiple iterationsThe method comprises the steps of carrying out a first treatment on the surface of the When the convergence condition is not satisfied +.>And continuing the next iteration until the convergence condition is met.
8. The method for measuring sheet resistance of a contact battery according to claim 7, wherein the step S1064 is specifically:
calculating the square resistance distribution of the edge area of the battery piece to be measured according to the following formula:
wherein ,ρrepresentation ofThe electrical resistivity of the material is determined by the electrical resistivity,R s the square resistance is represented by the square resistance,wand representing the thickness of the battery piece to be tested.
9. A contact battery sheet resistance measurement system for performing the contact battery sheet resistance measurement method of any one of claims 1 to 8.
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| CN117805644A (en) * | 2023-12-28 | 2024-04-02 | 江苏森标科技有限公司 | Non-contact nondestructive method for measuring resistivity of battery piece |
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| JP2001004678A (en) * | 1999-06-16 | 2001-01-12 | Sanyo Electric Co Ltd | Resistivity measuring method for resistant film |
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| JP2001004678A (en) * | 1999-06-16 | 2001-01-12 | Sanyo Electric Co Ltd | Resistivity measuring method for resistant film |
| CN114325053A (en) * | 2021-12-30 | 2022-04-12 | 广州昆德半导体测试技术有限公司 | Four-probe resistivity and sheet resistance tester |
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