JP2019100931A - Processing device and processing method - Google Patents

Abstract

To accurately specify the surface resistivity in each direction of a sheet member having anisotropy.SOLUTION: The present invention comprises: a measurement unit 12 for supplying a measuring signal to two supply positions on the surface of a sheet member 100 and measuring the potential at a plurality of measurement positions on the surface; and a processing unit 15 for specifying surface resistivities ρ1, ρ2 in two directions on the surface on the basis of the measured potential values Va, Vb. The processing unit 15 repeatedly executes an evaluation value calculation process of calculating an evaluation value on the basis of each measured value and the theoretical value of potential at each measurement position calculated by assigning, to a calculation formula that is a solution of formula (1), a component of position vector indicating each measurement position and a first and a second set value having been discretionarily set assuming surface resistivities ρ1, ρ2, while changing the first and the second set values, and specifies the first and the second set values when the evaluation value satisfies a prescribed condition respectively as surface resistivities ρ1, ρ2. Formula (1): X*(σ'XV down-arrow (down-arrow up-arrow down-arrow r down-arrow))=-I(δ(up-arrow r-up-arrow r down-arrow s)-δ(up-arrow r-up-arrow r down-arrow d)).SELECTED DRAWING: Figure 1

Description

  The present invention relates to a processing apparatus and processing method for performing a surface resistivity identification process for identifying a first surface resistivity in a first direction and a second surface resistivity in a second direction on the surface of a sheet.

  As a method of specifying the surface resistivity (sheet resistance) of a sheet body, a specific method disclosed in Non-Patent Document 1 below is known. In this particular method, the four probes are brought into contact with the surface of the sheet so that they are aligned along a straight line on the surface of the sheet (sample in the form of a sheet) which is extremely thin and infinite (sufficiently large). A constant DC current is supplied through the two probes, and the voltage between the two inner probes is measured. Next, the sheet resistance (surface resistivity) of the sheet is calculated by multiplying the ratio between the measured voltage and the current value of the supplied current by the correction coefficient π / ln2. In this specific method, it is possible to calculate an accurate sheet resistance by multiplying the ratio of the voltage to the current by the correction coefficient.

ARTHUR UHLIR, JR, "The Potentials of Infinite System of Source and Numerical Solutions of Problems in Semiconductor Engineering", THE BELL SYSTEM TECHNICAL JOURNAL, January 1955, p. 105-128.

  However, the above-described method of specifying the surface resistivity has the following problems to be improved. Specifically, for a sheet having no anisotropy (or a low anisotropy), the correction value is multiplied by the resistance value (the ratio of the measured voltage value to the current value) in the direction in which the probes are arranged. Thus, the correct surface resistivity can be determined. However, in this specific method, when a sheet having anisotropy different in surface resistivity depending on the direction is targeted, even if the resistance value in the direction different from the direction in which the probes are lined is multiplied by the correction coefficient, Correcting the surface resistivity in different directions may be difficult. Therefore, in this method of specifying the surface resistivity, it is difficult to accurately specify the surface resistivity in each direction in the sheet body having anisotropy. In addition, although this method of specifying the surface resistivity can accurately specify the surface resistivity for an infinite (sufficiently) wide sheet body, the size can not be applied to a sheet body having a finite size. It is difficult to accurately identify the surface resistivity of a finite sheet body.

  The present invention has been made in view of such improvements, and its main object is to provide a processing apparatus and processing method capable of accurately specifying the surface resistivity in each direction in a sheet having anisotropy. .

In order to achieve the above object, the processing apparatus according to claim 1 is configured to supply the measurement signal through a pair of supply probes respectively contacting two supply positions on the surface of the sheet body. A measurement unit that measures the potential at each measurement position via a plurality of measurement probes that are respectively in contact with a plurality of measurement positions in the first and second measurement values on the surface based on measurement values of the potential measured by the measurement unit A processing unit for executing a surface resistivity identification process for identifying a first surface resistivity in one direction and a second surface resistivity in a second direction different from the first direction on the surface; In the surface resistivity identification process, a component of a position vector indicating the measurement position, the first surface resistivity, and the second surface resistivity are parameters of the solution of the following equation (1). In the calculation equation, a component of a position vector indicating each measurement position, a first set value arbitrarily set as the first surface resistivity, and a second set value arbitrarily set as the second surface resistivity Evaluation to calculate the theoretical value of the potential at each measurement position by substitution, and to evaluate the degree of agreement between each measured value specified based on each measured value and each theoretical value and each theoretical value The first set value when the evaluation value calculation process for calculating a value is repeatedly executed while changing the first set value and the second set value, and the evaluation value satisfies a prescribed condition defined in advance. And the second set value is specified as the first surface resistivity and the second surface resistivity, respectively.
∇ · (σ′∇V _{(↑ r)} ) = − I (δ (↑ r− ↑ r _s ) −δ (↑ r− ↑ r _d )) (1) where σ ′ is the above-mentioned measurement position Represents a quadratic square matrix having elements of the conductivity of the sheet corresponding to the components of the position vector rr shown, where ∇ is a nabla operator and V _{(↑ r)} is represented by the position vector rr Represents the potential at the measurement position, I represents the current value of the measurement signal, δ represents the delta function, ↑ r _s represents a position vector indicating the supply position on the source side, and ↑ r _d represents the drain It represents a position vector indicating the supply position on the side.

In the processing device according to claim 2, in the processing device according to claim 1, in the evaluation value calculation process, the processing unit performs one of the first direction and the second direction in the xy orthogonal coordinate system. The above equation is a solution of the following equation (2) in which the above equation (1) is modified with the x direction in the x direction and the other in the first direction and the second direction as the y direction in the xy orthogonal coordinate system The theoretical value is calculated using.
(1 / ρ _x ) (∂ ² / ∂ _x ² ) V (x, y) + (1 / ρ _y ) (∂ ² / ∂ _y ² ) V (x, y) =-I (δ (x-x) _{s 2} ) δ (y-y _s ) -δ (x-x _d ) δ (y-y _d ) (2) where x represents the x coordinate of the measurement position in the xy orthogonal coordinate system, y Represents the y-coordinate of the measurement position in the xy orthogonal coordinate system, ρ _x represents one of the first surface resistivity and the second surface resistivity, and _{y y} represents the first surface resistivity and the first surface resistivity. Represents the other of the second surface resistivity, ∂ represents a partial differential symbol, V (x, y) represents a change in potential with x and y as parameters, and I represents a current value of the measurement signal, δ represents the delta function, x _s represents the x-coordinate of the position of supplying the source side of the xy rectangular coordinate system, y _s is the source in the xy rectangular coordinate system Y coordinate of the position of supplying, x _d represents the x-coordinate of the position of supplying the drain side in the xy rectangular coordinate system, the y _d a y coordinate of the position of supplying the drain side in the xy rectangular coordinate system Represent.

Further, in the processing apparatus according to claim 3, in the processing apparatus according to claim 2, the processing unit performs the following (3) as the calculation equation which is a solution of the equation (2) in the evaluation value calculation process. The theoretical value is calculated using the equation).
_{V (x, y, ρ x} , ρ y) = V 0 - (I / L x L y) Σ 'nx, ny (4/2 δnx, 0 + δ0, ny) [1 / (λ nx 2 / ρ x + λ ^{_{ny 2 / ρ y)] (}} cosλ nx x d cosλ ny y d -cosλ nx x s cosλ ny y s) cosλ nx xcosλ ny y ... (3) formula where, x is the measured position in the xy rectangular coordinate system represents an x coordinate, y represents ay coordinate of the measurement position in the xy orthogonal coordinate system, ρ _x represents any one of the first surface resistivity and the second surface resistivity, and _{y y} represents the second surface resistivity 1 represents the other of the surface resistivity and the second surface resistivity, and V (x, y, _x x, y _y ) represents a change in potential with x, y, _{x x} , _{y y} as a parameter, V ₀ Is a constant independent of x and y, and I represents the current value of the signal for measurement. L _x represents the length of the sheet in the xy orthogonal coordinate system in the x-axis direction, L _y represents the length of the sheet in the xy orthogonal coordinate system in the y-axis direction, and n is each Represents the number given to each measurement position, Σ 'represents the sum excluding the term nx = ny = 0, δ represents the Kronecker delta, λ _nx is nxπ / L _x , and λ _ny is nyπ / L _y , x _d represents the x-coordinate of the supply position on the drain side in the xy Cartesian coordinate system, y _d represents the y-coordinate of the supply position on the drain side in the xy Cartesian coordinate system, x _s Represents the x coordinate of the supply position on the source side in the xy rectangular coordinate system, and y _s represents the y coordinate of the supply position on the source side in the xy rectangular coordinate system.

  Further, in the processing apparatus according to any one of claims 1 to 3, in the processing apparatus according to claim 4, in the evaluation value calculation process, the measuring unit measures the measured value and the theoretical value at each measurement position. The residual sum of squares of difference values of is calculated as the evaluation value.

  In the processing apparatus according to claim 5, in the processing apparatus according to any one of claims 1 to 4, the processing unit is configured to continue the process until the evaluation value as the defined condition satisfies the condition of not more than the defined value. The evaluation value calculation process is repeatedly executed.

In the processing method according to the sixth aspect, a plurality of measurement positions on the surface in a state where the measurement signal is supplied via the pair of supply probes respectively contacting the two supply positions on the surface of the sheet body. The potential at each measurement position is measured via a plurality of measurement probes respectively brought into contact with each other, and based on the measured value of the measured potential, the first surface resistivity in the first direction on the surface, and the surface In the surface resistivity identification process for identifying a second surface resistivity in a second direction different from the first direction, a component of a position vector indicating the measurement position, which is a solution of the following equation (1), A first set value arbitrarily set as a component of a position vector indicating each measurement position and the first surface resistivity in a calculation formula using the first surface resistivity and the second surface resistivity as parameters The theoretical value of the potential at each measurement position is calculated by substituting a second set value arbitrarily set as the second surface resistivity, and the specific value is specified based on each measurement value and each theoretical value. An evaluation value calculation process for calculating an evaluation value for evaluating the degree of agreement between each measured value and each theoretical value is repeatedly executed while changing the first set value and the second set value, and the evaluation value is The first set value and the second set value when the predetermined condition defined in advance is defined are specified as the first surface resistivity and the second surface resistivity, respectively.
∇ · (σ′∇V _{(↑ r)} ) = − I (δ (↑ r− ↑ r _s ) −δ (↑ r− ↑ r _d )) (1) where σ ′ is the above-mentioned measurement position Represents a quadratic square matrix having elements of the conductivity of the sheet corresponding to the components of the position vector rr shown, where ∇ is a nabla operator and V _{(↑ r)} is represented by the position vector rr Represents the potential at the measurement position, I represents the current value of the measurement signal, δ represents the delta function, ↑ r _s represents a position vector indicating the supply position on the source side, and ↑ r _d represents the drain It represents a position vector indicating the supply position on the side.

  In the processing apparatus according to claim 1 and the processing method according to claim 6, the theoretical value of the potential calculated by substituting the first set value and the second set value into the calculation equation which is the solution of equation (1) Evaluation value calculation processing for calculating an evaluation value based on the measured value of potential is repeatedly executed while changing the first set value and the second set value, and the first setting when the evaluation value satisfies the prescribed condition The value and the second set value are specified as a first surface resistivity and a second surface resistivity, respectively. For this reason, according to this processing apparatus and processing method, the surface resistivity can be determined depending on the direction by arbitrarily defining the first direction and the second direction on the surface of the sheet and measuring the potential at at least two measurement positions. Even when a sheet having different anisotropy is treated, the first surface resistivity in the first direction and the second surface resistivity in the second direction can be accurately identified.

  Further, in the processing apparatus according to the second aspect, one of the first direction and the second direction is taken as the x-axis direction in the xy orthogonal coordinate system, and the other in the first direction and the second direction is taken as y in the xy orthogonal coordinate system. The theoretical value is calculated using a calculation equation which is a solution of the following equation (2) obtained by modifying the equation (1) as the axial direction. Therefore, according to this processing apparatus and processing method, by setting the direction of one side of the rectangular sheet body as the x-axis direction and the direction of the other side orthogonal to the one side as the y-axis direction, The first surface resistivity and the second surface resistivity in the y-axis direction can be accurately identified.

  Moreover, in the processing apparatus of Claim 3, a theoretical value is calculated using (3) Formula as a calculation formula. In this case, since the equation (3) is a calculation equation obtained by solving the equation (2) by an analytical solution method, the theoretical value is accurately calculated by comparison with the calculation equation obtained by solving the equation (2) by a numerical solution method can do. Therefore, according to this processing apparatus and processing method, the first surface resistivity and the second surface resistivity can be specified more accurately.

  Further, according to the processing apparatus of claim 4, a difference (a disagreement between the measured value and the theoretical value) is calculated by calculating the residual square sum of the difference value between the measured value and the theoretical value at each measurement position as the evaluation value. Can be accurately evaluated, and therefore, by using this evaluation value, the first surface resistivity in the first direction and the second surface resistivity in the second direction can be more accurately identified.

  Further, according to the processing apparatus of claim 5, the evaluation value calculation process is repeatedly executed until the evaluation value satisfies the condition of the predetermined value or less, thereby defining the predetermined value to be an appropriate value. It is possible to prevent a decrease in processing efficiency due to an increase in the number of times the value calculation process is repeatedly performed.

FIG. 2 is a configuration diagram showing a configuration of a processing device 1 FIG. 2 is a plan view of a sheet body 100 and a probe unit 11; 5 is a flowchart of surface resistivity identification processing 50;

  Hereinafter, embodiments of the processing apparatus and the processing method will be described with reference to the attached drawings.

  First, the configuration of the processing apparatus 1 shown in FIG. 1 will be described. The processing apparatus 1 is an example of a processing apparatus, and, for example, as shown in FIG. 2, the surface resistivity (sheet resistance) of the sheet 100 having a rectangular planar shape can be specified. In this case, in the processing apparatus 1, when the sheet 100 has physical properties in which the surface resistivity is different depending on the direction, surfaces in two directions (a first direction and a second direction different from the first direction) The resistivity can be specified according to the processing method described later. In the following description, the surface resistivity in the first direction (first surface resistivity) is also referred to as surface resistivity 11, and the surface resistivity in the second direction (second surface resistivity) is also referred to as surface resistivity 22. .

  Further, as shown in FIG. 1, the processing apparatus 1 is configured to include a probe unit 11, a measurement unit 12, a storage unit 13, a display unit 14, and a processing unit 15.

  As shown in FIG. 2, the probe unit 11 includes two supply probes 21a and 21b (hereinafter also referred to as "supply probes 21" when not distinguished from each other) and two measurement probes 22a and 22b (hereinafter referred to as When it does not distinguish, it is comprised also with the support part 23 which supports each probe 21 for measurement, and each probe 22 for measurement, and also "a probe 22 for measurement."

  In this case, when each supply probe 21 specifies the surface resistivity 1,1 and 22, two supply positions 71a and 71b on the surface 101 of the sheet 100 (see FIG. 2; ), And is used to supply a direct current as an example of the measurement signal. In this example, the supply position 71a is defined on the source side, and the supply position 71b is defined on the drain side. When the measurement probe 22 specifies the surface resistivity ρ1 and 22 of the sheet 100, the two measurement positions 72a and 72b on the surface 101 of the sheet 100 (refer to FIG. (Also referred to as “position 72”) and used to measure the potential of each measurement position 72.

  The measurement unit 12 includes a power supply unit (not shown) that outputs a direct current as a measurement signal, and is a supply probe of the probe unit 11 in contact with the supply positions 71a and 71b on the surface 101 of the sheet 100. The measurement probes 22a and 22b of the probe unit 11 in contact with the measurement positions 72a and 72b of the surface 101 in a state where the direct current output from the power supply unit is supplied to the sheet body 100 through 21a and 21b. A measurement process is performed to measure each potential of the measurement positions 72a and 72b. The measured values of the potential with respect to the reference potential (for example, ground potential) at the measurement positions 72a and 72b are also referred to as "measured values Va and Vb", respectively, and when the measured values Va and Vb are not distinguished, they are also referred to as "measured value V".

The storage unit 13 stores information indicating the shape of the sheet 100 shown in FIG. Specifically, the length Lx of the sheet 100 shown in the figure in the x direction (an example of the first direction) and the length Ly of the sheet 100 in the y direction (an example of the second direction) orthogonal to the x direction. Remember. The storage unit 13 also stores the measurement values Va and Vb measured by the measurement unit 12. In addition, the storage unit 13 stores surface resistivity ρ1 and ρ2 of the sheet 100 identified by the processing unit 15. Furthermore, the storage unit 13 further includes coordinates x _a and y _{a of} the measurement position 72 a, coordinates x _b and y _{b of} the measurement position 72 _b , and coordinates x _s and y _s of the supply position 71 a on the source side in an xy orthogonal coordinate system described later. The coordinates x _d and y _d of the supply position 71 _b on the drain side are stored.

  The display unit 14 displays various information such as surface resistivity 抵抗 1 and ρ2 specified by the processing unit 15 according to the control of the processing unit 15.

  The processing unit 15 controls the measurement unit 12, the storage unit 13, and the display unit 14. Further, the processing unit 15 executes the surface resistivity identification processing 50 shown in FIG. 3 to identify the surface resistivity 1,1 and ρ2 of the sheet 100.

  Next, a method (processing method) of specifying the surface resistivities 1,1 and 22 of the sheet 100 shown in FIG. 2 using the processing apparatus 1 will be described.

  First, as shown in FIG. 2, the sheet member 100 is placed on a mounting table (not shown) with the surface 101 facing upward, and then the tip portions of the supply probes 21a and 21b and the measurement probes 22a and 22b are The probe unit 11 is placed on the sheet 100 in a state of being directed downward. At this time, as shown in the figure, the supply probes 21a and 21b respectively contact the supply positions 71a and 71b on the surface 101 of the sheet 100, and the measurement probes 22a and 22b on the measurement positions 72a and 72b on the surface 101. Contact each other.

  Subsequently, an operation unit (not shown) is operated to instruct start of measurement. In response to this, the processing unit 15 causes the measuring unit 12 to execute measurement processing. In this measurement process, the measurement unit 12 outputs a direct current as a measurement signal from the power supply unit (not shown), and the supply probes 21a and 21b (see FIG. 2) that are in contact with the supply positions 71a and 71b (see FIG. 2). A direct current is supplied to the supply positions 71a and 71b via the same reference). The measurement unit 12 also measures the potentials at the measurement positions 72a and 72b via the measurement probes 22a and 22b (see the same drawing) that are in contact with the measurement positions 72a and 72b (see the same drawing). Subsequently, the processing unit 15 stores the measurement values Va and Vb of the potential measured by the measurement unit 12 in the storage unit 13.

  Subsequently, the operation unit is operated to instruct execution of a process of specifying the surface resistivity of the sheet 100. In response to this, the processing unit 15 executes the surface resistivity identification process 50 shown in FIG. In the surface resistivity identification process 50, the processing unit 15 reads the measured values Va and Vb measured by the measurement unit 12 from the storage unit 13 (step 51).

  Next, the processing unit 15 executes an evaluation value calculation process (steps 52 to 54 described later). In this evaluation value calculation process, the set value rr1 (first set value) corresponding to the predicted value of the surface resistivity 11 (first surface resistivity) and the predicted value of the surface resistivity 22 (second surface resistivity) are used. The corresponding set value r r2 (second set value) is arbitrarily set (step 52). The surface resistivities 1,1 and 22 are used when calculating the theoretical value V ′ of the potential at the measurement position 72 by substituting the calculation formula described later. Subsequently, the processing unit 15 calculates the theoretical value V 'of the potential at the measurement position 72 (step 53).

Here, a calculation formula used to calculate the theoretical value V ′ will be described. First, a position vector indicating the measurement position 72 is ↑ r, and a quadratic square matrix (conductivity matrix) having elements of the conductivity of the sheet 100 corresponding to the components of the position vector r r is σ ′. the potential at position 72 and V _{(↑ r),} the current value of the measurement signal (direct current) and I, the position vector indicating the supply position 71a on the source side and ↑ r _s, indicating a supply position 71b of the drain-side When the position vector and ↑ r _d, the following equation (1) (Poisson equation) holds.
∇ · (σ′∇V _{(↑ r)} ) = − I (δ (↑ r− ↑ r _s ) −δ (↑ r− ↑ r _d )) (1) In the equation (1), ∇ Represents the nabla operator, and δ represents the delta function.

Next, as shown in FIG. 2, the direction of one side in the rectangular sheet 100 (x direction as the first direction shown in the same figure) is taken as the x-axis direction in the xy orthogonal coordinate system, and the other side in the sheet 100 is Assuming that the direction of y (the y direction as the second direction shown in the same figure) is the y-axis direction in the xy orthogonal coordinate system, the equation (1) is transformed into an equation for the xy orthogonal coordinate system. The first order partial differential equation is obtained.
(1 / ρ _x ) (∂ ² / ∂ _x ² ) V (x, y) + (1 / ρ _y ) (∂ ² / ∂ _y ² ) V (x, y) =-I (δ (x-x) _{s 2} ) δ (y-y _s ) -δ (x-x _d ) δ (y-y _d ) (2) where, x is the x of measurement position 72 in the xy orthogonal coordinate system Y represents the y coordinate of the measurement position 72 in the xy orthogonal coordinate system, and ρ _x represents the surface resistivity in the x direction in the xy orthogonal coordinate system (corresponding to the theoretical value of the surface resistivity 1 1) _y represents the surface resistivity (corresponding to the theoretical value of the surface resistivity 22) in the y direction in the xy orthogonal coordinate system, and V (x, y) takes x (x coordinate) and y (y coordinate) as parameters I represents the change in potential, I represents the current value of the measurement signal (direct current), x _s represents the x coordinate of the supply position 71a on the source side in the xy orthogonal coordinate system, y _s represents the y coordinate of the source side supply position 71a in the xy orthogonal coordinate system, x _d represents the x coordinate of the drain side supply position 71 _b in the xy orthogonal coordinate system, and y _d is the drain side in the xy orthogonal coordinate system Represents the y-coordinate of the supply position 71b of In equation (2), ∂ is a partial differential symbol, and δ represents a delta function.

Here, the inventor solves the above-mentioned equation (2) by an analytical solution, and obtains the following equation (3) as a calculation equation (equation for calculating the theoretical value V ′) which is a solution of the equation (2) Succeeded.
_{V (x, y, ρ x} , ρ y) = V 0 - (I / L x L y) Σ 'nx, ny (4/2 δnx, 0 + δ0, ny) [1 / (λ nx 2 / ρ x + λ ^{_{ny 2 / ρ y)] (}} cosλ nx x d cosλ ny y d -cosλ nx x s cosλ ny y s) cosλ nx xcosλ ny y ... (3) equation However, in (3), x, y, [rho _x , _{Y y} , x _s , y _s , x _d , y _d , I respectively represent the same contents as the same symbols in the above-mentioned equation (2), and V (x, y, _{x x} , _{y y} ) is x, represents a change in potential with y, _{x x} , _{y y} as parameters, V ₀ is a constant independent of x and y, and L _x is a length in the x-axis direction in the xy rectangular coordinate system of the sheet 100 represents see FIG. 2), L _y is the length of the y-axis direction in the xy Cartesian coordinate system of the sheet member 100 (FIG. N represents the number given to the measurement position 72 (in this case, n in the measurement position 72a is “1” and n in the measurement position 72b is “2”), and Σ ′ is nx Represents the sum excluding the term = ny = 0, and δ represents Kronecker's delta. Also, λ _nx is nxπ / L _x and λ _ny is nyπ / L _y .

The processing unit 15 substitutes the x coordinate and y coordinate (component of the position vector indicating the measurement position 72) of the measurement position 72 into x and y of the above equation (3), respectively, and arbitrarily sets in step 52 described above. The theoretical values V 'of the potential at the measurement position 72 are calculated by substituting the set values ρ r1 and 式 r2 into ρ _x and _{y y} in equation (3).

Next, the processing unit 15 reads out the measured value V measured by the measuring unit 12 from the storage unit 13 and evaluates the evaluation value J (evaluation function based on the theoretical value V 'and the measured value V calculated in step 53 described above. ) Is calculated (step 54). In this case, the processing unit 15 calculates the evaluation value J by the following equation (4) as an example.
J = Σ (V _n −V _n ′) ² (4) where V _n is the measurement position 72 to which n is added (in this case, n in the measurement position 72 a is 1), The n of the measurement position 72 b is 2), and V _n ′ represents the theoretical value of the potential at the measurement position 72 to which n is added. That is, the residual square sum of the difference value between the measurement value V of the potential at each measurement position 72 and the theoretical value V ′ of the potential at each measurement position 72 is calculated as the evaluation value J by the above equation (4).

Subsequently, the processing unit 15 determines whether the evaluation value J calculated in the above-described step 54 is less than or equal to a prescribed value ε (for example, ε = 10 ⁻⁵ ) defined in advance (step 55). In this case, when the processing unit 15 determines that the evaluation value J is larger than the specified value ε, the processing unit 15 executes the above-described step 52 to change the set values rr1 and rr2, and then performs the above-described steps 53 to 55. Run. Hereinafter, the processing unit 15 repeats steps 52 to 55 (that is, evaluation value calculation processing) while changing the set values rr1 and rr2 each time it determines that the evaluation value J is larger than the specified value ε in step 55. Do.

  On the other hand, when it is determined in step 56 that the evaluation value J is equal to or less than the specified value ε, the set values rr1 and rr2 set at the time of the determination are specified as surface resistivity ρ1 and 22, respectively (step 56). Subsequently, the processing unit 15 stores the identified surface resistivity 1,1 and ρ2 in the storage unit 13 (Step 57), and ends the surface resistivity identification process 50.

  As described above, in the processing apparatus 1 and the processing method, based on the theoretical value V 'of the potential and the measured value V calculated by substituting the set values rr1 and rr2 into the calculation equation which is a solution of the equation (1) The evaluation value calculation processing for calculating the evaluation value J is repeatedly executed while changing the set values rr1 and rr2, and the set values ρr1 and rr2 when the evaluation value J satisfies the defined conditions are respectively surface resistivity ρ1 and 22 Identify as Therefore, according to the processing apparatus 1 and the processing method, the first direction and the second direction are arbitrarily defined on the surface 101 of the sheet 100, and the potentials at at least two measurement positions 72 are measured. Even when the sheet 100 having different anisotropy in surface resistivity is to be treated, the surface resistivity 11 in the first direction and the surface resistivity ρ2 in the second direction can be accurately identified.

  Further, in the processing apparatus 1 and the processing method, the solution of the equation (2) in which the first direction is the x-axis direction in the xy orthogonal coordinate system and the second direction is the y-axis direction in the xy orthogonal coordinate system The theoretical value V ′ is calculated using the calculation formula Therefore, according to the processing apparatus 1 and the processing method, the direction of one side of the rectangular sheet 100 is the x-axis direction, and the direction of the other side orthogonal to the one side is the y-axis direction. The surface resistivity 11 in the direction and the surface resistivity ρ2 in the y-axis direction can be accurately identified.

  Further, in the processing device 1 and the processing method, the evaluation value is calculated using the equation (3) as a calculation equation. In this case, since the equation (3) is a calculation equation obtained by solving the equation (2) by an analytical solution method, the theoretical value V 'is accurately compared with the calculation equation obtained by solving the equation (2) by a numerical solution method Can be calculated. Therefore, according to the processing apparatus 1 and the processing method, the surface resistivity ρ1 and ρ2 can be specified more accurately.

  Further, according to the processing device 1 and the processing method, by calculating the residual square sum of the difference value between the measurement value V and the theoretical value V ′ at each measurement position 72 as the evaluation value J, the measurement value V and the theory are calculated. Since the difference (mismatch) with the value V 'can be accurately evaluated, by using this evaluation value J, the surface resistivity 11 in the first direction and the surface resistivity ρ2 in the second direction can be more accurately determined. It can be identified.

  Further, according to the processing apparatus 1 and the processing method, the definition value ε is defined to be an appropriate value by repeatedly executing the evaluation value calculation process until the evaluation value J satisfies the condition of the specified value ε or less. Thus, it is possible to prevent a decrease in processing efficiency due to an increase in the number of times of execution of the evaluation value calculation process repeatedly.

  The processing apparatus and the processing method are not limited to the above configurations and methods. For example, the theory is based on a calculation equation which is a solution of equation (2) in which the first direction is the x-axis direction of the xy orthogonal coordinate system, and the second direction is the y-axis direction of the xy orthogonal coordinate system. Although the example of calculating the value V ′ has been described above, one axial direction in a coordinate system in which two axes are not orthogonal is set as a first direction, and the other axial direction in the coordinate system is set as a second direction (1) It is also possible to adopt a configuration and a method of calculating the theoretical value V ′ using a calculation formula that is a solution of that formula. In this configuration and method, it is possible to accurately specify the first surface resistivity and the second surface resistivity in two directions in a non-rectangular quadrilateral or non-tetragonal polygonal sheet body.

  In addition, the equation (1) is modified by taking the radial direction centered at the origin as the first direction and the circumferential direction centered at the origin as the second direction (corresponding to the polar coordinate system), and solving the equation The configuration and method of calculating the theoretical value V ′ using a calculation formula can also be adopted. In this configuration and method, by setting the radial direction of the circular sheet as the first direction and the circumferential direction as the second direction, the first surface resistivity in the radial direction of the circular sheet and the first surface resistivity in the circumferential direction can be obtained. (2) The surface resistivity can be accurately identified.

  In addition, although the electric potentials at two measurement positions 72a and 72b are measured and the surface resistivity ρ1 and 22 are specified using the respective measured values Va and Vb, the electric potentials at three or more measurement positions are measured. The surface resistivity ρ1 and ρ2 can also be specified using each measurement value.

  Moreover, although the above describes the example which calculates theoretical value V 'using (3) which solved (2) formula by analytical solution, the formula which solved (2) formula by numerical solution is used as a calculation formula The configuration and method of calculating the theoretical value V ′ can also be adopted.

  In addition, although the above has described the example in which the residual square sum of the difference value between the measurement value V and the theoretical value V ′ at each measurement position 72 is calculated as the evaluation value J in the evaluation value calculation process, other values are evaluated value J It is also possible to adopt the configuration and method of calculating as As an example, a configuration and method may be adopted in which the ratio between the measurement value V and the theoretical value V ′ at each measurement position 72 is calculated, and the average value of each ratio is calculated as the evaluation value J. When this configuration and method are adopted, the evaluation value calculation process is repeated until the evaluation value J satisfies the conditions of the upper and lower limit values close to 1 instead of the condition that the evaluation value J is less than or equal to the specified value ε. Configurations and methods to implement can be employed.

  Moreover, the sheet-like object made into the object of this processing apparatus and processing method also includes a plate-like body.

DESCRIPTION OF SYMBOLS 1 processing apparatus 12 measurement part 15 processing part 21a, 21b supply probe 22a, 22b measurement probe 50 surface resistivity identification process 71a, 71b supply position 72a, 72b measurement position 100 sheet body 101 surface J evaluation value Va, Vb measured value V 'Theoretical value ε Specified value ρ1, 22 Surface resistivity

Claims (6)

For a plurality of measurements which are respectively in contact with a plurality of measurement positions on the surface while supplying measurement signals through a pair of supply probes which are respectively in contact with two supply positions on the surface of the sheet body A measurement unit that measures the potential at each measurement position via the probe;
Identifying a first surface resistivity in a first direction on the surface and a second surface resistivity in a second direction different from the first direction on the surface based on the measurement value of the potential measured by the measurement unit A processing unit that executes surface resistivity identification processing;
The processing unit is a solution of the following equation (1) in the surface resistivity identification process, and includes a component of a position vector indicating the measurement position, the first surface resistivity, and the second surface resistivity. In the calculation formula using the parameter as a parameter, a component of a position vector indicating each measurement position, a first set value arbitrarily set as the first surface resistivity, and a second set value arbitrarily set as the second surface resistivity And calculate the theoretical value of the potential at each measurement position, and evaluate the degree of agreement between each measurement value specified based on each measurement value and each theoretical value and each theoretical value The evaluation value calculation process for calculating the evaluation value to be performed is repeatedly executed while changing the first set value and the second set value, and the first value when the evaluation value satisfies a prescribed condition defined in advance. Set value and second set value Processor for identifying a first surface resistivity and the second surface resistivity.
∇ · (σ′∇V _{(↑ r)} ) = − I (δ (↑ r− ↑ r _s ) −δ (↑ r− ↑ r _d )) (1) where σ ′ is the above-mentioned measurement position Represents a quadratic square matrix having elements of the conductivity of the sheet corresponding to the components of the position vector rr shown, where ∇ is a nabla operator and V _{(↑ r)} is represented by the position vector rr Represents the potential at the measurement position, I represents the current value of the measurement signal, δ represents the delta function, ↑ r _s represents a position vector indicating the supply position on the source side, and ↑ r _d represents the drain It represents a position vector indicating the supply position on the side. In the evaluation value calculation process, the processing unit sets one of the first direction and the second direction as an x-axis direction in the xy orthogonal coordinate system, and the other in the first direction and the second direction. The processing apparatus according to claim 1, wherein the theoretical value is calculated using the calculation equation which is a solution of the following equation (2) obtained by modifying the equation (1) as the y-axis direction in the xy orthogonal coordinate system.
(1 / ρ _x ) (∂ ² / ∂ _x ² ) V (x, y) + (1 / ρ _y ) (∂ ² / ∂ _y ² ) V (x, y) =-I (δ (x-x) _{s 2} ) δ (y-y _s ) -δ (x-x _d ) δ (y-y _d ) (2) where x represents the x coordinate of the measurement position in the xy orthogonal coordinate system, y Represents the y-coordinate of the measurement position in the xy orthogonal coordinate system, ρ _x represents one of the first surface resistivity and the second surface resistivity, and _{y y} represents the first surface resistivity and the first surface resistivity. Represents the other of the second surface resistivity, ∂ represents a partial differential symbol, V (x, y) represents a change in potential with x and y as parameters, and I represents a current value of the measurement signal, δ represents the delta function, x _s represents the x-coordinate of the position of supplying the source side of the xy rectangular coordinate system, y _s is the source in the xy rectangular coordinate system Y coordinate of the position of supplying, x _d represents the x-coordinate of the position of supplying the drain side in the xy rectangular coordinate system, the y _d a y coordinate of the position of supplying the drain side in the xy rectangular coordinate system Represent. The processing apparatus according to claim 2, wherein the processing unit calculates the theoretical value using the following equation (3) as the calculation equation which is a solution of the equation (2) in the evaluation value calculation process.
_{V (x, y, ρ x} , ρ y) = V 0 - (I / L x L y) Σ 'nx, ny (4/2 δnx, 0 + δ0, ny) [1 / (λ nx 2 / ρ x + λ ^{_{ny 2 / ρ y)] (}} cosλ nx x d cosλ ny y d -cosλ nx x s cosλ ny y s) cosλ nx xcosλ ny y ... (3) formula where, x is the measured position in the xy rectangular coordinate system represents an x coordinate, y represents ay coordinate of the measurement position in the xy orthogonal coordinate system, ρ _x represents any one of the first surface resistivity and the second surface resistivity, and _{y y} represents the second surface resistivity 1 represents the other of the surface resistivity and the second surface resistivity, and V (x, y, _x x, y _y ) represents a change in potential with x, y, _{x x} , _{y y} as a parameter, V ₀ Is a constant independent of x and y, and I represents the current value of the signal for measurement. L _x represents the length of the sheet in the xy orthogonal coordinate system in the x-axis direction, L _y represents the length of the sheet in the xy orthogonal coordinate system in the y-axis direction, and n is each Represents the number given to each measurement position, Σ 'represents the sum excluding the term nx = ny = 0, δ represents the Kronecker delta, λ _nx is nxπ / L _x , and λ _ny is nyπ / L _y , x _d represents the x-coordinate of the supply position on the drain side in the xy Cartesian coordinate system, y _d represents the y-coordinate of the supply position on the drain side in the xy Cartesian coordinate system, x _s Represents the x coordinate of the supply position on the source side in the xy rectangular coordinate system, and y _s represents the y coordinate of the supply position on the source side in the xy rectangular coordinate system.   The said measurement part calculates the residual value square sum of the difference value of the said measured value in each said measurement position, and the said theoretical value in an evaluation value calculation process as said evaluation value in any one of Claim 1 to 3 Processing unit.   The processing apparatus according to any one of claims 1 to 4, wherein the processing unit repeatedly executes the evaluation value calculation process until the evaluation value as the defined condition satisfies the condition that the evaluated value is less than or equal to the defined value. A plurality of measurement probes respectively brought into contact with a plurality of measurement positions on the surface while supplying measurement signals through a pair of supply probes respectively brought into contact with the two supply positions on the surface of the sheet body The potential at each measurement position is measured, and a first surface resistivity in a first direction on the surface and a second direction different from the first direction on the surface are measured based on the measured value of the measured potential. In the surface resistivity identification process for identifying the second surface resistivity,
It is a solution of the following equation (1), and each measurement position is calculated using a component of a position vector indicating each measurement position, the first surface resistivity, and the second surface resistivity as parameters. The theory of the potential at each of the measurement positions by substituting the component of the position vector to be shown, the first setting value arbitrarily set as the first surface resistivity, and the second setting value arbitrarily set as the second surface resistivity Evaluation value calculation processing for calculating a value and calculating an evaluation value for evaluating the degree of coincidence between each of the measured values specified based on the measured values and the theoretical values and the theoretical value; 1) The first set value and the second set value are repeatedly executed while changing the first set value and the second set value, and the first set value and the second set value are each set to the first value when the evaluation value satisfies a predetermined condition defined and defined in advance. The surface resistivity and the second surface resistivity Processing method for specifying Te.
∇ · (σ′∇V _{(↑ r)} ) = − I (δ (↑ r− ↑ r _s ) −δ (↑ r− ↑ r _d )) (1) where σ ′ is the above-mentioned measurement position Represents a quadratic square matrix having elements of the conductivity of the sheet corresponding to the components of the position vector rr shown, where ∇ is a nabla operator and V _{(↑ r)} is represented by the position vector rr Represents the potential at the measurement position, I represents the current value of the measurement signal, δ represents the delta function, ↑ r _s represents a position vector indicating the supply position on the source side, and ↑ r _d represents the drain It represents a position vector indicating the supply position on the side.

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