Evaluation program of electrode arrangement design, polishing device and evaluation method of electrode arrangement design

Abstract

To provide an evaluation program of electrode arrangement design which enables an operator to appropriately recognize a cross-sectional shape of a wafer during machining.SOLUTION: An evaluation program 100 for evaluating the arrangement design of a pair of electrodes for detecting a resonance frequency of a wafer of a piezoelectric material during polishing of the wafer allows a computer to execute: electrode track calculation processing 101 of calculating electrode tracks which are tracks of the pair of electrodes when an object wafer is polished for a predetermined time, on the basis of predetermined information including an arrangement condition of the pair of electrodes; overlapping section calculation processing 102 of calculating overlapping sections passing on the object wafer, among the electrode tracks; effective section calculation processing 103 for calculating an effective section where the pair of electrodes simultaneously face the object wafer, among the overlapping sections; and ratio calculation processing 104 of calculating an effective ratio which is a ratio of the effective section in the overlapping section.SELECTED DRAWING: Figure 7

Description

Technical Field

[0001] The present invention relates to an evaluation program for evaluating the arrangement design of electrodes for detecting the resonance frequency of a wafer during polishing, a polishing apparatus for polishing a wafer, and a method for evaluating the arrangement design of electrodes.

Background Art

[0002] Conventionally, for example, a polishing apparatus is known that measures the thickness of a wafer by optical means such as the optical reflection interference method, and generates and displays a shape drawing line indicating the cross-sectional shape of the wafer based on the acquired thickness data (see, for example, Patent Document 1).

[0003] Also, it is known that the resonance frequency of a piezoelectric material such as quartz is determined depending on its thickness dimension. Therefore, when polishing a wafer made of a piezoelectric material, in order to process it to a predetermined thickness that can obtain desired frequency characteristics, a pair of electrodes are provided on the surface plate, a predetermined frequency sweep signal is applied from one electrode, and the frequency sweep signal that has passed through the wafer is acquired via the other electrode to obtain the resonance frequency of the wafer. A polishing apparatus capable of this is known (see, for example, Patent Documents 2 and 3).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0005] Incidentally, when measuring the thickness of a wafer by optical means in a polishing apparatus, it is necessary that the polishing liquid used is permeable. In a polishing environment using a non-permeable polishing liquid, the light that should originally be irradiated onto the wafer is blocked by the polishing liquid, and the purpose of thickness measurement cannot be achieved. Also, in the method of measuring the thickness of a wafer using optical means, based on the origin (center) positions of each of the internal gear, sun gear, surface plate, etc., the position of the wafer and the position of the thickness measuring device are grasped, and an example is common where a shape drawing line is generated while collating the irradiation position of the measurement light by the thickness measuring device with the position of the internal gear etc. in the polishing apparatus. In such measuring means for grasping position information, the origin position information of each gear and surface plate, the set position information of the wafer, the origin position information of the carrier, etc. are basically required.

[0006] On the other hand, in the case of measuring means for acquiring the resonance frequency of a wafer, regardless of whether the polishing liquid is permeable or not, it is possible to measure the resonance frequency of the wafer as long as a certain degree of conductivity from the measuring device to the wafer can be ensured. Also, in the device configuration, even when not calculating the position information etc. of the wafer, it is theoretically possible to obtain information on the cross-sectional shape of the wafer due to the characteristic of the continuity of the resonance frequency data. On the other hand, in a conventional polishing apparatus using a measuring device, a shape drawing line showing the cross-sectional shape of the wafer has not been generated from the resonance frequency data of the wafer. Therefore, it has been difficult for the operator of the polishing apparatus to grasp the cross-sectional shape of the wafer during polishing.

[0007] Furthermore, when the arrangement of the electrodes for detecting the resonance frequency changes, the trajectory of the electrodes during wafer polishing changes, resulting in fluctuations in the measurement results such as fluctuations in the signal intensity for detecting the resonance frequency or the inability to obtain a signal. In addition, a situation may occur where the electrodes cannot pass properly over the wafer, and the opportunity for measurement is not obtained or decreases. That is, the detection accuracy of the resonance frequency of the wafer varies depending on the electrode arrangement design, and the situation of generating the shape drawing line indicating the cross-sectional shape of the wafer also changes depending on the electrode arrangement design. Therefore, in order to accurately let the operator grasp the cross-sectional shape of the wafer during processing, in addition to using a system for measuring the resonance frequency of the wafer, it is required to perform an appropriate electrode arrangement design.

[0008] The present invention has been made paying attention to the above problems, and an object thereof is to provide an evaluation program for electrode arrangement design, a polishing apparatus, and an evaluation method for electrode arrangement design that can appropriately let the operator of the polishing machine recognize the cross-sectional shape of the wafer during processing.

Means for Solving the Problems

[0009] To achieve the above object, the evaluation program for electrode arrangement design of the present invention is an evaluation program for evaluating the electrode arrangement design in a polishing apparatus in which a pair of electrodes for detecting the resonance frequency of a wafer made of a piezoelectric material is attached to a surface plate. The evaluation program includes: an electrode trajectory calculation process for calculating an electrode trajectory, which is the trajectory of the pair of electrodes when an arbitrary wafer is polished for a predetermined time, based on predetermined information including the arrangement conditions of the pair of electrodes; a overlapping section calculation process for calculating the length of an overlapping section, which is a section passing over the arbitrary wafer, among the electrode trajectories; a valid section calculation process for calculating the length of a valid section, which is a section where the pair of electrodes simultaneously face the arbitrary wafer, among the overlapping sections; and a ratio calculation process for calculating a valid ratio, which is the ratio of the valid section in the overlapping section, and causing a computer to execute these processes.

[0010] To achieve the above object, a polishing apparatus of the present invention includes a polishing machine that polishes a wafer made of a piezoelectric material with a surface plate, a first electrode and a second electrode attached to the surface plate and having tip surfaces facing the wafer, a frequency calculation unit that applies a predetermined frequency sweep signal from the first electrode to the wafer and calculates the resonance frequency of the wafer based on the frequency sweep signal received by the second electrode, a shape drawing unit that generates a shape drawing line indicating the cross-sectional shape of the wafer based on the resonance frequency, and a display that displays the shape drawing line.

[0011] To achieve the above object, an evaluation method for the electrode arrangement design of the present invention is an evaluation method for the electrode arrangement design in a polishing apparatus in which a pair of electrodes for detecting the resonance frequency of a wafer made of a piezoelectric material during polishing of the wafer are attached to a surface plate, and is executed by a computer equipped with an evaluation program for evaluating the electrode arrangement design. Based on predetermined information including the arrangement conditions of the pair of electrodes, a step of calculating an electrode trajectory that is the trajectory of the pair of electrodes when an arbitrary wafer is polished for a predetermined time, a step of calculating the length of an overlapping section that is a section passing over the arbitrary wafer among the electrode trajectories, a step of calculating the length of an effective section that is a section where the pair of electrodes face the arbitrary wafer simultaneously among the overlapping sections, a step of calculating an effective ratio that is the ratio of the effective section in the overlapping section, and a step of comparing the effective ratio with a predetermined threshold value and evaluating the electrode arrangement design.

Advantages of the Invention

[0012] In the evaluation program for the electrode arrangement conditions, the polishing apparatus, and the evaluation method for the electrode arrangement conditions of the present invention, the cross-sectional shape of the wafer can be appropriately recognized by the operator of the polishing machine during processing.

Brief Description of the Drawings

[0013]

Figure 1

Figure 2

Figure 3

Figure 4A

Figure 4B

Figure 4C

Figure 5A

Figure 5B

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10A

Figure 10B

Figure 10C

Figure 11

Embodiments for Carrying Out the Invention

[0014] Hereinafter, embodiments for implementing the polishing apparatus, the evaluation program for the electrode arrangement design, and the evaluation method for the electrode arrangement design of the present invention will be described based on Example 1 shown in the drawings.

[0015] [Polishing Apparatus] The polishing apparatus 1 of Example 1 is a double-sided polishing apparatus that polishes the front and back surfaces of a thin plate disk-shaped wafer W made of a piezoelectric material such as quartz or ceramic. Note that the "piezoelectric material" is a crystal material that can generate an electric current when pressure is applied.

[0016] As shown in FIG. 1, the polishing apparatus 1 includes a polishing machine 10, a frequency detector 20, and a control unit 30.

[0017] The polishing machine 10 sandwiches the wafer W between a lower platen 11 and an upper platen 12 disposed opposite to the lower platen 11, and relatively moves the lower platen 11, the upper platen 12, and the wafer W in a state where a load is applied to the wafer W to simultaneously polish the front and back surfaces of the wafer W. Note that the polishing machine 10 may be a single-sided polishing apparatus that polishes one surface of the wafer W by the lower platen 11 or the upper platen 12.

[0018] The polishing machine 10 includes a donut disk-shaped lower platen 11 and an upper platen 12 concentrically arranged with the axis L1 at the center, a sun gear 13 rotatably disposed at the central portion of the lower platen 11, an internal gear 14 disposed on the outer peripheral side of the lower platen 11, and a disk-shaped carrier plate 15 disposed between the lower platen 11 and the upper platen 12 and having a wafer holding hole 15a (see FIG. 2). A polishing pad 11a is attached to the upper surface of the lower platen 11, and a polishing pad 12a is attached to the lower surface of the upper platen 12. Further, the upper platen 12 is provided with a supply hole (not shown) for supplying polishing slurry.

[0019] The carrier plate 15 has gears formed on its outer peripheral edge and meshes with the sun gear 13 and the internal gear 14 as shown in FIG. 2. Then, as the sun gear 13 and the internal gear 14 rotate, the carrier plate 15 rotates (revolves) around the axis L1 while rotating on its own axis.

[0020] The wafer W is disposed inside the wafer holding hole 15a of the carrier plate 15. Then, with the wafer W sandwiched between the polishing pad 11a attached to the rotating lower platen 11 and the polishing pad 12a attached to the rotating upper platen 12, the carrier plate 15 rotates on its own axis and revolves, causing the lower platen 11 and the upper platen 12 and the wafer W to move relative to each other, and the wafer W is polished by the polishing pads 11a and 12a. That is, the surfaces of the polishing pads 11a and 12a become polishing surfaces for polishing the wafer W.

[0021] Note that the polishing pads 11a and 12a are used when polishing the wafer W by polishing. The polishing pads 11a and 12a may not be used when the wafer W is polished by lapping. Here, "lapping" means polishing at a relatively high rate using coarse abrasive grains, and "polishing" means polishing at a relatively low rate using fine abrasive grains to improve the surface quality.

[0022] The upper platen 12 is fixed to the rod 16 via the support studs 16a and the mounting members 16b attached to the upper surface. The rod 16 is extended and contracted along the vertical direction by the fifth driving device M5, and the upper platen 12 moves up and down as the rod 16 extends and contracts. Then, a predetermined load is applied to the wafer W from the upper platen 12 according to the extended and contracted length of the rod 16.

[0023] Further, at the center of the polishing machine 10, a first drive shaft 17a standing along the axis L1 is arranged. The first drive shaft 17a is a shaft that is rotated by a first drive device M1. A driver 18 is fixed to the upper end of the first drive shaft 17a, and the driver 18 rotates integrally with the first drive shaft 17a. Further, a groove portion (not shown) for engaging with a hook 12b provided on the upper surface plate 12 is formed on the outer peripheral surface of the driver 18. When the rod 16 extends and the upper surface plate 12 moves downward and the hook 12b engages with the groove portion of the driver 18, the driver 18 and the upper surface plate 12 can rotate integrally.

[0024] A second drive shaft 17b is fixed in a penetrating state to a hole 13a at the center of the sun gear 13. The second drive shaft 17b is a hollow tube with both ends open, and the first drive shaft 17a penetrates therethrough rotatably. Further, the second drive shaft 17b is rotated by a second drive device M2.

[0025] A third drive shaft 17c is formed at the lower part of the center of the lower surface plate 11. The third drive shaft 17c is a hollow tube with both ends open, and the first drive shaft 17a and the second drive shaft 17b penetrate therethrough rotatably. Further, the third drive shaft 17c is rotated by a third drive device M3.

[0026] Further, a fourth drive shaft 17d is formed on the internal gear 14. The fourth drive shaft 17d is a hollow tube with both ends open, and the first drive shaft 17a, the second drive shaft 17b, and the third drive shaft 17c penetrate therethrough rotatably. Further, the fourth drive shaft 17d is rotated by a fourth drive device M4.

[0027] Furthermore, a pair of electrode holes are formed in the upper surface plate 12. Each electrode hole penetrates through the upper surface plate 12 and the polishing pad 12a, and a pair of electrodes (first electrode 21a, second electrode 21b) of the frequency detector 20 are inserted therein respectively.

[0028] As shown in FIG. 1, the frequency detector 20 includes a pair of electrodes (first electrode 21a and second electrode 21b) and a frequency calculation unit 22, and detects the resonance frequency of the wafer W during polishing by the frequency sweep method.

[0029] Here, the "frequency sweep method" is defined as a method for detecting the resonance frequency of the wafer W performed according to the following procedure. That is, first, during the polishing of the wafer W, a circuit is formed between a pair of electrodes (first electrode 21a and second electrode 21b) attached to the upper platen 12, the wafer W, and the lower platen 11, and a frequency sweep signal is applied to the wafer W via the first electrode 21a. Then, a response signal is acquired based on the signal received by the second electrode 21b. Here, when the frequency of the applied frequency sweep signal changes (sweeps) within an appropriate range, a resonance phenomenon occurs when the frequency approaches the natural vibration frequency of the wafer W, and the impedance decreases. Here, the signal intensity of the response signal varies according to the impedance. Therefore, the signal intensity of the acquired response signal is calculated, and when a variation in the signal intensity of a predetermined level or more is observed (when the influence of the impedance decrease phenomenon is confirmed), the frequency of the frequency sweep signal is detected as the resonance frequency (natural vibration frequency) of the wafer W at the position of the midpoint O3 (see FIG. 3) of the pair of electrodes (first electrode 21a and second electrode 21b).

[0030] The first electrode 21a is composed of a cylindrical metal member whose peripheral surface is covered with an insulating coating, and is inserted into one of the electrode holes and attached to the upper platen 12. The first electrode 21a has a tip surface exposed from the insulating coating facing the wafer W and is electrically connected to the frequency calculation unit 22. The first electrode 21a applies the frequency sweep signal output from the frequency calculation unit 22 toward the wafer W.

[0031] The second electrode 21b is composed of a cylindrical metal member whose peripheral surface is covered with an insulating coating, is inserted into the other electrode hole, and is attached to the upper platen 12. The tip surface of the second electrode 21b that is exposed from the insulating coating faces the wafer W and is electrically connected to the frequency calculation unit 22. The second electrode 21b receives the frequency sweep signal output from the first electrode 21a. Note that the configurations of the first electrode 21a and the second electrode 21b are not limited to the above configurations. Any electrodes that can appropriately apply and receive the frequency sweep signal between the first electrode 21a and the second electrode 21b can be used.

[0032] The positions where the first electrode 21a and the second electrode 21b are arranged are defined by the arrangement conditions including the condition of the distance between the first electrode 21a and the second electrode 21b (hereinafter referred to as "electrode distance ID"), the condition of the angle between the first electrode 21a and the second electrode 21b (hereinafter referred to as "electrode angle θ"), and the condition of the position of the midpoint O3 between the first electrode 21a and the second electrode 21b with respect to the center (axis L1) of the upper platen 12 (hereinafter referred to as "platen radial position").

[0033] As shown in FIG. 3, the electrode distance ID is the distance between the center O1 of the first electrode 21a and the center O2 of the second electrode 21b. Also, as shown in FIG. 3, the electrode angle θ is the angle formed by the straight line α connecting the center O1 of the first electrode 21a and the center O2 of the second electrode 21b and the tangent line β drawn in the circumferential direction r concentric with the upper platen 12 passing through the center O1 of the first electrode 21a. The midpoint O3 is the central position between the center O1 of the first electrode 21a and the center O2 of the second electrode 21b on the straight line α. The platen radial position is the position of the midpoint O3 on the straight line γ connecting the center (axis L1) of the upper platen 12 and the midpoint O3. The platen radial position is represented by a value that is 0% at the inner peripheral end 12x of the upper platen 12 and 100% at the outer peripheral end 12y of the upper platen 12, and is smaller the closer it is to the inner peripheral end 12x and larger the closer it is to the outer peripheral end 12y.

[0034] Further, as will be described later, the polishing apparatus 1 of Example 1 generates a shape drawing line indicating the cross-sectional shape of the wafer W based on the resonance frequency of the wafer W. When generating the shape drawing line, the polishing apparatus 1 of Example 1 can generate a clearer shape drawing line if the resonance frequency of the wafer W is appropriately detected. Therefore, in order to improve the generation accuracy of the shape drawing line, it is necessary to appropriately detect the resonance frequency of the wafer W by the frequency detector 20. On the other hand, in the electrode arrangement design, it has been found that by changing the inter-electrode distance ID, the inter-electrode angle θ, and the platen radial position respectively, the detection accuracy of the resonance frequency of the wafer W changes, and the generation accuracy of the shape drawing line fluctuates.

[0035] That is, the inter-electrode distance ID, the inter-electrode angle θ, and the platen radial position are all parameters that vary the generation accuracy of the shape drawing line of the wafer W. The reasons why each parameter varies the generation accuracy of the shape drawing line of the wafer W are as follows.

[0036] As shown in FIG. 4(A), when the inter-electrode distance ID is set to an appropriate distance, the frequency sweep signal (indicated by the broken line) output from the first electrode 21a passes through the wafer W and is received by the second electrode 21b. Therefore, when the inter-electrode distance ID is set to an appropriate distance, the frequency detector 20 can acquire a stable response signal and can appropriately detect the resonance frequency. Therefore, it becomes possible to generate a clear shape drawing line.

[0037] On the one hand, when the distance between the first electrode 21a and the second electrode 21b is sufficiently small, it is presumed that the frequency sweep signal is input directly from the first electrode 21a to the second electrode 21b through only the polishing slurry (without passing through the wafer W) with less resistance than being received by the second electrode 21b through the wafer W. Therefore, as shown in Fig. 4(B), when the inter-electrode distance ID is set shorter than the appropriate distance (the electrodes are too close to each other), the proportion of the frequency sweep signal short-circuiting without passing through the wafer W increases. In this case, compared with the case where the inter-electrode distance ID is set to the appropriate distance, the peak value of the response signal may become smaller or the response signal may become unstable. As a result, the frequency detector 20 cannot appropriately detect the resonance frequency, and the generated shape drawing line is likely to be disturbed.

[0038] Also, the frequency sweep signal may pass not only through the wafer W but also through the polishing slurry and the carrier plate 15 before being output from the first electrode 21a and received by the second electrode 21b. However, the presence of the polishing slurry and the carrier plate 15 is a factor contributing to the resistance of signal transmission. Therefore, as shown in Fig. 4(C), when the inter-electrode distance ID is set longer than the appropriate distance (the electrodes are too far from each other), the resistance of the intermediate path until the frequency sweep signal output from the first electrode 21a is received by the second electrode 21b increases, or the transmission path of the frequency sweep signal becomes complicated, so that variations in the response signal are likely to occur. Furthermore, it becomes difficult for the first electrode 21a and the second electrode 21b to simultaneously face the wafer W. As a result, compared with the case where the inter-electrode distance ID is set to the appropriate distance, the peak value of the response signal becomes smaller, the frequency detector 20 cannot appropriately detect the resonance frequency, and variations are likely to occur in the generation accuracy of the shape drawing line.

[0039] In this way, the detection accuracy of the resonance frequency of the frequency detector 20 changes according to the electrode gap ID, and as a result, the generation accuracy of the shape drawing line of the wafer W fluctuates. Therefore, it can be said that the electrode gap ID is a parameter that varies the generation accuracy of the shape drawing line of the wafer W. The appropriate distance of the electrode gap ID is preferably 1 mm to 500 mm regardless of the surface plate size, more preferably the electrode gap ID is 6 mm to 150 mm, and even more preferably the electrode gap ID is 10 mm to 30 mm.

[0040] On the other hand, in the frequency detector 20, it is possible to acquire the response signal more stably when the response signal is acquired in a state where both the first electrode 21a and the second electrode 21b face the wafer W simultaneously than when the response signal is acquired in a state where only one of the first electrode 21a or the second electrode 21b faces the wafer W.

[0041] On the contrary, when the wafer W moves relative to the first electrode 21a and the second electrode 21b as the wafer W is polished, when the relative movement of the wafer W and the first electrode 21a and the second electrode 21b is along the circumferential direction r concentric with the upper surface plate 12, when the inter-electrode angle θ is incident on the wafer W at 0°, as shown in FIG. 5A, after the first electrode 21a faces the wafer W, it takes time until both the first electrode 21a and the second electrode 21b face the wafer W. Therefore, the time during which the pair of electrodes (the first electrode 21a, the second electrode 21b) face the wafer W simultaneously is relatively short, and the acquisition of the response signal tends to be unstable.

[0042] On the other hand, when the relative movement of the wafer W, the first electrode 21a, and the second electrode 21b is performed along the circumferential direction r concentric with the upper dead center 12, when the inter-electrode angle θ is incident on the wafer W at 90°, as shown in FIG. 5B, both the first electrode 21a and the second electrode 21b begin to face the wafer W almost simultaneously, and at almost the same timing, the first electrode 21a and the second electrode 21b completely face the wafer W. Therefore, the time during which the pair of electrodes (the first electrode 21a and the second electrode 21b) face the wafer W can be made relatively long, and it becomes possible to stably acquire the response signal. That is, when the first electrode 21a and the second electrode 21b relatively approach the wafer W, it is desirable that the two electrodes (the first electrode 21a and the second electrode 21b) begin to face the wafer W as simultaneously as possible.

[0043] As described above, depending on the relative movement trajectory of the wafer W, the first electrode 21a, and the second electrode 21b and the inter-electrode angle θ, the time required from when at least one of the first electrode 21a or the second electrode 21b begins to face the wafer W until both the first electrode 21a and the second electrode 21b are in a state of completely facing the wafer W is different, and the stability of acquiring the response signal changes. Therefore, it can be said that the inter-electrode angle θ is a parameter that varies the generation accuracy of the shape drawing line of the wafer W. Note that the appropriate numerical range of the inter-electrode angle θ may change depending on conditions such as the inter-electrode distance ID and the position in the chuck diameter direction.

[0044] Furthermore, the higher the number of times the response signal is acquired by the frequency detector 20, the higher the generation accuracy of the shape drawing line. However, while the carrier plate 15 rotates around the axis L1 while rotating (revolving) around the axis L1, the wafer W performs a planetary motion around the axis L1. For this reason, when the position in the radial direction of the surface plate is different, the orbits of the first electrode 21a and the second electrode 21b with respect to the wafer W change, and the number of times the response signal is acquired by the frequency detector 20 fluctuates. Here, when the position in the radial direction of the surface plate is set close to the inner peripheral end 12x or the outer peripheral end 12y of the upper surface plate 12, the number of times the response signal is acquired tends to decrease. Therefore, it can be said that the position in the radial direction of the surface plate is a parameter that varies the generation accuracy of the shape drawing line of the wafer W. And from the viewpoint of the acquisition frequency of these response signals, it is desirable that the position in the radial direction of the surface plate is set in the range of 10% to 80%, and it is more desirable that it is set in the range of 20% to 45% or 55% to 80%.

[0045] Also, in the polishing apparatus 1 of the first embodiment, according to the electrode arrangement design evaluated by the evaluation program 100 for electrode arrangement design described later and determined to be effective for generating the shape drawing line of the wafer W, the first electrode 21a and the second electrode 21b are arranged at predetermined positions on the upper surface plate 12.

[0046] As shown in FIG. 1, the frequency calculation unit 22 includes a frequency sweep unit 23, a signal detection unit 24, and a data processing unit 25.

[0047] The frequency sweep unit 23 generates and outputs a frequency sweep signal whose frequency is changed (swept) within a predetermined frequency range specified in advance.

[0048] Based on the frequency sweep signal received by the second electrode 21b, the signal detection unit 24 acquires a response signal that varies according to the impedance between the second electrode 21b and the lower surface plate 11. The response signal is input to the data processing unit 25.

[0049] The data processing unit 25 calculates the resonance frequency of the wafer W from the signal strength of the response signal input from the signal detection unit 24 and the frequency of the frequency sweep signal when the response signal is acquired. That is, the data processing unit 25 continuously monitors the signal strength while the frequency of the frequency sweep signal changes within a predetermined frequency range. Then, the frequency at which fluctuations in the signal strength associated with the resonance phenomenon are observed is taken as the resonance frequency at the position facing the midpoint O3 between the first electrode 21a and the second electrode 21b of the wafer W. The data of the resonance frequency is input to the control unit 30.

[0050] Then, the calculation of the resonance frequency by the data processing unit 25 is performed each time the frequency of the frequency sweep signal changes within a predetermined frequency range. That is, the resonance frequency data is continuously acquired at time intervals when the frequency of the frequency sweep signal changes. Note that the data processing unit 25 does not calculate the resonance frequency if the maximum value of the signal strength acquired while the frequency of the frequency sweep signal changes within a predetermined frequency range is less than a predetermined value. This is because it is estimated that the midpoint O3 between the first electrode 21a and the second electrode 21b is not facing the wafer W in this case.

[0051] The control unit 30 consists of a CPU (Central Processing Unit) etc. As shown in FIG. 1, it includes a device control unit 31, a shape drawing unit 32, a display control unit 33, a memory 34, etc. Further, an input device 41 operable by the operator of the polishing apparatus 1 and a display 42 visible to the operator are connected to the control unit 30.

[0052] The device control unit 31 outputs control commands to the first to fifth drive devices M1 to M5 based on the processing target and various conditions of the wafer W input by the operator via the input device 41, the program stored in the memory 34, the cross-sectional shape information of the wafer W calculated by the shape drawing unit 32, etc., and controls the operation of the polishing machine 10.

[0053] The shape drawing unit 32 utilizes the fact that the resonance frequency (natural frequency) of the wafer W varies depending on the thickness of the wafer W, calculates the cross-sectional shape of the wafer W based on the data of the resonance frequency of the wafer W detected by the frequency detector 20, and generates a cross-sectional shape line T1 as shown in FIG. 6. The cross-sectional shape line T1 is a shape drawing line indicating the cross-sectional shape of the wafer W, and is periodically generated at regular time intervals during the polishing process of the wafer W.

[0054] Also, the shape drawing unit 32 generates the cross-sectional shape line T1 without grasping the position information of the wafer W during the polishing process of the wafer W. Here, the cross-sectional shape line T1 is output as long as an appropriate resonance frequency is continuously obtained sufficiently when the first electrode 21a and the second electrode 21b pass over the wafer. Further, the shape drawing unit 32 instantaneously converts the resonance frequency data input from the frequency detector 20 into thickness data of the wafer W, and can display the cross-sectional shape line T1 obtained by plotting the obtained thickness data at equal intervals on the screen as the shape drawing line of the wafer W. At that time, the start point and the end point of the continuous thickness data of the wafer W may be used as the values of the outer peripheral end portions of the cross-sectional shape of the wafer W, respectively.

[0055] Note that a shape drawing line generated based on the data of the resonance frequency obtained at a position deviated from the vicinity of the center of the wafer W is not suitable as a shape drawing line indicating the cross-sectional shape of the wafer W. Therefore, the shape drawing unit 32 of the first embodiment does not use the data of the resonance frequency obtained at a position deviated from the vicinity of the center of the wafer W for generating the shape drawing line. As a result, the shape drawing unit 32 can generate a more accurate shape drawing line.

[0056] Here, the shape drawing unit 32 of Example 1 does not grasp the position information of the wafer W. Therefore, in order not to use the resonance frequency data obtained at a position deviated from the vicinity of the center of the wafer W for generating the shape drawing line, specifically, when the resonance frequency data is continuously input from the frequency detector 20 a predetermined number of times (for example, any number from 5 to 20 times can be set) or more, the shape drawing unit 32 generates a shape drawing line based on the resonance frequency data. And when the resonance frequency data is not continuously input a predetermined number of times or more, it is estimated that the data is when the midpoint O3 of the first electrode 21a and the second electrode 21b passes through the edge of the wafer W, and the shape drawing unit 32 does not generate a shape drawing line of the wafer W. As a result, the shape drawing unit 32 can exclude the resonance frequency data obtained at a position deviated from the vicinity of the center of the wafer W from the generation of the shape drawing line. This is one of the methods to improve the reliability of the shape drawing line.

[0057] The display control unit 33 controls the display content displayed on the display 42. The display control unit 33 causes the display 42 to promptly display the shape drawing line (cross-sectional shape line T1) of the wafer W generated by the shape drawing unit 32 each time it is generated. That is, each time a new shape drawing line of the wafer W is generated, the display 42 switches to and displays the new shape drawing line. Thereby, the operator of the polishing apparatus 1 can grasp the cross-sectional shape of the wafer W that changes moment by moment during the polishing process almost simultaneously (in real time) with the polishing operation of the wafer W by visually recognizing the shape drawing line of the wafer W displayed on the display 42, and can recognize the transition of the shape change.

[0058] [Evaluation Program for Electrode Arrangement Design] The evaluation program 100 for the electrode arrangement design of Example 1 is installed in any computer (personal computer, notebook or tablet computer, smartphone, cloud server, non-cloud server device, etc.). And the evaluation program 100 for the electrode arrangement design of Example 1 is used when designing the electrode arrangement in a polishing apparatus 1 etc. where a pair of electrodes (first electrode 21a, second electrode 21b) for detecting the resonance frequency of the wafer W is attached to the upper platen 1 during the polishing of the wafer W made of a piezoelectric material. It causes a computer to execute a plurality of processes described later to evaluate the electrode arrangement design in the polishing apparatus 1 etc.

[0059] That is, as shown in FIG. 7, the evaluation program 100 for the electrode arrangement design of Example 1 causes a computer to execute an electrode trajectory calculation process 101, an overlapping section calculation process 102, an effective section calculation process 103, a ratio calculation process 104, and a design evaluation process 105 in this order.

[0060] The electrode trajectory calculation process 101 is a process of calculating an electrode trajectory EO (see FIG. 9), which is the trajectory of the midpoint O3 (see FIG. 3) of a pair of electrodes (first electrode 21a, second electrode 21b) when an arbitrary wafer W is polished for a predetermined time, based on predetermined information including the arrangement conditions of the pair of electrodes (first electrode 21a, second electrode 21b).

[0061] Note that the arrangement conditions of the pair of electrodes (first electrode 21a, second electrode 21b) used when calculating the electrode trajectory EO in the electrode trajectory calculation process 101 include at least the inter-electrode distance ID, the inter-electrode angle θ, and the position in the radial direction of the platen. Also, the predetermined information other than the arrangement conditions includes, for example, device data such as the polishing apparatus 1 etc., polishing conditions, information on the wafer W to be polished, and the like.

[0062] The overlapping section calculation process 102 calculates the length of an overlapping section S OV (see FIG. 9), which is a section that passes over an arbitrary wafer W during a predetermined time.

[0063] The effective interval calculation process 103 calculates the length of the effective interval S OV which is the interval in which a pair of electrodes (the first electrode 21a and the second electrode 21b) simultaneously face an arbitrary wafer W VA (see FIG. 9) among the overlapping intervals S calculated by the overlapping interval calculation process 102.

[0064] The ratio calculation process 104 calculates the effective ratio ER which is the ratio of the effective interval S OV in the overlapping interval S VA to the overlapping interval S.

[0065] The design evaluation process 105 compares the effective ratio ER calculated by the ratio calculation process 104 with a preset predetermined threshold value, and evaluates the electrode arrangement design in the polishing apparatus 1. In the design evaluation process 105, the evaluation result of the electrode arrangement design may be displayed on a display device included in the computer or a display device provided separately from the computer.

[0066] [Evaluation method of electrode arrangement design] The evaluation procedure of the evaluation method of the electrode arrangement design in the evaluation program 100 of Example 1 is shown in the flowchart shown in FIG. 8. The evaluation method shown in FIG. 8 is executed by a computer equipped with the evaluation program 100 of the electrode arrangement design when designing the electrode arrangement in the polishing apparatus 1 or the like.

[0067] Hereinafter, the evaluation method of the electrode arrangement design of Example 1 will be described based on the flowchart shown in FIG. 8.

[0068] In step S1, the computer reads predetermined information necessary to calculate the trajectories of the wafer W and the pair of electrodes (first electrode 21a and second electrode 21b) during polishing, and proceeds to step S2. Here, the information read by the computer includes at least information regarding the device data of the polishing apparatus 1 that polishes the wafer W, information regarding the polishing conditions of the wafer W polished by the polishing apparatus 1, information regarding the wafer W polished by the polishing apparatus 1, and information regarding the arrangement conditions of the pair of electrodes (first electrode 21a and second electrode 21b) attached to the polishing apparatus 1. Each piece of information may be appropriately input by an operator of the computer, or may be read from a memory installed in the computer.

[0069] Note that the device data is, for example, the respective diameter dimensions (sizes) of the lower platen 11, upper platen 12, sun gear 13, internal gear 14, and carrier plate 15 in the polishing apparatus 1, etc., and the respective number of teeth of the sun gear 13, internal gear 14, and carrier plate 15, etc. Also, the polishing conditions are, for example, the respective rotational speeds of the lower platen 11, upper platen 12, sun gear 13, and internal gear 14, etc. Further, the wafer information is, for example, the size and shape of the wafer W to be polished, the arrangement position information of the wafer W within the carrier plate 15, etc. The polishing conditions and wafer information may be standard information determined according to the polishing apparatus 1, etc.

[0070] And the arrangement conditions of the pair of electrodes (first electrode 21a and second electrode 21b) differ according to the electrode arrangement design in the polishing apparatus 1, and include at least the electrode interval ID, the electrode angle θ, and the position in the platen diameter direction.

[0071] In step S2, following the reading of the predetermined information in step S1, the computer calculates the electrode trajectory EO (see FIG. 9) and proceeds to step S3. Here, the "electrode trajectory EO" is the trajectory of the midpoint O3 when an arbitrary wafer W (hereinafter referred to as "target wafer W'") polished at an arbitrary position on the lower platen 11 is polished for a preset predetermined time (for example, 250 seconds to 350 seconds). The electrode trajectory EO is calculated, for example, according to the following procedure.

[0072] First, the computer calculates the rotation orbit of the target wafer W´ (shown hatched in FIGS. 10A to 10C) with respect to the center (axis L1) of the upper platen 12 based on the following formulas (1) and (2). Note that the "rotation orbit of the target wafer W´" is the orbit of the center of the target wafer W´ when the target wafer W´ is polished for a predetermined time. Xwafer = C radius × cos(C revolution × i × UT × π / 180) + W position × cos(C rotation × i × UT × π / 180) ···(1) Ywafer = C radius × sin(C revolution × i × UT × π / 180) + W position × sin(C rotation × i × UT × π / 180) ···(2) Here, Xwafer: X coordinate of the target wafer W´ at the center of the upper platen Ywafer: Y coordinate of the target wafer W´ at the center of the upper platen C radius: Radius of the central orbit during polishing of the carrier plate 15 C revolution: Revolution speed of the carrier plate 15 [rpm] C rotation: Rotation speed of the carrier plate 15 [rpm] W position: Distance between the center of the carrier plate 15 and the center of the target wafer W´ i: Arbitrary integer UT: Arbitrary time unit [msec] Let it be so.

[0073] Next, the computer calculates the rotation orbit RO1 (see FIG. 10A) of the first electrode 21a and the second electrode 21b with respect to the center (axis L1) of the upper platen 12 based on the following formulas (3) and (4). Note that the rotation orbit of the first electrode 21a and the rotation orbit of the second electrode 21b are calculated individually, but in FIGS. 10A to 10C, each rotation orbit is shown overlapping. Also, the "rotation orbit of the first electrode 21a" is the orbit of the center O1 of the first electrode 21a when the target wafer W´ is polished for a predetermined time. The "rotation orbit of the second electrode 21b" is the orbit of the center O2 of the second electrode 21b when the target wafer W´ is polished for a predetermined time. X electrode = D radius × cos(U rotation × i × UT × π / 180) ···(3) Y electrode = D radius × sin(U rotation × i × UT × π / 180) ···(4) Here, X electrode: the X coordinate of the first electrode 21a or the second electrode 21b at the center of the upper platen Y electrode: the Y coordinate of the first electrode 21a or the second electrode 21b at the center of the upper platen D radius: the radius of the central orbit during polishing of the first electrode 21a or the second electrode 21b U rotation: the rotation speed of the upper platen 12 [rpm] Let it be so.

[0074] Subsequently, the computer converts the rotation orbit RO1 of the first electrode 21a and the second electrode 21b with respect to the center (axis L1) of the upper platen 12 into an orbit RO2 (see FIG. 10B) on the coordinates with respect to the center W' of the target wafer W' based on the following formulas (5) and (6). O to the orbit RO2 (see FIG. 10B) on the coordinates with respect to the center W' of the target wafer W'. X electrode 2 = X electrode - Xwafer ···(5) Y electrode 2 = Y electrode - Ywafer ···(6) Here, X electrode 2: the X coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W' Y electrode 2: the Y coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W' Let it be so.

[0075] Then, the computer cancels the rotation of the carrier plate 15 and obtains the rotation orbit RO3 (see FIG. 10C) of the first electrode 21a and the second electrode 21b shown by fixing the positional relationship between the carrier plate 15 holding the target wafer W' and the target wafer W' based on the following formulas (7) and (8). X electrode 3 = X electrode 2 × cos(-C rotation × i × UT × π / 180) - Y electrode 2 × sin(-C rotation × i × UT × π / 180) ···(7) Y electrode 3 = X electrode 2 × sin(-C rotation × i × UT × π / 180) + Y electrode 2 × cos(-C rotation × i × UT × π / 180) ···(8) Here, X electrode 3: the X coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W' when the positional relationship between the carrier plate 15 and the wafer W is fixed Y electrode 3: The Y coordinate of the first electrode 21a or the second electrode 21b at the center of the target wafer W' when the positional relationship between the carrier plate 15 and the wafer W is fixed shall be used.

[0076] Then, the computer obtains the rotation orbit RO3 of the first electrode 21a and the orbit at the central position of the rotation orbit RO3 of the second electrode 21b as the "electrode orbit EO", which is the orbit of the midpoint O3.

[0077] In step S3, following the calculation of the electrode orbit EO in step S2, the computer determines whether the calculated electrode orbit EO passes over a reference region (the region inside the circle A indicated by the dashed line in FIG. 9) set on the target wafer W'. When the computer determines YES (passes over the reference region), it proceeds to step S4. When it determines NO (does not pass over the reference region), it proceeds to END.

[0078] Here, the "reference region" is a similar shape that coincides with the center of the target wafer W', and its radius is of a size that is a predetermined magnification (0.5 times to 0.7 times) of the radius of the target wafer W'. Note that when the electrode orbit EO does not pass over the reference region, the resonance frequency data is acquired only at positions deviated from the vicinity of the center of the wafer W, so that an accurate shape drawing line cannot be obtained. The size of the reference region can be set arbitrarily.

[0079] In step S4, following the determination in step S3 that the electrode orbit EO passes over the reference region, the computer extracts the overlapping section S OV (see FIG. 9) from the electrode orbit EO calculated in step S2 and proceeds to step S5. Here, the "overlapping section S OV " is a section that passes over the target wafer W' during a preset predetermined time (for example, 250 seconds to 350 seconds) among the electrode orbits EO calculated in step S2.

[0080] In step S5, for the overlapping section S in step S4 OVFollowing the extraction of the overlapping section S in step S4, the computer OV Then, the length of the overlapping section S is calculated, and the process proceeds to step S6. OV If multiple are extracted, the overlapping interval S OV Calculate the length for each.

[0081] In step S6, the overlapping section S in step S5 is OV Following the calculation of VA (see FIG. 9) and proceed to step S7. VA " refers to the overlapping section S extracted in step S4. OV In this section, a pair of electrodes (first electrode 21a and second electrode 21b) simultaneously face the target wafer W'. Also, as shown in FIG. 9, the overlapping section S OV If multiple are extracted, the overlapping interval S OV Each valid section S VA Extract the valid section S VA is an interval in which the following expressions (9) and (10) are simultaneously satisfied. First distance≦radius of target wafer W′ (9) second distance≦radius of target wafer W′ (10) Here, the first distance is the distance from the center O1 of the first electrode 21a to the center W' of the target wafer W'. O Distance to Second distance: from the center O2 of the second electrode 21b to the center W' of the target wafer W' O Distance to Let us assume that.

[0082] In step S7, the valid section S in step S6 is VA Following the extraction of the valid interval S, the computer VA Then, the length of the valid section S is calculated, and the process proceeds to step S8. VA If multiple are extracted, the validity interval S VA Calculate the length for each.

[0083] In step S8, the valid section S in step S7 isVA Following the operation of VA , the computer calculates the effective ratio ER and proceeds to step S9. Here, the "effective ratio ER" refers to the ratio of the length of the effective interval S OV to the length of the overlapping interval S VA . The effective ratio ER is calculated by the following formula (11). As shown in FIG. 9, when multiple overlapping intervals S OV are extracted, the effective ratio ER is calculated for each overlapping interval S OV , and the average value of the calculated multiple effective ratios ER is taken as the final effective ratio ER. Effective ratio ER [%] = Effective interval S VA ÷ Overlapping interval S OV × 100 ··· (11)

[0084] In step S9, following the calculation of the effective ratio ER in step S8, the computer compares the effective ratio ER calculated in step S8 with a preset predetermined threshold value to evaluate the electrode arrangement design of a pair of electrodes (the first electrode 21a and the second electrode 21b) in the polishing apparatus 1, and proceeds to the end. Note that the evaluation result of the electrode arrangement design evaluated in step S9 may be displayed on a display device provided in the computer or a display device connected to the computer by wire or wirelessly.

[0085] Here, the threshold value compared with the effective ratio ER is set to an arbitrary value. For example, based on an effective region set within a predetermined range from the center of the wafer W, it is set to a value between 90% and 85%.

[0086] Hereinafter, the operation of the polishing apparatus 1 of Example 1 will be described.

[0087] In the polishing apparatus 1 of Example 1, in order to improve the processing accuracy of the wafer W and appropriately perform the setting management of the polishing conditions, it is desired to appropriately let the operator grasp the state and shape of the wafer W during the polishing process in real time (substantially simultaneously with the polishing operation of the wafer W by the polishing apparatus 1).

[0088] On the other hand, the polishing apparatus 1 of Example 1 includes a polishing machine 10 that polishes a wafer W made of a piezoelectric material by means of a surface plate (lower surface plate 11 and upper surface plate 12), a first electrode 21a and a second electrode 21b that are attached to a predetermined position of the upper surface plate 12 and whose tip surfaces face the wafer W, a frequency calculation unit 22 that applies a predetermined frequency sweep signal from the first electrode 21a to the wafer and calculates the resonance frequency of the wafer W based on the frequency sweep signal received by the second electrode 21b, a shape drawing unit 32 that generates a shape drawing line indicating the cross-sectional shape of the wafer W based on the resonance frequency, and a display 42 that displays the shape drawing line.

[0089] Accordingly, the polishing apparatus 1 of Example 1 can detect the resonance frequency of the wafer W by the frequency sweep method during the polishing of the wafer W, generate a shape drawing line indicating the cross-sectional shape of the wafer W based on the detected resonance frequency, and display it on the display 42. Here, when the shape drawing line is generated based on the resonance frequency, the polishing apparatus 1 does not need to grasp the position information of the wafer W and the like. That is, the polishing apparatus 1 of Example 1 can generate a shape drawing line indicating the cross-sectional shape of the wafer W by instantaneously converting the continuously input resonance frequency data into thickness data of the wafer W and plotting it.

[0090] Accordingly, the polishing apparatus 1 of Example 1 can shorten the time required to generate the shape drawing line compared to the case where the thickness of the wafer W is measured by optical means or the like to generate the shape drawing line, and can generate and display the shape drawing line almost simultaneously (in real time) with the polishing operation of the wafer W. Then, by visually observing the shape drawing line displayed on the display 42, the operator can recognize the cross-sectional shape of the wafer W being polished almost in real time. Therefore, the polishing apparatus 1 of Example 1 can appropriately allow the operator to grasp the cross-sectional shape of the wafer W during processing.

[0091] And by appropriately allowing the operator to grasp the cross-sectional shape of the wafer during processing, the operator can accurately adjust the polishing conditions, polishing time, etc., and obtain a desired wafer W.

[0092] Further, when detecting the resonance frequency of the wafer W by the frequency sweep method, if the polishing apparatus 1 cannot sufficiently acquire the data of the resonance frequency of the wafer W, the shape drawing line may become unclear, or there may be variations in the generation accuracy of the shape drawing line, and an appropriate shape drawing line cannot be generated. As a result, the operator may not be able to appropriately grasp the cross-sectional shape of the wafer W during processing.

[0093] That is, in order to generate a clear shape drawing line or suppress variations in the generation accuracy of the shape drawing line, it is necessary to accurately detect the resonance frequency of the wafer W at predetermined intervals by the frequency detector 20. However, depending on the arrangement conditions of the pair of electrodes (the first electrode 21a and the second electrode 21b), the resonance frequency cannot be continuously detected, and as a result, there is a problem that an appropriate shape drawing line cannot be generated.

[0094] Furthermore, the arrangement positions of the pair of electrodes (the first electrode 21a and the second electrode 21b) are restricted in practice due to the design convenience in manufacturing the polishing machine 10. That is, in order to prevent interference between the pair of electrodes (the first electrode 21a and the second electrode 21b) and other components other than the electrodes provided on the upper surface plate 12, or to suppress deterioration of maintainability, there are restrictions on the arrangement positions of the first electrode 21a and the second electrode 21b. Therefore, among various restrictions, a design aimed at obtaining an optimal shape drawing line of the wafer W is desired for the arrangement design of the first electrode 21a and the second electrode 21b.

[0095] On the other hand, in the polishing apparatus 1 of the first embodiment, when designing the electrode arrangement, it is evaluated by the evaluation program 100 for the electrode arrangement design of the first embodiment. That is, in the polishing apparatus 1 of the first embodiment, a pair of electrodes (the first electrode 21a and the second electrode 21b) are arranged at predetermined positions on the upper surface plate 12 according to the electrode arrangement design evaluated by the evaluation program 100 of the first embodiment. Moreover, in the first embodiment, the arrangement positions of the first electrode 21a and the second electrode 21b are determined according to the electrode arrangement design determined to be effective for generating the shape drawing line of the wafer W by the evaluation program 100.

[0096] Thus, in the polishing apparatus 1 of Example 1, it is possible to manufacture after confirming in advance whether an appropriate shape drawing line of the wafer W can be obtained during polishing with an arbitrarily designed electrode arrangement. Then, by arranging the first electrode 21a and the second electrode 21b according to the arrangement design evaluated to be capable of obtaining an appropriate shape drawing, the polishing apparatus 1 of Example 1 can generate and display an appropriate shape drawing line of the wafer W during polishing, and can appropriately let the operator grasp the wafer shape.

[0097] Hereinafter, the operation of the evaluation program 100 for the electrode arrangement design and the evaluation method of Example 1 will be described.

[0098] As described above, in the polishing apparatus 1 of Example 1 in which a pair of electrodes (first electrode 21a, second electrode 21b) for detecting the resonance frequency of the wafer W are attached to the upper surface plate 12 during polishing of the wafer W made of a piezoelectric material, the calculation accuracy of the resonance frequency of the wafer W changes according to the position where the pair of electrodes (first electrode 21a, second electrode 21b) are arranged, and accordingly, the generation accuracy of the shape drawing line indicating the cross-sectional shape of the wafer W fluctuates. Therefore, when designing and manufacturing the polishing apparatus 1, it is required to evaluate the effectiveness of an arbitrarily designed electrode arrangement design with respect to the generation accuracy of the shape drawing line, and to determine whether the designed electrode arrangement is suitable for generating the shape drawing line.

[0099] On the other hand, the evaluation program 100 for the electrode arrangement design of Example 1 is installed in an arbitrary computer and is used when designing the electrode arrangement in the polishing apparatus 1 of Example 1 and the like.

[0100] That is, the evaluation program 100 for the electrode arrangement design of Example 1 calculates an electrode trajectory EO, which is the trajectory of the midpoint O3 of the pair of electrodes 21a and 21b when an arbitrary target wafer W' is polished for a predetermined time, based on predetermined information including the arrangement conditions of the pair of electrodes (first electrode 21a, second electrode 21b), and an overlapping section S, which is a section passing over the target wafer W' during a predetermined time, among the electrode trajectories EO OVThe overlapping interval operation process 102 for calculating the length of, and the overlapping interval S OV Among them, the effective interval S which is the interval in which a pair of electrodes 21a and 21b simultaneously face the target wafer W´ VA The effective interval operation process 103 for calculating the length of, and the overlapping interval S OV The effective interval S occupied in the overlapping interval S VA The ratio calculation process 104 for calculating the effective ratio ER which is the ratio of, are executed by the computer.

[0101] Thereby, designers of the polishing apparatus 1 etc. can, based on the effective ratio ER output from the computer, before actually manufacturing the polishing apparatus 1 etc., confirm whether the electrode arrangement design arbitrarily designed is effective for the generation accuracy of the shape drawing line generated during polishing, that is, whether it is an electrode arrangement design that can obtain an appropriate shape drawing line. And, by designing and manufacturing the polishing apparatus 1 etc. according to the electrode arrangement design whose effectiveness has been confirmed with respect to the generation accuracy of the shape drawing line of the wafer W, an appropriate shape drawing line can be generated during polishing, and as a result, the operator of the polishing apparatus 1 etc. can appropriately grasp the cross-sectional shape of the wafer W during processing.

[0102] Also, the evaluation program 100 of Example 1 causes the computer to execute a design evaluation process 105 for evaluating the electrode arrangement design by comparing the effective ratio ER with a predetermined threshold value.

[0103] Therefore, the evaluation program 100 of Example 1 can cause the computer to mechanically perform the evaluation of the electrode arrangement design. Thereby, for example, it is possible to prevent the evaluation result of the electrode arrangement design from changing due to the subjectivity of the designer of the polishing apparatus 1 etc. or the evaluation result from becoming ambiguous, and it is possible to stably evaluate according to a certain standard.

[0104] Fig. 11 illustrates the differences in the shape drawing lines of the wafer W when the effective ratio ER is different.

[0105] The prototype device 1 is a polishing device in which the first electrode 21a and the second electrode 21b are arranged according to an electrode arrangement design with an effective ratio ER of 90.6%. When polishing the target wafer W' using the prototype device 1, the electrode track EO (overlapping section S OV ) and the effective section S VA (shown by the thick line) have a trajectory prediction diagram as shown in Fig. 11. Furthermore, the shape drawing line prediction diagram in this case is the prediction diagram 1001 shown in Fig. 11. Comparing the prediction diagram 1001 with the wafer cross-sectional shape drawing line 1003 measured on the machine after actually polishing the target wafer W', they have almost the same shape, and it is presumed that the prototype device 1 can appropriately grasp the cross-sectional shape of the wafer during polishing. Therefore, it can be seen that the electrode arrangement design in the prototype device 1 is effective for the shape drawing line of the wafer W.

[0106] On the other hand, the prototype device 2 is a polishing device in which the first electrode 21a and the second electrode 21b are arranged according to an electrode arrangement design with an effective ratio ER of 51.5%. When polishing the target wafer W' using the prototype device 2, the electrode track EO (overlapping section S OV ) and the effective section S VA (shown by the thick line) have a trajectory prediction diagram as shown in Fig. 11. Furthermore, the shape drawing line prediction diagram in this case is the prediction diagram 1002 shown in Fig. 11. Comparing the prediction diagram 1002 with the wafer cross-sectional shape drawing line 1003 measured on the machine after actually polishing the target wafer W', they have completely different shapes, and it is presumed that it is difficult for the prototype device 2 to appropriately grasp the cross-sectional shape of the wafer during polishing. Therefore, it can be seen that the electrode arrangement design in the prototype device 2 is not effective for the shape drawing line of the wafer W.

[0107] Thus, when designing the polishing device 1 or the like, by evaluating the arrangement design of a pair of electrodes (the first electrode 21a, the second electrode 21b) using the evaluation program 100 for the electrode arrangement design of Example 1, it is possible to manufacture a polishing device 1 or the like that can appropriately generate the shape drawing line of the wafer W.

[0108] The evaluation program for the electrode arrangement conditions, the polishing apparatus, and the method for evaluating the electrode arrangement conditions of the present invention have been described based on Example 1. However, the specific configuration is not limited to this example, and design changes, additions, etc. are allowed as long as the gist of the invention according to each claim is not deviated from.

[0109] In the evaluation program 100 of Example 1, an example was shown in which the computer was made to execute the design evaluation process 105 that compares the effective ratio ER with a preset predetermined threshold value and evaluates the electrode arrangement design in the polishing apparatus 1. However, the evaluation program 100 does not necessarily have to make the computer execute the design evaluation process 105. For example, in the ratio calculation process 104, the calculated effective ratio ER may be displayed on a display device possessed by the computer or a display device provided separately from the computer, and the designer of the polishing apparatus 1 or the like may visually recognize it. In this case, the designer can determine the effectiveness of the electrode arrangement design based on the effective ratio ER.

[0110] Also, in the evaluation program 100 of Example 1, when a plurality of overlapping intervals S OV and effective intervals S VA are extracted, an example was shown in which the length is calculated for each overlapping interval S OV and effective interval S VA . However, the overlapping interval S OV may be, for example, a value obtained by summing a plurality of overlapping intervals S OV , and the effective interval S VA may be a value obtained by summing a plurality of effective intervals S VA .

[0111] Also, in Example 1, an example was shown in which the electrode orbit EO is the orbit of the midpoint O3 between a pair of electrodes (the first electrode 21a and the second electrode 21b). However, the electrode orbit EO only needs to be an orbit showing the movement of a pair of electrodes (the first electrode 21a and the second electrode 21b), and is not limited to the orbit of the midpoint O3. For example, the orbit of either the first electrode 21a or the second electrode 21b may be the "electrode orbit EO", or the orbit at an arbitrary position between the first electrode 21a and the second electrode 21b may be the "electrode orbit EO".

[0112] In the polishing apparatus 1 of Example 1, an example was shown in which resonance frequency data was converted into thickness data of the wafer W, and a shape drawing line of the wafer W was generated by plotting the converted thickness data. However, the generation of the shape drawing line is not limited to this. For example, the shape drawing unit 32 may use, as the shape drawing line, an approximate curve obtained by averaging a plurality of cross-sectional shape lines T1 generated by plotting thickness data over a predetermined time.

[0113] In the polishing apparatus 1 of Example 1, an example was shown in which the first electrode 21a and the second electrode 21b were attached to the upper surface plate 12. However, the first electrode 21a and the second electrode 21b may be attached to the lower surface plate 11, or may be provided on both the lower surface plate 11 and the upper surface plate 12.

[0114] In the polishing apparatus 1 of Example 1, an example was shown in which a disk-shaped wafer W was polished. However, the shape of the wafer W is not limited to a disk shape, and may be, for example, a rectangular shape or the like.

Explanation of Reference Numerals

[0115] 1 Polishing apparatus 10 Polishing machine 11 Lower surface plate (surface plate) 12 Upper surface plate (surface plate) 20 Frequency detector 21a First electrode 21b Second electrode 22 Frequency calculation unit 30 Control unit 32 Shape drawing unit 33 Display control unit 42 Display 100 Evaluation program for electrode arrangement design 101 Electrode trajectory calculation process 102 Overlapping interval calculation process 103 Effective interval calculation process 104 Ratio calculation process 105 Design evaluation process W Wafer

Claims

1. An evaluation program for evaluating the electrode arrangement design in a polishing apparatus in which a pair of electrodes for detecting the resonance frequency of a wafer made of a piezoelectric material are attached to a surface plate during polishing of the wafer, comprising: an electrode trajectory calculation process for calculating an electrode trajectory, which is the trajectory of the pair of electrodes when an arbitrary wafer is polished for a predetermined time, based on predetermined information including the arrangement conditions of the pair of electrodes; an overlapping section calculation process for calculating the length of an overlapping section, which is a section passing over the arbitrary wafer, among the electrode trajectories; an effective section calculation process for calculating the length of an effective section, which is a section where the pair of electrodes face the arbitrary wafer simultaneously, among the overlapping sections; a ratio calculation process for calculating an effective ratio, which is the ratio of the effective section to the overlapping section; and causing a computer to execute the above, characterized in that it is an evaluation program.

2. In the evaluation program according to Claim 1, a design evaluation process for evaluating the electrode arrangement design by comparing the effective ratio with a predetermined threshold value is caused to be executed by the computer the above, characterized in that it is an evaluation program.

3. A polishing machine for polishing a wafer made of a piezoelectric material with a surface plate; a first electrode and a second electrode attached to the surface plate and having tip surfaces facing the wafer; a frequency calculation unit that applies a predetermined frequency sweep signal from the first electrode to the wafer and calculates the resonance frequency of the wafer based on the frequency sweep signal received by the second electrode; a shape drawing unit that generates a shape drawing line indicating the cross-sectional shape of the wafer based on the resonance frequency; and a display for displaying the shape drawing line. A polishing apparatus, characterized by comprising the above.

4. In the polishing apparatus according to Claim 3, the first electrode and the second electrode are arranged at predetermined positions on the surface plate according to the electrode arrangement design evaluated by the evaluation program according to Claim 1 or Claim 2 the above, characterized in that it is a polishing apparatus.

5. In the polishing apparatus according to Claim 3, the electrode distance, which is the distance between the center of the first electrode and the center of the second electrode, is set to 1 mm to 500 mm the above, characterized in that it is a polishing apparatus.

6. In the polishing apparatus according to Claim 4, the electrode distance, which is the distance between the center of the first electrode and the center of the second electrode, is set to 1 mm to 500 mm the above, characterized in that it is a polishing apparatus.

7. In the polishing apparatus according to Claim 3, The radial position of the center of the surface plate, the midpoint between the centers of the first electrode and the second electrode, on the straight line connecting them, is set in the range of 10% to 80% when the inner peripheral end of the surface plate is set to 0% and the outer peripheral end of the surface plate is set to 100%. A polishing apparatus characterized by the above.

8. In the polishing apparatus according to claim 4, The radial position of the center of the surface plate, the midpoint between the centers of the first electrode and the second electrode, on the straight line connecting them, is set in the range of 10% to 80% when the inner peripheral end of the surface plate is set to 0% and the outer peripheral end of the surface plate is set to 100%. A polishing apparatus characterized by the above.

9. An evaluation method executed by a computer equipped with an evaluation program for evaluating the electrode arrangement design in a polishing apparatus in which a pair of electrodes for detecting the resonance frequency of a wafer made of a piezoelectric material is attached to a surface plate, Calculating an electrode trajectory, which is the trajectory of the pair of electrodes when an arbitrary wafer is polished for a predetermined time, based on predetermined information including the arrangement conditions of the pair of electrodes; Calculating the length of an overlapping section, which is a section passing over the arbitrary wafer, among the electrode trajectories; Calculating the length of an effective section, which is a section where the pair of electrodes face the arbitrary wafer simultaneously, among the overlapping sections; Calculating an effective ratio, which is the ratio of the effective section to the overlapping section; Comparing the effective ratio with a predetermined threshold value and evaluating the electrode arrangement design; An evaluation method characterized by comprising the above steps.

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