JP5824833B2 - Wafer polishing support device, wafer polishing support method and program - Google Patents

Description

The present invention relates to a wafer polishing support apparatus, a wafer polishing support method, and a program. In particular, the present invention relates to a wafer polishing support apparatus that supports polishing of a wafer, a wafer polishing support method, and a program that causes a computer to function as the wafer polishing support apparatus.

  The polishing rate in the wafer polishing step is usually calculated by measuring the film thickness before and after polishing the wafer with a film thickness measuring instrument and dividing the polishing amount obtained from the film thickness difference by unit time. However, in such a method, the polishing rate must be calculated by measuring the polishing amount of the wafer every time, which increases the number of manufacturing steps and deteriorates productivity.

  Therefore, at present, the polishing rate is estimated based on sensor data indicating various physical phenomena of the wafer polishing apparatus without measuring the film thickness before and after the wafer polishing. The technique described in Patent Document 1 is a technique for estimating a polishing rate by regression analysis using a physical quantity obtained from various sensors of a wafer polishing apparatus as an explanatory variable and a polishing amount of a test wafer as an objective variable. In the method described in this document, as explanatory variables, the torque value of the motor that rotates the polishing table for polishing the wafer in the polishing apparatus, the surface temperature on the polishing table for polishing the wafer, and the wafer is pushed onto the polishing table during polishing. An average value of physical phenomena such as a pressure value applied is obtained, a statistical model of regression analysis is created, and a subsequent polishing rate is estimated. Patent Documents 2 and 3 are also known as documents related to the wafer polishing apparatus.

  FIG. 8 shows an example of the change in the polishing pad usage time and wafer polishing rate value. However, as shown in FIG. 8, the estimated polishing rate value with respect to the usage time of the polishing pad on the polishing table used for wafer polishing cannot be distinguished whether it is immediately after the start of use of the polishing pad or when the polishing pad is deteriorated. This is because immediately after the start of use of the polishing pad, the degree of penetration of the polishing liquid entering between the grooves of the polishing pad is low and the polishing rate value is low. Therefore, for example, in the case where the life management of the polishing pad is performed based on the estimated polishing rate, it is impossible to determine whether the polishing pad is immediately after the start of use or has deteriorated only by the estimated polishing rate value.

JP 2005-328441 A JP 2004-047747 A JP 2004-220842 A

  As described above, the polishing rate value is the same immediately after the start of use of the polishing pad and at the time of deterioration (see FIG. 8). For this reason, the deterioration state and replacement period of the polishing pad cannot be determined only from the estimated value of the polishing rate.

  More specifically, the wafer is polished while the surface of the semiconductor film is scientifically changed by the polishing liquid contained in the polishing pad. Immediately after the use of the polishing pad is started, since the degree of penetration of this polishing liquid is low, the polishing rate value also becomes low. When the usage time elapses to some extent, the polishing liquid sufficiently penetrates into the polishing pad and the polishing rate value increases. When the usage time further elapses, the polishing rate value decreases due to deterioration of the polishing pad.

  FIG. 9 shows the difference in the change in the polishing rate value when the polishing pad is normal and abnormal. For example, in the case where the life of the polishing pad is managed based on the estimated polishing rate, when the polishing rate is estimated using a polishing pad with an extremely fast deterioration as shown in FIG. It cannot be determined whether the influence is due to the degree of liquid penetration or the abnormal deterioration of the polishing pad, and appropriate polishing pad replacement cannot be performed.

In order to solve the above-described problem, according to the first aspect of the present invention, a wafer polishing support apparatus for supporting wafer polishing , wherein polishing is performed from statistical models and explanatory variables that have been created in advance by multiple regression analysis. A prediction unit for calculating an estimated value of the performed polishing rate of the wafer, and a physical quantity indicating a normal state in which the polishing member is not deteriorated from a plurality of physical quantities representing a deterioration characteristic of the polishing member in the wafer polishing apparatus for performing the wafer polishing process. An initial set generation unit that generates a set and calculates an average and variance of the set, a polishing vector generation unit that generates a multidimensional vector from physical quantities at the time of wafer polishing, and an average and variance of the set generated by the initial set generation unit , based on the multi-dimensional vector polishing vector generation unit is generated, and the Mahalanobis distance calculating unit which calculates a Mahalanobis distance, the estimated polishing rate prediction portion is calculated If, based on the Mahalanobis distance Mahalanobis distance calculation unit has calculated, to exchange determination of the polishing member, the estimated value of the polishing rate is lower than the threshold, if the Mahalanobis distance is greater than 1, the polishing member And a polishing member replacement determination unit that determines that replacement is to be performed .

According to a second aspect of the present invention, there is provided a wafer polishing support method for supporting wafer polishing, wherein a polishing rate of a polished wafer is estimated from a statistical model and explanatory variables created in advance by multiple regression analysis. A set of physical quantities indicating a normal state in which the polishing member is not deteriorated is generated from a plurality of physical quantities representing a deterioration characteristic of the polishing member in the wafer polishing apparatus that performs the polishing process of the wafer and a polishing process of the wafer, and the average of the set And initial set generation stage for calculating variance, polishing vector generation stage for generating multi-dimensional vectors from physical quantities at the time of wafer polishing, average and variance of sets generated in the initial set generation stage, and generation in the polishing vector generation stage based on the multi-dimensional vectors, and Mahalanobis distance calculation step of calculating a Mahalanobis distance, polished calculated in the prediction step The estimated value of over preparative, based on the Mahalanobis distance calculated in the Mahalanobis distance calculation step, to exchange determination of the polishing member, the estimated value of the polishing rate is lower than the threshold, if the Mahalanobis distance is greater than 1 Includes a polishing member replacement determination step for determining that the polishing member should be replaced.

According to a third aspect of the present invention, there is provided a program for causing a computer to function as a wafer polishing support apparatus for supporting wafer polishing, wherein the computer is preliminarily created from a statistical model and explanatory variables created by multiple regression analysis. , A prediction unit for calculating an estimated value of the polishing rate of the polished wafer, and a normal state in which the polishing member is not deteriorated from a plurality of physical quantities representing a deterioration characteristic of the polishing member in the wafer polishing apparatus for polishing the wafer An initial set generation unit that generates a set of physical quantities and calculates an average and variance of the set, a polishing vector generation unit that generates a multidimensional vector from physical quantities at the time of wafer polishing, and an average and variance of sets generated by the initial set generation unit Mahalanobis distance calculation unit polishing vector generation unit based on the multi-dimensional vector generated, to calculate the Mahalanobis distance, the prediction unit And the estimated value of the calculated polishing rate, based on the Mahalanobis distance Mahalanobis distance calculation unit has calculated, to exchange determination of the polishing member, the estimated value of the polishing rate is lower than the threshold, the Mahalanobis distance is greater than 1 In this case, it is made to function as a polishing member replacement determination unit that determines that the polishing member should be replaced .

  In addition, as described above, the summary of the invention does not enumerate all necessary features of the present invention, and sub-combinations of these feature groups can also be the invention.

  As is apparent from the above description, the present invention can increase cost and productivity as compared with known techniques.

It is a figure which shows an example of the distance which consists of the data of 2 variables, and a point. It is a figure which shows an example of the relationship between deterioration of a polishing pad and a polishing rate value. It is a figure which shows an example of the utilization environment of the wafer grinding | polishing assistance apparatus 100 which concerns on one Embodiment. It is a figure which shows an example of the block configuration of the wafer grinding | polishing assistance apparatus. It is a figure which shows an example of the change of the detected temperature of the thermometer. It is a figure which shows an example of the discrimination method of the polishing pad at the time of normal. It is a figure which shows an example of the discrimination method of the polishing pad at the time of abnormality. It is a figure which shows an example of the usage time of a polishing pad, and the change of a wafer polishing rate value. It is a figure which shows the difference in the change of the polishing rate value at the time of normality of a polishing pad, and abnormality. An example of a hardware configuration when the wafer polishing support apparatus 100 is configured by an electronic information processing apparatus such as a computer is shown.

  Hereinafter, the present invention will be described through embodiments of the invention. However, the following embodiments do not limit the invention according to the scope of claims, and are combinations of features described in the embodiments. Not all are essential to the solution of the invention.

  Mahalanobis distance is a kind of distance used in statistics. More specifically, the Mahalanobis distance indicates the degree of similarity between the known sample data and the new sample data as a distance based on a multivariable correlation.

FIG. 1 shows an example of a set of two variable data and the distance between points. The set U in this example is a set of normal data A and data B in a certain event. Further, u (a0, b0) in this example is an average value of the set U. In this example, σ _a ² is a range in which data A is dispersed. Further, in this example, σ _b ² and data B are in a dispersed range. In such a case, in general, the distance from the average value u of the set U to the point X1 (a1, b1) can be obtained as the Euclidean distance _Du by Equation (1).

However, at the Euclidean distance _Du , X1 outside the set U and X2 included in the set U are the same distance, and the difference between the two points cannot be seen. On the other hand, the Mahalanobis distance D _M is consideration of variations of the data A, B, by dividing the elements of data in the standard deviation of the data, and performs the distance calculation from performing normalization of data. Therefore, the Mahalanobis distance D _M from the average value u to extension of the set U is always 1. The formula for the Mahalanobis distance D _M from the average value u to X1 referred to equation (2).

As described above, the Mahalanobis distance D1 from the average value u to X1 and the Mahalanobis distance D2 from the average u to X2 are D2 <1 <D1, and the data can be classified by the distance. In FIG. 1, the set in the case of two variables and the Mahalanobis distance D _M of points are described. However, the equation for obtaining the Mahalanobis distance D _M (x) in the case of two or more variables is as follows.

  In the present invention, immediately after the start of use of the polishing pad is defined as a normal state in which the polishing pad is not deteriorated. A set of normal states is created from a plurality of physical quantities representing the deterioration state of the polishing pad. Then, the Mahalanobis distance between the average of the set in the normal state and the plurality of physical quantity vectors at the time of wafer polishing is obtained, and whether the polishing pad is normal or abnormal, that is, whether the polishing pad is deteriorated is determined.

  What is important when performing discrimination processing using the Mahalanobis distance is the creation of a reference set. When a reference set is created using a variable with large variation, the set becomes large, and there is a high possibility that abnormal data is determined as normal data. In addition, when the number of samples for creating a reference set is small, it is not possible to represent all the states in which the set is a reference, and there is a high possibility that normal data is determined to be abnormal. Therefore, the Mahalanobis distance includes an error depending on how to set a reference set.

  There are individual differences in the polishing pad used in the wafer polishing apparatus, and variations in physical quantities at the time of wafer polishing differ for each polishing pad. For this reason, when a normal set of all polishing pads is generated, the set becomes large due to variations among polishing pads.

  Further, when a normal set is created from the physical quantity immediately after the polishing pad is replaced, it is not possible to create a set representing all normal times.

  FIG. 2 shows an example of the relationship between the deterioration of the polishing pad and the polishing rate value. Due to the error included in the Mahalanobis distance, only the numerical value of the Mahalanobis distance cannot be used to make an appropriate polishing pad replacement determination even though the state change from the time when the set is created can be seen.

  Therefore, in the present invention, the polishing pad replacement determination is performed with high accuracy even in the above case by combining the estimation result of the deterioration determination of the polishing pad and the estimated polishing rate value.

  FIG. 3 shows an example of the usage environment of the wafer polishing support apparatus 100 according to an embodiment. When performing polishing pad replacement determination, the wafer polishing support apparatus 100 performs polishing pad replacement determination independent of the usage time of the polishing pad based on the estimated polishing rate value and the polishing pad deterioration estimation, thereby effectively using the polishing pad. Is made possible.

  The wafer polishing apparatus 200 holds and transports a polishing table 210 on which a polishing pad for polishing a wafer is mounted, a table motor 220 that rotates the polishing table 210, and a polishing surface of the wafer facing the polishing table 210. A polishing head 230 having a function of pressing and polishing the wafer while pressing the wafer against the polishing table 210, a head motor 240 for rotating the polishing head 230, and dressing of the polishing pad on the polishing table 210 after polishing. A dresser head 250 to be performed; a dresser motor 260 that rotates the dresser head 250; a slurry feeder 270 that supplies a slurry as a polishing liquid onto the polishing table 210; heat generated by the wafer polishing; Mechanically generated by friction with table 210 It consists thermometer 280 Metropolitan measuring the temperature change of the polishing table 210 by the heat.

  FIG. 4 shows an example of a block configuration of the wafer polishing support apparatus 100. The wafer polishing support apparatus 100 collects the motor torque data of the table motor 220, the head motor 240, and the dresser motor 260 and the temperature data of the thermometer 280, and transmits the data to the data storage unit 120. A data storage unit 120 for accumulating data collected by the collection unit 110, a polishing data acquisition unit 130 for acquiring various sensor data at a constant time period during polishing, and a sensor data acquired by the polishing data acquisition unit 130 for representative value processing A conversion unit 140 that performs the calculation, a prediction unit 150 that calculates a predicted value of the polishing rate from the representative value calculated by the conversion unit 140 and a statistical model obtained in advance by multiple regression analysis, and a plurality of characteristics representing characteristics of a polishing mechanism that polishes the wafer The polishing rate is estimated based on a statistical model with the physical quantity of The polishing member deterioration estimation unit 160 that estimates the deterioration of the polishing member in the wafer polishing apparatus 200 that performs the polishing process of C, and the polishing member replacement determination unit 26 that performs the polishing pad replacement determination from the predicted polishing rate value and the Mahalanobis distance Is done.

  The polishing member deterioration estimation unit 160 includes an initial set generation unit 161 that generates a representative value set indicating a normal state in which the polishing pad is not deteriorated from the representative value, and a polishing vector generation unit 162 that generates a multidimensional vector from the representative value. A Mahalanobis distance calculation unit 163 that calculates the Mahalanobis distance from the average of the initial space and the polishing vector.

  Next, the operation of the wafer polishing apparatus will be described. First, the data collection unit 110 rotates the rotation torque data of the table motor 220 when the wafer is being polished on the polishing table 210, the rotation torque data of the head motor 240 that is also being polished, and the polishing table 210 that is also being polished. Data of the thermometer 280 that measures the upper temperature is sampled at a constant sampling period and stored in the data storage unit 120. Further, the rotational torque data of the dresser motor 260 at the time of dressing the polishing table 210 by the dresser head 250 performed after the wafer polishing is also stored in the data storage unit 120.

  FIG. 5 shows an example of a change in temperature detected by the thermometer 280. For example, in the temperature data of the thermometer 280, the sampling data stored in the data storage unit 120 is two-dimensional data representing changes in table temperature data with respect to time data as shown in FIG. Other motor rotation torque values and the like are also two-dimensional data representing changes in torque values with respect to time data.

  Then, the rotational torque data of the table motor 220 and the head motor 240 during polishing, the polishing table temperature data of the thermometer 280, and the dresser motor 260 at the time of dressing, which are stored in the data storage unit 120 by the polishing data acquisition unit 130. The rotational torque data is extracted and output to the conversion unit 140. The conversion unit 140 performs representative value processing such as an average value and a difference value for a predetermined time for each acquired data for each wafer polishing process.

  Next, the prediction unit 150 first acquires from the conversion unit 140 as representative variables polishing data such as table temperature and various motor rotation torques when the wafer whose polishing rate is estimated is polished. Next, an estimated value of the polishing rate of the polished wafer is calculated from a statistical model and explanatory variables that have been created in advance by multiple regression analysis.

  Next, the initial set generation unit 161 acquires representative polishing data such as a table temperature and various motor rotation torques when the wafer immediately after the start of the use of the polishing pad is polished from the conversion unit 140, and before the deterioration. A set of representative values representing a normal polishing pad state is generated. Also, the variance and average of the set are calculated.

  Next, the polishing vector generation unit 162 acquires from the conversion unit 140 representative polishing data such as a table temperature and various motor rotation torques when the polished wafer is polished at the time when it is desired to obtain the state of the polishing pad. Then, a multidimensional vector is generated.

  Next, the Mahalanobis distance calculation unit 25 calculates the Mahalanobis distance between the variance and average of the set obtained by the initial set generation unit 161 and the multidimensional vector obtained by the vector generation unit 24.

  Finally, the polishing member replacement determination unit 26 determines the replacement of the polishing pad based on the estimated polishing rate value obtained by the prediction unit 150 and the Mahalanobis distance obtained by the Mahalanobis distance calculation unit 25.

  FIG. 6 shows an example of a normal polishing pad discrimination method. FIG. 7 shows an example of a method of discriminating the polishing pad at the time of abnormality. Examples of the initial set generation unit 161, the polishing vector generation unit 162, the Mahalanobis distance calculation unit 25, and the polishing member replacement determination unit 26 will be described in detail with respect to the embodiment described in the above embodiment.

  In the initial set generation unit 161, first, a set of representative polishing data such as a table temperature and various motor rotation torques when five polished wafers are polished immediately after the use of the polishing pad is acquired from the conversion unit 140. To do. Next, a multidimensional set is created from the set of sensor representative values. This means that the polishing pad immediately after the start of use is defined as being in a normal state before deterioration, and the normal state of the polishing pad is represented by generating a representative value space.

  Next, the polishing vector generation unit 162 will be described in detail. In the polishing vector generation unit 162, the unit in the representative polishing data such as the table temperature and various motor rotation torques when the polished wafer is polished when it is desired to estimate the deterioration of the polishing pad after the initial set generation is performed. This is expressed as a multidimensional vector using representative values constituting the space. This represents the state of the polishing pad during wafer polishing.

  Next, the Mahalanobis distance calculation unit 25 will be described in detail. The Mahalanobis distance calculation unit 25 calculates the Mahalanobis distance using the variance and average obtained by the initial set generation unit 161 and the multidimensional vector obtained by the polishing vector generation unit 162. The distance obtained here represents the state of the polishing pad. Specifically, when the Mahalanobis distance exceeds 1, it is determined that the polishing pad has deteriorated.

  Finally, the polishing member replacement determination unit 26 will be described in detail. The polishing member replacement determination unit 26 performs polishing pad replacement determination based on the predicted rate value obtained by the prediction unit 150 and the Mahalanobis distance obtained by the Mahalanobis distance calculation unit 25. Specifically, in the case of a normal polishing pad, when the predicted rate value is low and the Mahalanobis distance exceeds 1, as shown in FIG. 6, it is determined that the polishing pad should be replaced, and processing is performed. In the case of an abnormal polishing pad, the Mahalanobis distance is increased similarly to the polishing rate as shown in FIG. 7, so that when the predicted rate is low and the Mahalanobis distance exceeds 1, as in the case of a normal polishing pad, polishing is performed. It is determined that the pad should be replaced and processing is performed.

  The effect of the present invention is that the deterioration of the polishing pad and the replacement determination of the polishing pad can be estimated without depending on the usage time of the polishing pad, thereby increasing the cost and productivity as compared with the conventional one.

  As an application example of the present invention, the present invention is used in a wafer polishing apparatus that performs a polishing process on a wafer.

  FIG. 10 shows an example of a hardware configuration when the wafer polishing support apparatus 100 is configured by an electronic information processing apparatus such as a computer. Wafer polishing support apparatus 100 includes a CPU (Central Processing Unit) peripheral part, an input / output part, and a legacy input / output part. The CPU peripheral section includes a CPU 802, a RAM (Random Access Memory) 803, a graphic controller 804, and a display device 805 that are connected to each other by a host controller 801. The input / output unit includes a communication interface 807, a hard disk drive 808, and a CD-ROM (Compact Disk Read Only Memory) drive 809 connected to the host controller 801 by the input / output controller 806. The legacy input / output unit includes a ROM (Read Only Memory) 810, a flexible disk drive 811, and an input / output chip 812 connected to the input / output controller 806.

  The host controller 801 connects the RAM 803, the CPU 802 that accesses the RAM 803 at a high transfer rate, and the graphic controller 804. The CPU 802 operates based on programs stored in the ROM 810 and the RAM 803 to control each unit. The graphic controller 804 acquires image data generated by the CPU 802 or the like on a frame buffer provided in the RAM 803 and displays the image data on the display device 805. Alternatively, the graphic controller 804 may include a frame buffer for storing image data generated by the CPU 802 or the like.

  The input / output controller 806 connects the host controller 801 to the hard disk drive 808, the communication interface 807, and the CD-ROM drive 809, which are relatively high-speed input / output devices. The hard disk drive 808 stores programs and data used by the CPU 802. The communication interface 807 is connected to the network communication device 891 to transmit / receive programs or data. The CD-ROM drive 809 reads a program or data from the CD-ROM 892 and provides it to the hard disk drive 808 and the communication interface 807 via the RAM 803.

  The input / output controller 806 is connected to the ROM 810, the flexible disk drive 811, and the relatively low-speed input / output device of the input / output chip 812. The ROM 810 stores a boot program executed when the wafer polishing support apparatus 100 is started, a program depending on the hardware of the wafer polishing support apparatus 100, and the like. The flexible disk drive 811 reads a program or data from the flexible disk 893 and provides it to the hard disk drive 808 and the communication interface 807 via the RAM 803. The input / output chip 812 connects various input / output devices via the flexible disk drive 811 or a parallel port, serial port, keyboard port, mouse port, and the like.

  A program executed by the CPU 802 is stored in a recording medium such as a flexible disk 893, a CD-ROM 892, or an IC (Integrated Circuit) card and provided by a user. The program stored in the recording medium may be compressed or uncompressed. The program is installed in the hard disk drive 808 from the recording medium, read into the RAM 803, and executed by the CPU 802. The program executed by the CPU 802 causes the wafer polishing support apparatus 100 to execute the data collection unit 110, the data storage unit 120, the polishing data acquisition unit 130, the conversion unit 140, the prediction unit 150, and the like described with reference to FIGS. The polishing member deterioration estimation unit 160 (the initial set generation unit 161, the polishing vector generation unit 162, and the Mahalanobis distance calculation unit 163) and the polishing member replacement determination unit 170 are caused to function.

  The program shown above may be stored in an external storage medium. As a storage medium, in addition to a flexible disk 893 and a CD-ROM 892, an optical recording medium such as a DVD (Digital Versatile Disk) or a PD (Phase Disk), a magneto-optical recording medium such as an MD (MiniDisk), a tape medium, and an IC card A semiconductor memory or the like can be used. Further, a storage medium such as a hard disk or a RAM provided in a server system connected to a dedicated communication network or the Internet may be used as a recording medium and provided as a program via the network.

  As mentioned above, although this invention was demonstrated using embodiment, the technical scope of this invention is not limited to the range as described in the said embodiment. It will be apparent to those skilled in the art that various modifications or improvements can be added to the above embodiment. It is apparent from the scope of the claims that the embodiments added with such changes or improvements can be included in the technical scope of the present invention.

100 Wafer Polishing Support Device 110 Data Collection Unit 120 Data Storage Unit 130 Polishing Data Acquisition Unit 140 Conversion Unit 150 Prediction Unit 160 Polishing Member Degradation Estimation Unit 161 Initial Set Generation Unit 162 Polishing Vector Generation Unit 163 Mahalanobis Distance Calculation Unit 170 Polishing Member Replacement Determination Unit 200 Wafer polishing apparatus 210 Polishing table 220 Table motor 230 Polishing head 240 Head motor 250 Dresser head 260 Dresser motor 270 Slurry feeder 280 Thermometer 801 Host controller 802 CPU
803 RAM
804 Graphic controller 805 Display device 806 Input / output controller 807 Communication interface 808 Hard disk drive 809 CD-ROM drive 810 ROM
811 Flexible disk drive 812 I / O chip 891 Network communication device 892 CD-ROM
893 Flexible disk

Claims (5)

A wafer polishing support device for supporting wafer polishing,
A prediction unit that calculates an estimated value of the polishing rate of a polished wafer from a statistical model and explanatory variables that have been created in advance by multiple regression analysis;
An initial stage for generating a set of physical quantities indicating a normal state in which the polishing member is not deteriorated from a plurality of physical quantities representing the deterioration characteristics of the polishing member in a wafer polishing apparatus that performs wafer polishing, and calculating an average and variance of the set A set generation unit;
A polishing vector generation unit that generates a multidimensional vector from the physical quantity at the time of wafer polishing;
A Mahalanobis distance calculation unit that calculates a Mahalanobis distance based on the average and variance of the set generated by the initial set generation unit and the multidimensional vector generated by the polishing vector generation unit;
Based on the estimated polishing rate value calculated by the prediction unit and the Mahalanobis distance calculated by the Mahalanobis distance calculation unit, the polishing member replacement determination is performed, and the estimated polishing rate value is lower than a threshold value. A wafer polishing assistance apparatus comprising: a polishing member replacement determination unit that determines that the polishing member should be replaced when the Mahalanobis distance exceeds 1. The initial set generation unit includes, as a plurality of physical quantities representing deterioration characteristics of the polishing member, temperature information in a polishing portion as heat generation amount information by polishing, and at least one of a plurality of motors provided in a polishing mechanism portion. The wafer polishing support apparatus according to claim 1, wherein torque information is used. It further comprises a conversion unit that converts various sensor data into representative value processed data ,
The prediction unit, the transform unit is obtained by converting data with the explanatory variables, the wafer polishing support device according to claim 1 or 2 for calculating the estimated value of the polishing rate. A wafer polishing support method for supporting wafer polishing,
A prediction stage for calculating an estimated value of the polishing rate of a polished wafer from statistical models and explanatory variables created by multiple regression analysis in advance,
An initial stage for generating a set of physical quantities indicating a normal state in which the polishing member is not deteriorated from a plurality of physical quantities representing the deterioration characteristics of the polishing member in a wafer polishing apparatus that performs wafer polishing, and calculating an average and variance of the set A set generation stage;
A polishing vector generation stage for generating a multidimensional vector from the physical quantity at the time of wafer polishing;
A Mahalanobis distance calculating step of calculating a Mahalanobis distance based on the average and variance of the set generated in the initial set generating step and the multidimensional vector generated in the polishing vector generating step;
Based on the estimated value of the polishing rate calculated in the prediction step and the Mahalanobis distance calculated in the Mahalanobis distance calculation step, the replacement determination of the polishing member is performed, and the estimated value of the polishing rate is more than a threshold value And a polishing member replacement determination step for determining that the polishing member should be replaced when the Mahalanobis distance is greater than 1. A program for causing a computer to function as a wafer polishing support device for supporting wafer polishing,
The computer,
A prediction unit that calculates an estimated value of the polishing rate of a polished wafer from statistical models and explanatory variables created by multiple regression analysis in advance,
An initial stage for generating a set of physical quantities indicating a normal state in which the polishing member is not deteriorated from a plurality of physical quantities representing the deterioration characteristics of the polishing member in a wafer polishing apparatus that performs wafer polishing, and calculating an average and variance of the set Set generation unit,
A polishing vector generation unit that generates a multidimensional vector from the physical quantity at the time of wafer polishing,
A Mahalanobis distance calculation unit that calculates a Mahalanobis distance based on the average and variance of the set generated by the initial set generation unit and the multidimensional vector generated by the polishing vector generation unit,
Based on the estimated polishing rate value calculated by the prediction unit and the Mahalanobis distance calculated by the Mahalanobis distance calculation unit, the polishing member replacement determination is performed, and the estimated polishing rate value is lower than a threshold value. When the Mahalanobis distance exceeds 1, the program functions as a polishing member replacement determination unit that determines that the polishing member should be replaced.

Images