Patent Publication Number: US-2019181025-A1

Title: Monitoring system, learning apparatus, learning method, monitoring apparatus, and monitoring method

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application claims priority to Japanese Patent Application No. 2017-238786 filed on Dec. 13, 2017. The entire disclosure of Japanese Patent Application No. 2017-238786 is hereby incorporated herein by reference. 
     FIELD 
     The disclosure relates to a monitoring system, a learning apparatus, a learning method, a monitoring apparatus, and a monitoring method. 
     BACKGROUND 
     Conventionally, various methods for monitoring the state of a component used in an etching apparatus have been proposed. For example, JP 2003-031456A proposes a method for monitoring the state of a consumable component using a relation that predicts the etching rate uniformity from the amount of time the consumable component is used. Specifically, according to the method proposed in JP 2003-031456A, a predicted value of the etching rate uniformity is calculated by substituting the amounts of time respective consumable components are used into a predetermined relation, and a combination of consumable components to be replaced is calculated based on the calculated predicted value of the etching rate uniformity. With this method, the timing of replacement of a consumable component can be specified based on the amount of time the consumable component is used. 
     JP 2003-031456A is an example of background art. 
     In a wet etching apparatus, when a chemical solution, which is a consumable component, deteriorates, a phenomenon (hereinafter referred to as “removal unevenness”) in which a portion of a target area of the etching process remains unremoved will occur. The inventors have found that, since the removal unevenness cannot be appropriately predicted with the above-described etching rate uniformity, there is a problem in that, if replacement of the chemical solution is performed when a predicted value of the etching rate uniformity exceeds a threshold value, even chemical solutions that are still well usable will be replaced. That is to say, the inventors have found that there is a problem with a conventional method in that it is difficult to appropriately predict the timing at which removal unevenness will occur, and replacement of the chemical solution is performed more frequently than necessary, resulting in an increased wet etching cost. 
     SUMMARY 
     One or more embodiments have been made in view of the foregoing situation in an aspect, and aims to provide a technique that enables the timing at which removal unevenness will occur in a wet etching apparatus to be appropriately predicted. 
     To achieve the above-stated object, an aspect may employ the following configuration. 
     That is to say, a monitoring system according to an aspect is a monitoring system for monitoring the state of a chemical solution used in an etching process performed by a wet etching apparatus, the monitoring system including: a learning data acquisition unit configured to acquire, as learning data, a set of normal values of:
     an accumulated operating time indicating the accumulated time for which the wet etching apparatus has operated from when the chemical solution has been replaced to when the etching process has been applied to a wafer,   an accumulated number of processed wafers indicating the accumulated number of wafers that have been processed from when the chemical solution has been replaced to when the etching process has been applied to the wafer, and   a removal amount indicating the amount that has been removed by etching from the wafer to which the etching process has been applied; a model construction unit configured to construct a predictive model that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers, based on the normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data; an actual value acquisition unit configured to acquire actual values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount with respect to the wet etching apparatus when it is in operation; an indicator value calculation unit configured to calculate a predicted value of the removal amount by inputting the acquired actual values of the accumulated operating time and the accumulated number of processed wafers to the predictive model, and calculate the difference between the calculated predicted value and the acquired actual value of the removal amount, as an indicator value serving as a measure of how necessary it is to replace the chemical solution; and an output unit configured to output information regarding replacement of the chemical solution based on the calculated indicator value.   

     A predictive model that predicts a value of the removal amount removed by etching depending on values of the accumulated operating time and the accumulated number of processed wafers can be constructed by analyzing data that is obtained while the wet etching apparatus is operating normally. The inventors have found that the greater the discrepancy between a predicted value of the removal amount derived from the predictive model and a corresponding actual value of the removal amount, the more likely that removal unevenness will occur in a target wet etching apparatus. That is to say, the inventors have found that the occurrence of removal unevenness can be predicted based on whether or not the difference between a predicted value of the removal amount obtained by inputting actual values of the accumulated operating time and the accumulated number of processed wafers to the predictive model and a corresponding actual value of the removal amount exceeds a certain value. 
     Note that the term “accumulated operating time” refers to the accumulated time for which the wet etching apparatus has operated from when the chemical solution has been replaced to immediately before the etching process has been applied to the wafer. The term “accumulated number of processed wafers” refers to the accumulated number of wafers that have been processed from when the chemical solution has been replaced to immediately before the etching process has been applied to the wafer. The term “removal amount” refers to the amount that has been removed by etching from the wafer to which the etching process has been applied by the wet etching apparatus. 
     Thus, the monitoring system according to the above-described configuration acquires a combination of normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount as learning data, and constructs a predictive model that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers, based on the acquired learning data. That is to say, the predictive model is constructed such that, upon input of values of the accumulated operating time and the accumulated number of processed wafers, the predictive model outputs a value of the removal amount removed by etching predicted from the input values of the accumulated operating time and the accumulated number of processed wafers. 
     Also, the monitoring system according to the above-described configuration acquires actual values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount with respect to a wet etching apparatus when it is in operation, and calculates a predicted value of the removal amount removed by etching, by inputting the acquired actual values of the accumulated operating time and the accumulated number of processed wafers to the predictive model. Then, the monitoring system according to the above-described configuration calculates the difference between the predicted value and the actual value of the removal amount, as an indicator value serving as a measure of how necessary it is to replace the chemical solution, and outputs information regarding replacement of the chemical solution based on the calculated indicator value. 
     Therefore, the monitoring system according to the above-described configuration can appropriately construct a predictive model that predicts a value of the removal amount from values of the accumulated operating time and the accumulated number of processed wafers. Moreover, the monitoring system according to the above-described configuration can derive a predicted value of the removal amount with respect to a wet etching apparatus when it is in operation, using the constructed predictive model, calculate the difference between the predicted value and an actual value of the removal amount, and outputs information regarding replacement of the chemical solution based on the calculated difference. Thus, with the monitoring system according to the above-described configuration, the timing at which removal unevenness will occur in a wet etching apparatus can be appropriately predicted based on the above-described findings of the inventors. Moreover, use of the monitoring system according to the above-described configuration can suppress excessive replacement of the chemical solution in the target wet etching apparatus, and can reduce the wet etching cost. 
     Note that the difference (i.e., indicator value) between the predicted value and the actual value of the removal amount may be expressed as the result of subtraction of the predicted value and the actual measured value, or may be expressed as the ratio between the predicted value and the actual value. Also, the predictive model is configured to indicate the relationship of the accumulated operating time and the accumulated number of processed wafers with the removal amount, by statistically analyzing the learning data. The type of the predictive model needs not be limited and may be selected as appropriate, depending on an embodiment, as long as the predictive model is obtained through such statistical analysis. Examples of the predictive model may include a regression model, a neural network, a decision tree model, and the like. 
     In the monitoring system according to an aspect, the output unit may be configured to compare the calculated indicator value and a threshold value and to output a message for prompting replacement of the chemical solution as the information regarding replacement of the chemical solution, if it is judged that the indicator value exceeds the threshold value as a result of the comparison. With this configuration, a monitoring system that prompts replacement of the chemical solution at appropriate timing can be provided. 
     In the monitoring system according to an aspect, the threshold value may be set based on the difference between an output value obtained by inputting values of the accumulated operating time and the accumulated number of processed wafers when an abnormality has occurred during the etching process in the wet etching apparatus to the predictive model and a value of the removal amount when the abnormality has occurred. With this configuration, a threshold value constituting an indicator used to determine the timing of replacement of the chemical solution can be set appropriately. 
     In the monitoring system according to an aspect, the model construction unit may be configured to construct the predictive model by performing regression analysis of normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data. With this configuration, a predictive model that predicts the removal amount from the accumulated operating time and the accumulated number of processed wafers can be constructed appropriately. 
     In the monitoring system according to an aspect, the wet etching apparatus may include a chemical solution replacement unit configured to perform replacement of the chemical solution. Moreover, in the monitoring system according to an aspect, the output unit may be configured to output an instruction to replace the chemical solution to the chemical solution replacement unit of the wet etching apparatus, as the information regarding replacement of the chemical solution. With this configuration, replacement of the chemical solution can be automated. 
     Note that one or more embodiments of the monitoring system may also include an information processing method and a program that realize the above respective configurations, and a storage medium that stores such a program and can be read by a computer or another kind of apparatus, machine, or the like. Here, a storage medium that can be read by a computer or the like is a medium that accumulates information such as a program by means of an electric, magnetic, optical, mechanical, or chemical effect. Moreover, the monitoring system according to one or more embodiments may be constituted by one or more information processing apparatuses. Furthermore, it is also possible to extract some constituent elements of the monitoring system according to one or more embodiments and construct an apparatus, a method, a program, and a storage medium storing the program according to one or more embodiments. 
     For example, a learning apparatus according to an aspect includes a learning data acquisition unit configured to acquire, as learning data, a set of normal values of:
     an accumulated operating time indicating the accumulated time for which a wet etching apparatus has operated from when a chemical solution has been replaced to when an etching process has been applied to a wafer,   an accumulated number of processed wafers indicating the accumulated number of wafers that have been processed from when the chemical solution has been replaced to when the etching process has been applied to the wafer, and   a removal amount indicating the amount that has been removed by etching from the wafer to which the etching process has been applied; and a model construction unit configured to construct a predictive model that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers, based on the normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data.   

     Also, for example, a learning method according to an aspect is a learning method including: a step of acquiring, as learning data, a set of normal values of:
     an accumulated operating time indicating the accumulated time for which a wet etching apparatus has operated from when a chemical solution has been replaced to when an etching process has been applied to a wafer,   an accumulated number of processed wafers indicating the accumulated number of wafers that have been processed from when the chemical solution has been replaced to when the etching process has been applied to the wafer, and   a removal amount indicating the amount that has been removed by etching from the wafer to which the etching process has been applied; and a step of constructing a predictive model that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers, based on the normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data, the steps being executed by a computer.   

     Also, for example, a monitoring apparatus according to an aspect includes an actual value acquisition unit configured to acquire, with respect to a wet etching apparatus when it is in operation, actual values of:
     an accumulated operating time indicating the accumulated time for which the wet etching apparatus has operated from when a chemical solution has been replaced to when an etching process has been applied to a wafer,   an accumulated number of processed wafers indicating the accumulated number of wafers that have been processed from when the chemical solution has been replaced to when the etching process has been applied to the wafer, and   a removal amount indicating the amount that has been removed by etching from the wafer to which the etching process has been applied; an indicator value calculation unit configured to calculate a predicted value of the removal amount by inputting the acquired actual values of the accumulated operating time and the accumulated number of processed wafers to a predictive model that is constructed so as to predict a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers, and calculate the difference between the calculated predicted value and the acquired actual value of the removal amount, as an indicator value serving as a measure of how necessary it is to replace the chemical solution; and an output unit configured to output information regarding replacement of the chemical solution based on the calculated indicator value.   

     Also, for example, a monitoring method according to an aspect is a monitoring method including: a step of acquiring, with respect to a wet etching apparatus when it is in operation, actual values of:
     an accumulated operating time indicating the accumulated time for which the wet etching apparatus has operated from when a chemical solution has been replaced to when an etching process has been applied to a wafer,   an accumulated number of processed wafers indicating the accumulated number of wafers that have been processed from when the chemical solution has been replaced to when the etching process has been applied to the wafer, and   a removal amount indicating the amount that has been removed by etching from the wafer to which the etching process has been applied; a step of calculating a predicted value of the removal amount by inputting the acquired actual values of the accumulated operating time and the accumulated number of processed wafers to a predictive model that is constructed so as to predict a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers; a step of calculating the difference between the calculated predicted value and the acquired actual value of the removal amount, as an indicator value serving as a measure of how necessary it is to replace the chemical solution; and a step of outputting information regarding replacement of the chemical solution based on the calculated indicator value, the steps being executed by a computer.   

     One or more aspects can provide a technique that enables the timing at which removal unevenness will occur in a wet etching apparatus to be appropriately predicted. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram schematically illustrating an example of an instance according to one or more embodiments. 
         FIG. 2A  is a diagram illustrating results of measurement of an accumulated operating time, an accumulated number of processed wafers, and a removal amount. 
         FIG. 2B  is a diagram illustrating results of calculation of differences between predicted values and actual values of a removal amount. 
         FIG. 3  is a diagram schematically illustrating an example of a hardware configuration of a monitoring system according to one or more embodiments. 
         FIG. 4  is a diagram schematically illustrating an example of a software configuration of a monitoring system according to one or more embodiments. 
         FIG. 5  is a diagram illustrating an example of a processing procedure performed by a monitoring system according to one or more embodiments when constructing a predictive model. 
         FIG. 6  is a diagram schematically illustrating an example of operation data indicating an operation state of a wet etching apparatus according to one or more embodiments. 
         FIG. 7  is a diagram schematically illustrating an example of a data table for managing learning data according to one or more embodiments. 
         FIG. 8  is a diagram schematically illustrating an example of a data table for managing a predictive model according to one or more embodiments. 
         FIG. 9  is a diagram illustrating an example of a processing procedure performed by a monitoring system according to one or more embodiments when monitoring a state of a chemical solution in a wet etching apparatus. 
         FIG. 10  is a diagram schematically illustrating an example of results of calculation of an indicator value according to one or more embodiments. 
         FIG. 11  is a diagram schematically illustrating an example of a software configuration of a monitoring system according to a modification. 
         FIG. 12  is a diagram schematically illustrating an example of a configuration of a monitoring system according to a modification. 
         FIG. 13  is a diagram schematically illustrating an example of a configuration of a wet etching apparatus according to a modification. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments according to an aspect (also referred to as “an embodiment” or “one or more embodiments” below) will be described based on the drawings. However, the embodiments described below is merely an example of the present invention in every respect. Needless to say, various improvements and modifications may be made without departing from the scope of the present invention. That is to say, to implement the present invention, a specific configuration corresponding to one or more embodiments may also be employed as appropriate. Note that, although data that is used in one or more embodiments is described using natural language, more specifically, the data is defined by pseudo-language, commands, parameters, machine language, or the like that can be recognized by a computer. 
     § 1 Application Example 
     First, an example of an instance according to one or more embodiments will be described using  FIG. 1 .  FIG. 1  schematically shows an example of an instance of using a monitoring system  1  according to one or more embodiments. 
     The monitoring system  1  according to one or more embodiments is an information processing apparatus for monitoring the state of a chemical solution for use in an etching process performed by a wet etching apparatus  3 . The type of the wet etching apparatus  3  needs not be limited, and may be selected as appropriate, depending on an embodiment. A known wet etching apparatus may be used as the wet etching apparatus  3 . 
     In order to specify the situations in which removal unevenness is likely to occur, data on an accumulated operating time, an accumulated number of processed wafers, and a removal amount was collected under the following conditions using a known wet etching apparatus. 
     &lt;Data Collecting Conditions&gt; 
     
         
         Wet etching apparatus: DIP type (batch processing) wet bench 
         Type of chemical solution: iodine/potassium iodide etchant for Au 
         Type of wafer: silicon wafer 
         Processing of wafer: Au is deposited on a silicon wafer through sputtering, and an interconnect pattern is formed using a photoresist. 
         Replacement frequency of chemical solution: at least once a month (this changed for a while in the sixth month and thereafter) 
       
    
     The term “accumulated operating time” as used herein refers to the accumulated time for which the wet etching apparatus was operated from when the chemical solution was replaced to immediately before the etching process was applied to a wafer. The term “accumulated number of processed wafers” refers to the accumulated number of wafers that have been processed from when the chemical solution was replaced to immediately before the etching process was applied to the wafer. The term “removal amount” refers to the amount that has been removed by etching from the wafer to which the etching process was applied by the wet etching apparatus. 
     While data was collected, each time the chemical solution was replaced, the values of the accumulated operating time and the accumulated number of processed wafers were reset to 0. Dimensions between electrodes of a wafer change as a result of performing the etching process. The resistance value between the electrodes varies in accordance with the change in the dimensions between the electrodes. Thus, the resistance value of a wafer was measured before and after the etching process was performed, the amount of change in the resistance value of the wafer was calculated from the difference between the obtained measured values, and, based on the calculated amount of change in the resistance value of the wafer, the removal amount removed by etching from the wafer was obtained. Note that the wet etching apparatus used to collect the data houses a single lot of wafers (three wafers) in its magazine and etches the wafers in a single lot together, and therefore, the removal amount was measured through sampling from each lot. 
       FIG. 2A  shows the collected data. During a period in which the wet etching apparatus operated normally, that is, during a period in which removal unevenness did not occur on wafers, the removal amount removed from a wafer basically decreased in accordance with the accumulated operating time and the accumulated number of processed wafers. On the other hand, in the sixth month and thereafter when the frequency of replacement of the chemical solution was reduced, at the time when the accumulated operating time and the accumulated number of processed wafers had increased to a certain extent, the removal amount removed from a wafer that had been decreasing started to increase. Then, removal unevenness occurred during a period indicated in  FIG. 2A . 
     These trends showed that a situation in which, although the accumulated operating time and the accumulated number of processed wafers are increasing, the removal amount removed from a wafer is increasing may increase the risk of removal unevenness. Thus, a predictive model that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers was constructed, using data collected during a period in which the removal amount removed from a wafer tended to decrease. The data was analyzed using regression analysis to construct the predictive model (regression model). Then, the differences between predicted values of the removal amount derived from the constructed predictive model and actual measured values (data in  FIG. 2A ) of the removal amount were calculated. 
       FIG. 2B  shows the results of the calculation of the differences between the predicted values and the actual values of the removal amount. As shown in  FIG. 2B , it was found that the higher the risk of removal unevenness, the greater the difference between a predicted value of the removal amount derived from the predictive model and a corresponding actual measured value of the removal amount. Therefore, the inventors have found that the risk of removal unevenness can be predicted by using the difference between a predicted value of the removal amount derived from a predictive model and a corresponding actual measured value of the removal amount, as an indicator value. 
     Thus, as shown in  FIG. 1 , in a learning phase, the monitoring system  1  acquires a set of normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount with respect to the wet etching apparatus  3 , as learning data. Then, based on the acquired learning data, the monitoring system  1  constructs a predictive model that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers. The predictive model is constructed such that, upon input of values (actual values) of the accumulated operating time and the accumulated number of processed wafers, the predictive model outputs a value (predicted value) of the removal amount removed by etching predicted from the input values of the accumulated operating time and the accumulated number of processed wafers. 
     On the other hand, in a monitoring phase, the monitoring system  1  acquires actual values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount with respect to the wet etching apparatus  3  when it is in operation. Subsequently, the monitoring system  1  inputs the acquired actual values of the accumulated operating time and the accumulated number of processed wafers to the predictive model, thereby calculating a predicted value of the removal amount removed by etching with respect to the wet etching apparatus  3 . Then, the monitoring system  1  calculates the difference between the calculated predicted value and the acquired actual value of the removal amount as an indicator value serving as a measure of how necessary it is to replace the chemical solution, and outputs information regarding replacement of the chemical solution, based on the calculated indicator value. 
     In this manner, the monitoring system  1  according to one or more embodiments can appropriately construct a predictive model that predicts the value of the removal amount from the values of the accumulated operating time and the accumulated number of processed wafers with respect to the wet etching apparatus  3 . Also, the monitoring system  1  according to one or more embodiments can derive a predicted value of the removal amount with respect to the wet etching apparatus  3  when it is in operation, by using the constructed predictive model, calculate the difference between the predicted value and a corresponding actual value of the removal amount, and output information regarding replacement of the chemical solution based on the calculated difference. 
     Therefore, according to one or more embodiments, the timing at which removal unevenness will occur in the wet etching apparatus  3  can be appropriately predicted based on the above-described findings of the inventors. Accordingly, use of the monitoring system  1  according to one or more embodiments can suppress excessive replacement of the chemical solution in the wet etching apparatus  3 , and can reduce the wet etching cost. 
     Note that the wet etching apparatus  3  of the learning phase may be different from the wet etching apparatus  3  of the monitoring phase. That is to say, the wet etching apparatus from which learning data is acquired to construct a predictive model and the wet etching apparatus to be monitored for the occurrence of removal unevenness may be different. 
     §2 Configuration Example 
     [Hardware Configuration] 
     Next, an example of a hardware configuration of the monitoring system  1  according to one or more embodiments will be described using  FIG. 3 .  FIG. 3  schematically shows an example of the hardware configuration of the monitoring system  1  according to one or more embodiments. 
     As shown in  FIG. 3 , the monitoring system  1  according to one or more embodiments is a computer in which a control unit  11 , a storage unit  12 , an external interface  13 , an input device  14 , an output device  15 , and a drive  16  are electrically connected to one another. Note that, in  FIG. 3 , the external interface is denoted as “external I/F”. 
     The control unit  11  includes a CPU (Central Processing Unit), which is a hardware processor, a RAM (Random Access Memory), a ROM (Read Only Memory), and the like, and controls the constituent elements as appropriate for information processing. The storage unit  12  is an auxiliary storage such as a hard disk drive or a solid-state drive, for example, and stores various kinds of information such as a program  8  to be executed by the control unit  11 . The program  8  is a program for causing the monitoring system  1  to execute learning processing ( FIG. 5 ) and monitoring processing ( FIG. 9 ), which will be described later. The details will be described later. 
     The external interface  13  is a dedicated port, a USB (Universal Serial Bus) port, or the like, for example, and is an interface for connection to an external device. The type and number of external interfaces  13  may be determined as appropriate, depending on an embodiment. The monitoring system  1  is connected to the wet etching apparatus  3  via the external interface  13 . 
     The input device  14  is a device for performing input, such as a mouse or a keyboard, for example. The output device  15  is a device for performing output, such as a display or a speaker, for example. An operator can operate the monitoring system  1  via the input device  14  and the output device  15 . 
     The drive  16  is a CD drive, a DVD drive, or the like, for example, and is a drive device for loading a program stored in a storage medium  9 . The type of the drive  16  may be selected as appropriate in accordance with the type of storage medium  9 . The program  8  may also be stored in this storage medium  9 . 
     The storage medium  9  is a medium that accumulates information such as that of a program by means of an electric, magnetic, optical, mechanical, or chemical effect, so that a computer or other kinds of apparatuses, machines, or the like can read the recorded information such as that of a program. The monitoring system  1  may also acquire the program  8  from this storage medium  9 . 
     Here,  FIG. 3  shows a disk-type storage medium such as a CD or DVD as an example of the storage medium  9 . However, the type of the storage medium  9  is not limited to a disk type, and may also be a type other than a disk type. Examples of a storage medium of a type other than a disk type may include a semiconductor memory such as a flash memory. 
     Note that, regarding the specific hardware configuration of the monitoring system  1 , constituent elements may be omitted, replaced, and added as appropriate, depending on an embodiment. For example, the control unit  11  may also include a plurality of processors. The monitoring system  1  may also be constituted by a plurality of information processing apparatuses. The monitoring system  1  may also be an information processing apparatus designed exclusively for a service to be provided, as well as a general-purpose server device, a PC (Personal Computer), or the like. 
     [Software Configuration] 
     Next, an example of a software configuration of the monitoring system  1  according to one or more embodiments will be described using  FIG. 4 .  FIG. 4  schematically shows an example of the software configuration of the monitoring system  1  according to one or more embodiments. 
     The control unit  11  in the monitoring system  1  loads the program  8  stored in the storage unit  12  to the RAM. The control unit  11  then interprets and executes the program  8  loaded to the RAM, using the CPU, and controls the constituent elements. Thus, as shown in  FIG. 4 , the monitoring system  1  according to one or more embodiments is configured as a computer including a learning data acquisition unit  111 , a model construction unit  112 , an actual value acquisition unit  113 , an indicator value calculation unit  114 , and an output unit  115 , as software modules. 
     In the learning phase, the learning data acquisition unit  111  acquires a set of normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount as learning data  121 . The model construction unit  112  constructs a predictive model  122  that predicts the value of the removal amount depending on the values of the accumulated operating time and the accumulated number of processed wafers, based on the normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data  121 . 
     Next, in the monitoring phase, the actual value acquisition unit  113  acquires actual values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount with respect to the wet etching apparatus  3  when it is in operation. The indicator value calculation unit  114  calculates a predicted value of the removal amount by inputting the acquired actual values of the accumulated operating time and the accumulated number of processed wafers to the predictive model  122 , and calculates the difference between the calculated predicted value and the acquired actual value of the removal amount, as an indicator value serving as a measure of how necessary it is to replace the chemical solution. The output unit  115  outputs information regarding replacement of the chemical solution based on the calculated indicator value. 
     The software modules of the monitoring system  1  will be described in detail in an operation example, which will be described later. Note that one or more embodiments describes an example in which all of the software modules of the monitoring system  1  are realized by a general-purpose CPU. However, some or all of those software modules may also be realized by one or more dedicated processors. Regarding the software configuration of the monitoring system  1 , software modules may be omitted, replaced, and added as appropriate, depending on an embodiment. 
     §3 Operation Example 
     Next, an operation example of the monitoring system  1  will be described. The monitoring system  1  according to one or more embodiments performs two types of operations: the operation of the learning phase in which the predictive model  122  is constructed and the operation of the monitoring phase in which the state of the chemical solution in the wet etching apparatus  3  is monitored using the predictive model  122  constructed in the learning phase. Hereinafter, processing procedures of the respective phases will be described. 
     [Learning Phase] 
     First, a processing procedure of the learning phase, in which the predictive model  122  is constructed, will be described using  FIG. 5 .  FIG. 5  shows an example of the processing procedure of the learning phase of the monitoring system  1  according to one or more embodiments. The processing procedure of the learning phase described below is an example of a “learning method” of one or more embodiments. However, the processing procedure described below is merely an example, and processing may be modified to the extent possible. Regarding the processing procedure described below, steps may be omitted, replaced, and added as appropriate, depending on an embodiment. 
     Step S 101   
     First, in step S 101 , the control unit  11  functions as the learning data acquisition unit  111 , and acquires a set of normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount as the learning data  121 . 
     The method for acquiring the learning data  121  may be selected as appropriate, depending on an embodiment. For example, the control unit  11  may acquire operation data that indicates the operation state of the wet etching apparatus  3  during a period in which an abnormality such as removal unevenness does not occur. The control unit  11  may then extract the values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount from the acquired operation data and thereby acquire the learning data  121 . Note that the operation data needs not be acquired in real time, and the control unit  11  may also acquire the operation data after the wet etching apparatus  3  stops operating. 
       FIG. 6  schematically shows an example of the operation data of the wet etching apparatus  3 . The control unit  11  can acquire the operation data from, for example, the wet etching apparatus  3  itself, a known checking apparatus (not shown) that checks the operation of the wet etching apparatus  3 , or the like. The operation data shown as an example in  FIG. 6  has fields storing the values of “check time”, “lot ID”, “batch ID”, “accumulated operating time”, “accumulated number of processed wafers”, “removal amount”, “amount of chemical solution”, and “solution concentration”, respectively. 
     “Check time” indicates the time at which the operation state of the wet etching apparatus  3  is checked. “Lot ID” and “batch ID” are identifiers for identifying wafers that have been etched in the wet etching apparatus  3 . “Amount of chemical solution” indicates the amount of the chemical solution used in the etching process. “Solution concentration” indicates the concentration of the chemical solution used in the etching process. 
     The control unit  11  can extract the fields storing the check time, the accumulated operating time, the accumulated number of processed wafers, and the removal amount from the above-described operation data and thereby acquire the learning data  121 . The control unit  11  may then store the acquired learning data  121  in the storage unit  12  in a predetermined format. 
       FIG. 7  schematically shows an example of a data table for managing the learning data  121 . The data table shown as an example in  FIG. 7  has fields storing the values of “check time”, “accumulated operating time”, “accumulated number of processed wafers”, “removal amount”, and “flag”, respectively. The control unit  11  may store the learning data  121  in such a data table format. However, the data format used to manage the learning data  121  needs not be limited to a table format such as that described above, and may be selected as appropriate, depending on an embodiment. After acquiring the learning data  121 , the control unit  11  advances the processing to the next step S 102 . 
     Note that the flag indicates whether or not that record (line data) is to be used as the learning data  121 . In  FIG. 7 , “FALSE” indicates that the record is not to be used as the learning data  121 , and “TRUE” indicates that the record is to be used as the learning data  121 . In this step S 101 , when extracting values of the above-described fields from the operation data, the control unit  11  may select whether or not to use respective records extracted from the operation data as the learning data  121 . 
     This selection may also be performed by the operator, for example. In this case, the control unit  11  outputs the records extracted from the operation data to the output device  15  and receives selections with regard to whether or not the respective records are to be used as the learning data  121 . The operator operates the input device  14  to select whether or not to use the respective records as the learning data  121 . The control unit  11  judges whether or not to use the respective records extracted from the operation data as the learning data  121 , based on the operation of the input device  14  that is performed by the operator. 
     Moreover, from  FIGS. 2A and 2B  above, when the removal amount removed by etching tends to decrease as the accumulated operating time and the accumulated number of processed wafers increase, there is substantially no risk of removal unevenness, whereas when the removal amount tends to increase as the accumulated operating time and the accumulated number of processed wafers increase, it is predicted that the risk of removal unevenness increases. Thus, the control unit  11  may judge whether or not to use the respective records extracted from the operation data as the learning data  121 , based on the value of the removal amount and without resorting to the selection performed by the operator. For example, the control unit  11  may refer to the value of the removal amount of certain records, and judge that those records are to be used as the learning data  121 , if the value of the removal amount tends to decrease. On the other hand, the control unit  11  may judge that those records are not to be used as the learning data  121 , if the value of the removal amount tends to increase. However, the method for selecting the learning data  121  is not limited to this example, and a portion of the data during a period in which the value of the removal amount tends to increase may also be used as the learning data  121 . 
     Step S 102   
     In the next step S 102 , the control unit  11  functions as the model construction unit  112 , and constructs the predictive model  122  that predicts a value of the removal amount depending on values of the accumulated operating time and the accumulated number of processed wafers, based on the normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data  121  acquired in step S 101 . The type of the predictive model  122  may be selected as appropriate, depending on an embodiment. For example, a regression model may be employed as the predictive model  122 . The regression model can be expressed by the following mathematical equation (1): 
         y=c   0   +c   1   x   1   +c   2   x   2   (1)
 
     Note that y corresponds to the removal amount, x 1  corresponds to the accumulated operating time, and x 2  corresponds to the accumulated number of processed wafers. The items to which x 1  and x 2  correspond may also be exchanged. Also, C 0  is an intercept, and C 1  and C 2  are regression coefficients. The control unit  11  calculates the values of C 0  to C 2  by performing regression analysis of normal values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the learning data  121 , and thereby constructs the predictive model  122  (regression model). The control unit  11  may store the calculated values of C 0  to C 2  in a predetermined format in the storage unit  12  in order to save the constructed predictive model  122 . 
       FIG. 8  schematically shows an example of a data table for managing the predictive model  122 . The data table shown as an example in  FIG. 8  has fields storing the values of C 0  to C 2  and a standard deviation (Rsd), respectively. The control unit  11  may save the predictive model  122  in such a data table format. However, the data format used to manage the predictive model  122  needs not be limited to a table format such as that described above, and may be selected as appropriate, depending on an embodiment. After constructing the predictive model  122 , the control unit  11  ends the processing of the learning phase according to this operation example. 
     Note that the standard deviation (Rsd) field stores a standard deviation of errors of the predictive model  122  (regression model) relative to the learning data  121 . The control unit  11  can calculate the value of the standard deviation based on the predictive model  122  constructed through the regression analysis and the learning data  121 . However, the value of the standard deviation is not a constituent element of the predictive model  122 . Therefore, calculation of the standard deviation may also be omitted. That is to say, the standard deviation (Rsd) field may also be omitted from the above-described data table. 
     Moreover, the type of the predictive model  122  needs not be limited to a specific type, as long as the predictive model  122  is obtained through statistical analysis that can derive the relationship of the accumulated operating time and the accumulated number of processed wafers with the removal amount. That is to say, the type of the predictive model  122  needs not be limited to the above-described regression model, and may be selected as appropriate, depending on an embodiment, as long as the predictive model  122  can output, in response to input of values of the accumulated operating time and the accumulated number of processed wafers, a value of the removal amount predicted from the input values of the accumulated operating time and the accumulated number of processed wafers. The above-described regression model, as well as a neural network, a decision tree model (a regression tree, a random forest, etc.), or the like, for example, can be used as the predictive model  122 . 
     [Monitoring Phase] 
     Next, a processing procedure of the monitoring phase, in which the state of the chemical solution in the wet etching apparatus  3  is monitored using the constructed predictive model  122 , will be described using  FIG. 9 .  FIG. 9  shows an example of a processing procedure of the monitoring phase of the monitoring system  1  according to one or more embodiments. The processing procedure of the monitoring phase described below is an example of a “monitoring method” of one or more embodiments. However, the processing procedure described below is merely an example, and processing may be modified to the extent possible. Regarding the processing procedure described below, steps may be omitted, replaced, and added as appropriate, depending on an embodiment. 
     Step S 201   
     First, in step S 201 , the control unit  11  functions as the actual value acquisition unit  113 , and acquires actual values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount with respect to the wet etching apparatus  3  when it is in operation. 
     The method for acquiring the actual values may be selected as appropriate, depending on an embodiment. For example, the control unit  11  may acquire the same operation data as in the above-described step S 101  in real time from the wet etching apparatus  3  when it is in operation, a checking apparatus (not shown), or the like. The control unit  11  then extracts values of the respective fields of the accumulated operating time, the accumulated number of processed wafers, and the removal amount contained in the acquired operation data, and can thereby acquire actual values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount. After acquiring the actual values, the control unit  11  advances the processing to the next step S 202 . 
     Step S 202   
     In the next step S 202 , the control unit  11  functions as the indicator value calculation unit  114 , and calculates a predicted value of the removal amount by inputting the actual values of the accumulated operating time and the accumulated number of processed wafers that have been acquired in step S 201  to the predictive model  122 . 
     This step S 202  is performed as appropriate in accordance with the type of the predictive model  122  that has been constructed in the above-described step S 102 . According to one or more embodiments, the predictive model  122  is constructed using the above-described regression model. Therefore, the control unit  11  performs calculation processing of the predictive model  122  (regression model) expressed by the mathematical equation (1) above, by substituting the actual values of the accumulated operating time and the accumulated number of processed wafers that have been obtained in step S 201  for x 1  and x 2 , respectively, and using the values of C 0  to C 2  that have been calculated in step S 102 . In this manner, the control unit  11  can calculate the predicted value of the removal amount. After calculating the predicted value of the removal amount, the control unit  11  advances the processing to the next step S 203 . 
     Step S 203   
     In the next step S 203 , the control unit  11  calculates the difference between the predicted value of the removal amount calculated in step S 202  and the actual value of the removal amount acquired in step S 201 , thereby acquiring an indicator value serving as a measure of how necessary it is to replace the chemical solution in the wet etching apparatus  3 . Note that the difference between the predicted value and the actual value of the removal amount may be expressed as the result of subtraction of the predicted value and the actual value, or may be expressed as the ratio between the predicted value and the actual value. 
       FIG. 10  schematically shows an example of the results of calculation of an indicator value. A data table shown as an example in  FIG. 10  has fields storing the actual values acquired in step S 201 , the predicted value of the removal amount calculated in step S 202 , and the indicator value calculated in step S 203 . One record indicates one calculation result. The control unit  11  may save the results of processing in steps S 201  to S 203  in such a data table format in the storage unit  12 . However, the data format used to save the results of calculation of the indicator value needs not be limited to a table format such as that described above, and may be selected as appropriate, depending on an embodiment. After calculating the indicator value, the control unit  11  advances the processing to the next step S 204 . 
     Step S 204   
     In the next step S 204 , the control unit  11  functions as the output unit  115 , and compares the indicator value calculated in step S 203  with a preset threshold value. Then, as a result of this comparison, if the control unit  11  judges that the indicator value exceeds the threshold value, the processing is advanced to the next step S 205 . On the other hand, if the control unit  11  judges that the indicator value does not exceed the threshold value, the processing of the next step S 205  is skipped, and the processing of the monitoring phase according to this operation example is ended. 
     Note that the threshold value may be determined as appropriate. For example, the control unit  11  may set an n-fold (e.g., threefold) value of the standard deviation that has been calculated in the above-described step S 102 , as the threshold value. Moreover, for example, the threshold value may also be set based on the difference between an output value obtained by inputting the values of the accumulated operating time and the accumulated number of processed wafers when an abnormality has occurred in the etching process of the wet etching apparatus  3  to the predictive model  122  and the value of the removal amount when the abnormality has occurred. Note that the control unit  11  can acquire the values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount when an abnormality such as the removal unevenness has occurred, from the operation data when the abnormality has occurred. Also, the control unit  11  can acquire the operation data as in the above-described steps S 101  and S 201 . 
     Step S 205   
     In the next step S 205 , the control unit  11  functions as the output unit  115 , and outputs information regarding replacement of the chemical solution based on the indicator value calculated in step S 203 . According to one or more embodiments, the control unit  11  outputs a message for prompting replacement of the chemical solution, as the information regarding replacement of the chemical solution. 
     The destination to which the message is to be output may be selected as appropriate, depending on an embodiment. For example, the control unit  11  may output the message via the output device  15 . Specifically, the control unit  11  may display the message on a display, or may output the message by voice from a loudspeaker. Also, for example, the control unit  11  may output the message to an external device by electronic mail or the like. In this case, the address of the external device serving as the destination of the message may be stored in the storage unit  12 , for example. 
     Upon completion of the output of the information regarding replacement of the chemical solution, the control unit  11  ends the processing of the monitoring phase according to this operation example. Note that, after ending the processing of the monitoring phase, the control unit  11  may again execute processing from step S 201 . In this manner, the monitoring system  1  may continuously monitor the state of the chemical solution in the wet etching apparatus  3 . 
     [Features] 
     As described above, in one or more embodiments, a predictive model that predicts the value of the removal amount from the values of the accumulated operating time and the accumulated number of processed wafers can be appropriately constructed through processing of steps S 101  and S 102  above. Also, through processing of steps S 201  to S 205  above, a predicted value of the removal amount with respect to the wet etching apparatus  3  when it is in operation can be derived using the constructed predictive model, the difference between the predicted value and a corresponding actual value of the removal amount can be calculated as an indicator value, and information regarding replacement of the chemical solution can be output based on the calculated indicator value. 
     Therefore, according to one or more embodiments, the timing at which removal unevenness will occur in the wet etching apparatus  3  can be appropriately predicted based on the above-described findings of the inventors. Accordingly, use of the monitoring system  1  according to one or more embodiments can suppress excessive replacement of the chemical solution in the wet etching apparatus  3 , and can reduce the wet etching cost. 
     § 4 Modifications 
     Although embodiments have been described above in detail, the above descriptions are merely examples of the present invention in all aspects. Needless to say, various improvements and modifications may be made without departing from the scope of the present invention. For example, the following modifications are possible. Note that, in the following description, the same constituent elements as the constituent elements described in the above embodiments are assigned the same signs, and descriptions of the same points as the points described in the above embodiments are omitted as appropriate. The following modifications may be combined as appropriate. 
     4.1 
     In  FIGS. 3 and 4  above, the monitoring system  1  according to one or more embodiments is constituted by a single computer. However, the configuration of the monitoring system  1  needs not be limited to this example, and may be selected as appropriate, depending on an embodiment. For example, it is also possible to extract constituent elements corresponding to the learning phase or the monitoring phase of the monitoring system  1  and construct a system, an apparatus, a method, a program, and a storage medium storing the program according to another embodiment. 
       FIG. 11  schematically shows an example of a software configuration of a monitoring system  1 A according to a modification. The monitoring system  1 A is constituted by a learning apparatus  21  and a monitoring apparatus  22 . The learning apparatus  21  and the monitoring apparatus  22  may respectively have the same hardware configurations as those of the monitoring system  1  described above. The learning apparatus  21  and the monitoring apparatus  22  each may be an information processing apparatus designed exclusively for a service to be provided, as well as a general-purpose server device, a PC, a PLC (programmable logic controller), or the like. 
     The learning apparatus  21  is configured as a computer including the learning data acquisition unit  111  and the model construction unit  112  as software modules that are realized by the computer executing a program stored in a storage unit, using a control unit (CPU). On the other hand, the monitoring apparatus  22  is configured as a computer including the actual value acquisition unit  113 , the indicator value calculation unit  114 , and the output unit  115  as software modules that are realized by the computer executing a program stored in a storage unit, using a control unit. 
     Thus, the learning apparatus  21  executes the processing of the above-described steps S 101  and S 102  of the learning phase. The monitoring apparatus  22  executes the processing of the above-described steps S 201  to S 205  of the monitoring phase. Note that the predictive model  122  constructed by the learning apparatus  21  may be transmitted from the learning apparatus  21  to the monitoring apparatus  22  as appropriate. Data that indicates the predictive model  122  may be transmitted via a network or the like, for example. In this case, the learning apparatus  21  and the monitoring apparatus each include a communication interface for performing data communication via a network, as appropriate. 
     4.2 
     In one or more embodiments, the control unit  11  compares the indicator value and the threshold value (step S 204 ), and if the indicator value exceeds the threshold value, the control unit  11  outputs a message for prompting replacement of the chemical solution, as the information regarding replacement of the chemical solution (step S 205 ). However, the output method and contents of the information regarding replacement of the chemical solution need not be limited to this example, and may also be determined as appropriate, depending on an embodiment. For example, step S 204  may be omitted. Also, the control unit  11  may output the indicator value calculated in step S 203  on an as-is basis, as the information regarding replacement of the chemical solution. 
     4.3 
     In one or more embodiments, in each of the learning phase and the monitoring phase, the monitoring system  1  acquires the values of the accumulated operating time, the accumulated number of processed wafers, and the removal amount based on the operation data of the wet etching apparatus  3 . However, the method for acquiring these values needs not be limited to this example, and may be selected as appropriate, depending on an embodiment. 
     For example, the monitoring system  1  may acquire the value of the accumulated operating time by counting time from when the chemical solution has been replaced to immediately before the etching process has been applied to a wafer, based on a timer (not shown) or the like. Also, the monitoring system  1  may acquire the value of the accumulated number of processed wafers by counting the number of wafers to which the etching process has been applied after replacement of the chemical solution. 
     Moreover, the monitoring system  1  may also measure the resistance value of a wafer before and after the etching process is performed, calculate the amount of change in the resistance value of the wafer using the difference between the obtained measured values, and derive the removal amount removed by etching from the wafer, based on the calculated amount of change in the resistance value of the wafer. With this method, the removal amount removed from the wafer can be simply and accurately measured. However, the method for specifying the removal amount needs not be limited to this example, and may be selected as appropriate, depending on an embodiment. For example, the monitoring system  1  may also measure the weight of a wafer before and after the etching process is performed, and calculate the removal amount removed by etching from the wafer, using the difference between the obtained measured values. Moreover, for example, the monitoring system  1  may also measure a step that has been formed on a wafer as a result of the etching process, and derive the removal amount removed by etching based on the depth of the step. Furthermore, for example, the monitoring system  1  may also measure the width of a pattern that has been formed on the wafer as a result of the etching process, and derive the removal amount removed by etching based on the measured value of the width. 
     4.4 
     In the above-described step S 205 , the control unit  11  of the monitoring system  1  functions as the output unit  115 , and outputs a message for prompting replacement of the chemical solution, as the information regarding replacement of the chemical solution. However, the information regarding replacement of the chemical solution needs not be limited to such a message, and may be determined as appropriate, depending on an embodiment. 
       FIG. 12  schematically shows an example of a configuration of a monitoring system  1 B according to a modification.  FIG. 13  schematically shows an example of a configuration of a wet etching apparatus  3 B according to this modification. In this modification, the wet etching apparatus  3 B includes a chemical solution replacement unit  31  configured to perform replacement of the chemical solution. In the example in  FIG. 13 , the wet etching apparatus  3 B further includes a treatment bath  32  configured to enable the etching process of a wafer to be performed therein, and a chemical solution reservoir  33  configured to store a chemical solution for use in the etching process and supply the chemical solution to the treatment bath  32 . The chemical solution replacement unit  31  according to this modification is constituted by a solution supply valve  311 , a solution discharge valve  312 , and a valve control unit  313 . The valve control unit  313  controls the operation of the valves ( 311  and  312 ). The solution supply valve  311  is provided on piping that connects the chemical solution reservoir  33  and the treatment bath  32 , and supplies the chemical solution from the chemical solution reservoir  33  to the treatment bath  32  in response to an instruction from the valve control unit  313 . The solution discharge valve  312  is provided on piping that connects the treatment bath  32  and a waste solution tank (not shown), and discharges the chemical solution from the treatment bath  32  to the waste solution tank in response to an instruction from the valve control unit  313 . On the other hand, an output unit  115 B of the monitoring system  1 B outputs an instruction to replace the chemical solution to the chemical solution replacement unit  31  of the wet etching apparatus  3 B, as the information regarding replacement of the chemical solution. Note that, except that the contents of the output are different, the monitoring system  1 B has the same configuration as the above-described monitoring system  1 . 
     In this case, the control unit of the monitoring system  1 B executes the processing of steps S 101  and S 102  and the processing of steps S 201  to S 204  in the same manner as the above-described monitoring system  1 . Then, in step S 205 , the control unit of the monitoring system  1 B functions as the output unit  115 B, and outputs an instruction to replace the chemical solution to the chemical solution replacement unit  31  of the wet etching apparatus  3 B. Upon receiving this instruction, the chemical solution replacement unit  31  of the wet etching apparatus  3 B executes replacement of the chemical solution. Specifically, upon receiving the instruction from the monitoring system  1 B, the valve control unit  313  opens the solution discharge valve  312  and controls the discharge of the chemical solution from the treatment bath  32  to the waste solution tank. After the discharge of the chemical solution has been completed, the valve control unit  313  opens the solution supply valve  311  and controls the supply of the chemical solution from the chemical solution reservoir  33  to the treatment bath  32 . Thus, replacement of the chemical solution can be automated. Note that the configuration of the chemical solution replacement unit  31  needs not be limited to the above-described example, and may be determined as appropriate, depending on an embodiment.