Prediction algorithm generating device, information processing device, prediction algorithm generating method and processing condition determination method

Abstract

A predictor generating device comprises a first data acquisition unit that acquires a plurality of first data sets and a first determination unit that determines a first parameter by applying the plurality of first data sets to a predetermined first function and performing regression analysis, wherein each of the plurality of first data sets includes a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and a first processing condition, wherein the first processing result includes the difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and the first function represents the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate using the first processing condition and the first parameter.

Description

Technology Field

[0001] The present invention relates to a prediction algorithm generation device, an information processing device, a prediction algorithm generation method, and a processing condition determination method. Background Technology

[0002] In the semiconductor manufacturing process, there is a cleaning process. In the cleaning process, the film thickness of the coating formed on the substrate is adjusted through an etching treatment in which a chemical solution is applied to the substrate. In this film thickness adjustment, it is important to perform the etching treatment in a way that ensures the surface of the substrate is uniform. Furthermore, it is also important to adjust the film thickness to obtain a desired thickness distribution, such as by increasing the amount of etching near the edges of the substrate. When the etching solution is ejected from a nozzle onto a portion of the substrate, it is necessary to move the nozzle in the radial direction relative to the substrate. However, the etching treatment is a complex process in which the throughput of the film changes depending on the difference in the operation of the nozzle movement. Moreover, the throughput of the film processed by the etching treatment is determined only after the substrate has been processed. For this reason, setting the nozzle movement operation requires trial and error by technicians. Determining the optimal nozzle operation requires significant cost and time.

[0003] Patent Document 1 describes an apparatus for determining scan speed information from a target throughput by using a machine-trained model with training data in which "input" is throughput (etching amount) and "output" is scan speed information. According to this technology, scan speed information is determined from a target throughput. Prior art literature

[0004] Japanese Patent Publication No. 2021-108367 The problem to be solved

[0005] Meanwhile, it is known that in etching a film formed on a substrate, the temperature of the processing solution, the rotation speed of the substrate, and the flow rate of the processing solution affect the etching throughput. The completed learning model described in Patent Document 1 does not take into account the temperature of the processing solution, the rotation speed of the substrate, and the flow rate of the processing solution, and therefore cannot handle cases where the temperature of the processing solution, the rotation speed of the substrate, and the flow rate of the processing solution are different. Furthermore, since the completed learning model is a black box, different completed learning models are generated depending on differences in the training data used for machine learning. For this reason, there is a problem that it is not easy to collect and determine appropriate training data to generate a completed learning model.

[0006] One of the objectives of the present invention is to provide a prediction algorithm generation device and a prediction algorithm generation method that can easily generate a prediction algorithm suitable for a substrate processing device.

[0007] Another objective of the present invention is to provide an information processing device and a method for determining processing conditions that are capable of presenting a plurality of processing conditions for the processing results of a complex process for processing a substrate. means of solving the problem

[0008] A prediction algorithm generating device according to one aspect of the present invention comprises a first data acquisition unit for acquiring a plurality of first data sets and a first determination unit for determining a first parameter by applying the plurality of first data sets to a predetermined first function and performing regression analysis, wherein each of the plurality of first data sets includes a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and a first processing condition, wherein the first processing result includes the difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and the first function represents the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate using the first processing condition and the first parameter.

[0009] An information processing device according to another aspect of the present invention is an information processing device for managing a substrate processing device, wherein the substrate processing device performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, and has a processing condition determining unit that determines a first processing condition for the substrate processing device to perform processing of the film by using a prediction algorithm, wherein the prediction algorithm is a first function that calculates the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate on which the substrate processing device performs processing of the film from the first processing condition using a first parameter, the first parameter is obtained by applying a plurality of first data sets to the first function and performing regression analysis, and each of the plurality of first data sets includes a first processing result obtained after driving the substrate processing device with the first processing condition and performing processing of the film, and a first processing condition, wherein the first processing result includes the difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and the processing condition determining unit from a temporary first processing condition using a prediction algorithm If the first processing result produced satisfies the allowable condition, the temporary first processing condition is determined as the first processing condition for driving the substrate processing device.

[0010] A method for generating a prediction algorithm according to another aspect of the present invention comprises a step of acquiring a plurality of first data sets and a step of determining a first parameter by applying the plurality of first data sets to a first function and performing regression analysis, wherein each of the plurality of first data sets includes a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and a first processing condition, wherein the first processing result includes a difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and a first function is predetermined to represent the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate using the first processing condition and the first parameter.

[0011] A method for determining processing conditions according to another aspect of the present invention is a method for determining processing conditions executed by an information processing device managing a substrate processing device, wherein the substrate processing device processes a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, and has a processing condition determination step for determining a first processing condition for the substrate processing device to perform the processing of the film by using a prediction algorithm, wherein the prediction algorithm is a first function that calculates a first processing result from a first processing condition using a first parameter, and the first processing result includes the difference in film thickness before and after the processing of the film is performed at each of a plurality of different positions in the diameter direction of the substrate, and the first parameter is obtained by applying a plurality of first data sets to the first function and performing regression analysis, and each of the plurality of first data sets includes a first processing result obtained after the substrate processing device performs the processing of the film according to the first processing condition and a first processing condition, and the processing condition determination step is such that when the first processing result calculated from a temporary first processing condition using a prediction algorithm satisfies an allowable condition, the temporary It includes determining the processing condition as a first processing condition for driving the substrate processing device. Effects of the invention

[0012] According to the present invention, a prediction algorithm generating device and a prediction algorithm generating method that enable easy generation of a prediction algorithm suitable for a substrate processing device can be provided.

[0013] In addition, an information processing device and a method for determining processing conditions can be provided, which are capable of presenting multiple processing conditions for the processing results of a complex process for processing a substrate. Brief explanation of the drawing

[0014] FIG. 1 is a drawing for explaining the configuration of a substrate processing system related to an embodiment of the present invention. Figure 2 is a diagram showing an example of the configuration of an information processing device. Figure 3 is a diagram showing an example of the configuration of a prediction algorithm generation device. FIG. 4 is a drawing showing an example of the functional configuration of a substrate processing system related to one embodiment. Figure 5 is a diagram illustrating the processing results. FIG. 6 is a diagram showing an example of a function of generating a prediction algorithm that considers back-side discharge processing among the functions of a prediction algorithm generating unit related to the present embodiment. Figure 7 is a diagram showing an example of the result of the first processing. Figure 8 is a diagram showing the first function F1(x). FIG. 9 is a drawing showing the first influence diagram at each of multiple different positions in the diameter direction of the substrate W. Figure 10 is a diagram showing an example of the second function F2(x). Figure 11 is a diagram illustrating the behavior of the etching solution regarding the operation of the surface nozzle of a substrate processing device. Figure 12 is a diagram showing the coverage rate obtained from a plurality of second processing results according to variation conditions. Figure 13 is a diagram showing an example of the third function H(x). FIG. 14 is a diagram showing an example of a function of generating a prediction algorithm that does not consider back discharge processing among the functions of a prediction algorithm generation unit. Figure 15 is a flowchart showing an example of the flow of the prediction algorithm generation process. Figure 16 is a flowchart showing an example of the flow of the first function decision process. Figure 17 is a flowchart showing an example of the flow of the second function decision processing. FIG. 18 is a flowchart showing an example of the flow of a third function determination process considering back discharge processing. FIG. 19 is a flowchart showing an example of the flow of a third function determination process that does not consider back-side discharge processing. FIG. 20 is a third figure showing an example of the function of a prediction algorithm generation unit. Specific details for implementing the invention

[0015] Hereinafter, a substrate processing system related to an embodiment of the present invention will be described in detail with reference to the drawings. In the following description, the term "substrate" refers to a semiconductor substrate (semiconductor wafer), a substrate for an FPD (Flat Panel Display) such as a liquid crystal display device or an organic EL (Electro Luminescence) display device, a substrate for an optical disc, a substrate for a magnetic disc, a substrate for an optical magnetic disc, a substrate for a photomask, a ceramic substrate, or a substrate for a solar cell, etc.

[0016] (1) Overall configuration of the substrate processing system

[0017] FIG. 1 is a diagram illustrating the configuration of a substrate processing system related to an embodiment of the present invention. The substrate processing system (1) of FIG. 1 includes an information processing device (100), a prediction algorithm generating device (200), and a substrate processing device (300). The prediction algorithm generating device (200) is, for example, a server, and the information processing device (100) is, for example, a personal computer.

[0018] The prediction algorithm generating device (200) and the information processing device (100) are used to manage the substrate processing device (300). Additionally, the substrate processing device (300) managed by the prediction algorithm generating device (200) and the information processing device (100) is not limited to one unit, and multiple substrate processing devices (300) may be managed.

[0019] In the substrate processing system (1) related to the present embodiment, the information processing device (100), the prediction algorithm generating device (200), and the substrate processing device (300) are connected to each other by a wired or wireless communication line or a communication network. The information processing device (100), the prediction algorithm generating device (200), and the substrate processing device (300) are each connected to a network so that data can be transmitted and received from each other. For example, a local area network (LAN) or a wide area network (WAN) is used as the network. In addition, the network may be the Internet. In addition, the information processing device (100) and the substrate processing device (300) may be connected via a dedicated communication network. The network connection type may be a wired connection or a wireless connection.

[0020] Additionally, the prediction algorithm generating device (200) does not necessarily need to be connected to the substrate processing device (300) and the information processing device (100) via a communication line or a communication network. In this case, data generated by the substrate processing device (300) may be transferred to the prediction algorithm generating device (200) through a recording medium. Also, data generated by the prediction algorithm generating device (200) may be transferred to the information processing device (100) through a recording medium.

[0021] A substrate processing device (300) is formed with a display device, a voice output device, and an operating unit, which are not shown. The substrate processing device (300) is operated according to predetermined processing conditions (processing recipe).

[0022] (2) Overview of the substrate processing device

[0023] A substrate processing device (300) comprises a control device (10) and a plurality of substrate processing units WU. The control device (10) controls the plurality of substrate processing units WU. The plurality of substrate processing units WU perform processing of the film on the substrate W by supplying a processing solution of a constant flow rate to the substrate W on which the film is formed. In this embodiment, the substrate W to be processed has a diameter of 300 mm, but the present invention is not limited thereto. The processing solution includes an etching solution, and the substrate processing unit WU performs an etching process. The etching solution is a chemical solution. The etching solution is, for example, hydronitrate (a mixture of hydrofluoric acid (HF) and nitric acid (HNO3)), hydrofluoric acid, buffered hydrofluoric acid (BHF), ammonium fluoride, HFEG (a mixture of hydrofluoric acid and ethylene glycol), or phosphoric acid (H3PO4).

[0024] The substrate processing unit WU comprises a spin chuck SC, a spin motor SM, a surface nozzle (311), a nozzle movement mechanism (301), and a back nozzle (312). The spin chuck SC includes a disc-shaped spin base SB maintained in a horizontal position and a plurality of chuck pins (306) capable of maintaining a substrate W in a horizontal position above the spin base SB. Thus, the spin chuck SC maintains the substrate W horizontally. The substrate W is held in the spin chuck SC such that the center of the substrate W coincides with the first rotation axis AX1 of the spin motor SM. The spin motor SM has a first rotation axis AX1. The first rotation axis AX1 extends in the vertical direction. The spin chuck SC is mounted on the upper end of the first rotation axis AX1 of the spin motor SM. When the spin motor SM rotates, the spin chuck SC rotates around the first rotation axis AX1. The spin motor SM is a stepping motor. The substrate W held by the spin chuck SC rotates around the first rotation axis AX1. Therefore, the rotational speed of the substrate W is the same as the rotational speed of the stepping motor. Additionally, if an encoder is formed to generate a rotational speed signal indicating the rotational speed of the spin motor, the rotational speed of the substrate W may be obtained from the rotational speed signal generated by the encoder. In this case, the spin motor SM may use a motor other than a stepping motor.

[0025] The surface nozzle (311) supplies etching solution to the surface (upper surface) of the substrate W held in the spin chuck SC. Etching solution is supplied to the surface nozzle (311) from an etching solution supply unit not shown. The surface nozzle (311) discharges the etching solution toward the surface of the rotating substrate W. The back nozzle (312) supplies etching solution to the back surface (lower surface) of the substrate W held in the spin chuck SC. Etching solution is supplied to the back nozzle (312) from an etching solution supply unit not shown and discharges the etching solution toward the back surface of the rotating substrate W. Hereinafter, the process of discharging the etching solution from the back nozzle (312) is referred to as the back discharge process.

[0026] The nozzle moving mechanism (301) moves the surface nozzle (311) in an approximately horizontal direction. Specifically, the nozzle moving mechanism (301) has a nozzle motor (303) having a second rotation axis AX2 and a nozzle arm (305). The nozzle motor (303) is positioned so that the second rotation axis AX2 follows an approximately vertical direction. The nozzle arm (305) has a rectangular shape that extends in a straight line. One end of the nozzle arm (305) is mounted on the top of the second rotation axis AX2 so that the longitudinal direction of the nozzle arm (305) is different from the direction of the second rotation axis AX2. The surface nozzle (311) is mounted on the other end of the nozzle arm (305) so that the discharge port of the etching liquid faces downward.

[0027] When the nozzle motor (303) operates, the nozzle arm (305) rotates in a horizontal plane around the second rotation axis AX2. As a result, the surface nozzle (311) mounted on the other end of the nozzle arm (305) moves (rotates) in a horizontal direction around the second rotation axis AX2. While moving in a horizontal direction, the surface nozzle (311) discharges an etching solution toward the substrate W. The nozzle motor (303) is, for example, a stepping motor.

[0028] The control unit (10) includes a CPU (central processing unit) and memory, and controls the entire substrate processing unit (300) by the CPU executing a program stored in memory. The control unit (10) controls the spin motor (SM) and the nozzle motor (303).

[0029] Experimental data from a substrate processing device (300) is input to a prediction algorithm generating device (200). The prediction algorithm generating device (200) generates a prediction algorithm using the experimental data and outputs the prediction algorithm to an information processing device (100). In this embodiment, the prediction algorithm is composed of an algorithm including a first function F(x), a second function F2(x), and a third function F3(x) described below.

[0030] The information processing device (100) uses a prediction algorithm to determine processing conditions for processing a substrate for a substrate that the substrate processing device (300) is scheduled to process from now on. The information processing device (100) outputs the determined processing conditions to the substrate processing device (300).

[0031] FIG. 2 is a diagram showing an example of the configuration of an information processing device. Referring to FIG. 2, the information processing device (100) is composed of a CPU (101), RAM (random access memory) (102), ROM (read-only memory) (103), a memory device (104), an operating unit (105), a display device (106), and an input / output I / F (interface) (107). The CPU (101), RAM (102), ROM (103), memory device (104), operating unit (105), display device (106), and input / output I / F (107) are connected to a bus (108).

[0032] RAM (102) is used as a work area for the CPU (101). A system program is stored in ROM (103). A memory device (104) includes a storage medium such as a hard disk or semiconductor memory and stores a program. The program may be stored in ROM (103) or another external memory device.

[0033] A CD-ROM (109) is removable from the memory device (104). The recording medium for storing the program executed by the CPU (101) is not limited to a CD-ROM (109) but may be a medium such as an optical disc (MO (Magnetic Optical Disc) / MD (Mini Disc) / DVD (Digital Versatile Disc)), an IC card, an optical card, a mask ROM, or a semiconductor memory such as an EPROM (Erasable Programmable ROM). Additionally, the CPU (101) may download a program from a computer connected to a network and store it in the memory device (104), or a computer connected to a network may record a program in the memory device (104), load the program stored in the memory device (104) into the RAM (102), and execute it by the CPU (101). The program referred to here includes not only a program that can be directly executed by the CPU (101), but also source programs, compressed programs, encrypted programs, etc.

[0034] The control unit (105) is an input device such as a keyboard, mouse, or touch panel. By operating the control unit (105), the user can give a predetermined instruction to the information processing device (100). The display device (106) is a display device such as a liquid crystal display and displays a GUI (Graphical User Interface), etc., for receiving instructions from the user. The input / output I / F (107) is connected to a network.

[0035] FIG. 3 is a diagram showing an example of the configuration of a prediction algorithm generating device. Referring to FIG. 3, the prediction algorithm generating device (200) is composed of a CPU (201), RAM (202), ROM (203), memory device (204), operation unit (205), display device (206), and input / output I / F (207). The CPU (201), RAM (202), ROM (203), memory device (204), operation unit (205), display device (206), and input / output I / F (207) are connected to a bus (208).

[0036] RAM (202) is used as a work area for the CPU (201). A system program is stored in ROM (203). A memory device (204) includes a storage medium such as a hard disk or semiconductor memory and stores a program. The program may be stored in ROM (203) or another external memory device. A CD-ROM (209) is removable from the memory device (204).

[0037] The control unit (205) is an input device such as a keyboard, mouse, or touch panel. The input / output I / F (207) is connected to a network.

[0038] (3) Functional configuration of the substrate processing system

[0039] FIG. 4 is a drawing showing an example of the functional configuration of a substrate processing system related to one embodiment. Referring to FIG. 4, a control device (10) provided by a substrate processing device (300) controls a substrate processing unit WU to perform a coating treatment on a substrate W according to processing conditions during the processing time. The processing time is a time determined for the coating treatment on the substrate. In this embodiment, the processing time is the time while the surface nozzle (311) discharges an etching solution onto the substrate W. The processing conditions are conditions used when the substrate processing unit WU performs the coating treatment.

[0040] The processing conditions include the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, the rotational speed R of the substrate W, and the position of the surface nozzle (311). The concentration C of the etching solution is represented by the mixing ratio of a plurality of chemical solutions. The position of the surface nozzle (311) is represented by the relative position of the surface nozzle (311) and the substrate W at each of a plurality of points in time during the processing of the film. The relative position of the surface nozzle (311) and the substrate W is represented by the rotation angle of the nozzle motor (303).

[0041] Processing conditions include fixed conditions that do not change over time and variable conditions that change over time. In this embodiment, the fixed conditions are the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, and the rotational speed R of the substrate W, and the variable conditions are the relative positions of the surface nozzle (311) and the substrate W that change over time.

[0042] The prediction algorithm generation device (200) includes an experimental data acquisition unit (211), a prediction algorithm generation unit (213), and a transmission unit (215). The function provided by the prediction algorithm generation device (200) is realized by the CPU (201) by the CPU (201) provided by the prediction algorithm generation device (200) executing a prediction algorithm generation program stored in RAM (202).

[0043] The experimental data acquisition unit (211) acquires experimental data from the substrate processing device (300). The experimental data includes processing conditions, a processing result ER indicating the result of the substrate processing device (300) performing film treatment on the substrate W under said processing conditions, and a processing type indicating whether or not back-side discharge treatment is performed. The processing result ER represents the difference in film thickness before and after the film treatment is performed at each of a plurality of different positions in the diameter direction of the substrate W with respect to the film formed on the substrate W.

[0044] Experimental data is input to the prediction algorithm generation unit (213) from the experiment data acquisition unit (211). The prediction algorithm generation unit (213) generates a prediction algorithm using the experiment data and outputs the generated prediction algorithm to the transmission unit (215). Details of the prediction algorithm generation unit (213) will be described later. The transmission unit (215) transmits the prediction algorithm generated by the prediction algorithm generation unit (213) to the information processing device (100).

[0045] Here, the processing result ER is described. FIG. 5 is a diagram illustrating the processing result ER. In FIG. 5, the vertical axis represents the film thickness, and the horizontal axis represents the radial position of the substrate. Additionally, the origin of the horizontal axis represents the center of the substrate. The film thickness of the film formed on substrate W before processing by the substrate processing device (300) is shown as a solid line. In the processing of the film, the film thickness of the film formed on substrate W is adjusted by applying an etching solution according to processing conditions by the substrate processing device (300). The film thickness of the film formed on substrate W after the film processing by the substrate processing device (300) is shown as a dotted line.

[0046] The difference between the film thickness of the film formed on the substrate W before processing by the substrate processing device (300) and the film thickness of the film formed on the substrate W after processing by the substrate processing device (300) is the processing result ER (etching amount). In other words, the processing result ER represents the film thickness reduced at each of multiple positions in the diameter direction of the substrate W by the processing of the film by the substrate processing device (300).

[0047] In the treatment of the film of the aforementioned substrate processing device (300), when back-side discharge treatment is performed by the back-side nozzle (312) (see FIG. 1), the temperature of the substrate W changes due to the etching solution discharged from the back-side nozzle (312). Therefore, the presence or absence of back-side discharge treatment affects the amount of film thickness reduced by the treatment of the film. Accordingly, the ER of the treatment result differs depending on the presence or absence of back-side discharge treatment.

[0048] In the following description, a processing condition in which back-side discharge processing is not performed in the processing of a film is called the first processing condition, and a processing condition in which back-side discharge processing is performed in the processing of a film is called the second processing condition. The second processing condition is a processing condition in which the back-side discharge condition of the back-side discharge processing is added to the first processing condition. Also, among the processing result ERs, the processing result ER obtained by the substrate processing device (300) performing film processing according to the first processing condition is called the first processing result ER1, and the processing result ER obtained by the substrate processing device (300) performing film processing according to the second processing condition is called the second processing result ER2.

[0049] Next, the detailed configuration of the prediction algorithm generation unit (213) will be described. FIG. 6 is a diagram showing an example of a function of generating a prediction algorithm that considers back-side discharge processing among the functions of the prediction algorithm generation unit related to the present embodiment. Referring to FIG. 6, the prediction algorithm generation unit (213) includes a first decision unit (220), a second decision unit (230), and a third decision unit (240).

[0050] The first determination unit (220) identifies a first function F1(x) with the position x of the substrate W as a variable based on the first processing condition and the first processing result ER1. Specifically, the first determination unit (220) includes a first data acquisition unit (221), a first condition-based classification unit (223), a first reference parameter determination unit (225), and a first parameter determination unit (227). The first data acquisition unit (221) acquires multiple sets of first data sets including the first processing condition and the first processing result ER1 obtained under the first processing condition from the experimental data acquisition unit (211).

[0051] The first condition-based classification unit (223) classifies multiple sets of first data acquired by the first data acquisition unit (221) into multiple groups according to processing conditions. The first condition-based classification unit (223) classifies multiple sets of first data that have the same first processing condition into the same group. In addition, the first condition-based classification unit (223) may define multiple ranges by dividing the range in which the value of each of the multiple items of the first processing condition can take into multiple ranges, define multiple groups by combining the ranges between the multiple items, and classify multiple sets of first data into any of the multiple groups. For example, when the temperature T of the etching solution, the concentration C of the etching solution, and the flow rate D of the etching solution are each divided into three ranges, 27 groups are defined. In this case, multiple sets of first data are classified into any of the 27 groups.

[0052] The first reference parameter determination unit (225) determines a first function F1(x) that approximates one or more first data sets classified into groups for each of the plurality of groups defined by the first conditional classification unit (223). Here, the first function F1(x) is described.

[0053] FIG. 7 is a diagram showing an example of a first treatment result. In FIG. 7, the vertical axis represents the difference in film thickness before and after the treatment of the film, and the horizontal axis represents the position in the radial direction of the substrate W. The origin represents the center O of the substrate W. In addition, a plurality of first treatment results ER1 are shown as being normalized from 0 to 1. As shown in FIG. 7, if the temperature T of the etching solution, the concentration C of the etching solution, and the flow rate D of the etching solution are different, the first treatment result ER1 is different. As shown in FIG. 7, the plurality of first treatment result ER1s are large near the center O of the substrate W, where the difference in film thickness before and after the treatment of the film is large, and decreases as they approach the outer edge of the substrate W.

[0054] FIG. 8 is a diagram showing the first function F1(x). The horizontal axis represents the position in the diameter direction of the substrate, and the vertical axis represents the difference in film thickness before and after the film treatment. Referring to FIG. 8, the position indicated by XE on the horizontal axis represents the outer edge of the substrate W. The first function F1(x) shown in FIG. 8 is a function discovered by the inventor as a function approximated by the first treatment result ER1 shown in FIG. 7.

[0055] The first function F1(x) is a function representing the difference in film thickness before and after the film treatment is performed at any position in the diameter direction of substrate W when the substrate processing device performs film treatment on substrate W under the first processing condition. The first function F1(x) is represented by the following equation (1).

[0056]

[0057] The first function F1(x) is expressed using the radial position x of the substrate W as a variable and the first reference parameters α and β. The first function F1(x) is a function of the variable x following n1 (n1 is a defined integer).

[0058] Returning to FIG. 6, the first reference parameter determining unit (225) determines, for each of the plurality of groups, in other words, for each of the plurality of first processing conditions, an integer n1 and first reference parameters α and β, respectively, for which the first function F1(x) is closest to the first processing result ER1. The integer n1 and the first reference parameters α and β are obtained by regression analysis. The first reference parameter determining unit (225) corresponds to each of the plurality of groups and outputs the first processing condition and the first reference parameters α and β obtained corresponding to the first processing condition to the first parameter determining unit (227).

[0059] Regarding the determination of the integer n1, for example, the first reference parameter determination unit (225) determines the integer n1 such that the error between the first processing result ER1 and the first function F1(x) for each of the first data sets is minimized by the least squares method. Regarding the determination of the first reference parameters α and β, for example, the first reference parameter determination unit (225) determines them by performing regression analysis by comparing the average value of the first processing result ER1 for each first data set and the average value of the first function F1(x) of Equation (1), and the difference between the maximum and minimum values ​​of the first processing result ER1 for each first data set and the difference between the maximum and minimum values ​​of the first function F1(x) of Equation (1). Additionally, the first function F1(x) may be determined using methods such as fluid analysis.

[0060] In the first parameter determining unit (227), a plurality of sets of the first processing condition and the first reference parameter are input from the first reference parameter determining unit (225). The first parameter determining unit (227) determines the first parameters α1 to α3 and β1 to β3 by applying a plurality of sets of the first processing condition and the first reference parameter to the first sub-functions shown in the following equations (2) and (3) and performing regression. In other words, the first parameter determining unit (227) determines the first parameters α1 to α3 and β1 to β3 by bringing the first parameters α1 to α3 and β1 to β3 to the same value between a plurality of first sub-functions to which a plurality of sets of the first processing condition and the first reference parameter are each applied.

[0061]

[0062] In addition, the first parameters α1 to α3 and β1 to β3 are values ​​that depend on the concentration C of the etching solution. Here, the first sub-function is described. The first sub-function includes a function representing the relationship between the first reference parameter α and the first parameters α1 to α3 as indicated by Equation (2), and a function representing the relationship between the first reference parameter β and the first parameters β1 to β3 as indicated by Equation (3). The first sub-function is a function in which the temperature T of the etching solution, the concentration C of the etching solution, and the flow rate D of the etching solution are variables among the first treatment conditions, and is a function determined by the inventor based on the qualitative trend of the first treatment result.

[0063] In the first parameter determining unit (227), a first processing condition and a set of first reference parameters α and β are input from the first reference parameter determining unit (225) in the number of first processing conditions. The first parameter determining unit (227) determines the first parameters α1 to α3 and β1 to β3 by bringing each of the first parameters α1 to α3 and β1 to β3 close to the same value among the plurality of first processing conditions.

[0064] Specifically, the first parameter determining unit (227) substitutes the first reference parameters α and β and the first processing condition into the first sub-function for each of the plurality of first processing conditions. By doing so, the same number of expressions (2) and (3) as the first processing condition are generated. The first parameter determining unit (227) determines the first parameters α1 to α3 by bringing each of the first parameters α1 to α3 close to the same value between the same number of expressions (2) as the first processing condition, and also determines the first parameters β1 to β3 by bringing each of the first parameters β1 to β3 close to the same value in the same number of expressions (3) as the first processing condition. A method such as the least squares method may be used for determining the first parameters α1 to α3 and β1 to β3 of the first parameter determining unit (227). Thus, the first function F1(x) is determined. The first parameter determination unit (227) assigns the determined first function F1(x) to the second determination unit (230).

[0065] The second determination unit (230) generates a second function F2(x) based on the second processing condition and the second processing result ER2. The second function F2(x) is a function with the position of the substrate W as a variable. The second determination unit (230) identifies the second function F2(x) based on the second processing condition and the second processing result ER2.

[0066] Specifically, the second determination unit (230) includes a second data acquisition unit (231), a second conditional classification unit (233), a first transformation unit (235), a second reference parameter determination unit (237), and a second parameter determination unit (239). The second data acquisition unit (231) acquires multiple sets of second data sets including a second processing condition and a second processing result ER2 from the experimental data acquisition unit (211).

[0067] The second condition-based classification unit (233) classifies multiple sets of second data acquired by the second data acquisition unit (231) into multiple groups according to processing conditions. The second condition-based classification unit (233) classifies multiple sets of second data that have the same second processing condition into the same group. In addition, the second condition-based classification unit (233) may define multiple ranges by dividing the range in which the value of each of the multiple items of the second processing condition can take into multiple ranges, define multiple groups by combining the ranges between the multiple items, and classify multiple sets of second data into any of the multiple groups. For example, when the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, and the rotation speed R of the substrate W are each divided into three ranges, 81 groups are defined. In this case, multiple sets of second data are classified into any of the 81 groups.

[0068] The second reference parameter determination unit (237) determines a second function F2(x) based on one or more second data sets classified into groups for each of the plurality of groups defined by the second conditional classification unit (233). Here, the second function F2(x) is described.

[0069] The order of determining the second function F2(x) is as follows. By performing treatment of the film under multiple second treatment conditions in which the values ​​of the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, and the rotation speed R of the substrate W are each different, multiple second treatment results ER2 are obtained. The value of the second treatment result ER2 at a radial position of the substrate W is expressed as follows using the first function F1(x) and the second function F2(x) represented by Equation (1).

[0070]

[0071] Here, by modifying Equation (4), the second function F2(x) becomes equivalent to the value obtained by dividing the second processing result ER2 by the first function F1(x). Since the second function F2(x) is the value obtained by dividing the second processing result ER2 by the first function F1(x), it can be said to represent the influence of the discharge treatment. Hereinafter, the influence of the discharge treatment is referred to as the first influence degree.

[0072] FIG. 9 is a diagram showing the first influence degree at each position in the radial direction of the substrate W. The vertical axis represents the first influence degree, and the horizontal axis represents the position in the radial direction of the substrate W. In addition, the first influence degree is shown as normalized from 0 to 1. As shown in FIG. 9, if the second processing condition is different, the first influence degree is different.

[0073] The first transformation unit (235) outputs to the second reference parameter determination unit (237) a first influence degree calculated by dividing the second processing result ER2 of one or more second data sets classified into the group by the first determination unit (220) by the first function F1(x) determined by the second determination unit (220), for each of the plurality of groups defined by the second conditional classification unit (233).

[0074] FIG. 10 is a diagram showing an example of a second function F2(x). Referring to FIG. 10, the horizontal axis represents a position in the diameter direction of the substrate, and the vertical axis represents a first influence degree. The position indicated by XE on the horizontal axis represents the outer edge of the substrate W. The second function F2(x) shown in FIG. 10 is a function discovered by the inventor as a function approximated by the first influence degree shown in FIG. 9.

[0075] The second function F2(x) is represented by the following equation (5).

[0076]

[0077] The second function F2(x) is represented by the product of the first configuration function f21(x) represented by Equation (6) and the second configuration function f22(x) represented by Equation (7). The first configuration function f21(x) is a hyperbolic function for the variable x representing the radial position of the substrate W. The second configuration function f22(x) is a function of the variable x following n2 (n2 is a defined integer). The first configuration function f21(x) and the second configuration function f22(x) are each represented using the variable x representing the radial position of the substrate W and the second reference parameters γ, δ, ε, ξ. In other words, the second function F2(x) is represented using the variable x representing the radial position of the substrate W and the second reference parameters γ, δ, ε, ξ.

[0078] Returning to FIG. 6, the second reference parameter determination unit (237) determines, for each of the multiple groups, in other words, for each of the multiple second processing conditions, the second function F2(x) shown in Equation (5) most approximates the first influence shown in FIG. 9, and each of the second reference parameters γ, δ, ε, ξ. The integers n2 and the second reference parameters γ, δ, ε, ξ are obtained by regression analysis.

[0079] An example of determining the second reference parameters γ, δ, ε, and ξ is described. First, the second reference parameter determining unit (237) regresses ξ of the second configuration function f22(x) from the minimum value of each of the plurality of first influence degrees calculated by the first transformation unit (235). Next, regarding the outer side of the substrate W, it can be seen that the influence of the first configuration function f21(x) is small from the shape of the outer side of the substrate W of the first influence degree shown in FIG. 10. Therefore, ε of the second configuration function f22(x) is regressed for each of the outer side of the substrate W of the plurality of first influence degrees. Thus, the second configuration function f22(x) is determined. Next, the plurality of first influence degrees are normalized to 0 to 1 to exclude the influence of γ. In this state, δ is regressed from the shape near the center O of the substrate W of the multiple normalized first influence degrees. With δ regressed, the normalization of the multiple first influence degrees is released, and γ is regressed from the shape of the multiple first influence degrees. In this way, the first configuration function f21(x) is determined.

[0080] The second reference parameter determination unit (237) corresponds to each of the plurality of groups and outputs the second processing condition and the set of second reference parameters γ, δ, ε, and ξ obtained in response to the second processing condition to the second parameter determination unit (239).

[0081] The second parameter determining unit (239) receives a set of second processing conditions and second reference parameters from the second reference parameter determining unit (237). The second parameter determining unit (239) applies a plurality of sets of second processing conditions and second reference parameters to the second sub-functions shown in Equations (8) to (11) to determine the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, ξ1 to ξ4.

[0082]

[0083] In addition, the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4 are values ​​that depend on the temperature T of the etching solution. Here, the second sub-function is described. The second sub-function includes a function representing the relationship between the second reference parameter γ and the second parameters γ1 to γ4 as indicated by Equation (8), a function representing the relationship between the second reference parameter δ and the second parameters δ1 to δ4 as indicated by Equation (9), a function representing the relationship between the second reference parameter ε and the second parameters ε1 to ε4 as indicated by Equation (10), and a function representing the relationship between the second reference parameter ξ and the second parameters ξ1 to ξ4 as indicated by Equation (11). The second sub-function is a function in which the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, and the rotation speed R of the substrate W are variables among the second processing conditions, and is a function determined by the inventor based on the qualitative trend of the first influence degree.

[0084] In the second parameter determining unit (239), sets of second processing conditions and second reference parameters γ, δ, ε, and ξ are input from the second reference parameter determining unit (237) in the number of second processing conditions. The second parameter determining unit (239) determines the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4 by bringing the second parameters close to the same value among the plurality of second processing conditions.

[0085] Specifically, the second parameter determining unit (239) substitutes the second reference parameters γ, δ, ε, ξ and the second processing condition into the second sub-function for each of the multiple second processing conditions. In this way, the same number of equations (8) to (11) as the second processing condition is generated. The second parameter determining unit (239) determines the second parameters γ1 to γ4 by bringing each of the second parameters γ1 to γ4 close to the same value between the same number of equations (8) as the second processing condition. Also, the second parameter determining unit (239) determines the second parameters δ1 to δ4 by bringing each of the second parameters δ1 to δ4 close to the same value between the same number of equations (9) as the second processing condition. Additionally, the second parameter determining unit (239) determines the second parameters ε1 to ε4 by bringing each of the second parameters ε1 to ε4 to the same value between the same number of expressions (10) as the second processing condition. Additionally, the second parameter determining unit (239) determines the second parameters ξ1 to ξ4 by bringing each of the second parameters ξ1 to ξ4 to the same value between the same number of expressions (11) as the second processing condition. For determining the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4 of the second parameter determining unit (239), methods such as the least squares method may be used. The second parameter determination unit (239) assigns the second function F2(x) to the third determination unit (240).

[0086] Here, the second processing result ER2 obtained by the processing of the film by the substrate processing device (300) is described in detail. Regarding the processing of the film by the substrate processing device (300), an etching solution is supplied from the surface nozzle (311) to the substrate W on which the film is formed. Specifically, in the processing of the film, the film formed on the substrate W is removed by the etching solution coming into contact with the film formed on the substrate W. Here, when the processing of the film begins, the surface nozzle (311) moves from the outer edge of the substrate W toward the center of the substrate W. Therefore, during the period until the surface nozzle (311) moves from the outer edge of the substrate W toward the center of the substrate W, a period occurs during which the etching solution does not reach the film formed on the substrate W. For this reason, the time during which the etching solution does not come into contact after the processing of the film begins affects the processing result of the film processing.

[0087] FIG. 11 is a diagram illustrating the behavior of the etching solution in relation to the operation of the surface nozzle (311) of the substrate processing device (300). FIG. 11 shows a cross-section of the substrate W in the movement range of the surface nozzle (311), from the outer end XE of the substrate W to the center O of the substrate W. When the processing of the film begins, the surface nozzle (311) moves horizontally from the outer end XE of the substrate W toward the center O of the substrate W and discharges the etching solution toward the substrate W.

[0088] The surface nozzle (311) is positioned above the outer end XE of the substrate W prior to the start of the coating treatment. When the start of the coating treatment is commanded to the substrate treatment device (300), the substrate W rotates, and the surface nozzle (311) discharges an etching solution from above the outer end XE of the rotating substrate W. In this way, the etching solution is supplied to the vicinity of the surface of the outer end XE of the substrate W.

[0089] Next, the surface nozzle (311) moves from a position above the outer edge XE of the substrate W toward a position above the center O of the substrate W while discharging the etching solution. The movement speed of the surface nozzle (311) during the processing time of this embodiment is predetermined. In this case, the relative position of the surface nozzle (311) with respect to the substrate W is represented as S(t) with time t as a variable. In other words, the distance between the center O of the substrate W and the surface nozzle (311) is represented as S(t) with t as a variable. The variable t represents the elapsed time since the processing of the film began. S(t) is a variable condition.

[0090] When etching solution is supplied to substrate W, most of the supplied etching solution moves toward the outside of substrate W due to the centrifugal force of the rotating substrate W. Meanwhile, the etching solution that collides with substrate W spreads horizontally on substrate W due to the discharge of the etching solution by the surface nozzle (311). Because of this, some of the etching solution supplied to substrate W moves toward the inside of substrate W from the position where it collides with substrate W. At this time, the distance between the center O of substrate W and the outer edge IE of the etching solution that has moved toward the center of the substrate is called the first distance h1. Also, the distance between the outer edge IE of the etching solution that has moved toward the inside and the position where the etching solution collides with substrate W is called the second distance h2. In addition, since the first distance h1 and the second distance h2 are values ​​related to the distance S(t) between the center O of the substrate W and the surface nozzle (311), they can be expressed as the first distance function h1(t) and the second distance function h2(t) using the variable t.

[0091] When the outer edge IE of the etching solution reaches the center O of the substrate W as the surface nozzle (311) moves toward a position above the center O of the substrate W, the etching solution is supplied over the entire substrate W by the centrifugal force of the rotating substrate W. After that, the surface nozzle (311) moves toward a position above the outer edge XE on the opposite side of the outer edge relative to the center O of the substrate W.

[0092] In this way, while the outer edge IE of the etching solution supplied to the substrate W moves from the outer edge XE of the substrate W to the center O in conjunction with the movement of the surface nozzle (311), there is a time when the etching solution is not actually supplied to each of the radial positions of the substrate W.

[0093] Returning to FIG. 6, the third determining unit (240) generates a third function H(x) that considers back-side discharge processing based on the second processing condition and the second processing result ER2. The second processing condition includes a variation condition. The third function H(x) that considers back-side discharge processing is a function in which the radial position of the substrate W is the variable x. The third determining unit (240) identifies the third function H(x) that considers back-side discharge processing based on the second processing condition and the second processing result ER2.

[0094] Specifically, the third determination unit (240) includes a third data acquisition unit (241), a nozzle operation classification unit (243), a second conversion unit (245), a third reference parameter determination unit (247), and a third parameter determination unit (249). The third data acquisition unit (241) acquires multiple sets of second data sets including second processing conditions and second processing result ER2 from the experimental data acquisition unit (211).

[0095] The nozzle operation classification unit (243) classifies multiple sets of second data sets acquired by the third data acquisition unit (241) into multiple groups according to variation conditions. The nozzle operation classification unit (243) classifies multiple sets of second data sets with the same variation conditions into the same group.

[0096] The third reference parameter determination unit (247) and the third parameter determination unit (249) determine a third function H(x) that considers back-side discharge processing based on one or more second data sets classified into groups for each of the plurality of groups defined by the nozzle operation classification unit (243). Here, the third function H(x) that considers back-side discharge processing is described.

[0097] The order of determining the third function H(x) considering back-side discharge treatment is as follows. By performing treatment of the film under a plurality of second treatment conditions in which the values ​​of the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, and the rotational speed R of the substrate W are each different, and also the variation conditions appearing at the relative position of the surface nozzle (311) and the substrate W that fluctuate over time are each different, a plurality of second treatment results ER2 are obtained. The value of the second treatment result ER2 at the radial position of the substrate W is expressed as follows using the first function F1(x) and the second function F2(x) represented by Equation (1) and the third function H(x) considering back-side discharge treatment.

[0098]

[0099] Here, by modifying Equation (12), the third function H(x) considering back-side discharge processing becomes equivalent to the value obtained by dividing the value of the second processing result ER2 by the first function F1(x) and the second function F2(x). Therefore, the value obtained by dividing the value of the second processing result ER2 by the first function F1(x) and the second function F2(x) can be said to be the influence on the second processing result ER2 of the time during which the etching solution is not actually supplied to the substrate W due to nozzle operation during the processing time. Hereinafter, the value obtained by dividing the value of the second processing result ER2 by the first function F1(x) and the second function F2(x) is referred to as the second influence (or coverage rate of the etching solution).

[0100] FIG. 12 is a diagram showing the coverage rate obtained from multiple second processing results ER2 according to variation conditions. The vertical axis represents the coverage rate, and the horizontal axis represents the position in the radial direction of the substrate W. In addition, the coverage rate is shown as normalized from 0 to 1. As shown in FIG. 12, if the variation conditions are different, the coverage rate is different.

[0101] The second conversion unit (245) calculates a second influence by dividing the second processing result ER2 of one or more second data sets classified into groups by the nozzle operation classification unit (243) by the first function F1(x) determined by the first determination unit (220) and the second function F2(x) determined by the second determination unit (230), and outputs the calculated second influence to the third reference parameter determination unit (247).

[0102] FIG. 13 is a diagram showing an example of the third function H(x). Referring to FIG. 13, the horizontal axis represents the position in the diameter direction of the substrate, the first vertical axis on the left represents the coverage rate, and the second vertical axis on the right represents the elapsed time since the film treatment began. Additionally, the elapsed time is shown from top to bottom on the second vertical axis. The third function H(x) is shown as a solid line. Also, S(t), which represents the position of the surface nozzle (311) relative to the substrate W, is shown as a dashed line. Additionally, the film treatment begins when the elapsed time is 0. The third function H(x) shown in FIG. 13 is a function discovered by the inventor as a function that approximates the second influence shown in FIG. 12.

[0103] The third function H(x) considering the discharge treatment on the back side is represented by the following equation (13).

[0104]

[0105] Here, in the third function H(x) considering the back-side discharge process, while the outer edge IE of the etching solution supplied to the substrate W moves from the outer edge XE of the substrate W to the center O, the first distance function h1(t) is valid when tdelay < t < tcenter, provided that tcenter is the time when the surface nozzle (311) first reaches the center O of the substrate W and tdelay is the time from when the film processing begins until the etching solution is actually supplied to the substrate W. This can be expressed by Equation (14) using the position S(t) of the surface nozzle (311) at time t and the third reference parameter ν. The inverse function h1 of the first distance function h1(t). ―1(x) represents the time the etching solution exists at position x on substrate W. The third reference parameter ν is the distance from the position where the etching solution struck substrate W (a position below the surface nozzle (311)) to the outer edge of the etching solution.

[0106] The third sub-function shown in Equation (15) is a function that represents the third reference parameter ν using a variable x representing the radial position of the substrate W. The third sub-function is an exponential function of the variable x representing the radial position of the substrate W, and is represented using the third parameters ν1 to ν4. The third sub-function is a function that takes the flow rate D of the etching solution and the rotational speed R of the substrate W as variables among the second processing conditions, and is a function that the inventor discovered through the qualitative trend of the second influence.

[0107] The third function H(x), which takes into account the back-side discharge process of Equation (13), is a function representing the coverage rate of the etching solution. In reality, for the position where the etching solution has already reached at the time tdelay when the etching solution begins to be supplied to the substrate W, there is no need to consider the third function H(x). For this reason, the third function H(x) for the range where the variable x is greater than or equal to the first distance function h1(tdelay) is represented as 1.

[0108] Meanwhile, the third function H(x) for a range where the variable x is smaller than the first distance function h1(tdelay) is the inverse function h1 of the first distance function h1(t). ―1(x) is obtained by dividing tproc - tdelay, which represents the time the etching solution exists on substrate W. Also, tproc represents the elapsed time from when the film treatment begins until when the film treatment ends, and tdelay represents the time from when the film treatment begins until the etching solution is actually supplied to substrate W. Based on these, the third function H(x) is expressed using the variable x representing the radial position of substrate W and the third parameters ν1 to ν4.

[0109] Regarding the second processing result ER2, the etching solution is sufficiently supplied to the position in the diameter direction of the substrate W, which is greater than the first distance h1. According to this, it is assumed that the shape of the second processing result ER2 changes significantly when the variable x is the first distance h1. Therefore, attention is paid to point P1, which corresponds to the inflection point of the third function H(x). Since the inflection point is a point where the rate of change of the coverage rate changes rapidly, it is a characteristic point of the third function H(x). The value of the horizontal axis of point P1 represents the value of the first distance function h1(t). Also, the distance from point P1 to S(t) on the horizontal axis corresponds to the third reference parameter ν, which represents the second distance h2. In this embodiment, the third parameter is determined by finding the third reference parameter ν at this inflection point P.

[0110] Returning to FIG. 6, the third reference parameter determining unit (247) determines the value of the third reference parameter ν for each of the multiple groups, in other words, for each of the multiple variation conditions, for the coverage rate obtained from the multiple second processing result ER2 shown in FIG. 12. The third parameter determining unit (249) determines each of the third parameters ν1 to ν4 for each of the multiple groups, in other words, for each of the multiple second processing conditions. The third parameter determining unit (249) determines the third parameters ν1 to ν4 by applying the third reference parameter and the second processing condition to the third sub-function shown in Equation (15) and performing regression analysis. In other words, the third reference parameter determination unit (247) determines the third parameters ν1 to ν4 by bringing each of the third parameters ν1 to ν4 to the same value among the same number of expressions (15) as the second processing condition.

[0111] Through the series of operations described above, the prediction algorithm generation unit (213) generates a prediction algorithm. The prediction algorithm is represented as the product of a first function F1(x) determined by the first decision unit (220), a second function F2(x) determined by the second decision unit (230), and a third function H(x) determined by the third decision unit (240) considering back discharge processing.

[0112] FIG. 14 is a diagram illustrating an example of a function of a prediction algorithm generation unit that generates a prediction algorithm without considering back-side discharge processing. Referring to FIG. 14, the prediction algorithm generation unit (213) includes a first decision unit (220) and a fourth decision unit (250). Since the function of the first decision unit (220) is the same as the function described above, the explanation here is not repeated.

[0113] The fourth determination unit (250) generates a third function H(x) that does not consider back-side discharge processing based on the first processing condition and the first processing result ER1. Specifically, the fourth determination unit (250) includes a fourth data acquisition unit (251), a nozzle operation classification unit (253), a third conversion unit (255), a fourth reference parameter determination unit (257), and a fourth parameter determination unit (259).

[0114] The fourth data acquisition unit (251) acquires multiple sets of a first data set including a first processing condition and a first processing result ER1 from the experimental data acquisition unit (211). The first processing condition includes a variation condition.

[0115] The nozzle operation classification unit (253) classifies multiple sets of first data sets acquired by the fourth data acquisition unit (251) into multiple groups according to variation conditions. The nozzle operation classification unit (253) classifies multiple sets of first data sets with the same variation conditions into the same group.

[0116] The fourth reference parameter determination unit (257) and the fourth parameter determination unit (259) determine a third function H(x) that does not consider back-side discharge processing based on one or more first data sets classified into groups for each of the plurality of groups defined by the nozzle operation classification unit (253).

[0117] The order of determination for the third function H(x) without considering back-side discharge treatment is as follows. By performing treatment of the film under a plurality of first treatment conditions in which the values ​​of the temperature T of the etching solution, the concentration C of the etching solution, the flow rate D of the etching solution, and the rotational speed R of the substrate W are each different, and also the variation conditions appearing at the relative position of the surface nozzle (311) and the substrate W that fluctuate over time are each different, a plurality of first treatment results ER1 are obtained. The value of the first treatment result ER1 at the radial position of the substrate W is expressed as follows using the first function F1(x) represented by Equation (1) and the third function H(x) without considering back-side discharge treatment.

[0118]

[0119] Here, by modifying Equation (12A), the third function H(x), which does not consider back-side discharge processing, becomes equivalent to the value obtained by dividing the value of the first processing result ER1 by the first function F1(x). Therefore, the value obtained by dividing the value of the first processing result ER1 by the first function F1(x) can be said to be the influence on the first processing result ER1 during the time when the etching solution is not actually supplied to the substrate W due to nozzle operation during the processing time. Hereinafter, the value obtained by dividing the value of the first processing result ER1 by the first function F1(x) is referred to as the third influence.

[0120] The third conversion unit (255) calculates a third influence by dividing the first processing result ER1 of one or more first data sets classified by the group defined by the nozzle operation classification unit (253) by the first function F1(x) determined by the first determination unit (220), and outputs the calculated third influence to the fourth reference parameter determination unit (257).

[0121] The fourth reference parameter determination unit (257) determines the value of the third reference parameter ν for each of the multiple groups, in other words, for each of the multiple variation conditions, regarding the third influence obtained from the first processing result ER1. In addition, regarding the method of determining the value of the third reference parameter ν, the same method as the method of determination performed by the third reference parameter determination unit (247) is used. The fourth parameter determination unit (259) determines each of the third parameters ν1 to ν4 among the multiple groups, in other words, for each of the multiple first processing conditions. The fourth parameter determination unit (259) determines the third parameters ν1 to ν4 by applying the third reference parameter and the first processing condition to the third sub-function represented by Equation (15) and performing regression analysis. In other words, the fourth parameter determination unit (259) determines the third parameters ν1 to ν4 by bringing each of the third parameters ν1 to ν4 to the same value among the same number of expressions (15) as the first processing condition.

[0122] By going through a series of these operations, the prediction algorithm generation unit (213) can generate a prediction algorithm represented as the product of a first function F1(x) and a third function H(x) that does not consider the back discharge processing determined by the fourth decision unit (250).

[0123] Here, referring again to FIG. 5, for example, the film thickness formed by the substrate processing device (300) is desired to be uniform across the entire surface of the substrate W. For this reason, a target film thickness is determined for the processing performed by the substrate processing device (300). The target film thickness is indicated by a dotted line. The deviation characteristic is the difference between the film thickness of the film formed on the substrate W after processing by the substrate processing device (300) and the target film thickness. The deviation characteristic includes the difference at each of a plurality of positions in the diameter direction of the substrate W.

[0124] Returning to FIG. 4, the information processing device (100) includes a processing condition determining unit (151), a receiving unit (155), a prediction unit (159), an evaluation unit (161), and a processing condition transmitting unit (163). The function provided by the information processing device (100) is realized by the CPU (101) provided by the information processing device (100) by executing a processing condition determining program stored in RAM (102). The receiving unit (155) receives a prediction algorithm transmitted from a prediction algorithm generating device (200) and outputs the received prediction algorithm to the prediction unit (159).

[0125] The processing condition determination unit (151) determines the processing conditions for the substrate W to be processed by the substrate processing device (300) and outputs the processing conditions, including the variation conditions for back-side discharge processing, to the prediction unit (159).

[0126] The prediction unit (159) estimates an etching profile from processing conditions including variation conditions. Specifically, the prediction unit (159) uses a prediction algorithm to predict an etching profile from processing conditions including variation conditions input from the processing condition determination unit (151), and outputs the etching profile to the evaluation unit (161).

[0127] The evaluation unit (161) evaluates the etching profile input from the prediction unit (159) and outputs the evaluation result to the processing condition determination unit (151). Specifically, the evaluation unit (161) obtains the film thickness characteristics of the substrate W before processing, which the substrate processing device (300) plans to process. The evaluation unit (161) calculates the film thickness characteristics predicted after etching processing from the etching profile input from the prediction unit (159) and the film thickness characteristics of the substrate W before processing, and compares them with the target film thickness characteristics. If the result of the comparison satisfies the evaluation criteria, the processing conditions determined by the processing condition determination unit (151) are output to the processing condition transmission unit (163). For example, the evaluation unit (161) calculates the discrepancy characteristics (see FIG. 5) and determines whether the discrepancy characteristics satisfy the evaluation criteria. The divergence characteristic is the difference between the film thickness characteristic of the substrate (W) after etching treatment and the target film thickness characteristic. The evaluation criteria can be determined arbitrarily. For example, the evaluation criteria may be whether the maximum difference in the divergence characteristic is below a threshold value, or whether the average difference is below a threshold value.

[0128] The processing condition transmitting unit (163) transmits a processing condition including a variation condition determined by the processing condition determining unit (151) to the control unit (10) of the substrate processing device (300). The substrate processing device (300) processes the substrate W according to the processing condition including the variation condition.

[0129] If the evaluation result does not satisfy the evaluation criteria, the evaluation unit (161) outputs the evaluation result to the processing condition determination unit (151). The evaluation result includes the film thickness characteristic predicted after etching treatment or the difference between the film thickness characteristic predicted after etching treatment and the target film thickness characteristic.

[0130] The processing condition determination unit (151) determines a new processing condition to be predicted by the prediction unit (159) based on the evaluation result input from the evaluation unit (161). The processing condition determination unit (151) selects one set of processing conditions from a plurality of processing conditions including pre-prepared variation conditions using experimental design, pairwise method, or Bayes estimation, and transmits the selected processing condition to the prediction unit (159).

[0131] An example is described in which a processing condition determination unit (151) searches for processing conditions including variation conditions using Bayesian estimation. For example, when multiple evaluation results are output by an evaluation unit (161), there are multiple sets of processing conditions including variation conditions and evaluation results. From the trends of the etching profiles in each of the multiple sets, a processing condition in which the film thickness of the film becomes uniform, or a processing condition in which the difference between the film thickness characteristic predicted after etching treatment and the target film thickness characteristic is minimized is searched.

[0132] Specifically, the processing condition determination unit (151) searches for processing conditions to minimize the objective function. The objective function is a function representing the uniformity of the film thickness of the film or a function representing the consistency between the film thickness characteristics of the film and the target film thickness characteristics. For example, the objective function is a function that represents the difference between the film thickness characteristics predicted after etching treatment and the target film thickness characteristics as a parameter. The parameter here is a corresponding variation condition. The corresponding variation condition is a variation condition used to estimate the etching profile using a prediction algorithm. The processing condition determination unit (151) selects a variation condition that is a parameter determined by searching among a plurality of variation conditions, and determines the selected variation condition and the processing condition.

[0133] FIG. 15 is a flowchart illustrating an example of the flow of a prediction algorithm generation process. The prediction algorithm generation process is a process executed by the CPU (201) by the CPU (201) equipped in the prediction algorithm generation device (200) by executing a prediction algorithm generation program stored in RAM (202).

[0134] Referring to FIG. 15, the CPU (201) provided by the prediction algorithm generating device (200) acquires experimental data (step S01). The CPU (201) acquires experimental data from the substrate processing device (300) by controlling the input / output I / F (107). The experimental data may be acquired by reading experimental data recorded on a recording medium such as a CD-ROM (209) from the memory device (104). The experimental data includes a plurality of first data sets and a plurality of second data sets. The first data set includes a first processing condition and a first processing result ER1. The second data set includes a second processing condition and a second processing result ER2.

[0135] In the following step S02, a first function generation process is executed, and the process proceeds to step S03. The details of the first function generation process will be described later, but it is a process of generating a first function F1(x) based on multiple sets of the first data set. In step S03, it is determined whether a back-side discharge process is performed in the processing of the film of the substrate processing device (300).

[0136] In step S03, if it is determined that back-side discharge processing is performed by processing the film of the substrate processing device (300), the process proceeds to step S04. In step S04, a second function generation process is executed, and the process proceeds to step S05A. The details of the second function generation process will be described later, but it is a process of generating a second function F2(x) based on multiple sets of the second data set. In step S05A, a third function generation process considering back-side discharge processing is executed, and the process proceeds to step S06. The details of the third function generation process considering back-side discharge processing will be described later, but it is a process of generating a third function H(x) based on multiple sets of the second data set.

[0137] In step S03, if it is determined that back-side discharge processing is not performed due to the processing of the film of the substrate processing device (300), the processing proceeds to step S05B. In step S05B, a third function generation process that does not consider back-side discharge processing is executed, and the processing proceeds to step S06. The details of the third function generation process that does not consider back-side discharge processing will be described later, but it is a process that generates a third function H(x) based on multiple sets of the first data set.

[0138] In step S06, the CPU (201) determines a prediction algorithm. If the processing proceeds from step S05A, the prediction algorithm is determined using the first function determined in step S02, the second function determined in step S04, and the third function determined in step S05A that takes into account the back discharge processing. If the processing proceeds from step S05B, the prediction algorithm is determined using the first function determined in step S01 and the third function determined in step S05B that does not take into account the back discharge processing. In the following step S07, the CPU (201) transmits the determined prediction algorithm to the information processing device (100) and terminates the processing.

[0139] FIG. 16 is a flowchart illustrating an example of the flow of the first function determination process. The equations (1) to (3) described above are stored in advance in the memory (204) of the prediction algorithm generating device (200). First, the CPU (201) acquires multiple sets of first data from experimental data and classifies the acquired multiple sets of first data into multiple groups according to processing conditions (step S11).

[0140] Next, the CPU (201) selects a first processing condition by selecting one group to be processed from among a plurality of groups (step S12). The CPU (201) determines a first reference parameter corresponding to the selected first processing condition (step S13) and proceeds to step S14 for processing. Specifically, the CPU (201) determines the first reference parameters α, β and an integer n1 corresponding to the first processing condition by applying the first processing condition to the expression (1) stored in the memory device (204) and returning to the first processing result ER1.

[0141] Next, the CPU (201) determines a first sub-function (step S14) and proceeds to step S15. Here, the first sub-function for the first processing condition is determined by substituting the first reference parameters α and β determined in step S13 and the first processing condition selected as the processing target into the first sub-function (equations (2), (3)) stored in the memory device (204). In step S15, it is determined whether there is a first processing condition that is not selected as the processing target. If there is an unselected first processing condition, the processing returns to step S12, but otherwise, the processing proceeds to step S16.

[0142] Steps S12 to S14 are repeated as many times as there are multiple first processing conditions, thereby determining multiple first sub-functions corresponding to each of the multiple first processing conditions. In step S16, the CPU (201) determines first parameters α1 to α3 and β1 to β3. After that, the processing returns to the prediction algorithm generation process. Specifically, the CPU (201) determines first parameters α1 to α3 and β1 to β3 by performing regression analysis on multiple first sub-functions corresponding to each of the multiple first processing conditions. In other words, first parameters α1 to α3 and β1 to β3 are determined by bringing each of the first parameters α1 to α3 and β1 to β3 closer to the same value among the multiple first sub-functions. As the first parameters α1 to α3 and β1 to β3 are determined, the first function F1(x) represented by Equation (1) is determined using Equation (2) and Equation (3). Because of this, by applying an arbitrary first processing condition to the first function F1(x), it becomes possible to predict a processing result that represents the difference in film thickness before and after processing when the substrate processing device (300) performs film processing under the first processing condition.

[0143] FIG. 17 is a flowchart illustrating an example of the flow of the second function determination process. The equations (4) to (7) described above are stored in advance in the memory (204) of the prediction algorithm generating device (200). First, the CPU (201) acquires multiple sets of second data from the experimental data and classifies the acquired multiple sets of second data into multiple groups according to processing conditions (step S21).

[0144] Next, the CPU (201) selects a second processing condition by selecting one group to be processed from among a plurality of groups (step S22). The CPU (201) calculates a first influence using the second processing result ER2 obtained by the selected second processing condition and the first function F1(x) generated by the first function generation process (step S23). The CPU (201) determines a second reference parameter corresponding to the selected second processing condition (step S24) and proceeds to step S25. Specifically, the CPU (201) determines the second reference parameters γ, δ, ε, ξ and the integer n2 corresponding to the second processing condition by applying the second processing condition to equations (6) and (7) stored in memory (204) and regressing to approximate the calculated first influence.

[0145] Next, the CPU (201) determines a second sub-function (step S25) and proceeds to step S26. Here, the second sub-function for the second processing condition is determined by substituting the second reference parameters γ, δ, ε, ξ determined in step S24 and the second processing condition selected as the processing target into the second sub-function (equations (8), (9), (10), (11)) stored in the memory device (204). In step S26, it is determined whether there is a second processing condition that is not selected as the processing target. If there is an unselected second processing condition, the processing returns to step S22, but otherwise, the processing proceeds to step S27.

[0146] Steps S22 to S25 are repeated as many times as there are multiple second processing conditions, thereby determining multiple second sub-functions corresponding to each of the multiple second processing conditions. In step S27, the CPU (201) determines the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4. After that, the processing returns to the prediction algorithm generation processing. Specifically, the CPU (201) determines the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4 by performing regression analysis on the multiple second sub-functions corresponding to each of the multiple second processing conditions. Thus, the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, and ξ1 ~ ξ4 are determined such that the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, and ξ1 ~ ξ4 are identical among the multiple second sub-functions. As the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, and ξ1 ~ ξ4 are determined, the second function F2(x) represented by Equation (5) is determined by using Equations (6), (7) and Equations (8) ~ (11). For this reason, by applying an arbitrary second processing condition to the second function F2(x), it becomes possible to predict a processing result that indicates the difference in film thickness before and after processing when the substrate processing device (300) performs film processing with the second processing condition.

[0147] FIG. 18 is a flowchart showing an example of the flow of a third function determination process considering back-side discharge processing. The equations (12) to (15) described above are stored in advance in the memory (204) of the prediction algorithm generation device (200). First, the CPU (201) acquires multiple sets of second data from experimental data and classifies the acquired multiple sets of second data into multiple groups according to variation conditions (step S31).

[0148] Next, the CPU (201) selects a variation condition by selecting one group to be processed from among a plurality of groups (step S32). The CPU (201) calculates a second influence (coverage rate) using the second processing result ER2 obtained by the second processing condition corresponding to the selected variation condition, the first function F1(x) generated by the first function generation process, and the second function F2(x) generated by the second function generation process (step S33). The CPU (201) determines a third reference parameter ν corresponding to the variation condition (step S34) and proceeds to step S35. Specifically, the CPU (201) sets the inflection point of the calculated second influence as a feature point. The inflection point is determined by taking the second derivative of the second influence. Also, the CPU (201) determines the distance between the inflection point and the position of the surface nozzle (311) in the diameter direction of the substrate W as the third reference parameter ν.

[0149] Next, the CPU (201) determines a third sub-function (step S35) and proceeds to step S36. Here, the third reference parameter ν determined in step S34, the variation condition selected as the processing target, and the second processing condition corresponding to the variation condition are substituted into the third sub-function (equation (15)) stored in the memory device (204). By doing so, the third sub-function for the variation condition is determined. In step S36, it is determined whether there is a variation condition that is not selected as the processing target. If there is an unselected variation condition, the processing returns to step S32, but otherwise, the processing proceeds to step S37.

[0150] Steps S32 through S35 are repeated as many times as there are multiple variation conditions, thereby determining multiple third sub-functions corresponding to each of the multiple variation conditions. In step S37, the CPU (201) determines third parameters ν1 through ν4. After that, the processing returns to the prediction algorithm generation process. Specifically, the CPU (201) determines the third parameters ν1 through ν4 by performing regression analysis on the multiple third sub-functions corresponding to each of the multiple variation conditions. In other words, the third parameters ν1 through ν4 are determined by bringing the third parameters ν1 through ν4 close to the same value among the multiple third sub-functions. Once the third parameters ν1 through ν4 are determined, the third function H(x) considering the back discharge processing represented by Equation (13) is determined using Equation (14) and Equation (15). For this reason, by applying arbitrary variation conditions to the third function H(x) considering back-side discharge processing, it becomes possible to predict the processing result showing the difference in film thickness before and after processing when the substrate processing device (300) (with back-side discharge processing) performs film processing with those variation conditions.

[0151] FIG. 19 is a flowchart illustrating an example of the flow of a third function determination process that does not consider back-side discharge processing. The equations (12A) and (13) through (15) described above are stored in advance in the memory (204) of the prediction algorithm generation device (200). First, the CPU (201) acquires multiple sets of first data from experimental data and classifies the acquired multiple sets of first data into multiple groups according to variation conditions (step S41).

[0152] Next, the CPU (201) selects a variation condition by selecting one group to be processed from among a plurality of groups (step S42). The CPU (201) calculates a third influence (coverage rate) using a first processing result ER1 obtained by a first processing condition corresponding to the selected variation condition and a first function F1(x) generated by a first function generation process (step S43). The CPU (201) determines a third reference parameter ν corresponding to the variation condition (step S44) and proceeds to step S45. Specifically, the CPU (201) sets the inflection point of the calculated third influence as a feature point. The inflection point is determined by taking the second derivative of the third influence. Also, the CPU (201) determines the distance between the inflection point and the position of the surface nozzle (311) in the diameter direction of the substrate W as the third reference parameter ν.

[0153] Next, the CPU (201) determines a third sub-function (step S45) and proceeds to step S46. Here, the third reference parameter ν determined in step S44, the variation condition selected as the processing target, and the first processing condition corresponding to the variation condition are substituted into the third sub-function (equation (15)) stored in the memory device (204). By doing so, the third sub-function for the variation condition is determined. In step S46, it is determined whether there is a variation condition that is not selected as the processing target. If there is an unselected variation condition, the processing returns to step S42, but otherwise, the processing proceeds to step S47.

[0154] Steps S42 to S45 are repeated as many times as there are multiple variation conditions, thereby determining multiple third sub-functions corresponding to each of the multiple variation conditions. In step S47, the CPU (201) determines the third parameters ν1 to ν4. After that, the processing returns to the prediction algorithm generation process. Specifically, the CPU (201) determines the third parameters ν1 to ν4 by performing regression analysis on the multiple third sub-functions corresponding to each of the multiple variation conditions. In other words, the third parameters ν1 to ν4 are determined by bringing each of the third parameters ν1 to ν4 closer to the same value among the multiple third sub-functions. As the third parameters ν1 to ν4 are determined, the third function H(x) that does not consider the back discharge processing represented by Equation (13) is determined using Equation (14) and Equation (15). For this reason, by applying arbitrary variation conditions to the third function H(x) that does not consider back-side discharge treatment, it becomes possible to predict the treatment result showing the difference in film thickness before and after treatment when the substrate processing device (300) (no back-side discharge treatment) performs film treatment with those variation conditions.

[0155] (4) Effects of the embodiment

[0156] According to the prediction algorithm generating device (200) of the above embodiment, the first reference parameters α, β and the first parameters α1 to α3, β1 to β3 of the predetermined first function F1(x) are determined based on a plurality of sets of first data sets including the first processing condition and the first processing result ER1. By doing so, the first function F1(x) that predicts the first processing result ER1 from the first processing condition can be fitted to each substrate processing device (300). In addition, since the first processing result ER1 is calculated from the first processing condition using the first function F1(x), the reliability of the first processing result ER1 predicted by the first function F1(x) is improved compared to estimating the first processing result ER1 using an inference model lacking explanatory power, such as a black box.

[0157] In addition, a first sub-function is determined for each of the multiple first processing conditions, and since the first parameters α1 to α3 and β1 to β3 are determined by bringing them close to the same value between the multiple first processing conditions, the first function F1(x) can be easily obtained.

[0158] In addition, the second reference parameters γ, δ, ε, ξ and the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, ξ1 ~ ξ4 of the predetermined second function F2(x) are determined based on multiple sets of second data sets. The first influence is a value calculated by applying a second processing condition to the first function F1(x) and is obtained by dividing the second processing result ER2, thus representing the influence that the back-side discharge process exerts on the second processing result ER2. By doing so, the second function F2(x), which estimates the influence of the process of supplying a processing liquid to the back-side of the substrate on the second processing result ER2, can be fitted to each substrate processing device.

[0159] In addition, a second sub-function is determined for each of the multiple second processing conditions, and by bringing the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, and ξ1 ~ ξ4 closer to the same value among the multiple second processing conditions, the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, and ξ1 ~ ξ4 are determined, so the second function F2(x) can be easily obtained.

[0160] In addition, the third reference parameter ν and the third parameters ν1 to ν4 of the predetermined third function H(x) are determined based on the second influence. Since the second influence is the value obtained by dividing the second processing result ER2 by the value calculated by applying the second processing condition to the first function F1(x) and the value calculated by applying the second processing condition to the second function F2(x), it represents the influence that moving the position of the nozzle supplying the processing liquid to the substrate over time has on the second processing result ER2. By doing so, the third function H(x), which estimates the influence that moving the position of the nozzle supplying the processing liquid to the substrate over time has on the second processing result ER2, can be fitted to each substrate processing device.

[0161] In addition, a third sub-function is determined for each of the multiple variation conditions, and since the third parameters ν1 to ν4 are determined by bringing them close to the same value between the multiple variation conditions, the third function H(x) can be easily obtained.

[0162] (5) Other embodiments

[0163] (5-1) FIG. 20 is a third diagram showing an example of the function of a prediction algorithm generation unit. The function of the prediction algorithm generation unit of FIG. 6 and the function of the prediction algorithm generation unit of FIG. 20 are different. The function of the prediction algorithm generation unit of FIG. 20 does not have the first reference parameter determination unit (225) of the first determination unit (220), the second reference parameter determination unit (237) of the second determination unit (230), and the third reference parameter determination unit (247) of the third determination unit (240). In Equation (1) of the above embodiment, the first function F1(x) is expressed using first reference parameters α and β, and in Equations (2) and (3), the first reference parameters α and β are expressed using first parameters α1 to α3 and β1 to β3 by the first sub-function, but the present invention is not limited thereto. For example, the first function F1(x) may be expressed using first parameters α1 to α3 and β1 to β3 without passing through the first sub-function, as shown in the following Equation (16).

[0164]

[0165] The first parameter determination unit (227) of FIG. 20 determines the integer n1 and the first parameters α1 to α3 and β1 to β3, respectively, for which the first function F1(x) shown in Equation (16) is closest to the first processing result ER1. The integer n1 and the first parameters α1 to α3 and β1 to β3 can be obtained by regression analysis.

[0166] In addition, in the above embodiments, the second function F2(x) includes the first constituent function f21(x) and the second constituent function f22(x), and is represented using the second reference parameters γ, δ, ε, and ξ of the first constituent function f21(x) and the second constituent function f22(x), and the second reference parameters γ, δ, ε, and ξ are represented using the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4 by the second sub-functions shown in the above embodiments (8) to (11), but the present invention is not limited thereto. For example, the first constituent function f21(x) and the second constituent function f22(x) of the second function F2(x) may be expressed using the second parameters γ1 ~ γ4, δ1 ~ δ4, ε1 ~ ε4, and ξ1 ~ ξ4 without passing through the second sub-function, as shown in the following equations (17) and (18).

[0167]

[0168] The second parameter determination unit (239) of FIG. 20 determines the integer n2 and the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4, respectively, for which the first constituent function f21(x) and the second constituent function f22(x) of the second function F2(x) shown in Equations (17) and (18) are closest to the second processing result ER2. The integer n2 and the second parameters γ1 to γ4, δ1 to δ4, ε1 to ε4, and ξ1 to ξ4 can be obtained by regression analysis.

[0169] In addition, in Equation (13) of the above embodiment, the third function H(x) is the inverse function h1 of the first distance function h1(t). ―1(x) is used to represent the first distance function h1(x), and the third reference parameter ν is used to represent the third reference parameter ν, and the third reference parameter ν is used to represent the third parameters ν1 to ν4 by the third sub-function shown in Equation (15), but the present invention is not limited thereto. For example, as shown in the following Equation (19), the first distance function h1(x) of the third function H(x) may be represented using the third parameters ν1 to ν4 without passing through the third sub-function.

[0170]

[0171] The third parameter determination unit (249) of FIG. 20 determines each of the third parameters ν1 to ν4 for which the first distance function h1(x) of the third function H(x) shown in Equation (19) is closest to the second processing result ER2. The third parameters ν1 to ν4 are obtained by regression analysis.

[0172] (5-2) In the above embodiment, an example is described in which a prediction algorithm generated by the prediction algorithm generation unit (213) of the prediction algorithm generation device (200) is input to the prediction unit (159) of the information processing device (100), the prediction unit (159) inputs processing conditions including variation conditions to the prediction algorithm, and outputs an etching profile output by the prediction algorithm to the evaluation unit (161), but the present invention is not limited thereto. For example, a prediction algorithm including a first function F1(x), a second function F2(x), and a third function H(x) represented by Equations (1) to (15) may be stored in the prediction unit. In this case, it is possible to realize the function of the prediction unit (159) by inputting each parameter determined by the prediction algorithm generation unit (213) of the prediction algorithm generation device (200) to the prediction unit (159) of the information processing device (100).

[0173] (6) Overall of the embodiments

[0174] (Claim 1) A prediction algorithm generating device according to one aspect of the present invention,

[0175] A first data acquisition unit that acquires a first data set of multiple sets, and

[0176] A first determination unit is provided for determining a first parameter by applying a plurality of the above-mentioned first data sets to a predetermined first function and performing regression analysis, and

[0177] Each of the plurality of first data sets comprises a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and said first processing condition.

[0178] The above first processing result includes the difference in film thickness before and after the processing of the film is performed at each of a plurality of different locations in the diameter direction of the substrate, and

[0179] The first function above represents the difference between the film thickness before and after the treatment of the film at any position in the diameter direction of the substrate using the first treatment condition and the first parameter.

[0180] According to the prediction algorithm generating device described in claim 1, since the first parameter of a predetermined first function is determined based on multiple sets of a first data set including a first processing condition and a first processing result, a first function that predicts a first processing result from a first processing condition can be adapted to each substrate processing device. Furthermore, since the first processing result is calculated from the first processing condition using the first function, the reliability of the first processing result predicted by the first function is improved compared to estimating the first processing result using an inference model lacking explanatory power, such as a black box. As a result, a prediction algorithm generating device capable of easily generating a prediction algorithm suitable for a substrate processing device can be provided.

[0181] (Clause 2) In the prediction algorithm generating device described in Clause 1,

[0182] The above first function is a function using a first reference parameter represented by a first sub-function using the above first processing condition and the above first parameter, and

[0183] The first determination unit comprises a first reference parameter determination unit that determines the first reference parameter corresponding to the first processing condition by applying the first processing result corresponding to the first processing condition to the first function and performing regression analysis for each of the plurality of the first processing conditions, and

[0184] In each of the plurality of the above-mentioned first processing conditions, a first parameter determining unit may be included to determine the first parameter by applying the first reference parameter determined in correspondence with the first processing condition and the first processing condition to the first sub-function and performing regression analysis.

[0185] According to the prediction algorithm generating device described in claim 2, a first sub-function is determined for each of the plurality of first processing conditions, and since the first parameter is determined by bringing the first parameter close to the same value between the plurality of first processing conditions, the first function can be easily obtained.

[0186] (Clause 3) In the prediction algorithm generating device described in Clause 1,

[0187] The treatment of the above film includes a back surface discharge treatment that supplies a treatment solution to the back surface of the substrate, and

[0188] A second data acquisition unit that acquires a second data set of multiple sets, and

[0189] A second determination unit is additionally provided for determining a second parameter by applying a first influence degree and a second processing condition corresponding to each of the plurality of second data sets to a predetermined second function and performing regression analysis.

[0190] Each of the plurality of second data sets comprises, when the substrate processing device performs the processing of the film including the back-side discharge process, a second processing result obtained after the substrate processing device performs the processing of the film including the back-side discharge process according to the second processing condition in which the back-side discharge condition is added to the first processing condition, and the second processing condition.

[0191] The second processing result above includes a difference in film thickness before and after the processing of the film, including the back-side discharge processing at each of a plurality of different locations in the diameter direction of the substrate, and

[0192] The above second function represents the first influence degree obtained by subtracting the second processing result from the value calculated by applying the second processing condition to the above first function, and

[0193] The above second function may represent the first influence degree at any position in the diameter direction of the substrate using the second processing condition and the second parameter.

[0194] According to the prediction algorithm generating device described in claim 3, a second parameter of a predetermined second function is determined based on a plurality of second data sets. The first influence is a value obtained by applying the second processing condition to the first function and subtracting the second processing result, so it represents the influence that the back-side discharge process exerts on the second processing result. In this way, a second function that estimates the influence of the process of supplying a processing liquid to the back-side of a substrate on the second processing result can be fitted to each substrate processing device.

[0195] (Clause 4) In the prediction algorithm generating device described in Clause 3,

[0196] The above second function is a function using a second reference parameter represented by a second sub-function using the above second processing condition and the above second parameter, and

[0197] The second determination unit comprises a second reference parameter determination unit that determines the second reference parameter corresponding to the second processing condition by applying the first influence degree corresponding to the second processing condition to the second function and performing regression analysis for each of the plurality of the second processing conditions, and

[0198] It may include a second parameter determining unit that determines the second parameter by applying the second reference parameter determined in correspondence with the second processing condition and the second processing condition to the second sub-function and performing regression analysis for each of the plurality of the above second processing conditions.

[0199] According to the prediction algorithm generating device described in claim 4, a second sub-function is determined for each of the plurality of second processing conditions, and since the second parameter is determined by the second parameter approaching the same value between the plurality of second processing conditions, the second function can be easily obtained.

[0200] (Clause 5) In the prediction algorithm generating device described in Clause 3,

[0201] When the substrate processing device performs the processing of the film including the back-side discharge process, it moves the position of the nozzle supplying the processing liquid to the substrate over time, and

[0202] The second processing condition above includes a variation condition indicating the relative position of the nozzle with respect to the substrate that varies over time, and

[0203] A third determination unit is additionally provided for determining a third parameter by applying a second influence degree and a second processing condition corresponding to each of the plurality of the above fluctuation conditions to a predetermined third function and performing regression analysis.

[0204] The third function represents the second influence degree obtained by subtracting the second processing result from the value calculated by applying the second processing condition to the first function and the value calculated by applying the second processing condition to the second function, and

[0205] The above third function may represent the second influence degree at any position in the diameter direction of the substrate using the second processing condition and the third parameter.

[0206] According to the prediction algorithm generating device described in claim 5, a third parameter of a predetermined third function is determined based on a second influence. Since the second influence is a value obtained by applying a second processing condition to a first function and a value obtained by applying a second processing condition to a second function and subtracting the second processing result from the second processing result, it represents the influence that a process of moving the position of a nozzle supplying a processing liquid to a substrate over time has on the second processing result. By doing so, a third function that estimates the influence of a process of moving the position of a nozzle supplying a processing liquid to a substrate over time on the second processing result can be fitted to each substrate processing device.

[0207] (Clause 6) In the prediction algorithm generating device described in Clause 5, the third function is a function using a third reference parameter represented by a third sub-function using the second processing condition and the third parameter, and

[0208] The third determination unit comprises a third reference parameter determining unit that determines the third reference parameter based on a feature point of the second influence degree corresponding to the variation condition for each of the plurality of variation conditions, and

[0209] For each of the plurality of the above-mentioned variation conditions, a third parameter determining unit may be included to determine the third parameter by applying the third reference parameter determined in response to the variation condition and the second processing condition corresponding to the variation condition to the third sub-function and performing regression analysis.

[0210] According to the prediction algorithm generating device described in claim 6, a third sub-function is determined for each of the plurality of variation conditions, and since the third parameter is determined by bringing the third parameter close to the same value between the plurality of variation conditions, the third function can be easily obtained.

[0211] (Clause 7) In a prediction algorithm generating device described in Clause 1 or 2,

[0212] When performing the treatment of the film, the above substrate processing device moves the position of the nozzle supplying the processing liquid to the substrate over time, and

[0213] The first processing condition above includes a variation condition indicating the relative position of the nozzle with respect to the substrate that varies over time, and

[0214] A fourth determination unit is additionally provided for determining a third parameter by applying a third influence degree corresponding to each of the plurality of the above-mentioned fluctuation conditions and the first processing condition to a predetermined third function and performing regression analysis.

[0215] The above third function represents the above third influence degree obtained by subtracting the above first processing result from the value calculated by applying the above first processing condition to the above first function, and

[0216] The above third function may represent the third influence degree at any position in the diameter direction of the substrate using the first processing condition and the third parameter.

[0217] According to the prediction algorithm generating device described in claim 7, a third parameter of a predetermined third function is determined based on a third influence. Since the third influence is a value calculated by applying a first processing condition to a first function and subtracting the first processing result, it represents the influence that a process of moving the position of a nozzle supplying a processing liquid to a substrate over time has on the first processing result. By doing so, a third function that estimates the influence of a process of moving the position of a nozzle supplying a processing liquid to a substrate over time on the first processing result can be fitted to each substrate processing device.

[0218] (Clause 8) In the prediction algorithm generating device described in Clause 7,

[0219] The above third function is a function using a third reference parameter represented by a third sub-function using the above first processing condition and the above third parameter, and

[0220] The fourth determination unit comprises a fourth reference parameter determination unit that determines the third reference parameter based on the characteristic point of the third influence degree corresponding to the variation condition for each of the plurality of variation conditions, and

[0221] For each of the plurality of the above-mentioned variation conditions, a fourth parameter determining unit may be included to determine the third parameter by applying the third reference parameter determined in response to the variation condition and the first processing condition corresponding to the variation condition to the third sub-function and performing regression analysis.

[0222] According to the prediction algorithm generating device described in claim 8, a third sub-function is determined for each of the plurality of variation conditions, and since the third parameter is determined by bringing the third parameter close to the same value between the plurality of variation conditions, the third function can be easily obtained.

[0223] (Clause 9) An information processing device according to another aspect of the present invention is,

[0224] As an information processing device that manages a substrate processing device,

[0225] The above substrate processing device processes the film by supplying a processing solution to the upper surface of the substrate on which the film is formed, and

[0226] Using a prediction algorithm, the substrate processing device comprises a processing condition determining unit that determines a first processing condition for executing the processing of the film, and

[0227] The above prediction algorithm is a first function that calculates the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate where the substrate processing device performs the processing of the film, using a first parameter from the first processing condition, and

[0228] The above first parameter is obtained by applying a plurality of first data sets to the above first function and performing regression analysis, and

[0229] Each of the plurality of first data sets comprises a first processing result obtained after processing the film by driving the substrate processing device under the first processing condition and the first processing condition, and

[0230] The above first processing result includes the difference in film thickness before and after the processing of the film is performed at each of a plurality of different locations in the diameter direction of the substrate, and

[0231] The processing condition determination unit determines the temporary first processing condition as the first processing condition for driving the substrate processing device when the first processing result calculated from the temporary first processing condition using the prediction algorithm satisfies the allowable condition.

[0232] According to the information processing device described in claim 9, when a first processing condition is applied to a first function and the first processing result produced by the first function satisfies an allowable condition, a temporary first processing condition is determined as a first processing condition for driving a substrate processing device. Accordingly, a plurality of temporary first processing conditions can be determined for a first processing result that satisfies an allowable condition. As a result, it becomes possible to present a plurality of appropriate processing conditions to a substrate processing device in which a complex process is executed.

[0233] (Clause 10) A method for generating a prediction algorithm according to another aspect of the present invention is,

[0234] A step of acquiring a first data set of multiple sets, and

[0235] The method comprises a step of determining a first parameter by applying a plurality of the above-mentioned first data sets to a first function and performing regression analysis, and

[0236] Each of the plurality of first data sets comprises a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and said first processing condition.

[0237] The above first processing result includes the difference in film thickness before and after the processing of the film is performed at each of a plurality of different locations in the diameter direction of the substrate, and

[0238] The first function is predetermined to represent the difference between the film thickness before and after the treatment of the film at any position in the diameter direction of the substrate using the first treatment condition and the first parameter.

[0239] According to the method for generating a prediction algorithm described in claim 10, since the first parameter of a predetermined first function is determined based on multiple sets of a first data set including a first processing condition and a first processing result, a first function that predicts a first processing result from a first processing condition can be fitted to each substrate processing device. In addition, since the first processing result is calculated from the first processing condition using the first function, the reliability of the first processing result predicted by the first function is improved compared to estimating the first processing result using an inference model lacking explanatory power, such as a black box.

[0240] (Clause 11) A method for determining processing conditions according to another aspect of the present invention is,

[0241] A method for determining processing conditions executed by an information processing device that manages a substrate processing device,

[0242] The above substrate processing device processes the film by supplying a processing solution to the upper surface of the substrate on which the film is formed, and

[0243] Using a prediction algorithm, the substrate processing device comprises a processing condition determination step for determining a first processing condition for executing the processing of the film, and

[0244] The above prediction algorithm is a first function that produces a first processing result from the above first processing condition using a first parameter, and

[0245] The above first processing result includes the difference in film thickness before and after the processing of the film is performed at each of a plurality of different locations in the diameter direction of the substrate, and

[0246] The above first parameter is obtained by applying a plurality of first data sets to the above first function and performing regression analysis, and

[0247] Each of the plurality of first data sets comprises the first processing result obtained after the substrate processing device performs the processing of the film according to the first processing condition, and the first processing condition.

[0248] The above processing condition determination step includes determining the temporary first processing condition as the first processing condition for driving the substrate processing device when the first processing result calculated from the temporary first processing condition using the above prediction algorithm satisfies the allowable condition.

[0249] According to the method for determining processing conditions described in claim 11, when a first processing condition is applied to a first function and the first processing result produced by the first function satisfies an allowable condition, a temporary first processing condition is determined as a first processing condition for driving a substrate processing device. Accordingly, a plurality of temporary first processing conditions can be determined for a first processing result that satisfies an allowable condition. As a result, it becomes possible to present a plurality of appropriate processing conditions for a substrate processing device in which a complex process is executed.

Claims

Claim 1 A prediction algorithm generating device comprising a first data acquisition unit for acquiring a plurality of first data sets and a first determination unit for determining a first parameter by applying the plurality of first data sets to a predetermined first function and performing regression analysis, wherein each of the plurality of first data sets includes a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and the first processing condition, wherein the first processing result includes the difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and the first function represents the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate using the first processing condition and the first parameter. Claim 2 A prediction algorithm generating device according to claim 1, wherein the first function is a function using a first reference parameter represented by a first sub-function using the first processing condition and the first parameter, and the first determination unit comprises a first reference parameter determining unit that determines the first reference parameter corresponding to the first processing condition by applying the first processing result corresponding to the first processing condition to the first function and performing regression analysis for each of the plurality of the first processing conditions, and a first parameter determining unit that determines the first parameter by applying the first processing condition and the first reference parameter determined corresponding to the first processing condition to the first sub-function and performing regression analysis for each of the plurality of the first processing conditions. Claim 3 In claim 1, the treatment of the film includes a back-side discharge treatment that supplies a treatment solution to the back side of the substrate, and further comprises a second data acquisition unit that acquires a plurality of second data sets, and a second determination unit that determines a second parameter by applying a first influence degree and a second treatment condition corresponding to each of the plurality of second data sets to a predetermined second function and performing regression analysis, wherein each of the plurality of second data sets includes a second treatment result obtained after the substrate processing device performs the treatment of the film including the back-side discharge treatment according to the second treatment condition in which the back-side discharge condition is added to the first treatment condition when the substrate processing device performs the treatment of the film including the back-side discharge treatment, and the second treatment condition, wherein the second treatment result includes the difference in film thickness before and after the treatment of the film including the back-side discharge treatment is performed at each of a plurality of different positions in the diameter direction of the substrate, and the second function is the first function with the A prediction algorithm generating device that represents the first influence degree obtained by subtracting the second processing result from the value calculated by applying the second processing condition, and the second function represents the first influence degree at any position in the diameter direction of the substrate using the second processing condition and the second parameter. Claim 4 In claim 3, the second function is a function using a second reference parameter represented by a second sub-function using the second processing condition and the second parameter, and the second determination unit comprises a second reference parameter determination unit that determines the second reference parameter corresponding to the second processing condition by applying a first influence degree corresponding to the second processing condition to the second function and performing regression analysis for each of the plurality of the second processing conditions, and a second parameter determination unit that determines the second parameter by applying the second reference parameter determined corresponding to the second processing condition to the second sub-function and performing regression analysis for each of the plurality of the second processing conditions. Claim 5 In claim 3, the substrate processing device, when performing the processing of the film including the back-side discharge process, moves the position of the nozzle supplying the processing liquid to the substrate over time, the second processing condition includes a variation condition indicating the relative position of the nozzle with respect to the substrate that varies over time, and further comprises a third determination unit that determines a third parameter by applying a second influence degree corresponding to each of the plurality of variation conditions and the second processing condition to a predetermined third function and performing regression analysis, wherein the third function represents the second influence degree obtained by subtracting the second processing result from the value calculated by applying the second processing condition to the first function and the value calculated by applying the second processing condition to the second function, and the third function represents the second influence degree at any position in the diameter direction of the substrate using the second processing condition and the third parameter. Claim 6 A prediction algorithm generating device according to claim 5, wherein the third function is a function using a third reference parameter represented by a third sub-function using the second processing condition and the third parameter, and the third determination unit comprises a third reference parameter determining unit that determines the third reference parameter based on a feature point of the second influence degree corresponding to the fluctuation condition for each of the plurality of fluctuation conditions, and a third parameter determining unit that determines the third parameter by applying the third reference parameter determined corresponding to the fluctuation condition and the second processing condition corresponding to the fluctuation condition to the third sub-function and performing regression analysis for each of the plurality of fluctuation conditions. Claim 7 A prediction algorithm generating device according to claim 1 or 2, wherein, when performing the processing of the film, the substrate processing device moves the position of a nozzle supplying a processing liquid to the substrate over time, the first processing condition includes a variation condition indicating the relative position of the nozzle with respect to the substrate that varies over time, and further comprises a fourth determination unit that determines a third parameter by applying a third influence degree corresponding to each of the plurality of variation conditions and the first processing condition to a predetermined third function and performing regression analysis, wherein the third function represents the third influence degree obtained by subtracting the first processing result from the value calculated by applying the first processing condition to the first function, and the third function represents the third influence degree at any position in the diameter direction of the substrate using the first processing condition and the third parameter. Claim 8 A prediction algorithm generating device according to claim 7, wherein the third function is a function using a third reference parameter represented by a third sub-function using the first processing condition and the third parameter, and the fourth determination unit comprises a fourth reference parameter determining unit that determines the third reference parameter based on a feature point of the third influence degree corresponding to the fluctuation condition for each of the plurality of fluctuation conditions, and a fourth parameter determining unit that determines the third parameter by applying the third reference parameter determined corresponding to the fluctuation condition and the first processing condition corresponding to the fluctuation condition to the third sub-function and performing regression analysis for each of the plurality of fluctuation conditions. Claim 9 As an information processing device for managing a substrate processing device, the substrate processing device processes a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, and has a processing condition determining unit that determines a first processing condition for the substrate processing device to execute the processing of the film using a prediction algorithm, wherein the prediction algorithm is a first function that calculates the difference in film thickness before and after processing of the film at any position in the diameter direction of the substrate where the substrate processing device executes the processing of the film from the first processing condition using a first parameter, wherein the first parameter is obtained by applying a plurality of first data sets to the first function and performing regression analysis, and each of the plurality of first data sets includes a first processing result obtained after driving the substrate processing device with the first processing condition to perform the processing of the film and the first processing condition, and the first processing result includes the difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and the processing condition determining unit An information processing device that determines the first processing condition as the first processing condition for driving the substrate processing device when the first processing result calculated from the first processing condition using a prediction algorithm satisfies an allowable condition. Claim 10 A method for generating a prediction algorithm, comprising a step of acquiring a plurality of first data sets and a step of determining a first parameter by applying the plurality of first data sets to a first function and performing regression analysis, wherein each of the plurality of first data sets includes a first processing result obtained after a substrate processing device, which performs processing of a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, performs processing of the film according to a first processing condition, and the first processing condition, wherein the first processing result includes the difference in film thickness before and after processing of the film at each of a plurality of different positions in the diameter direction of the substrate, and the first function is predetermined to represent the difference between the film thickness before and after processing of the film at any position in the diameter direction of the substrate using the first processing condition and the first parameter. Claim 11 A method for determining processing conditions executed by an information processing device managing a substrate processing device, wherein the substrate processing device processes a film by supplying a processing liquid to the upper surface of a substrate on which a film is formed, and comprises a processing condition determination step that determines a first processing condition for the substrate processing device to execute the processing of the film using a prediction algorithm, wherein the prediction algorithm is a first function that calculates a first processing result from the first processing condition using a first parameter, and the first processing result includes the difference in film thickness before and after the processing of the film is executed at each of a plurality of different positions in the diameter direction of the substrate, wherein the first parameter is obtained by applying a plurality of first data sets to the first function and performing regression analysis, and each of the plurality of first data sets includes the first processing result obtained after the substrate processing device executes the processing of the film according to the first processing condition and the first processing condition, and wherein the processing condition determination step determines that the first processing result calculated from the temporary first processing condition using the prediction algorithm is an acceptable condition A method for determining a processing condition, comprising determining the above temporary first processing condition as the first processing condition for driving the substrate processing device when satisfied.

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