Information processing device, information processing method, and program

Abstract

To provide a device capable of predicting a process result with high accuracy.SOLUTION: An information processing device is provided, including a model acquisition part for acquiring a mathematical model corresponding to a process result by a substrate processing device, a data acquisition part for acquiring measurement data showing the process result measured by using the substrate processing device, a fitting part for fitting a parameter of the mathematical model on the basis of the measurement data, and a prediction part for predicting the process result on the basis of the mathematical model with the fitted parameter set.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present disclosure relates to an information processing apparatus, an information processing method, and a program.

Background Art

[0002] There is known a technique for optimizing the process conditions of a substrate processing apparatus by predicting the process results of the substrate processing apparatus. For example, Patent Document 1 discloses an information processing apparatus that creates a machine learning model of a semiconductor manufacturing apparatus that executes processing according to process conditions, and searches for process conditions capable of achieving a target process result using the machine learning model.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] The present disclosure provides an apparatus capable of accurately predicting a process result.

Means for Solving the Problems

[0005] According to one aspect of the present disclosure, there is provided an information processing apparatus including: a model acquisition unit that acquires a mathematical model corresponding to a process result of a substrate processing apparatus; a data acquisition unit that acquires measurement data indicating a process result measured using the substrate processing apparatus; a fitting unit that fits parameters of the mathematical model based on the measurement data; and a prediction unit that predicts a process result based on the mathematical model with the fitted parameters set.

Effects of the Invention

[0006] In one aspect, the process result can be accurately predicted.

Brief Description of the Drawings

[0007]

Figure 1

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Figure 13

Modes for Carrying Out the Invention

[0008] Hereinafter, embodiments for carrying out the present disclosure will be described with reference to the drawings. In each drawing, the same reference numerals are given to the same components, and redundant descriptions may be omitted.

[0009] [Embodiment] One embodiment of the present disclosure is a substrate processing system including a substrate processing apparatus that processes a substrate as an example of an object to be processed. In the present embodiment, the substrate processing system includes an optimization apparatus that optimizes process conditions based on a process result by the substrate processing apparatus.

[0010] The substrate processing apparatus executes a predetermined process according to process conditions. The process conditions are optimized so that a good process result can be obtained by the substrate processing apparatus. The optimization of the process conditions is often performed based on the knowledge of an expert who is familiar with the substrate processing apparatus or the process. Further, the optimization of the process conditions may be performed based on machine learning. In the optimization of the process conditions based on machine learning, for example, a process result using a regression method or the like is predicted, and process conditions that can obtain a predicted result satisfying a target are searched for.

[0011] The optimization by an expert depends on the expert's empirical values, and the man-hours required to find process conditions that can obtain a predicted result satisfying a target differ. Further, since the optimization by an expert is highly personal, it is difficult to optimize the process conditions in an environment where there is no optimal expert.

[0012] In the optimization by machine learning, since the accuracy of the regression model strongly depends on the number of experiments, a large number of experiments are required to ensure sufficient accuracy. For example, in linear regression, if the number of experiments is not sufficient, the physical phenomena occurring during the process cannot be accurately reproduced. Further, for example, in non-linear regression, since the prediction accuracy of extrapolation is low, it is necessary to repeat experiments over a wide range. Furthermore, generally, the regression model has low robustness, so it is difficult to use it generally. Note that low robustness means characteristics such as being unable to cope with changes over time of the apparatus or being unable to be applied to different apparatuses.

[0013] The present embodiment predicts a process result using a model suitable for the physical phenomena occurring during the process. Further, the present embodiment fits the parameters of the model based on the data obtained by measuring the process result by the substrate processing apparatus.

[0014] On one hand, according to this embodiment, since the physical phenomena occurring during the process can be accurately reproduced, the process results can be accurately predicted. Also, according to this embodiment, since the model can be generated with a small number of experiments, the process results can be efficiently predicted. Furthermore, according to this embodiment, even an expert who is not familiar with the device or process can optimize the process conditions in a short period of time. As a result, the lead time for process development is significantly shortened.

[0015] <System Configuration> The overall configuration of the substrate processing system in this embodiment will be described with reference to FIG. 1. FIG. 1 is a block diagram showing an example of the overall configuration of the substrate processing system.

[0016] As shown in FIG. 1, the substrate processing system 100 includes substrate processing apparatuses 120a1 to 120a3 and control apparatuses 121a1 to 121a3 in factory a. The substrate processing apparatuses 120a1 to 120a3 and the control apparatuses 121a1 to 121a3 are connected by wire or wirelessly.

[0017] Also, the substrate processing system 100 includes substrate processing apparatuses 120b1, 120b2 and control apparatuses 121b1, 121b2 in factory b. The substrate processing apparatuses 120b1, 120b2 and the control apparatuses 121b1, 121b2 are connected by wire or wirelessly.

[0018] Also, the substrate processing system 100 includes substrate processing apparatuses 120c1, 120c2 and control apparatuses 121c1, 121c2 in factory c. The substrate processing apparatuses 120c1, 120c2 and the control apparatuses 121c1, 121c2 are connected by wire or wirelessly.

[0019] The substrate processing apparatuses 120a1 to 120a3, the substrate processing apparatuses 120b1 and 120b2, and the substrate processing apparatuses 120c1 and 120c2 are connected to the host apparatuses 110a, 110b, and 110c via the networks N1 to N3, respectively. Each substrate processing apparatus executes substrate processing under the control of each control apparatus based on instructions from the host apparatuses 110a, 110b, and 110c. The host apparatuses 110a, 110b, and 110c are connected to the server apparatus 150 via a network N4 such as the Internet.

[0020] In the following description, the substrate processing apparatuses 120a1 to 120a3, 120b1, 120b2, 120c1, and 120c2 are also collectively referred to as the substrate processing apparatus 120. Also, the control apparatuses 121a1 to 121a3, 121b1, 121b2, 121c1, and 121c2 are also collectively referred to as the control apparatus 121. The host apparatuses 110a, 110b, and 110c are also collectively referred to as the host apparatus 110.

[0021] It is assumed that the substrate processing apparatuses 120a1 to 120a3, the substrate processing apparatuses 120b1 and 120b2, and the substrate processing apparatuses 120c1 and 120c2 store a wide variety of data managed by each of them in the apparatus itself.

[0022] By being connected to the substrate processing apparatus 120 including the substrate processing apparatus 120a1, the optimization apparatus 140 continuously acquires the stored data stored in each of the substrate processing apparatuses 120. The example of FIG. 1 shows a state where the optimization apparatus 140 is connected to the substrate processing apparatus 120a1, but it is not limited to this. Hereinafter, in the present embodiment, details of the case where the optimization apparatus 140 is connected to the substrate processing apparatus 120a1 will be described.

[0023] The substrate processing system 100 shown in FIG. 1 is an example, and it goes without saying that there are various system configuration examples depending on the application and purpose. The classification of devices such as the host device 110, the substrate processing device 120, the control device 121, the optimization device 140, and the server device 150 shown in FIG. 1 is an example. For example, the number of factories, the number of host devices 110, the number of substrate processing devices 120, the number of control devices 121, the number of optimization devices 140, etc. are examples and are not limited thereto.

[0024] For example, the substrate processing system 100 can have various configurations, such as a configuration in which at least two of the host device 110, the substrate processing device 120, the control device 121, the optimization device 140, and the server device 150 are integrated, or a further divided configuration. For example, the control device 121 may be configured to control a plurality of substrate processing devices 120 collectively, may be provided one-to-one for the substrate processing devices 120, or may be integrated with the substrate processing devices 120.

[0025] The optimization device 140 may be realized by the host device 110 or may be realized by the server device 150. In this case, the optimization device 140 becomes unnecessary. Also, the optimization device 140 may be realized by the control device 121. The optimization device 140 may be realized by a control device (not shown) that controls a plurality of control devices 121 collectively.

[0026] <Substrate processing device> An example of the substrate processing device in this embodiment will be described with reference to FIG. 2. FIG. 2 is a schematic cross-sectional view showing a vertical heat treatment device which is an example of the substrate processing device.

[0027] The vertical heat treatment device 120 in this embodiment is a substrate processing device that accommodates a large number of semiconductor wafers W, which are an example of the object to be processed, at once and performs heat treatments such as oxidation, diffusion, and reduced-pressure CVD. As shown in FIG. 2, the vertical heat treatment device 120 includes a processing container 10, a gas supply unit 20, an exhaust unit 30, a heating unit 40, a cooling unit 50, a control device 121, and the like.

[0028] The processing container 10 has a substantially cylindrical shape. The processing container 10 includes an inner tube 11, an outer tube 12, a manifold 13, an injector 14, a gas outlet 15, a lid 16, etc. The inner tube 11 has a substantially cylindrical shape. The outer tube 12 has a substantially cylindrical shape with a ceiling, and the inner tube 11 and the outer tube 12 constitute a double-tube structure. The inner tube 11 and the outer tube 12 are formed of a heat-resistant material such as quartz, for example.

[0029] The manifold 13 has a substantially cylindrical shape. The manifold 13 supports the lower ends of the inner tube 11 and the outer tube 12. The manifold 13 is formed of, for example, stainless steel. The injector 14 extends horizontally into the inner tube 11 through the manifold 13 and bends in an L shape and extends upward within the inner tube 11. The base end of the injector 14 is connected to the gas introduction pipe 24, and the tip is open. The injector 14 discharges the processing gas (hereinafter also simply referred to as "gas") introduced through the gas introduction pipe 24 into the inner tube 11 from the opening at the tip. A plurality of injectors 14 may be provided.

[0030] The gas outlet 15 is formed in the manifold 13. The processing gas is exhausted by the exhaust unit 30 through the gas outlet 15. The lid 16 airtightly closes the opening at the lower end of the manifold 13. The lid 16 is formed of, for example, stainless steel. A wafer boat (substrate holder) 18 is placed on the lid 16 via a heat-insulating cylinder 17. The heat-insulating cylinder 17 and the wafer boat 18 are formed of a heat-resistant material such as quartz, for example.

[0031] The wafer boat 18 holds a plurality of semiconductor wafers W substantially horizontally at a predetermined interval in the vertical direction. The wafer boat 18 is carried (loaded) into the processing container 10 by the lifting mechanism 19 raising the lid 16 and is accommodated in the processing container 10. The wafer boat 18 is carried out (unloaded) from the processing container 10 by the lifting mechanism 19 lowering the lid 16.

[0032] The gas supply unit 20 includes a gas source 21, an IGS 22 (Integrated Gas System), an external pipe 23, and a gas introduction pipe 24. The gas source 21 is a supply source of the processing gas, and includes, for example, a film formation gas source, a cleaning gas source, and a purge gas source. The IGS 22 is an integrated circuit of gas pipes, and a group of pipes respectively connected to the film formation gas source, the cleaning gas source, the purge gas source, etc. of the gas source 21 is integrated therein. A flow rate control unit is installed in the IGS 22 to control the flow rate of the gas flowing through each pipe. The flow rate control unit includes, for example, a mass flow controller and an on-off valve.

[0033] The IGS 22 is connected to the external pipe 23. The external pipe 23 is connected to the gas introduction pipe 24. A heater (not shown) is wound around the outer periphery of the external pipe 23 and is configured to heat the external pipe 23. The gas introduction pipe 24 is connected to the processing vessel 10 and introduces gas into the inside of the processing vessel 10. That is, the flow rate of the processing gas from the gas source 21 is controlled by the flow rate control unit in the IGS 22, heated when flowing through the external pipe 23, flowed into the gas introduction pipe 24, and supplied into the processing vessel 10 from the gas introduction pipe 24 via the injector 14. The injector 14 functions as a gas inlet of the processing vessel 10.

[0034] Near the gas inlet of the processing vessel 10, a joint 82 for the gas pipe connected to the gas introduction pipe 24 is provided. The temperature sensor 80 is configured to penetrate the joint 82. The temperature sensor 80 is configured to measure the temperature of the gas in the gas introduction pipe 24. The temperature sensor 80 transmits the measured temperature to the control device 121. Further, a second heater 81 is disposed in the gas introduction pipe 24, and the second heater 81 is configured to heat the gas in the gas introduction pipe 24.

[0035] The exhaust section 30 includes an exhaust device 31, an exhaust pipe 32, and a pressure controller 33. The exhaust device 31 is a vacuum pump such as a dry pump or a turbo molecular pump. The pressure controller 33 is installed in the exhaust pipe 32 and controls the pressure inside the processing container 10 by adjusting the conductance of the exhaust pipe 32. The pressure controller 33 is, for example, an automatic pressure control valve.

[0036] The heating section 40 includes a heat insulating material 41, a first heater 42, and an outer skin 43. The heat insulating material 41 has a substantially cylindrical shape and is provided around the outer pipe 12. The heat insulating material 41 is formed mainly of silica and alumina. The first heater 42 has a linear shape and is provided spirally or meanderingly on the inner circumference of the heat insulating material 41. The first heater 42 is configured to be capable of temperature control by dividing it into a plurality of zones in the height direction of the processing container 10. The outer skin 43 is provided so as to cover the outer circumference of the heat insulating material 41. The outer skin 43 holds the shape of the heat insulating material 41 and reinforces the heat insulating material 41. The outer skin 43 is formed of a metal such as stainless steel. Further, in order to suppress the heat influence to the outside of the heating section 40, a water-cooled jacket (not shown) may be provided on the outer circumference of the outer skin 43. Such a heating section 40 heats the inside of the processing container 10 by the first heater 42 generating heat.

[0037] The cooling section 50 supplies a cooling fluid toward the processing container 10 and cools the semiconductor wafer W inside the processing container 10. The cooling fluid may be, for example, air. The cooling section 50 supplies a cooling fluid toward the processing container 10, for example, when rapidly cooling the semiconductor wafer W after heat treatment. The cooling section 50 has a fluid flow path 51, a blowout hole 52, a distribution flow path 53, a flow rate adjustment section 54, and a heat exhaust port 55.

[0038] A plurality of fluid flow paths 51 are formed in the height direction between the heat insulating material 41 and the outer skin 43. The fluid flow path 51 is, for example, a flow path formed along the circumferential direction outside the heat insulating material 41. The blowout holes 52 are formed to penetrate the heat insulating material 41 from each fluid flow path 51, and blow out the cooling fluid into the space between the outer tube 12 and the heat insulating material 41. The distribution flow path 53 is provided outside the outer skin 43, and distributes and supplies the cooling fluid to each fluid flow path 51. The flow rate adjustment unit 54 is interposed in the distribution flow path 53, and adjusts the flow rate of the cooling fluid supplied to the fluid flow path 51.

[0039] The exhaust heat port 55 is provided above the plurality of blowout holes 52, and discharges the cooling fluid supplied to the space between the outer tube 12 and the heat insulating material 41 to the outside of the processing container 10. The cooling fluid discharged to the outside of the processing container 10 is cooled by, for example, a heat exchanger and supplied again to the distribution flow path 53. However, the cooling fluid discharged to the outside of the processing container 10 may be discharged without being reused.

[0040] The temperature sensor 60 detects the temperature inside the processing container 10. The temperature sensor 60 is provided, for example, inside the inner tube 11. However, the temperature sensor 60 may be provided at a position where it can detect the temperature inside the processing container 10, and may be provided, for example, in the space between the inner tube 11 and the outer tube 12. The temperature sensor 60 has, for example, a plurality of temperature measuring parts provided at different positions in the height direction corresponding to a plurality of zones. The plurality of temperature measuring parts may be, for example, thermocouples or resistance temperature detectors. The temperature sensor 60 transmits the temperatures detected by the plurality of temperature measuring parts to the control device 121.

[0041] The control device 121 controls the operation of the vertical heat treatment apparatus 120 to control the semiconductor process executed in the vertical heat treatment apparatus 120. The control device 121 may be, for example, a computer.

[0042] <Computer> The host device 110, control device 121, optimization device 140, and server device 150 included in the substrate processing system 100 shown in FIG. 1 are realized by a computer having a hardware configuration as shown in FIG. 3, for example. FIG. 3 is a block diagram showing an example of the hardware configuration of a computer.

[0043] As shown in FIG. 3, the computer 500 includes an input device 501, an output device 502, an external I / F (interface) 503, a RAM (Random Access Memory) 504, a ROM (Read Only Memory) 505, a CPU (Central Processing Unit) 506, a communication I / F 507, and an HDD (Hard Disk Drive) 508, etc., and each is interconnected by a bus B. Note that the input device 501 and the output device 502 may be connected and used when necessary.

[0044] The input device 501 is a keyboard, mouse, touch panel, etc., and is used for an operator or the like to input each operation signal. The output device 502 is a display or the like, and displays the processing result by the computer 500. The communication I / F 507 is an interface for connecting the computer 500 to a network. The HDD 508 is an example of a non-volatile storage device that stores programs and data.

[0045] The external I / F 503 is an interface with an external device. The computer 500 can read and / or write a recording medium 503a such as an SD (Secure Digital) memory card via the external I / F 503. The ROM 505 is an example of a non-volatile semiconductor memory (storage device) in which programs and data are stored. The RAM 504 is an example of a volatile semiconductor memory (storage device) that temporarily holds programs and data.

[0046] The CPU 506 is an arithmetic unit that realizes the control and functions of the entire computer 500 by reading programs and data from storage devices such as the ROM 505 and the HDD 508 onto the RAM 504 and executing processing.

[0047] <Functional configuration> The functional configuration of the optimization device in this embodiment will be described with reference to FIG. 4. FIG. 4 is a block diagram showing an example of the functional configuration of the optimization device.

[0048] As shown in FIG. 4, the optimization device 140 includes a model input unit 201, a model storage unit 202, an instruction input unit 203, a model acquisition unit 204, an experimental design unit 205, a data acquisition unit 206, a fitting unit 207, a prediction unit 208, and an optimization unit 209.

[0049] The model input unit 201, the instruction input unit 203, the model acquisition unit 204, the experimental design unit 205, the data acquisition unit 206, the fitting unit 207, the prediction unit 208, and the optimization unit 209 are realized, for example, by the CPU 506 shown in FIG. 3 executing a program loaded on the RAM 504.

[0050] The model storage unit 202 is realized, for example, by the RAM 504 or the HDD 508 shown in FIG. 3.

[0051] The model input unit 201 receives the input of model equations. The model input unit 201 may receive the input of a plurality of model equations. The model input unit 201 stores the received one or more model equations in the model storage unit 202.

[0052] The model equation may be a mathematical model representing a physical phenomenon. The physical phenomenon may include a physical phenomenon related to the process executed by the substrate processing apparatus 120. The physical phenomenon related to the process is a physical phenomenon that can occur during the execution of the process. It can also be said that the physical phenomenon related to the process is a physical phenomenon that affects the process result. The physical phenomenon may include, for example, chemical reactions, gas-phase reactions, or surface reactions that occur in the processing chamber 10 of the substrate processing apparatus 120.

[0053] As an example, the model formula may be a mathematical model related to the reaction rate of chemical vapor deposition (CVD) that follows the Arrhenius equation. Equation (1) is an example of a mathematical model related to the reaction rate.

[0054]

Number

[0055] However, DR is the reaction rate, Q is the supply gas flow rate, T is the reaction surface temperature, P is the pressure inside the processing vessel, and α, β, n, γ are adjustable parameters.

[0056] Also, as an example, the model formula may be a mathematical model related to resistivity. Equation (2) is an example of a mathematical model related to resistivity.

[0057]

Number

[0058] However, ρ0 is the electrical resistivity in the solid (bulk), α is a coefficient, N is the impurity concentration in the crystal, β is the reflectivity of electrons at the interface, and d is the film thickness. Note that if the reflectivity β is zero, it is total reflection, and if it exceeds zero, it indicates that diffuse reflection occurs.

[0059] The model formulas shown in Equation (1) and Equation (2) are just examples and are not limited to these. The model formula may be any mathematical model that represents the physical phenomena related to the process results by the substrate processing apparatus 120.

[0060] A model group including a plurality of model formulas is stored in the model storage unit 202. The model group stored in the model storage unit 202 includes the model formula received by the model input unit 201.

[0061] The instruction input unit 203 receives an input of instruction information indicating an optimization target. The instruction information may include information indicating the substrate processing apparatus 120, information indicating the process, and information indicating the objective variable. The instruction information may include information indicating a plurality of objective variables. Each piece of information included in the instruction information may be specified by the user.

[0062] The objective variable may be a physical quantity indicating the process result by the substrate processing apparatus 120. The physical quantity indicating the process result may be a physical quantity measurable by the substrate processing apparatus 120 during the execution of the process. The physical quantity indicating the process result may be a physical quantity measurable from the processed object. As an example, the physical quantity indicating the process result includes film formation amount (film formation rate, in-plane uniformity, etc.), electrical characteristics (resistivity, dielectric constant, breakdown field, residual polarization, etc.), etching rate (WER, DER, etc.), optical constants (refractive index, attenuation rate, etc.), coverage, and film composition, etc.

[0063] Based on the instruction information input to the instruction input unit 203, the model acquisition unit 204 acquires a model formula from the model storage unit 202. Specifically, the model acquisition unit 204 reads out from the model storage unit 202 the model formula corresponding to the objective variable indicated in the instruction information. When a plurality of objective variables are indicated in the instruction information, the model acquisition unit 204 acquires model formulas corresponding to each of the plurality of objective variables.

[0064] Based on the model formula acquired by the model acquisition unit 204, the experimental design unit 205 generates an experimental design. As an example, the experimental design unit 205 may generate an experimental design based on an experimental design method. Specifically, the experimental design unit 205 may generate a plurality of values at a predetermined number of levels for each factor, with each variable included in each model formula as a factor, and generate an experimental design by combining those values.

[0065] The experimental design unit 205 may select variables to be the subject of experimental design based on the contribution rate to the process result. The variables to be the subject of experimental design may be selected according to the user's specification. For example, for variables with a low contribution rate to the process result (in other words, variables that have a small impact on the process result), the experimental design unit 205 may set them as fixed values. By setting some variables as fixed values, the number of experimental conditions to be included in the experimental design can be reduced.

[0066] Regarding the experimental design in this embodiment, it will be described with reference to FIGS. 5 to 8. FIGS. 5 and 6 are diagrams showing an example of experimental design according to the prior art. FIGS. 7 and 8 are diagrams showing an example of experimental design according to this embodiment.

[0067] Here, as an example, consider generating an experimental design based on the model formula of formula (3). Formula (3) is an example of a mathematical model regarding the reaction rate of chemical vapor deposition.

[0068]

Number

[0069] However, k is the reaction rate coefficient, Q1 is the reaction gas inflow rate, Q2 is the gas inflow rate that does not contribute to the reaction, P is the pressure inside the processing container, T is the reaction surface temperature, and α, n, β are adjustable parameters.

[0070] Note that the variable k in formula (3) is the reaction rate coefficient, and the film thickness can be calculated by formula (4).

[0071]

Number

[0072] However, thickness is the film thickness, t is the reaction time, and C is the influence of the incubation time.

[0073] Since the four factors Q1, Q2, P, and T in Equation (3) have strong non-linearity, each factor shall take on values at three levels. In the prior art, in order to learn a regression model including interactions and the like, all combinations of three levels and four factors are required. FIG. 5 shows a state where all combinations of the values of the factors Q1, Q2, P, and T are used as experimental conditions. FIG. 6 shows combinations of the values of the factors Q1, Q2, P, and T that are experimental conditions in the prior art. In FIG. 5, the cube represents the design space, and the black dots represent the experimental conditions included in the experimental design. As shown in FIGS. 5 and 6, the number of experimental conditions required in the prior art is 3 to the power of 4 (= 81).

[0074] On the other hand, in the present embodiment, in addition to the central conditions, it is sufficient to assign values to Q1 at two levels, Q2 at two levels, P at two levels, and T at two levels. FIG. 7 shows the experimental conditions included in the experimental conditions in the present embodiment. FIG. 8 shows combinations of the values of the factors Q1, Q2, P, and T that are experimental conditions in the present embodiment. In FIG. 7, as in FIG. 5, the cube represents the design space, and the black dots represent the experimental conditions included in the experimental design. As shown in FIGS. 7 and 8, the number of experimental conditions required in the present embodiment is 2m + 1 (= 9), where m is the number of factors (= 4). Comparing FIGS. 5 and 6 or FIGS. 7 and 8, it can be seen that the experimental conditions in the present embodiment are significantly reduced compared to the prior art.

[0075] The data acquisition unit 206 acquires measurement data indicating the process result by the substrate processing apparatus 120. The measurement data is data measured using the substrate processing apparatus 120 according to the experimental plan generated by the experimental planning unit 205. The data acquisition unit 206 may acquire the measurement data input by the user. The data acquisition unit 206 may also acquire the measurement data from the log information stored in the substrate processing apparatus 120.

[0076] The measurement data may be measured by an experiment using the substrate processing apparatus 120. The measurement data may also be data measured by various sensors mounted on the substrate processing apparatus 120. The measurement data may also be data obtained by measuring the processed object processed by the substrate processing apparatus 120 with various measuring instruments.

[0077] Based on the measurement data acquired by the data acquisition unit 206, the fitting unit 207 fits the parameters of the model formula acquired by the model acquisition unit 204. When a plurality of model formulas are acquired by the model acquisition unit 204, the fitting unit 207 fits the parameters for each of the plurality of model formulas.

[0078] The fitting unit 207 may fit each parameter included in the model formula individually. The fitting unit 207 may also fit a plurality of parameters together. For example, in the model formula shown in Equation (3), T can be fitted individually. Also, for (Q1 / Q1 + Q2*P), it can be fitted together by separating the adjustment knobs. Furthermore, since α is merely a coefficient, it may be ignored when targeting correlation and can be adjusted independently.

[0079] Based on the model formula with the fitted parameters by the fitting unit 207, the prediction unit 208 predicts the objective variable indicated in the instruction information. The prediction unit 208 acquires a plurality of process conditions to be predicted, and for each of the plurality of process conditions, predicts the objective variable based on the model formula. The prediction unit 208 may acquire the process conditions specified by the user as the prediction target. The prediction unit 208 may also randomly generate the process conditions to be predicted.

[0080] Based on the predicted value of the objective variable by the prediction unit 208, the optimization unit 209 optimizes the process conditions of the process indicated in the instruction information. As an example, the optimization unit 209 may optimize the process conditions based on an optimization method such as the Newton method or an evolutionary algorithm. These optimization methods are just examples, and any optimization method may be used.

[0081] Specifically, the optimization unit 209 identifies the process conditions under which a predicted value that satisfies a predetermined target condition is obtained among the predicted values of the target variable. As an example, the predetermined target condition may be that the best process result is obtained, or the process result may be improved compared to the existing process conditions. When a plurality of target variables are indicated in the instruction information, the best process result may be determined based on any criterion, or may be determined in consideration of the balance of the predicted values of the respective target variables.

[0082] The optimization unit 209 presents the optimization result to the user. The optimization result may include a predicted value that satisfies a predetermined target condition and the process conditions corresponding to the predicted value. The optimization result may include all the predicted values predicted by the prediction unit 208 and all the process conditions corresponding to those predicted values.

[0083] <Processing procedure> The optimization method executed by the substrate processing system 100 in the present embodiment will be described with reference to FIGS. 9 and 10. The optimization method in the present embodiment includes a modeling process (see FIG. 9) and an optimization process (see FIG. 10).

[0084] ≪Modeling process≫ FIG. 9 is a flowchart showing an example of the modeling process. The modeling process is a process of creating model equations included in a model group.

[0085] In step S1, the user of the substrate processing system 100 acquires device information regarding the substrate processing apparatus 120. For example, the user may acquire the device information by investigating the setting information or log information of the substrate processing apparatus 120.

[0086] The device information includes information regarding the substrate processing apparatus 120 and information regarding the process executed by the substrate processing apparatus 120. As an example, the information regarding the substrate processing apparatus 120 may include the type, model, and device configuration of the substrate processing apparatus 120. As an example, the information regarding the process may include the type of process and process conditions.

[0087] In step S2, the user creates a model formula based on the device information obtained in step S1. The user may create a plurality of model formulas. For example, the user may identify one or more physical phenomena that affect the process result based on the relationship between the device configuration and the process of the substrate processing apparatus 120, and create a model formula representing each of the identified physical phenomena. In creating the model formula, for example, known physical laws may be used. Also, in creating the model formula, for example, preconditions regarding the substrate processing apparatus or the process may be assumed.

[0088] As an example, the model formula regarding the reaction rate of chemical vapor deposition shown in formula (3) will be described. Generally, in the substrate processing apparatus 120, the volume of the processing chamber 10 is fixed. It can be assumed that the supply gas is supplied at a constant flow rate. On the other hand, the pressure and temperature inside the processing chamber 10 are adjustable. Also, the type or amount of the dilution gas is adjustable. At this time, when the film formation rate is the target variable, the user can create a model formula (3) regarding the reaction rate according to the Arrhenius equation.

[0089] In step S3, the user checks the accuracy of the model formula created in step S2. Specifically, the user calculates the error between the measured value of the process result measured by the substrate processing apparatus 120 and the predicted value of the process result predicted based on the model formula for various process conditions. If the error between the measured value and the predicted value is within the threshold, the user may determine that the accuracy of the model formula is sufficient. On the other hand, if the error between the measured value and the predicted value exceeds the threshold, the user may determine that the accuracy of the model formula is insufficient.

[0090] If the accuracy of the model formula is sufficient (YES), the user proceeds to step S4. On the other hand, if the accuracy of the model formula is insufficient (NO), the user returns the process to step S2. After returning the process to step S2, the user reconsiders the model formula. For example, the user may review the assumed preconditions, adjust the fixed parameters, or change the underlying physical laws.

[0091] In step S4, the user inputs the model formula created in step S2 into the optimization device 140. In the optimization device 140, the model input unit 201 receives the input of the model formula. The model input unit 201 stores the received model formula in the model storage unit 202.

[0092] ≪Optimization Process≫ FIG. 6 is a flowchart showing an example of the optimization process. The optimization process is a process of optimizing process conditions based on the model formula created in the modeling process.

[0093] In step S11, the instruction input unit 203 of the optimization device 140 receives the input of instruction information indicating the optimization target. The instruction input unit 203 sends the input instruction information to the model acquisition unit 204.

[0094] The instruction input unit 203 may receive the input of instruction information according to the user's operation on the optimization support tool. The optimization support tool is an example of a tool provided to the user of the substrate processing system 100 in order to optimize process conditions. The optimization support tool may be executed in the optimization device 140. The optimization support tool may be executed in another information processing device that can communicate with the optimization device 140 via a communication network.

[0095] In step S12, the model acquisition unit 204 of the optimization device 140 receives the instruction information from the instruction input unit 203. Next, the model acquisition unit 204 reads out the model formula corresponding to the objective variable indicated in the received instruction information from the model storage unit 202. Then, the model acquisition unit 204 sends the read model formula to the experimental design unit 205 and the fitting unit 207.

[0096] In step S13, the experimental design unit 205 of the optimization device 140 receives a model formula from the model acquisition unit 204. Next, the experimental design unit 205 generates an experimental design based on the received model formula. Then, the experimental design unit 205 presents the generated experimental design to the user. For example, the experimental design unit 205 displays the experimental design on the optimization support tool.

[0097] In step S14, the user conducts an experiment using the substrate processing apparatus 120 according to the presented experimental design. As a result, measurement data indicating the process result by the substrate processing apparatus 120 is generated.

[0098] In step S15, the data acquisition unit 206 of the optimization device 140 acquires the measurement data generated in step S14. Next, the data acquisition unit 206 sends the acquired measurement data to the fitting unit 207.

[0099] In step S16, the fitting unit 207 of the optimization device 140 receives a model formula from the model acquisition unit 204. Also, the fitting unit 207 receives measurement data from the data acquisition unit 206. Next, the fitting unit 207 fits the parameters of the model formula based on the measurement data. Subsequently, the fitting unit 207 sets the fitted parameters in the model formula. Then, the fitting unit 207 sends the model formula with the fitted parameters set to the prediction unit 208.

[0100] The fitting unit 207 may store the model formula with the fitted parameters set in the model storage unit 202. The fitting unit 207 may store only the fitted parameters in the model storage unit 202 in association with the model formula. By storing the fitted parameters, steps S13 to S16 can be omitted when instruction information indicating the same optimization target is input.

[0101] In step S17, the prediction unit 208 of the optimization device 140 receives the model formula with the fitted parameters set from the fitting unit 207. Next, the prediction unit 208 acquires a plurality of process conditions to be predicted. Subsequently, for each of the plurality of process conditions, the prediction unit 208 predicts the objective variable based on the acquired model formula. Then, the prediction unit 208 sends the predicted value of the objective variable to the optimization unit 209.

[0102] In step S18, the optimization unit 209 of the optimization device 140 receives the predicted value of the objective variable from the prediction unit 208. Next, the optimization unit 209 optimizes the process conditions based on the received predicted value of the objective variable. For example, the optimization unit 209 identifies the predicted values that satisfy a predetermined target condition among the predicted values of the objective variable.

[0103] Subsequently, the optimization unit 209 presents the optimization result to the user. For example, the optimization unit 209 displays the optimization result on the optimization support tool.

[0104] The user can refer to the presented optimization result and use it for process development. Also, the user may set the process conditions shown in the presented optimization result in the substrate processing apparatus 120 and cause the substrate processing apparatus 120 to execute a process according to the process conditions. The substrate processing apparatus 120 executes a process on the substrate according to the optimized process conditions. Therefore, the user can obtain a good process result.

[0105] <User Interface> The user interface of the substrate processing system 100 in the present embodiment will be described with reference to FIG. 11. FIG. 11 is a diagram showing an example of an optimization support tool.

[0106] As shown in FIG. 11, the optimization support tool 600 has a model selection area 610, an experimental design area 620, a fitting result area 630, and an optimization result area 640.

[0107] The model selection area 610 has a device selection column 611, a process selection column 612, target value selection columns 613, 614, and a confirmation button 615. In FIG. 11, two target value selection columns 613, 614 are shown, but the number of target value selection columns can be arbitrarily set and may be increased or decreased by the user's operation.

[0108] In the device selection column 611, options for the substrate processing apparatus 120 that can be the optimization target are displayed. In the process selection column 612, options for the processes executed by the substrate processing apparatus 120 selected in the device selection column 611 are displayed. In the target value selection columns 613, 614, options for the target variables related to the process selected in the process selection column 612 are displayed.

[0109] When the user selects the device selection column 611, the process selection column 612, and the target value selection columns 613, 614 and then presses the confirmation button 615, instruction information including the information selected in each selection column is input to the optimization apparatus 140.

[0110] The experimental design area 620 displays the experimental design 621 generated by the optimization apparatus 140. The user can perform experiments with the substrate processing apparatus 120 according to the experimental design 621 displayed in the experimental design area 620.

[0111] The fitting result area 630 has a model formula display column 631, a result input button 632, and a parameter display column 633.

[0112] The model formula display column 631 displays the model formula obtained by the optimization apparatus 140. The model formula displayed in the model formula display column 631 is the model formula corresponding to the target variables selected in the target value selection columns 613, 614.

[0113] When the user presses the result input button 632, a screen for inputting the measurement data obtained in the experiment is launched. The screen for inputting the measurement data may be an input screen having input fields for inputting the measured values of each target variable for each experimental condition, or may be a selection screen having a selection field for selecting the electronic data in which the measurement data is recorded. When the user inputs the measurement data on the launched screen, the measurement data is input to the optimization device 140.

[0114] The parameter display column 633 displays the parameters of the model formula fitted by the optimization device 140. The user may verify the validity of the parameters displayed in the parameter display column 633.

[0115] The optimization result area 640 has a prediction result display column 641 and a process condition display column 642.

[0116] The prediction result display column 641 displays the predicted values included in the optimization result by the optimization device 140. The prediction result display column 641 may display the predicted values for all the process conditions to be predicted. The prediction result display column 641 may highlight the predicted values that satisfy a predetermined target condition. The prediction result display column 641 shown in FIG. 11 displays the process conditions with the best predicted values as white circles and the predicted values for the other process conditions as black circles.

[0117] The process condition display column 642 displays the process conditions included in the optimization result by the optimization device 140. The process condition display column 642 may display the process conditions for which predicted values satisfying a predetermined target condition are obtained. The process condition display column 642 may display the process conditions corresponding to the predicted values selected by the user in the prediction result display column 641.

[0118] <Prediction accuracy> The prediction accuracy by the optimization device 140 in the present embodiment will be described with reference to FIGS. 12 and 13. FIG. 12 is a diagram showing an example of the prediction accuracy according to the prior art. FIG. 13 is a diagram showing an example of the prediction accuracy according to the embodiment.

[0119] FIG. 12 is a graph showing the prediction accuracy of the reaction rate by polynomial multiple regression. The polynomial multiple regression is performed by Lasso regression. In the graph shown in FIG. 12, the horizontal axis represents the measured value (Actual), the vertical axis represents the predicted value (Estimation), and each process condition is plotted. The white circle plots in the graph indicate the process conditions with strong interaction.

[0120] As shown in FIG. 12, the prediction accuracy of the reaction rate by polynomial multiple regression has a coefficient of determination R 2 of 0.7669. It can be seen that in the process conditions with strong interaction, the points deviate from the approximate curve, indicating that the prediction accuracy is not high.

[0121] FIG. 13 is a graph showing the prediction accuracy of the reaction rate by the model formula shown in Equation (1). As shown in FIG. 13, the prediction accuracy of the reaction rate by the model formula has a coefficient of determination R 2 of 0.973, which is higher than the prediction accuracy by polynomial multiple regression. It can be seen that even in the process conditions with strong interaction, the points are near the approximate curve, indicating that the prediction accuracy is high.

[0122] From FIGS. 12 and 13, it is shown that by using the model formula according to this embodiment, the prediction accuracy of the process result is improved compared to the conventional method.

[0123] <Effects of the Embodiment> The optimization device 140 in this embodiment fits the parameters of the mathematical model corresponding to the process result by the substrate processing device 120 based on the measurement data indicating the process result measured using the substrate processing device 120, and predicts the process result based on the mathematical model with the fitted parameters set. By fitting the mathematical model corresponding to the process result, a high-precision model can be created. According to this embodiment, the process result can be predicted accurately.

[0124] The mathematical model may include a model formula that represents physical phenomena related to the processes executed by the substrate processing apparatus 120. According to this embodiment, a model with guaranteed validity and high robustness of the model formula can be generated. Further, according to this embodiment, when there are parameters specific to the substrate processing apparatus 120, physical meaningful parameters can be obtained by fitting the parameters of the model formula so as to comply with physical laws.

[0125] The optimization apparatus 140 may generate an experimental plan based on the mathematical model and acquire measurement data obtained by measuring process results according to the experimental plan. The optimization apparatus 140 may generate an experimental plan based on the contribution rate of each variable of the mathematical model. According to this embodiment, since the model can be created with a small number of experiments, the process results can be efficiently predicted.

[0126] The optimization apparatus 140 may output the process conditions of the substrate processing apparatus 120 based on the predicted values of the process results. The optimization apparatus 140 may output the process conditions for which predicted values satisfying predetermined target conditions are obtained. According to this embodiment, the process conditions can be optimized efficiently and with high precision. Further, according to this embodiment, the process conditions can be easily optimized even by a non-expert.

[0127] Furthermore, the mathematical model may be a model formula that can be solved algebraically. Although it takes an enormous amount of time to numerically analyze the search for process conditions, the use of a model formula that can be solved algebraically can increase the calculation speed of parameter fitting or process prediction.

[0128] Also, when the mathematical model includes a differential equation with no solution, a machine learning model such as a neural network may be utilized. Therefore, according to this embodiment, the model formula has high versatility and can also handle physical phenomena that can only be solved numerically.

[0129] According to this embodiment, the number of experiments performed to optimize the process conditions for each substrate processing apparatus can be significantly reduced. For example, when using a model formula with fitted parameters, the number of experiments required for optimizing the process conditions is 2m + 1, where m is the number of adjustable parameters. Also, when using a model formula that requires parameter fitting, the number of experiments required for optimizing the process conditions is 3m + 1. Note that when constructing a regression model from scratch, the number of experiments required for optimizing the process conditions is 3 to the power of m. Therefore, according to this embodiment, the larger the number of adjustable parameters, the fewer the number of experiments required for optimizing the process conditions.

[0130] [Supplementary Explanation] The information processing apparatus and the substrate processing apparatus according to the embodiment disclosed this time are illustrative in all respects and not restrictive. The embodiment can be modified and improved in various forms without departing from the scope and gist of the appended claims. Matters described in the above plurality of embodiments can also adopt other configurations and can be combined within a non - conflicting range.

[0131] The substrate processing apparatus that executes the process including the substrate processing method of the present disclosure is not limited to a heat treatment apparatus. The substrate processing apparatus can be applied to any type of apparatus such as an Atomic Layer Deposition (ALD) apparatus, a Capacitively Coupled Plasma (CCP), an Inductively Coupled Plasma (ICP), a Radial Line Slot Antenna (RLSA), an Electron Cyclotron Resonance Plasma (ECR), and a Helicon Wave Plasma (HWP).

[0132] In addition, the substrate processing apparatus of the present disclosure can be applied to any apparatus that uses plasma or does not use plasma, as long as it is an apparatus for performing a predetermined process (for example, film formation process, etching process, etc.) on a substrate. Further, the substrate processing apparatus of the present disclosure can be applied to any of a single wafer apparatus that processes substrates one by one, a batch apparatus that processes a plurality of substrates collectively, and a semi-batch apparatus that processes a plurality of substrates fewer than the number of substrates processed collectively by the batch apparatus.

Explanation of Reference Numerals

[0133] 100: Substrate processing system 110: Host device 120: Substrate processing apparatus 121: Control device 140: Optimization device 150: Server device 201: Model input unit 202: Model storage unit 203: Instruction input unit 204: Model acquisition unit 205: Experimental design unit 206: Data acquisition unit 207: Fitting unit 208: Prediction unit 209: Optimization unit

Claims

1. A model acquisition unit configured to acquire a mathematical model corresponding to a process result by a substrate processing apparatus; A data acquisition unit configured to acquire measurement data indicating the process result measured using the substrate processing apparatus; A fitting unit configured to fit parameters of the mathematical model based on the measurement data; A prediction unit configured to predict the process result based on the mathematical model with the fitted parameters set; An information processing apparatus comprising the above.

2. The information processing apparatus according to Claim 1, wherein the mathematical model includes a model formula representing a physical phenomenon related to a process executed by the substrate processing apparatus. An information processing apparatus.

3. The information processing apparatus according to Claim 1, further comprising an experimental design unit configured to generate an experimental design based on the mathematical model, wherein the data acquisition unit is configured to acquire the measurement data obtained by measuring the process result according to the experimental design. An information processing apparatus.

4. The information processing apparatus according to Claim 3, wherein the experimental design unit is configured to select the process result for generating the experimental design based on the contribution rate of each variable of the mathematical model. An information processing apparatus.

5. The information processing apparatus according to any one of Claims 1 to 4, further comprising an optimization unit configured to output process conditions of the substrate processing apparatus based on a predicted value of the process result. An information processing apparatus.

6. The information processing apparatus according to Claim 5, wherein the optimization unit is configured to output the process conditions for which the predicted value satisfying a predetermined target condition is obtained. An information processing apparatus.

7. An information processing method in which an information processing apparatus executes: a procedure for acquiring a mathematical model corresponding to a process result by a substrate processing apparatus; a procedure for acquiring measurement data indicating the process result measured using the substrate processing apparatus; a procedure for fitting parameters of the mathematical model based on the measurement data; a procedure for predicting the process result based on the mathematical model with the fitted parameters set. An information processing method.

8. In an information processing apparatus: a procedure for acquiring a mathematical model corresponding to a process result by a substrate processing apparatus; A procedure for acquiring measurement data indicating the process results measured using the substrate processing apparatus; A procedure for fitting the parameters of the mathematical model based on the measurement data; A procedure for predicting the process results based on the mathematical model with the fitted parameters set; A program for causing the above to be executed.

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