Prediction method, prediction device, learning device, learning method, and program

Abstract

Provided is a prediction method for predicting properties of a precursor capable of forming a polymer that is polyimide and / or polybenzoxazole, the prediction method comprising: a step for predicting the i-line transmittance Tx of a precursor x of interest; a step for predicting the dissolution rate Sx of the precursor x of interest; and a step for predicting properties of the precursor x of interest on the basis of the i-line transmittance Tx and the dissolution rate Sx.

Description

Prediction method, prediction device, learning device, learning method, and program

[0001] This disclosure relates to a prediction method, a prediction device, a learning device, a learning method, and a program.

[0002] Resins that form heterocyclic rings containing nitrogen atoms, such as polybenzoxazoles and polyimides, have excellent heat resistance and insulating properties, and are therefore used in various applications such as interlayer insulating films, encapsulants, and protective films for semiconductor devices. In these applications, photosensitive resin compositions containing resin precursors are used. For example, after being applied to a substrate by coating, exposure, development, heating, etc., can be performed as needed to cause a ring-closing reaction of the precursor and form a cured resin on the substrate.

[0003] In recent years, with the increasing functionality and miniaturization of semiconductor devices, there has been a demand for cured films with finer patterns on interlayer insulating films and the like, and for photosensitive resin compositions that exhibit good contrast performance.

[0004] To date, a photosensitive resin composition has been reported that includes (A) a specific polyimide precursor containing a phenylenediamine derivative or bisphenylenediamine derivative unit having a fluoroalcohol group, and (B) a photosensitive agent, with the aim of providing a photosensitive resin composition that contains a polyimide precursor having high solvent solubility and has a high exposure dissolution rate and dissolution contrast (for example, Patent Document 1).

[0005] Japanese Patent Publication No. 2021-060461

[0006] However, while the prior art described in Patent Document 1 exhibits excellent dissolution rate of the precursor in alkaline developer, it does not evaluate i-line transmittance. Therefore, there is room to develop a photosensitive precursor that can achieve both excellent i-line transmittance and dissolution rate.

[0007] The present disclosure aims to provide a prediction method that can predict a precursor that can achieve an excellent balance between i-line transmittance and dissolution rate.

[0008] Means for solving the above problems are as follows. That is, <1> A prediction method for predicting the characteristics of a precursor capable of forming a polymer that is polyimide and / or polybenzoxazole, wherein the calculated value A of the absorption intensity at 365 nm of the plurality of polymers is obtained by quantum chemical calculation based on the structural units of the plurality of polymers 1...n １ ...A ｎ A step of calculating; the calculated value A of the absorption intensity at 365 nm of the plurality of polymers １ ...A ｎ And a step of obtaining a first regression equation based on the measured values T of the i-line transmittance of the plurality of precursors １ ...T ｎ When the coefficient of determination R2 in the first regression equation is greater than 0.4, based on the first regression equation and the calculated value A of the absorption intensity at 365 nm of the precursor x to be predicted ｘ And a step of predicting the i-line transmittance T of the precursor x ｘ By molecular dynamics calculation based on the structures of the plurality of precursors 1...n, the calculated value E of the solvation energy of the plurality of precursors １ ...E ｎ A step of calculating; the calculated value E of the solvation energy of the plurality of precursors １ ...E ｎ And a step of obtaining a second regression equation based on the measured values S of the dissolution rates of the plurality of precursors １ ...S ｎ When the coefficient of determination R2 in the second regression equation is greater than 0.4, based on the second regression equation and the calculated value E of the solvation energy of the precursor x to be predicted ｘ And a step of predicting the dissolution rate S of the precursor x ｘ Based on the i-line transmittance T ｘ And the dissolution rate S ｘ And a step of predicting the characteristics of the precursor x to be predicted, characterized by having. <2> In the step of predicting the characteristics of the precursor x to be predicted based on the i-line transmittance T ｘ And the dissolution rate S ｘ When the i-line transmittance T ｘ Is 80% or more, and the dissolution rate S ｘA prediction method according to <1>, wherein the properties of the precursor x to be predicted are excellent when the speed is 320 nm / s or higher. <3> A prediction device comprising: an intermediate prediction unit configured to predict the intermediate parameters based on a first machine learning model whose objective variable is an intermediate parameter that functions on the properties of a polymer and a precursor; and a property prediction unit configured to predict the properties by inputting the predicted values ​​of the intermediate parameters into a second machine learning model which includes the intermediate parameters as explanatory variables and the properties as the objective variable, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor. <4> A prediction device according to <3>, wherein the intermediate parameters further include the physical properties of the polymer and the precursor, the manufacturing conditions of the polymer and the precursor, or the usage conditions of the polymer and the precursor. <5> A prediction device according to <3> or <4>, wherein the intermediate parameters are selected based on a mechanism diagram relating to the properties. <6> A prediction device according to any one of <3> to <5>, wherein the intermediate parameters are selected based on the results of statistical analysis of a dataset including a plurality of parameters and the properties. <7> The prediction device according to any one of <3> to <6>, wherein the intermediate parameters are selected based on the result of querying a trained language model for the intermediate parameters. <8> A learning device comprising: a selection unit configured to select intermediate parameters that function for the properties of a polymer and a precursor; an intermediate learning unit configured to generate a first machine learning model with the intermediate parameters as the objective variable; and a property learning unit configured to generate a second machine learning model with the intermediate parameters as explanatory variables and the properties as the objective variable, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.<9> A prediction method characterized in that a computer performs the steps of: predicting intermediate parameters based on a first machine learning model in which intermediate parameters that function for the properties of a polymer and a precursor are objective variables; and predicting the properties by inputting the predicted values ​​of the intermediate parameters into a second machine learning model in which the intermediate parameters are explanatory variables and the properties are objective variables, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor. <10> A learning method characterized in that a computer performs the steps of: selecting intermediate parameters that function for the properties of a polymer and a precursor; generating a first machine learning model in which the intermediate parameters are objective variables; and generating a second machine learning model in which the intermediate parameters are explanatory variables and the properties are objective variables, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor. <11> A program for causing a computer to perform the following steps: predict intermediate parameters based on a first machine learning model in which intermediate parameters function for the properties of a polymer and a precursor are the target variables; and predict the properties by inputting the predicted values ​​of the intermediate parameters into a second machine learning model in which the intermediate parameters are the explanatory variables and the properties are the target variables, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor. <12> A program for causing a computer to perform the following steps: select intermediate parameters that function for the properties of a polymer and a precursor; generate a first machine learning model in which the intermediate parameters are the target variables; and generate a second machine learning model in which the intermediate parameters are the explanatory variables and the properties are the target variables, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

[0009] According to this disclosure, a prediction method can be provided that can predict a precursor that can achieve an excellent balance between i-line transmittance and dissolution rate.

[0010] Figure 1 is a flowchart showing an example of the prediction method of this embodiment. Figure 2 is a flowchart showing another example of the prediction method of this embodiment. Figure 3 is a block diagram showing an example of the overall configuration of the prediction system of this embodiment. Figure 4 is a block diagram showing an example of a computer. Figure 5 is a block diagram showing an example of the functional configuration of the prediction system. Figure 6 is a diagram showing an example of a mechanism development diagram. Figure 7 is a scatter plot of the measured i-line transmittance of the precursor in the example and the calculated absorption intensity at 365 nm. Figure 8 shows the calculated value A of polymer x, which is the target of prediction, compared to Figure 7. ｘ and predicted value T ｘ This is a scatter plot with additional plots. Figure 9 is a scatter plot of the measured values ​​of the dissolution rate of the precursor and the calculated values ​​of the solvation energy in the example. Figure 10 shows the calculated values ​​A of polymer x, which is the target of prediction, compared to Figure 9. ｘ and predicted value T ｘ This is a scatter plot with additional plots.

[0011] Hereinafter, embodiments of this disclosure will be described with reference to the accompanying drawings. In this specification and drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant descriptions will be omitted.

[0012] (Prediction Method) The prediction method of this disclosure is a prediction method for predicting the properties of a precursor capable of forming a polymer which is polyimide and / or polybenzoxazole, wherein the i-line transmittance T of the precursor x to be predicted ｘ Step (S1) to predict the dissolution rate S of the precursor x to be predicted. ｘ The process of predicting (S2) and the i-line transmittance T ｘ And, dissolution rate S ｘ The prediction method includes a step (S3) of predicting the characteristics of the precursor x to be predicted based on the above, and further includes other steps as necessary. Preferably, the prediction method is configured so that each step is performed by a computer.

[0013] According to the prediction method of this disclosure, it is possible to predict precursors that can excellently balance i-line transmittance and dissolution rate. Therefore, based on the structural data of the polymer to be predicted and the precursors capable of forming the polymer, it is possible to develop polymers and precursors with good contrast performance (high resolution).

[0014] Here, if the i-line transmittance is low, for example, if the i-line transmittance is 50% or less for a precursor film with a thickness of 10 μm, there is a problem that the i-line does not transmit uniformly in the thickness direction of the precursor film during i-line exposure, and therefore the cured film cannot be formed uniformly. This may result in defects in fine patterning. On the other hand, according to the prediction method of this disclosure, it is possible to predict a precursor with excellent i-line transmittance.

[0015] Furthermore, considering the regulations on perfluorooctanesian-fluorinated compounds (PFAS), the inventors have found that when evaluating polymers obtained by removing fluorine from known fluorine-containing polymers, i-ray transmittance and dissolution rate tend to decrease. According to the prediction method of this disclosure, even in the need to develop polymers and precursors that do not contain fluorine, it is possible to predict precursors that can excellently balance i-ray transmittance and dissolution rate.

[0016] -Polyimides and Polyamic Acids- Polyimides (PI) are polymers having a structural unit represented by general formula (1), and are resins having heterocyclic rings containing nitrogen atoms. Polyamic acids are precursors of polyimides and have a structural unit represented by general formula (1').

[0017] In general formula (1), R １ This exhibits a tetravalent group with 2 or more carbon atoms, R ２ This represents a divalent group with two or more carbon atoms.

[0018] In general formula (1'), R １ This exhibits a tetravalent group with 2 or more carbon atoms, R ２ This represents a divalent group having two or more carbon atoms. The polyamic acid may also be a polyamic acid ester having an ester bond in the acid-derived portion of the amide bond of the polyamic acid.

[0019] The polyimide represented by general formula (1) is first formed by the reaction of an acid anhydride represented by general formula (1A) and a diamine represented by general formula (1B), as shown in the reaction formula (I) below. This reaction first forms a polyamic acid represented by general formula (1') as a precursor to a polyimide having an open heterocycle. Subsequently, the polyimide represented by general formula (1) is obtained by the ring-closing reaction (imidization) of the polyamic acid.

[0020]

[0021] In general formula (1A), R １ This exhibits a tetravalent group with two or more carbon atoms.

[0022] In general formula (1B), R ２ This represents a divalent group with two or more carbon atoms.

[0023] In general formula (1), R １ (CO) ４ The portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R ２ (N) ２ The portion represents a tetravalent group derived from a divalent diamine having two or more carbon atoms. The acid anhydride represented by general formula (1A) may also be a hydrolyzed tetracarboxylic acid.

[0024] R １ The tetravalent group can be appropriately selected depending on the purpose, as long as it has two or more carbon atoms. Examples include alkyl groups which may have substituents, cycloalkyl groups which may have substituents, aromatic rings which may have substituents, and heterocycles which may have substituents.

[0025] R ２ The divalent group having two or more carbon atoms can be appropriately selected depending on the purpose, and examples include alkyl groups which may have substituents, cycloalkyl groups which may have substituents, aromatic rings which may have substituents, and heterocycles which may have substituents.

[0026] -Polybenzoxazoles and polyamic acids- Polybenzoxazole (PBO) is a polymer having a structural unit represented by general formula (2), and is a resin having a heterocycle containing a nitrogen atom. Polyhydroxyamide is a precursor of polybenzoxazole and has a structural unit represented by general formula (2').

[0027] In general formula (2), R ３ This indicates a divalent group with 2 or more carbon atoms, R ４ This exhibits a tetravalent group with two or more carbon atoms.

[0028] In general formula (2'), R ３ This indicates a divalent group with 2 or more carbon atoms, R ４ This exhibits a tetravalent group with two or more carbon atoms.

[0029] As shown in reaction equation (II) below, polybenzoxazole represented by general formula (2) is first formed by the reaction of a dicarboxylic acid derivative represented by general formula (2A) and bis(o-aminophenol) represented by general formula (2B), forming a polyhydroxyamide represented by general formula (2') as a precursor to polybenzoxazole having an open heterocycle. Then, the polyhydroxyamide undergoes a ring-closing reaction to form an oxazole ring, yielding polybenzoxazole represented by general formula (2).

[0030]

[0031] In general formula (2A), R ３ X represents a divalent group with two or more carbon atoms, and X represents a monovalent group.

[0032] In general formula (2B), R ４ This exhibits a tetravalent group with two or more carbon atoms.

[0033] R ３ The divalent group having two or more carbon atoms can be appropriately selected depending on the purpose, and examples include alkyl groups which may have substituents, cycloalkyl groups which may have substituents, aromatic rings which may have substituents, and heterocycles which may have substituents.

[0034] R ４ The tetravalent group can be appropriately selected depending on the purpose, as long as it has two or more carbon atoms. Examples include alkyl groups which may have substituents, cycloalkyl groups which may have substituents, aromatic rings which may have substituents, and heterocycles which may have substituents.

[0035] X can be appropriately selected depending on the purpose, as long as it is a monovalent group that has reactivity with the amino group in general formula (2B) bis(o-aminophenol), for example, chloride (Cl), thionyl chloride (SOCl) ２ ) are some examples.

[0036] One embodiment of the prediction method of this disclosure will be described with reference to Figures 1 and 2. Figure 1 is a flowchart of an example of the prediction method of this embodiment. Figure 2 is a flowchart of another example of the prediction method of this embodiment.

[0037] Here, when there are n types of polymers that serve as training data, they can be identified by denoting them as, for example, polymer 1, polymer 2, ... polymer n (where n is an integer of 3 or more). n is preferably 10 or more, and preferably 20 or more. For polymer i (where i is an integer from 1 to n), the corresponding precursor is denoted as precursor i. For polymer i and precursor i, the i-line transmittance (measured value) is given by T. ｉ The absorption intensity at 365 nm (calculated value) is A ｉ , Dissolution rate (measured value) S ｉ , and the solvation energy (calculated value) E ｉ They can be identified by writing them as follows. Furthermore, the polymer to be predicted and the corresponding precursor are denoted as polymer x and precursor x, respectively, and the i-ray transmittance (estimated value) for polymer x and precursor x is given as T ｘ The absorption intensity at 365 nm (calculated value) is A ｘ , the dissolution rate (estimated value) is S ｘ , and the solvation energy (calculated value) E ｘ These are written as , respectively.

[0038] <Step S1> Step S1 is the i-line transmittance T of the precursor x to be predicted.ｘ This is a process for predicting the i-line transmittance T of the precursor x to be predicted, as shown in Figure 1, and may also include step S1-0 as needed, as shown in Figure 2. In step S1, based on a plurality of polymers that serve as training data, the i-line transmittance T of the precursor x to be predicted is predicted. ｘ It can be predicted.

[0039] <<Step S1-0>> Step S1-0 is the measured value T of the i-line transmittance of multiple precursors 1...n. １ ...T ｎ This is the process of obtaining the i-line transmittance. There are no particular restrictions on the method of measuring the actual i-line transmittance, and it can be appropriately selected according to the purpose. For example, the following methods for measuring i-line transmittance can be given.

[0040] -Method for measuring i-line transmittance- A precursor solution is applied to a glass plate and spin-coated. At this time, the precursor solution concentration and the spin-coating rotation speed are adjusted so that the average thickness of the coated film is 10 μm.

[0041] The precursor film obtained by spin coating is heated and dried on a hot plate, and then irradiated with i-line light (365 nm light). The i-line transmittance is measured using an uncoated glass plate as a reference.

[0042] On the other hand, it is possible to use known measured i-line transmittance data or a database containing such data without performing step S1-0. Furthermore, the measured i-line transmittance values ​​measured in step S1-0 can be added to existing measured data or databases and used in subsequent steps.

[0043] <<Step S1-1>> Step S1-1 is performed by quantum chemical calculations based on the structural units of the plurality of polymers 1...n, and the calculated value A of the absorption intensity of the plurality of polymers at 365 nm. １ ...A ｎ This is the process of calculating the absorption intensity at 365 nm. There are no particular restrictions on the method of calculating the absorption intensity of a polymer at 365 nm by quantum chemical calculations based on the structural units of the polymer, and it can be appropriately selected according to the purpose. For example, the following methods for calculating the absorption intensity at 365 nm can be cited.

[0044] - Calculation method for absorption intensity at 365 nm - By performing time-dependent density functional theory (DFT) calculations at the ωB97xd / 6-31+G(d) level using the general-purpose quantum chemistry calculation program Gaussian16Brev.01 for the selected polymer structural units, the absorption intensity of the polymer structural units at 365 nm can be obtained.

[0045] <<Step S1-2>> Step S1-2 is the calculated value A of the absorption intensity of the plurality of polymers at 365 nm. １ ...A ｎ And the measured value T of the i-line transmittance of the plurality of precursors. １ ...T ｎ This is the process of obtaining the first regression equation based on the above.

[0046] One method for obtaining the first regression equation is, for example, a set of n types of values: absorption intensity at 365 nm and calculated values ​​of measured i-line transmittance [A ｉ , T ｉ One method involves creating a scatter plot using [ ] and obtaining a linearly approximated regression equation and coefficient of determination R2. In this case, if the coefficient of determination R2 of the regression equation exceeds the reference value, proceed to the next step; otherwise, increase the number of polymers n that serve as training data to obtain a regression equation in which the coefficient of determination R2 exceeds the reference value. The reference value for the coefficient of determination R2 is preferably 0.4, more preferably 0.5, and even more preferably 0.6.

[0047] <<Step S1-3>> Step S1-3 is performed when the coefficient of determination R2 in the first regression equation is greater than 0.4, and the first regression equation and the calculated value A of the absorption intensity of the polymer x to be predicted at 365 nm. ｘ Based on this, the i-line transmittance T of precursor x ｘ This is a process to predict the i-line transmittance T of the precursor x to be predicted, based on multiple polymers that serve as training data. ｘ This can be predicted. The i-line transmittance T of precursor x. ｘ One method for determining this is to use the first regression equation and the calculated value A of the absorption intensity at 365 nm. ｘSubstitute the value of and the corresponding T ｘ It is possible to calculate this.

[0048] <Step S2> Step S2 is the dissolution rate S of the precursor x to be predicted. ｘ This is a process for predicting the dissolution rate S of the precursor x to be predicted, and as shown in Figure 1, it has steps S2-1 to S2-3, and may also have step S2-0 as needed, as shown in Figure 2. In step S1, based on a plurality of polymers that serve as learning data, the dissolution rate S of the precursor x to be predicted is predicted. ｘ It can be predicted.

[0049] <<Step S2-0>> Step S2-0 is the measured value S of the dissolution rate of multiple precursors 1...n. １ ...S ｎ This is the process of obtaining [the substance]. There are no particular restrictions on the method of measuring the actual dissolution rate, and it can be appropriately selected according to the purpose. For example, the following methods for measuring the dissolution rate can be given.

[0050] -Method for measuring dissolution rate- The precursor solution is applied to a silicon substrate and spin-coated. The coated film obtained by spin-coating is heated on a hot plate and dried, and the average thickness of the precursor film is measured.

[0051] Next, the precursor film obtained in the above procedure is immersed in a 2.3% by mass aqueous solution of tetramethylammonium hydroxide (TMAH). At this time, the precursor gradually dissolves from the film and interference fringes appear on the silicon substrate. The time from when the precursor film is immersed in the TMAH aqueous solution until these interference fringes disappear can be measured, and the dissolution rate can be calculated by dividing the film thickness by the interference fringe disappearance time.

[0052] <<Step S2-1>> Step S2-1 is performed by molecular dynamics calculations based on the structures of the multiple precursors 1...n, and calculates the solvation energy E of the multiple precursors. １ ...E ｎ This is the process of calculating the solvation energy of the precursor. There are no particular restrictions on the method of calculating the solvation energy of the precursor by molecular dynamics calculations based on the structure of the precursor, and it can be appropriately selected according to the purpose. For example, the following method for calculating the solvation energy at 365 nm can be used.

[0053] - Calculation method for solvation energy - For the selected precursor structural units, monomer model (single unit constituting the polymer) precursor structural unit data is created using the multiscale simulation software J-OCTA version 7.1 (JSOL Corporation), and a GAFF force field is assigned.

[0054] For monomer models to which a force field has been assigned, charge calculations are performed using quantum chemical calculations at the RHF / 6-31G(d) level, and charges are assigned to each atom of the monomer model by electrostatic potential fitting. The charge-assigned monomer models are then extended using the polymer modeling function of J-OCTA to create polyhydroxyamide structure data with a degree of polymerization of 10 as a precursor polymer model.

[0055] Using the "$ gmx insert-molecules" function of the GROMACS software, distributed under the GNU Lesser General Public License version 2.1, one molecule of the obtained precursor polymer model and 5,000 molecules of water are randomly packed to create a computational cell in the form of a cube.

[0056] The obtained calculation cells are subjected to a 10 ns (nanosecond) calculation using an NPT ensemble at a temperature of 300 K and a pressure of 1 atmosphere. The obtained calculation results can then be used to determine the solvation energy of water relative to the precursor using the Ermod program, which is distributed under the GNU General Public License version 2.0.

[0057] <<Step S2-2>> Step S2-2 is the calculated value E of the solvation energy of the plurality of precursors. １ ...E ｎ And the measured value S of the dissolution rate of the plurality of precursors. １ ...S ｎ This is the process of obtaining a second regression equation based on the above.

[0058] As a method for obtaining the second regression equation, for example, a scatter diagram is created using n sets [E ｉ , S ｉ of the calculated value of the solvation energy and the measured value of the dissolution rate, and a regression equation and a determination coefficient R2 obtained by linear approximation are determined. At this time, if the determination coefficient R2 of the regression equation exceeds the reference value, the process proceeds to the next step. If it does not exceed, the number n of a plurality of polymers serving as learning data is increased to obtain a regression equation in which the determination coefficient R2 exceeds the reference value. As the reference value of the determination coefficient R2, 0.4 is preferable, 0.5 is more preferable, and 0.6 is still more preferable.

[0059] <<Step S2-3>> Step S2-3 is a step of predicting the dissolution rate S ｘ of the precursor x to be predicted based on the second regression equation, the calculated value E ｘ of the solvation energy of the precursor x to be predicted, and. By step S2-3, the dissolution rate S ｘ of the precursor x to be predicted can be predicted. As a method for obtaining the dissolution rate S ｘ of the precursor x, the value of the calculated value E ｘ of the solvation energy is substituted into the second regression equation, and the corresponding S ｘ can be calculated.

[0060] <Step S3> Step S3 is a step of predicting the characteristics of the precursor x to be predicted based on the i-line transmittance T ｘ and the dissolution rate S ｘ . Here, the reference value for determining the characteristics is not particularly limited and can be appropriately selected according to the purpose. From the viewpoint of exhibiting good contrast performance, it is preferable that both the i-line transmittance and the dissolution rate are high.

[0061] As the i-line transmittance, 80% or more is preferable, and 90% or more is more preferable. When the i-line transmittance is 80% or more, the i-line uniformly penetrates in the thickness direction of the precursor film during exposure with the i-line, and a polymer film uniformly cured in the thickness direction can be formed. In addition, when forming a fine pattern by i-line exposure, the curing of the exposed portion proceeds uniformly, and a fine pattern can be formed.

[0062] The dissolution rate is preferably 320 nm / s or higher, more preferably 400 nm / s or higher, and even more preferably 500 nm / s or higher. When the dissolution rate is 320 nm / s or higher, the precursor coating film can be formed uniformly, the exposed areas (solubilized in alkaline solution) during i-line exposure can be easily removed, and fine patterns can be formed.

[0063] By evaluating whether both the reference value for i-line transmittance and the reference value for dissolution rate are met, it is possible to predict precursors that can achieve excellent balance between i-line transmittance and dissolution rate. Therefore, based on the structural data of the polymer to be predicted and the precursors capable of forming the polymer, it is possible to develop polymers and precursors with good contrast performance (high resolution).

[0064] (Prediction System) The prediction system of this disclosure is a prediction system that predicts the properties of a precursor capable of forming a polymer which is polyimide and / or polybenzoxazole.

[0065] Polymers and precursors are manufactured to meet good contrast performance requirements. To check whether they meet good contrast performance requirements, the i-line transmittance and dissolution rate of the polymers and precursors are evaluated.

[0066] According to the prediction system of this disclosure, it is possible to predict precursors that can achieve an excellent balance between i-line transmittance and dissolution rate. Therefore, based on the structural data of the polymer to be predicted and the precursors capable of forming the polymer, it is possible to develop polymers and precursors with good contrast performance (high resolution).

[0067] Precursors capable of forming polymers with predicted properties may be manufactured using the prediction system of this disclosure. More specifically, precursors predicted to have superior properties may be manufactured without human judgment of adoption or rejection. Preferably, precursors predicted to have an i-line transmittance Tx of 80% or more and a dissolution rate Sx of 320 nm / s or more may be automatically adopted as manufacturing conditions.

[0068] <Overall Configuration> The overall configuration of the prediction system according to this embodiment will be described with reference to Figure 3. Figure 3 is a block diagram showing an example of the overall configuration of the prediction system.

[0069] As shown in Figure 3, the prediction system 1000 includes a learning device 10, a prediction device 20, and a terminal device 30. The learning device 10, the prediction device 20, and the terminal device 30 are connected via a communication network N to enable data communication. The communication network N may be, for example, a LAN (Local Area Network), a VPN (Virtual Private Network), or the Internet.

[0070] The learning device 10 is an example of an information processing device such as a personal computer, workstation, or server that learns a predictive model. The predictive model is an example of a machine learning model that predicts the properties of polymers and precursors.

[0071] The prediction model includes a characteristic prediction model that predicts characteristics and an intermediate prediction model that predicts intermediate parameters. The intermediate parameters include the i-ray transmittance of the precursor and the dissolution rate of the precursor, and may further include other parameters as needed. The prediction model may include an intermediate prediction model that predicts the i-ray transmittance of the precursor and an intermediate model that predicts the dissolution rate of the precursor, and may also include an intermediate prediction model that predicts other parameters.

[0072] Other parameters are those that function in determining the properties and can be appropriately selected depending on the purpose. Examples include the physical properties of the polymer and precursor, the manufacturing conditions of the polymer and precursor, and the usage conditions of the polymer and precursor. As physical properties of the polymer and precursor, for example, the substitution ratio of polar groups such as carbonyl groups and the intramolecular conjugation length can be considered.

[0073] An intermediate prediction model is a machine learning model that uses intermediate parameters as its dependent variable. The explanatory variables of an intermediate prediction model can be any variables that can predict the intermediate parameters. For example, the explanatory variables of an intermediate prediction model may include one or more parameters related to polymers and precursors.

[0074] A characteristic prediction model is a machine learning model that includes intermediate parameters as explanatory variables and a characteristic as the dependent variable. The explanatory variables for the characteristic may include parameters other than the intermediate parameters. The parameters other than the intermediate parameters may include one or more parameters relating to the polymer and precursor. For example, the parameters relating to the polymer and precursor may include at least one of the following: information describing the material, the physical properties of the material, the manufacturing conditions of the polymer and precursor, or the usage conditions of the polymer and precursor.

[0075] The characteristic prediction model and the intermediate prediction model may be any type of machine learning model. Examples of machine learning model types include Gaussian process regression, linear regression, or random forest. The characteristic prediction model and the intermediate prediction model may be the same type of machine learning model, or they may be different types of machine learning models. If the prediction model includes multiple intermediate prediction models, the intermediate prediction models may be the same type of machine learning model, or they may be different types of machine learning models.

[0076] The prediction device 20 is an example of an information processing device such as a personal computer, workstation, or server that predicts the properties of polymers and precursors. The prediction device 20 may predict the properties of polymers and precursors based on a trained prediction model. The trained prediction model may be generated by the learning device 10.

[0077] The prediction device 20 may predict intermediate parameters based on a trained intermediate prediction model. The prediction device 20 may also predict the properties of the polymer and precursor by inputting the predicted values ​​of the intermediate parameters into a property prediction model.

[0078] Terminal device 30 is an example of an information processing terminal such as a personal computer, smartphone, or tablet terminal operated by a user of the prediction system 1000. Terminal device 30 may accept input of explanatory variables for the intermediate prediction model and transmit them to the prediction device 20. Terminal device 30 may also receive prediction results from the prediction device 20 and present them to the user.

[0079] The overall configuration of the prediction system 1000 shown in Figure 3 is just one example, and various system configurations are possible depending on the application and purpose. For example, one or more of the learning device 10, prediction device 20, and terminal device 30 may be included in the prediction system 1000. For example, the prediction system 1000 may include a single information processing device that integrates the learning device 10 and the prediction device 20.

[0080] For example, the learning device 10 or the prediction device 20 may be implemented using multiple computers, or as a cloud computing service. For example, the learning device 10 and the prediction device 20 may be implemented using standalone computers. The classification of devices such as the learning device 10, prediction device 20, and terminal device 30 shown in Figure 3 is just one example.

[0081] <Hardware Configuration> The hardware configuration of the prediction system 1000 will be explained with reference to Figure 4. The learning device 10, the prediction device 20, and the terminal device 30 are implemented, for example, by a computer. Figure 4 is a block diagram showing an example of the computer's hardware configuration.

[0082] As shown in Figure 4, the computer 500 includes a CPU (Central Processing Unit) 501, ROM (Read Only Memory) 502, RAM (Random Access Memory) 503, HDD (Hard Disk Drive) 504, input device 505, display device 506, communication interface 507, and external interface 508. The CPU 501, ROM 502, and RAM 503 form what is known as a computer. Each piece of hardware in the computer 500 is interconnected via a bus line 509. The input device 505 and display device 506 may also be used by connecting them to the external interface 508.

[0083] The CPU 501 is a computing device that reads programs and data from a storage device such as ROM 502 or HDD 504 onto RAM 503 and executes processing to realize the overall control and functions of the computer 500. The computer 500 may have a GPU (Graphics Processing Unit) in addition to or instead of the CPU 501.

[0084] ROM 502 is an example of a non-volatile semiconductor memory (storage device) that can retain programs and data even when the power is turned off. ROM 502 functions as the main memory, storing various programs and data necessary for the CPU 501 to execute the various programs installed on HDD 504. Specifically, ROM 502 stores boot programs such as BIOS (Basic Input Output System) and EFI (Extensible Firmware Interface) that are executed when the computer 500 starts up, as well as data such as OS (Operating System) settings and network settings.

[0085] RAM 503 is an example of volatile semiconductor memory (storage device) whose programs and data are erased when the power is turned off. RAM 503 can be, for example, DRAM (Dynamic Random Access Memory) or SRAM (Static Random Access Memory). RAM 503 provides a workspace that is expanded when various programs installed on HDD 504 are executed by CPU 501.

[0086] HDD 504 is an example of a non-volatile storage device that stores programs and data. The programs and data stored in HDD 504 include the OS, which is the basic software that controls the entire computer 500, and applications that provide various functions on the OS. Note that the computer 500 may use a storage device that uses flash memory as its storage medium (for example, an SSD: Solid State Drive) instead of HDD 504.

[0087] The input device 505 includes a touch panel used by the user to input various signals, operation keys and buttons, a keyboard and mouse, and a microphone for inputting sound data such as voice.

[0088] The display device 506 consists of a display such as a liquid crystal or organic EL (Electro-Luminescence) that displays a screen, and a speaker that outputs sound data such as audio.

[0089] Communication I / F 507 is an interface that connects to a communication network and allows the computer 500 to perform data communication.

[0090] External I / F 508 is an interface to external devices. External devices include drive devices 510, etc.

[0091] The drive device 510 is a device for setting the recording medium 511. The recording medium 511 here includes media that record information optically, electrically, or magnetically, such as CD-ROMs, flexible disks, and magneto-optical disks. The recording medium 511 may also include semiconductor memory that records information electrically, such as ROMs and flash memory. This allows the computer 500 to read and / or write to the recording medium 511 via the external interface 508.

[0092] The various programs to be installed on the HDD 504 are installed, for example, when the distributed recording medium 511 is set in a drive device 510 connected to an external I / F 508, and the various programs recorded on the recording medium 511 are read by the drive device 510. Alternatively, the various programs to be installed on the HDD 504 may be installed by downloading them via the communication I / F 507 from the communication network N or another network different from the communication network N.

[0093] <Functional Configuration> The functional configuration of the prediction system 1000 will be explained with reference to Figure 5. Figure 5 is a block diagram showing an example of the functional configuration of the prediction system.

[0094] <<Learning Device>> As shown in Figure 5, the learning device 10 includes a data storage unit 101, a selection unit 110, an intermediate learning unit 120, a characteristic learning unit 130, and a model output unit 140. The learning device 10 functions as the data storage unit 101, selection unit 110, intermediate learning unit 120, characteristic learning unit 130, and model output unit 140 when a pre-installed learning program is executed.

[0095] For example, the data storage unit 101 is implemented by the HDD 504 shown in Figure 4. For example, the selection unit 110, intermediate learning unit 120, characteristic learning unit 130, and model output unit 140 are implemented by a process in which a program loaded from the HDD 504 shown in Figure 4 onto the RAM 503 is executed by the CPU 501.

[0096] The data storage unit 101 stores a dataset. The dataset is a collection of training data used to build a predictive model. The training data may include multiple parameters relating to the polymer and precursor, and the ground truth values ​​of the properties of the polymer and precursor. The ground truth values ​​of the properties may include at least one of the measured values ​​obtained from experiments using the polymer and precursor, or the calculated values ​​obtained from simulations.

[0097] The selection unit 110 selects intermediate parameters. The selection unit 110 may select intermediate parameters from a plurality of parameters relating to the polymer and precursor. The selection unit 110 may select multiple intermediate parameters. The number of intermediate parameters selected by the selection unit 110 is not limited.

[0098] The selection unit 110 may select intermediate parameters based on a mechanism diagram. The selection unit 110 may select intermediate parameters based on a mechanism diagram relating to the properties. A mechanism diagram is a document that describes the relationship between the properties of polymers and precursors, the functions that affect those properties, and the parameters that affect those functions. The mechanism diagram may be written based on hypotheses. The selection unit 110 may accept input of intermediate parameters selected by the user of the prediction system 1000 based on the mechanism diagram.

[0099] The selection unit 110 may select intermediate parameters based on the results of statistical analysis of the dataset. The selection unit 110 may also perform statistical analysis on the dataset read from the data storage unit 101. The selection unit 110 may obtain the results of the statistical analysis of the dataset from another information processing device.

[0100] For example, the selection unit 110 may select parameters with a high correlation coefficient with the characteristic as intermediate parameters. For instance, the selection unit 110 may select a predetermined number of parameters with high correlation coefficients as intermediate parameters. Alternatively, the selection unit 110 may select parameters with a correlation coefficient above a threshold as intermediate parameters.

[0101] As another example, the selection unit 110 may construct a machine learning model based on the dataset, using parameters related to polymers and precursors as explanatory variables and properties as the objective variable, and select parameters with high importance among the explanatory variables in that machine learning model as intermediate parameters. For example, the selection unit 110 may select a predetermined number of parameters with high importance as intermediate parameters. Alternatively, the selection unit 110 may select parameters with importance above a threshold as intermediate parameters.

[0102] The selection unit 110 may select intermediate parameters based on a trained language model. The selection unit 110 may also select intermediate parameters based on the results of querying the trained language model for intermediate parameters. For example, the selection unit 110 may query the trained language model for parameters that are effective in predicting characteristics.

[0103] The language model may be a large language model (LLM) trained to perform various language processing tasks, or a small language model (SLM) trained to perform a specific language processing task. The trained language model may be built into the learning device 10, or it may be held by another information processing device that can communicate via the communication network N.

[0104] The intermediate learning unit 120 generates an intermediate prediction model. The intermediate learning unit 120 may generate an intermediate prediction model based on a dataset read from the data storage unit 101. The intermediate learning unit 120 may generate an intermediate prediction model in which the intermediate parameters selected by the selection unit 110 are the target variables. The intermediate learning unit 120 may generate multiple intermediate prediction models for each of the multiple intermediate parameters selected by the selection unit 110.

[0105] The explanatory variables of the intermediate prediction model may include any variables that can predict the intermediate parameters. For example, the intermediate learning unit 120 may select the explanatory variables of the intermediate prediction model based on a mechanism diagram. The intermediate learning unit 120 may select the explanatory variables of the intermediate prediction model based on the results of statistical analysis of the dataset. The intermediate learning unit 120 may select the explanatory variables of the intermediate prediction model based on a trained language model.

[0106] The characteristic learning unit 130 generates a characteristic prediction model. The characteristic learning unit 130 may generate a characteristic prediction model based on a dataset read from the data storage unit 101. The explanatory variables of the characteristic prediction model may include intermediate parameters selected by the selection unit 110. The explanatory variables of the characteristic prediction model may include all of the multiple intermediate parameters selected by the selection unit 110.

[0107] The model output unit 140 outputs the trained prediction model. The model output unit 140 may output a prediction model that includes the intermediate prediction model generated by the intermediate learning unit 120 and the characteristic prediction model generated by the characteristic learning unit 130. The model output unit 140 may transmit the trained prediction model to the prediction device 20. The trained prediction model may be stored in the model storage unit 201 of the prediction device 20.

[0108] <<Prediction Device>> As shown in Figure 5, the prediction device 20 comprises a model storage unit 201, a request reception unit 210, an intermediate prediction unit 220, a characteristic prediction unit 230, and a result output unit 240. The prediction device 20 functions as the model storage unit 201, request reception unit 210, intermediate prediction unit 220, characteristic prediction unit 230, and result output unit 240 when a pre-installed prediction program is executed.

[0109] For example, the model storage unit 201 is implemented by the HDD 504 shown in Figure 4. For example, the request reception unit 210, the intermediate prediction unit 220, the characteristic prediction unit 230, and the result output unit 240 are implemented by a process in which a program loaded from the HDD 504 shown in Figure 4 onto the RAM 503 is executed by the CPU 501.

[0110] The model storage unit 201 stores a trained prediction model. The model storage unit 201 may already have a pre-trained prediction model stored in it. The prediction model stored in the model storage unit 201 may be generated by the learning device 10.

[0111] The request receiving unit 210 receives prediction requests. A prediction request is information or a signal requesting the prediction of a characteristic. The request receiving unit 210 may receive prediction requests from the terminal device 30. The request receiving unit 210 may also receive input of prediction requests via the input device 505 of the prediction device 20.

[0112] The prediction request may include parameters relating to the polymer and precursor to be predicted. The prediction request may also include parameters that serve as explanatory variables for the intermediate prediction model. The prediction request may also include parameters entered by the user of the prediction system 1000 into the terminal device 30.

[0113] The intermediate prediction unit 220 predicts intermediate parameters. The intermediate prediction unit 220 may predict intermediate parameters based on intermediate prediction models included in the prediction model. The intermediate prediction unit 220 may predict multiple intermediate parameters for each of the multiple intermediate prediction models included in the prediction model. The intermediate prediction unit 220 may predict intermediate parameters based on prediction requests received by the request reception unit 210. The intermediate prediction unit 220 may predict intermediate parameters by inputting the parameters included in the prediction request into the intermediate prediction model.

[0114] The property prediction unit 230 predicts the properties of the polymer and precursor. The property prediction unit 230 may predict the properties of the polymer and precursor based on the property prediction model included in the prediction model. The property prediction unit 230 may also predict the properties of the polymer and precursor by inputting predicted values ​​of intermediate parameters into the property prediction model. The predicted values ​​of intermediate parameters may be predicted by the intermediate prediction unit 220.

[0115] The result output unit 240 outputs the prediction results. The prediction results may include predicted values ​​of the characteristics. The prediction results may include the confidence level of the predicted values ​​of the characteristics. The prediction results may include the information used for the prediction. The information used for the prediction may include predicted values ​​of intermediate parameters. The information used for the prediction may include the parameters used for predicting the intermediate parameters.

[0116] - Mechanism Diagram - The mechanism diagram used by the selection unit 110 will be explained with reference to Figure 6. Figure 6 is a diagram showing an example of a mechanism diagram.

[0117] Figure 6 shows an example of a mechanism diagram relating to the contrast performance of a precursor. As shown in Figure 6, the mechanism diagram describes the relationship between the properties of the polymer and precursor, the functions that affect those properties, and the parameters that affect those functions. In Figure 6, the relationship between properties, functions, and parameters is shown in a tree format as an example, but the notation of the mechanism diagram is not limited to this.

[0118] Figure 6 shows that the contrast performance of a precursor is influenced by its ability to transmit i-lines and its ability to dissolve in alkaline solutions. Furthermore, Figure 6 shows that the ability of the precursor to transmit i-lines is influenced by its absorption intensity at 365 nm, and its ability to dissolve in alkaline solutions is influenced by its solvation energy.

[0119] [Supplement] Each function of the embodiments described above can be realized by one or more processing circuits. Hereinafter, "processing circuit" in this specification includes processors programmed to execute each function by software, such as CPUs (Central Processing Units) or GPUs (Graphics Processing Units) implemented by electronic circuits, as well as devices such as ASICs (Application Specific Integrated Circuits), DSPs (Digital Signal Processors), FPGAs (Field Programmable Gate Arrays), and conventional circuit modules designed to execute each function described above.

[0120] The present invention will be described more specifically below based on examples, but the present invention is not limited to the following examples.

[0121] The properties of polybenzoxazoles (PBOs) and their corresponding precursors, polyhydroxyamides, were predicted using the following procedure. The training data consisted of 47 types of polybenzoxazoles (PBOs) and their precursors, synthesized from combinations of dicarboxylic acids No. 1-26 (shown in Tables 1-2) and bis(o-aminophenol) No. 1-10 (shown in Table 3), as shown in Tables 4-9.

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] (Prediction of i-line transmittance) <Acquisition of i-line transmittance of precursors> Using the following i-line transmittance measurement method, the measured i-line transmittance T of 47 types of polyhydroxyamides, which are precursors of polybenzoxazoles (PBOs), was obtained for precursors 1...n. １ ...T ｎ Obtained (Step S1-0).

[0132] -Method for measuring i-line transmittance- A 30% to 50% by mass N-methylpyrrolidone (NMP) precursor solution was applied to a glass plate and spin-coated. At this time, the precursor solution concentration and the spin-coating rotation speed were adjusted so that the average thickness of the precursor film after drying was 10 μm.

[0133] The precursor film obtained by spin coating was dried by heating it on a hot plate at 120°C for 3 minutes. The precursor film was then irradiated with i-line light (365 nm light), and the i-line transmittance was measured using an uncoated glass plate as a reference.

[0134] <Calculation of Absorption Intensity at 365 nm> Next, for each polymer whose i-line transmittance was measured, the absorption intensity at 365 nm was calculated using the following calculation method (Step S1-1).

[0135] - Calculation method for absorption intensity at 365 nm - For the selected PBO structural unit (ring-closed benzoxazole structure), the absorption intensity of the PBO structural unit at 365 nm was obtained by performing time-dependent DFT calculations at the ωB97xd / 6-31+G(d) level using the general-purpose quantum chemistry calculation program Gaussian16Brev.01.

[0136] <Obtaining the first regression equation> Next, the measured value of i-line transmittance and the calculated value of absorption intensity at 365 nm are obtained in n sets [T ｉ , A ｉA scatter plot was created using [ ] to obtain the first regression equation and the coefficient of determination R2 (step S1-2). The results are shown in Figure 7. Figure 7 is a scatter plot of the measured i-line transmittance of the precursor in the example and the calculated absorption intensity at 365 nm. At this time, the first regression equation was T = -0.0024 × Ax + 85.961, and the coefficient of determination R2 of the first regression equation was 0.6913. Since the coefficient of determination R2 exceeded 0.4, we proceeded to the next step S1-3.

[0137] Furthermore, as shown in Figure 7, in the polybenzoxazole represented by general formula (2), R ３ It was found that when the material has an adamantyl group or an n-alkylene group (hexylene group), the i-ray transmittance is high, at 90% or more. Therefore, R ３ When saturated hydrocarbons are present and the influence of conjugation by the aromatic rings of the polymer is low, a tendency for high i-line transmittance was observed.

[0138] <Linear transmittance T in the polymer to be predicted> ｘ Prediction > Using polybenzoxazole represented by the following structural formula (2x) as the polymer x to be predicted, the calculated value A of the absorption intensity at 365 nm is obtained using the calculation method described above. ｘ The following was calculated: Calculated value A ｘ Substitute this into the first regression equation and obtain the predicted value T of the i-line transmittance corresponding to this value. ｘ The value A was calculated (Step S1-3). ｘ This is 0.0493 (unitless), and the predicted value T ｘ The result was 86%. The results are shown in Figure 8. Figure 8 shows the calculated value A of polymer x, which is the target of prediction, in Figure 7. ｘ and predicted value T ｘ This is a scatter plot with additional plots.

[0139]

[0140] (Prediction of dissolution rate) <Acquisition of precursor dissolution rate> Using the following dissolution rate measurement method, the measured dissolution rate S of precursor 1...n was obtained for 47 types of polyhydroxyamides, which are precursors of polybenzoxazole (PBO). １ ...S ｎ Obtained (Step S2-0).

[0141] -Method for measuring dissolution rate- An NMP solution of 30% to 50% by mass of the precursor was applied to a silicon substrate and spin-coated. The coated film obtained by spin-coating was heated on a hot plate at 120°C for 3 minutes to dry, and the average thickness of the precursor film was measured.

[0142] Next, the precursor film obtained in the above procedure was immersed in a 2.3% by mass aqueous solution of tetramethylammonium hydroxide (TMAH). At this time, the precursor gradually eluted from the film, and interference fringes appeared on the surface of the TMAH aqueous solution. The time from when the precursor film was immersed in the TMAH aqueous solution until these interference fringes disappeared was measured, and the dissolution rate was calculated by dividing the film thickness by the interference fringe disappearance time.

[0143] <Calculation of Solvation Energy> Next, for each polymer whose dissolution rate was measured, the solvation energy was calculated using the following solvation energy calculation method (Step S2-1).

[0144] - Calculation method for solvation energy - For the ring-opened polyhydroxyamide skeleton, which is the precursor of the selected PBO skeleton, monomer model (single unit constituting the polymer) hydroxyamide structure data was created using the multiscale simulation software J-OCTA version 7.1 (JSOL Corporation), and a GAFF force field was assigned.

[0145] For monomer models to which a force field was assigned, charge calculations were performed using quantum chemical calculations at the RHF / 6-31G(d) level, and charge was assigned to each atom of the monomer model by electrostatic potential fitting. The charge-assigned monomer models were extended using the polymer modeling function of J-OCTA, and polyhydroxyamide structural data with a degree of polymerization of 10 was created as a precursor polymer model.

[0146] Using the "$ gmx insert-molecules" function of the GROMACS software, distributed under the GNU Lesser General Public License version 2.1, one molecule of the obtained precursor polymer model and 5,000 molecules of water were randomly packed to create a computational cell in the form of a cube.

[0147] The obtained computational cells were subjected to 10 ns (nanosecond) calculations using an NPT ensemble at a temperature of 300 K and a pressure of 1 atm. The solvation energy of water for the precursor polyhydroxyamide was then determined using the Ermod program, which is distributed under the GNU General Public License version 2.0, based on the obtained computational results.

[0148] <Obtaining the second regression equation> Next, we obtain n sets of measured values ​​of dissolution rate and calculated values ​​of solvation energy [S ｉ , E ｉ A scatter plot was created using [ ] and the second regression equation and coefficient of determination R2 were obtained (Step S2-2). The results are shown in Figure 9. Figure 9 is a scatter plot of the measured values ​​of the dissolution rate of the precursor and the calculated values ​​of the solvation energy in the example. At this time, the second regression equation is S = -1.0993 × E ｘ The result was -328.99, and the coefficient of determination R² of the second regression equation was 0.4007. Since the coefficient of determination R² exceeded 0.4, we proceeded to the next step S2-3.

[0149] Furthermore, as shown in Figure 9, in the polybenzoxazole represented by general formula (2), R ３ It has an ether group, R ４ It was found that when the polymer has a sulfonyl group and therefore has strong polarity, the dissolution rate is high, at 400 nm / s or more. On the other hand, R ４ Even if it has a highly polar methyl fluoride group, R ３ When saturated hydrocarbons are present, a lower dissolution rate was observed, suggesting that a lower polarity of the polymer as a whole leads to a lower dissolution rate.

[0150] <Dissolution rate S in the predictive precursor>ｘ Prediction > Using a polyhydroxyamide represented by the following structural formula (2'x) as the precursor x to be predicted, the solvation energy E is calculated using the calculation method described above. ｘ The calculated value E was obtained. ｘ Substitute this into the second regression equation and obtain the corresponding predicted value S of the dissolution rate. ｘ The calculated value E was calculated (step S2-3). ｘ The value is -856.1 [kcal / mol], and the predicted value S ｘ The value was 612 [nm / s]. The results are shown in Figure 10. Figure 10 shows the calculated value A of polymer x, which is the target of prediction, compared to Figure 9. ｘ and predicted value T ｘ This is a scatter plot with additional plots.

[0151]

[0152] <Prediction of Precursor Properties> The predicted i-line transmittance for precursor x was 86%, and the dissolution rate was 612 [nm / s]. Both exceeded the standard values ​​of 80% for i-line transmittance and 320 [nm / s] for dissolution rate, which were set from the perspective of having good contrast performance. Therefore, it was predicted that the polyhydroxyamide represented by the structural formula (2'x), which is precursor x, is a precursor that can excellently balance i-line transmittance and dissolution rate, and can be used as a polymer and precursor with good contrast performance (high resolution).

[0153] While embodiments of the present disclosure have been described in detail above, the embodiments disclosed herein are illustrative and not restrictive in all respects. The embodiments can be modified and improved in various ways without departing from the scope and spirit of the appended claims. The features described in the above embodiments can be combined in any way that is not inconsistent with other configurations.

[0154] This application claims priority to Japanese Patent Application No. 2024-230564, filed with the Japan Patent Office on 26 December 2024, which is incorporated herein by reference to its entire contents.

[0155] 10: Learning device 20: Prediction device 30: Terminal device 101: Data storage unit 110: Selection unit 120: Intermediate learning unit 130: Characteristic learning unit 140: Model output unit 201: Model storage unit 210: Request reception unit 220: Intermediate prediction unit 230: Characteristic prediction unit 240: Result output unit 1000: Prediction system

Claims

1. A prediction method for predicting the properties of a precursor capable of forming a polymer that is a polyimide and / or a polybenzoxazole, comprising: calculating a calculated value A of the absorption intensity at 365 nm of the plurality of polymers based on quantum chemical calculations of the structural units of the plurality of polymers 1... n ｘ ...A ｎ a step of calculating; a calculated value A of the absorption intensity at 365 nm of the plurality of polymers １ ...A ｎ and an actually measured value T of the i-line transmittance of a plurality of precursors １ ...T ｎ and obtaining a first regression equation based thereon; when the coefficient of determination R2 in the first regression equation is greater than 0.4, the first regression equation and a calculated value A of the absorption intensity at 365 nm of the precursor x to be predicted ｘ and predicting the i-line transmittance T of the precursor x based thereon ｘ ; calculating a calculated value E of the solvation energy of the plurality of precursors by molecular dynamics calculations based on the structures of the plurality of precursors 1... n １ ...E ｎ a step of calculating; a calculated value E of the solvation energy of the plurality of precursors １ ...E ｎ and an actually measured value S of the dissolution rate of the plurality of precursors １ ...S ｎ and obtaining a second regression equation based thereon; when the coefficient of determination R2 in the second regression equation is greater than 0.4, the second regression equation and a calculated value E of the solvation energy of the precursor x to be predicted ｘ and predicting the dissolution rate S of the precursor x based thereon ｘ ; and predicting the properties of the precursor x to be predicted based on the i-line transmittance T ｘ and the dissolution rate S ｘ characterized by comprising a step of predicting.

2. i-line transmittance T ｘ And, dissolution rate S ｘ In the process of predicting the characteristics of the target precursor x based on the i-line transmittance T ｘ If the content is 80% or more, and the dissolution rate is S ｘ The prediction method according to claim 1, wherein when the frequency is 320 nm / s or higher, it is predicted that the characteristics of the precursor x to be predicted are excellent.

3. A prediction device comprising: an intermediate prediction unit configured to predict intermediate parameters based on a first machine learning model whose objective variable is an intermediate parameter that functions in the properties of a polymer and a precursor; and a property prediction unit configured to predict the property by inputting the predicted values ​​of the intermediate parameters into a second machine learning model which includes the intermediate parameters as explanatory variables and the property as the objective variable, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

4. The prediction apparatus according to claim 3, wherein the intermediate parameters further include the physical properties of the polymer and precursor, the manufacturing conditions of the polymer and precursor, or the usage conditions of the polymer and precursor.

5. The prediction device according to claim 3 or 4, wherein the intermediate parameters are selected based on a mechanism diagram relating to the characteristics.

6. The prediction device according to any one of claims 3 to 5, wherein the intermediate parameters are selected based on the results of a statistical analysis of a dataset including a plurality of parameters and the characteristics.

7. The prediction device according to any one of claims 3 to 6, wherein the intermediate parameters are selected based on the results of querying a trained language model for the intermediate parameters.

8. A learning device comprising: a selection unit configured to select intermediate parameters that function for the properties of a polymer and a precursor; an intermediate learning unit configured to generate a first machine learning model with the intermediate parameters as the objective variable; and a property learning unit configured to generate a second machine learning model with the intermediate parameters as the explanatory variables and the properties as the objective variable, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

9. A prediction method characterized in that a computer performs the following steps: predict intermediate parameters based on a first machine learning model in which intermediate parameters functioning on the properties of a polymer and a precursor are the objective variables; and predict the properties by inputting the predicted values ​​of the intermediate parameters into a second machine learning model in which the intermediate parameters are the explanatory variables and the properties are the objective variables, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

10. A learning method characterized in that a computer performs the following steps: selecting intermediate parameters that function on the properties of a polymer and a precursor; generating a first machine learning model with the intermediate parameters as the objective variable; and generating a second machine learning model that includes the intermediate parameters as explanatory variables and the properties as the objective variable, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

11. A program for causing a computer to perform the following steps: predict intermediate parameters based on a first machine learning model in which intermediate parameters functioning on the properties of a polymer and a precursor are the target variables; and predict the properties by inputting the predicted values ​​of the intermediate parameters into a second machine learning model in which the intermediate parameters are the explanatory variables and the properties are the target variables, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

12. A program for causing a computer to perform the following steps: selecting intermediate parameters that function on the properties of a polymer and a precursor; generating a first machine learning model with the intermediate parameters as the objective variable; and generating a second machine learning model that includes the intermediate parameters as explanatory variables and the properties as the objective variable, wherein the intermediate parameters include the absorption intensity of the precursor at 365 nm and the solvation energy of the precursor.

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