JP7769965B2 - Plasmonic material exploration method and plasmonic material exploration device - Google Patents

Description

The present invention relates to a plasmonic material exploration method and a plasmonic material exploration device.

Plasmonic materials have been used in a variety of fields, from stained glass in the past to biochemical sensors, detection of lesions such as cancer, near-infrared shielding materials, metamaterials, and more recently. Plasmonic materials utilize the plasmon resonance characteristic, so conductive materials such as metals, alloys, and carrier-doped semiconductors are preferred.

Another important characteristic of plasmonic materials is the extent to which the electric field is enhanced in response to incident light due to plasmon resonance.

Such plasmonic materials include metals such as gold and silver, and carrier-doped semiconductors such as antimony-doped tin oxide and tin-doped indium oxide. However, these plasmonic materials have problems such as high cost due to the inclusion of precious and rare metals, and issues with weather resistance. Therefore, the discovery of new plasmonic materials is desired.

One method for searching for new plasmonic materials is to measure the dielectric function of a material and determine whether it is a plasmonic material from that dielectric function. To maximize the electric field enhancement due to plasmon resonance, materials with low energy loss within the material, that is, materials with low absorption of irradiated electromagnetic waves, are preferred. Energy loss within a material is described by the imaginary part of the material's dielectric function. Therefore, measuring the dielectric function of candidate plasmonic materials makes it possible to search for plasmonic materials. However, experimentally measuring the dielectric function of all candidate materials using methods such as spectroscopic ellipsometry requires a great deal of effort.

Another method for exploring new plasmonic materials is to calculate the dielectric function of a material using first-principles calculations such as density functional theory (DFT). For example, Non-Patent Document 1 shows that the dielectric function can be calculated with high accuracy using first-principles calculations using hybrid functionals.

Furthermore, Non-Patent Document 2 shows that by using machine learning, it is possible to search for plasmonic materials from a large number of conductive materials in a short period of time.

S. Yoshio, K. Maki, and K. Adachi, The Journal of Chemical Physics, 144, 234702 (2016). T. Yoshida, R. Maezono, and K. Hongo, ACS Applied Nano Materials, 4, 1932 (2021).

One method for exploring plasmonic materials is to determine the dielectric function of conductive materials using first-principles calculations and machine learning.

However, semiconductors doped with carriers, such as antimony-doped tin oxide and tin-doped indium oxide, are not considered candidate materials in the first place because the parent material is a non-conductive material. Possible methods for doping carriers into non-conductive materials include element substitution, defect introduction, and element insertion into vacancies. However, performing first-principles calculations for all of these cases requires a great deal of effort. Therefore, there was a need for a simple method to explore whether non-conductive materials doped with carriers are suitable for use as plasmonic materials.

In view of the problems inherent in the above-mentioned conventional techniques, one aspect of the present invention aims to provide a plasmonic material search method that can efficiently search for plasmonic materials from among materials that use non-conductive materials as parent materials.

In order to solve the above problem, according to one aspect of the present invention,
a predictive electromagnetic wave absorption calculation step of calculating, by first-principles calculation, electromagnetic wave absorption when a unit lattice of a non-conductive material of the first non-conductive material group is virtually doped with carriers;
a prediction model generation step of generating a prediction model using information on the non-conductive material of the first non-conductive material group and the electromagnetic wave absorption calculated in the prediction electromagnetic wave absorption calculation step when the non-conductive material of the first non-conductive material group is virtually doped with carriers;
a prediction step of predicting electromagnetic wave absorption when a non-conductive material of the second non-conductive material group is virtually doped with carriers based on the prediction model;
a candidate material selection step of selecting, from the non-conductive materials of the second non-conductive material group, a non-conductive material whose electromagnetic wave absorption predicted in the prediction step is equal to or less than a preset threshold, as a candidate material;
an electromagnetic wave absorption calculation step of calculating electromagnetic wave absorption when the candidate material is virtually doped with carriers using a hybrid functional;
and a selection step of selecting, from the candidate substances, a non-conductive substance whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation step is equal to or less than the threshold value.

One aspect of the present invention provides a plasmonic material search method that can efficiently search for plasmonic materials from among materials that use non-conductive materials as parent materials.

FIG. 1 is a flowchart of a plasmonic material searching method according to the first embodiment. FIG. 2 shows an example of the process of calculating electromagnetic wave absorption for prediction in the first embodiment. FIG. 3 is a flowchart of a plasmonic material searching method according to the second embodiment. FIG. 4 is an image diagram of transfer learning. FIG. 5 is a diagram showing the hardware configuration of a plasmonic material exploration apparatus according to an embodiment of the present invention. FIG. 6 is a block diagram showing the functions of a plasmonic material exploration apparatus according to an embodiment of the present invention.

Hereinafter, embodiments for carrying out the present invention will be described, but the present invention is not limited to the following embodiments, and various modifications and substitutions can be made to the following embodiments without departing from the scope of the present invention.
[Plasmonic material exploration method]
(1) First Embodiment Hereinafter, a plasmonic material searching method according to this embodiment will be described with reference to a flowchart 100 in FIG. 1 and a flowchart 200 in FIG.

Figure 1 is a flowchart of the plasmonic material exploration method according to the first embodiment. Figure 2 shows an example of the process for calculating electromagnetic wave absorption for prediction according to the first embodiment.

The plasmonic material searching method according to the first embodiment includes a predictive electromagnetic wave absorption calculation step, a prediction model generation step, a prediction step, a candidate substance selection step, an electromagnetic wave absorption calculation step, and a selection step.
(Prediction electromagnetic wave absorption calculation step: S1)
In the first embodiment, first, a step of calculating electromagnetic wave absorption for prediction can be executed.

The predicted electromagnetic wave absorption calculation step uses first-principles calculations to calculate the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is hypothetically doped with carriers (step S1).

Here, first-principles calculation refers to a method of calculating the movement of electrons in a material using a computer in accordance with the Schrödinger equation of quantum mechanics. For first-principles calculation, for example, generalized gradient approximation, hybrid functionals, etc. can be used.

A non-conductive material refers to a material with a band gap greater than 0 eV, such as a semiconductor material. It is particularly preferable for the non-conductive material to be a wide-gap semiconductor, with a band gap within the range of 3 eV ± 0.2 eV.

Virtual carrier doping can be performed by increasing (electron doping) or decreasing (hole doping) the number of valence electrons in a material. By performing virtual carrier doping, it is possible to calculate the electromagnetic wave absorption when carriers are doped into a semiconductor without considering various cases such as element substitution, defect formation, and element insertion into vacancies. More specifically, virtual carrier doping can be performed by adding or removing a predetermined number of electrons to or from the unit lattice of a non-conductive material to be virtually doped.

In the predictive electromagnetic wave absorption calculation process, first, the crystal structures of N non-conductive materials are obtained from a database storing the crystal structures of M non-conductive materials that are search candidates (Figure 1, step S1). Here, M and N represent the numbers required to create a model. Furthermore, N represents an integer of 2 or greater and smaller than M. The N non-conductive materials are examples of non-conductive materials in the first non-conductive material group in this embodiment. In other words, the M non-conductive materials are non-conductive materials that make up the material group of non-conductive materials prepared in advance when carrying out the plasmonic material search method of this embodiment. The non-conductive materials in the first non-conductive material group are non-conductive materials that are part of the material group of non-conductive materials prepared in advance.

The non-conductive materials in the second non-conductive material group, described below, are the remaining non-conductive materials from the group of non-conductive materials prepared in advance, excluding the non-conductive materials in the first non-conductive material group.

Specifically, the process for calculating electromagnetic wave absorption for prediction can be carried out, for example, according to the flow shown in Figure 2, and can include a first calculation process and a second calculation process.

In the first calculation step, the dielectric function ε when each non-conductive material in the first group of non-conductive materials is virtually doped with carriers can be calculated using first-principles calculations using hybrid functionals, using the N crystal structures obtained (Figure 2, step S11).

Next, in the second calculation step, the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is virtually doped with carriers can be calculated from the imaginary part Im[ε] of the calculated dielectric function ε based on the following equation (1) (Figure 2, step S12).

Electromagnetic wave absorption = ∫Im[ε]dλ (1)
Here, electromagnetic wave absorption refers to the value obtained by integrating the imaginary part of the dielectric function with respect to wavelength. In other words, the dielectric function ε is a quantity that depends on the wavelength λ. The wavelength integration range can be selected depending on the purpose. For example, if a plasmonic material is intended to be used in the visible light wavelength range, the integration range can be set to 380 nm to 780 nm.
(Prediction model generation step: S2)
Next, a prediction model generation step can be executed. In the prediction model generation step, a prediction model is generated using information on the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated in the predictive electromagnetic wave absorption calculation step when the non-conductive materials in the first non-conductive material group are virtually doped with carriers (FIG. 1, step S2). Here, the generated prediction model is a model that predicts the electromagnetic wave absorption when the non-conductive material is virtually doped with carriers.

The information on non-conductive materials used to generate the prediction model is not particularly limited. For example, the weighted average, maximum, minimum, or average value of certain physical property values of each element contained in the non-conductive material, the radial distribution function of the crystal, or CGCNN (Crystal Graph Convolutional Neural Network) can be used.

The method for generating the prediction model is not particularly limited. For example, a prediction model can be generated using information about the non-conductive material in the first non-conductive material group as an explanatory variable and the electromagnetic wave absorption calculated in the step of calculating the predicted electromagnetic wave absorption when the non-conductive material in the first non-conductive material group is virtually doped with carriers as a response variable. For example, neural networks or Gaussian process regression can be used to generate such a prediction model.
(Prediction step: S3)
Next, a prediction step can be performed. In the prediction step, electromagnetic wave absorption when non-conductive materials in the second non-conductive material group are virtually doped with carriers is predicted based on the prediction model ( FIG. 1 , step S3). Here, the non-conductive materials in the second non-conductive material group correspond to the non-conductive materials (M−N non-conductive materials) obtained by subtracting the N non-conductive materials constituting the first non-conductive material group from the M non-conductive materials described above. Therefore, in the prediction step, the prediction model generated in the prediction model generation step is used to predict electromagnetic wave absorption when M−N non-conductive materials are virtually doped with carriers.
(Candidate substance selection step: S4)
Next, a candidate material selection step can be performed. In the candidate material selection step, non-conductive materials in the second non-conductive material group whose electromagnetic wave absorption predicted in the prediction step is equal to or less than a preset threshold are selected as candidate materials (FIG. 1, step S4). Specifically, in the candidate material selection step, it is determined whether the electromagnetic wave absorption when the M-N non-conductive materials predicted in the prediction step are virtually doped with carriers is equal to or less than a threshold δ.

The threshold value δ can be changed as appropriate depending on the conditions, but is set to, for example, δ = 3.5, taking into account preferred plasmonic materials.

In the candidate substance selection step, if the predicted electromagnetic wave absorption is equal to or less than the threshold δ, the process proceeds to the electromagnetic wave absorption calculation step (FIG. 1, step S5) described below. On the other hand, if the predicted electromagnetic wave absorption exceeds the threshold δ, the process returns to the prediction step (FIG. 1, step S3), and the prediction step and the candidate substance selection step can be repeated (FIG. 1, steps S3 and S4).
(Electromagnetic wave absorption calculation step: S5)
Next, an electromagnetic wave absorption calculation step is performed. In the electromagnetic wave absorption calculation step, the electromagnetic wave absorption when the candidate substance selected in the candidate substance selection step is virtually doped with carriers is calculated using a hybrid functional (FIG. 1, step S5). Specifically, the dielectric function when the candidate substance selected in the candidate substance selection step is virtually doped with carriers is calculated by first-principles calculation using the hybrid functional. Then, the electromagnetic wave absorption when the candidate substance is virtually doped with carriers is calculated from the imaginary part Im[ε] of the calculated dielectric function ε.

The method for calculating the dielectric function when a candidate substance is virtually doped with carriers using first-principles calculations based on hybrid functionals is not particularly limited, and any method can be used. For example, the calculation can be performed in the same manner as when the dielectric function when a non-conductive substance in the first non-conductive substance group described above is virtually doped with carriers (see Figure 2, step S11).

Furthermore, the method for calculating the electromagnetic wave absorption of the candidate material from the imaginary part of the dielectric function is not particularly limited, and any method can be used. For example, the calculation can be performed in the same manner as in the case of calculating the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is hypothetically doped with carriers (see FIG. 2 , step S12).
(Selection process: S6)
Next, a selection step can be performed. In the selection step, non-conductive substances whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation step is equal to or less than a threshold can be selected from the candidate substances. The method for selecting non-conductive substances whose electromagnetic wave absorption is equal to or less than a threshold is not particularly limited, but for example, the calculation can be performed in the same manner as when selecting candidate substances in the candidate substance selection step described above (see FIG. 1 , step S4).

In the selection process, non-conductive materials whose calculated electromagnetic wave absorption is below the threshold value δ can be recorded as preferred plasmonic materials. At this time, for example, the crystal structure of the selected non-conductive material, its dielectric function when virtually doped with carriers, and its electromagnetic wave absorption can also be output and recorded.

On the other hand, if the electromagnetic wave absorption of the candidate substance subjected to the selection process exceeds the threshold value δ, the process can return to the prediction process (Figure 1, step S3) and repeat the prediction process, candidate substance selection process, electromagnetic wave absorption calculation process, and selection process (Figure 1, steps S3 to S6).

Then, if the above prediction process, candidate material selection process, electromagnetic wave absorption calculation process, and selection process (steps S3 to S6) have been performed for all M-N substances, the search for plasmonic materials ends. On the other hand, if the above steps S3 to S6 have not been performed for all M-N substances, the process returns to step S3 and the subsequent steps can be repeated (Figure 1, steps S3 to S6).

In the plasmonic material search method of this embodiment, by performing the above-mentioned predictive electromagnetic wave absorption calculation process, prediction model generation process, prediction process, candidate substance selection process, electromagnetic wave absorption calculation process, and selection process (steps S1 to S6), it becomes possible to search for plasmonic materials from a large number of non-conductive candidate substances in a short period of time. Therefore, according to this embodiment, it is possible to efficiently search for plasmonic materials whose parent substance is a non-conductive substance.

Furthermore, in the plasmonic material exploration method of this embodiment, as described above, the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is virtually doped with carriers is calculated from the imaginary part of the dielectric function when a non-conductive material obtained by first-principles calculation using a hybrid functional is virtually doped with carriers ( FIG. 2 , steps S11 and S12), thereby making it possible to search for plasmonic materials whose parent material is a non-conductive material with high accuracy from among a large number of candidate materials.
(2) Second Embodiment Hereinafter, a plasmonic material searching method according to this embodiment will be described with reference to a flowchart 300 in FIG.

Figure 3 is a flowchart of the plasmonic material exploration method according to the second embodiment.

In the plasmonic material exploration method according to the second embodiment, explanations of parts common to the first embodiment will be omitted. In the second embodiment, the electromagnetic wave absorption calculation step (S1) can include a first electromagnetic wave absorption calculation step and a second electromagnetic wave absorption calculation step.

In the plasmonic material exploration method according to the second embodiment, the prediction model generation step (S2) can include a first prediction model generation step and a second prediction model generation step.
(First predictive electromagnetic wave absorption calculation step: S21)
In the first electromagnetic wave absorption calculation step of the electromagnetic wave absorption calculation step, the electromagnetic wave absorption when a non-conductive material in the third non-conductive material group is virtually doped with carriers can be calculated using a generalized gradient approximation ( FIG. 3 , step S21). The non-conductive materials in the third non-conductive material group can be L non-conductive materials among the M non-conductive materials that are search candidates. L represents the number required for model generation in the first prediction model generation step described below. Furthermore, L is greater than N and represents an integer equal to or greater than 2, and the N non-conductive materials in the first non-conductive material group are included in the third non-conductive material group.

The generalized gradient approximation is not particularly limited, and for example, the PBE functional (exchange-correlation functional) can be used.

In calculating the electromagnetic wave absorption when a non-conductive material of the third non-conductive material group is virtually doped with carriers, the imaginary part of the dielectric function when a non-conductive material of the third non-conductive material group is virtually doped with carriers can be calculated by first-principles calculation using the generalized gradient approximation instead of the hybrid functional described in the first embodiment. Then, from the imaginary part of the dielectric function, the electromagnetic wave absorption when a non-conductive material of the third non-conductive material group is virtually doped with carriers can be calculated (see FIG. 2 , steps S11 and S12).
(Second predictive electromagnetic wave absorption calculation step: S22)
In the second predicted electromagnetic wave absorption calculation step of the predicted electromagnetic wave absorption calculation step, a hybrid functional can be used to calculate the electromagnetic wave absorption when a non-conductive material of the first non-conductive material group, which is part of a non-conductive material of the third non-conductive material group, is virtually doped with carriers (FIG. 3, step S22).

As in the first embodiment, the non-conductive materials in the first group of non-conductive materials correspond to the N non-conductive materials obtained from the M non-conductive materials described above, and are part of the non-conductive materials that make up the third group of non-conductive materials.

The hybrid functional is not particularly limited, and for example, the HSE06 functional can be used.

In the second predictive electromagnetic wave absorption calculation step, the dielectric function when a non-conductive material in the first non-conductive material group is virtually doped with carriers can be calculated by first-principles calculation using a hybrid functional.

Then, from the imaginary part of the dielectric function, the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is virtually doped with carriers can be calculated.

In other words, in the second electromagnetic wave absorption calculation step for prediction, the calculation of the electromagnetic wave absorption when a non-conductive material from the first non-conductive material group is virtually doped with carriers can be calculated from the imaginary part of the dielectric function when a non-conductive material from the first non-conductive material group is virtually doped with carriers, as obtained by first-principles calculations using hybrid functionals, as in the first embodiment (see Figure 2, steps S11 and S12).

In the plasmonic material exploration method according to the second embodiment, the prediction model generation step can include a first prediction model generation step and a second prediction model generation step.
(First prediction model generation step: S23)
In the first prediction model generation step of the prediction model generation process, a first prediction model can be generated in which information about the non-conductive materials in the third non-conductive material group is used as an explanatory variable and the electromagnetic wave absorption calculated in the first prediction electromagnetic wave absorption calculation step is used as a target variable.

The information on the non-conductive materials in the third non-conductive material group used to generate the first prediction model is not particularly limited, and for example, a weighted average value of certain physical property values of each element contained in the non-conductive materials in the third non-conductive material group can be used, as in the first embodiment. The method for generating the first prediction model is also not particularly limited, and for example, a neural network or Gaussian process regression can be used, as in the first embodiment. In particular, it is preferable to generate the first prediction model using a neural network in the first prediction model generation step, since this allows for generation of a prediction model with particularly high accuracy.
(Second prediction model generation step: S24)
In the second prediction model generation step of the prediction electromagnetic wave absorption calculation step, the first prediction model can be transferred to the second prediction model by transfer learning using information on the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated in the second prediction electromagnetic wave absorption calculation step (Figure 3, step S22).

The non-conductive materials in the first group of non-conductive materials correspond to the N non-conductive materials described above. Furthermore, the information on the non-conductive materials used to generate the second prediction model is not particularly limited; for example, as in the first embodiment, a weighted average value of certain physical property values of each element contained in the non-conductive materials in the first group of non-conductive materials can be used.

Here, transfer learning is a general term for a technique for generating highly accurate models in categories with little data by transferring a predictive model from a category where there is a large amount of data and it is possible to generate a highly accurate predictive model to a category where there is little data and it is difficult to generate a highly accurate predictive model.

In this embodiment, a first prediction model generated using, for example, a PBE functional as a generalized gradient approximation can be transferred to create a second prediction model generated using a hybrid functional. The dielectric function calculated using the PBE functional does not closely match the measured value, but the calculation time is several tenths to several tens of times shorter than that of the hybrid functional, making it possible to generate a sufficient amount of data in a short period of time to create a highly accurate prediction model.

For example, if the first prediction model is a neural network, the transfer method involves transferring a trained neural network model with information about the non-conductive material as the explanatory variable and the electromagnetic wave absorption when the non-conductive material is virtually doped with carriers, calculated using a PBE functional, as the objective variable, to the second prediction model generated using the hybrid functional described above.

Specifically, as shown in Figure 4, in the neural network 10, the parameters of the hidden layer 11 (number of layers, number of nodes, weights) are fixed, and a predictor (not shown) is added that uses as input the values output from the final hidden layer 12. This predictor can use, for example, linear regression, decision tree regression, Lasso regression, Ridge regression, Elastic-Net regression, gradient boosting regression, or random forest regression. The electromagnetic wave absorption when a non-conductive material is virtually doped with carriers, calculated using a hybrid functional, can be used to train the predictor.

Furthermore, if the first prediction model is Gaussian process regression, it is transferred to the second prediction model using co-kriging and trained using electromagnetic wave absorption calculated using a hybrid functional.

Using the prediction model (second prediction model) obtained in this way, the prediction process (Figure 1, step S3) is then carried out, as in the first embodiment, and the prediction process, candidate substance selection process, electromagnetic wave absorption calculation process, and selection process are executed, and these processes can be repeated as necessary (see Figure 1, steps S3 to S6).

In the plasmonic material discovery method according to the second embodiment, by creating a prediction model by transfer learning as described above, a prediction model that can be used for the discovery of plasmonic materials can be generated from a small number of non-conductive substances. Therefore, the plasmonic material discovery method according to this embodiment can discover plasmonic materials whose parent substance is a non-conductive substance in a shorter period of time.
[Plasmonic material exploration device]
The plasmonic material searching apparatus of this embodiment can have the following predictive electromagnetic wave absorption calculator, predictive model generator, predictor, candidate substance selector, electromagnetic wave absorption calculator, and selector.

The predictive electromagnetic wave absorption calculation unit can use first-principles calculations to calculate the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is hypothetically doped with carriers.

The prediction model generation unit can generate a prediction model using information about the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated by the prediction electromagnetic wave absorption calculation unit when the non-conductive materials in the first non-conductive material group are virtually doped with carriers.

The prediction unit can predict the electromagnetic wave absorption when a non-conductive material in the second non-conductive material group is virtually doped with carriers based on the prediction model.

The candidate material selection unit can select as candidate materials non-conductive materials from the second group of non-conductive materials whose electromagnetic wave absorption predicted by the prediction unit is below a preset threshold.

The electromagnetic wave absorption calculation unit can use hybrid functionals to calculate the electromagnetic wave absorption when a candidate material is virtually doped with carriers.

The selection unit can select, from among the candidate materials, non-conductive materials whose electromagnetic wave absorption calculated by the electromagnetic wave absorption calculation unit is below the threshold.

As shown in the hardware configuration diagram in Figure 5, the plasmonic material exploration device 50 of this embodiment is composed of, for example, an information processing device (computer) and can be physically configured as a computer system including a CPU (Central Processing Unit: Processor) 51, which is an arithmetic processing unit, a RAM (Random Access Memory) 52 and a ROM (Read Only Memory) 53, which are main storage devices, an auxiliary storage device 54, an input/output interface 55, and a display device 56, which is an output device. These are interconnected by a bus 57. The auxiliary storage device 54 and the display device 56 may also be provided externally.

The CPU 51 controls the overall operation of the plasmonic material exploration device 50 and performs various information processing. The CPU 51 executes, for example, the plasmonic material exploration method or a program (plasmonic material exploration program) stored in the ROM 53 or the auxiliary storage device 54, to calculate the dielectric function and electromagnetic wave absorption, generate a prediction model, and predict electromagnetic wave absorption using the prediction model.

RAM 52 is used as a work area for CPU 51 and may include non-volatile RAM for storing key control parameters and information.

ROM 53 can store programs (plasmonic material search programs) and the like.

The auxiliary storage device 54 is a storage device such as an SSD (Solid State Drive) or HDD (Hard Disk Drive), and can store various data, files, etc. necessary for the operation of the plasmonic materials exploration device. Specifically, it can store data on the crystal structure of non-conductive materials, for example.

The input/output interface 55 includes both a user interface such as a touch panel, keyboard, display screen, and operation buttons, and a communication interface that imports information from external data recording servers and outputs analysis information to other electronic devices.

The display device 56 is a monitor display or the like. The display device 56 displays an analysis screen, and the screen is updated in response to input/output operations via the input/output interface 55.

The functions of the plasmonic material exploration device 50 shown in Figure 5 can be realized by loading a program (plasmonic material exploration program) from a main storage device such as RAM 52 or ROM 53 or an auxiliary storage device 54, and executing it with the CPU 51, thereby reading and writing data from RAM 52, etc., and operating the input/output interface 55 and display device 56.

Note that the plasmonic material exploration device 50 can also be configured so that each of the components described below is configured with an individual CPU and associated devices, with each component connected by a cable or other means capable of transferring data.

Figure 6 shows a functional block diagram of the plasmonic material exploration device 50 of this embodiment.

As shown in FIG. 6 , the plasmonic material exploration device 50 can have a reception unit 61, a processing unit 62, and an output unit 63. These units are realized by software and hardware working together in an information processing device such as a personal computer equipped with a CPU, storage device, various interfaces, etc., which the plasmonic material exploration device 50 has, by the CPU executing a pre-stored program, such as the plasmonic material exploration method described above, or the like.

The configuration of each part will be explained below.
(A) Reception Unit The reception unit 61 receives input of commands and data from the user related to the processing executed by the processing device 62. Examples of the reception unit 61 include a keyboard or mouse operated by the user to input commands, a communication device for inputting data via a network, and a reading device for inputting data from various storage media such as a CD-ROM or DVD-ROM.
(B) Processing Device The processing device 62 can have a predictive electromagnetic wave absorption calculation unit 621, a prediction model generation unit 622, a prediction unit 623, a candidate substance selection unit 624, an electromagnetic wave absorption calculation unit 625, and a selection unit 626. The processing device can also have any other components as necessary.
(B-1) Prediction Electromagnetic Wave Absorption Calculation Unit The prediction electromagnetic wave absorption calculation unit 621 can calculate, by first-principles calculation, the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is virtually doped with carriers. That is, the prediction electromagnetic wave absorption calculation step described above can be performed.

The prediction electromagnetic wave absorption calculation unit may also be configured to include a first calculation unit and a second calculation unit.

In this case, the first calculation unit can calculate the dielectric function when a non-conductive material in the first non-conductive material group is virtually doped with carriers, through first-principles calculations using hybrid functionals. The second calculation unit can calculate the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is virtually doped with carriers, from the imaginary part of the dielectric function calculated by the first calculation unit.

The electromagnetic wave absorption prediction calculator may also be configured to include a first electromagnetic wave absorption prediction calculator and a second electromagnetic wave absorption prediction calculator.

In this case, the first predictive electromagnetic wave absorption calculation unit can use the generalized gradient approximation to calculate the electromagnetic wave absorption when a non-conductive material in the third non-conductive material group is virtually doped with carriers.

In addition, the second predictive electromagnetic wave absorption calculation unit can use a hybrid functional to calculate the electromagnetic wave absorption when a non-conductive material from the first non-conductive material group, which is part of a non-conductive material from the third non-conductive material group, is virtually doped with carriers.

The second predictive electromagnetic wave absorption calculation unit can calculate the dielectric function when a non-conductive material in the first non-conductive material group is virtually doped with carriers by first-principles calculations using hybrid functionals.

Then, from the imaginary part of the dielectric function, it is possible to calculate the electromagnetic wave absorption when a non-conductive material of the first non-conductive material group is virtually doped with carriers.
(B-2) Prediction Model Generator The prediction model generator 622 can generate a prediction model using information on the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated by the prediction electromagnetic wave absorption calculator when the non-conductive materials in the first non-conductive material group are virtually doped with carriers. In other words, the prediction model generator 622 can perform the prediction model generation process described above.

In addition, if the prediction electromagnetic wave absorption calculation unit has a first prediction electromagnetic wave absorption calculation unit and a second prediction electromagnetic wave absorption calculation unit, the prediction model generation unit may also have a first prediction model generation unit and a second prediction model generation unit.

The first prediction model generation unit can generate a first prediction model using information about the non-conductive materials in the third non-conductive material group as an explanatory variable and the electromagnetic wave absorption calculated by the first prediction electromagnetic wave absorption calculation unit as a target variable.

The second prediction model generation unit can transfer the first prediction model to the second prediction model by transfer learning using information on the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated by the second prediction electromagnetic wave absorption calculation unit. In this case, the prediction unit (described later) can use the second prediction model as a prediction model.
(B-3) Prediction Unit The prediction unit 623 can predict the electromagnetic wave absorption when a non-conductive material of the second non-conductive material group is virtually doped with carriers, based on the prediction model generated by the prediction model generation unit 622. In other words, the prediction step described above can be performed.
(B-4) Candidate substance selection unit The candidate substance selection unit 624 can select, from the non-conductive substances in the second non-conductive substance group, a non-conductive substance whose electromagnetic wave absorption predicted by the prediction unit is equal to or less than a preset threshold, as a candidate substance. In other words, the candidate substance selection step described above can be performed.
(B-5) Electromagnetic Wave Absorption Calculation Unit The electromagnetic wave absorption calculation unit 625 can calculate the electromagnetic wave absorption when a candidate substance is virtually doped with carriers using a hybrid functional. That is, the electromagnetic wave absorption calculation step described above can be performed.
(B-6) Selection Unit The selection unit 626 can select, from among the candidate materials, non-conductive materials whose electromagnetic wave absorption calculated by the electromagnetic wave absorption calculation unit is equal to or less than a threshold value. That is, the above-mentioned selection step can be performed.
(C) Output Unit The output unit 63 may have, for example, a display. The search results obtained by the selection unit 626 can be output to the output unit 63. There are no particular limitations on the content of the search results to be output. For example, for the non-conductive substance selected by the selection unit 626, the crystal structure of the non-conductive substance, the dielectric function when virtually doped with carriers, and the electromagnetic wave absorption can be output and displayed on the output unit 63.

The output unit 63 can also be configured to simply record data on the selected non-conductive materials, etc., in various storage devices, without displaying the search results on a display or the like.

The plasmonic material exploration device of this embodiment described above makes it possible to comprehensively explore plasmonic materials whose parent material is a non-conductive substance in a short period of time.

Furthermore, by creating a prediction model by transfer learning as described above, the plasmonic material exploration apparatus of this embodiment can generate a prediction model that can be used to explore plasmonic materials from a small number of non-conductive substances. In this case, the plasmonic material exploration apparatus of this embodiment can explore plasmonic materials whose parent substance is a non-conductive substance in a shorter period of time.
[program]
Next, the program of this embodiment will be described.

The program of this embodiment relates to a program for searching for plasmonic materials, and can cause a computer to function as a predictive electromagnetic wave absorption calculation unit, a predictive model generation unit, a prediction unit, a candidate substance selection unit, an electromagnetic wave absorption calculation unit, and a selection unit.
(Prediction electromagnetic wave absorption calculation unit)
The electromagnetic wave absorption calculation unit for prediction can calculate the electromagnetic wave absorption when a non-conductive material of the first non-conductive material group is hypothetically doped with carriers by first-principles calculation, i.e., can perform the above-mentioned electromagnetic wave absorption calculation step for prediction.

The prediction electromagnetic wave absorption calculation unit may also be configured to include a first calculation unit and a second calculation unit.

In this case, the first calculation unit can calculate the dielectric function when a non-conductive material in the first non-conductive material group is virtually doped with carriers, through first-principles calculations using hybrid functionals. The second calculation unit can calculate the electromagnetic wave absorption when a non-conductive material in the first non-conductive material group is virtually doped with carriers, from the imaginary part of the dielectric function calculated by the first calculation unit.

The electromagnetic wave absorption prediction calculator may also be configured to include a first electromagnetic wave absorption prediction calculator and a second electromagnetic wave absorption prediction calculator.

In this case, the first predictive electromagnetic wave absorption calculation unit can use the generalized gradient approximation to calculate the electromagnetic wave absorption when a non-conductive material in the third non-conductive material group is virtually doped with carriers.

In addition, the second predictive electromagnetic wave absorption calculation unit can use a hybrid functional to calculate the electromagnetic wave absorption when a non-conductive material from the first non-conductive material group, which is part of a non-conductive material from the third non-conductive material group, is virtually doped with carriers.

The second predictive electromagnetic wave absorption calculation unit can calculate the dielectric function when a non-conductive material in the first non-conductive material group is virtually doped with carriers by first-principles calculations using hybrid functionals.

Then, from the imaginary part of the dielectric function, it is possible to calculate the electromagnetic wave absorption when a non-conductive material of the first non-conductive material group is virtually doped with carriers.
(Prediction model generation unit)
The prediction model generating unit can generate a prediction model using information on the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated by the prediction electromagnetic wave absorption calculating unit when the non-conductive materials in the first non-conductive material group are virtually doped with carriers, i.e., can perform the prediction model generating step described above.

In addition, if the prediction electromagnetic wave absorption calculation unit has a first prediction electromagnetic wave absorption calculation unit and a second prediction electromagnetic wave absorption calculation unit, the prediction model generation unit may also have a first prediction model generation unit and a second prediction model generation unit.

The first prediction model generation unit can generate a first prediction model using information about the non-conductive materials in the third non-conductive material group as an explanatory variable and the electromagnetic wave absorption calculated by the first prediction electromagnetic wave absorption calculation unit as a target variable.

The second prediction model generation unit can transfer the first prediction model to the second prediction model by transfer learning using information on the non-conductive materials in the first non-conductive material group and the electromagnetic wave absorption calculated by the second prediction electromagnetic wave absorption calculation unit. In this case, the prediction unit (described later) can use the second prediction model as a prediction model.
(Prediction Department)
The prediction unit can predict the electromagnetic wave absorption when a non-conductive material of the second non-conductive material group is virtually doped with carriers based on the prediction model, i.e., can perform the prediction step described above.
(Candidate substance selection section)
The candidate material selection unit can select, as a candidate material, a non-conductive material from the second non-conductive material group whose electromagnetic wave absorption predicted by the prediction unit is equal to or less than a preset threshold value, i.e., can perform the candidate material selection step described above.
(Electromagnetic wave absorption calculation section)
The electromagnetic wave absorption calculation unit can calculate the electromagnetic wave absorption when the candidate material is virtually doped with carriers using a hybrid functional, i.e., can perform the electromagnetic wave absorption calculation step described above.
(Selection section)
The selection unit can select, from among the candidate materials, non-conductive materials whose electromagnetic wave absorption calculated by the electromagnetic wave absorption calculation unit is equal to or less than a threshold value, i.e., can perform the above-described selection step.

The program of this embodiment can be stored in various storage media, such as the RAM or ROM of the main memory or auxiliary memory of the plasmonic material exploration device described above. Then, by loading the program and executing it with the CPU, data can be read and written to the RAM, etc., and the input/output interface and display device can be operated and executed. Therefore, a description of the matters already described for the plasmonic material exploration device will be omitted.

The program of this embodiment described above may be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network. The program of this embodiment may also be configured to be provided and distributed via a network such as the Internet.

The program of this embodiment may be distributed in a state stored on a recording medium such as an optical disc such as a CD-ROM or a semiconductor memory.

The program of this embodiment described above makes it possible to comprehensively search for plasmonic materials whose parent material is a non-conductive substance in a short period of time.

Furthermore, by creating a predictive model using transfer learning as described above, the program of this embodiment can also generate a predictive model that can be used to search for plasmonic materials from a small number of non-conductive substances. In this case, the program of this embodiment can search for plasmonic materials whose parent substance is a non-conductive substance in a shorter period of time.

Specific examples are provided below, but the present invention is not limited to these examples.

Below, plasmonic materials were searched for using the plasmonic material search device 50 and the plasmonic material search method described above. As candidates for parent materials for plasmonic materials, a total of 2,329 binary, ternary, and quaternary substances registered in the materials database "Materials Project" as substances with a band gap greater than 0 were prepared. Note that these 2,329 substances correspond to the M non-conductive substances described above.

The target wavelength was set to visible light, and the integral range of electromagnetic wave absorption was set to 380 nm to 780 nm. The weighted average, weighted variance, weighted sum, maximum value, and minimum value of the physical property values of each element contained in the composition were used as information on the non-conductive material to create the prediction model. For example, in the case of a binary material A _wA B _wB , the physical property value f is expressed as follows using the physical property values f _A and f _B of elements A and B:
Weighted average: f _ave = (wAf _A + wBf _B )/(wA + wB)
Weighted variance: f _var = [wA (f _A - _{f ave} ) ² + wB (f _B - _{f ave} ) ² ] / (wA + wB)
Weighted sum: f _sum = wAf _A + wBf _B
Maximum value: f _max = max(f _A , f _B )
Minimum value: f _min =min(f _A , f _B )
The physical property value f is the period, number of protons, atomic number, atomic radius, atomic radius according to Rahm, atomic volume, atomic mass, atomic volume according to the Inorganic Crystal Structure Database (ICSD), lattice constant, van der Waals (vdW) radius, vdW radius according to Alvarez, vdW radius according to Batsanov, vdW radius according to Bondi, vdW radius according to Dreiding FF, MM3 FF vdW radius, Rowland and Taylor vdW radius, Truhlar vdW radius, UFF vdW radius, Bragg covalent radius, Cerdero covalent radius, Pyykko single bond distance, Pyykko double bond distance, Pyykko triple bond distance, Slater covalent radius, vdW coefficient C6, Gould and Bucko vdW coefficient C6, Density at 295 K, Proton affinity, Dipole polarizability, Electron affinity, Electronegativity, Allen scale electronegativity, Ghosh scale electronegativity, Mulliken scale electronegativity The following data were used: viscosities, DFT band gap, DFT energy, DFT BCC lattice constant, DFT FCC lattice constant, DFT magnetic moment, DFT volume, HHI coefficient, specific heat at 20 ° C, gas phase basicity, first ionization energy, heat of fusion, heat of formation, molar specific heat capacity, specific heat capacity, heat of vaporization, thermal expansion coefficient, boiling point, Brinell hardness, compressibility, melting point, single bond distance of metallic bond radius, closest distance of metallic bond radius, thermal conductivity at 25 ° C, speed of sound, Vickers hardness, polarizability, Young's modulus, Poisson's ratio, molar volume, total number of unoccupied electrons, total number of valence electrons, number of unoccupied d electrons, number of d valence electrons, number of unoccupied f electrons, number of f valence electrons, number of unoccupied p electrons, number of p electrons, number of unoccupied s electrons, and number of s valence electrons. The Python library XenonPy was used to calculate the information on non-conductive materials.

Transfer learning using neural networks was selected as a method for creating a predictive model to predict electromagnetic wave absorption when non-conductive materials are virtually doped with carriers.

Specifically, first, for 1,000 of the M non-conductive materials described above, the electromagnetic wave absorption when virtually doped with carriers was calculated using first-principles calculations using the generalized gradient approximation (first electromagnetic wave absorption calculation step for prediction, first electromagnetic wave absorption calculation unit for prediction). Note that these 1,000 materials correspond to the L non-conductive materials that make up the previously described third non-conductive material group. Virtual carrier doping was performed by adding one electron to the unit cell of each material.

The calculations were performed using the Vienna Ab initio Simulation Package (VASP), a plane-wave based first-principles calculation software, with a PBE functional (exchange-correlation functional) in the DFT category. A PAW (projector augmented wave) potential was used, with a planar cutoff of 520 eV and a k-point density of 0.4 ^Å .

Using these results, a first prediction model of electromagnetic wave absorption using generalized gradient approximation was created (first prediction model generation process, first prediction model generation unit).

For N (163) non-conductive materials in the first non-conductive material group out of the L (1,000) materials that make up the third non-conductive material group, the electromagnetic wave absorption when virtually doped with carriers was calculated using a hybrid functional (second prediction electromagnetic wave absorption calculation step, second prediction electromagnetic wave absorption calculation unit).

The calculation was performed using VASP, a plane wave basis first-principles calculation software, in the category of DFT, with the HSE06 functional. The PAW potential was used, with a plane cutoff of 520 eV and a k-point density of 0.6 ^Å . This calculation is an example of a first-principles calculation using the hybrid functional described above.

By transfer learning, the first prediction model of electromagnetic wave absorption using generalized gradient approximation was transferred to a second prediction model of electromagnetic wave absorption using hybrid functionals, and the model was trained using data on electromagnetic wave absorption using hybrid functionals for 163 non-conductive materials in the first non-conductive material group (second prediction model generation process, second prediction model generation unit). The Python library XenonPy was used for transfer learning.

Using the second prediction model described above as a prediction model, the electromagnetic wave absorption of 2,166 non-conductive materials in the second non-conductive material group, obtained by excluding the N non-conductive materials that make up the first non-conductive material group from the M non-conductive materials, was predicted when virtually doped with carriers (prediction process, prediction unit). Note that the 2,166 materials obtained by excluding the N non-conductive materials that make up the first non-conductive material group from the M non-conductive materials correspond to the M-N non-conductive materials obtained by excluding the N non-conductive materials (163 materials) from the M non-conductive materials (2,329 materials) described above.

Among the non-conductive materials in the second non-conductive material group, non-conductive materials whose electromagnetic wave absorption predicted in the prediction step was equal to or less than a preset threshold were selected as candidate materials (candidate material selection step, candidate material selection unit). The threshold used was the electromagnetic wave absorption of cesium tungstate ( _Cs0.33WO3 ), a plasmonic material whose known parent material is a non-conductive material; specifically, the threshold δ was set to 3.5. There were 287 materials whose predicted values of electromagnetic wave absorption by the hybrid functional in the prediction step were equal to or less than _the threshold δ.

For the above 287 materials, the electromagnetic wave absorption when virtually doped with carriers was calculated using hybrid functionals (electromagnetic wave absorption calculation process, electromagnetic wave absorption calculation section).

The calculation was performed using VASP, a plane wave basis first-principles calculation software, in the category of DFT, using the HSE06 functional. In addition, a PAW potential was used, with a plane cutoff of 520 eV and a k-point density of 0.4 ^Å . This calculation is an example of a first-principles calculation using a hybrid functional in the electromagnetic wave absorption calculation section.

Among the candidate substances, non-conductive substances whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation step was below the threshold were selected (selection step, selection unit). The threshold δ was set to δ = 3.5. There were 17 substances whose electromagnetic wave absorption by the hybrid functional was below the threshold. These 17 substances can be said to be suitable materials as plasmonic materials whose parent substance is a non-conductive substance. Examples of plasmonic materials whose parent substance is a non-conductive substance discovered in this example include Mg( _SbO3 ) ₂ , _SrZnO2 , and _SrSnO3 .

This example enabled us to comprehensively search and discover, in a short period of time, 2,329 substances that could be used as plasmonic materials in the visible light region by doping them with carriers. Furthermore, this example confirmed that the development period can be shortened because it allows us to comprehensively search for plasmonic materials whose parent substance is a non-conductive substance in a short period of time.

50 Plasmonic material exploration device 621 Prediction electromagnetic wave absorption calculation unit 622 Prediction model generation unit 623 Prediction unit 624 Candidate substance selection unit 625 Electromagnetic wave absorption calculation unit 626 Selection unit

Claims (6)

a predictive electromagnetic wave absorption calculation step of calculating, by first-principles calculation, electromagnetic wave absorption when a unit lattice of a non-conductive material of the first non-conductive material group is virtually doped with carriers;
a prediction model generation step of generating a prediction model using information on the non-conductive material of the first non-conductive material group and the electromagnetic wave absorption calculated in the prediction electromagnetic wave absorption calculation step when the non-conductive material of the first non-conductive material group is virtually doped with carriers;
a prediction step of predicting electromagnetic wave absorption when a non-conductive material of the second non-conductive material group is virtually doped with carriers based on the prediction model;
a candidate material selection step of selecting, from the non-conductive materials of the second non-conductive material group, a non-conductive material whose electromagnetic wave absorption predicted in the prediction step is equal to or less than a preset threshold, as a candidate material;
an electromagnetic wave absorption calculation step of calculating electromagnetic wave absorption when the candidate material is virtually doped with carriers using a hybrid functional;
a selection step of selecting, from the candidate substances, a non-conductive substance whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation step is equal to or less than the threshold. In the step of calculating the electromagnetic wave absorption for prediction,
calculating a dielectric function when a non-conductive material of the first non-conductive material group is virtually doped with carriers by first-principles calculation using a hybrid functional;
The plasmonic material exploration method according to claim 1 , further comprising calculating electromagnetic wave absorption when a non-conductive material of the first non-conductive material group is virtually doped with carriers from the imaginary part of the dielectric function. The predictive electromagnetic wave absorption calculation step includes:
a first predictive electromagnetic wave absorption calculation step of calculating electromagnetic wave absorption when a non-conductive material of the third non-conductive material group is virtually doped with carriers using a generalized gradient approximation;
a second predictive electromagnetic wave absorption calculation step of calculating, using a hybrid functional, electromagnetic wave absorption when a non-conductive material of the first non-conductive material group, which is a part of a non-conductive material of the third non-conductive material group, is virtually doped with carriers,
The prediction model generation step includes:
a first prediction model generating step of generating a first prediction model using information on the non-conductive materials of the third non-conductive material group as an explanatory variable and the electromagnetic wave absorption calculated in the first prediction electromagnetic wave absorption calculating step as a response variable;
a second prediction model generation step of transferring the first prediction model to a second prediction model by transfer learning using information on the non-conductive materials of the first non-conductive material group and the electromagnetic wave absorption calculated in the second prediction electromagnetic wave absorption calculation step,
The plasmonic material exploration method according to claim 1 , wherein the prediction step uses the second prediction model as the prediction model. The plasmonic material exploration method according to claim 3, wherein the first prediction model generation step uses a neural network to generate the first prediction model. In the second predictive electromagnetic wave absorption calculation step,
calculating a dielectric function when a non-conductive material of the first non-conductive material group is virtually doped with carriers by first-principles calculation using a hybrid functional;
5. The plasmonic material exploration method according to claim 3, further comprising calculating electromagnetic wave absorption when a non-conductive material of the first non-conductive material group is virtually doped with carriers from the imaginary part of the dielectric function. a prediction electromagnetic wave absorption calculation unit that calculates electromagnetic wave absorption when a unit lattice of a non-conductive material of the first non-conductive material group is virtually doped with carriers by first-principles calculation;
a prediction model generating unit that generates a prediction model using information on the non-conductive material of the first non-conductive material group and the electromagnetic wave absorption calculated by the prediction electromagnetic wave absorption calculating unit when the non-conductive material of the first non-conductive material group is virtually doped with carriers;
a prediction unit that predicts electromagnetic wave absorption when a non-conductive material of the second non-conductive material group is virtually doped with carriers based on the prediction model;
a candidate material selection unit that selects, from the non-conductive materials of the second non-conductive material group, a non-conductive material whose electromagnetic wave absorption predicted by the prediction unit is equal to or less than a preset threshold, as a candidate material;
an electromagnetic wave absorption calculation unit that calculates electromagnetic wave absorption when the candidate material is virtually doped with carriers using a hybrid functional;
a selection unit that selects, from the candidate materials, a non-conductive material whose electromagnetic wave absorption calculated by the electromagnetic wave absorption calculation unit is equal to or less than the threshold.