Plasmonic material search method and plasmonic material search device

Abstract

To efficiently search a plasmonic material.SOLUTION: A plasmonic material search method includes the steps of: calculating electromagnetic wave absorption of a conductive substance using hybrid functional; generating a prediction model using information on the conductive substance as an explanatory variable and using the electromagnetic wave absorption as an objective variable; predicting electromagnetic wave absorption of an arbitrary conductive substance on the basis of the prediction model; selecting the conductive substance of which the predicted electromagnetic wave absorption is a predetermined threshold or less; calculating the electromagnetic wave absorption of the selected conductive substance using the hybrid functional; and selecting the conductive substance of which the calculated electromagnetic wave absorption is the predetermined threshold or less.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for searching for plasmonic materials and an apparatus for searching for plasmonic materials.

Background Art

[0002] Plasmonic materials have been used in various fields such as stained glass in the past, and in recent years, in biochemical sensors, detection of diseased sites such as cancer, near-infrared shielding materials, and metamaterials. Since plasmonic materials utilize plasmon resonance as their characteristic, they are preferably conductive materials such as metals and alloys. Also, how much the electric field is enhanced with respect to incident light due to plasmon resonance is an important characteristic of plasmonic materials.

[0003] As such plasmonic materials, metals such as gold and silver, and semiconductors doped with carriers such as antimony-doped tin oxide and indium tin oxide are used. However, these plasmonic materials have problems such as high cost because they contain precious metals and rare metals, and problems with weather resistance. Therefore, discovery of new plasmonic materials is desired.

[0004] As a method for searching for new plasmonic materials, there is a method of measuring the dielectric function of a substance and determining a plasmonic material from the dielectric function. In order to increase the electric field enhancement due to plasmon resonance, a material with less energy loss in the substance, that is, a material with small absorption of irradiated electromagnetic waves, is preferable. The energy loss in the substance is described by the imaginary part of the dielectric function of the substance. Therefore, it is possible to search for plasmonic materials by measuring the dielectric function of candidate substances for plasmonic materials. However, experimentally measuring the dielectric function by a method such as spectroscopic ellipsometry for all candidate substances requires a great deal of labor.

[0005] As another method for searching for novel plasmonic materials, there is a method of calculating the dielectric function of a substance by 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 by first-principles calculations using a hybrid functional. However, first-principles calculations using a hybrid functional have a very high computational cost, and it is substantially impossible to carry out this method on a realistic time scale for all candidate substances.

Prior Art Documents

Non-Patent Documents

[0006]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] As methods for searching for plasmonic materials, there are several methods for obtaining the dielectric function of a substance. However, since the dielectric function must be obtained for an extremely large number of substances in any method, it is difficult to carry out both experimentally and computationally.

[0008] An object of the present invention is to efficiently search for plasmonic materials.

Means for Solving the Problems

[0009] To achieve the above object, the plasmonic material search method of the present invention includes The computer uses a predicted electromagnetic wave absorption calculation step of calculating the electromagnetic wave absorption of a conductive substance in a first conductive substance group by first-principles calculations, and information on the conductive substances in the first conductive substance group as the explanatory variable and the electromagnetic wave absorption of the conductive substances in the first conductive substance group calculated in the predicted electromagnetic wave absorption calculation step as the objective variable to create a neural network A prediction model generation step of generating a prediction model using the same, a prediction step of predicting the electromagnetic wave absorption of the conductive materials in the second conductive material group based on the prediction model, and among the conductive materials in the second conductive material group, a candidate material selection step of selecting, as candidate materials, the conductive materials whose electromagnetic wave absorption predicted in the prediction step is equal to or less than a preset threshold value, an electromagnetic wave absorption calculation step of calculating the electromagnetic wave absorption of the candidate materials using a hybrid function, and a selection step of selecting, from among the candidate materials, the conductive materials whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation step is equal to or less than the threshold value.

Advantages of the Invention

[0010] According to one aspect of the present invention, plasmonic materials can be efficiently explored.

Brief Description of the Drawings

[0011]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Modes for Carrying Out the Invention

[0012] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings.

[0013] <Plasmonic Material Exploration Method> FIG. 1 is a flowchart of a plasmonic material search method according to the first embodiment. FIG. 2 is an example of a step of calculating predicted electromagnetic wave absorption in the first embodiment. The plasmonic material search method of the first embodiment includes a step of calculating predicted electromagnetic wave absorption, a step of generating a prediction model, a prediction step, a step of selecting candidate substances, a step of calculating electromagnetic wave absorption, and a selection step.

[0014] In the first embodiment, first, a step of calculating predicted electromagnetic wave absorption is executed. In the step of calculating predicted electromagnetic wave absorption, the electromagnetic wave absorption of the conductive substances in the first conductive substance group is calculated by first-principles calculation (step S1). Here, the first-principles calculation refers to a method of calculating the motion of electrons in a substance by a computer according to the Schrödinger equation of quantum mechanics. For the first-principles calculation, for example, a general functional, a hybrid functional, or the like can be used.

[0015] In the present embodiment, crystal structures of N conductive substances are obtained from a database in which crystal structures of M conductive substances to be search candidates are stored (FIG. 1, step S1). Here, M and N indicate the numbers necessary for model creation. Also, N indicates an integer of 2 or more that is smaller than M. The N conductive substances are an example of the conductive substances in the first conductive substance group in the present embodiment.

[0016] Specifically, as shown in FIG. 2, using the obtained N crystal structures, the dielectric function ε of each conductive substance is calculated from first-principles calculation using a hybrid functional (FIG. 2, step S11). Then, from the imaginary part Im[ε] of the calculated dielectric function ε, electromagnetic wave absorption is calculated based on the following formula (1) (FIG. 2, step S12).

[0017] Electromagnetic wave absorption = ∫Im[ε]dλ (1)

[0018] Here, the electromagnetic wave absorption indicates a value obtained by integrating the imaginary part of the dielectric function with respect to the wavelength. That is, the dielectric function ε is a quantity that depends on the wavelength λ. The integration range of the wavelength can be selected according to the purpose. For example, when it is desired to use as a plasmonic material in the wavelength region of visible light, the integration range can be set to 380 nm to 780 nm.

[0019] Next, the prediction model generation step is executed. In the prediction model generation step, a prediction model is generated using the information of the conductive materials in the first conductive material group and the electromagnetic wave absorption of the conductive materials in the first conductive material group calculated in the electromagnetic wave absorption calculation step for prediction (FIG. 1, step S2). Here, the prediction model is a model for predicting the electromagnetic wave absorption of a conductive material.

[0020] The information of the conductive material used for generating the prediction model is not particularly limited. For example, the weighted average value, maximum value, minimum value, average value, radial distribution function of the crystal, CGCNN (Crystal Graph Convolutional Neural Network), etc. of certain physical property values of each element contained in the conductive material can be used.

[0021] The method for generating the prediction model is not particularly limited. For example, a prediction model is created with the information of the conductive material as the explanatory variable and the electromagnetic wave absorption of the conductive material calculated in the electromagnetic wave absorption calculation step for prediction as the target variable. For creating such a prediction model, for example, a neural network or Gaussian process regression can be used.

[0022] Next, the prediction step is executed. In the prediction step, the electromagnetic wave absorption of the conductive materials in the second conductive material group is predicted based on the prediction model (FIG. 1, step S3). Here, the conductive materials in the second conductive material group correspond to the conductive materials (M - N conductive materials) obtained by removing N conductive materials from the above-mentioned M conductive materials. Specifically, the electromagnetic wave absorption of the M - N conductive materials is predicted using the prediction model generated in the prediction model generation step.

[0023] Next, a candidate substance selection step is executed. In the candidate substance selection step, among the conductive substances in the second conductive substance group, a conductive substance whose electromagnetic wave absorption predicted in the prediction step is equal to or less than a preset threshold is selected as a candidate substance (FIG. 1, step S4). Specifically, it is determined whether the electromagnetic wave absorption of the predicted M - N conductive substances is equal to or less than the threshold δ. Note that the value of the threshold δ can be appropriately changed according to conditions, but considering a preferable plasmonic material, for example, δ = 3.5 is determined.

[0024] 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 an electromagnetic wave absorption calculation step (FIG. 1, step S5) described later. 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 are repeated (FIG. 1, steps S3 - S4).

[0025] Next, an electromagnetic wave absorption calculation step is executed. In the electromagnetic wave absorption calculation step, the electromagnetic wave absorption of the candidate substance selected in the candidate substance selection step is calculated using a hybrid functional (FIG. 1, step S5). Specifically, the dielectric function of the candidate substance selected in the candidate substance selection step is calculated by first - principle calculation using a hybrid functional. Then, the electromagnetic wave absorption of the candidate substance is calculated from the imaginary part Im[ε] of the calculated dielectric function ε.

[0026] Note that the method of calculating the dielectric function of the candidate substance by first - principle calculation using a hybrid functional is arbitrary. For example, it can be calculated in the same manner as when calculating the dielectric function of the conductive substances in the first conductive substance group described above (see FIG. 2, step S11). Also, the method of calculating the electromagnetic wave absorption of the candidate substance from the imaginary part of the dielectric function is arbitrary, but for example, it can be calculated in the same manner as when calculating the electromagnetic wave absorption of the conductive substances in the first conductive substance group described above (see FIG. 2, step S12).

[0027] Next, the selection process is executed. In the selection process, among the candidate substances, a conductive substance whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation process is equal to or less than the threshold value is selected. The method of selecting a conductive substance whose electromagnetic wave absorption is equal to or less than the threshold value is arbitrary. For example, it can be calculated in the same manner as when selecting candidate substances in the above-described candidate substance selection process (see FIG. 1, step S4).

[0028] In the selection process, for a conductive substance whose calculated electromagnetic wave absorption is equal to or less than the threshold value δ, as a preferable plasmonic material, the crystal structure, dielectric function, and electromagnetic wave absorption of the conductive substance are output and recorded. On the other hand, when the calculated electromagnetic wave absorption exceeds the threshold value δ, the process returns to the prediction process (FIG. 1, step S3), and the prediction process, candidate substance selection process, electromagnetic wave absorption calculation process, and selection process are repeated (FIG. 1, steps S3 to S6).

[0029] When the above-described prediction process, candidate substance selection process, electromagnetic wave absorption calculation process, and selection process (steps S5 to S6) are performed for all of the M - N substances, the search for the plasmonic material is terminated. On the other hand, when steps S5 to S6 have not been performed for all of the M - N substances, the process returns to step S5, and the subsequent steps are repeated (FIG. 1, steps S5 to S6).

[0030] In the plasmonic material search method of the present embodiment, by executing the above-described electromagnetic wave absorption calculation process for prediction, prediction model generation process, prediction process, candidate substance selection process, electromagnetic wave absorption calculation process, and selection process (each process of steps S1 to S6), it is possible to search for a plasmonic material from among a large number of candidate substances in a short period of time. Therefore, according to the present embodiment, a plasmonic material can be efficiently searched for.

[0031] Further, in the plasmonic material search method of the present embodiment, as described above, by calculating the electromagnetic wave absorption of the conductive substances in the first conductive substance group from the imaginary part of the dielectric function of the conductive substances obtained by first-principles calculation using a hybrid functional (FIG. 2, steps S11, step S12), a plasmonic material can be searched for with high accuracy from among a large number of candidate substances.

[0032] Figure 3 is a flowchart of a plasmonic material search method according to the second embodiment. In the second embodiment, descriptions of parts common to the first embodiment are omitted. In the second embodiment, the predicted electromagnetic wave absorption calculation step includes a first predicted electromagnetic wave absorption calculation step and a second predicted electromagnetic wave absorption calculation step.

[0033] In the first predicted electromagnetic wave absorption calculation step of the predicted electromagnetic wave absorption calculation step, the electromagnetic wave absorption of the conductive materials in the first group of conductive materials is calculated using a general-purpose function. The conductive materials in the first group of conductive materials can be N out of the M conductive materials that are search candidates, similar to the first embodiment.

[0034] The general-purpose function is not particularly limited, and for example, a PBE function (exchange-correlation function) or the like can be used. The calculation of the electromagnetic wave absorption of the conductive materials in the first group of conductive materials can be calculated from the imaginary part of the dielectric function of the conductive materials in the first group of conductive materials by first-principles calculation using a general-purpose function instead of the hybrid function in the first embodiment (see FIG. 2, step S11, step S12).

[0035] In the second predicted electromagnetic wave absorption calculation step of the predicted electromagnetic wave absorption calculation step, the electromagnetic wave absorption of some of the conductive materials in the first group of conductive materials is calculated using a hybrid function (FIG. 3, step S21). Some of the conductive materials in the first group of conductive materials correspond to L conductive materials obtained from the above-mentioned N conductive materials N. Here, L represents the number required for model creation. Also, L represents an integer of 2 or more that is smaller than N.

[0036] The hybrid function is not particularly limited, and for example, an HSE06 function or the like can be used. Also, the calculation of the electromagnetic wave absorption of some of the conductive materials in the first group of conductive materials can be calculated from the imaginary part of the dielectric function of the conductive materials in the first group of conductive materials obtained by first-principles calculation using a hybrid function, similar to the first embodiment (see FIG. 2, step S11, step S12).

[0037] In the first embodiment, the prediction model generation process includes a first prediction model generation process and a second prediction model generation process. In the first prediction model generation process of the prediction model generation process, a first prediction model is generated using the information of the conductive materials in the first conductive material group as explanatory variables and the electromagnetic wave absorption calculated in the first electromagnetic wave absorption calculation process for prediction as the objective variable.

[0038] The information of the conductive materials used for generating the first prediction model is not particularly limited. For example, similar to the first embodiment, the weighted average value of certain physical property values of each element contained in the conductive materials of the first conductive material group can be used. Also, the method for generating the first prediction model is not particularly limited. For example, similar to the first embodiment, a neural network or Gaussian process regression can be used.

[0039] In the second prediction model generation process of the electromagnetic wave absorption calculation process for prediction, the first prediction model is transferred to the second prediction model by transfer learning using the information of some of the conductive materials in the first conductive material group and the electromagnetic wave absorption calculated in the second electromagnetic wave absorption calculation process for prediction (FIG. 3, step S22).

[0040] Some of the conductive materials in the first conductive material group correspond to L of the N conductive materials described above. Also, the information of the conductive materials used for generating the second prediction model is not particularly limited. For example, similar to the first embodiment, the weighted average value of certain physical property values of each element partially contained in the conductive materials of the first conductive material group can be used.

[0041] Here, transfer learning is a general term for a technique of generating a highly accurate model in a category with a small amount of data by transferring a prediction model from a category with a large amount of data where a highly accurate prediction model can be generated to a category with a small amount of data where it is difficult to generate a highly accurate prediction model.

[0042] In this embodiment, a first prediction model generated using generalized gradient approximation as a general function is transferred, and a second prediction model generated using a hybrid function is created. The dielectric function calculated by generalized gradient approximation does not match the measured values well, but since the calculation time is one-tenth to several tens of times that of the hybrid function, it is possible to create a sufficient amount of data for creating a highly accurate prediction model in a short period of time.

[0043] For example, when the first prediction model is a neural network, the method of transfer is to transfer the neural network of a learned model that uses information on the conductive material as an explanatory variable and the electromagnetic wave absorption of the conductive material calculated by generalized gradient approximation as an objective variable to the second prediction model generated using the above-described hybrid function.

[0044] Specifically, as shown in FIG. 4, in the neural network 10, a parameter (the number of layers, the number of nodes, the weight) of the hidden layer 11 is fixed, and a predictor (not shown) that takes as input the value output from the last hidden layer 12 is added. For this predictor, for example, linear regression, decision tree regression, Lasso regression, Ridge regression, Elastic-Net regression, gradient boost regression, random forest regression, etc. are used. For the learning of the predictor, the electromagnetic wave absorption of the conductive material calculated by the hybrid function is used.

[0045] When the first prediction model is a Gaussian process regression, it is transferred to the second prediction model by co-kriging and learned with the electromagnetic wave absorption calculated by the hybrid function.

[0046] Using the thus obtained prediction model (second prediction model), hereinafter, in the same manner as in the first embodiment, the process proceeds to the prediction step (FIG. 1, step S3), and the prediction step, candidate material selection step, electromagnetic wave absorption calculation step, and selection step are executed, and these steps are repeated as necessary (see FIG. 1, steps S3 to S6).

[0047] In the plasmonic material search method of the second embodiment, by creating a prediction model through transfer learning as described above, a prediction model that can be used for searching plasmonic materials can be generated from a small number of conductive substances. Therefore, according to this embodiment, plasmonic materials can be searched in a shorter period of time.

[0048] <Plasmonic Material Search Device> FIG. 5 is a schematic diagram of a plasmonic material search device according to an embodiment. In the plasmonic material search device of this embodiment, the aforementioned plasmonic material search method is implemented, and plasmonic materials can be searched. Therefore, the description of overlapping parts of matters already described may be omitted.

[0049] As shown in FIG. 5, the plasmonic material search device 20 of this embodiment includes a data storage unit 21, an electromagnetic wave absorption prediction unit 22, a candidate substance determination unit 23, an electromagnetic wave absorption calculation unit 24, and a conductive substance selection unit 25.

[0050] The following describes each part.

[0051] (Data Storage Unit) The data storage unit 21 stores data on the crystal structures of conductive substances. The data storage unit 21 includes, for example, RAM (Random Acess Memory), ROM (Read Only Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), etc. Note that the data on the crystal structures of conductive substances stored in the data storage unit 21 can be appropriately input by an input means (not shown).

[0052] (Electromagnetic Wave Absorption Prediction Unit) The electromagnetic wave absorption prediction unit 22 predicts the electromagnetic wave absorption of the conductive materials in the second conductive material group based on a prediction model generated using the information on the conductive materials in the first conductive material group and the electromagnetic wave absorption of the conductive materials in the first conductive material group calculated by first-principles calculation. Specifically, the electromagnetic wave absorption calculation step for prediction, the prediction model generation step, and the prediction step in the plasmonic material search method according to the above-described embodiment are executed (FIG. 1, steps S1 to S3).

[0053] The electromagnetic wave absorption prediction unit 22 can acquire the crystal structure of the conductive material from the data storage unit 21 as information on the conductive materials in the first conductive material group. In the electromagnetic wave absorption prediction unit 22, the electromagnetic wave absorption of the conductive materials in the first conductive material group calculated by first-principles calculation may be those stored in the storage device 222 in advance.

[0054] The electromagnetic wave absorption prediction unit 22 is, for example, a type of computer and can include a CPU (Central Processing Unit) 221, a storage device 222, and an input interface 223 for receiving signals from external devices such as a keyboard. Examples of the storage device 222 include RAM, ROM, HDD, and SSD.

[0055] As shown in FIG. 5, the electromagnetic wave absorption prediction unit 22 can be connected to the data storage unit 21 by a cable 26 so as to be able to exchange data with the data storage unit 21.

[0056] The CPU 221 can create a prediction model for predicting the electromagnetic wave absorption of the conductive material as described above from the crystal structure data acquired from the data storage unit 21 and the electromagnetic wave absorption of the conductive material (the conductive material in the first conductive material group), and perform control to store it in the storage device 222.

[0057] (Candidate substance determination unit) The candidate substance determination unit 23 determines, as candidate substances, the conductive substances in the second conductive substance group whose predicted electromagnetic wave absorption is equal to or less than a preset threshold value. Specifically, the candidate substance selection step in the plasmonic material search method according to the above-described embodiment is executed (FIG. 1, step S4).

[0058] The candidate substance determination unit 23 can be, for example, a type of computer and can include a CPU 231, a storage device 232, and an input interface 233 for receiving signals from external devices such as a keyboard. Examples of the storage device 232 include a RAM, a ROM, an HDD, an SSD, and the like.

[0059] The preset threshold value is stored in the storage device 232, and the electromagnetic wave absorption prediction unit 22 can acquire the preset threshold value from the data storage unit 21.

[0060] As shown in FIG. 5, the candidate substance determination unit 23 can be connected to the electromagnetic wave absorption prediction unit 22 by a cable 26 so as to be able to exchange data with the electromagnetic wave absorption prediction unit 22.

[0061] The CPU 231 can acquire the conductive substances in the second conductive substance group from the electromagnetic wave absorption prediction unit 22, select candidate substances from the conductive substances in the second conductive substance group, and perform control to store the data of the selected candidate substances in the storage device 232.

[0062] (Electromagnetic Wave Absorption Calculation Unit) The electromagnetic wave absorption calculation unit 24 calculates the electromagnetic wave absorption of the candidate substances using a hybrid functional. Specifically, the electromagnetic wave absorption calculation step in the plasmonic material search method according to the above-described embodiment is executed (FIG. 1, step S5).

[0063] The electromagnetic wave absorption calculation unit 24 can be, for example, a type of computer and can include a CPU 241 and a storage device 242. Examples of the storage device 242 include a RAM, a ROM, an HDD, an SSD, and the like.

[0064] As shown in FIG. 5, the electromagnetic wave absorption calculation unit 24 can be connected to the candidate substance determination unit 23 via a cable 26 so that data can be exchanged between the candidate substance determination unit 23 and the electromagnetic wave absorption calculation unit 24.

[0065] The CPU 241 can obtain the electromagnetic wave absorption of the candidate substance from the candidate substance determination unit 23, calculate the electromagnetic wave absorption of the candidate substance, and control to store the result in the storage device 242.

[0066] (Conductive Substance Selection Unit 25) The conductive substance selection unit 25 selects a conductive substance among the candidate substances whose electromagnetic wave absorption calculated by the electromagnetic wave absorption calculation unit is equal to or less than a threshold value. Specifically, the selection process in the plasmonic material search method according to the above-described embodiment is executed (FIG. 1, step S6).

[0067] The conductive substance selection unit 25 can be, for example, a type of computer and can include a CPU 251, a storage device 252, and an input interface 253 for receiving signals from external devices such as a keyboard. Examples of the storage device 252 include a RAM, a ROM, an HDD, an SSD, and the like.

[0068] As shown in FIG. 5, the conductive substance selection unit 25 can be connected to the electromagnetic wave absorption calculation unit 24 via a cable 26 so that data can be exchanged between the electromagnetic wave absorption calculation unit 24 and the conductive substance selection unit 25.

[0069] The CPU 251 can obtain the electromagnetic wave absorption of the candidate substance from the electromagnetic wave absorption calculation unit 24, select a conductive substance suitable as a plasmonic material from the electromagnetic wave absorption of the candidate substance, and control to store the selection result in the storage device 252.

[0070] The conductive substance selection unit 25 can be connected to a display device 27 and output and display the crystal structure, dielectric function, and electromagnetic wave absorption of the substance on the display device 27. Further, the conductive substance selection unit 25 can be connected to the data storage unit 21 via a cable or the like (not shown) and store the selection result of the conductive substance suitable as a plasmonic material in the data storage unit 21.

[0071] In the plasmonic material search device according to the present embodiment, in the electromagnetic wave absorption prediction unit 22, the dielectric function of the conductive material in the first conductive material group is calculated by first-principles calculation using a hybrid functional, and the electromagnetic wave absorption of the conductive material in the first conductive material group is calculated from the imaginary part of the dielectric function (FIG. 2, step S11, step S12).

[0072] Also, in the plasmonic material search device according to the present embodiment, in the electromagnetic wave absorption prediction unit, the electromagnetic wave absorption of the conductive material in the first conductive material group is calculated using a general functional, the electromagnetic wave absorption of some of the conductive materials in the first conductive material group is calculated using a hybrid functional, a first prediction model is generated with the information of the conductive material in the first conductive material group as the explanatory variable and the electromagnetic wave absorption of the conductive material in the first conductive material group as the target variable, and the first prediction model is transferred to a second prediction model by transfer learning using the information of some of the conductive materials in the first conductive material group and the electromagnetic wave absorption of some of the conductive materials in the first conductive material group (FIG. 3, step S21 to step S24).

[0073] Specifically, the first predicted electromagnetic wave absorption calculation step and the second predicted electromagnetic wave absorption calculation step in the predicted electromagnetic wave absorption calculation step, and the first prediction model generation step and the second prediction model generation step in the prediction model generation step in the plasmonic material search method according to the above-described embodiment are executed (FIG. 3, step S21 to step S24).

[0074] The plasmonic material search device according to the present embodiment includes such an electromagnetic wave absorption prediction unit 22, a candidate material determination unit 23, an electromagnetic wave absorption calculation unit 24, and a conductive material selection unit 25 (FIG. 1, step S1 to step S6). Thereby, in the plasmonic material search device according to the present embodiment, the search for plasmonic materials can be comprehensively performed in a short period of time.

[0075] In the plasmonic material search device of the present embodiment, as described above, the electromagnetic wave absorption of the conductive substances in the first conductive substance group is calculated from the imaginary part of the dielectric function of the conductive substances obtained by first-principles calculations using a hybrid functional (FIG. 2, step S11, step S12). Thus, in the plasmonic material search device of the present embodiment, a plasmonic material can be searched for with high accuracy from among a large number of candidate substances.

[0076] Also, in the plasmonic material search device of the present embodiment, as described above, by creating a prediction model through transfer learning, a prediction model that can be used for searching for plasmonic materials can be generated from a small number of conductive substances (FIG. 3, step S21 to step S24). Therefore, according to the plasmonic material search device of the present embodiment, a plasmonic material can be searched for in a shorter period of time.

Example

[0077] Hereinafter, a plasmonic material was searched for using the plasmonic material search device 20. As candidates for plasmonic materials, 9026 candidate substances of binary and ternary substances registered with a band gap of 0 in the material database "Materials Project" were prepared. Note that these 9026 substances correspond to the above-described M conductive substances.

[0078] The target wavelength was set to visible light, and the integration range of electromagnetic wave absorption was set to 380 nm to 780 nm. As information on the conductive substances used for creating the prediction model, the weighted average, weighted variance, weighted sum, maximum value, and minimum value of the physical property values of each element included in the composition were used. For example, for the binary substance A wA B wB in the case of, for the physical property value f, the physical property values f A and f B of elements A and B are used and shown as follows.

[0079] Weighted average: f ave =(wAf A +wBf B ) / (wA + wB) Weighted variance: fvar =[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 )

[0080] The physical property value f is the period, the number of protons, the atomic number, the atomic radius, the atomic radius by Rahm, the atomic volume, the atomic mass, the atomic volume of the Inorganic Crystal Structure Database (ICSD), the lattice constant, the van der Waals (vdW) radius, the vdW radius by Alvarez, the vdW radius by Batsanov, the vdW radius by Bondi, the vdW radius of DREIDING FF, the vdW radius of MM3 FF, the vdW radius by Rowland and Taylor, the vdW radius by Truhlar, the vdW radius of UFF, the covalent bond radius by Bragg, the covalent bond radius by Cerdero, the single bond distance of the covalent bond radius by Pyykko, the double bond distance of the covalent bond radius by Pyykko, the triple bond distance of the covalent bond radius by Pyykko, the covalent bond radius by Slater, the vdW coefficient C6, the vdW coefficient C6 by Gould and Bucko, the density at 295K, the proton affinity, the dipole polarizability, the electron affinity, the electronegativity, the electronegativity on the Allen scale, the electronegativity on the Ghosh scale, the electronegativity on the Mulliken scale, the band gap of DFT, the energy of DFT, the lattice constant of BCC by DFT, the lattice constant of FCC by DFT, the magnetic moment of DFT, the volume of DFT, the HHI coefficient, the specific heat at 20°C, the gas phase basicity, the first ionization energy, the heat of fusion, the heat of formation, the molar specific heat capacity, the specific heat capacity, the heat of vaporization, the coefficient of thermal expansion, the boiling point, the Brinell hardness, the compressibility, the melting point, the single bond distance of the metallic bond radius, the nearest neighbor distance of the metallic bond radius, the thermal conductivity at 25°C, the speed of sound, the Vickers hardness, the polarizability, the Young's modulus, the Poisson's ratio, the molar volume, the total number of unoccupied electrons, the total number of valence electrons, the number of unoccupied d electrons, the number of d valence electrons, the number of unoccupied f electrons, the number of f valence electrons, the number of unoccupied p electrons, the number of p electrons, the number of unoccupied s electrons, and the number of s valence electrons. For the calculation of the information of the conductive substance, the Python library XenonPy was used.

[0081] As a method for creating a prediction model for predicting the electromagnetic wave absorption of a conductive substance, transfer learning using a neural network was selected. For 971 substances, the electromagnetic wave absorption was calculated by the generalized gradient approximation. Note that these 971 substances correspond to the above-mentioned N conductive substances.

[0082] The calculations were performed within the framework of DFT using the PBE functional (exchange-correlation functional) with the plane-wave basis first-principles calculation software VASP (Vienna Ab initio Simulation Package). The PAW (projector augmented wave) potential was used, with a plane-wave cutoff of 520 eV and a k-point density of 0.4 Å -1 Using these results, a prediction model for electromagnetic wave absorption based on the generalized gradient approximation was created. This calculation is an example of a first-principles calculation using a general functional in the above-described electromagnetic wave absorption calculation step for prediction or the prediction model generation section.

[0083] For 163 substances out of the above 971 substances, the electromagnetic wave absorption was calculated using a hybrid functional. Note that these 163 substances correspond to the above-mentioned L conductive substances.

[0084] The calculations were performed within the framework of DFT using the HSE06 functional with the plane-wave basis first-principles calculation software VASP. The PAW potential was used, with a plane-wave cutoff of 520 eV and a k-point density of 0.6 Å -1 This calculation is an example of a first-principles calculation using the above-described hybrid functional.

[0085] By transfer learning, the prediction model for electromagnetic wave absorption based on the generalized gradient approximation was transferred to a prediction model for electromagnetic wave absorption using a hybrid functional, and learning was performed using the data of electromagnetic wave absorption of 163 substances using the hybrid functional. The Python library XenonPy was used for transfer learning.

[0086] For the remaining 8863 substances, the electromagnetic wave absorption using the hybrid functional was predicted using the prediction model for electromagnetic wave absorption using the hybrid functional. Note that these 8863 substances correspond to M - L conductive substances obtained by excluding L conductive substances (163 substances) from the above-mentioned M conductive substances (9026 substances).

[0087] The threshold value was set to δ = 3.5, and the selection or determination of candidate substances was carried out. Note that for the threshold value (δ = 3.5), the electromagnetic wave absorption of cesium tungstate (Cs 2 WO 4 ), which is a known plasmonic material, was used. There were 82 substances for which the predicted value of electromagnetic wave absorption by the hybrid functional was equal to or less than the threshold value δ.

[0088] For the above 82 substances, the electromagnetic wave absorption was calculated using the hybrid functional. The calculation was performed in the scope of DFT using the HSE06 functional with the plane-wave basis first-principles calculation software VASP. Also, the PAW potential was used, the plane cut-off was 520 eV, and the k-point density was 0.4 Å -1 . This calculation is an example of the first-principles calculation using the hybrid functional in the above-described electromagnetic wave absorption calculation step or electromagnetic wave absorption calculation unit.

[0089] The threshold value was set to δ = 3.5, and the selection or determination of conductive substances with electromagnetic wave absorption equal to or less than the threshold value was carried out. There were 46 substances for which the electromagnetic wave absorption by the hybrid functional was equal to or less than the threshold value. These 46 substances can be said to be suitable materials as plasmonic materials. Note that examples of the plasmonic materials discovered by this embodiment include Ba 2 CuO 3 .

[0090] According to this example, substances that become plasmonic materials in the visible light region could be comprehensively searched for and discovered from among 9026 substances in a short period. Also, according to this embodiment, since the search for plasmonic materials can be comprehensively carried out in a short period, the development period can be shortened.

[0091] As described above, the embodiments of the present invention have been explained, but the present invention is not limited to specific embodiments, and various modifications and changes are possible within the scope of the invention described in the claims.

Explanation of Reference Numerals

[0092] 20 Plasmonic Material Search Device 21 Data storage unit 22 Electromagnetic wave absorption prediction unit 23 Candidate substance determination unit 24 Electromagnetic wave absorption calculation unit 25 Conductive substance selection unit 26 Cable 27 Display device

Claims

1. A computer performs a predicted electromagnetic wave absorption calculation step of calculating the electromagnetic wave absorption of the conductive materials in the first conductive material group by first-principles calculation; a prediction model generation step of generating a prediction model using a neural network, with the information of the conductive materials in the first conductive material group as explanatory variables and the electromagnetic wave absorption of the conductive materials in the first conductive material group calculated in the predicted electromagnetic wave absorption calculation step as the objective variable; a prediction step of predicting the electromagnetic wave absorption of the conductive materials in the second conductive material group based on the prediction model; a candidate material selection step of selecting, as candidate materials, the conductive materials among the conductive materials in the second conductive material group whose electromagnetic wave absorption predicted in the prediction step is equal to or less than a preset threshold; an electromagnetic wave absorption calculation step of calculating the electromagnetic wave absorption of the candidate materials using a hybrid functional; a selection step of selecting, among the candidate materials, the conductive materials whose electromagnetic wave absorption calculated in the electromagnetic wave absorption calculation step is equal to or less than the threshold, A method for exploring plasmonic materials.

2. In the predicted electromagnetic wave absorption calculation step, the dielectric function of the conductive materials in the first conductive material group is calculated by first-principles calculation using a hybrid functional, and the electromagnetic wave absorption of the conductive materials in the first conductive material group is calculated from the imaginary part of the dielectric function. The method for exploring plasmonic materials according to Claim 1.

3. The predicted electromagnetic wave absorption calculation step includes a first predicted electromagnetic wave absorption calculation step of calculating the electromagnetic wave absorption of the conductive materials in the first conductive material group using a general functional, and a second predicted electromagnetic wave absorption calculation step of calculating the electromagnetic wave absorption of some of the conductive materials in the first conductive material group using a hybrid functional. The prediction model generation step includes a first prediction model generation step of generating a first prediction model with the information of the conductive materials in the first conductive material group as explanatory variables and the electromagnetic wave absorption calculated in the first predicted electromagnetic wave absorption calculation step as the objective variable, and a second prediction model generation step of transferring the first prediction model to a second prediction model by transfer learning using the information of some of the conductive materials in the first conductive material group and the electromagnetic wave absorption calculated in the second predicted electromagnetic wave absorption calculation step. In the prediction step, the second prediction model is used as the prediction model. The method for exploring plasmonic materials according to Claim 1.

4. In the second predicted electromagnetic wave absorption calculation step, the dielectric function of some of the conductive materials in the first conductive material group is calculated by first-principles calculation using a hybrid functional, Calculating the electromagnetic wave absorption of some conductive materials in the first conductive material group from the imaginary part of the dielectric function The plasmonic material search method according to claim 3

5. An electromagnetic wave absorption prediction unit that predicts the electromagnetic wave absorption of the conductive materials in the second conductive material group based on a prediction model generated using a neural network, with the information of the conductive materials in the first conductive material group as the explanatory variable and the electromagnetic wave absorption of the conductive materials in the first conductive material group calculated by first-principles calculation as the objective variable A candidate substance determination unit that determines, as candidate substances, the conductive materials among the conductive materials in the second conductive material group whose predicted electromagnetic wave absorption is equal to or less than a preset threshold An electromagnetic wave absorption calculation unit that calculates the electromagnetic wave absorption of the candidate substances using a hybrid functional A conductive material selection unit that selects, from among the candidate substances, the conductive materials whose calculated electromagnetic wave absorption is equal to or less than the threshold A plasmonic material search device

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