JP2013156030A - Scattered wave calculation system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate an electromagnetic field formed by scattered waves from a dielectric having a variety of structures highly accurately with a smaller amount of data processing.SOLUTION: A scattered wave calculation system has a structure specification part and an electromagnetic field calculation part. The structure specification part represents an area of a dielectric to be a calculation object of an electromagnetic field formed by scattered waves occurring when electromagnetic waves are made incident as an area composed by a reference area and a plurality of finite areas which comprise a part or a space of the dielectric respectively and do not intersect one another. The electromagnetic field calculation part successively adds the plurality of finite areas to the reference area in batches and obtains an electromagnetic field formed by scattered waves when the electromagnetic wave is made incident to the dielectric by calculation in which an electromagnetic field generated by each of the finite areas added are successively added to the electromagnetic field formed by the reference area.

Description

  The present invention relates to a scattered wave calculation system, a scattered wave calculation method, and a scattered wave calculation program.

  Conventionally, various methods have been proposed as a method for calculating an electromagnetic field of a scattered wave generated when an electromagnetic wave is incident on a dielectric. For example, when the dielectric structure is sufficiently large with respect to the wavelength of the incident electromagnetic wave, the electromagnetic field of the scattered wave is approximately obtained by adding a phase distribution according to the shape of the dielectric to the incident wave. Can do. This method is called scalar wave approximation.

  On the other hand, when calculating the electromagnetic field of scattered waves generated by a dielectric having a fine structure that is about the wavelength of the incident electromagnetic wave or less than the wavelength of the electromagnetic wave, correctly consider the boundary condition of the electromagnetic field at the boundary of the dielectric It is effective to use a vector electromagnetic simulation method capable of The vector electromagnetic field simulation method is a calculation method that handles an electromagnetic field as a vector.

  Vector electromagnetic field simulation methods are classified into various methods such as time-domain finite difference method (FDTD method), finite element method, boundary element method, volume integration method, and differential field boundary element method. The

  The FDTD method is a method of dividing the inside of a region to be subjected to calculation of an electromagnetic field with a grid and tracking the temporal development of the electromagnetic field at each grid point of the grid. Since the FDTD method tends to increase the data processing time, measures such as parallel processing are taken to reduce the data processing time.

  The finite element method is a method that uses a variational method to obtain an electromagnetic field formed by scattered waves. Even in the finite element method, an area to be subjected to electromagnetic field calculation is divided into a plurality of analysis areas. Therefore, in order to reduce the amount of data processing while maintaining accuracy, an appropriate finite element creation method has been proposed.

  The boundary element method is a technique for obtaining an electromagnetic field by discretizing only the boundary of the analysis region or the boundary of the refractive index, not the inside of the analysis region that is the calculation target of the electromagnetic field. The boundary element method uses a Green's function and an integral method to solve differential equations for electromagnetic field analysis. Since the boundary element method has one dimension less than the method of discretizing the inside of the analysis region, the data processing amount is small. Therefore, the boundary element method is useful when the boundary distribution is sparse and the boundary length is finite, such as when electromagnetic waves are incident on the dielectric from infinity.

  The volume integration method is a method for calculating a scattered electromagnetic field generated in a dielectric having a periodic structure at high speed.

  The difference field boundary element method is a method developed from the conventional boundary element method (see, for example, Non-Patent Document 1). The difference field boundary element method calculates the electromagnetic field after the change of the structure by obtaining the difference of the electromagnetic field distribution that changes due to the change of the structure when a slight change is added to the simple structure with the known electromagnetic field. This is a technique for indirectly obtaining. In the difference field boundary element method, the target of discretization is only the boundary around the part where the structure is changed. For this reason, in the differential field boundary element method, the number of analysis regions can be reduced. The differential field boundary element method is suitable for the calculation of the scattered electromagnetic field of a large-scale dielectric having locally different structures.

  These electromagnetic field simulation techniques are typically used for photolithography and diffractive optical element simulation. In the photolithography simulation, a scattered electromagnetic field from a fine pattern on the surface of the reticle is calculated for the design and inspection of the reticle. Then, a light intensity pattern obtained by imaging the scattered electromagnetic field from the reticle is acquired.

  A diffraction grating, which is one of diffractive optical elements, is used in a spectroscope or the like, and requires high-precision spectral characteristics. Therefore, it is necessary to design and analyze the diffraction grating by performing an accurate simulation. In the calculation of the scattered wave of the diffraction grating, a rigorous coupled wave analysis method using the spatial periodicity of the structure is widely used. The exact coupled wave analysis method is a technique that uses Bloch's theorem by applying periodic boundary conditions to the analysis region. According to this rigorous coupled wave analysis method, it is possible to accurately calculate the polarization characteristics only by considering the structure of one period of the diffraction grating.

Junichiro Sugisaka, Toyohiko Yatagai, Proceedings of the 72nd JSAP Scientific Meeting, p03-002, 1p-ZG-3, (2011)

  However, in the conventional scattered electromagnetic field calculation method, the amount of data processing becomes enormous and the data processing time may be long. In particular, when a scattered electromagnetic field is calculated from a huge dielectric that exists in an open region such as a reticle or a diffraction grating and has a fine structure, an increase in data processing amount is significant. For this reason, depending on the calculation conditions, the calculation resource overflows or the calculation is virtually impossible. Or a large-scale computational resource is required.

  In addition, some conventional methods for calculating scattered electromagnetic fields require special conditions. For example, in the finite element method, the analysis region cannot be divided because an absorption boundary such as the FDTD method cannot be applied. Further, in the finite element method, the scattered electromagnetic field from the open region cannot be calculated. For these reasons, it is difficult to calculate the scattered electromagnetic field from a huge dielectric by the finite element method.

  Furthermore, the volume integration method requires that the dielectric structure be periodic. Therefore, it is impossible to calculate the scattered electromagnetic field from an irregular dielectric material having no periodicity.

  As described above, the calculation of the scattered electromagnetic field may be difficult even if any conventionally known method is used.

  Therefore, the present invention provides a scattered wave calculation system and a scattered wave calculation method capable of calculating an electromagnetic field formed by scattered waves from dielectrics having various structures with high accuracy with a smaller amount of data processing. An object of the present invention is to provide a scattered wave calculation program.

The scattered wave calculation system according to the embodiment of the present invention includes a structure specifying unit and an electromagnetic field calculation unit. The structure specifying part is composed of a reference region and a region of the dielectric, which is an object of calculation of an electromagnetic field formed by scattered waves generated when electromagnetic waves are incident, and a space or a part of the dielectric, respectively, and A plurality of finite regions that do not intersect with each other are represented as a combined region. The electromagnetic field calculation unit sequentially adds the plurality of finite regions to the reference region in a plurality of times, and sequentially adds the electromagnetic field generated by each added finite region to the electromagnetic field formed by the reference region. An electromagnetic field formed by a scattered wave generated when the electromagnetic wave is incident on the dielectric is calculated.
Further, the scattered wave calculation method according to the embodiment of the present invention includes a dielectric region that is an object of calculation of an electromagnetic field formed by scattered waves generated when an electromagnetic wave is incident, a reference region, The step of representing as a region composed of a plurality of finite regions composed of a part of a dielectric material and not intersecting with each other, and sequentially adding the plurality of finite regions to the reference region in a plurality of times. Obtaining an electromagnetic field formed by a scattered wave generated when the electromagnetic wave is incident on the dielectric by calculation of sequentially adding the electromagnetic field respectively generated by the finite region to the electromagnetic field formed by the reference region. .
The scattered wave calculation program according to the embodiment of the present invention causes a computer to function as the above-described structure specifying unit and electromagnetic field calculation unit.

  According to the scattered wave calculation system, the scattered wave calculation method, and the scattered wave calculation program according to the embodiment of the present invention, the electromagnetic field formed by the scattered wave from the dielectric having various structures can be reduced in the data processing amount. Can be calculated with high accuracy.

The functional block diagram of the scattered wave calculation system which concerns on the 1st Embodiment of this invention. The flowchart which shows the calculation procedure of the scattered electromagnetic field in the scattered wave calculation system shown in FIG. Sectional drawing which shows the example which represented the area | region of the dielectric material used as the calculation object of a scattered electromagnetic field in the scattered wave calculation system shown in FIG. 1 as an area | region which synthesize | combined several finite area | regions which do not mutually cross | intersect. The figure explaining the calculation method of the scattered electromagnetic field in the electromagnetic field calculation part shown in FIG. The figure which shows an example of the simulation result by the scattered wave calculation system shown in FIG. The figure which compared the calculation accuracy of the scattered wave calculation system shown in FIG. 1, the calculation accuracy of a scattered electromagnetic field, and the calculation accuracy of the scattered electromagnetic field by the conventional FDTD method. Sectional drawing which shows the example which represented the area | region of the dielectric material used as the calculation object of a scattered electromagnetic field in the scattered wave calculation system in 2nd Embodiment as an area | region which synthesize | combined several finite space which does not mutually cross | intersect. The figure explaining the calculation method of the scattered electromagnetic field by the electromagnetic field calculation part in 2nd Embodiment. The figure which shows the structural example suitable for the area | region division | segmentation method of a dielectric material as shown in FIG. Sectional drawing which shows the structural example of the reticle used as the calculation object of a scattered electromagnetic field in the scattered wave calculation system in 3rd Embodiment. The figure explaining the calculation method of the scattered electromagnetic field by the electromagnetic field calculation part in 3rd Embodiment. The figure explaining the calculation method of the scattered electromagnetic field from the diffraction grating by the scattered wave calculation system in 4th Embodiment. Calculation of scattered electromagnetic field when second dielectric material having different dielectric constant is partially embedded in first dielectric material having single dielectric constant by scattered wave calculation system according to one embodiment of the present invention. Sectional drawing explaining a method. A method for calculating a scattered electromagnetic field when a second dielectric having a different dielectric constant is completely embedded in a first dielectric having a single dielectric constant by a scattered wave calculation system according to an embodiment of the present invention. FIG. The perspective view explaining an example of the calculation method of the scattered electromagnetic field from 3D dielectric material by the scattered wave calculation system which concerns on one Embodiment of this invention.

  A scattered wave calculation system, a scattered wave calculation method, and a scattered wave calculation program according to embodiments of the present invention will be described with reference to the accompanying drawings.

(First embodiment)
(Configuration and function)
FIG. 1 is a functional block diagram of a scattered wave calculation system according to the first embodiment of the present invention.

  The scattered wave calculation system 1 is a system for calculating an electromagnetic field formed by a scattered wave generated when an electromagnetic wave is incident on a dielectric. Therefore, the scattered wave calculation system 1 can also be called a scattered electromagnetic field simulation system. More specifically, the scattered wave calculation system 1 shown in FIG. 1 calculates the scattered electromagnetic field generated when a plane wave is incident on the surface of an infinitely large plate-like dielectric material that has been irregularly processed. be able to.

  The scattered wave calculation system 1 can be constructed by reading a scattered wave calculation program into a computer 6 having an input device 2, a display device 3, a storage device 4, and an arithmetic device 5. The scattered wave calculation program can be recorded on an information recording medium and distributed as a program product so that a general-purpose computer can be used as the scattered wave calculation system 1. Of course, the scattered wave calculation program can also be downloaded to the computer 6 via a network without going through an information recording medium. However, a suitable circuit may be used to configure the scattered wave calculation system 1.

  The computing device 5 of the computer 6 functions as a dielectric structure definition unit 7, a dielectric structure acquisition unit 8, a structure identification unit 9, and an electromagnetic field calculation unit 10 by a scattered wave calculation program. The storage device 4 functions as the reference electromagnetic field storage unit 11 and the target electromagnetic field storage unit 12. In other words, the scattered wave calculation system 1 includes the dielectric structure definition unit 7, the dielectric structure acquisition unit 8, the structure identification unit 9, the electromagnetic field calculation unit 10, the reference electromagnetic field storage unit 11, and the target electromagnetic field storage unit 12. Have.

  In addition, the scattered wave calculation system 1 can be connected to a desired device such as another computer 13 or a recording medium driving device 14 via a network. Of course, the recording medium driving device 14 may be a component of the scattered wave calculation system 1.

  The dielectric structure defining unit 7 has a function of defining a structure of a dielectric that is a calculation target of the scattered electromagnetic field according to information input from the input device 2. The dielectric structure defining unit 7 can define a finite or semi-infinite dielectric. For this reason, for example, a huge plate-like structure subjected to irregular unevenness processing can be defined as a dielectric structure.

  The dielectric structure acquisition unit 8 has a function of acquiring a predefined dielectric structure as a calculation target of the scattered electromagnetic field from another computer 13 or the recording medium driving device 14 via the network. Therefore, instead of defining the dielectric structure that is the object of calculation of the scattered electromagnetic field in the dielectric structure definition unit 7, it is also possible to input from the outside of the scattered wave calculation system 1.

  The structure specifying unit 9 synthesizes a dielectric region that is an electromagnetic field calculation target acquired by the dielectric structure definition unit 7 or the dielectric structure acquisition unit 8 and a plurality of finite regions that do not intersect with each other. It has the function of representing as a region. The reference area can be a finite or semi-infinite area.

  The electromagnetic field calculation unit 10 sequentially adds a plurality of finite regions in a plurality of times to the reference region specified by the structure specifying unit 9, and an electromagnetic field generated by each of the added finite regions is formed by the reference region. It has a function of analytically obtaining the scattered electromagnetic field of the target dielectric by calculation that is sequentially added to the electromagnetic field. That is, the electromagnetic field calculation unit 10 has a function of repeating the calculation by the difference field boundary element method while sequentially adding a plurality of finite regions to the reference region in a plurality of times.

  The difference field boundary element method calculates the electromagnetic field difference that occurs when the analysis region changes and adds it to the electromagnetic field formed by the analysis region before the change, thereby forming the electromagnetic field formed by the analysis region after the change. This is a method for calculating.

  More specifically, the electromagnetic field calculation unit 10 first adds a single or a plurality of finite regions using the reference region as the initial calculation region, and calculates the difference in the electromagnetic field distribution due to the region change by the difference field boundary element method. Calculate as an electromagnetic field. Then, by adding the differential electromagnetic field to the electromagnetic field formed by the reference region, it is possible to calculate the electromagnetic field formed by the region in which a single or a plurality of finite regions are added to the reference region.

  Next, another single or a plurality of finite regions are added with the region where the single or a plurality of finite regions are added to the reference region as an initial region. Then, the differential electromagnetic field is similarly calculated by the differential field boundary element method, and the differential electromagnetic field generated by the addition of another single or plural finite regions is added to the already calculated electromagnetic field. Thereby, an electromagnetic field formed by a region obtained by adding a finite region to the reference region can be calculated. Similarly, by repeating the addition of the finite region, the calculation of the differential electromagnetic field, and the addition of the differential electromagnetic field as many times as the addition of the finite region, the scattered electromagnetic field formed by the target dielectric material before decomposition is obtained analytically. be able to.

  That is, the electromagnetic field calculation unit 10 obtains a reference electromagnetic field formed by scattered waves generated when electromagnetic waves are incident on the reference region, and sequentially obtains at least one of a plurality of finite regions from the reference region. Electromagnetic waves formed by scattered waves generated when electromagnetic waves are incident on a dielectric by sequentially adding the displacements of electromagnetic fields formed by scattered waves generated when electromagnetic waves are incident on different areas, respectively. Configured to seek the world.

  Note that data processing can be simplified by sequentially adding a plurality of finite areas one by one to the reference area. Therefore, hereinafter, an example in which a single finite area is sequentially added to the reference area will be described. However, even when a plurality of finite regions are sequentially added to the reference region, the scattered electromagnetic field from the dielectric can be analytically determined by a similar method if the calculation formula is adapted.

  The reference electromagnetic field storage unit 11 stores a scattered electromagnetic field based on the reference region according to the simulation conditions such as the shape of the reference region and the dielectric constant of the dielectric. Therefore, once the scattered electromagnetic field formed by the reference region defined as the desired region is calculated, it can be reused by being stored in the reference electromagnetic field storage unit 11.

  The target electromagnetic field storage unit 12 has a function of storing the electromagnetic field of the scattered wave acquired as a calculation result by the electromagnetic field calculation unit 10. The stored scattered electromagnetic field can be output externally via a network or a recording medium.

(Operation and action)
Next, the operation and action of the scattered wave calculation system 1 will be described.

  FIG. 2 is a flowchart showing a calculation procedure of the scattered electromagnetic field in the scattered wave calculation system 1 shown in FIG.

  First, in step S1, the dielectric structure defining unit 7 defines the structure of the dielectric that is the subject of the calculation of the scattered electromagnetic field. The dielectric structure defining unit 7 may input the predefined dielectric structure to the dielectric structure obtaining unit 8 via a network or a recording medium without defining the dielectric structure.

  Next, in step S2, the structure specifying unit 9 represents the dielectric region in which the structure is defined as a region obtained by combining the reference region and a plurality of finite regions that do not intersect each other. Here, a case will be described as an example where the structure of the dielectric to be calculated is represented separately as a simple semi-infinite reference region having only a plane boundary and a plurality of finite closed regions that do not intersect each other.

  FIG. 3 is a cross-sectional view showing an example in which the region of the dielectric material for which the scattered electromagnetic field is calculated in the scattered wave calculation system 1 shown in FIG. 1 is expressed as a region synthesized with a plurality of finite regions that do not intersect with each other. FIG.

  As shown in FIG. 3A, when a dielectric having irregularly provided convex portions having a constant height or concave portions having a constant depth on the surface of a flat substrate is a calculation object, it is semi-infinite. The dielectric can be divided into a reference area b0 composed of a flat rectangular area and M finite rectangular areas b1, b2, b3,..., BM. In this case, the heights of the rectangular regions b1, b2, b3,..., BM are constant, and the lengths and intervals are irregular. In the case of manufacturing a semiconductor, a dielectric having a constant unevenness is used as shown in FIG.

  On the other hand, as shown in FIG. 3 (B), even if a dielectric having irregularly provided convex portions with non-constant heights or concave portions with non-constant depths on the surface of a flat substrate is to be calculated, The dielectric can be divided into a reference region b0 composed of an infinite rectangular region and M finite rectangular regions b1, b2, b3,..., BM. In the example shown in FIG. 3B, the heights, lengths, and intervals of the rectangular regions b1, b2, b3,..., BM are irregular.

  Furthermore, as shown in FIG. 3 (C), if a dielectric having irregularly provided convex portions on the surface of a flat substrate is a calculation target, a reference region b0 composed of a semi-infinite rectangular region and The dielectric can be divided into M finite regions b1, b2, b3,..., BM having various shapes.

  As described above, when a dielectric having unevenness on its surface is decomposed along the bottom of the unevenness, a semi-infinite plate-like dielectric substrate region, which is independent of the shape, height and interval of the protrusions, and It can be divided into independent small finite regions surrounded by closed curves.

  In FIG. 3, the lengths of the reference region b0 and the finite regions b1, b2, b3,..., BM in the depth direction perpendicular to the paper surface are treated as infinite. That is, FIG. 3 shows an example in which the structure of the dielectric is expressed by combining a plurality of two-dimensional (2D) regions. Therefore, in FIG. 3, the recess has a groove-like structure provided in the dielectric.

  However, similarly, a dielectric structure can be expressed by combining a plurality of three-dimensional (3D) regions. When the dielectric is divided into a plurality of 3D regions, the dielectric is divided into a semi-infinite flat 3D region and an independent minute 3D region surrounded by a closed curved surface such as a rectangular parallelepiped. That is, the dielectric region can be expressed as a region obtained by combining a 3D reference region and a plurality of 3D finite regions that do not intersect each other. If the dielectric is treated as a composite region of the 3D region, it is possible to calculate the scattered electromagnetic field of the dielectric having various structures.

  However, in the following, for the purpose of simplifying the calculation, a dielectric having the structure shown in FIG. 3 (A) is a target for calculating the scattered electromagnetic field, and the dielectric is divided into a 2D reference region and a plurality of 2D finite regions. Will be described.

  When the dielectric is divided into the reference area b0 and M finite rectangular areas b1, b2, b3,..., BM, the electromagnetic field calculation unit 10 calculates the scattered electromagnetic field using the differential field boundary element method. Is possible.

  FIG. 4 is a diagram for explaining a method of calculating the scattered electromagnetic field in the electromagnetic field calculation unit 10 shown in FIG.

  First, in step S3 of FIG. 2, the electromagnetic field calculation unit 10 scatters from the flat reference region b0 when the rectangular regions b1, b2, b3,..., BM as shown in FIG. Calculate the electromagnetic field. The scattered electromagnetic field formed by reflected and transmitted waves from a semi-infinite dielectric substrate having a simple planar boundary can be easily calculated analytically from the Fresnel formula. As a result, the electromagnetic field distribution f (r) at each position r that is an object of calculation of the electromagnetic field distribution is obtained.

  Next, the electromagnetic field calculation unit 10 sequentially adds M rectangular regions b1, b2, b3,..., BM to the reference region b0, and each rectangular region b1, b2, b3,. ..., repeatedly calculate the scattered electromagnetic field after adding bM. When all the rectangular regions b1, b2, b3,..., BM are added, the scattered electromagnetic field of the target dielectric can be obtained.

  For this purpose, one rectangular area bi (i = 1, 2, 3,..., M) to be first added to the reference area b0 by the electromagnetic field calculation unit 10 in step S4 in FIG. Choose from. The selection method of the finite area is arbitrary, but the method of selecting one by one from the rectangular area b1 at the end to the rectangular area bM at the other end is simple and the calculation is easy. In this case, the rectangular area b1 is selected as an initial addition area to the reference area b0. As a result, as shown in FIG. 4B, a region obtained by adding a rectangular region b1 to the reference region b0 is defined as a calculation target region.

  Then, the electromagnetic field calculation unit 10 can calculate the scattered electromagnetic field from the region obtained by adding the rectangular region b1 to the reference region b0 by the differential field boundary element method.

  For this purpose, the differential electromagnetic field generated by adding the rectangular region b1 to the reference region b0 in step S5 of FIG. 2 is calculated.

In order to calculate the differential electromagnetic field, as shown in FIG. 4B, the surface boundary C ₀ having a predetermined length of the reference region b0 around the rectangular region b1, the rectangular region b1 and the reference region b0 The electromagnetic field calculation unit 10 specifies the boundary C ₁ between them and the surface boundary C ₂ of the rectangular region b ₁ . These boundaries C ₀ , C ₁ and C ₂ are used as integration paths for boundary integration in the difference field boundary element method. Then, the differential electromagnetic fields f _s1 and f _s2 on each boundary C ₀ and the electromagnetic fields f _s3 on each boundary C ₁ and C ₂ are calculated by solving the integral equation shown in Expression (1).

・・・(1)

... (1)

  However, it shall be defined like Formula (2) in Formula (1).

・・・(2)

... (2)

Further, in the equation (1) and (2), G _n is the free space Green's function of the region S _n shown in FIG. 4, epsilon _n is the relative dielectric constant of the area S _n, f is the magnetic field in a direction perpendicular to the plane It is a component. The region S ₁ is a region that is an integration range in the reference region b 0, the region S ₂ is a region of the integration range outside the dielectric, and the region S ₃ is a region in the rectangular region b 1.

  Expressions (1) and (2) are expressions for obtaining a scattered electromagnetic field when p (parallel) polarized light whose vibration direction of an electric field component is parallel to the incident surface is incident on the dielectric. When s (senkrecht) polarized light whose field component oscillation direction is perpendicular to the incident surface is incident on the dielectric, calculate the scattered electromagnetic field using the formula in which the relative permittivity in formula (1) is replaced with the permeability. Can do. However, in the case of s-polarized light, f in equations (1) and (2) is an electric field component in a direction perpendicular to the paper surface. In the following equations, the p-polarization equation can be rewritten into the s-polarization equation by replacing the relative permittivity with the permeability.

In order to solve the integral equation shown in Equation (1), the values at the boundaries C ₁ and C ₂ of the electromagnetic field distribution formed by the reference region b0 before the addition of the rectangular region b1 and the reference region b0 side in the normal direction, That is, in FIG. 4, a differential coefficient with the downward direction being positive is used. Thereby, the differential electromagnetic fields f _s1 and f _s2 on the respective boundaries C ₀ and the electromagnetic fields f _s3 on the respective boundaries C ₁ and C ₂ in the area obtained by adding the rectangular area b1 to the reference area b0 can be obtained.

Next, the differential electromagnetic field at an arbitrary position r outside the rectangular region b1 can be calculated by using an expression including the integral expression shown in Expression (3) using the electromagnetic fields f _s1 , f _s2 , and f _s3 .

・・・(3)

... (3)

F _s1 (S ₁ ) obtained by Equation (3) is the differential electromagnetic field inside the reference region b0, f _s2 (S ₂ ) is the differential electromagnetic field outside the reference region b0 and the rectangular region b1, and f _s3 (S ₃ ) is The electromagnetic field is not a difference inside the rectangular region b1.

Upon solving integral equations, infinite when the value of the electromagnetic field is required at the far, it is possible to find the far field in the unit vector i _p direction by using the extreme value of the formula (4).

・・・(4)

···(Four)

  Then, the differential electromagnetic field distribution outside the rectangular region b1 and the electromagnetic field distribution inside the rectangular region b1 can be obtained by performing the calculation shown in Equation (1) or Equation (3) while changing the position r.

The above-described calculation is equivalent to dividing the dielectric boundary into a plurality of boundary elements and discretizing the electromagnetic field on the boundary. Therefore, the amount of computation required to calculate the differential electromagnetic field distribution, when the discretized at discrete number N rectangular region b1, the order of N ^3.

Further, the length of the surface boundary C ₀ of the reference region b0 is a length corresponding to the integration range. In the integral equation, the surface boundary of the reference region b0 sufficiently far from the reference region b0 is ignored, and the electromagnetic field is regarded as zero outside the integration range. Therefore, as the length of the surface boundary C ₀ is increased, the integration range is widened, and the scattered electromagnetic field can be calculated with high accuracy. Therefore, the length of the surface boundary C ₀ of the reference area b0 may be determined at an appropriate distance according to the required scattered electromagnetic field calculation accuracy.

The wavelength of the electromagnetic wave suitable for use varies depending on the irradiation position of the electromagnetic wave, and the calculation accuracy of the scattered electromagnetic field varies depending on the wavelength. Accordingly, the appropriate length of the surface boundary C ₀ varies depending on other conditions such as the wavelength of the electromagnetic wave.

  Next, in step S6 of FIG. 2, the electromagnetic field calculator 10 calculates the difference electromagnetic field distribution f1 (r) at each position r outside the rectangular region b1 generated by adding the rectangular region b1 to the reference region b0. Add to the scattered electromagnetic field distribution f (r) generated only by the reference region b0. As a result, an electromagnetic field distribution at each position r generated by the area obtained by adding only the rectangular area b1 to the reference area b0 is obtained. Then, the electromagnetic field calculator 10 calculates the electromagnetic field distribution f (r) before the addition of the differential electromagnetic field distribution f1 (r) as shown in FIG. 4B after the addition of the differential electromagnetic field distribution f1 (r). To the electromagnetic field distribution f (r) + f1 (r).

  Next, in step S7 of FIG. 2, the electromagnetic field calculator 10 determines whether or not all M rectangular regions b1, b2, b3,..., BM have been added to the reference region b0. As illustrated in FIG. 2, this determination may be a determination as to whether or not the identification information i of the rectangular area bi added to the reference area b0 immediately before is the identification information M of the last rectangular area bM. it can.

  If it is determined in step S7 that all the rectangular areas b1, b2, b3,..., BM are not added to the reference area b0, the next rectangular area bi is determined as an addition target in step S8. . When the rectangular areas bi are added in order, i = i + 1 may be set. And the process in step S5 and step S6 is performed in the electromagnetic field calculation part 10 again.

  More specifically, if only the first rectangular area b1 is added to the reference area b0, the second rectangular area b2 is the next additional area. Then, the calculation by the difference field boundary element method in step S5 is performed again using the area obtained by adding the first rectangular area b1 to the reference area b0 as the initial area.

When the second rectangular area b2 is added, as shown in FIG. 4C, the surface boundary of the area obtained by adding the first rectangular area b1 to the reference area b0 is C ₀ , and the second rectangular area boundary between the b2 and the reference region b0 surface boundary of C _1, 2-th rectangular area b2 is C _2. That is, the surface boundary C ₀ is defined as a boundary along the surfaces of the first rectangular region b1 and the reference region b0.

  Then, the differential electromagnetic field distribution f2 (r) at each position r outside the second rectangular region b2 can be obtained by the same calculation as when the first rectangular region b1 is added to the reference region b0. Then, as shown in FIG. 4C, the electromagnetic field distribution f (r) is updated by adding the differential electromagnetic field distribution f2 (r) by the second rectangular region b2 to the electromagnetic field distribution f (r). . As a result, an electromagnetic field distribution f (r) at each position r generated by a region obtained by adding two rectangular regions b1 and b2 to the reference region b0 is obtained.

Then, as shown in FIGS. 2 and 4, (D) and (E), the last rectangular region bM is added, and the calculation in steps S5 and S6 by the difference field boundary element method is performed until it is determined that i = M. Repeated. If it is determined in step S7 in FIG. 2 that all rectangular regions b1, b2, b3,..., BM have been added to the reference region b0, the last electromagnetic field distribution calculated by the differential field boundary element method f (r) is the scattered electromagnetic field distribution f _total (r) generated by the dielectric.

  Then, the scattered electromagnetic field distribution generated by the dielectric in step S9 can be output to a desired output destination such as the display device 3 or the media or another computer 13. Moreover, it can preserve | save in the target electromagnetic field preservation | save part 12 as needed.

  FIG. 5 is a diagram showing an example of a simulation result by the scattered wave calculation system 1 shown in FIG.

  5A and 5B, each vertical axis represents the relative intensity of the electromagnetic field, and each horizontal axis represents the radiation angle of the scattered electromagnetic field. 5A shows the relative intensity of the scattered light reflected by the dielectric in the far field, and FIG. 5B shows the relative intensity of the scattered light transmitted through the dielectric in the far field. That is, FIG. 5A is an angular spectrum of scattered light reflected by the dielectric, and FIG. 5B is an angular spectrum of transmitted light that has passed through the dielectric. The intensity of the scattered light obtained as an angular spectrum is the result of Fourier transforming the electromagnetic field in the vicinity of the dielectric.

  Number M of rectangular regions bi = 12, Refractive index inside dielectric, 2.5, Relative length and spacing of rectangular regions bi from 0.4l to 2.4l, Relative height of rectangular region bi 0.8l, Incident on dielectric As a result of the simulation of plotting the intensity of the scattered light emitted from the dielectric with respect to the radiation direction by the scattered wave calculation system 1 with the electromagnetic wave to be generated as a plane wave with an incident angle of 45 degrees and the observation position as an infinite point, FIG. The analysis results shown in (B) and (B) were obtained.

  Further, when a plane wave having an incident angle of 45 degrees is incident on the reference area b0 without the rectangular area bi, both reflected light and transmitted light become plane waves having a constant emission angle. Each of these plane waves is included in the angular spectrum as a component represented by a delta function. Therefore, the components of these plane waves are indicated by arrows in FIGS. 5 (A) and 5 (B). On the other hand, each differential electromagnetic field f1 (r), f2 (r), f3 (r),..., FM (r) is a finite continuous function expressed by the equation (3). Therefore, the components of the differential electromagnetic fields f1 (r), f2 (r), f3 (r),..., FM (r) are indicated by solid lines in FIGS.

  According to the simulation results shown in FIGS. 5 (A) and 5 (B), it is confirmed that the scattered electromagnetic field intensity from the dielectric having an irregular concavo-convex structure can be calculated with good accuracy by the scattered wave calculation system 1. it can.

  That is, the scattered wave calculation system 1 as described above treats the structure of a dielectric having irregular irregularities as a structure obtained by adding a local change multiple times to a simple structure, and adds a difference field while changing the simple structure. This is a system for obtaining the vector electromagnetic field of the scattered wave by repeating the calculation by the boundary element method. That is, in the scattered wave calculation system 1, the differential electromagnetic field resulting from the change of the dielectric structure is sequentially calculated by the differential field boundary element method, and the differential electromagnetic field is sequentially added from the dielectric having the target structure. The scattered electromagnetic field can be determined.

(effect)
For this reason, according to the scattered wave calculation system 1, the electromagnetic field formed by the scattered waves from the dielectrics having various structures can be calculated with a small amount of data processing with high accuracy. In particular, the differential electromagnetic field of the vector scattered electromagnetic field to be calculated in the differential field boundary element method can be calculated at high speed using an integral equation using boundary integral. For this reason, it is possible to calculate the vector scattered electromagnetic field with high accuracy with a smaller calculation resource.

For example, the calculation amount necessary for calculating the angular spectrum shown in FIG. 5 is the difference electromagnetic fields f1 (r), f2 (r), f3 (r),. This is the total amount of calculation required to calculate r). Also, assuming that each rectangular region bi is discretized by a discrete number N, the calculation required to calculate each differential electromagnetic field f1 (r), f2 (r), f3 (r), ..., fM (r) The quantity is on the order of N ³ each. Therefore, it can be estimated that the calculation amount necessary for calculating the angular spectrum shown in FIG. 5 is the calculation amount when the calculation amount of the N ³ order is calculated M times, that is, the order of MN ³ .

On the other hand, when the scattered electromagnetic field is calculated by the conventional simple difference field boundary element method, the M rectangular regions bi are discretized at N points, respectively. Therefore, the total discrete number is MN. In the differential field boundary element method, two unknowns at each point are obtained by simultaneous equations. For this reason, it is considered that the amount of calculation required to solve the simultaneous equations is on the order of (MN) ³ . Therefore, compared with the calculation by conventional simple differential field boundary element method, according to the scattered wave computing system 1, it is possible to reduce the amount of calculation to 1 / M ^2.

  Next, the scattered wave calculation method by the scattered wave calculation system 1 is compared with the conventional FDTD method.

  FIG. 6 is a diagram comparing the scattered wave calculation system 1 shown in FIG. 1 with the calculation accuracy of the scattered electromagnetic field and the calculation accuracy of the scattered electromagnetic field by the conventional FDTD method.

  In FIG. 6, the vertical axis indicates the relative error [%] of the scattered electromagnetic field, and the horizontal axis indicates the calculation time [s] of the scattered electromagnetic field. In FIG. 6, triangles indicate the relationship between the relative error of the scattered electromagnetic field by the conventional FDTD method and the calculation time. Further, in FIG. 6, circles indicate the relationship between the relative error of the scattered electromagnetic field and the calculation time when the difference field boundary element method is repeatedly calculated by the scattered wave calculation system 1.

  In the conventional FDTD method, the calculation accuracy of the scattered electromagnetic field improves as the analysis region becomes longer. Therefore, the relationship between the calculation time and the relative error in the conventional FDTD method was plotted while changing the length of the analysis region.

On the other hand, in the method of the scattered wave computing system 1 repeats the difference field boundary element method, as set longer the length of the surface boundary C ₀ of the reference area b0 as described above, the weak difference electromagnetic in the distance from each of the rectangular regions bi The world is considered. For this reason, as the length of the surface boundary C ₀ of the reference region b ₀ is set longer, the calculation accuracy of the scattered electromagnetic field as well as the differential electromagnetic field is improved. Therefore, the relationship between the calculation time and the relative error was plotted while changing the length of the surface boundary C ₀ .

  The relative error is an error from the convergence value of the scattered electromagnetic field that converges as the calculation time increases. The convergence value of the scattered electromagnetic field can be obtained by fitting the calculated value of the scattered electromagnetic field with an exponential function.

  According to FIG. 6, if the calculation time is the same, it can be confirmed that the calculation accuracy by the scattered wave calculation system 1 is about five digits higher than the calculation accuracy in the conventional FDTD method. Conversely, in the scattered wave calculation system 1, the calculation time required to make the relative error of the scattered electromagnetic field 0.1% is about 1/360 of the calculation time required in the conventional FDTD method. Therefore, it can be said that the calculation speed of the scattered wave calculation system 1 is about 360 times the calculation speed in the conventional FDTD method.

  For this reason, according to the scattered wave calculation system 1, even a dielectric having an irregular and large-scale structure, which is unrealistic with the conventional method, can be used as a strict vector field as a scattered electromagnetic field. The field can be calculated with good accuracy. In particular, it is effective when calculating a vector scattered electromagnetic field from a dielectric having a fine structure that is the same as or smaller than the wavelength of the incident electromagnetic wave.

  For example, when trying to make the various structures shown in FIG. 3 into the analysis area of the conventional boundary element method, the analysis area cannot be limited, so that the infinitely long dielectric boundary is reduced to a fraction of the wavelength of the incident electromagnetic wave. It is necessary to discretize with a boundary element of length. Therefore, the amount of calculation becomes infinite, and calculation by the boundary element method becomes impossible. That is, in the conventional boundary element method, calculation is virtually impossible when the boundary length or the boundary area is large.

  Also in the FDTD method, the analysis region must be discretized at intervals of a fraction of the wavelength of the incident electromagnetic wave. Moreover, it is necessary to store the electromagnetic field values at all discrete points during the calculation. For this reason, the FDTD method may require a huge amount of memory and calculation time. As a result, when the dielectric is very large with respect to the wavelength of the incident electromagnetic wave, it cannot often be calculated by the FDTD method. In addition, it is possible to reduce the amount of memory required by limiting the analysis area to a narrow range in the FDTD method, but this causes a deterioration in calculation accuracy as shown in FIG.

  In the conventional differential field boundary element method, the dielectric is decomposed into a reference region and a single finite region, and the scattered electromagnetic field from the dielectric is calculated by calculating the differential electromagnetic field of the single finite region. The Therefore, it is impossible to calculate a scattered electromagnetic field from a dielectric material that is decomposed into a plurality of finite regions.

  Unlike such a conventional method, the scattered wave calculation system 1 calculates a scattered electromagnetic field by a dielectric even if the dielectric is decomposed into a plurality of finite regions or a dielectric having a very long boundary length. be able to. That is, according to the scattered wave calculation system 1, the scattered electromagnetic field can be calculated regardless of the shape of the dielectric.

  In addition, the scattered wave calculation system 1 can calculate a scattered electromagnetic field generated by an incident wave having an arbitrary polarization state.

(Second Embodiment)
In the scattered wave calculation system in the second embodiment, the detailed functions of the structure specifying unit and the electromagnetic field calculation unit are different from the scattered wave calculation system 1 in the first embodiment. Therefore, only the detailed functions of the structure specifying unit and the electromagnetic field calculation unit in the second embodiment will be described.

  The structure specifying unit of the scattered wave calculation system according to the second embodiment is a region in which a dielectric region that is a target of calculation of a scattered electromagnetic field is combined with a flat reference region and a plurality of finite spaces that do not intersect each other. As a function. That is, the plurality of finite regions are not limited to the region occupied by the dielectric, but may be voids where no dielectric exists. In other words, each finite region can be composed of a part of a dielectric or a space.

  FIG. 7 shows an example in which the region of the dielectric that is the target of calculation of the scattered electromagnetic field in the scattered wave calculation system according to the second embodiment is expressed as a region synthesized with a plurality of finite spaces that do not intersect with each other. It is sectional drawing.

  As shown in FIG. 7, when a dielectric having irregularly provided convex portions having a constant height or concave portions having a constant depth on the surface of a flat substrate is an object of calculation, a semi-infinite flat plate A region occupied by the dielectric can be represented as a combined region of the reference region b0 formed of a rectangular region and M finite rectangular space regions b1, b2, b3,..., BM. In this case, the depth of each rectangular space region b1, b2, b3,..., BM is constant, and the length and interval are irregular.

  Similarly to the example shown in FIGS. 3B and 3C, the finite space regions b1, b2, b3,... It can be a shape. That is, instead of the convex portions as shown in FIG. 3, a plurality of concave portions having a desired shape can be formed as a plurality of finite regions b1, b2, b3,.

  FIG. 7 shows an example in which a 2D space having a finite area surrounded by a closed curve is defined as each finite space region b1, b2, b3,..., BM. A finite 3D space may be used as each finite space region b1, b2, b3, ..., bM.

  The electromagnetic field calculation unit in the second embodiment uses a method similar to that in the first embodiment to add a plurality of rectangular spaces to the reference region as shown in FIG. By repeating the calculation by the method, the scattered electromagnetic field of the target dielectric is analytically obtained. Therefore, the calculation flow of the scattered electromagnetic field of the dielectric is the same as the flow shown in the flowchart shown in FIG.

  FIG. 8 is a diagram for explaining a calculation method of the scattered electromagnetic field by the electromagnetic field calculation unit in the second embodiment.

  As shown in FIG. 8, even when a plurality of rectangular spaces b1, b2, b3,..., BM are sequentially added to the flat reference region b0, the flow is the same as in the first embodiment shown in FIG. The scattered electromagnetic field of the dielectric can be calculated.

  That is, first, using the Fresnel equation, the electromagnetic field f (r (r) at the position r generated by the flat reference region b0 without the rectangular spaces b1, b2, b3,..., BM as shown in FIG. ). Subsequently, as shown in FIGS. 8B to 8E, rectangular spaces b1, b2, b3,..., BM are sequentially added. Then, using the differential field boundary element method, each of the differential electromagnetic fields f1 (r), f2 (r), f3 (r), ... with the addition of each rectangular space b1, b2, b3, ..., bM sequentially. , fM (r) is calculated.

However, when the rectangular spaces b1, b2, b3,..., BM are added as shown in FIG. 8, the integration path is defined as shown in FIGS. That is, the surface boundary C ₀ having a predetermined length of the dielectric region around the rectangular space bi, the surface boundary C ₁ of the rectangular space bi, and the boundary C ₂ between the rectangular space bi and the reference region b0 are boundary integrals. Defined as integration path. Furthermore, the area S ₁ is an area where the integration range of the dielectric region, the region S ₂ is the area of integration range in the reference region b0 outside region S ₃ is rectangular space b1 to be added subject, b2, b3, ..., each defined as a region in bM.

  Further, when a plurality of rectangular spaces b1, b2, b3,..., BM are sequentially added as the recesses, the equation (5) is used instead of the equation (1) as the integral equation.

・・・(5)

···(Five)

  Further, equation (6) is used instead of equation (3).

・・・(6)

... (6)

Then, as shown in FIG. 8, each differential electromagnetic field f1 (r), f2 (r), f3 (r),..., FM (r) calculated by the integral equation is changed to an electromagnetic field f (( By sequentially adding and updating to r), the scattered electromagnetic field distribution f _total (r) generated by the dielectric having the target structure can be obtained.

  According to such a scattered wave calculation system in the second embodiment, the same effect as that of the scattered wave calculation system in the first embodiment can be obtained.

  FIG. 9 is a diagram showing a structural example suitable for the dielectric region division method as shown in FIG.

  As shown in FIG. 9A, when the dielectric is divided into a flat reference region b0 and rectangular regions b1, b2, b3,. There may be cases where it is not finite. Therefore, as shown in FIG. 9B, if the dielectric is divided into a flat reference region b0 and a finite rectangular space b1, b2, b3,. The scattered electromagnetic field of the dielectric can be obtained by repeating the calculation according to.

(Third embodiment)
In the scattered wave calculation system in the third embodiment, the detailed functions of the structure specifying unit and the electromagnetic field calculation unit are different from the scattered wave calculation system 1 in the first embodiment. For this reason, only the detailed functions of the structure specifying unit and the electromagnetic field calculation unit in the third embodiment will be described.

  The structure specifying unit of the scattered wave calculation system according to the third embodiment includes a dielectric region with a non-constant dielectric constant that is a calculation target of the scattered electromagnetic field, a flat reference region, and a plurality of finite regions that do not intersect with each other. Has a function of expressing as a synthesized region. For this reason, the electromagnetic field calculation unit in the third embodiment is configured to obtain an electromagnetic field formed by scattered waves generated when electromagnetic waves are incident on dielectrics having a plurality of different dielectric constants.

  A typical example of a dielectric having a plurality of different dielectric constants is a reticle used in photolithography. Therefore, here, a case will be described in which an electromagnetic field formed by scattered waves generated when electromagnetic waves are incident on the reticle is obtained.

  FIG. 10 is a cross-sectional view showing an example of the structure of a reticle that is a calculation target of the scattered electromagnetic field in the scattered wave calculation system according to the third embodiment.

  The reticle 20 is configured by depositing a metal thin film 22 on a flat glass substrate 21 and providing a plurality of openings 23 in the metal thin film 22. The lengths and intervals of the openings 23 are irregular, and the surface of the glass substrate 21 is exposed at the openings 23. The dielectric constants of the glass substrate 21 and the metal thin film 22 are different from each other. Therefore, the reticle 20 can be regarded as a two-layer semi-infinite dielectric plate having two dielectric constants.

  Therefore, the scattered electromagnetic field of the reticle 20 having a two-layer dielectric structure can be calculated in the same manner as in the first or second embodiment. That is, the reticle 20 is represented as a composite region of a reference region and a plurality of finite regions, and the scattered electromagnetic field is changed to a vector field by repeating the calculation by the difference field boundary element method while adding a single or a plurality of finite regions to the reference region. Can be calculated as

  Here, for ease of calculation, a case will be described as an example where each opening 23 of reticle 20 is a finite region configured by a space, and each finite region is added to a flat reference region one by one.

  FIG. 11 is a diagram for explaining a calculation method of the scattered electromagnetic field by the electromagnetic field calculation unit in the third embodiment.

  Assuming that the finite regions b1, b2, b3,..., BM in which the openings 23 are sequentially added to the reference region b0, the reference region b0 has a dielectric constant of 2 in the thickness direction as shown in FIG. It becomes a flat region of two layers of values. Therefore, the electromagnetic field distribution f (r) at the position r when there is no opening 23 corresponds to the electromagnetic field distribution generated by the three-layer dielectric multilayer film of glass, metal thin film, and air.

  The electromagnetic field distribution f (r) generated by the dielectric multilayer film can be calculated by any method. From the viewpoint of calculation amount and accuracy, for example, calculation by the transmission matrix method is suitable.

Next, as shown in FIG. 11B, the first opening 23 is added to the reference region b0 as a finite region b1. Further, as the integral path of the boundary integral, the glass substrate 21 and the boundary C ₀ of predetermined length between the metal thin film 22, the boundary C ₁ between the glass substrate 21 and a finite area b1 (opening 23), a finite region b1 boundary C ₂ of the metal thin film 22, the surface boundary C ₄ of the surface boundary C ₃ and the reference area b0 finite area b1 (metal film 22) is defined. That is, the lengths of the boundaries C ₀ and C ₄ are set according to the integration range. That is, a boundary sufficiently far from the finite region b1 is ignored.

Further, the region S ₁ is a region that is an integration range in the glass substrate 21, the region S ₂ is a region that is an integration range in the metal thin film 22, and the region S ₃ is a region that is an integration range outside the reference region b0, area S ₄ are respectively defined as the area within the rectangular space b1 to be added subject.

Then, the differential electromagnetic field on each defined boundary C ₀ , C ₄ and the electromagnetic field on each boundary C ₁ , C ₂ , C ₃ can be obtained by solving the integral equation shown in Equation (7) .

・・・(7)

... (7)

In addition, using the differential electromagnetic field on each boundary C ₀ , C ₄ calculated by Equation (7) and the electromagnetic field on each boundary C ₁ , C ₂ , C ₃ , the outside of the rectangular space b1 by Equation (8) It is possible to calculate the differential electromagnetic field f1 (r) at an arbitrary position r and the electromagnetic field inside the rectangular space b1.

・・・(8)

... (8)

  Then, the differential electromagnetic field f1 (r) generated by the addition of the rectangular space b1 and the electromagnetic field distribution f (r) generated by the reference region b0 are added. Then, the electromagnetic field distribution f (r) is updated to an added value with the differential electromagnetic field f1 (r). Thereby, the electromagnetic field distribution f (r) formed by the region obtained by adding the rectangular space b1 to the reference region b0 as shown in FIG. 11B can be obtained.

  Subsequently, similarly, the second and subsequent finite regions bi are sequentially added. Then, the electromagnetic field distribution f (r) is calculated by calculating the differential electromagnetic field fi (r) corresponding to the finite region bi added in the same flow and adding the differential electromagnetic field f1 (r) and the electromagnetic field distribution f (r). ) Is repeated.

  However, when the permittivity of the reference region b0 is binary, the calculation formula such as the integral equation differs depending on whether or not the added finite region bi is included in the integration range. Therefore, the electromagnetic field calculation unit determines whether or not the added finite region bi is included in the integration range. As a result, as shown in FIG. 11 (C), the finite region bi-1 that has already been added to the integration range is not included, and the finite region bi that has already been added to the integration range as shown in FIG. 11 (D). Cases can be classified when -1 is included.

  In this case, the determination process for classification can be performed by an arbitrary algorithm. For example, cases can be classified by threshold processing in which the length of the integration range is used as a threshold and the distance between the finite regions bi is compared with the threshold.

As shown in FIG. 11C, when a boundary C ₀ having a predetermined length can be set between the glass substrate 21 and the metal thin film 22, that is, when the boundary C ₀ does not straddle the adjacent finite region bi-1. Can be calculated by the above-described calculation formula. On the other hand, as shown in FIG. 11 (D), when there are three or more boundaries C ₀ between the integration range glass substrate 21 and the metal thin film 22 due to the existence of the adjacent finite region bi-1, the above-mentioned case is described. The calculation cannot be performed using the formula. The same applies to the case where the boundary C ₀ between the glass substrate 21 and the metal thin film 22 is not the end of the integration range.

That is, as shown in FIG. 11D, when a long boundary C ₀ between the glass substrate 21 and the metal thin film 22 extends over the adjacent finite region bi-1, a calculation formula such as an integral equation is used. Are different expressions. Therefore, it is necessary to set the calculation formula for obtaining the differential electromagnetic field fi (r) corresponding to the finite region bi as the calculation formula corresponding to the boundary and the region surrounded by the boundary. For example, a region S ₂ shown in FIG. 11 (C) in the example shown in FIG. 11 (D), are divided in the region S _2a and the region S _2b. Therefore, the calculation formula for obtaining the differential electromagnetic field fi (r) is an equation using integral equations and integrals for each region surrounding each region S _2a , S _2b .

When the boundary C ₀ between the glass substrate 21 and the metal thin film 22 extends over the adjacent finite region bi-1, the number of types of integration paths increases, and the amount of calculation is limited to the boundary C _0. It is almost the same as when not straddling 1. In addition, even when the boundary C ₀ extends over a plurality of finite regions bi-1, bi-2, bi-3, ... that have been added, similarly define the boundary element and the region surrounded by the boundary, It can be calculated with the corresponding calculation formula.

  When the reference region b0 has a binary dielectric constant, such determination process and calculation of the differential electromagnetic field fi (r) by a calculation formula corresponding to the boundary are repeated. Similarly, even when the reference region b0 has a multivalued dielectric constant, the differential electromagnetic field fi (r) corresponding to the finite region bi is sequentially calculated using the determination process and the calculation formula corresponding to the number of dielectric constants. can do.

When the calculation for the last finite region bM is completed, the scattered electromagnetic field distribution f _total (r) generated by the reticle 20 having a plurality of irregular openings 23 as shown in FIG. Can be requested.

  Alternatively, the metal thin film 22 may be a plurality of convex finite regions, and the finite region constituted by the metal thin film 22 may be sequentially added to the flat reference region. In this case, the dielectric constant of the reference region and the dielectric constant of the finite region are different from each other. Therefore, it is only necessary to solve the integral equation corresponding to the case where the dielectric constants are different. Further, the calculation formula is a formula obtained by rewriting the calculation formula of the first embodiment when the dielectric constant is binary.

  As described above, according to the scattered wave calculation system in the third embodiment, not only a dielectric having a single dielectric constant but also a finite or semi-infinite dielectric having a plurality of dielectric constants is used. The field can be calculated.

  For this reason, according to the scattered wave calculation system in the third embodiment, it is possible to perform imaging simulation of photolithography, which was difficult with the conventional method, at high speed with good accuracy. That is, an electromagnetic field formed by scattered waves generated when an electromagnetic wave is incident on a reticle 20 used for photolithography which is important in the semiconductor industry can be obtained with good accuracy.

  In particular, in the calculation by the conventional differential field boundary element method, the scattered electromagnetic field is calculated by adding the differential electromagnetic field generated by a single opening and the electromagnetic field generated by the reference region. Here, if the differential electromagnetic field generated by all the openings is calculated and added to the electromagnetic field generated by the reference region, if the scattering effect by the openings is weak, the differential electromagnetic field and the differential electromagnetic field There is a difference in magnitude between the electromagnetic field to be added. For this reason, in the conventional method in which the calculation by the differential field boundary element method is performed once, a weak scattered light component may be lost and an imaging pattern may not be accurately obtained.

  On the other hand, according to the scattered wave calculation system in the third embodiment, the electromagnetic field f (r) having a relatively large intensity and the differential electromagnetic field fi (r) having a weak intensity are calculated individually. Therefore, it is possible to obtain an imaging pattern that accurately reflects a weak scattered light component. As a result, it is possible to design a photomask that is increasingly miniaturized so as to have a smaller error, and to shorten the photomask design time. Then, semiconductor microfabrication technology can be developed.

  In the third embodiment, the reference region b0 and the finite regions b1, b2, b3,..., BM can be handled as 3D regions. In that case, the scattered electromagnetic field can be calculated as each finite region b1, b2, b3,..., BM surrounded by the closed surface of the opening 23 or the metal thin film 22 of the reticle 20.

  In addition, the simulation of the scattered electromagnetic field in the third embodiment can be used to detect foreign matter and defects mixed in the photomask. Specifically, it is possible to obtain a scattered electromagnetic field by assuming a plurality of dielectric constants and positions of a region where a foreign substance or a defect exists, and to associate each scattered electromagnetic field with a state where the foreign substance or the defect exists. Then, it is possible to infer the presence and position of a foreign substance or a defect by comparing the measured value of the scattered electromagnetic field of the actual photomask with the simulation result of the scattered electromagnetic field.

(Fourth embodiment)
In the scattered wave calculation system in the fourth embodiment, the detailed functions of the structure specifying unit and the electromagnetic field calculation unit are different from the scattered wave calculation system 1 in the first embodiment. Therefore, only the detailed functions of the structure specifying unit and the electromagnetic field calculation unit in the fourth embodiment will be described.

  The structure specifying unit of the scattered wave calculation system in the fourth embodiment synthesizes the area of the dielectric that is the target of calculation of the scattered electromagnetic field, with a reference area having a non-flat shape and a plurality of finite areas that do not intersect each other. Have the function of representing as a region. For this reason, the electromagnetic field calculation unit according to the fourth embodiment is based on the differential field boundary element method while sequentially adding a plurality of finite regions composed of a part of a dielectric or a space to a reference region having a non-flat shape. It has a function to repeat calculations.

  A typical example of a dielectric material that preferably defines a reference region having a non-planar shape for obtaining a scattered electromagnetic field is a diffraction grating. Therefore, here, a case where the electromagnetic field calculation unit obtains an electromagnetic field formed by a scattered wave generated when an electromagnetic wave is incident on the diffraction grating will be described.

  FIG. 12 is a diagram for explaining a method for calculating a scattered electromagnetic field from a diffraction grating by the scattered wave calculation system in the fourth embodiment.

  FIG. 12A is a cross-sectional view of a rectangular diffraction grating 30. In the diffraction grating 30 shown in FIG. 12A, a simple dielectric and space are added as examples of irregular foreign matters and defects. For example, a semicircular foreign matter 31A is added to the leftmost convex shape portion, and a triangular foreign matter 31B is added to the right side of the second convex shape portion from the left. Further, a semicircular defect 32A is added to the leftmost concave portion, and a triangular defect 32B is added to the left side of the second convex shape portion from the left.

  As in the diffraction grating 30 shown in FIG. 12A, a dielectric having a structure that repeats the same shape with periodicity or a dielectric having a shape change applied to such a dielectric is a target for calculating the scattered electromagnetic field. In some cases, the reference region b0 is preferably a structure that repeats with periodicity.

  Therefore, as shown in FIG. 12B, the structure specifying unit defines the ideal periodic structure of the diffraction grating 30 as the reference region b0. That is, an ideal region of the diffraction grating 30 in which rectangular irregularities having a certain length and interval and a certain height are repeated is defined as the reference region b0.

  Next, the structure specifying unit extracts a closed region surrounded by the boundary of the surface of the target diffraction grating 30 and the reference region b0. As a result, the foreign matter 31A, 31B and the defects 32A, 32B of the diffraction grating 30 are separated from the diffraction grating 30 as a plurality of finite regions b1, b2, b3,.

  Next, the electromagnetic field calculation unit generates a scattered electromagnetic field generated by an ideal diffraction grating 30 without any finite regions b1, b2, b3,. Calculate The diffraction grating 30 has a periodic structure. For this reason, the electromagnetic field f (r (r) corresponding to the reference region b0 can be easily obtained by a conventional method such as a rigorous coupled wave analysis method using the periodic boundary condition of the diffraction grating 30 even if the size of the diffraction grating 30 is infinite. ).

  Next, as shown in FIG. 12C, the first finite area b1 corresponding to the foreign matter 31A is added to the reference area b0. Then, the first finite region b1 becomes a dielectric convex portion added to the reference region b0. Therefore, the integration path and region can be determined by the same method as in the first embodiment, and the differential electromagnetic field f1 (r) corresponding to the first finite region b1 can be calculated by the differential field boundary element method.

That is, as shown in FIG. 12C, the surface boundary C _{0 of} the reference region b0 having a predetermined length, the boundary C ₁ between the reference region b0 and the first finite region b1, and the first finite region. surface boundary C ₂ of b1 is defined as the integral path. Further, a region S ₁ in the reference region b 0, a dielectric outer region S _2, and a region S ₃ in the finite region b 1 are defined. Surface boundary C ₀ of the reference area b0 is determined according to the required calculation accuracy.

  Then, the differential electromagnetic field f1 (r) can be calculated by the equations (1) and (2). The obtained differential electromagnetic field f1 (r) is added to the electromagnetic field f (r) corresponding to the reference region b0, and the electromagnetic field f (r) is updated. As a result, the electromagnetic field f (r) is an electromagnetic field generated by a region where the first finite region b1 is added to the reference region b0, that is, a region where only the foreign matter 31A is added to the ideal diffraction grating.

  Subsequently, as shown in FIG. 12D, the second finite area b2 corresponding to the defect 32A is added to the area obtained by synthesizing the first finite area b1 with the reference area b0. Then, the second finite region b2 becomes a concave portion of the dielectric added as a finite space to the reference region b0. Therefore, the integration path and region can be determined by the same method as in the second embodiment, and the differential electromagnetic field f2 (r) corresponding to the second finite region b2 can be calculated by the differential field boundary element method.

That is, as shown in FIG. 12 (D), a surface boundary C _0, the second surface boundary C ₁ and the reference area b0 and second finite area b2 finite region b2 of the reference area b0 having a predetermined length boundary C ₂ is defined as the integral path between. In addition, a region S _{1 in} the reference region b 0, an external region S _{2 in the} reference region b 0, and a region S ₃ in the second finite region b 2 are defined.

  Then, the differential electromagnetic field f2 (r) can be calculated by the equations (5) and (6). The obtained difference electromagnetic field f2 (r) is added to the electromagnetic field f (r), and the electromagnetic field f (r) is updated. As a result, the electromagnetic field f (r) is a region obtained by adding the first and second finite regions b1 and b2 to the reference region b0, that is, a region where only the foreign matter 31A and the defect 32A are added to the ideal diffraction grating. The electromagnetic field generated by

Similarly, the addition of the finite region bi, the calculation of the differential electromagnetic field fi (r), and the addition of the differential electromagnetic field fi (r) to the electromagnetic field f (r) are repeated. Thereby, the scattered electromagnetic field distribution f _total (r) generated by the diffraction grating 30 having the structure shown in FIG. 12A can be obtained.

  It is also possible to calculate the scattered electromagnetic field from a dielectric having a periodic structure other than the diffraction grating 30 by appropriately defining the shapes of the finite regions b1, b2, b3,..., BM. For example, the scattered electromagnetic field of the mesa structure can be calculated by defining the triangular foreign matter 31B or the defect 32B as the finite regions b3 and b4.

  According to such a scattered wave calculation system in the fourth embodiment, a scattered electromagnetic field from a dielectric having a periodic structure such as a diffraction grating to which a specific shape such as a foreign substance, a defect, or a manufacturing error is irregularly added. It is possible to calculate with high accuracy with a realistic data processing amount. For this reason, the scattered wave calculation system can be used to detect foreign matters and defects in an optical element such as a diffraction grating.

  In other words, the scattered electromagnetic field can be simulated under a plurality of typical conditions in which a foreign object or defect exists in the optical element, and the change in the scattered electromagnetic field due to the influence of the foreign object or defect can be examined. And the position and magnitude | size of a foreign material or a defect are detectable by comparing the scattered electromagnetic field of the optical element actually manufactured, and the simulation result.

  The diffraction wave of an ideal diffraction grating can also be calculated by rigorous coupled wave analysis, which is one of the conventional methods. On the other hand, there is a need to analyze the nature of how the diffraction characteristics of a diffraction grating deteriorate when foreign matter or defects adhere to or mix in the diffraction grating. However, if the periodicity of the structure of the diffraction grating is lost due to irregular inclusion of foreign matter or defects, the strict coupled wave analysis cannot be applied.

  In addition, when the conventional FDTD method is applied to the analysis of a diffraction grating having a defect and the calculation range is limited to a region near the defect, the diffracted wave from the diffraction grating varies depending on the size of the calculation range. For this reason, if the FDTD method is used to analyze a diffraction grating having defects, an influence due to the limitation of the calculation range occurs, and it is difficult to accurately obtain a diffraction wave from the diffraction grating.

  On the other hand, according to the scattered wave calculation system in the fourth embodiment, as described above, it is a diffracted wave from a diffraction grating that includes irregular foreign matters and defects and whose structure has a disordered spatial periodicity. Can be calculated with high accuracy in a short time.

In addition, when there are M abnormal parts such as foreign matters on the diffraction grating, when trying to calculate the scattered electromagnetic field by the conventional differential field boundary element method, if the number of points to be discretized is N, approximately (MN ) Requires ³ orders of calculation. On the other hand, in the case of the scattered wave calculation system in the fourth embodiment, it can be estimated that the calculation amount is in the order of MN ³ . Therefore, compared with the conventional calculation based on the simple difference field boundary element method, according to the scattered wave calculation system in the fourth embodiment, the calculation amount can be reduced to 1 / M ² .

(Other embodiments)
Although specific embodiments have been described above, the described embodiments are merely examples, and do not limit the scope of the invention. The novel methods and apparatus described herein can be implemented in a variety of other ways. Various omissions, substitutions, and changes can be made in the method and apparatus described herein without departing from the spirit of the invention. The appended claims and their equivalents include such various forms and modifications as are encompassed by the scope and spirit of the invention.

  For example, as suggested above, the dielectric decomposition method and the scattered electromagnetic field calculation method in each embodiment can be combined. For example, when the first embodiment and the second embodiment are combined, the corresponding calculation formulas may be used properly depending on whether the finite region is a part of a dielectric or a space. Then, by simply adding the differential electromagnetic field corresponding to each finite region composed of a dielectric or space, the scattered electromagnetic field from the dielectric having the target structure can be calculated. That is, if the dielectric constant of the dielectric is constant, the case division according to the integration range as described in the third embodiment is unnecessary.

  On the other hand, if the dielectric constant of the dielectric is not constant, a calculation formula such as a corresponding integral equation may be properly used depending on whether or not a closed region having the same dielectric constant exists in the integration range. Therefore, not only a simple two-layer dielectric as shown in the third embodiment, but also a multilayer dielectric or a dielectric with a foreign substance having a different dielectric constant locally attached or mixed inside, As long as each dielectric constant is known, the scattered electromagnetic field can be calculated using a calculation formula according to the conditions.

  When the dielectric is a multilayer, the foreign material is often made of the same material as any one of the layers of the dielectric. Therefore, the dielectric constant of the foreign substance can be assumed to be the dielectric constant of any layer of the dielectric. For this reason, the scattered wave calculation system can be used for the detection of adhesion and contamination of foreign substances having different dielectric constants.

  FIG. 13 shows scattering when a second dielectric having a different dielectric constant is partially embedded in a first dielectric having a single dielectric constant by a scattered wave calculation system according to an embodiment of the present invention. It is sectional drawing explaining the calculation method of an electromagnetic field.

  A simple case in which the lower half of the cylindrical second dielectric 42 is embedded in the semi-infinite plate-like first dielectric 40 as shown in FIG. 13A will be described as an example. In this case, as shown in FIG. 13B, a flat semi-infinite rectangular region in which the second dielectric 42 is not embedded in the first dielectric 40 is used as the reference region b0, while the cylindrical first Two dielectrics 42 can be defined as a finite region b1.

Accordingly, as shown in FIG. 13A, the surface boundary of the predetermined length of the first dielectric 40 is C ₀ , and the boundary corresponding to the intersection of the reference region b 0 and the second dielectric 41 is C ₁ , The surface boundary of the second dielectric 41 is C ₂ , the boundary between the first dielectric 40 and the second dielectric 41 is C ₃ , and the region within the integration range in the first dielectric 40 is S. ₁ , the region within the integration range outside the first dielectric 40 and the second dielectric 42 can be defined as S ₂ , and the region inside the second dielectric 41 can be defined as S ₃ .
In this case, the integral equation corresponding to Equation (1) is Equation (9).

  Further, an expression including an integral expression corresponding to Expression (3) is Expression (10).

  FIG. 14 shows scattered electromagnetic waves when a second dielectric having a different dielectric constant is completely embedded in a first dielectric having a single dielectric constant by the scattered wave calculation system according to an embodiment of the present invention. It is sectional drawing explaining the calculation method of a field.

  As shown in FIG. 14A, a simple case in which the cylindrical second dielectric 42 is completely embedded inside the semi-infinite plate-shaped first dielectric 40 is also partially embedded. The scattered electromagnetic field can be calculated in the same manner as in the case. That is, as shown in FIG. 14B, a flat semi-infinite rectangular area where the second dielectric 42 is not embedded in the first dielectric 40 is used as the reference area b0, while the cylindrical second The dielectric 42 can be defined as a finite region b1.

Therefore, as shown in FIG. 14A, the surface boundary of the predetermined length of the first dielectric 40 is C ₀ , and the boundary between the first dielectric 40 and the second dielectric 41 is C ₁ , The region within the integration range in the first dielectric 40 is S ₁ , the region within the integration range outside the first dielectric 40 and the second dielectric 42 is S ₂ , and the inside of the second dielectric 41 the area can be defined as S _3.

  In this case, the integral equation corresponding to Equation (9) is Equation (11).

・・・(11)

... (11)

  Further, an expression including an integral expression corresponding to Expression (10) is Expression (12).

・・・(12)

... (12)

  In FIG. 13 and FIG. 14, when a plurality of second dielectrics 42 are present at equal intervals or unequal intervals, they are sequentially added as finite regions b1, and the same calculation may be performed. If the single or plural second dielectrics 42 are assumed to be a foreign substance, the detection of the foreign substance can be supported by referring to the scattered electromagnetic field pattern. That is, when a scattered electromagnetic field showing the same tendency as the simulated scattered electromagnetic field is measured, it can be determined that a foreign object exists.

  In addition, various conditions can be changed by adapting calculation formulas including integral equations. For example, in each of the above-described embodiments, the case where the electromagnetic wave is incident on the dielectric as a plane wave has been described. The scattered electromagnetic field can be calculated.

  On the other hand, a reference region b0 having a curved surface such as a spherical surface, an elliptical surface, or a cylindrical side surface as the surface shape can be defined for the dielectric. For this reason, the above-described scattered wave calculation system can be applied to detection of defects generated in an optical element such as a lens.

  Further, as described above, the reference region and the finite region can be treated as a 2D region or a 3D region regardless of whether the dielectric constant is constant or has a plurality of dielectric constants. When a scattered electromagnetic field is calculated by defining a 3D region, a dielectric region is represented as a region obtained by combining a 3D reference region and a plurality of 3D finite regions that do not intersect each other. Then, a three-dimensional or 3D space having a constant dielectric constant or a plurality of values is sequentially added to a 3D reference region having a constant dielectric constant or a plurality of values to calculate a differential electromagnetic field.

  FIG. 15 is a perspective view illustrating an example of a method for calculating a scattered electromagnetic field from a 3D dielectric by the scattered wave calculation system according to the embodiment of the present invention.

  As shown in FIG. 15, when a dielectric material to be calculated can be decomposed into a semi-infinite flat reference region b0 in a biaxial direction and finite regions b1, b2, b3,. Will be described as an example. This corresponds to the case where the example shown in FIG. 4 is extended to 3D.

  When calculating the scattered electromagnetic field from the 3D region, all the variables in the mathematical formula are 3D electric field vectors or 3D magnetic field vectors. Further, the equation including the integral equation corresponding to equation (1) and the integral expression corresponding to equation (3) is a double integral equation. Therefore, the boundary element that becomes the integration path is not a line element but an area element as in the case of 2D.

As a specific example, as shown in FIG. 15, if the calculation is performed by adding the second finite area b2, the predetermined area obtained by adding the first finite area b1 to the reference area b0 is used. Define the surface of the 3D region as C ₀ , the interface between the 3D region obtained by adding the first finite region b1 to the reference region b0 and the finite region b2 as C ₁ , and the surface of the finite region b2 as C _2. Can perform calculations involving integral equations. In this case, each boundary surface C ₁ , C ₂ , C ₃ and each region divided by the integration range are also defined using parameters.

  In addition to the above-described examples, the reference region and the plurality of finite regions are approximated without strictly defining the reference region and the plurality of finite regions by closely simulating the structure of the actual dielectric that is the object of calculation of the scattered electromagnetic field. An area may be defined. For example, the scattered electromagnetic field can be calculated by ignoring a finite region in which it can be determined that the influence on the scattered electromagnetic field is relatively small. In this case, the time required for calculating the scattered electromagnetic field can be shortened. Judgment whether or not the influence on the scattered electromagnetic field is relatively small is made uniformly by threshold processing for indices indicating the contribution to the scattered electromagnetic field such as dielectric constant, area, volume, boundary length, and shape of a finite region. Can be done.

  Therefore, when the index indicating the contribution to the scattered electromagnetic field for a certain finite area is less than or less than the threshold value, the electromagnetic field calculation unit does not add the differential electromagnetic field generated by the addition of the finite area. What is necessary is just to obtain a scattered electromagnetic field. This is because the structure specifying unit approximates the dielectric region to a reference region and a plurality of finite regions by using a plurality of finite regions where the index indicating the degree of contribution to the scattered electromagnetic field is equal to or greater than the threshold value or exceeds the threshold value. Is substantially the same as expressing the region as a synthesized region. By such threshold processing, it is possible to calculate the scattered electromagnetic field at higher speed while omitting slight irregularities on the dielectric surface.

  And by adapting the scattered wave calculation system to various conditions as described above, it has various structures such as reticle, diffraction grating, optical waveguide processed on the substrate, light scattering from rough surface, biological tissue, etc. The scattered electromagnetic field from the dielectric can be calculated in a short time with the required accuracy.

  The scattered wave calculation system is particularly useful when calculating the electromagnetic field of a scattered wave generated by a dielectric having a fine structure approximately equal to or less than the wavelength of the incident electromagnetic wave. However, even if the dielectric has a sufficiently large structure with respect to the wavelength of the incident electromagnetic wave, the electromagnetic field of the scattered wave can be calculated by the scattered wave calculation system.

DESCRIPTION OF SYMBOLS 1 Scattered wave calculation system 2 Input device 3 Display device 4 Storage device 5 Arithmetic device 6 Computer 7 Dielectric structure definition part 8 Dielectric structure acquisition part 9 Structure specification part 10 Electromagnetic field calculation part 11 Reference electromagnetic field preservation | save part 12 Target electromagnetic field Storage unit 13 Computer 14 Recording medium driving device 20 Reticle 21 Glass substrate 22 Metal thin film 23 Opening 30 Diffraction gratings 31A and 31B Foreign matter 32A and 32B Defect 40 First dielectric 41 Second dielectric

Claims (8)

A dielectric region that is an object of calculation of an electromagnetic field formed by scattered waves generated when electromagnetic waves are incident is composed of a reference region and a part or space of each of the dielectrics, and a plurality of regions that do not intersect each other. A structure specifying unit that represents a region combined with a finite region;
A plurality of finite regions are sequentially added to the reference region in a plurality of times, and an electromagnetic field generated by each added finite region is sequentially added to the electromagnetic field formed by the reference region. An electromagnetic field calculator for obtaining an electromagnetic field formed by scattered waves generated when the electromagnetic wave is incident;
A scattered wave calculation system.   2. The scattered wave calculation according to claim 1, wherein the electromagnetic field calculation unit is configured to obtain an electromagnetic field formed by a scattered wave generated when the electromagnetic wave is incident on a dielectric having a plurality of different dielectric constants. system.   When the index indicating the degree of contribution to the electromagnetic field formed by the scattered wave for a certain finite region is less than or less than the threshold, the electromagnetic field calculation unit calculates the electromagnetic field generated by the addition of the finite region. The scattered wave calculation system according to claim 1, wherein the scattered wave calculation system is configured to obtain an electromagnetic field formed by the scattered wave without adding.   The structure specifying unit is configured to represent the region of the dielectric as a region obtained by combining a three-dimensional reference region and a plurality of three-dimensional finite regions that do not intersect with each other. Scattered wave calculation system described in 1.   5. The electromagnetic field calculation unit according to claim 1, wherein the electromagnetic field calculation unit is configured to obtain an electromagnetic field formed by a scattered wave generated when the electromagnetic wave is incident on a reticle or diffraction grating used in photolithography. The scattered wave calculation system according to item 1.   The electromagnetic field calculation unit is obtained by sequentially combining at least one of the plurality of finite regions in the reference region with a reference electromagnetic field formed by scattered waves generated when the electromagnetic wave is incident on the reference region. Scattered waves generated when the electromagnetic waves are incident on the dielectric by sequentially adding displacement amounts of electromagnetic fields formed by the scattered waves generated when the electromagnetic waves are incident on a plurality of different regions. The scattered wave calculation system according to any one of claims 1 to 6, wherein the scattered wave calculation system is configured to obtain an electromagnetic field formed by: A dielectric region that is an object of calculation of an electromagnetic field formed by scattered waves generated when electromagnetic waves are incident is composed of a reference region and a part or space of each of the dielectrics, and a plurality of regions that do not intersect each other. Representing a finite region as a composite region;
A plurality of finite regions are sequentially added to the reference region in a plurality of times, and an electromagnetic field generated by each added finite region is sequentially added to the electromagnetic field formed by the reference region. Obtaining an electromagnetic field formed by scattered waves generated when the electromagnetic wave is incident;
Scattered wave calculation method having Computer
A dielectric region that is an object of calculation of an electromagnetic field formed by scattered waves generated when electromagnetic waves are incident is composed of a reference region and a part or space of each of the dielectrics, and a plurality of regions that do not intersect each other. A structure specifying unit that represents a region combined with a finite region, and the plurality of finite regions are sequentially added to the reference region in multiple times, and an electromagnetic field generated by each added finite region is formed by the reference region. An electromagnetic field calculation unit for obtaining an electromagnetic field formed by a scattered wave generated when the electromagnetic wave is incident on the dielectric by calculation to sequentially add to the electromagnetic field to be performed;
Scatter wave calculation program to function as.

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