JP6733231B2 - Spectral reflectance design method, spectral reflectance design device, and spectral reflectance design program - Google Patents

Description

The present invention relates to a spectral reflectance design method, a spectral reflectance design device, and a spectral reflectance design program.

A technique for controlling the spectral reflectance of a thin film using the theory of thin film interference is known. The thin film interference is a phenomenon in which light reflected on the upper surface and the lower surface of the thin film interferes with each other, and light having a wavelength corresponding to the film thickness strengthens or weakens. For example, Patent Document 1 describes that an antireflection property is imparted by forming a thin film having a thickness of about the wavelength of light on the surface of a product. Patent Document 2 describes that the antireflection performance is enhanced by appropriately controlling the thickness of the thin film.

JP, 2010-286657, A JP, 2005-210308, A

In the conventional method, the value of the spectral reflectance is designed using an approximate expression when the film thickness is constant. Therefore, only a simple spectral reflectance waveform can be designed. Further, in the conventional method, a uniform film thickness is an essential condition for realizing the designed waveform. However, since the actual film thickness varies, the waveform as designed is not always realized.

An object of the present invention is to provide a spectral reflectance designing method, a spectral reflectance designing apparatus, and a spectral reflectance designing program capable of designing spectral reflectances of various waveforms.

A spectral reflectance design method according to one aspect of the present invention is a weighted average spectral reflectance that calculates a weighted average spectral reflectance by performing a weighted average of theoretical values of spectral reflectance for each film thickness of a thin film with a distribution function including distribution parameters. A rate calculation step; and an analysis step of applying the weighted average spectral reflectance to the design value of the spectral reflectance of the thin film to calculate the distribution parameter.

With this configuration, it is possible to design the spectral reflectance of the thin film having a film thickness distribution (film thickness variation). Therefore, it is possible to design the spectral reflectances of various waveforms as compared with the case where the spectral reflectances are designed by a simple model in which the film thickness is constant. Further, since the design value is approximated by the weighted average spectral reflectance in consideration of the film thickness distribution, the design value and the calculated value (weighted average spectral reflectance) are likely to match. Therefore, the difference between the calculated spectral reflectance and the actual spectral reflectance is unlikely to occur.

In the spectral reflectance design method according to one aspect of the present invention, the distribution parameter is calculated using, for example, a regression analysis method. As the distribution function, a distribution function which has an average value and whose probability distribution is calculated based on the variance value is preferably used. The film thickness distribution changes depending on the film forming conditions. Therefore, it is preferable to adopt an appropriate distribution function according to the film forming conditions. In consideration of the deviation of the film thickness distribution that occurs in the film forming process, it is possible to add a function or coefficient that can uniquely define the deviation to the above distribution function.

With this configuration, the weighted average spectral reflectance can be mechanically applied to the design value having an arbitrary wavelength dispersion, and the approximation accuracy is also high.

In the spectral reflectance design method according to one aspect of the present invention, for example, the distribution function is a distribution function exhibiting a Gaussian distribution or a Laplace distribution.

According to this configuration, it is possible to accurately approximate the film thickness distribution by using a highly probable distribution function.

In the spectral reflectance designing method according to one aspect of the present invention, the weighted average spectral reflectance is applied to the design value in the wavelength range of 300 nm to 3000 nm, for example.

For example, the weighted average spectral reflectance is applied to the design value in the visible light range. According to this configuration, the target spectral reflectance is likely to be realized in the visible light range. Therefore, it is possible to perform an appropriate design in applications where spectral reflectance in the visible light range is important, such as antireflection films. In other applications, spectral reflectance in the ultraviolet or infrared may be important. In that case, the weighted average spectral reflectance may be applied to the design value in the ultraviolet region or the infrared region.

In the spectral reflectance design method according to an aspect of the present invention, for example, based on a film forming table showing a correspondence relationship between the film forming conditions of the thin film and the distribution parameter, the distribution parameter calculated in the analysis step, The method has a film forming condition determining step for determining the film forming condition to be realized.

With this structure, the structure of the thin film having a desired spectral reflectance can be easily designed.

In the spectral reflectance design method according to an aspect of the present invention, for example, before the film forming condition determination step, using the actual measurement value of the spectral reflectance of the sample of the thin film formed under known film forming conditions. There is a film forming table creating step for creating the film forming table, and the film forming table creating step establishes a known relationship between the theoretical value of the spectral reflectance for each film thickness of the thin film and the distribution parameter. A second weighted average spectral reflectance calculating step of calculating a second weighted average spectral reflectance by weighted averaging with a second distribution function including a second distribution parameter having, and an actual measurement value of the spectral reflectance of the sample. And a second analysis step of applying the second weighted average spectral reflectance to calculate the second distribution parameter.

According to this configuration, the actual measurement value of the spectral reflectance of the sample is analyzed by the same routine as the analysis routine for designing the spectral reflectance. Therefore, the processing unit that designs the spectral reflectance and the processing unit that creates the film formation table can be shared.

Further, with this configuration, the film thickness distribution in the measurement region can be obtained by measuring the spectral reflectance once. Since the range that can be measured at one time is wide and the actual measurement value can be easily analyzed, the film thickness distribution in a wide range can be efficiently measured. Therefore, the work of forming the film forming table becomes easy.

Further, since the measured value is approximated by the second weighted average spectral reflectance in consideration of the film thickness distribution, the measured value and the calculated value (second weighted average spectral reflectance) are likely to match. Therefore, an error is unlikely to occur between the calculated film thickness distribution and the actual film thickness distribution. Therefore, the film forming condition and the film thickness distribution can be accurately associated with each other.

In the spectral reflectance design method according to an aspect of the present invention, for example, in the second analysis step, the second weight is added to the measured value in a wavelength range other than the absorption wavelength range of the base material on which the sample is arranged. Apply the average spectral reflectance.

According to this configuration, the second weighted average spectral reflectance can be accurately applied to the measured value. Therefore, an error is unlikely to occur between the calculated film thickness distribution and the actual film thickness distribution.

In the spectral reflectance designing method according to one aspect of the present invention, for example, the actual measurement value is a measurement value of the spectral reflectance in a measurement region of 1 mm ² or more.

According to this configuration, the film thickness distribution in a large measurement region of 1 mm ² or more can be obtained by measuring the spectral reflectance once. Therefore, even when the measurement is sequentially performed on a plurality of two-dimensionally arranged measurement regions, the measurement is completed in a short time.

In the spectral reflectance design method according to one aspect of the present invention, for example, the actual measured value of the spectral reflectance of the laminate of a plurality of samples is used, in the second weighted average spectral reflectance calculation step. , Setting the second distribution function for each sample, calculating the second weighted average spectral reflectance for each sample, the sum of the second weighted average spectral reflectance of each sample the laminate Is calculated as the second weighted average spectral reflectance, and in the second analysis step, the second weighted average spectral reflectance of the laminate is applied to the measured value to obtain the second distribution function of each sample. To calculate the second distribution parameter.

According to this configuration, the film thickness distributions of the plurality of samples are acquired by one measurement. It is not necessary to repeat the measurement for each sample. Therefore, it becomes easy to create a film forming table.

In the spectral reflectance design method according to an aspect of the present invention, for example, the thin film is composed of a plurality of layers, in the weighted average spectral reflectance calculation step, the distribution function is set for each layer, each layer To calculate the weighted average spectral reflectance, to calculate the sum of the weighted average spectral reflectance of each layer as the weighted average spectral reflectance of the thin film, in the analysis step, the design value to the weighted average spectral reflectance of the thin film. The distribution parameters included in the distribution function of each layer are calculated by applying the ratio.

With this configuration, it is possible to design the spectral reflectance of a thin film having a plurality of layers having a film thickness distribution (film thickness variation). Therefore, as compared with the case where the spectral reflectance is designed with only one thin film, the variation of the spectral reflectance that can be designed increases. Further, since the design value is approximated by the weighted average spectral reflectance in consideration of the film thickness distribution of each layer, the design value and the calculated value (weighted average spectral reflectance) are likely to match. Therefore, the difference between the calculated spectral reflectance and the actual spectral reflectance is unlikely to occur.

A spectral reflectance designing apparatus according to an aspect of the present invention is a weighted average spectral reflectance that calculates a weighted average spectral reflectance by performing a weighted average of theoretical values of spectral reflectance for each film thickness of a thin film with a distribution function including distribution parameters. A rate calculation unit and an analysis unit that calculates the distribution parameter by applying the weighted average spectral reflectance to the design value of the spectral reflectance of the thin film.

With this configuration, it is possible to design the spectral reflectance of the thin film having a film thickness distribution (film thickness variation). Therefore, it is possible to design the spectral reflectances of various waveforms as compared with the case where the spectral reflectances are designed by a simple model in which the film thickness is constant. Further, since the design value is approximated by the weighted average spectral reflectance in consideration of the film thickness distribution, the design value and the calculated value (weighted average spectral reflectance) are likely to match. Therefore, the difference between the calculated spectral reflectance and the actual spectral reflectance is unlikely to occur.

A spectral reflectance design program according to an aspect of the present invention is a weighted average spectral reflectance that calculates a weighted average spectral reflectance by performing a weighted average of theoretical values of spectral reflectance for each film thickness of a thin film with a distribution function including distribution parameters. A computer is made to perform the rate calculation step and the analysis step of applying the weighted average spectral reflectance to the design value of the spectral reflectance of the thin film to calculate the distribution parameter.

With this configuration, it is possible to design the spectral reflectance of the thin film having a film thickness distribution (film thickness variation). Therefore, it is possible to design the spectral reflectances of various waveforms as compared with the case where the spectral reflectances are designed by a simple model in which the film thickness is constant. Further, since the design value is approximated by the weighted average spectral reflectance in consideration of the film thickness distribution, the design value and the calculated value (weighted average spectral reflectance) are likely to match. Therefore, the difference between the calculated spectral reflectance and the actual spectral reflectance is unlikely to occur.

According to the present invention, it is possible to provide a spectral reflectance designing method, a spectral reflectance designing apparatus, and a spectral reflectance designing program capable of designing spectral reflectances of various waveforms.

FIG. 1 is a schematic diagram of a spectral reflectance design device according to the first embodiment. FIG. 2 is a diagram for explaining the principle of thin film interference. FIG. 3 is a diagram showing an example of the waveform of the spectral reflectance. FIG. 4 is a diagram showing how the spectral reflectance is measured for a thin film including a plurality of regions having different film thicknesses. FIG. 5 is a diagram showing the spectral reflectances of the first region and the second region. FIG. 6 is a diagram showing an example of the film thickness distribution of the thin film. FIG. 7 is a diagram showing an example of theoretical values of the spectral reflectance for each film thickness of the thin film. FIG. 8 is a diagram showing an example of the weighted average spectral reflectance of the thin film. FIG. 9 is a flowchart for explaining the spectral reflectance design method. FIG. 10 is a conceptual diagram showing a spectral reflectance designing method according to the second embodiment. FIG. 11 is a flowchart for explaining the spectral reflectance design method. FIG. 12 is a schematic diagram of a spectral reflectance design device according to the third embodiment. FIG. 13 is a diagram showing a plurality of measurement regions provided in the sample. FIG. 14 is a flowchart illustrating a method for detecting the second distribution parameter. FIG. 15 is a diagram showing a comparison result between the actual measurement value and the second weighted average spectral reflectance in Example 1. FIG. 16 is a diagram showing a comparison result between the actual measurement value and the second weighted average spectral reflectance in Example 2. FIG. 17 is a diagram showing a comparison result between the actual measurement value and the second weighted average spectral reflectance in Example 3. FIG. 18 is a diagram showing a comparison result between the actual measurement value and the second weighted average spectral reflectance in Example 4. FIG. 19 is a diagram showing film forming conditions, measured values of root mean square deviation, average film thickness and dispersion according to this analysis method in Examples 1 to 4. FIG. 20 is a diagram showing the relationship between the variance and the root mean square deviation. 21: is a figure which shows the comparison result of the actually measured value in Example 5, and a 2nd weighted average spectral reflectance. 22: is a figure which shows the comparison result of the measured value and the 2nd weighted average spectral reflectance in Example 6. FIG. FIG. 23 is a diagram showing the film forming conditions of Examples 5 and 6, and the average film thickness and dispersion according to this analysis method. FIG. 24 is a conceptual diagram showing a method of creating a film formation table according to the fourth embodiment. FIG. 25 is a flowchart illustrating a method for detecting the second distribution parameter of each layer. 26: is a figure which shows the comparison result of the measured value and the 2nd weighted average spectral reflectance in Example 7. FIG. FIG. 27 is a diagram showing values of parameters used for analysis of the sample of Example 7. FIG. 28 is a diagram showing variations of the distribution function. FIG. 29 is a diagram showing variations of the distribution function. FIG. 30 is a conceptual diagram of a single-layer film optical system. FIG. 31 is a conceptual diagram of a multilayer film optical system.

[First embodiment]
FIG. 1 is a schematic diagram of a spectral reflectance design device 1 according to the first embodiment.

The spectral reflectance design device 1 includes a processing unit 20, an input unit 30, a data storage unit 31, and a display unit 32. The processing unit 20 acquires the design information ID related to the design value RD of the spectral reflectance of the target thin film via the input unit 30. The processing unit 20 analyzes the design information ID, and detects the distribution information D regarding the film thickness distribution of the thin film with which the design value RD is obtained.

FIG. 2 is a diagram for explaining the principle of thin film interference. FIG. 3 is a diagram showing an example of the waveform of the spectral reflectance. In the following description, the surface of the thin film 40 on the side on which the illumination light Li enters is referred to as the upper surface 40a, and the surface of the thin film 40 on the side opposite to the side on which the illumination light Li enters (interface with the base material BM) is the lower surface 40b. Say.

The processing unit 20 designs the spectral reflectance of the thin film 40 using the theory of thin film interference. The thin film interference refers to a phenomenon in which the light L1 reflected on the upper surface 40a of the thin film 40 and the light L2 reflected on the lower surface 40b interfere with each other to intensify or weaken the light having the wavelength λ according to the film thickness t. A phase difference φ proportional to the film thickness t occurs between the light L1 and the light L2. Therefore, the intensity of the reflected light Lr changes periodically according to the size of the film thickness t. When the film thickness t is changed, the wavelength λ at which the intensity of the reflected light Lr has an extreme value changes.

The materials of the thin film 40 and the base material BM are not particularly limited. The thin film 40 and the base material BM may be made of materials having different refractive indexes. For example, as the base material BM, an inorganic material such as silver, aluminum and silica can be used, or an organic material such as polycarbonate and acrylic can be used. The thin film 40 preferably contains no scattering agent. However, a weak scattering agent that does not significantly impair the interference between the light L1 and the light L2 may be included in the thin film 40.

The spectral reflectance R is represented by the intensity ratio of the illumination light Li and the reflected light Lr. In a simple model in which the film thickness t is constant, the theoretical value RT of the spectral reflectance R is calculated by the calculation method using the matrix method described later. For details of the calculation method, refer to the section [Arithmetic Treatment of Interference Phenomena] below. The spectral reflectance R is represented by the following formula (1), for example. The theoretical value RT has a waveform as shown in FIG.

In the formula (1), R ₀ is the absorptance of the thin film 40. n _f is the refractive index of the thin film 40. α is a constant determined by the incident angle of the illumination light Li. Although the absorptance R ₀ is a function of the wavelength λ, it is treated as a constant in this embodiment. The value of α changes depending on the incident angle of the illumination light Li. In the present embodiment, for example, the illumination light Li is vertically incident on the thin film 40. Therefore, the value of α is 1.

When the influence of the base material BM is taken into consideration, the refractive index of the base material BM may be included in the theoretical value R. When the base material BM is polycarbonate, the refractive index of the base material BM is 1.59. Since the magnitude of the refractive index changes depending on the wavelength λ, an accurate theoretical value R can be obtained by describing the refractive indexes of the thin film 40 and the base material BM as a function of the wavelength λ. For simplification, the wavelength dependence of the refractive index can be corrected by the Abbe number. It is preferable to make the refractive index constant regardless of the wavelength because the accuracy of the calculation result is improved.

FIG. 4 is a diagram showing how the spectral reflectance is measured for the thin film 40 including a plurality of regions (first region FA, second region FB) having different film thicknesses.

The reflected light Lra from the first area FA and the reflected light Lrb from the second area FB are simultaneously observed by the observer. Therefore, the value of the spectral reflectance RTa of the reflected light Lra and the value of the spectral reflectance RTb of the reflected light Lrb simultaneously contribute to the observed value of the spectral reflectance observed by the observer. When the areas of the first area FA and the second area FB are reduced, the film thickness can be regarded as uniform in each area. Therefore, the spectral reflectance RTa and the spectral reflectance RTb are represented by the theoretical value RT shown in the equation (1).

FIG. 5 is a diagram showing the spectral reflectances of the first area FA and the second area FB.

The film thickness ta of the first area FA and the film thickness tb of the second area FB are different. Therefore, the waveform of the spectral reflectance RTa and the waveform of the spectral reflectance RTb are different. Therefore, when the spectral reflectance RTa and the spectral reflectance RTb are added, the wavelength λ showing the extreme value and the spectral reflectance value change. A large number of regions having different film thicknesses exist in one measurement region MA, and the observed value of the spectral reflectance is the sum of the spectral reflectances of the respective regions.

If there is variation in the film thickness, the waveform of the observed value changes according to the magnitude of the variation. Therefore, by properly controlling the variation in film thickness (film thickness distribution), it is possible to design spectral reflectances having various waveforms that have not been available in the past. For example, by intentionally increasing the variation in the film thickness, it becomes possible to increase or decrease the magnitude of the spectral reflectance over a wide wavelength range. The processing unit 20 detects the target design value RD of the spectral reflectance on the basis of the design information ID, and detects the film thickness distribution of the thin film such that the waveform of the target design value RD is obtained.

6 to 8 are diagrams showing the design principle of the spectral reflectance. FIG. 6 is a diagram showing an example of the film thickness distribution of the thin film 40. FIG. 7 is a diagram showing an example of the theoretical value RT of the spectral reflectance for each film thickness t of the thin film 40. FIG. 8 is a diagram showing an example of the weighted average spectral reflectance R _av of the thin film 40. The configuration of the processing unit 20 will be described below with reference to FIG. 1 with reference to FIGS. 6 to 8. The processing unit 20 is a computer including a processor and a memory. The memory includes a RAM (Random Access Memory) and a ROM (Read Only Memory).

As shown in FIG. 1, the processing unit 20 includes a distribution function creation unit 21, a non-distribution spectral reflectance creation unit 22, a weighted average spectral reflectance calculation unit 23, a design data acquisition unit 24, and an analysis unit 25. An output unit 26, a film forming condition determination unit 27, a table storage unit 28, and a program storage unit 29.

The distribution function creation unit 21 creates a distribution function f(t, P) indicating the film thickness distribution of the thin film 40 using the distribution parameter P that characterizes the film thickness distribution of the thin film 40. The distribution function f(t,P) indicates the ratio (occupancy rate) of the occupied area of the region where the film thickness of the thin film 40 is t in the measurement region MA. The distribution parameter P is expressed as a combination of _q (q is an integer of 1 or more) element parameters P _{1 to} P _q that characterize the film thickness distribution of the thin film 40. The value of each element parameter is calculated by analyzing the design value RD by the analysis unit 25. As shown in FIG. 6, the film thickness distribution may be a continuous distribution CD or a discrete distribution DD.

The non-distribution spectral reflectance creation unit 22 creates a theoretical value RT(λ, t) of the spectral reflectance for each film thickness t of the thin film 40 based on the equation (1). As shown in FIGS. 6 and 7, the non-distribution spectral reflectance creation unit 22 calculates theoretical values RT(λ, t) for a plurality of film thickness values (t ₁ , t ₂ ,..., T _N ), respectively. .. The plurality of film thickness values are set for each Δt within a range in which the film thickness distribution exists. The range in which the film thickness distribution exists and the magnitude of the film thickness pitch Δt are input from the input unit 30, for example.

The weighted average spectral reflectance calculation unit 23 performs a weighted average of the theoretical value RT(λ, t) of the spectral reflectance for each film thickness t of the thin film 40 with the distribution function f(t, P) to obtain the weighted average spectral reflectance R. Calculate _av (λ, P). The weighted average spectral reflectance R _av (λ, P) is an approximate expression that approximates the design value RD of the spectral reflectance. FIG. 8 is a diagram showing an example of the weighted average spectral reflectance R _av (λ, P) when the film thickness distribution is a Gaussian distribution.

The design data acquisition unit 24 acquires the design information ID input by the input unit 30. The design data acquisition unit 24 creates data on the spectral reflectance based on the design information ID and supplies it to the analysis unit 25 as a design value RD(λ).

The analysis unit 25 applies the weighted average spectral reflectance R _av (λ, P) to the design value RM(λ) of the spectral reflectance of the thin film 40 to calculate the distribution parameter P. The analysis unit 25 supplies the distribution parameter P to the output unit 26 and the film formation condition determination unit 27.

The output unit 26 detects the distribution information D regarding the film thickness distribution using the distribution parameter P. The distribution information D is, for example, the values of some or all of the element parameters that make up the distribution parameter P. The distribution information D may be a distribution function f(t,P) including a distribution parameter P. The output unit 26 supplies the distribution information D to the data storage unit 31 and the display unit 32 in association with the film forming conditions MC of the thin film 40, which will be described later.

The film forming condition determining unit 27 realizes the distribution parameter P calculated by the analyzing unit 25 based on the film forming table 28a indicating the correspondence between the film forming condition MC of the thin film 40 and the distribution parameter P. Determine the MC. The film formation table 28a is stored in the film formation table storage unit 28. The film formation table 28a defines a correspondence relationship between at least one of the q element parameters forming the distribution parameter P and the film formation condition MC. The film forming condition determining unit 27 determines the film forming condition MC that realizes the distribution parameter P calculated by the analyzing unit 25 based on the correspondence between the element parameters shown in the film forming table 28a and the film forming condition MC. decide.

The program storage unit 29 stores a spectral reflectance design program and data for the processing unit 20 to perform various kinds of processing. The spectral reflectance design program is a program that causes a computer to execute the spectral reflectance design method according to the present embodiment. The processing unit 20 performs various processes according to the spectral reflectance design program stored in the program storage unit 29. By executing the spectral reflectance design program, the processing unit 20 executes the distribution function creation unit 21, the non-distribution spectral reflectance creation unit 22, the weighted average spectral reflectance calculation unit 23, the design data acquisition unit 24, the analysis unit 25, It functions as the output unit 26 and the film formation condition determination unit 27.

The input unit 30 inputs information necessary for the processing unit 20 to execute various processes to the processing unit 20. The input unit 30 may input information acquired from an external storage device to the processing unit 20 via a communication line, or may input information input by the user using a touch panel, a keyboard, or the like to the processing unit 20.

The input unit 30 inputs design information regarding the design value RD to the design data acquisition unit 24, for example. The design information may be the design value RD itself or a feature value characterizing the waveform of the design value RD. The input unit 30 inputs information such as the type of the distribution function, the variation range of the element parameters forming the distribution parameter P, and the range in which the film thickness distribution exists, to the distribution function creation unit 21, for example. The input unit 30 inputs information such as the refractive index n _f of the thin film 40, the range in which the film thickness distribution exists, and the film thickness pitch Δt to the non-distribution spectral reflectance creation unit 22, for example. When the theoretical value includes the refractive index of the base material BM, the input unit 30 also inputs information about the refractive index of the base material BM to the non-distribution spectral reflectance creation unit 22.

The data storage unit 31 stores, for example, the distribution information D in association with the film forming conditions MC of the thin film 40 and the like. The data storage unit 31 may store the design information ID and the design value RD. The data storage unit 31 may store information necessary for the processing unit 20 to execute various types of processing. The data storage unit 31 is a storage device such as a semiconductor memory or a hard disk, for example.

The display unit 32 displays the distribution information D on the display screen, for example. The display unit 32 may display the distribution information D in association with the film forming conditions MC of the thin film 40, the design value RD of the spectral reflectance, and the like. The display unit 32 is a display device such as a liquid crystal display.

FIG. 9 is a flowchart illustrating the spectral reflectance design method of this embodiment.

First, the input unit 30 inputs the design information ID into the processing unit 20 (input step S1). The input unit 30 also inputs to the processing unit 20 information necessary for the processing unit 20 to execute various processes. For example, information such as the type of distribution function, the variation range of the element parameters that make up the distribution parameter P, and the range in which the film thickness distribution exists is input to the distribution function creation unit 21. Information such as the refractive index n _f of the thin film 40, the range in which the film thickness distribution exists, and the film thickness pitch Δt are input to the non-distribution spectral reflectance creation unit 22. When the theoretical value includes the refractive index of the base material BM, information about the refractive index of the base material BM is also input to the non-distribution spectral reflectance creation unit 22.

Next, the distribution function creating unit 21 creates a distribution function f(t, P) indicating the film thickness distribution using the distribution parameter P that characterizes the film thickness distribution of the thin film 40 (distribution function creating step S2). For example, the distribution function creating unit 21 creates a distribution function corresponding to the continuous distribution CD in FIG. The film thickness distribution of FIG. 6 is, for example, a Gaussian distribution. The film thickness distribution can be accurately approximated by using a highly probable distribution function such as Gaussian distribution. The distribution parameter P includes, for example, the average film thickness tA and the variance σ as element parameters.

Next, the non-distribution spectral reflectance creation unit 22 creates a theoretical value RT(λ, t) of the spectral reflectance for each film thickness t of the thin film 40 using Equation (1) (non-distribution spectral reflectance). Creation step S3). For example, based on the information from the input unit 30, the non-distribution spectral reflectance creation unit 22 has a plurality of film thickness values (t ₁ , t ₂ ,..., T) at a pitch of Δt in the range where the film thickness distribution exists. _N ) is set. The non-distribution spectral reflectance creation unit 22 creates a theoretical value RT(λ, t) corresponding to each film thickness value.

Next, the weighted average spectral reflectance calculation unit 23 weights the theoretical value RT(λ, t) of the spectral reflectance for each film thickness t of the thin film 40 with the distribution function f(t, P) including the distribution parameter P. Then, the weighted average spectral reflectance R _av (λ, P) is calculated (weighted average spectral reflectance calculation step S4). The weighted average spectral reflectance R _av (λ, P) of the thin film 40 is represented by the following equation (2).

Next, the analysis unit 25 applies the weighted average spectral reflectance R _av (λ, P) to the design value RD(λ) of the spectral reflectance of the thin film 40 to calculate the distribution parameter P (analyzing step S5). For example, the analysis unit 25 calculates the distribution parameter P using a regression analysis method. As the regression analysis method, a known method such as the least square method can be used.

For example, the analysis unit 25 applies the weighted average spectral reflectance R _av (λ, P) to the design value RD(λ) in the visible light range. This makes it easy to achieve the target spectral reflectance in the visible light range.

The analysis unit 25 refers to the result of comparison between the weighted average spectral reflectance R _av (λ, P) and the design value RD (λ) to determine the distribution parameter P (average film thickness tA and variance σ that are element parameters). Change. The analysis unit 25 determines, as the distribution parameter P of the thin film 40, the distribution parameter P in which the difference between the weighted average spectral reflectance R _av (λ, P) and the design value RD(λ) is the smallest. Thereby, the distribution parameter P of the thin film 40 is calculated. The analysis unit 25 outputs the calculated distribution parameter P to the output unit 26 and the film formation condition determination unit 27.

Next, the film formation condition determination unit 27 realizes the distribution parameter P calculated in the analysis step S5 based on the film formation table 28a showing the correspondence between the film formation condition MC of the thin film 40 and the distribution parameter P. The film forming condition MC is determined (film forming condition determining step S6). The film forming condition determination unit 27 supplies the determined film forming condition MC to the output unit 26.

Next, the output unit 26 detects the distribution information D using the distribution parameter P. The output unit 26 supplies the distribution information D to the data storage unit 31 and the display unit 32 in association with the film forming conditions MC of the thin film 40 (output step S7).

As described above, according to the spectral reflectance designing method of this embodiment, it is possible to design the spectral reflectance of the thin film 40 having a film thickness distribution (film thickness variation). Therefore, the spectral reflectances of various waveforms can be designed as compared with the case where the spectral reflectances are designed by a simple model in which the film thickness t is constant. Further, since the design value RD is approximated by the weighted average spectral reflectance R _av in consideration of the film thickness distribution, the design value RD and the calculated value (weighted average spectral reflectance R _av ) are likely to match. Therefore, the difference between the calculated spectral reflectance and the actual spectral reflectance is unlikely to occur.

In this embodiment, the distribution parameter P is calculated using a regression analysis method. Therefore, the weighted average spectral reflectance R _av can be mechanically applied to the measured value RM having an arbitrary wavelength dispersion, and the approximation accuracy is high.

In the present embodiment, the film forming condition MC for realizing the distribution parameter P is determined based on the film forming table 28a showing the correspondence between the film forming condition MC of the thin film 40 and the distribution parameter P of the thin film 40. Therefore, the thin film 40 having a desired spectral reflectance can be easily manufactured.

[Second embodiment]
FIG. 10 is a conceptual diagram showing a spectral reflectance designing method according to the second embodiment. In this embodiment, the same components as those in the first embodiment are designated by the same reference numerals, and detailed description thereof will be omitted.

The difference between the present embodiment and the first embodiment is that the thin film 40 is composed of a plurality of layers 41. Thin film 40 includes, for example, as a plurality of layers 41, a layer of M from a second layer 41 ₁ to M th layer 41 _M (M is an integer of 2 or more). The refractive indexes of the adjacent layers 41 are different from each other.

FIG. 11 is a flowchart for explaining the spectral reflectance designing method of this embodiment. Hereinafter, the configuration and operation of the processing unit 20 will be described focusing on the differences from the first embodiment with reference to the flowchart.

First, the input unit 30 inputs the design information ID into the processing unit 20 (input step S11). The input unit 30 also inputs to the processing unit 20 information necessary for the processing unit 20 to execute various processes. For example, information such as the type of distribution function, the variation range of the element parameters that make up the distribution parameter P, and the range in which the film thickness distribution exists is input to the distribution function creation unit 21. Information such as the refractive index n _f of the thin film 40, the range in which the film thickness distribution exists, and the film thickness pitch Δt are input to the non-distribution spectral reflectance creation unit 22.

Next, the distribution function creation unit 21 sets a distribution function for each layer 41 (distribution function creation step S12). For example, for the i-th layer 41 _i (i is an integer from 1 to M), a distribution function f _i (t indicating the film thickness distribution is used by using a distribution parameter P _i that characterizes the film thickness distribution of the layer 41 _i. , P _i ). The distribution function f _i (t, P _i ) indicates the ratio (occupancy ratio) of the occupied area of the region where the film thickness of the layer 41 _i is t. The distribution parameter P _i is represented as a combination of q (q is an integer of 1 or more) element parameters P _{i1 to} P _iq that characterize the film thickness distribution of the layer 41 _i .

The film thickness distribution may be a continuous distribution CD or a discrete distribution DD. For example, the distribution function creating unit 21 creates a distribution function corresponding to the continuous distribution CD in FIG. The film thickness distribution of FIG. 6 is, for example, a Gaussian distribution. The distribution parameter P includes, for example, the average film thickness tA and the variance σ as element parameters.

Next, the non-distribution spectral reflectance creation unit 22 creates a theoretical value of the spectral reflectance for each layer 41 based on the equation (1) (non-distribution spectral reflectance creation step S13). For example, for the i-th layer 41 _i , the theoretical value RT _i (λ, t) of the spectral reflectance for each film thickness t of the layer 41 _i is created. Based on the information from the input unit 30, the non-distribution spectral reflectance creation unit 22 has a plurality of film thickness values (t ₁ , t ₂ ,..., T _N ) at a pitch of Δt in the range where the film thickness distribution exists. To set. The non-distribution spectral reflectance creation unit 22 creates a theoretical value RT _i (λ, t) for each film thickness value.

Next, the weighted average spectral reflectance calculation unit 23 calculates the weighted average spectral reflectance of each layer 41, and calculates the sum of the weighted average spectral reflectances of each layer 41 as the weighted average spectral reflectance of the thin film 40 (weighted. Average spectral reflectance calculation step S14). For example, for the i-th layer 41 _i , the theoretical value RT _i (λ, t) of the spectral reflectance for each film thickness t of the layer 41 _i is weighted by the distribution function f _i (t, P _i ) and weighted. The average spectral reflectance R _avi (λ, P _i ) is calculated. The weighted average spectral reflectance R _avi (λ, P _i ) of the layer 41 _i is represented by the following formula (3). The weighted average spectral reflectance R _avt (λ, P ₁ ,..., P _M ) of the thin film is represented by the following formula (4).

Next, the analysis unit 25 applies the weighted average spectral reflectance R _avt (λ, P ₁ ,..., P _M ) of the thin film 40 to the design value RD(λ) to calculate the distribution function f ₁ (t, Distribution parameters P _{1 to} P _M included in P ₁ ) to f _M (t, P _M ) are calculated (analysis step S15). For example, the analysis unit 25 calculates the distribution parameters P _{1 to} P _M by using a regression analysis method.

For example, the analysis unit 25 applies the weighted average spectral reflectance R _avt (λ, P ₁ ,..., P _M ) to the design value RD(λ) in the visible light range. This makes it easy to achieve the target spectral reflectance in the visible light range.

From the above, the distribution parameters P _{1 to} P _{M of} each layer 41 are calculated. The analysis unit 25 outputs the calculated distribution parameters P _{1 to} P _M of each layer 41 to the output unit 26 and the film formation condition determination unit 27.

Next, the film formation condition determination unit 27, for each layer 41, based on the film formation table 28a indicating the correspondence between the film formation conditions and the distribution parameters, the distribution parameters P _{1 to} P _M calculated in the analysis step S15. A film forming condition MC for realizing is determined (film forming condition determining step S16). The film forming table 28a is provided with a film forming table area for each layer 41, the film forming table showing the correspondence between the film forming conditions and the distribution parameters. The film formation table 28a is stored in the film formation table storage unit 28.

The film formation condition determination unit 27 determines the film formation conditions MC for realizing the distribution parameters P _{1 to} P _M calculated by the analysis unit 25 for each layer 41 while referring to the respective film formation table areas. The film forming condition determination unit 27 supplies the film forming condition MC determined for each layer 41 to the output unit 26.

Next, the output unit 26 detects the distribution information D of each layer 41 using the distribution parameters P _{1 to} P _M for each layer 41. The output unit 26 supplies the distribution information D of each layer 41 to the data storage unit 31 and the display unit 32 in association with the film forming conditions MC of each layer 41 (output step S17).

As described above, according to the spectral reflectance designing method of this embodiment, it is possible to design the spectral reflectance of the thin film 40 having the plurality of layers 41 having the film thickness distribution (film thickness variation). Therefore, as compared with the case where the spectral reflectance is designed with only one thin film, the variation of the spectral reflectance that can be designed increases. Further, since the design value RD is approximated by the weighted average spectral reflectance R _avt considering the film thickness distribution of each layer 41, the design value RD and the calculated value (weighted average spectral reflectance R _avt ) are likely to match. Therefore, the difference between the calculated spectral reflectance and the actual spectral reflectance is unlikely to occur.

[Third embodiment]
FIG. 12 is a schematic diagram of the spectral reflectance design device 2 according to the third embodiment. In this embodiment, the same components as those in the first embodiment are designated by the same reference numerals, and detailed description thereof will be omitted.

The difference between the present embodiment and the first embodiment is that the spectral reflectance designing device 2 uses the actual measurement value RM of the spectral reflectance of the sample 40D of the thin film 40 formed under known film forming conditions to form a film. This is the point of creating the table 28a. The film forming table forming step of forming the film forming table 28a is executed before the film forming condition determining step S6 shown in FIG.

The spectral reflectance design device 2 includes a measurement unit 10, a processing unit 50, an input unit 30, a data storage unit 31, a display unit 32, and a table creation unit 33.

The measurement unit 10 measures the spectral reflectance of the sample 40D. The measurement unit 10 includes, for example, a light source 11, a spectroscope 12, and a half mirror 13. The light source 11 is, for example, a white light source that emits white illumination light Li. The illumination light Li emitted from the light source 11 enters the sample 40D via the half mirror 13. The illumination light Li (reflected light Lr) reflected by the sample 40D enters the spectroscope 12 via the half mirror 13. The spectroscope 12 supplies the data MD of the spectral intensity of the reflected light Lr to the processing unit 50. The processing unit 50 analyzes the spectral intensity data MD measured by the measuring unit 10 and detects the second distribution parameter P _D of the sample 40D.

The wavelength range that can be measured by the measuring unit 10 is, for example, 300 nm to 3000 nm. Thereby, the samples 40D having various film thicknesses can be measured. The wavelength range actually measured by the measuring unit 10 depends on the wavelength region where the peak of the reflectance appears due to the film thickness and the refractive index, but the difference between the minimum wavelength and the maximum wavelength of the measurement wavelength range is 100 nm or more and 800 nm or less. It is preferable. This makes it possible to detect one or more peaks required for analysis in a short measurement time. However, depending on the film thickness to be measured and the refractive index, a region where the difference between the minimum wavelength and the maximum wavelength in the measurement wavelength range is 800 nm or more may be required. The measurement wavelength interval is preferably 50 nm or less, more preferably 10 nm or less, and further preferably 5 nm or less. In the measurement, it is preferable to perform the baseline alignment by setting the reflectance of a white plate such as alumina or barium sulfide as a reference plate to a reference value of 100%.

FIG. 13 is a diagram showing a plurality of measurement areas MA provided in the sample 40D.

The sample 40D is provided with a plurality of measurement areas MA. In Figure 13, for example, as a plurality of measurement areas MA, XY number of measurement areas _MA 11 _{to MA XY} is provided which is arranged two-dimensionally in X rows and Y rows. The measurement unit 10 sequentially measures a plurality of two-dimensionally arranged measurement areas MA. The measurement area MA is an area where the illumination light Li is irradiated by one measurement. The size of one measurement area MA is, for example, 1 mm ² or more. The processing unit 50 detects the second distribution parameter P _D in one measurement area MA for each measurement.

The second distribution parameter P _D is a distribution parameter that characterizes the film thickness distribution of the sample 40D. The second distribution parameter P _D , like the distribution parameter P described above, is represented as a combination of one or more element parameters that characterize the film thickness distribution of the sample 40D. The second distribution parameter P _D is used to create the film formation table. Therefore, the processing unit 50, a second distribution parameter P _D, detecting a second distribution parameter P _D having a known relationship between the distribution parameter P. The known relationship means a corresponding relationship recognized based on a theoretical formula or an empirical rule. The second distribution parameter P _D may be the same as or different from the distribution parameter P. The processing unit 50 _supplies the second distribution parameter P _D (P _{D11 to} P _DXY ) of each measurement area MA to the data storage unit 31 (see FIG. 12) in association with the position of the measurement area MA.

FIG. 14 is a flowchart illustrating a method of detecting the second distribution parameter P _D. Hereinafter, the method of forming the film forming table 28a will be mainly described with reference to FIGS. 12 and 14.

First, the measurement unit 10 sequentially measures the spectral reflectance in the plurality of measurement areas MA. The data MD of the spectral intensity of the reflected light Lr measured by the measurement unit 10 is acquired by the actual measurement data acquisition unit 51 provided in the processing unit 50. The actual measurement data acquisition unit 51 converts the spectral intensity data MD into spectral reflectance data and supplies the actual measurement value RM(λ) to the analysis unit 25. Thereby, the measured value RM(λ) of the spectral reflectance of each measurement area MA is obtained (measurement step S21).

Next, the input unit 30 inputs information necessary for the processing unit 50 to execute various processes to the processing unit 50 (input step S22). For example, information such as the type of distribution function, the variation range of the element parameters that make up the distribution parameter P, and the range in which the film thickness distribution exists is input to the distribution function creation unit 21. Information such as the refractive index n _f of the thin film 40, the range in which the film thickness distribution exists, and the film thickness pitch Δt are input to the non-distribution spectral reflectance creation unit 22.

Next, the distribution function creation unit 21 creates a second distribution function f _D (t, P _D ) indicating the film thickness distribution using the second distribution parameter P _D that characterizes the film thickness distribution of the sample 40D. (Second distribution function creating step S23). The second distribution function f _D (t, P _D ) may be the same as or different from the distribution function f(t, P) used in the analysis routine when designing the spectral reflectance. In the present embodiment, for example, the distribution function creating unit 21 creates a second distribution function similar to the distribution function corresponding to the continuous distribution CD in FIG. The film thickness distribution of FIG. 6 is, for example, a Gaussian distribution. The film thickness distribution can be accurately approximated by using a highly probable distribution function such as Gaussian distribution. The second distribution parameter P _D includes, for example, the average film thickness tA _D and the variance σ _D as element parameters, respectively.

Next, the non-distribution spectral reflectance creation unit 22 creates a theoretical value RT _D (λ, t) of the spectral reflectance for each film thickness t of the thin film 40 by using the equation (1) (non-distribution spectral reflection). Rate creation step S24). For example, based on the information from the input unit 30, the non-distribution spectral reflectance creation unit 22 has a plurality of film thickness values (t ₁ , t ₂ ,..., T) at a pitch of Δt in the range where the film thickness distribution exists. _N ) is set. The non-distribution spectral reflectance creation unit 22 creates a theoretical value RT _D (λ, t) corresponding to each film thickness value.

Next, the weighted average spectral reflectance calculation unit 23 calculates the theoretical value RT _D (λ, t) of the spectral reflectance for each film thickness t of the thin film 40 as the second distribution function f including the second distribution parameter P _D. The weighted average is calculated by _D (t, P _D ) to calculate the second weighted average spectral reflectance R _avD (λ, P _D ) (second weighted average spectral reflectance calculation step S25). The second weighted average spectral reflectance R _avD (λ, P _D ) is represented by the following formula (5).

Next, the analysis unit 25 applies the second weighted average spectral reflectance R _avD (λ, P _D ) to the measured value RM(λ) of the spectral reflectance of the sample 40D to calculate the second distribution parameter P _D. Yes (second analysis step S26). For example, the analysis unit 25 calculates the second distribution parameter P _D using a regression analysis method. As the regression analysis method, a known method such as the least square method can be used.

For example, the analysis unit 25 _adds the second weighted average spectral reflectance R _avD (λ, to the measured value RM(λ) in a wavelength range other than the absorption wavelength range of the thin film 40 and the base material BM on which the thin film 40 is arranged. fitting a P _D). As a result, the second weighted average spectral reflectance R _avD (λ, P _D ) can be accurately applied to the measured value RM(λ). Therefore, an error is unlikely to occur between the calculated film thickness distribution and the actual film thickness distribution.

The analysis unit 25 refers to the comparison result of the second weighted average spectral reflectance R _avD (λ, P _D ) and the actual measurement value RM(λ), and determines the second distribution parameter P _D (average which is an element parameter). The film thickness tA _D and the variance σ _D ) are changed. The analysis unit 25 determines the second distribution parameter P _D having the smallest difference between the second weighted average spectral reflectance R _avD (λ, P _D ) and the actual measurement value RM(λ) as the second distribution parameter P _D of the sample 40D. It is determined as the distribution parameter P _D. Thereby, the second distribution parameter P _{D of} one measurement area MA is calculated. The analysis unit 25 outputs the calculated second distribution parameter P _D to the output unit 26 in association with the position of the measurement area MA.

Next, the analysis unit 25 determines whether or not the second distribution parameters P _{D of} all the measurement areas MA set in the sample 40D have been calculated (determination step S27). When the analysis unit 25 determines that the second distribution parameters P _{D of} all the measurement areas MA have not been calculated (determination step S27: No), the procedure returns to the second distribution function creation step S23, and the same processing is performed. According to the procedure, the second distribution parameter P _D of the measurement area MA for which the second distribution parameter P _D has not been calculated is calculated. When the analysis unit 25 determines that the second distribution parameters P _{D of} all the measurement areas MA have been calculated (determination step S27: Yes), the analysis ends.

When the second distribution parameters P _{D of} all the measurement areas MA are calculated, the output unit 26 sets the second distribution parameters P _D of each measurement area MA to the position of the measurement area MA and the film forming conditions of the sample 40D. The data is associated and supplied to the data storage unit 31 and the display unit 32 (output step S28).

With the above, the analysis by the processing unit 50 ends. The second distribution parameter P _D supplied to the data storage unit 31 is acquired by the table creation unit 33. Table creation unit 33 based on the correspondence between the distribution parameter P and the second distribution parameter P _D, for detecting the distribution parameter P of the sample 40D. The table creating unit 33 creates the film forming table 28 a based on the correspondence relationship between the film forming conditions of the sample 40D and the distribution parameter P, and supplies the film forming table 28 a to the table storage unit 28. In the present embodiment, the film forming process in which the processing unit 50 and the table creating unit 33 create the film forming table 28a using the actual measurement value RM of the spectral reflectance of the sample 40D of the thin film 40 formed under known film forming conditions. Functions as a table creation unit.

15 to 18 are diagrams showing the results of comparison between the actual measurement value RM and the second weighted average spectral reflectance R _{avD in} Examples 1 to 4. The base material is polycarbonate. Since polycarbonate has an absorption wavelength range WR1 in the wavelength range on the short wavelength side of about 400 nm or less, fitting of the actual measurement value RM and the second weighted average spectral reflectance R _{avD in} the wavelength range WR2 other than the absorption wavelength range WR1. Is being done. When the sample 40D has a wavelength range in which absorption is large, it is preferable that the actual measurement value RM and the second weighted average spectral reflectance R _avD be fitted in a wavelength range other than the absorption wavelength range of the sample 40D.

FIG. 19 is a diagram showing film forming conditions, measured values of root mean square deviation S _q , average film thickness tA _D and variance σ _{D according} to this analysis method in Examples 1 to 4. FIG. 20 is a diagram showing the relationship between the variance σ _D and the root mean square deviation S _q .

In FIG. 19, “process A” means a process in which the sample is formed under the condition that the target film thickness is 180 nm. “Process B” means a process in which the sample is formed under the condition that the target film thickness is 120 nm. The film forming conditions indicate the number of times each step is performed. The greater the number of steps, the larger the film thickness.

The “process A” and the “process B” are performed using a gravure offset printing method. Gravure offset printing is a printing method in which a gravure plate cylinder having a specific depression pattern is transferred to a transfer blanket cylinder, and the ink on the transfer blanket cylinder is transferred to a substrate. In the gravure offset printing, by combining the characteristics of the gravure printing and the offset printing, it is possible to print on a hard material, a curved surface, and a fragile material that cannot be printed directly from the gravure plate cylinder. In the “process A”, a rough target film thickness was controlled by using a gravure plate cylinder having a 25 μm concave pattern. In the "process B", the approximate target film thickness was controlled by using a gravure plate cylinder having a recess pattern of 5 μm.

As shown in FIGS. 15 to 18, the waveform of the second weighted average spectral reflectance R _{avD and} the waveform of the actual measurement value RM match well. As shown in FIG. 19, the average thickness suggested by the film forming conditions, between the average thickness tA _D calculated by the calculation, there is a high correlation. Further, as shown in FIG. 20, there is a high correlation between the actual measurement value of the root mean square deviation S _q indicating the film thickness roughness and the variance σ _D calculated by the calculation. Therefore, it is expected that the film thickness distribution of the sample is accurately detected by the analysis method of this embodiment.

According to the study by the inventor, it has been confirmed that at least the actual measurement value RM of the thin film formed by the gravure coating method and the spin coating method is well approximated by the analysis method of the present embodiment. For example, FIGS. 15 to 18 show that the actually measured values of the thin film formed by the gravure offset printing are well approximated by the analysis method of the present embodiment. The inventor has conducted the same analysis for a thin film formed by spin coating. As a result, it has been confirmed that the actually measured value RM of the thin film formed by spin coating is well approximated by the analysis method of this embodiment.

21 and 22 are diagrams showing comparison results between the actual measurement value RM and the second weighted average spectral reflectance R _avD in the fifth and sixth embodiments. FIG. 23 is a diagram showing the film forming conditions (rotational speed of the coater) of Examples 5 and 6, the average film thickness tA and the dispersion σ by this analysis method. 21 and 22, the theoretical value RT of the spectral reflectance is also shown for comparison.

As shown in FIGS. 21 and 22, the waveform of the second weighted average spectral reflectance R _{avD and} the waveform of the actual measurement value RM match well. In the waveform of the theoretical value RT, although the peak positions are almost the same, the numerical value of the theoretical value RT is significantly different from the measured value.

The values of the average film thickness tA and the variance σ obtained by the analysis have a correlation with the average film thickness suggested by the film forming conditions. In spin coating, a base material coated with a coating material is rotated at high speed to thinly stretch the coating material. Therefore, the larger the rotation speed of the coater (rotation per minute: rpm), the smaller the film thickness and the larger the dispersion. The results in Figure 20 are consistent with this fact.

Since the film forming method does not affect the analysis method of this embodiment, it is considered that the analysis method of this embodiment can be applied to thin films formed by various methods. For example, other film forming methods include bar coating, sputtering, and CVD (Chemical Vapor Deposition). Moreover, it has been confirmed that, in the case of a single-layer thin film, the actual measurement value RM of the thin film of 20 nm to 2300 nm is well approximated by the analysis method of the present embodiment. Therefore, it is considered that the analysis method of this embodiment can be applied to a thin film having a film thickness of at least 10 nm to 5000 nm. By setting the measurement wavelength range to a long wavelength range of about 2000 nm to 3000 nm, it may be easier to confirm the peak of the spectral reflectance corresponding to the film thickness of about 40 μm. Therefore, it is preferable to select the wavelength range in which the peak can be easily confirmed and perform the measurement.

As described above, according to the spectral reflectance design method of the present embodiment, the actual measurement value RM of the spectral reflectance of the sample 40D is analyzed by the same routine as the analysis routine when designing the spectral reflectance. Therefore, the processing unit that designs the spectral reflectance and the processing unit that creates the film formation table 28a can be shared.

In addition, with this configuration, the film thickness distribution in the measurement region MA can be obtained by measuring the spectral reflectance once. Since the range that can be measured at one time is wide and the measured value RM can be easily analyzed, the film thickness distribution in a wide range can be efficiently measured. Therefore, the work of forming the film forming table 28a is facilitated.

_Further , since the measured value RM is approximated by the second weighted average spectral reflectance R _avD considering the film thickness distribution, the measured value RM and the calculated value (the second weighted average spectral reflectance R _avD ) match. Cheap. Therefore, an error is unlikely to occur between the calculated film thickness distribution and the actual film thickness distribution. Therefore, the film forming condition MC and the film thickness distribution can be accurately associated with each other.

In the present embodiment, the second weighted average spectral reflectance R _avD is applied to the measured value RM in the wavelength range WR2 other than the absorption wavelength range WR1 of the sample 40D and the base material BM on which the sample 40D is arranged. Therefore, the second weighted average spectral reflectance R _avD can be accurately applied to the measured value RM. Therefore, an error is unlikely to occur between the calculated film thickness distribution and the actual film thickness distribution.

In this embodiment, it is not necessary to reduce the size of the measurement area MA. Even if the measurement area MA is enlarged, the film thickness distribution of the entire measurement area MA is detected at one time. Therefore, the size of each measurement area MA can be increased to efficiently measure the film thickness distribution over a wide range. For example, in the present embodiment, the actual measurement value RM is a measurement value of the spectral reflectance of the measurement area MA of 1 mm ² or more. A single measurement of the spectral reflectance makes it possible to obtain a large film thickness distribution in the measurement area MA of 1 mm ² or more. Therefore, even when the measurement is sequentially performed on the plurality of two-dimensionally arranged measurement areas MA, the measurement is completed in a short time.

The size of the measurement area MA is grasped, for example, by visually observing the area where the sample 40D is irradiated with the illumination light Li. As a result of the observation by the inventor, the illumination light Li was applied to the sample 40D of each of Examples 1 to 6 in a rectangular region having a width of 1 mm and a length of 9 mm. Therefore, in actual measurement, the film thickness distribution of a very large measurement area MA of about 10 mm ² is measured at one time. As described above, the waveforms of the actually measured values in Examples 1 to 6 are in good agreement with the waveform of the second weighted average spectral reflectance. Therefore, it can be understood that the film thickness distribution of the very large measurement area MA of about 10 mm ² can be measured accurately in a short time.

[Fourth Embodiment]
FIG. 24 is a conceptual diagram showing a method of creating the film formation table 28a according to the second embodiment. In this embodiment, the same components as those in the third embodiment are designated by the same reference numerals, and detailed description thereof will be omitted.

The present embodiment is different from the third embodiment in that the thin film formed on the base material BM is a laminated body 40DS of a plurality of samples 40D, and the measured value RM(λ) is the spectral reflectance of the laminated body 40DS. Is the point at which the measured value of is used. The stacked body 40DS includes, for example, M samples (M is an integer of 2 or more) 40D from the _first sample 40D ₁ to the Mth sample 40D _M as the plurality of samples 40D. The adjacent samples 40D have different refractive indexes. The film thickness distribution of the plurality of samples 40D is acquired by one measurement. It is not necessary to repeat the measurement for each sample 40D. Therefore, the film forming table 28a can be easily created.

FIG. 25 is a flowchart illustrating a method for detecting the second distribution parameter P _D of each sample 40D. Hereinafter, the configuration and operation of the processing unit 50 will be described focusing on the differences from the third embodiment with reference to the flowchart.

First, the measurement unit 10 sequentially measures the spectral reflectance in the plurality of measurement areas MA. Thereby, the actual measurement value RM(λ) of the spectral reflectance of each measurement area MA is obtained (measurement step S31).

Next, the input unit 30 inputs information necessary for the processing unit 20 to execute various processes to the processing unit 20 (input step S32). For example, information such as the type of distribution function of each sample 40D, the variation range of the element parameters forming the second distribution parameter P _D , and the range in which the film thickness distribution exists is input to the distribution function creation unit 21. Information such as the refractive index n _f of each sample 40D, the range in which the film thickness distribution exists, and the film thickness pitch Δt are input to the non-distribution spectral reflectance creation unit 22.

Next, the distribution function creating unit 21 sets a second distribution function for each sample 40D (second distribution function creating step S33). For example, for the i-th sample 40D _i (i is an integer from 1 to M), the second distribution parameter P _Di that characterizes the film thickness distribution of the sample 40D _i is used to indicate the second film thickness distribution. Create a distribution function f _Di (t, P _Di ). The second distribution function f _Di (t, P _Di ) indicates the ratio (occupancy rate) of the occupied area of the region in which the film thickness of the sample 40D _i is t in the measurement region MA. The second distribution parameter P _Di is represented as a combination of q (q is an integer of 1 or more) element parameters P _{Di1 to} P _Diq characterizing the film thickness distribution of the sample 40D _i .

The film thickness distribution may be a continuous distribution CD or a discrete distribution DD. For example, the distribution function creation unit 21 creates a second distribution function corresponding to the continuous distribution CD of FIG. The film thickness distribution of FIG. 6 is, for example, a Gaussian distribution. The second distribution parameter P _D includes, for example, the average film thickness tA and the variance σ as element parameters.

Next, the non-distribution spectral reflectance creation unit 22 creates a theoretical value of the spectral reflectance for each sample 40D based on the equation (1) (non-distribution spectral reflectance creation step S34). For example, for the i-th sample 40D _i , the theoretical value RT _Di (λ, t) of the spectral reflectance for each film thickness t of the sample 40D _i is created. Based on the information from the input unit 30, the non-distribution spectral reflectance creation unit 22 has a plurality of film thickness values (t ₁ , t ₂ ,..., T _N ) at a pitch of Δt in the range where the film thickness distribution exists. To set. The non-distribution spectral reflectance creation unit 22 creates a theoretical value RT _Di (λ, t) for each film thickness value.

Next, the weighted average spectral reflectance calculation unit 23 calculates the second weighted average spectral reflectance for each sample 40D, and sums the second weighted average spectral reflectance of each sample 40D to the second of the stacked body 40DS. Is calculated as the weighted average spectral reflectance of (second weighted average spectral reflectance calculation step S35). For example, for the i-th sample 40D _i , the theoretical value RT _Di (λ, t) of the spectral reflectance for each film thickness t of the sample 40D _i is weighted average by the second distribution function f _Di (t, P _Di ). Then, the second weighted average spectral reflectance R _avDi (λ, P _Di ) is calculated. The second weighted average spectral reflectance R _avDi (λ, P _Di ) of the sample 40D _i is represented by the following formula (6). The second weighted average spectral reflectance R _avDt (λ, P _D1 ,..., P _DM ) of the laminated body 40DS is represented by the following formula (7).

Next, the analysis unit 25 applies the second weighted average spectral reflectance R _avDt (λ, P _D1 ,..., P _DM ) of the laminated body 40DS to the measured value RM(λ) of the spectral reflectance of the laminated body 40DS. Then, the second distribution parameters P _{D1 to} P _DM included in the second distribution functions f _D1 (t, P _D1 ) to f _DM (t, P _DM ) of each sample 40D are calculated (second analysis step). S36). For example, the analysis unit 25 calculates the second distribution parameters P _{D1 to} P _DM by using a regression analysis method.

For example, the analysis unit 25 _adds the second weighted average spectral reflectance R _avDt (to the measured value RM(λ) in a wavelength range other than the absorption wavelength range of each sample 40D and the base material BM on which each sample 40D is arranged. λ, P _D1 ,..., P _DM ). Thereby, the second weighted average spectral reflectance R _avDt (λ, P _D1 ,..., P _DM ) can be accurately applied to the measured value RM(λ). Therefore, an error is unlikely to occur between the film thickness distribution of each sample 40D calculated by calculation and the actual film thickness distribution of each sample 40D.

From the above, the second distribution parameters P _{D1 to} P _DM of each sample 40D in one measurement area MA are calculated. The analysis unit 25 outputs the calculated second distribution parameters P _{D1 to} P _DM of each sample 40D to the output unit 26 in association with the positions of the measurement area MA.

Next, the analysis unit 25 determines whether or not the second distribution parameters P _{D1 to} P _{DM of} all the measurement areas MA set in the stacked body 40DS have been calculated (determination step S37). When the analysis unit 25 determines that the second distribution parameters P _{D1 to} P _{DM of} all the measurement areas MA have not been calculated (determination step S37: No), the procedure returns to the second distribution function creation step S33. Then, according to the same procedure, the second distribution parameters P _{D1 to} P _DM of the measurement area MA in which the second distribution parameters P _{D1 to} P _DM have not been calculated are calculated. When the analysis unit 25 determines that the second distribution parameters P _{D1 to} P _{DM of} all the measurement areas MA have been calculated (determination step S37: Yes), the analysis ends.

When the second distribution parameters P _{D1 to} P _{DM of} all the measurement areas MA are calculated, the output unit 26 determines the second distribution parameters P _{D1 to} P _DM of each sample 40D for each measurement area MA. And the film forming conditions of each sample 40D and the like are supplied to the data storage unit 31 and the display unit 32 (output step S38).

With the above, the analysis by the processing unit 50 ends. The second distribution parameters P _{D1 to} P _DM of each sample 40D supplied to the data storage unit 31 are acquired by the table creation unit 33. The table creation unit 33 detects the distribution parameter P of each sample 40D based on the correspondence relationship between the distribution parameter P and the second distribution parameters P _{D1 to} P _DM . The table creating unit 33 creates the film forming table 28 a based on the correspondence relationship between the film forming conditions of each sample 40 D and the distribution parameter P of each sample 40 D, and supplies the film forming table 28 a to the table storage unit 28.

26: is a figure which shows the comparison result of the measured value RM in Example 7, and the 2nd weighted average spectral reflectance _RavDt . 27: is a figure which shows the value of the parameter used for the analysis of the laminated body 4DS of Example 7. FIG. In FIG. 26, the theoretical value RT of the spectral reflectance is also shown for comparison.

The laminated body 40DS of Example 7 is composed of the coating film 1 and the coating film 2. The configurations of the coating film 1 and the coating film 2 are as follows.

<Coating film 1>
The coating film 1 is a thin film obtained by spin coating a coating liquid in which the following raw materials are mixed.
Hollow silica (particle size 1 to 5 nm, [trade name, etc.] Excelpure BD-P01): 5% by weight
-Alcoholic solvent (ethanol): 30% by weight
-Alcoholic solvent (normal propyl alcohol): 30% by weight
-Alcoholic solvent (methanol): 5% by weight
-Ether solvent (propylene glycol monomethyl ether): 30% by weight

<Coating film 2>
The coating film 2 is a thin film obtained by spin coating a coating liquid in which the following raw materials are mixed.
Zirconium dioxide particles (particle size 15 to 25 nm, [trade name, etc.] Rio Duras TYZ): 17.5% by weight
Acrylic monomer (α-(allyloxymethyl)acrylate): 7.5% by weight
-Ether solvent (propylene glycol monomethyl ether): 74.5% by weight
-Photopolymerization initiator (acetophenone compound): 0.5% by weight

Since the base material has the absorption wavelength range WR1 on the short wavelength side, the actual measurement value RM and the second weighted average spectral reflectance R _avDt are fitted in the wavelength range WR2 other than the absorption wavelength range WR1. As shown in FIG. 26, the waveform of the second weighted average spectral reflectance R _{avDt and} the waveform of the actual measurement value RM match well. Therefore, even for a thin film having a multi-layer structure, it is expected that the film thickness distribution of each layer can be accurately detected by one measurement.

As described above, according to the method of creating the film formation table 28a of the present embodiment, the film thickness distributions of the plurality of samples 40D can be simultaneously calculated by measuring the spectral reflectance once. It is not necessary to repeat the measurement for each sample. Therefore, the film forming table 28a can be easily created. _Further , since the actual measurement value RM is approximated by the second weighted average spectral reflectance R _avDt considering the film thickness distribution of each sample 40D, the actual measurement value RM and the calculated value (second weighted average spectral reflectance R _avDt ) Is easy to match with. Therefore, an error is unlikely to occur between the film thickness distribution of each sample 40D calculated by calculation and the actual film thickness distribution of each sample 40D.

In FIG. 26, the analysis method of this embodiment is applied to a thin film having a two-layer structure, but the layer structure of the laminated body 40DS to be applied is not limited to the two-layer structure. It is considered that the analysis method of the present embodiment can be favorably applied to the laminated body 40DS having a laminated structure of three or more layers.

[First modification]
Hereinafter, modified examples of the first embodiment will be described. Constituent elements common to the first embodiment in this modified example are designated by the same reference numerals, and detailed description thereof will be omitted.

The difference of this modification from the first embodiment is that the film thickness distribution is the discrete distribution DD shown in FIG. The distribution function creation unit 21 illustrated in FIG. 1 discretely sets N (N is an integer of 2 or more) film thickness values from t ₁ to t _N for each Δt in a range in which the film thickness distribution exists. To do. The distribution function creation unit 21 sets the occupancy ratios f _{1 to} f _N corresponding to the respective film thicknesses t _{1 to} t _N as the distribution function f(t, P).

The distribution function f(t,P) is created as a combination of numerical values of the plurality of occupancy ratios f _{1 to} f _N corresponding to the film thicknesses t _{1 to} t _N. The distribution parameter P includes the occupation ratios f _{1 to} f _N of each film thickness as element parameters. The value (occupancy ratio f _{1 to} f _N ) of each element parameter is calculated by the analysis unit 25 analyzing the design value RD. The range in which the film thickness distribution exists and the size of the film thickness pitch Δt are input from the input unit 30, for example.

The weighted average spectral reflectance R _av (λ, P) is represented by the following formula (8).

The analysis unit 25 applies the weighted average spectral reflectance R _av (λ, P) to the design value RD(λ) of the spectral reflectance of the thin film 40 to calculate the distribution parameter P. Analyzing section 25, for example, discretely set by selecting N thickness value t ₁ ~t _N same number of wavelengths lambda ₁ to [lambda] _N was the value of the distribution parameter P using the following equation (9) To calculate.

By solving the simultaneous equations of formula (9), occupancy _f 1 ~f _N corresponding to the respective film thickness _t 1 ~t _N is calculated. λ _{1 to} λ _N can be set arbitrarily. λ _{1 to} λ _N are set as wavelengths in the visible light range, for example. As a result, the target spectral reflectance is likely to be achieved in the visible light range.

Also in this modification, the spectral reflectance of the thin film 40 having a film thickness distribution (film thickness variation) can be designed. Further, since the film thickness distribution is calculated by solving a simple simultaneous equation, the calculation is easy.

[Second modification]
28 and 29 are diagrams showing variations of the distribution function.

In the first and second embodiments, the Gaussian distribution as shown in FIG. 28 is used as the film thickness distribution, but the film thickness distribution is not limited to the Gaussian distribution. The Laplace distribution shown in FIG. 29 may be used as the film thickness distribution. As the distribution function, a distribution function which has an average value and whose probability distribution is calculated based on the variance value is preferably used. The film thickness distribution changes depending on the film forming conditions. Therefore, it is preferable to adopt an appropriate distribution function according to the film forming conditions. In consideration of the deviation of the film thickness distribution that occurs in the film forming process, it is possible to add a function or coefficient that can uniquely define the deviation to the above distribution function. The film thickness distribution can be accurately approximated by using a highly probable distribution function.

Although the preferred embodiment of the present invention has been described above, the present invention is not limited to such an embodiment. The contents disclosed in the embodiments are merely examples, and various modifications can be made without departing from the spirit of the present invention. Appropriate changes made without departing from the spirit of the present invention naturally belong to the technical scope of the present invention. All inventions that can be implemented by those skilled in the art by appropriately changing the design based on the above-described inventions also belong to the technical scope of the present invention as long as they include the gist of the present invention.

[Arithmetic treatment of interference phenomenon]
For the arithmetic treatment of the interference phenomenon, a calculation method generally called a matrix method is used. The values calculated by the matrix method are the interface reflectance, the interface transmittance, and the interface absorption rate. In the matrix method, the optical characteristics at the interface between two media are calculated. The symbols used in the calculation are described below. The following symbols have nothing to do with the symbols used in the above-described embodiments.

[A] Reflection and transmission of light at the interface
Reflection of light always occurs at the boundary surface between two different media. The amplitude reflection coefficient r at the interface between the medium having a refractive index of n0 and the medium having a refractive index of n1 is represented by the following formula (10). The amplitude transmission coefficient t is expressed by the following equation (11). ρ is the ratio of the complex refractive index of the interface.
r=(1-ρ)/(1+ρ) (10)
t=2/(1+ρ) (11)

When light is incident perpendicularly on the boundary surface, the reflectance R and the transmittance T are represented by the following equations (12) and (13) using the amplitude reflection coefficient r and the amplitude transmission coefficient t. ..
r=(N ₀ −N ₁ )/(N ₀ +N ₁ )... (12)
t=2N ₀ /(N ₀ +N ₁ ) (13)

When the refractive index N ₀ and the refractive index N ₁ are real numbers, that is, when the incident medium and the outgoing medium are transparent, the reflectance R and the transmittance T are calculated by the following equations (14) and (15). expressed.
^{_{R = r 2 = {(N}} 0 -N 1) / (N 0 + N 1)} 2 ··· (14)
T=N ₁ ·t ² /N ₀ =4N ₀ N ₁ /(N ₀ +N ₁ ) ² (15)

From equation (14) and equation (15), it can be seen that R+T=1.

[B] Physical quantity handled in optical calculation [B-1] Refractive index The refractive index N is defined by the ratio of the speed c of light in a vacuum to the speed v of light in a medium.
N=n-ik (16)

In Expression (13), i is an imaginary number and i ² =−1. N is called a complex refractive index, n is a real part of refractive index, and k is an imaginary part of refractive index. When dealing with a dielectric film, the thin film is a transparent body (that is, k=0), and thus n may be referred to as a refractive index.

k is a value expressing the absorption of the thin film. k has the following relationship with the absorption coefficient α.
α=4πk/λ (17)

In Expression (17), α is the reciprocal of the propagation distance that reduces the intensity of incident light to 1/e. λ is the wavelength of light.

[B-2] Phase Thickness The phase thickness δ expressing the change in phase when light propagates through the medium is expressed by the following equation.
δ=2πNdcos θ/λ (18)

In the equation (18), θ is the incident angle of light (angle formed with the normal line of the base material). λ is the wavelength of light. d is a physical film thickness.

[B-3] Matrix Calculation In the matrix method, the optical characteristics are calculated from the characteristic matrix defined by the optical constants that are the quantities specific to the thin film to be handled. In the case of a multilayer film, the product of the characteristic matrices of each layer is treated as the characteristic matrix of the entire multilayer film.

[C] Characteristic Matrix [C-1] Optical System of Single Layer Film The characteristic matrix M of the thin film in the optical system of the single layer film is represented by the following formula (19).

The characteristic matrix of the base material is represented by the following formula (20). In the following formula (20), Ns represents the complex refractive index of the base material.

[C-2] Calculation Method of Reflectance and Transmittance Hereinafter, a calculation method of reflectance and transmittance when a single-layer film is formed on a substrate will be described. FIG. 30 is a conceptual diagram of a single-layer film optical system.

The reflectance and the transmittance are calculated by obtaining a characteristic matrix of an optical system (optical system including a thin film and a base material) viewed from a medium into which light is incident. The characteristic matrix (B, C) of the optical system of the single-layer film is calculated as the product of the characteristic matrix M of the thin film and the matrix Ms of the base material. The calculation result is represented by the following formula (21).

The optical admittance Y is represented by the following formula (22). The optical admittance is a numerical value that can be treated in the same way as the refractive index.
Y=C/B (22)

Equations (10) and (11) can be used to determine the amplitude reflection coefficient r and the amplitude transmission coefficient t. The reflectance when a thin film is formed on the base material can be calculated by obtaining the reflectance at a simple interface between the input medium having the optical admittance η0 and the medium having the optical admittance Y.

Therefore, the amplitude reflection coefficient r from Expression (7) is expressed by the following Expression (23).
r=(η0−Y)/(η0+Y) (23)

The reflectance R is represented by the following formula (24).

From the expressions (23) and (24), the reflectance R is represented by the following expression (25). r* is a conjugate complex number of r.

The transmittance and the absorptance are represented by the following equation (26) and the following equation (27), respectively. ηs is the optical admittance of the substrate. real(η) is a calculation formula for obtaining the real part of η.

[C-3] Optical System of Multilayer Film The calculation method in the optical system of the multilayer film is the same as the calculation method in the optical system of the single layer film described above. FIG. 31 is a conceptual diagram of a multilayer film optical system. In FIG. 31, for example, the thin film is composed of p layers.

The characteristic matrix Mq of the q-th layer is calculated using the following equations (28) to (30).

The reflectance, the transmittance, and the absorptance are calculated using the equations (21), (22), (25), (26), and (27) as in the case of the single-layer film.

It should be noted that when the reflectance is calculated, the calculation considering the back surface of the base material cannot be performed. Therefore, only the reflection by the surface of the substrate is calculated. Further, the refractive index of a substance has a complicated wavelength dependence and cannot be expressed uniformly. Therefore, even if only the surface of the base material is used, it is difficult to accurately reproduce the actually measured reflectance by calculation.

In order to eliminate the influence of the substrate, it is preferable to calculate the difference between the reflectance of the substrate before forming the thin film and the reflectance after forming the thin film. Further, it is preferable to calculate a theoretical value of reflectance excluding the influence of the base material and compare this theoretical value with the above difference. Thereby, it is possible to accurately compare the theoretical value and the actually measured value.

When predicting the reflectance value, the following method can be used. First, using the measured reflectance of the base material as a baseline, the value that increases or decreases due to thin film interference is calculated. Then, how the reflectance changes based on the base line of the base material is calculated. This makes it possible to predict the reflectance value.

Similar estimation of the film thickness distribution can be performed using the transmittance data. When the thin film is a transparent material such as polycarbonate and acrylic, the transmittance increases or decreases due to thin film interference in the wavelength range where absorption is small. The film thickness distribution can be calculated by using the measured values of the reflectance and the transmittance.

1, 2 Spectral reflectance design device 21 Distribution function creating unit 23 Weighted average spectral reflectance calculating unit 25 Analyzing unit 28a Film forming table 40 Thin film 40D Sample 40DS Laminate 41 Layer BM Base material MA Measuring area MC Film forming condition P Distribution parameter P _D second distribution parameter R spectral reflectance _{R av, R avt} weighted average spectral reflectance RD spectral reflectance of the design value RM spectral reflectance measured value RT spectral reflectance of theory WR1 substrate absorption wavelength region of the WR2 Wavelength range other than absorption wavelength range of base material

Claims (11)

Shown by the formula (1), the theoretical values of the spectral reflectance of each film thickness of the thin film, viewing including the first distribution parameter characterizing the film thickness distribution of the thin film, the first distribution indicating a Gaussian or Laplacian distribution A weighted average spectral reflectance calculation step of calculating a first weighted average spectral reflectance represented by formula (2) by performing a weighted average using a function;
An analysis step of calculating the first distribution parameter by applying the first weighted average spectral reflectance to the design value of the spectral reflectance of the thin film,
And a method for designing spectral reflectance.

RT: theoretical value of spectral reflectance
φ: Phase difference
λ: wavelength
R ₀ : Absorption rate by thin film
n _f : Refractive index of thin film
α: constant determined by the incident angle of illumination light
t: thickness of thin film
R _av (λ,P): first weighted average spectral reflectance
f(t,P): first distribution function
P: first distribution parameter The spectral reflectance design method according to claim 1, wherein in the analyzing step, the first distribution parameter is calculated using a regression analysis method. Wherein in the analysis step, the spectral reflectance designing method according to claim 1 or 2 applying the first weighted average spectral reflectance of the designed value in the wavelength region in 300Nm～3000nm. A film forming condition for realizing the first distribution parameter calculated in the analyzing step is determined based on a film forming table showing a correspondence relationship between the film forming condition of the thin film and the first distribution parameter. spectral reflectivity designing method according to any one of claims 1 to 3 having a film condition determining step. Prior to the film forming condition determination step, a film forming table creating step of creating the film forming table using the actual measurement value of the spectral reflectance of the sample of the thin film formed under known film forming conditions,
The film forming table creating step,
The theoretical values of the spectral reflectance of each film thickness of the thin film, saw including a second distribution parameter having a known relationship between the first distribution parameter, a second distribution representing a Gaussian or Laplacian distribution A second weighted average spectral reflectance calculation step of calculating a second weighted average spectral reflectance shown in the following formula (3) by weighted averaging with a function;
A second analysis step of calculating the second distribution parameter by applying the second weighted average spectral reflectance to the measured value of the spectral reflectance of the sample;
The spectral reflectance design method according to claim 4 , further comprising:

RT _D (λ,t): theoretical value of spectral reflectance for each thickness of thin film
f _D (t, P _D ): second distribution function
P _D : second distribution parameter The spectral reflectance design according to claim 5 , wherein in the second analysis step, the second weighted average spectral reflectance is applied to the measured value in a wavelength range other than the absorption wavelength range of the base material on which the sample is arranged. Method. The measured values are spectral reflectance designing method according to claim 5 or 6 which is a measure of the spectral reflectance of 1 mm ² or more measurement regions. As the actual measurement value, the actual measurement value of the spectral reflectance of the laminate of a plurality of samples is used,
In the second weighted average spectral reflectance calculation step, the second distribution function is set for each sample, the second weighted average spectral reflectance is calculated for each sample, and the second of each sample is calculated. The sum of the weighted average spectral reflectance of the above is calculated as the second weighted average spectral reflectance of the laminate,
In the second analysis step, the second weighted average spectral reflectance of the laminate is applied to the measured value to calculate the second distribution parameter included in the second distribution function of each sample. Item 5. The spectral reflectance design method according to any one of items 5 to 7 . The thin film is composed of a plurality of layers,
In the weighted average spectral reflectance calculation step, the first distribution function is set for each layer, the first weighted average spectral reflectance is calculated for each layer, and the first weighted average spectrum of each layer is calculated. Calculate the sum of the reflectance as a weighted average spectral reflectance of the thin film,
In the analyzing step, said applying the weighted mean spectral reflectance of the thin film to the design value, claims 1 calculates the first distribution parameters included in the first distribution function of each layer 8 either 1 The spectral reflectance design method according to the item. Shown by the formula (1), the theoretical values of the spectral reflectance of each film thickness of the thin film, viewing including the first distribution parameter characterizing the film thickness distribution of the thin film, the first distribution indicating a Gaussian or Laplacian distribution A weighted average spectral reflectance calculation unit that calculates a first weighted average spectral reflectance represented by formula (2) by performing a weighted average using a function;
An analysis unit that calculates the first distribution parameter by applying the first weighted average spectral reflectance to the design value of the spectral reflectance of the thin film,
Spectral reflectance design device having.

RT: theoretical value of spectral reflectance
φ: Phase difference
λ: wavelength
R ₀ : Absorption rate by thin film
n _f : Refractive index of thin film
α: constant determined by the incident angle of illumination light
t: thickness of thin film
R _av (λ,P): first weighted average spectral reflectance
f(t,P): first distribution function
P: first distribution parameter Shown by the formula (1), the theoretical values of the spectral reflectance of each film thickness of the thin film, viewing including the first distribution parameter characterizing the film thickness distribution of the thin film, the first distribution indicating a Gaussian or Laplacian distribution A weighted average spectral reflectance calculation step of calculating a first weighted average spectral reflectance represented by formula (2) by performing a weighted average using a function;
An analysis step of calculating the first distribution parameter by applying the first weighted average spectral reflectance to the design value of the spectral reflectance of the thin film,
A spectral reflectance design program that causes a computer to execute.

RT: theoretical value of spectral reflectance
φ: Phase difference
λ: wavelength
R ₀ : Absorption rate by thin film
n _f : Refractive index of thin film
α: constant determined by the incident angle of illumination light
t: thickness of thin film
R _av (λ,P): first weighted average spectral reflectance
f(t,P): first distribution function
P: first distribution parameter

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