JP2018004534A - Film thickness distribution measurement method, film thickness distribution measurement device and film thickness distribution measurement program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a film thickness distribution measurement method that can efficiently measure a film thickness distribution of a broad range.SOLUTION: A film thickness distribution measurement method according to one embodiment of the present invention has: a spectral transmittance calculation step S5 that weight-averages a theoretical value TT(λ, t) of spectral transmittance for each film thickness t of a thin film by a distribution function f(t, P) including a distribution parameter P to calculate a weighted-average spectral transmittance T(λ, P); and an analysis step S6 that applies the weighted-average spectral transmittance T(λ, P) to an actual measurement value TM(λ) of the spectral transmittance of the thin film to calculate the distribution parameter P.SELECTED DRAWING: Figure 11

Description

  The present invention relates to a film thickness distribution measuring method, a film thickness distribution measuring apparatus, and a film thickness distribution measuring program.

  As an apparatus for measuring the thickness of a thin film, a transmission electron microscope (TEM: Transmission Electron Microscope, see Patent Document 1) and an atomic force microscope (AFM: Atomic Force Microscope, see Patent Document 2) are known. In these apparatuses, the range that can be measured at one time is very small, and the analysis of the measurement results is complicated. Therefore, it is difficult to efficiently measure a wide range of film thickness distribution.

  As a means for efficiently measuring a wide range, a reflection spectral film thickness meter is known. In the reflective spectral film thickness meter, the film thickness is measured using the theory of thin film interference. Thin film interference refers to a phenomenon in which light reflected from the upper surface of a thin film interferes with light reflected from the lower surface, and light having a wavelength corresponding to the film thickness is strengthened or weakened. Measurement is easy because the film thickness is measured by irradiating the thin film with light and detecting the peak wavelength of the reflection spectrum.

JP 2008-203001A JP 2011-220723 A

  In the conventional reflection spectral film thickness meter, the actual measurement value is approximated using the theoretical value of the spectral reflectance when the film thickness in the measurement range is constant. Therefore, the film thickness distribution cannot be obtained. In addition, since the actual measurement value is approximated using a theoretical value that does not consider the film thickness distribution, a divergence is likely to occur between the actual measurement value and the theoretical value. Therefore, an error is likely to occur between the film thickness obtained by calculation and the actual film thickness.

  The objective of this invention is providing the film thickness distribution measuring method, film thickness distribution measuring apparatus, and film thickness distribution measuring program which can measure the film thickness distribution of a wide range efficiently.

  The thickness distribution measuring method according to one aspect of the present invention is a weighted average spectral transmission that calculates a weighted average spectral transmittance by weighted averaging a theoretical value of spectral transmittance for each thin film thickness with a distribution function including distribution parameters. A rate calculating step, and an analyzing step of calculating the distribution parameter by applying the weighted average spectral transmittance to an actual measurement value of the spectral transmittance of the thin film.

  According to this configuration, the film thickness distribution in the measurement region can be obtained by measuring the spectral transmittance once. Since the range that can be measured at one time is wide and analysis of actual measurement values is easy, a wide range of film thickness distribution can be measured efficiently. In addition, since the actual measurement value is approximated by the weighted average spectral transmittance considering the film thickness distribution, the actual measurement value and the calculated value (weighted average spectral transmittance) are likely to coincide. Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

  In the film thickness distribution measuring method according to one aspect of the present invention, for example, in the analysis step, the distribution parameter is calculated using a regression analysis technique.

  According to this configuration, the weighted average spectral transmittance can be mechanically applied to an actual measurement value having an arbitrary wavelength dispersion, and the approximation accuracy is high.

  In the film thickness distribution measuring method according to one aspect of the present invention, for example, the distribution function is a distribution function indicating a Gaussian distribution or a Laplace distribution. As the distribution function, a distribution function having an average value and calculating a probability distribution based on the variance value is preferably used. The film thickness distribution varies depending on the film forming conditions. Therefore, it is preferable to employ an appropriate distribution function according to the film forming conditions. In consideration of the deviation of the film thickness distribution generated in the film forming process, it is possible to add a function or a coefficient that can uniquely define the deviation to the above distribution function.

  According to this configuration, the film thickness distribution can be accurately approximated by using a highly probable distribution function.

  In the film thickness distribution measuring method according to one aspect of the present invention, for example, in the analysis step, the weighted average spectral transmittance is applied to the measured value in a wavelength region other than the absorption wavelength region of the substrate on which the thin film is disposed. .

  According to this configuration, the weighted average spectral transmittance can be accurately applied to the actually measured value. Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

In the film thickness distribution measuring method according to one aspect of the present invention, for example, the actual measured value is a measured value of spectral transmittance in a measurement region of 1 mm ² or more.

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

  In the film thickness distribution measuring method according to one aspect of the present invention, for example, the thin film is configured by a plurality of layers, and in the weighted average spectral transmittance calculation step, the distribution function is set for each layer, and The weighted average spectral transmittance of the thin film is calculated as the weighted average spectral transmittance of the thin film. The weighted average spectral transmittance of the thin film is calculated as the weighted average spectral transmittance of the thin film. The distribution parameter included in the distribution function of each layer is calculated by applying a rate.

  According to this configuration, the film thickness distribution of a plurality of layers constituting the thin film can be calculated simultaneously by measuring the spectral transmittance once. In addition, since the actual measurement value is approximated by the weighted average spectral transmittance considering the film thickness distribution of each layer, the actual measurement value and the calculated value (weighted average spectral transmittance) are likely to match. Therefore, an error hardly occurs between the film thickness distribution of each layer calculated by the calculation and the actual film thickness distribution of each layer.

  A thickness distribution measuring apparatus according to an aspect of the present invention is a weighted average spectral transmittance that calculates a weighted average spectral transmittance by weighted averaging a theoretical value of spectral transmittance for each thin film thickness with a distribution function including a distribution parameter. A rate calculation unit, and an analysis unit that calculates the distribution parameter by applying the weighted average spectral transmittance to an actual measurement value of the spectral transmittance of the thin film.

  According to this configuration, the film thickness distribution in the measurement region can be obtained by measuring the spectral transmittance once. Since the range that can be measured at one time is wide and analysis of actual measurement values is easy, a wide range of film thickness distribution can be measured efficiently. In addition, since the actual measurement value is approximated by the weighted average spectral transmittance considering the film thickness distribution, the actual measurement value and the calculated value (weighted average spectral transmittance) are likely to coincide. Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

  The film thickness distribution measurement program according to an aspect of the present invention is a weighted average spectral transmittance that calculates a weighted average spectral transmittance by weighted averaging a theoretical value of spectral transmittance for each thin film thickness with a distribution function including distribution parameters. And causing the computer to execute a rate calculating step and an analysis step of calculating the distribution parameter by applying the weighted average spectral transmittance to an actual measured value of the spectral transmittance of the thin film.

  According to this configuration, the film thickness distribution in the measurement region can be obtained by measuring the spectral transmittance once. Since the range that can be measured at one time is wide and analysis of actual measurement values is easy, a wide range of film thickness distribution can be measured efficiently. In addition, since the actual measurement value is approximated by the weighted average spectral transmittance considering the film thickness distribution, the actual measurement value and the calculated value (weighted average spectral transmittance) are likely to coincide. Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

  ADVANTAGE OF THE INVENTION According to this invention, the film thickness distribution measuring method, film thickness distribution measuring apparatus, and film thickness distribution measuring program which can measure the film thickness distribution of a wide range efficiently can be provided.

FIG. 1 is a schematic view of a film thickness distribution measuring apparatus according to the first embodiment. FIG. 2 is a diagram showing a plurality of measurement regions provided in the thin film. FIG. 3 is a diagram illustrating the measurement principle of the measurement unit. FIG. 4 is a diagram illustrating an example of a waveform of measurement data. FIG. 5 is a diagram showing measured values and theoretical values of spectral transmittance. FIG. 6 is a diagram illustrating a state in which spectral transmittance is measured for a thin film including a plurality of regions having different film thicknesses. FIG. 7 is a diagram showing the spectral transmittance of the first region and the second region. FIG. 8 is a diagram showing an example of the film thickness distribution of the thin film. FIG. 9 is a diagram illustrating an example of a theoretical value of spectral transmittance for each film thickness of the thin film. FIG. 10 is a diagram illustrating an example of a weighted average spectral transmittance of a thin film. FIG. 11 is a flowchart for explaining the film thickness distribution measuring method. FIG. 12 is a diagram illustrating a comparison result between the actually measured value and the weighted average spectral transmittance in Example 1. FIG. 13 is a diagram illustrating a comparison result between the actually measured value and the weighted average spectral transmittance in Example 2. FIG. 14 is a diagram illustrating a comparison result between the actually measured value and the weighted average spectral transmittance in Example 3. FIG. 15 is a diagram illustrating a comparison result between the actually measured value and the weighted average spectral transmittance in Example 4. FIG. 16 is a diagram showing film forming conditions, measured values of root mean square deviation, average film thickness and dispersion according to the present analysis method in Examples 1 to 4. FIG. 17 is a diagram illustrating the relationship between variance and root mean square deviation. FIG. 18 is a conceptual diagram showing a film thickness distribution measuring method according to the second embodiment. FIG. 19 is a flowchart for explaining a film thickness distribution measuring method. FIG. 20 is a diagram illustrating a result of comparison between an actual measurement value of spectral transmittance and a weighted average spectral transmittance in Example 7. FIG. 21 is a diagram showing values of parameters used for the analysis of the thin film. FIG. 22 is a diagram showing variations of the distribution function. FIG. 23 is a diagram showing variations of the distribution function. FIG. 24 is a conceptual diagram of an optical system of a single layer film. FIG. 25 is a conceptual diagram of a multilayer optical system.

[First embodiment]
FIG. 1 is a schematic diagram of a film thickness distribution measuring apparatus 1 according to the first embodiment.

  The film thickness distribution measuring apparatus 1 includes a measurement unit 10, a processing unit 20, an input unit 30, a data storage unit 31, and a display unit 32.

  The measurement unit 10 includes, for example, a light source 11, a spectroscope 12, and a half mirror 13. The light source 11 is a white light source that emits white illumination light Li, for example. The illumination light Li emitted from the light source 11 passes through the thin film 40 and the base material BM, and then enters the reference plate RS via the half mirror 13. The illumination light Li (transmitted light Lt) reflected by the reference plate RS enters the spectroscope 12 via the half mirror 13. The spectral transmittance is calculated by dividing the spectral intensity of the transmitted light Lt by the spectral intensity of the transmitted light Lt0 when the thin film 40 and the base material BM are not disposed. The spectroscope 12 supplies the spectral intensity data MD of the transmitted light Lt to the processing unit 20. The processing unit 20 analyzes the spectral intensity data MD measured by the measurement unit 10 and detects distribution information D related to the film thickness distribution of the thin film 40.

  The wavelength range that can be measured by the measurement unit 10 is, for example, 300 nm to 3000 nm. Thereby, the thin film 40 of various film thickness can be measured. The wavelength range actually measured by the measurement unit 10 depends on the wavelength region where the transmittance peak appears depending on the film thickness and the refractive index, but the difference between the minimum wavelength and the maximum wavelength in the measurement wavelength range is 100 nm to 800 nm. preferable. Thereby, one or more peaks required for analysis can be detected 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 baseline matching with the reflectance of a white plate such as alumina or barium sulfide as the reference plate RS, with a reference value of 100%.

  FIG. 2 is a diagram showing a plurality of measurement areas MA provided in the thin film 40.

The thin film 40 is provided with a plurality of measurement areas MA. In Figure 2, 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 measurement areas MA that are two-dimensionally arranged. The measurement area MA is an area where the illumination light Li is irradiated in one measurement. The size of one measurement area MA is, for example, 1 mm ² or more. The processing unit 20 detects the distribution information D in one measurement area MA for each measurement.

The distribution information D is information relating to the ratio (occupancy) of the occupied area for each film thickness in the measurement area MA. The distribution information D may be, for example, a distribution function indicating the relationship between the film thickness and the occupation ratio, or may be an element parameter that characterizes the film thickness distribution. Examples of the element parameter include an average value of film thickness, a mode value of film thickness, and dispersion. The processing unit 20 supplies the distribution information D (D _{11 to} D _XY ) of each measurement area MA to the data storage unit 31 (see FIG. 1) in association with the position of the measurement area MA.

  FIG. 3 is a diagram illustrating the measurement principle of the measurement unit 10. FIG. 4 is a diagram illustrating an example of a waveform of measurement data. In the following description, the surface of the thin film 40 on the side on which the illumination light Li is incident 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 is incident (interface with the base material BM) is the lower surface 40b. That's it. The spectral intensity of the transmitted light Lt is calculated as the difference between the spectral intensity of the illumination light Li and the spectral intensity of the reflected light Lr.

  The measuring unit 10 measures the film thickness t of the thin film 40 using the theory of thin film interference. Thin film interference refers to a phenomenon in which light L1 reflected by the upper surface 40a of the thin film 40 and light L2 reflected by the lower surface 40b interfere with each other and light of a wavelength λ corresponding to the film thickness t is strengthened or weakened. A phase difference φ proportional to the film thickness t is generated between the light L1 and the light L2. The reflected light Lr includes light L1 and light L2. The transmitted light Lt is obtained by removing the light component that becomes the reflected light Lr from the illumination light Li. The measurement unit 10 measures the spectral intensity data MD of the transmitted light Lt and supplies it to the processing unit 20.

  In the wavelength region used for measurement by the measurement unit 10, it is preferable that the light absorption rate of the thin film 40 and the base material BM is small. The thin film 40 and the base material BM need only be formed of materials having different refractive indexes. For example, as the base material BM, an inorganic material such as glass can be used, and an organic material such as polycarbonate and acrylic can also be used. It is preferable that the thin film 40 does not contain a scattering agent. However, any thin 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. For example, in a hollow particle having air having a refractive index of 1.0 inside the particle, the apparent refractive index is low when the particle diameter is sufficiently small. As a particle diameter at this time, for example, a standard is 1/10 or less of the wavelength of light for which the thin film interference effect is desired. When such a material is used, it is possible to obtain a thin film interference effect without causing scattering while containing another material therein.

  The spectral transmittance T is represented by the intensity ratio between the illumination light Li and the transmitted light Lt. In a simple model in which the film thickness t is constant, the theoretical value TT of the spectral transmittance T is calculated by a calculation method using a matrix method described later. For details of the calculation method, refer to the section “Arithmetic treatment of interference phenomenon” described later. The spectral transmittance T is represented by the following formula (1), for example. The theoretical value TT shows a waveform as shown in FIG.

In Formula (1), R ₀ is the absorption rate by 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. The absorption rate R ₀ is a function of the wavelength λ, but is treated as a constant in this embodiment. The value of α varies depending on the incident angle of the illumination light Li. In the present embodiment, for example, the illumination light Li enters the thin film 40 perpendicularly. Therefore, the value of α is 1.

  In consideration of the influence of the base material BM, the refractive index of the base material BM may be included in the theoretical value T. 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, when the refractive index of the thin film 40 and the base material BM is described as a function of the wavelength λ, an accurate theoretical value T can be obtained. For simplification, the wavelength dependence of the refractive index can be corrected by the abbe number. Since the accuracy of the calculation result is improved rather than making the refractive index constant regardless of the wavelength, it is preferable.

FIG. 5 is a diagram showing the measured value TM and the theoretical value TT of the spectral transmittance. The actual measurement value TM is the spectral transmittance of the thin film 40 formed with a target film thickness of 107 nm. The theoretical value TT is a spectral transmittance obtained in an ideal model when the film is formed uniformly with no variation in target film thickness. The refractive index n _{f of the} thin film is 1.41.

  The measured value TM and the theoretical value TT both have a maximum value in the vicinity of the wavelength λ of 400 nm and a minimum value in the range of the wavelength λ from 550 mn to 600 nm. However, when examined in detail, the wavelength λ indicating the minimum value is around 550 nm in the theoretical value TT, but around 600 nm in the actual measurement value TM. Further, the absolute value of the spectral transmittance T is greatly different between the actual measurement value TM and the theoretical value TT.

  The actual measurement value TM and the theoretical value TT do not necessarily match well. As a result of examination by the inventors, it has been found that the variation in film thickness (film thickness distribution) in the measurement region MA greatly affects the waveform of the spectral transmittance. That is, the theoretical value TT is calculated on the assumption of an ideal model with a constant film thickness. However, in an actual thin film, there are a plurality of regions having different thicknesses, and light transmitted through each region is superimposed. Therefore, it is considered that the spectral transmittance having a waveform different from the theoretical value TT was measured.

  FIG. 6 is a diagram showing a state in which the spectral transmittance is measured for the thin film 40 including a plurality of regions (first region FA, second region FB) having different film thicknesses.

  The transmitted light Lta from the first area FA and the transmitted light Ltb from the second area FB are simultaneously incident on the spectroscope 12 (see FIG. 1). Therefore, the value of the spectral transmittance TTa of the transmitted light Lta and the value of the spectral transmittance TTb of the transmitted light Ltb simultaneously contribute to the actual measured value TM of the spectral transmittance of the entire measurement region MA. When the areas of the first region FA and the second region FB are reduced, the film thickness can be regarded as uniform within each region. For this reason, the spectral transmittance TTa and the spectral transmittance TTb are represented by the theoretical value TT represented by the equation (1).

  In FIG. 6, the symbol Lra indicates the reflected light from the first area FA. A symbol Lrb indicates reflected light from the second region FB. The symbol RTa indicates the spectral reflectance of the reflected light Lra. The symbol RTb indicates the spectral reflectance of the reflected light Lrb.

  FIG. 7 is a diagram showing the spectral transmittance of the first area FA and the second area FB.

  The film thickness ta of the first area FA is different from the film thickness tb of the second area FB. Therefore, the waveform of the spectral transmittance TTa and the waveform of the spectral transmittance TTb are different. Therefore, when the spectral transmittance TTa and the spectral transmittance TTb are added, the wavelength λ indicating the extreme value and the value of the spectral transmittance change. In one measurement area MA, there are a large number of areas having different film thicknesses, and the actual measurement value TM of the spectral transmittance of the entire measurement area MA is obtained by adding the spectral transmittances of the respective areas. If there is a variation in the film thickness, the spectral transmittance waveform changes according to the size of the variation. Therefore, if the waveform of the measured value TM of the spectral transmittance is analyzed, information on the film thickness distribution in the measurement area MA can be obtained.

8 to 10 are diagrams showing the measurement principle of the film thickness distribution. FIG. 8 is a diagram illustrating an example of the film thickness distribution of the thin film 40. FIG. 9 is a diagram illustrating an example of the theoretical value TT of the spectral transmittance for each film thickness t of the thin film 40. FIG. 10 is a diagram illustrating an example of the weighted average spectral transmittance T _av of the thin film 40. Hereinafter, the configuration of the processing unit 20 will be described with reference to FIGS. 8 to 10 and FIG. The processing unit 20 is a computer composed of 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-distributed spectral transmittance creation unit 22, a weighted average spectral transmittance calculation unit 23, an actual measurement data acquisition unit 24, and an analysis unit 25. And an output unit 26 and a program storage unit 29.

The distribution function creating unit 21 creates a distribution function f (t, P) indicating the film thickness distribution of the thin film 40 using the distribution parameter P characterizing the film thickness distribution of the thin film 40. The distribution function f (t, P) indicates the ratio (occupancy) of the occupied area of the region where the thickness of the thin film 40 is t in the measurement region MA. The distribution parameter P is expressed as a combination of _q element parameters P _{1 to} P _q that characterize the film thickness distribution of the thin film 40 (q is an integer of 1 or more). The value of each element parameter is calculated by analyzing the actual measurement value TM by the analysis unit 25. As shown in FIG. 8, the film thickness distribution may be a continuous distribution CD or a discrete distribution DD.

The non-distributed spectral transmittance creating unit 22 creates the theoretical value TT (λ, t) of the spectral transmittance for each film thickness t of the thin film 40 based on the formula (1). As shown in FIGS. 8 and 9, the non-distributed spectral transmittance creating unit 22 calculates theoretical values TT (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 where the film thickness distribution exists. 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 transmittance calculating unit 23 weights and averages the theoretical value TT (λ, t) of the spectral transmittance for each film thickness t of the thin film 40 using the distribution function f (t, P). _Av (λ, P) is calculated. The weighted average spectral transmittance T _av (λ, P) is an approximate expression that approximates the measured value TM of the spectral transmittance. FIG. 10 is a diagram illustrating an example of the weighted average spectral transmittance T _av (λ, P) when the film thickness distribution is a Gaussian distribution.

  The actual measurement data acquisition unit 24 acquires the spectral intensity data MD of the transmitted light Lt measured by the measurement unit 10. The actual measurement data acquisition unit 24 converts the spectral intensity data MD into spectral transmittance data, and supplies the spectral transmittance data MD to the analysis unit 25 as the actual measurement value TM (λ).

The analysis unit 25 calculates the distribution parameter P by applying the weighted average spectral transmittance T _av (λ, P) to the measured value TM (λ) of the spectral transmittance of the thin film 40. The analysis unit 25 supplies the distribution parameter P to the output unit 26.

  The output unit 26 uses the distribution parameter P to detect distribution information D related to the film thickness distribution. The distribution information D is, for example, 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 position of the measurement region MA and the film forming conditions of the thin film 40.

  The program storage unit 29 stores a film thickness distribution measurement program and data for the processing unit 20 to perform various processes. The film thickness distribution measurement program is a program that causes a computer to execute the film thickness distribution measurement method according to the present embodiment. The processing unit 20 performs various processes according to the film thickness distribution measurement program stored in the program storage unit 29. The processing unit 20 executes a film thickness distribution measurement program to thereby distribute a distribution function creation unit 21, a non-distributed spectral transmittance creation unit 22, a weighted average spectral transmittance calculation unit 23, an actual measurement data acquisition unit 24, an analysis unit 25, and It functions as the output unit 26.

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 the external storage device through the communication line to the processing unit 20 or may input information input by the user using a touch panel, a keyboard, or the like to the processing unit 20. For example, the input unit 30 inputs information such as the type of the distribution function, the variation range of the element parameters constituting 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-distributed spectral transmittance creating unit 22. When the theoretical value includes the refractive index of the base material BM, the input unit 30 also inputs information regarding the refractive index of the base material BM to the non-distributed spectral transmittance creating unit 22.

  For example, the data storage unit 31 stores the distribution information D in association with the position of the measurement region MA and the film forming conditions of the thin film 40. The data storage unit 31 may store spectral intensity data MD and spectral transmittance actual measurement values TM. The data storage unit 31 may store information necessary for the processing unit 20 to execute various processes. 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 of each measurement area MA on the display screen. The display unit 32 may display the distribution information D in association with the film forming conditions of the thin film 40 and the measured value TM of the spectral transmittance. The display unit 32 is a display device such as a liquid crystal display.

  FIG. 11 is a flowchart for explaining the film thickness distribution measuring method of the present embodiment.

  First, the measurement unit 10 sequentially measures the spectral transmittance in a plurality of measurement areas MA. Thereby, the actual measurement value TM (λ) of the spectral transmittance of each measurement area MA is obtained (measurement step S1).

Next, the input unit 30 inputs information necessary for the processing unit 20 to execute various processes to the processing unit 20 (input step S2). For example, information such as the type of distribution function, the variation range of element parameters constituting 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 is input to the non-distributed spectral transmittance creating unit 22. When the theoretical value includes the refractive index of the base material BM, information regarding the refractive index of the base material BM is also input to the non-distributed spectral transmittance creating 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 characterizing the film thickness distribution of the thin film 40 (distribution function creating step S3). For example, the distribution function creation unit 21 creates a distribution function corresponding to the continuous distribution CD in FIG. The film thickness distribution in FIG. 8 is, for example, a Gaussian distribution. By using a highly probable distribution function such as a Gaussian distribution, the film thickness distribution can be approximated with high accuracy. The distribution parameter P includes, for example, the average film thickness tA and the variance σ as element parameters.

Next, the non-distributed spectral transmittance creating unit 22 creates a theoretical value TT (λ, t) of the spectral transmittance for each film thickness t of the thin film 40 using the formula (1) (non-distributed spectral transmittance). Creating step S4). For example, the non-distributed spectral transmittance creating unit 22 creates a plurality of film thickness values (t ₁ , t ₂ ,..., T at a pitch of Δt in a range where the film thickness distribution exists based on information from the input unit 30. _N ). The non-distributed spectral transmittance creating unit 22 creates a theoretical value TT (λ, t) corresponding to each film thickness value.

Next, the weighted average spectral transmittance calculating unit 23 performs the weighted average of the theoretical value TT (λ, t) of the spectral transmittance 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 transmittance T _av (λ, P) is calculated (weighted average spectral transmittance calculating step S5). The weighted average spectral transmittance T _av (λ, P) of the thin film 40 is represented by the following formula (2).

Next, the analysis unit 25 calculates the distribution parameter P by applying the weighted average spectral transmittance T _av (λ, P) to the measured value TM (λ) of the spectral transmittance of the thin film 40 (analysis step S6). For example, the analysis unit 25 calculates the distribution parameter P using a regression analysis technique. As a method of regression analysis, a known method such as a least square method can be used.

For example, the analysis unit 25 sets the weighted average spectral transmittance T _av (λ, P) to the actual measurement value TM (λ) in a wavelength region other than the absorption wavelength region of the thin film 40 and the base material BM on which the thin film 40 is disposed. Apply. Thereby, the weighted average spectral transmittance T _av (λ, P) can be accurately applied to the actual measurement value TM (λ). Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

The analysis unit 25 refers to a comparison result between the weighted average spectral transmittance T _av (λ, P) and the actual measurement value TM (λ), and determines the distribution parameter P (the average film thickness tA and the variance σ, which are element parameters). Change. The analysis unit 25 determines the distribution parameter P that minimizes the difference between the weighted average spectral transmittance T _av (λ, P) and the actual measurement value TM (λ) as the distribution parameter P of the thin film 40. Thereby, the distribution parameter P of one measurement area MA is calculated. The analysis unit 25 outputs the calculated distribution parameter P to the output unit 26 in association with the position of the measurement region MA.

  Next, the analysis unit 25 determines whether or not the distribution parameters P of all measurement regions MA set on the thin film 40 have been calculated (determination step S7). When the analysis unit 25 determines that the distribution parameters P of all the measurement areas MA have not been calculated (determination step S7: No), the process returns to the distribution function creation step S3, and the distribution parameter P is set according to the same procedure. The distribution parameter P of the measurement area MA that has not been calculated is calculated. If the analysis unit 25 determines that the distribution parameters P of all the measurement areas MA have been calculated (determination step S7: Yes), the analysis ends.

  When the distribution parameters P of all the measurement areas MA are calculated, the output unit 26 detects the distribution information D for each measurement area MA using the distribution parameters P of each measurement area MA. The output unit 26 supplies the distribution information D of each measurement region MA to the data storage unit 31 and the display unit 32 in association with the position of the measurement region MA and the film forming conditions of the thin film 40 (output step S8).

FIGS. 12 to 15 are diagrams showing comparison results between the actual measurement value TM and the weighted average spectral transmittance T _av in the first to fourth embodiments. The substrate is polycarbonate. Since polycarbonate has an absorption wavelength region WR1 in a wavelength region of approximately 650 nm or less, the measured value TM and the weighted average spectral transmittance T _av are applied in a wavelength region WR2 other than the absorption wavelength region WR1. When the thin film has a wavelength region with large absorption, it is preferable to apply the measured value TM and the weighted average spectral transmittance T _{av in a} wavelength region other than the absorption wavelength region of the thin film.

The absorptance of polycarbonate is remarkably increased in the wavelength region on the short wavelength side of 400 nm or less. Therefore, a wavelength region of at least 400 nm or less is an inappropriate region that is not suitable for fitting the actual measurement value TM and the weighted average spectral transmittance T _av . However, even if the light absorptance is small, if the thickness of the base material BM increases, the total amount of absorption increases and the analysis result is affected. Therefore, when analyzing the measured value TM of the spectral transmittance, the improper region extends to a wavelength region longer than 400 nm. In the present embodiment, such an inappropriate region is set as the absorption wavelength region WR1.

Figure 16 is a diagram showing film forming conditions of Example 4 from Example 1, the measured value of the root mean square deviation S _q, the average thickness tA and variance σ by this analysis method. FIG. 17 is a diagram showing the relationship between the variance σ and the root mean square deviation _Sq .

  In FIG. 16, “Process A” means a process in which a thin film is formed under the condition that the target film thickness is 180 nm. “Process B” means a process in which a thin film is formed under the condition that the target film thickness is 120 nm. The number of times each process is performed is shown in the film forming conditions. The greater the number of steps, the greater the film thickness.

  “Step A” is performed using a gravure offset printing technique. Gravure offset printing is a printing technique in which a gravure plate cylinder having a specific dent pattern is transferred to a transfer blanket cylinder, and ink on the transfer blanket cylinder is transferred to a substrate. In gravure offset printing, by combining the characteristics of gravure printing and offset printing, it is possible to print on hard, curved, and fragile objects that cannot be printed directly from the gravure plate cylinder. In “Process A”, an approximate target film thickness was controlled by using a gravure plate cylinder having a 25 μm recess pattern. In “Process B”, an approximate target film thickness was controlled by using a gravure plate cylinder having a concave pattern of 54 μm.

As shown in FIGS. 12 to 15, the waveform of the weighted average spectral transmittance T _{av and} the waveform of the actual measurement value TM are in good agreement. As shown in FIG. 16, there is a high correlation between the average film thickness suggested by the film forming conditions and the average film thickness tA calculated by calculation. Further, as shown in FIG. 17, the measured value of the root mean square deviation S _q showing the film thickness roughness, also between the variance σ calculated by the calculation, there is a high correlation. Therefore, it is expected that the film thickness distribution of the thin film is accurately detected by the analysis method of this embodiment.

  According to the inventor's investigation, it has been confirmed that the measured value TM of the thin film formed by at least the gravure coating and spin coating techniques can be satisfactorily approximated by the analysis technique of this embodiment. For example, FIG. 12 to FIG. 15 show that the actual measurement value of the thin film formed by gravure offset printing can be satisfactorily approximated by the analysis method of this embodiment. The inventor has performed the same analysis on a thin film formed by spin coating. As a result, it has been confirmed that the actual measurement value TM of the thin film formed by spin coating is well approximated by the analysis method of this embodiment.

  Since the film formation 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). In the case of a single-layer thin film, it has been confirmed that the measured value TM of a thin film of 20 nm to 2300 nm is satisfactorily approximated by the analysis method of this embodiment. Therefore, it is considered that the analysis method of this embodiment can be applied to a thin film having a 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 easy to confirm the peak of the spectral transmittance corresponding to the film thickness of about 40 μm. Therefore, it is preferable to perform measurement by selecting a wavelength range in which a peak is easily confirmed.

As described above, according to the film thickness distribution measuring method of the present embodiment, the film thickness distribution in the measurement region MA can be obtained by measuring the spectral transmittance once. Since the range that can be measured at once is wide and analysis of the actual measurement value TM is easy, a wide range of film thickness distribution can be measured efficiently. In addition, since the actual measurement value TM is approximated by the weighted average spectral transmittance T _av considering the film thickness distribution, the actual measurement value TM and the calculated value (weighted average spectral transmittance T _av ) are likely to match. Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

In the present embodiment, the distribution parameter P is calculated using a regression analysis technique. Therefore, the weighted average spectral transmittance T _av can be mechanically applied to the actual measurement value TM having an arbitrary wavelength dispersion, and the approximation accuracy is high.

In the present embodiment, the weighted average spectral transmittance T _av is applied to the actual measurement value TM in a wavelength region WR2 other than the absorption wavelength region WR1 of the base material BM. Therefore, the weighted average spectral transmittance T _av can be accurately applied to the actual measurement value TM. Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

In the present 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 a time. Therefore, it is possible to efficiently measure a wide range of film thickness distribution by increasing the size of the measurement area MA per time. For example, in the present embodiment, the actual measurement value TM is a measurement value of the spectral transmittance of the measurement area MA of 1 mm ² or more. By measuring the spectral transmittance once, the film thickness distribution of the measurement area MA as large as 1 mm ² or more can be obtained. Therefore, even when the measurement is sequentially performed on a plurality of measurement areas MA arranged two-dimensionally, the measurement is completed in a short time.

The size of the measurement area MA is grasped by, for example, visually observing the area where the thin film 40 is irradiated with the illumination light Li. As a result of observation by the inventors, the thin film of Example 1 to Example 6 was irradiated with illumination light Li on a rectangular region having a width of about 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 a time. As described above, the waveform of the actually measured values in Examples 1 to 6 agrees well with the waveform of the weighted average spectral transmittance. Therefore, it can be seen that the film thickness distribution of a very large measurement area MA of about 10 mm ² can be measured with high accuracy in a short time.

[Second Embodiment]
FIG. 18 is a conceptual diagram showing a film thickness distribution measuring method according to the second embodiment. In this embodiment, the same components as those in the first embodiment are denoted by the same reference numerals, and detailed description thereof is omitted.

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

  FIG. 19 is a flowchart for explaining the film thickness distribution measuring method of the present embodiment. Hereinafter, the configuration and operation of the processing unit 20 will be described with a focus on differences from the first embodiment with reference to a flowchart.

  First, the measurement unit 10 sequentially measures the spectral transmittance in a plurality of measurement areas MA. Thereby, the actual measurement value TM (λ) of the spectral transmittance of each measurement area MA is obtained (measurement step S11).

Next, the input unit 30 inputs information necessary for the processing unit 20 to execute various processes to the processing unit 20 (input step S12). For example, information such as the type of distribution function of each layer 41, the variation range of element parameters constituting 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} each layer 41, the range in which the film thickness distribution exists, and the film thickness pitch Δt is input to the non-distributed spectral transmittance creating unit 22.

Next, the distribution function creation unit 21 sets a distribution function for each layer 41 (distribution function creation step S13). For example, for an 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 characterizing 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 in the measurement region MA. The distribution parameter P _i is expressed as a combination of q element parameters P _{i1 to} P _iq that characterize the film thickness distribution of the layer 41 _i (q is an integer of 1 or more).

  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 distribution function corresponding to the continuous distribution CD in FIG. The film thickness distribution in FIG. 8 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-distributed spectral transmittance creating unit 22 creates a theoretical value of the spectral transmittance for each layer 41 based on the formula (1) (non-distributed spectral transmittance creating step S14). For example, for the i-th layer 41 _i , a theoretical value TT _i (λ, t) of the spectral transmittance for each film thickness t of the layer 41 _i is created. Based on information from the input unit 30, the non-distributed spectral transmittance creating unit 22 has a plurality of film thickness values (t ₁ , t ₂ ,..., T _N ) at a pitch of Δt within a range where the film thickness distribution exists. Set. The non-distributed spectral transmittance creating unit 22 creates a theoretical value TT _i (λ, t) for each film thickness value.

Next, the weighted average spectral transmittance calculating unit 23 calculates the weighted average spectral transmittance for each layer 41, and calculates the sum of the weighted average spectral transmittance of each layer 41 as the weighted average spectral transmittance of the thin film 40 (weighted). Average spectral transmittance calculation step S15). For example, for the i-th layer 41 _i , the theoretical value TT _i (λ, t) of the spectral transmittance for each film thickness t of the layer 41 _i is weighted and averaged with the distribution function f _i (t, P _i ). The average spectral transmittance T _avi (λ, P _i ) is calculated. The weighted average spectral transmittance T _avi (λ, P _i ) of the layer 41 _i is represented by the following formula (3). The weighted average spectral transmittance T _avt (λ, P ₁ ,..., P _M ) of the thin film is expressed by the following formula (4).

Next, the analysis unit 25 applies the weighted average spectral transmittance T _avt (λ, P ₁ ,..., P _M ) of the thin film 40 to the measured value TM (λ) of the spectral transmittance of the thin film 40, and Distribution parameters P _{1 to} P _M included in the distribution functions f ₁ (t, P ₁ ) to f _M (t, P _M ) are calculated (analysis step S16). For example, the analysis unit 25 calculates the distribution parameter _P 1 to P _M using techniques regression analysis.

For example, the analysis unit 25 calculates the weighted average spectral transmittance T _avt (λ, P ₁ ,...) To the measured value TM (λ) in a wavelength region other than the absorption wavelength region of each layer 41 and the base material BM on which each layer 41 is disposed. , P _M ). Thereby, the weighted average spectral transmittance T _avt (λ, P ₁ ,..., P _M ) can be accurately applied to the actual measurement value TM (λ). Therefore, an error hardly occurs between the film thickness distribution of each layer 41 calculated by calculation and the actual film thickness distribution of each layer 41.

As described above, the distribution parameters P _{1 to} P _M of each layer 41 in one measurement region MA 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 in association with the position of the measurement region MA.

Next, the analyzing unit 25 determines whether the distribution parameter _P 1 to P _M of all the measurement areas MA, which is set to the thin film 40 is calculated (decision step S17). Analysis unit 25, when it is determined that the distribution parameter _P 1 to P _M of all the measurement regions MA not calculated (decision step S17: No), returns to the distribution function creating step S13, following the same procedure, The distribution parameters P _{1 to} P _M of the measurement area MA for which the distribution parameters P _{1 to} P _M are not calculated are calculated. Analysis unit 25, when it is determined that the distribution parameter _P 1 to P _M of all the measurement regions MA is calculated (decision step S17: Yes), the analysis is completed.

After distribution parameter _P 1 to P _M of all the measurement area MA is calculated, the output unit 26, using the distribution parameter _P 1 to P _M of each layer 41 of each measurement area MA, for each measurement area MA, the layers 41 distribution information D is detected. 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 position of the measurement region MA and the film forming conditions of each layer 41 (output step S18).

FIG. 20 is a diagram illustrating a comparison result between the actual measurement value TM and the weighted average spectral transmittance T _avt in Example 7. FIG. 21 is a diagram illustrating parameter values used in the analysis of the thin film of Example 7. In FIG. 20, the theoretical value TT of the spectral transmittance is also shown for comparison.

  The thin film of Example 7 is composed of the coating film 1 and the coating film 2. The composition of the coating film 1 and the coating film 2 is 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 1-5 nm, [trade name etc.] Excel Pure BD-P01): 5% by weight
・ Alcohol solvent (ethanol): 30% by weight
・ Alcohol solvent (normal propyl alcohol): 30% by weight
・ Alcohol 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.] Rioduras 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 an absorption wavelength region WR1 on the short wavelength side, the measured value TM and the weighted average spectral transmittance T _avt are applied in a wavelength region WR2 other than the absorption wavelength region WR1. As shown in FIG. 20, the waveform of the weighted average spectral transmittance T _{avt and} the waveform of the actual measurement value TM are in good agreement. Therefore, even for a thin film having a multilayer structure, it is expected that the film thickness distribution of each layer can be accurately detected by a single measurement.

As described above, according to the film thickness distribution measuring method of the present embodiment, the film thickness distributions of the plurality of layers 41 constituting the thin film 40 can be calculated simultaneously by measuring the spectral transmittance once. In addition, since the actual measurement value TM is approximated by the weighted average spectral transmittance T _avt considering the film thickness distribution of each layer 41, the actual measurement value TM and the calculated value (weighted average spectral transmittance T _avt ) are likely to match. Therefore, an error is unlikely to occur between the film thickness distribution of each layer 41 calculated by calculation and the actual film thickness distribution of each layer 41.

  In FIG. 20, the analysis method of the present embodiment is applied to a thin film having a two-layer structure, but the layer structure of the thin film 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 a thin film having a laminated structure of three or more layers.

[First modification]
Hereinafter, modifications of the first embodiment will be described. Constituent elements common to the first embodiment in this modification are given the same reference numerals, and detailed descriptions thereof are omitted.

In this modification, the difference from the first embodiment is that the film thickness distribution is the discrete distribution DD shown in FIG. Distribution function creating unit 21 shown in FIG. 1, the range where the film thickness distribution is present, discretely setting the film thickness value of N to t ₁ ~t _N (N is an integer of 2 or more) for each Δt To do. The distribution function creation unit 21 sets the occupation ratios f _{1 to} f _N corresponding to the 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 a plurality of occupation ratios f _{1 to} f _N corresponding to the film thicknesses t _{1 to} t _N. The distribution parameter P includes the occupancy rates f _{1 to} f _N of the respective film thicknesses as element parameters. The value of each element parameter (occupancy ratios f _{1 to} f _N ) is calculated by analyzing the actual measurement value TM by the analysis unit 25. 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 transmittance T _av (λ, P) is expressed by the following formula (5).

The analysis unit 25 calculates the distribution parameter P by applying the weighted average spectral transmittance T _av (λ, P) to the measured value TM (λ) of the spectral transmittance of the thin film 40. 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 (6) Is calculated.

By solving the simultaneous equations of formula (6), 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 a wavelength region other than the absorption wavelength region of the thin film 40 and the base material BM on which the thin film 40 is disposed, for example. Thereby, the approximate expression T _av (λ, P) can be accurately applied to the actual measurement value TM (λ). Therefore, an error hardly occurs between the film thickness distribution calculated by the calculation and the actual film thickness distribution.

  Also according to this modification, the film thickness distribution in the measurement region MA can be obtained by measuring the spectral transmittance once. Further, since the film thickness distribution is calculated by solving a simple simultaneous equation, the calculation is easy.

[Second modification]
22 and 23 are diagrams showing variations of the distribution function.

  In the first embodiment and the second embodiment, the Gaussian distribution as shown in FIG. 22 is used as the film thickness distribution, but the film thickness distribution is not limited to the Gaussian distribution. As the film thickness distribution, a Laplace distribution shown in FIG. 23 may be used. As the distribution function, a distribution function having an average value and calculating a probability distribution based on the variance value is preferably used. The film thickness distribution varies depending on the film forming conditions. Therefore, it is preferable to employ an appropriate distribution function according to the film forming conditions. In consideration of the deviation of the film thickness distribution generated in the film forming process, it is possible to add a function or a coefficient that can uniquely define the deviation to the above distribution function. By using a highly probable distribution function, the film thickness distribution can be accurately approximated.

  The preferred embodiment of the present invention has been described above, but the present invention is not limited to such an embodiment. The content disclosed in the embodiment is merely an example, 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 the inventions that can be implemented by those skilled in the art based on the above-described inventions are also within the technical scope of the present invention as long as they include the gist of the present invention.

[Arithmetic handling of interference phenomena]
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 interface reflectance, interface transmittance, and interface absorption rate. In the matrix method, optical properties at the interface between two media are calculated. The symbols used for calculation are described below. The following symbols are not related to the symbols used in the above-described embodiments.

[A] Reflection and transmission of light at the interface
Reflection of light always occurs at the interface between two different media. The amplitude reflection coefficient r at the boundary surface between the medium having the refractive index n0 and the medium having the refractive index n1 is expressed by the following formula (7). The amplitude transmission coefficient t is expressed by the following equation (8). ρ is the ratio of the complex refractive index of the interface.
r = (1−ρ) / (1 + ρ) (7)
t = 2 / (1 + ρ) (8)

When light is incident perpendicular to the boundary surface, the reflectance R and the transmittance T are expressed by the following formula (9) and the following formula (10) using the amplitude reflection coefficient r and the amplitude transmission coefficient t. .
r = (N ₀ −N ₁ ) / (N ₀ + N ₁ ) (9)
t = 2N ₀ / (N ₀ + N ₁ ) (10)

When the refractive index N ₀ and the refractive index N ₁ are real numbers, that is, when the incident medium and the output medium are transparent, the reflectance R and the transmittance T are expressed by the following expressions (11) and (12). expressed.
R = r ² = {(N ₀ −N ₁ ) / (N ₀ + N ₁ )} ² (11)
T = N ₁ · t ² / N ₀ = 4N ₀ N ₁ / (N ₀ + N ₁ ) ² (12)

  From Equation (11) and Equation (12), it is understood that R + T = 1.

[B] Physical quantities handled in optical calculation [B-1] Refractive index The refractive index N is defined by the ratio of the speed of light c in a vacuum to the speed of light v in a medium.
N = n−ik (13)

In formula (13), i is an imaginary number and i ² = −1. N is called the complex refractive index, n is the real part of the refractive index, and k is the imaginary part of the refractive index. When dealing with a dielectric film, since the thin film is a transparent body (ie, k = 0), n is sometimes 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 (14)

  In equation (14), α is the reciprocal of the propagation distance that reduces the intensity of the 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 as the following equation.
δ = 2πNd cos θ / λ (15)

  In the formula (15), θ is an incident angle of light (an angle formed with a 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, optical characteristics are calculated from a characteristic matrix defined by optical constants, which are quantities inherent to the thin film to be handled. In the case of a multilayer film, the product of the characteristic matrix of each layer is treated as the characteristic matrix of the entire multilayer film.

[C] Characteristic Matrix [C-1] Single Layer Film Optical System A thin film characteristic matrix M in the single layer film optical system is represented by the following formula (16).

  The characteristic matrix of the substrate is represented by the following formula (17). In following formula (17), Ns shows the complex refractive index of a base material.

[C-2] Method for calculating reflectance and transmittance Hereinafter, a method for calculating the reflectance and transmittance when a single-layer film is formed on a substrate will be described. FIG. 24 is a conceptual diagram of an optical system of a single layer film.

  The reflectance and transmittance are calculated by obtaining a characteristic matrix of an optical system (an optical system including a thin film and a base material) viewed from a light incident medium. 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 substrate. The calculation result is shown as the following formula (18).

The optical admittance Y is represented by the following formula (19). The optical admittance is a numerical value that can be handled in the same manner as the refractive index.
Y = C / B (19)

  In order to obtain the amplitude reflection coefficient r and the amplitude transmission coefficient t, Expression (7) and Expression (8) can be used. The reflectance when the thin film is formed on the substrate 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, from equation (7), the amplitude reflection coefficient r is expressed by the following equation (20).
r = (η0−Y) / (η0 + Y) (20)

The reflectance R is represented by the following formula (21).

  From the equations (20) and (21), the reflectance R is expressed by the following equation (22). r * is a conjugate complex number of r.

  The transmittance and the absorptance are represented by the following formula (23) and the following formula (24), respectively. ηs is the optical admittance of the substrate. real (η) is a calculation formula for obtaining the real part of η.

[C-3] Multilayer Optical System The calculation method in the multilayer optical system is the same as the calculation method in the single-layer optical system described above. FIG. 25 is a conceptual diagram of a multilayer optical system. In FIG. 25, for example, the thin film is composed of p layers.

  The characteristic matrix Mq of the q-th layer is calculated using the following formula (25) to the following formula (27).

  The reflectance, transmittance, and absorptance are calculated using Equation (18), Equation (19), Equation (22), Equation (23), and Equation (24), as in the case of the single layer film.

  In addition, when calculating a reflectance, the calculation which considered the back surface of the base material cannot be performed. Therefore, only the reflection from the surface of the substrate is calculated. Moreover, the refractive index of a substance has complicated wavelength dependence and cannot be expressed uniformly. Therefore, even if it is only the surface of the base material, it is difficult to accurately reproduce the measured reflectance by calculation.

  In order to eliminate the influence of the base material, it is preferable to calculate the difference between the reflectance of the base material before forming the thin film and the reflectance after forming the thin film. Further, it is preferable to calculate a theoretical value of the reflectance excluding the influence of the base material and compare this theoretical value with the above-mentioned difference. As a result, the theoretical value and the actual measurement value can be accurately compared.

  The substrate may be flat or curved. However, when evaluating a curved substrate, it is assumed that the optical path length varies depending on the incident angle during measurement with a spectrophotometer, and thus the calculated film thickness needs to be corrected.

  When predicting the reflectance value, the following method can be used. First, the value which increases / decreases by thin film interference is calculated | required by calculation by making the reflectance of the base material by measurement into a baseline. Then, how the reflectance varies based on the base line of the base material is calculated. Thereby, the value of reflectance can be predicted.

  A similar estimation of the film thickness distribution can also be performed using the transmittance data. In the case where the thin film is a transparent material such as polycarbonate and acrylic, an increase or decrease in the transmittance due to the thin film interference also appears in the transmittance in the wavelength region where the absorption is small. The film thickness distribution can be calculated using any measured value of reflectance and transmittance.

1 the film thickness distribution measuring device 21 distribution function creating unit 23 weighted mean spectral transmittance calculating unit 25 analyzing unit 40 thin film 41 layered MA measuring area P distribution parameter T spectral transmittance _{T av, T avt} weighted average spectral transmittance TM spectral transmittance Actual value TT Theoretical value of spectral transmittance WR1 Absorption wavelength region of substrate WR2 Wavelength region other than absorption wavelength region of substrate

Claims (8)

A weighted average spectral transmittance calculating step of calculating a weighted average spectral transmittance by weighted averaging a theoretical value of spectral transmittance for each film thickness of the thin film with a distribution function including a distribution parameter;
An analysis step of calculating the distribution parameter by applying the weighted average spectral transmittance to the measured value of the spectral transmittance of the thin film;
A method for measuring film thickness distribution. The film thickness distribution measuring method according to claim 1, wherein in the analyzing step, the distribution parameter is calculated using a regression analysis technique. The film thickness distribution measuring method according to claim 2, wherein the distribution function is a distribution function indicating a Gaussian distribution or a Laplace distribution. 4. The film thickness distribution according to claim 1, wherein in the analysis step, the weighted average spectral transmittance is applied to the actual measurement value in a wavelength region other than the absorption wavelength region of the substrate on which the thin film is disposed. Measuring method. The film thickness distribution measurement method according to any one of claims 1 to 4, wherein the actual measurement value is a measurement value of spectral transmittance in a measurement region of 1 mm ² or more. The thin film is composed of a plurality of layers,
In the weighted average spectral transmittance calculating step, the distribution function is set for each of the layers, the weighted average spectral transmittance is calculated for each of the layers, and the sum of the weighted average spectral transmittance of each layer is weighted of the thin film. Calculated as the average spectral transmittance,
6. The film thickness according to claim 1, wherein in the analysis step, the distribution parameter included in the distribution function of each layer is calculated by applying a weighted average spectral transmittance of the thin film to the actual measurement value. Distribution measurement method. A weighted average spectral transmittance calculating unit that calculates a weighted average spectral transmittance by weighted averaging a theoretical value of spectral transmittance for each thin film thickness with a distribution function including a distribution parameter;
An analyzer that calculates the distribution parameter by applying the weighted average spectral transmittance to the measured value of the spectral transmittance of the thin film;
A film thickness distribution measuring apparatus. A weighted average spectral transmittance calculating step of calculating a weighted average spectral transmittance by weighted averaging a theoretical value of spectral transmittance for each film thickness of the thin film with a distribution function including a distribution parameter;
An analysis step of calculating the distribution parameter by applying the weighted average spectral transmittance to the measured value of the spectral transmittance of the thin film;
Is a film thickness distribution measurement program that runs a computer.