JP2009036523A - Roughness measuring method and roughness measuring device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To measure nano-scale roughness of an interference of a transparent film formed on a substrate, optically and nondestructively in a noncontact state. <P>SOLUTION: A roughness measuring device 100 for measuring root mean square roughness of the interference of the transparent film 42 formed on the substrate 41 includes a light source 11 for irradiating light of the first wavelength having coherence to a transparent film formation surface of a substrate 41 on which the transparent film is formed and a reference mirror 19; a photodetector 23 for receiving interference light formed by synthesizing measuring light reflected by the transparent film formation surface with reference light reflected by a reference plane; and a roughness calculation part 33 for calculating root mean square roughness of the transparent film formation surface from a phase difference between the measuring light and the reference light based on an intensity change of the interference light received by the photodetector 23, and determining the root mean square roughness of the interference of the transparent film 42. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a roughness measuring method and a roughness measuring apparatus, and more particularly, a measuring method for optically measuring the nanoscale surface / interface roughness of a transparent film formed on a substrate in a non-destructive and non-contact manner. And a measuring apparatus.

  As a method for inspecting the surface roughness, there are a contact method using a stylus and a non-contact method using light or the like. In the former contact method, the surface must be scanned by bringing the stylus into contact with the surface to be inspected. For this reason, depending on the material of the surface to be inspected, the surface is damaged by the stylus and cannot be used for nondestructive inspection. Moreover, when measuring the surface roughness of the substrate surface on which the transparent film is formed, the substrate surface cannot be measured unless the transparent film is peeled off.

  On the other hand, since the latter non-contact method is a non-destructive inspection, there is an advantage that the surface to be inspected is not damaged. As this non-contact method, for example, an atomic force microscope, ellipsometry, spectral interferometry, optical interferometry, and the like are known. In an atomic force microscope, it is necessary to scan the surface to be inspected with a cantilever. For this reason, it takes an enormous time of several tens of minutes to measure an area of about several tens of μm square. Moreover, when measuring the surface roughness of the substrate surface on which the transparent film is formed, the substrate surface cannot be measured unless the transparent film is peeled off.

  Since the ellipsometry is a measurement using light, the surface of the transparent film and the substrate surface can be measured. However, since the spot size of light is large, there is a problem that the spatial resolution in the lateral direction is low. In addition, in the spectral interference method, the thickness of the transparent film can be measured, but from this result, the surface of the transparent film and the shape of the substrate surface cannot be separated. Further, in order to measure the surface roughness, it is necessary to assume that the substrate surface is flat. Also in this spectroscopic interferometry, since the measurement spot is large, only average information of a region having a diameter of about several tens of μm can be obtained. In the optical interference method using white light, the phase information on the transparent film surface and the phase information on the substrate surface are added to the optical interference intensity. For this reason, the surface roughness of the transparent film and the surface roughness of the substrate surface cannot be separated.

Depending on the type of the transparent film, there are some which are transparent with visible light but visible with i-line (wavelength 365 nm) and DUV (Deep Ultraviolet). However, it is considered that silicon oxide (SiO ₂ ) has a large measurement need in the semiconductor manufacturing process. When measuring this SiO ₂ , ultraviolet light having a wavelength of 150 nm or less is required. Therefore, it is not realistic to apply an optical system that realizes such short-wavelength ultraviolet light. In addition, as a measuring method of the shape and film thickness of a transparent film, it describes in patent documents 1-4.
JP 2006-138854 A JP 2006-84334 A JP 2004-361218 A JP 2004-317238 A

  The present invention has been made against the background of such circumstances, and the object of the present invention is to measure the nanoscale roughness of the interface of the transparent film formed on the substrate optically in a non-destructive and non-contact manner. An object of the present invention is to provide a roughness measuring method and a roughness measuring apparatus.

  The roughness measuring method according to the first aspect of the present invention is a measuring method for measuring the root mean square roughness of the interface of the transparent film formed on the substrate, the roughness measuring method for the substrate on which the transparent film is formed. Irradiating the transparent film forming surface and the reference surface with light having a first wavelength having coherence, and combining the measurement light reflected by the transparent film forming surface and the reference light reflected by the reference surface. Based on a change in intensity of the interference light, the root mean square roughness of the transparent film forming surface is calculated from the phase difference between the measurement light and the reference light, and the root mean square of the transparent film forming surface is calculated. Based on the roughness, the root mean square roughness of the interface of the transparent film is determined. Thereby, the roughness of the interface of a transparent film can be measured by non-destructive and non-contact.

  The roughness measuring method according to a second aspect of the present invention is the above roughness measuring method, wherein the transparent film forming surface and the reference surface are irradiated with light having a second wavelength different from the first wavelength, Based on the root mean square roughness of the transparent film forming surface calculated by irradiating one wavelength and the root mean square roughness of the transparent film forming surface calculated by irradiating the second wavelength, The root mean square roughness of both interfaces of the transparent film is determined simultaneously. Thereby, the roughness of both interfaces of the transparent film can be calculated in a short time.

に基づいて算出されることを特徴とする。ここで、Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ、Ｒｑ^{Ｌａｙｅｒ}：前記透明膜と媒質との界面の二乗平均平方根粗さ、Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ、ｎ_１：前記透明膜の屈折率、ｎ_０：前記媒質の屈折率、とする。このように、簡単な演算式により基板上に形成された透明膜の界面の粗さを算出することができる。 In the roughness measuring method according to the third aspect of the present invention, in the above roughness measuring method, the root mean square roughness of the interface of the transparent film is obtained for each of the first wavelength and the second wavelength. The following formula,

It is calculated based on. Here, Rq: root mean square roughness of the transparent film forming surface, Rq ^Layer : root mean square roughness of the interface between the transparent film and the medium, Rq ^Base : root mean square of the interface between the transparent film and the substrate Square root roughness, n ₁ : refractive index of the transparent film, n ₀ : refractive index of the medium. Thus, the roughness of the interface of the transparent film formed on the substrate can be calculated by a simple arithmetic expression.

  The roughness measuring method according to the fourth aspect of the present invention is the above roughness measuring method, wherein the root mean square roughness of the transparent film forming surface in the first medium is different from the refractive index of the first medium. Based on the root mean square roughness of the transparent film forming surface in the second medium, the root mean square roughness of both interfaces of the transparent film is simultaneously determined. Thereby, the roughness of both interfaces of the transparent film can be calculated in a short time.

に基づいて算出されることを特徴とする。ここで、Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ、Ｒｑ^{Ｌａｙｅｒ}：前記透明膜と前記第１媒質又は前記第２媒質との界面の二乗平均平方根粗さ、Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ、ｎ_１：前記透明膜の屈折率、ｎ_０：前記第１媒質の屈折率、ｎ_０'：前記第２媒質の屈折率とする。このように、簡単な演算式により、基板上に形成された透明膜の界面の粗さを算出することができる。 In the roughness measuring method according to the fifth aspect of the present invention, the root mean square roughness of the interface of the transparent film is the following two formulas:

It is calculated based on. Here, Rq: root mean square roughness of the transparent film forming surface, Rq ^Layer : root mean square roughness of the interface between the transparent film and the first medium or the second medium, Rq ^Base : the transparent film Root mean square roughness of the interface with the substrate, n ₁ : refractive index of the transparent film, n ₀ : refractive index of the first medium, n ₀ ′: refractive index of the second medium. Thus, the roughness of the interface of the transparent film formed on the substrate can be calculated with a simple arithmetic expression.

  A roughness measuring method according to a sixth aspect of the present invention is the roughness measuring method described above, wherein an optical distance between the transparent film forming surface and the reference surface is varied, and the measurement light and the reference light are changed. A plurality of phase differences are given between them to cause an intensity change of the interference light. Thereby, phase measurement can be performed with high resolution, and the roughness of the interface of the transparent film can be measured more accurately.

  A roughness measuring method according to a seventh aspect of the present invention is the above-described roughness measuring method, comprising a second transparent film formed on the transparent film and having a refractive index different from that of the transparent film, and the first wavelength. Further, based on the root mean square roughness of the transparent film forming surface calculated by further irradiating light of a third wavelength different from the second wavelength and irradiating light of the third wavelength, the second transparent It is characterized by determining the root mean square roughness of the film interface. Thereby, even when a plurality of transparent films having different refractive indexes are formed on the substrate, the roughness of the interface between the transparent films can be calculated.

に基づいて算出されることを特徴とする。
ここで、
Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ
Ｒｑ^{Ｌａｙｅｒ1}：前記第２透明膜と前記媒質との界面の二乗平均平方根粗さ
Ｒｑ^{Ｌａｙｅｒ2}：前記透明膜と前記第２透明膜との界面の二乗平均平方根粗さ
Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ
ｎ₂：前記透明膜の屈折率
ｎ_１：前記第２透明膜の屈折率
ｎ_０：前記媒質の屈折率
とする。 The roughness measuring method according to an eighth aspect of the present invention is the roughness measuring method described above, wherein the root mean square roughness of the interface of the second transparent film is the first wavelength, the second wavelength, and the second wavelength. The following formulas required for each of the three wavelengths:

It is calculated based on.
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer1 : root mean square roughness of the interface between the second transparent film and the medium Rq ^Layer2 : square of the interface between the transparent film and the second transparent film Average square root roughness Rq ^Base : root mean square roughness n ₂ of the interface between the transparent film and the substrate n ₂ : refractive index of the transparent film n ₁ : refractive index of the second transparent film n ₀ : refractive index of the medium And

  A roughness measuring apparatus according to a ninth aspect of the present invention is a roughness measuring apparatus for measuring a root mean square roughness of an interface of a transparent film formed on a substrate, wherein the transparent film is formed. A light source that emits light having a first wavelength having coherence to the transparent film forming surface and the reference surface of the substrate, the measurement light reflected by the transparent film forming surface, and the reference light reflected by the reference surface A photodetector that receives the interference light, and a root mean square of the transparent film forming surface based on a phase difference between the measurement light and the reference light based on a change in intensity of the interference light received by the photodetector. A calculation unit that calculates roughness and determines a root mean square roughness of the interface of the transparent film. Thereby, the roughness of the interface of a transparent film can be measured by non-destructive and non-contact.

  The roughness measuring apparatus according to a tenth aspect of the present invention is the roughness measuring apparatus, wherein the light source irradiates the transparent film forming surface and the reference surface with light having a second wavelength different from the first wavelength. The calculating unit calculates a root mean square roughness of the transparent film forming surface calculated by irradiating the first wavelength, and a square of the transparent film forming surface calculated by irradiating the second wavelength. The root mean square roughness of both interfaces of the transparent film is determined based on the mean square root roughness. Thereby, the roughness of both interfaces of the transparent film can be calculated in a short time.

に基づいて前記透明膜の界面の二乗平均平方根粗さを算出することを特徴とするものである。ここで、Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ、Ｒｑ^{Ｌａｙｅｒ}：前記透明膜と媒質との界面の二乗平均平方根粗さ、Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ、ｎ_１：前記透明膜の屈折率、ｎ_０：前記媒質の屈折率、とする。このように、簡単な演算式により基板上に形成された透明膜の界面の粗さを算出することができる。 The roughness measuring device according to an eleventh aspect of the present invention is the roughness measuring device described above, wherein the calculation unit has the following formula:

Based on the above, the root mean square roughness of the interface of the transparent film is calculated. Here, Rq: root mean square roughness of the transparent film forming surface, Rq ^Layer : root mean square roughness of the interface between the transparent film and the medium, Rq ^Base : root mean square of the interface between the transparent film and the substrate Square root roughness, n ₁ : refractive index of the transparent film, n ₀ : refractive index of the medium. Thus, the roughness of the interface of the transparent film formed on the substrate can be calculated by a simple arithmetic expression.

に基づいて、前記透明膜の界面の二乗平均平方根粗さを算出することを特徴とするものである。ここで、Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ、Ｒｑ^{Ｌａｙｅｒ}：前記透明膜と前記第１媒質又は前記第２媒質との界面の二乗平均平方根粗さ、Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ、ｎ_１：前記透明膜の屈折率、ｎ_０：前記第１媒質の屈折率、ｎ_０'：前記第２媒質の屈折率とする。 The roughness measuring apparatus according to a twelfth aspect of the present invention is the roughness measuring apparatus, wherein the calculation unit includes a root mean square roughness of the transparent film forming surface in the first medium, and the first medium. The root mean square roughness of both interfaces of the transparent film is simultaneously determined based on the mean square root roughness of the transparent film forming surface in the second medium different from the refractive index of the transparent film. Thereby, the roughness of both interfaces of the transparent film can be calculated in a short time.
The roughness measuring apparatus according to the thirteenth aspect of the present invention is the roughness measuring apparatus described above, wherein the calculation unit includes the following two formulas:

Based on the above, the root mean square roughness of the interface of the transparent film is calculated. Here, Rq: root mean square roughness of the transparent film forming surface, Rq ^Layer : root mean square roughness of the interface between the transparent film and the first medium or the second medium, Rq ^Base : the transparent film Root mean square roughness of the interface with the substrate, n ₁ : refractive index of the transparent film, n ₀ : refractive index of the first medium, n ₀ ′: refractive index of the second medium.

  A roughness measuring device according to a fourteenth aspect of the present invention is the above-described roughness measuring device, further comprising a fluctuation mechanism that varies an optical distance between the reference surface and the transparent film forming surface, A plurality of phase differences are provided between the reference light and the intensity of the interference light to change. Thereby, phase measurement can be performed with high resolution, and the roughness of the interface of the transparent film can be measured more accurately.

  In the roughness measuring apparatus according to the fifteenth aspect of the present invention, in the roughness measuring apparatus, a second transparent film having a refractive index different from that of the transparent film is formed on the transparent film on the transparent film forming surface. The light source emits light of a third wavelength different from the first wavelength and the second wavelength, and the calculation unit calculates a mean square of the transparent film formation surface calculated by irradiating the third wavelength. The root mean square roughness of the interface of the second transparent film is determined based on the square root roughness. Thereby, even when a plurality of transparent films having different refractive indexes are formed on the substrate, the roughness of the interface between the transparent films can be calculated.

に基づいて前記第２透明膜の界面の二乗平均平方根粗さを算出することを特徴とするものである。
ここで、
Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ
Ｒｑ^{Ｌａｙｅｒ1}：前記第２透明膜と前記媒質との界面の二乗平均平方根粗さ
Ｒｑ^{Ｌａｙｅｒ2}：前記透明膜と前記第２透明膜との界面の二乗平均平方根粗さ
Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ
ｎ₂：前記透明膜の屈折率
ｎ_１：前記第２透明膜の屈折率
ｎ_０：前記媒質の屈折率
とする。
これにより、簡単な演算式により基板上に屈折率が異なる複数の透明膜が形成されている場合でも、それぞれの透明膜の界面の粗さを算出することができる。 In the roughness measuring apparatus according to the sixteenth aspect of the present invention, the calculation unit has the following formula:

Based on the above, the root mean square roughness of the interface of the second transparent film is calculated.
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer1 : root mean square roughness of the interface between the second transparent film and the medium Rq ^Layer2 : square of the interface between the transparent film and the second transparent film Average square root roughness Rq ^Base : root mean square roughness n ₂ of the interface between the transparent film and the substrate n ₂ : refractive index of the transparent film n ₁ : refractive index of the second transparent film n ₀ : refractive index of the medium And
Thereby, even when a plurality of transparent films having different refractive indexes are formed on the substrate by a simple arithmetic expression, the roughness of the interface of each transparent film can be calculated.

  ADVANTAGE OF THE INVENTION According to this invention, the nanoscale roughness of the interface of the transparent film formed on the board | substrate can be measured optically nondestructively and non-contactingly.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. The following description shows preferred embodiments of the present invention, and the scope of the present invention is not limited to the following embodiments. In the following description, the same reference numerals denote the same contents.

  The configuration of the roughness measuring apparatus according to the embodiment of the present invention will be described with reference to FIGS. FIG. 1 is a diagram schematically showing a configuration of a roughness measuring apparatus 100 according to the present embodiment. FIG. 2 is a block diagram showing a configuration of the processing apparatus 30 used in the roughness measuring apparatus 100 according to the present embodiment. In this embodiment, an example using a Michelson type phase shift interferometer will be described as an example of an interferometer. The interferometer is not particularly limited, and other two-beam interferometers such as a Mirau interferometer and a Fizeau interferometer may be used. Further, any method can be adopted as long as the method can accurately measure the phase without being limited to the phase shift method.

  As shown in FIG. 1, the roughness measuring apparatus 100 according to the present embodiment includes a light source 11, a wavelength conversion unit 12, lenses 13, 22, beam splitters 14, 15, a measurement objective lens 16, a stage 17, and a reference. An objective lens 18, a reference mirror 19, a focus adjustment mechanism 20, an angle adjustment mechanism 21, a photodetector 23, and a processing device 30 are provided. As shown in FIG. 2, the processing apparatus 30 includes a stage drive unit 31, a wavelength conversion control unit 32, a roughness calculation unit 33, a memory 34, and the like.

In the roughness measuring apparatus 100 according to the present invention, the roughness of the measurement object 40 in which a transparent film is formed on a substrate such as a semiconductor wafer or glass is measured. Here, for example, a measurement object 40 is formed by forming silicon oxide (SiO ₂ ) on the surface of a Si substrate that has many needs for measurement in a semiconductor manufacturing process. FIG. 3 shows the configuration of the measurement object 40. As shown in FIG. 3, the measurement object 40 includes a substrate 41 and a transparent film 42 formed on the substrate 41. The surface of the substrate 41 covered with the transparent film 42 becomes the transparent film forming surface. In FIG. 3, the refractive index of the substrate 41 is n ₂ , the refractive index of the transparent film 42 is n ₁ , and the refractive index of air as a medium is n ₀ .

  In the present invention, by calculating the apparent root mean square roughness of the transparent film forming surface, the interface of the transparent film 42 (the interface between the transparent film 42 and the substrate 41, the interface between the transparent film 42 and air (medium)). Determine the root mean square roughness of. That is, the root mean square roughness of the surface of the transparent film 42 or the surface of the substrate 41 is measured. The apparent root mean square roughness of the transparent film forming surface is phase information that includes information on both interfaces of the transparent film 42 (the interface between the transparent film 42 and the air and the interface between the transparent film 42 and the substrate 41). From this, it is calculated as the roughness of the interface between the air and the solid (the substrate 41 covered with the transparent film 42) apparently. In the following description, a case where air is used as an example of the medium will be described. However, the present invention is not limited to this, and the measurement may be performed in another gas such as argon gas.

  Roughness measuring apparatus 100 according to the present embodiment measures the roughness of measurement object 40 using an interferometer. The roughness measuring apparatus 100 includes a Michelson interferometer in the optical system. The measurement light reflected by the substrate 41 and the transparent film 42 of the measurement object 40 (light reflected by the transparent film forming surface) and the reference light reflected by the reference mirror 19 serving as the reference surface are combined. It is receiving light.

  As the light source 11, a white light source such as a xenon lamp is used. For example, a xenon lamp having a wide continuous spectrum in the ultraviolet to infrared region (185 nm to 2000 nm) can be used. Note that the light source may not be a light source having a continuous spectrum, but may be a light source including a plurality of bright lines in the continuous spectrum, such as a mercury xenon lamp. Of course, the light source 11 is not limited to a xenon lamp, and a white diode, a white laser, or the like may be used. As will be described later, any light source may be used as long as the wavelength can be selected. The light emitted from the light source 11 is branched by the beam splitter 15 and applied to the measurement object 40 and the reference mirror 19. Then, the measurement light reflected by the measurement object 40 and the reference light reflected by the reference mirror 19 are combined by the beam splitter 15. The combined light of the measurement light and the reference light is received by the photodetector 23. Based on the phase difference between the measurement light and the reference light, the apparent root mean square roughness of the measurement object 40 is calculated. In the present invention, the root mean square roughness of the surface or interface of the transparent film 42 is determined from the root mean square roughness of the transparent film forming surface.

  First, an illumination optical system for illuminating the measurement object 40 and the reference mirror 19 with light from the light source 11 will be described. The light emitted from the light source 11 passes through the wavelength converter 12 and is converted into light having a predetermined first wavelength. As the wavelength converter 12, for example, a plurality of band-pass filters that selectively transmit light having a specific wavelength are provided. Thereby, light of a specific wavelength is selectively transmitted. The wavelength conversion control unit 32 of the processing device 30 changes the wavelength of light to be transmitted by switching a plurality of bandpass filters of the wavelength conversion unit 12. Then, the light having the first wavelength passes through the lens 13 and enters the beam splitter 14. The beam splitter 14 branches the light so that the amount of reflected light and transmitted light is approximately 1: 1 regardless of the polarization state. Accordingly, approximately half of the first wavelength light is reflected by the beam splitter 14.

  Note that a laser light source that emits single-wavelength laser light may be used as the light source 11, and a wavelength conversion element may be provided as the wavelength conversion unit 12. For example, wavelength conversion of single wavelength light from the light source 11 incident on the wavelength conversion element can be performed by second harmonic generation. Further, a variable wavelength laser can be used as the light source 11. Furthermore, a plurality of light sources that emit laser beams having different wavelengths may be provided, and light having a desired wavelength among the plurality of light sources may be emitted.

  The light reflected by the beam splitter 14 travels downward in FIG. 1 and enters the beam splitter 15. The beam splitter 15 branches the light so that the amount of reflected light and transmitted light is approximately 1: 1 regardless of the polarization state. Accordingly, approximately half of the light of the first wavelength is transmitted through the beam splitter 15, and the remaining approximately half is reflected by the beam splitter 15. Therefore, the incident light having the first wavelength is split into two light beams by the beam splitter 15. The reflecting surface of the beam splitter 15 is inclined 45 ° with respect to the optical axis. The light transmitted through the beam splitter 15 enters the measurement objective lens 16. That is, one of the two light beams branched by the beam splitter 15 is incident on the measurement objective lens 16. The measurement objective lens 16 condenses the incident light beam and emits it to the measurement object 40. That is, the light beam transmitted through the beam splitter 15 is reduced and projected onto the measurement object 40 by the measurement objective lens 16. Thereby, the measuring object 40 is illuminated with the light of the first wavelength.

  The measurement object 40 is placed on the stage 17. The stage 17 is an XYZ stage, and moves the measurement object 40 and the relative position of the illumination light based on a drive signal from a stage drive unit 31 provided in the processing apparatus 30. That is, the stage 17 on which the measurement object 40 is placed is driven using a piezoelectric element such as a piezoelectric element, and the distance between the measurement object 40 and the measurement objective lens 16 is changed. Thereby, the measurement object 40 can be scanned in the Z direction by the light beam. That is, a plurality of phase differences can be given between the measurement light and the reference light by mechanically changing the optical distance.

  The measurement objective lens 16 may be driven by a piezo element to change the distance between the measurement objective lens 16 and the measurement object 40. Further, instead of changing the distance between the measurement objective lens 16 and the measurement object 40, the distance between the reference objective lens 18 and the reference mirror 19 may be changed. In this way, by providing a phase difference between the measurement light and the reference light by mechanically changing the optical distance, non-polarized light can be used, and even a measurement object having optical anisotropy can be polarized. Therefore, the measurement light and the reference light can be accurately measured without causing a phase shift.

  As a method of giving a plurality of phase differences between the measurement light and the reference light, there are a method of giving a phase difference using polarization interference in addition to a method of mechanically changing the optical distance as described above. Specifically, in consideration of the rotation angle of the polarization of the measurement light and the reference light, a plurality of phase differences can be given between the measurement light and the reference light using a phase difference plate or the like. In this case, the beam splitter 15 shown in FIG. 1 is replaced with a polarization beam splitter so that the measurement light and the reference light become p-polarized light and s-polarized light, respectively. Further, a λ / 4 wavelength plate is inserted in front of the photodetector 22 so that these p-polarized light and s-polarized light interfere with each other. Note that a combination of a vibrating mirror such as a galvanometer mirror, an acoustooptic deflector, or the like may be used so that the illumination light scans the measurement object 40 in the XY direction.

  The light beam reflected by the beam splitter 15 enters a reference objective lens 18 provided on the side in FIG. That is, the reference objective lens 18 condenses the other light beam of the two light beams branched by the beam splitter 15 and makes it incident on the reference mirror 19. That is, the light beam reflected by the beam splitter 15 is reduced and projected onto the reference mirror 19 by the reference objective lens 18. Thereby, the reference mirror is illuminated by the light of the first wavelength. In this way, one of the light beams branched by the beam splitter 15 becomes illumination light for illuminating the measurement object 40, and the other becomes illumination light for illuminating the reference mirror 19.

  The reference mirror 19 is, for example, a flat mirror that is flat and has a reflectance of approximately 100%. Therefore, the reference mirror 19 regularly reflects almost all of the incident light. The reflectance of the reference mirror is preferably approximately the same as the reflectance of the measurement object. If the reflection intensity of the object to be measured and the reference mirror are equal, the contrast of the interference fringes becomes stronger and measurement with less noise becomes possible. Conversely, when the difference in reflectance between the reference mirror and the measurement object is large, the contrast of the interference fringes is deteriorated. Therefore, it is preferable that the reference mirror can be exchanged with a different reflectance in accordance with the reflectance of the measurement object. The reference objective lens 18 and the measurement objective lens 16 are, for example, the same type of objective lens, and are equal not only in focal length and optical path length but also in aberration characteristics such as wavefront aberration characteristics.

  A focus adjustment mechanism 20 and an angle adjustment mechanism 21 are attached to the back side of the reference mirror 19. The focus adjustment mechanism 20 includes a screw or the like for adjusting the focus. By rotating this screw, the reference mirror 19 is translated along the optical axis of the reference objective lens 18. Thereby, the focus of the reference objective lens 18 can be adjusted to the surface of the reference mirror 19. That is, the reference mirror 19 can be disposed at the focal point position of the reference objective lens 18. Focusing is performed by the focus adjusting mechanism 20. In order to adjust the angle of the reference mirror 19, the angle adjustment mechanism 21 includes, for example, a screw provided at the diagonal of the reference mirror 19. By rotating this screw, the angle of the reflecting surface of the reference mirror 19 can be changed. Thereby, the density of the interference fringe pattern based on the phase difference between the measurement light and the reference light can be changed. That is, when the reference objective lens 18 is tilted with respect to the optical axis, an optical path difference is generated according to the illumination position. Here, when the inclination angle is increased, the change in the optical path length is increased, and the density of the interference fringe pattern is increased. Thus, by providing the angle adjustment mechanism 21, the pitch between the bright part and the dark part of the interference fringe pattern can be adjusted.

  Next, a detection optical system for detecting light reflected by the measurement object 40 and light reflected by the reference mirror 19 will be described. As described above, a Michelson interferometer is inserted in the roughness measuring apparatus 100 according to the present embodiment. The Michelson interferometer is provided with a measurement objective lens 16 and a reference objective lens 18.

  The measurement light reflected by the measurement object 40 enters the measurement objective lens 16. Then, the measurement light enters the beam splitter 15 via the measurement objective lens 16. As described above, the beam splitter 15 branches the incident light substantially 1: 1 regardless of the polarization state. Accordingly, approximately half of the incident measurement light passes through the beam splitter 15. On the other hand, the reference light reflected by the reference mirror 19 enters the reference objective lens 18. That is, the reference mirror 19 reflects the light beam collected by the reference objective lens 18 and makes it incident on the reference objective lens 18 as reference light. The reference light then enters the beam splitter 15 via the reference objective lens 18. Approximately half of the incident reference light is reflected by the beam splitter 15.

  Accordingly, the measurement light and the reference light are combined by the beam splitter 15 to form one light beam. Here, one light beam combined by the beam splitter 15 is used as a combined wave. That is, the measurement light and the reference light are combined by the beam splitter 15 to generate combined light. As described above, in the Michelson interferometer, the illumination light is branched by the beam splitter 15, and the measurement light reflected by the measurement object 40 and the reference light reflected by the reference mirror 19 are transmitted by the beam splitter 15. It is synthesized into one light beam.

  The combined light emitted from the beam splitter 15 travels upward and enters the beam splitter 14. As described above, the beam splitter 14 branches the incident light approximately 1: 1 regardless of the polarization state. Accordingly, approximately half of the combined light incident on the beam splitter 14 is transmitted. That is, approximately half of the measurement light incident on the beam splitter 14 and approximately half of the reference light pass through the beam splitter 14. By this beam splitter 14, the combined light and the illumination light can be branched. That is, the combined light is separated from the optical path of the illumination light.

  The combined light separated from the illumination light enters the photodetector 23 via the lens 22. The lens 22 forms an image of the combined light on the light receiving surface of the photodetector 23. The photodetector 23 is, for example, a CCD sensor, and can be one provided with a light receiving element serving as a detection pixel. In the photodetector 23, signal charges corresponding to the amount of received light are accumulated for each pixel. By driving the stage 17 in the Z direction and scanning the measurement object 40, a plurality of phase differences can be given to the measurement light and the reference light, and a plurality of interference fringe patterns can be imaged.

  The photodetector 23 outputs a detection signal corresponding to the intensity of the incident light to the roughness calculation unit 33 of the processing device 30. A detection signal from the photodetector 23 is input to the processing device 30. The intensity of the detection signal output to the processing device 30 is based on the interference light intensity corresponding to the phase difference between the measurement light and the reference light. For example, the processing device 30 performs A / D conversion on the detection signal and stores it in the memory 34. The roughness calculation unit 33 uses the transparent film 42 on the substrate 41 of the measurement object 40 based on the phase difference between the measurement light and the reference light corresponding to the interference light intensity corresponding to the detection signal for each pixel stored in the memory 34. The apparent surface roughness of the transparent film forming surface on which is formed is calculated. Then, based on the apparent surface roughness of the transparent film forming surface, the roughness of the interface between the transparent film 42 and the substrate 41 and the interface between the transparent film 42 and air (the surface of the transparent film 42) are calculated. The treatment in the roughness calculation unit 33 will be described later. Note that the processing device 30 is not limited to a physically single device.

  Here, a method for measuring the roughness of the substrate 41 covered with the transparent film 42 will be described. In general, the surface roughness of a solid is measured by a stylus roughness meter, an atomic force microscope, a confocal microscope, an optical interferometer, or the like. The optical measurement method has an advantage that the surface roughness can be measured in a non-destructive and non-contact manner, but in the case of a film made of a transparent material, it is not usually applicable because light passes through the surface. Therefore, in the present invention, a method for measuring the surface roughness of the transparent film using the above-described optical interferometer is proposed. In the following description, it is assumed that the reflected light from the surface of the transparent film 42 is sufficiently weaker than the reflected light from the substrate 41. The interference between the reflected light of the substrate 41 and the multiple reflected light in the transparent film 42 can be canceled in principle by measurement using the phase shift interferometry.

First, consider a one-dimensional surface roughness for a solid surface in air. The definition of the root mean square roughness (Rq) of JIS standard is shown below. The height distribution of the surface and the arithmetic mean thereof are defined as h (x) and <h>, respectively. Here, if the section (reference length) for measuring roughness is 0 ≦ x ≦ Ln, Rq is expressed by Equation (1).

  When the interference intensity due to the reflected light on the surface of the transparent film forming surface can be measured using an optical interferometer, the phase change due to the reflection can be converted into the surface shape, so that Rq can be obtained according to the above definition formula. However, in the case of a transparent film as schematically shown in FIG. 3, the measured interference intensity can be considered almost as reflected light from the substrate 41. In this case, the phase distribution of the reflected light from the substrate 41 can be calculated as an apparent surface shape in the air. Therefore, the calculated Rq is an apparent value and includes the contributions of both the substrate 41 and the surface of the transparent film 42. That is, Rq is calculated from phase information that includes information on both interfaces of the transparent film 42 (the interface between the transparent film 42 and the air, and the interface between the transparent film 42 and the substrate 41). It is the apparent roughness of the film forming surface.

The geometrical heights of the transparent film 42 and the surface of the substrate 41 are respectively g (x) and f (x) as shown in FIG. The distance between the transparent film and the substrate at x = 0 is d _0, and the surface shape of the transparent film and the substrate shape are α (x) and β (x).

従って、式（５）、（７）より、Ｒｑ^ＢａｓｅとＲｑ^{Ｌａｙｅｒ}を求めるには、それぞれβ（ｘ）とα（ｘ）とが分かればよく、ｄ_０には依存しないことがわかる。 In this case, assuming that Rq of the substrate 41 and the transparent film 42 are Rq ^Base and Rq ^Layer , respectively, the following equations are obtained from the above equations (1) and (2).

Thus, equation (5) and ^(7), to determine the ^{Rq Base} and ^{Rq Layer,} it may be respectively β and (x) alpha and (x) is known, the _{d 0} seen to be independent.

As shown in FIG. 4, the distribution of the phase difference between the reflected light from the substrate 41 that passes through the transparent film 42 and the reflected light from the reference mirror 19 of the interferometer is φ (x). Let λ be a light source wavelength, and let n ₀ and n ₁ be the refractive index of air and the refractive index of the transparent film, respectively. The change in phase is expressed by Equation (9) when the refractive index of air n ₀ = 1.

これに式（９）を代入すると、以下の式（１１）になる。

When this phase change is converted into an apparent height in the air, Expression (10) is obtained.

Substituting equation (9) into this gives equation (11) below.

Thus, h (x) is represented by a linear combination of α (x) and β (x). Therefore, the arithmetic mean of h (x) can be written as in equation (12).

Substituting h and <h> into the root mean square roughness formulas (1) and (2), the apparent Rq is obtained.

Substituting Equation (14) into Equation (1), the apparent Rq ² of the transparent film forming surface is calculated as follows.

この透明膜形成面の見かけの二乗平均平方根粗さから、透明膜４２の表面又は透明膜４２と基板４１との界面（基板４１の表面）の二乗平均平方根粗さを決定することができる。 Thus, it can be seen that the apparent root mean square roughness Rp is a linear combination of the root mean square roughness of α (x) and β (x). That is, it means a primary combination of the surface roughness Rq ^Layer and the substrate roughness Rq ^Base . Therefore, as shown in Expression (16), the apparent surface roughness of the transparent film forming surface measured by the interferometer can be expressed as a primary combination of the roughness of the surface of the transparent film 42 and the roughness of the substrate 41. .

From the apparent root mean square roughness of the transparent film forming surface, the root mean square roughness of the surface of the transparent film 42 or the interface between the transparent film 42 and the substrate 41 (the surface of the substrate 41) can be determined.

The root mean square roughness of the surface of the transparent film 42 or the interface between the transparent film 42 and the substrate 41 can be determined as in the following two cases.
(1) When the roughness of the substrate 41 is known When the roughness of the substrate 41 is known, the surface roughness of the transparent film 42 can be written as in the following formula (17).

Rq ^Layer can be calculated by substituting Rq ^Base into this equation (17). In particular, when the roughness of the substrate 41 is sufficiently small and can be ignored, the Rq ^Layer is simplified as the following formula (18).

  On the contrary, when the roughness of the substrate 41 is unknown and the roughness of the transparent film 42 is known, the roughness of the substrate 41 can be similarly obtained from the equation (16). In this case, the roughness of the substrate 41 can be obtained without peeling off the transparent film 42 by measuring the root mean square roughness of the surface of the transparent film 42 using AFM or the like.

(2) When both the roughness of the substrate and the roughness of the transparent film are unknown,
Since equation (16) contains two unknowns, it cannot be solved any further as it is. Here, use of the wavelength dependence of the refractive index of the transparent film is considered. The same measurement as the measurement of optical interference using the wavelength λ is performed again at a different wavelength λ ′. In order to change the wavelength of the illumination light, the wavelength conversion control unit 32 switches the bandpass filter of the wavelength conversion unit 12. Thereby, the illumination light of the 2nd wavelength different from the 1st wavelength mentioned above can be irradiated. The wavelength of the illumination light having the second wavelength is λ ′. Assuming that the refractive index at the wavelength λ ′ is n ₁ ′ and the apparent roughness Rq ′, Expression (19) relating to λ ′ is obtained.

この連立方程式（２０）を解くことで、透明膜４２の粗さと、基板４１の粗さの両方が得られる。 The following simultaneous equations (20) are obtained from the equations (16) and (19).

By solving this simultaneous equation (20), both the roughness of the transparent film 42 and the roughness of the substrate 41 are obtained.

  Therefore, if the apparent roughness value obtained from the actual phase measurement result by the interferometer is measured separately at the two wavelengths and directly substituted into the equations (23) and (24), the transparent film 42 The root mean square roughness of the surface and the substrate 41 can be calculated independently. Although the difference in apparent roughness due to the wavelength is small, it is considered that the difference can be detected by performing high-resolution phase measurement such as phase shift interferometry. Further, the internal interference between the surface reflection of the transparent film 42 and the reflected light of the substrate 41 can be canceled by the phase shift interferometry.

  In the above description, the apparent roughness value obtained from the result of actual phase measurement by the interferometer is measured separately at two wavelengths, and the root mean square roughness of the surface of the transparent film 42 and the substrate 41 is measured. However, the present invention is not limited to this. For example, it is possible to obtain the root mean square roughness of the surface of the transparent film 42 and the substrate 41 by calculating the Rq separately for each medium using air and another gas having a sufficiently different refractive index from the air. it can. Thereby, the root mean square roughness of both interfaces of the transparent film 42 can be obtained without changing the wavelength of the illumination light.

  Thus, according to the present invention, the roughness of the interface of the transparent film can be measured in a short time without contact and nondestructively. Further, a visible light optical system can be used without using i-line or DUV. If the roughness of the substrate surface is measured in advance by a synthesis formula of the substrate roughness and the transparent film roughness, the roughness of the transparent film can be extracted from the interference measurement result. On the contrary, if the surface roughness of the transparent film is known, it is possible to extract the roughness of the substrate surface without peeling off the transparent film. When the interference measurement is performed independently for two wavelengths, the surface roughness of the transparent film and the surface roughness of the substrate can be separated, and the roughness of the substrate surface and the surface roughness of the transparent film can be determined simultaneously. it can.

ここで、Ｒｑ：前記透明膜形成面の二乗平均平方根粗さ、Ｒｑ^{Ｌａｙｅｒ1}：前記第２透明膜と前記媒質との界面の二乗平均平方根粗さ、Ｒｑ^{Ｌａｙｅｒ2}：前記透明膜と前記第２透明膜との界面の二乗平均平方根粗さ、Ｒｑ^Ｂａｓｅ：前記透明膜と前記基板との界面の二乗平均平方根粗さ、ｎ₂：前記透明膜の屈折率、ｎ_１：前記第２透明膜の屈折率、ｎ_０：前記媒質の屈折率とする。この３式の連立方程式を解くことにより、基板と１層目の透明膜の界面、１層目と２層目の透明膜の界面、２層目の透明膜の表面（２層目の透明膜と空気の界面）それぞれの二乗平均平方根粗さを決定することができる。 The present invention is not limited to the case where only one layer of the transparent film 42 is formed on the substrate 41. For example, when a plurality of transparent films 42 having different refractive indexes are formed on the substrate 41, the present invention can be applied to calculate the root mean square roughness of each interface of the transparent film 42. For example, when the first transparent film having a different refractive index is formed on the transparent film 42, the wavelength of the illumination light is switched twice, and the apparent roughness of the transparent film forming surface corresponding to each wavelength is changed. It is possible to calculate and obtain three linear combinations. In this case, three equations are obtained by calculating the root mean square roughness of the transparent film forming surface at each wavelength based on the following equation (25).

Here, Rq: root mean square roughness of the transparent film forming surface, Rq ^Layer1 : root mean square roughness of the interface between the second transparent film and the medium, Rq ^Layer2 : the transparent film and the second transparent film Mean square root roughness of the interface between the transparent film and the substrate, Rq ^Base : root mean square roughness of the interface between the transparent film and the substrate, n ₂ : refractive index of the transparent film, n ₁ : refractive index of the second transparent film. , N ₀ : Refractive index of the medium. By solving these three simultaneous equations, the interface between the substrate and the first transparent film, the interface between the first and second transparent films, the surface of the second transparent film (the second transparent film) The root mean square roughness of each of the air and air interfaces) can be determined.

  As described above, instead of switching the wavelength, the medium is replaced with another gas having a different refractive index, and the apparent roughness of each medium is calculated, whereby the interface between the substrate and the first transparent film is calculated. It is also possible to determine the root mean square roughness of the interface between the first and second transparent films and the surface of the second transparent film (interface between the second transparent film and air).

  In addition, when measuring the root mean square roughness of the interface of the transparent film formed on the transparent substrate, interference between the light transmitted through the sample and the reference light, such as a Mach-Zehnder interferometer and a Twyman green interferometer, is performed. A two-beam interferometer that measures roughness by the fringe intensity can be used.

It is a figure which shows typically the structure of the roughness measuring apparatus which concerns on embodiment. It is a block diagram which shows the structure of the processing apparatus of the roughness measuring apparatus which concerns on embodiment. It is a figure which shows typically the structure of a measuring device measuring object. It is a figure which shows the height of a measuring object.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 Light source 12 Wavelength conversion part 13, 22 Lens 14, 15 Beam splitter 16 Measurement objective lens 17 Stage 18 Reference objective lens 19 Reference mirror 20 Focus adjustment mechanism 21 Angle adjustment mechanism 23 Photo detector 30 Processing device 31 Stage drive part 32 Wavelength conversion control unit 33 Roughness calculation unit 34 Memory 40 Measurement object 41 Substrate 42 Transparent film

Claims (16)

A measurement method for measuring a root mean square roughness of an interface of a transparent film formed on a substrate,
Irradiating light having a first wavelength having interference to the transparent film forming surface and the reference surface of the substrate on which the transparent film is formed,
Receiving interference light obtained by combining the measurement light reflected by the transparent film forming surface and the reference light reflected by the reference surface;
Based on the intensity change of the interference light, from the phase difference between the measurement light and the reference light, calculate the root mean square roughness of the transparent film forming surface,
The roughness measuring method which determines the root mean square roughness of the interface of the said transparent film based on the root mean square roughness of the said transparent film formation surface. Irradiating the transparent film forming surface and the reference surface with light having a second wavelength different from the first wavelength;
Based on the root mean square roughness of the transparent film forming surface calculated by irradiating the first wavelength and the root mean square roughness of the transparent film forming surface calculated by irradiating the second wavelength. The roughness measurement method according to claim 1, wherein the root mean square roughness of both interfaces of the transparent film is determined simultaneously. The root mean square roughness of the interface of the transparent film is calculated by the following formulas obtained for each of the first wavelength and the second wavelength:

The roughness measuring method according to claim 2, wherein the roughness measuring method is calculated based on
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer : root mean square roughness of the interface between the transparent film and the medium Rq ^Base : root mean square roughness n ₁ of the interface between the transparent film and the substrate : Refractive index n _{0 of the} transparent film: Refractive index of the medium.   Based on the root mean square roughness of the transparent film forming surface in the first medium and the root mean square roughness of the transparent film forming surface in the second medium different from the refractive index of the first medium, the transparent The roughness measuring method according to claim 1, wherein the root mean square roughness of both interfaces of the film is determined simultaneously. The root mean square roughness of the transparent film interface is expressed by the following two formulas:

The roughness measuring method according to claim 4, wherein the roughness measuring method is calculated based on
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer : root mean square roughness of the interface between the transparent film and the first medium or the second medium Rq ^Base : interface between the transparent film and the substrate Root mean square roughness n ₁ : Refractive index n _{0 of the} transparent film: Refractive index n ₀ ′ of the first medium: Refractive index of the second medium.   The optical distance between the transparent film forming surface and the reference surface is varied to give a plurality of phase differences between the measurement light and the reference light, thereby causing a change in intensity of the interference light. The roughness measuring method of any one of Claims 1-5. A second transparent film formed on the transparent film and having a refractive index different from that of the transparent film;
Further irradiating light having a third wavelength different from the first wavelength and the second wavelength,
The root mean square roughness of the interface of the second transparent film is determined based on the root mean square roughness of the transparent film forming surface calculated by irradiating with the light of the third wavelength. The roughness measuring method of any one of Claims 1-6. The root mean square roughness of the interface of the second transparent film is calculated by the following formulas obtained for each of the first wavelength, the second wavelength, and the third wavelength:

The roughness measurement method according to claim 7, wherein the roughness measurement method is calculated based on
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer1 : root mean square roughness of the interface between the second transparent film and the medium Rq ^Layer2 : square of the interface between the transparent film and the second transparent film Average square root roughness Rq ^Base : root mean square roughness n ₂ of the interface between the transparent film and the substrate n ₂ : refractive index of the transparent film n ₁ : refractive index of the second transparent film n ₀ : refractive index of the medium And A roughness measuring device for measuring a root mean square roughness of an interface of a transparent film formed on a substrate,
A light source for irradiating light having a first wavelength having coherence on a transparent film forming surface and a reference surface of the substrate on which the transparent film is formed;
A photodetector that receives interference light obtained by combining the measurement light reflected by the transparent film forming surface and the reference light reflected by the reference surface;
Based on the intensity change of the interference light received by the photodetector, the root mean square roughness of the transparent film forming surface is calculated from the phase difference between the measurement light and the reference light, and the interface of the transparent film A roughness measuring apparatus comprising: a calculating unit that determines a root mean square roughness of The light source irradiates the transparent film forming surface and the reference surface with light having a second wavelength different from the first wavelength,
The calculation unit includes a root mean square roughness of the transparent film forming surface calculated by irradiating the first wavelength and a root mean square of the transparent film forming surface calculated by irradiating the second wavelength. The roughness measuring apparatus according to claim 9, wherein the root mean square roughness of both interfaces of the transparent film is determined based on the roughness. The calculation unit has the following formula:

The roughness measuring apparatus according to claim 9 or 10, wherein the root mean square roughness of the interface of the transparent film is calculated based on
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer : root mean square roughness of the interface between the transparent film and the medium Rq ^Base : root mean square roughness n ₁ of the interface between the transparent film and the substrate : Refractive index n _{0 of the} transparent film: Refractive index of the medium.   The calculating unit calculates a root mean square roughness of the transparent film forming surface in the first medium and a root mean square roughness of the transparent film forming surface in the second medium different from the refractive index of the first medium. The roughness measuring apparatus according to claim 9, wherein the root mean square roughness of both interfaces of the transparent film is simultaneously determined based on the basis. The calculation unit includes the following two formulas:

The roughness measuring method according to claim 12, wherein the root mean square roughness of the interface of the transparent film is calculated based on
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer : root mean square roughness of the interface between the transparent film and the first medium or the second medium Rq ^Base : interface between the transparent film and the substrate Root mean square roughness n ₁ : Refractive index n _{0 of the} transparent film: Refractive index n ₀ ′ of the first medium: Refractive index of the second medium.   A variation mechanism that varies an optical distance between the reference surface and the transparent film forming surface is further provided, and a plurality of phase differences are provided between the measurement light and the reference light, thereby causing a change in the intensity of the interference light. The roughness measuring apparatus according to claim 9, wherein A second transparent film having a refractive index different from that of the transparent film is formed on the transparent film on the transparent film forming surface,
The light source emits light of a third wavelength different from the first wavelength and the second wavelength,
The calculation unit determines the root mean square roughness of the interface of the second transparent film based on the root mean square roughness of the transparent film forming surface calculated by irradiating the third wavelength. The roughness measuring apparatus according to any one of claims 9 to 14, wherein: The calculation unit has the following formula:

The roughness measuring apparatus according to claim 15, wherein the root mean square roughness of the interface of the second transparent film is calculated based on
here,
Rq: root mean square roughness of the transparent film forming surface Rq ^Layer1 : root mean square roughness of the interface between the second transparent film and the medium Rq ^Layer2 : square of the interface between the transparent film and the second transparent film Average square root roughness Rq ^Base : root mean square roughness n ₂ of the interface between the transparent film and the substrate n ₂ : refractive index of the transparent film n ₁ : refractive index of the second transparent film n ₀ : refractive index of the medium And

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