JP2014035257A - Mueller matrix microscopic ellipsometer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a Mueller matrix microscopic ellipsometer capable of measuring the Mueller matrix of a sample if either one of an irradiation optical system side and a detection optical system side includes an active element.SOLUTION: An incident optical system 7 has a first lens system 11 for guiding parallel light to an object lens 1 and an active polarization element group 12 for independently controlling at least two elements of a first, a second and a third elements of a Stokes vector of the parallel light. An emission optical system 8 has a polarization element group and a second lens system 14 for forming an image of the image formed on a rear side focal plane 4 of the object lens 1 on a two-dimentional detector 9. The two-dimentional detector 9 images a plurality of images on the rear side focal plane 4 at a plurality of settings of the active polarization element group 12. A calculation device 15 calculates at least three elements of the vector indicating optical effects from the object lens 1 to the two-dimentional detector 9 on the basis of the plurality of images. The calculation device 15 calculates at least nine elements of the Mueller matrix of a sample 10 on the basis of an image corresponding to each of the elements of the vector.

Description

  The present invention relates to a Mueller matrix microscopic ellipsometer, and more particularly, uses a high numerical aperture objective lens, forms an image of a rear focal plane of the objective lens on a two-dimensional detector, and enters or exits the incident light on the objective lens. By modulating the Stokes vector of light by an active polarization element group and measuring the Stokes vector of light incident on the two-dimensional detector as a distribution in the back focal plane, the Stokes vector or objective of the light emitted from the objective lens The vector of the optical effect from the lens to the detector is obtained as a distribution in the rear focal plane, and from the azimuth angle dependency of the vector distribution, any multiple incident angles from the maximum incident angle determined by the numerical aperture of the objective lens In, the Mueller matrix element of the sample is calculated, and the optical constant and film thickness of the sample, as well as the offset of the objective lens used for the measurement On Mueller matrix microscopic ellipsometer seeking.

  The polarization characteristics of optical systems and materials can be divided into three types: dichroism, phase lag, and depolarization, and have three, three, and nine degrees of freedom, respectively. Liquid crystal / organic EL display elements, multilayer integrated circuits, and the like have complicated polarization characteristics, and advanced polarization analysis is required for process control and quality control. Further, the shape of the nanostructure can be analyzed by examining in detail the polarization characteristics of the periodic nanostructure such as a quantum crystal. For this reason, the Mueller matrix ellipsometer that can completely describe the polarization characteristics of optical systems and materials has attracted attention. In the field of life science, it is expected to be applied to diagnosis of retinal function and cancer tissue invasion, or tissue pathology.

  In recent years, semiconductor elements and recording media have been increasingly miniaturized, and the need for measuring polarization characteristics of materials in a finer area has increased. In the field of biotechnology, devices that combine fine sensors to measure biomolecules are being actively produced, and a method for examining the actual surface structure of the fabricated devices on the scale of several tens of nm to μm is necessary. Has been. In addition, in order to study the structure and function of cell membranes, using living cells or artificial bilayer membranes, the localization and binding of lipids and proteins to domains on the scale of several tens of nm to μm are present on the bilayer membrane. There is a need to develop techniques for detecting In particular, protein is difficult to label with dyes compared to DNA, so measurement that can examine the polarization characteristics of a sample with sub-μm-scale horizontal resolution and nm-scale depth resolution without using fluorescence from the sample. Technology is needed.

  The apparatus configuration of the Mueller matrix ellipsometer is the same as that of a normal ellipsometer. The incident optical system for irradiating the sample with light is provided with a polarization generator, and the exit optical system for analyzing light reflected or transmitted from the sample is provided with a polarization analyzer. In general, in order to analyze all 16 elements of the Mueller matrix, the first, second and third elements of the Stokes vector representing the polarization state of the light generated by the polarization generator are linearly independent from each other, and the polarization It is necessary for the analyzer to be able to measure the first, second and third elements of the reflected or transmitted Stokes vector.

  Here, general properties of the rear focal plane of the objective lens will be described. As shown in FIG. 1, the parallel light 2 incident on the objective lens 1 is focused on the sample surface 3, and the reflected light is emitted as parallel light through the objective lens 1. At this time, as shown in FIG. 2, the intensity of the emitted light is distributed on the polar coordinates (θ, φ) with the center of the objective lens as the origin in the rear focal plane 4. In the objective lens in which the aberration is corrected, the following relationship is established between the diameter d of the incident light on the rear focal plane and the angle θ on the sample surface.

Here, f is a focal length. Further, the angle φ formed with the x-axis on the rear focal plane is the azimuth angle of the incident light. That is, the incident angle θ and the azimuth angle φ of the light incident on the sample surface are determined by the position incident on the rear focal plane. Also, since the measurement resolution is equal to the objective lens resolution ε,

Given in. Here, λ is the wavelength of light, and NA is the numerical aperture of the objective lens. Therefore, when an objective lens having a high numerical aperture close to 1 is used, the resolution is almost equal to the wavelength of light, and measurement in a minute region of the sample is possible.

So far, methods have been developed that use the properties of the back focal plane of the objective lens to determine the thickness and refractive index of the thin film from the dependence of the reflectance on the incident angle. In this method, a one-dimensional distribution of light intensity in the x direction and the y direction is measured by a linear image sensor (Non-Patent Documents 1 and 2). Also, using a Michelson interferometer, the phase difference δ between p-polarized light and s-polarized light is obtained over the entire back focal plane of the objective lens, and light is perpendicular to the sample from the dependence of δ on the incident angle in the x and y directions. It obtains a phase difference [delta] ₀ when the incident further complex refractive index of the sample can be obtained (non-patent document 3). On the other hand, at a plurality of incident angles, the Fourier coefficient for the azimuth angle is obtained from the azimuth angle dependency of the light intensity, and the fitting with the theoretical value is performed by the method of least squares to determine the thickness of the sample (oxide film) on the silicon substrate. It was calculated | required (nonpatent literature 4).

  On the other hand, each of the polarization generation device on the irradiation optical system side and the polarization analysis device on the detection optical system side includes a polarizer and a pair of liquid crystal variable retarders, and includes an incident angle of 0 to 60 ° and all azimuth angles. Has developed a Mueller matrix microscopic ellipsometer that can measure all 16 elements of the Mueller matrix (Non-Patent Documents 5 to 7).

Appl. Phys. Lett. 60, 1301 (1992). J. Vac. Sci. Technol. A. 17, 380 (1999). Appl. Opt. 37, 1796 (1998). Opt. Express 26, 18056 (2007). Phys. Stat. Sol. A 205, 743 (2008). Appl. Opt. 48, 5025 (2009). Thin Solid Films 519, 2608 (2011). Surf. Sci. 96, 108 (1980).

  In the conventional Mueller matrix microscopic ellipsometers shown in Non-Patent Documents 5 to 7, active elements are required on both the irradiation optical system side and the detection optical system side in order to obtain the Mueller matrix of the sample. There was a problem that became expensive.

  The present invention has been made in order to solve the above-mentioned problems, and the object of the present invention is to measure the Mueller matrix of a sample if an active element is provided on either the irradiation optical system side or the detection optical system side. The object is to provide a Mueller matrix microscopic ellipsometer that is possible.

In order to achieve the above object, the Mueller matrix microscopic ellipsometer (1) according to the present invention comprises:
An infinity correction system objective lens, a non-polarizing beam splitter, a light source, an incident optical system, an exit optical system, a two-dimensional detector, and an arithmetic unit,
A sample to be measured is placed on the front focal plane of the objective lens,
The incident optical system independently controls at least two elements among a first lens system that enters parallel light into the objective lens and first to third elements of a Stokes vector of the parallel light. A polarizing element group,
The exit optical system includes a polarizer and a second lens system that forms an image of a rear focal plane of the objective lens on the two-dimensional detector,
The two-dimensional detector captures a plurality of images of the back focal plane in a plurality of settings of the active polarizing element group for changing elements of the Stokes vector;
The arithmetic unit calculates at least three elements of a vector representing an optical effect from the objective lens to the two-dimensional detector from the plurality of images;
The arithmetic unit calculates at least nine elements of the Mueller matrix of the sample from the image corresponding to each element of the optical effect vector.

The Mueller matrix microscopic ellipsometer (2) according to the present invention is:
An infinity correction system objective lens, a non-polarizing beam splitter, a light source, an incident optical system, an exit optical system, a two-dimensional detector, and an arithmetic unit,
A sample to be measured is placed on the front focal plane of the objective lens,
The incident optical system includes a first lens system for entering parallel light into the objective lens, and a polarizer.
The exit optical system controls a linearly independent contribution to the light intensity measured by the two-dimensional detector for at least two elements among the first to third elements of the Stokes vector of the exit light of the objective lens. An active polarizing element group; and a second lens system that forms an image of a rear focal plane of the objective lens on the two-dimensional detector;
The two-dimensional detector captures a plurality of images of the back focal plane in a plurality of settings of the active polarizing element group for changing elements of the Stokes vector;
The arithmetic unit calculates at least three elements of a Stokes vector of light emitted from the objective lens from a plurality of the images,
The arithmetic unit calculates at least nine elements of the Mueller matrix of the sample from the image corresponding to each element of the Stokes vector.

  Further, the Mueller matrix microscopic ellipsometer (3) according to the present invention is a polarizer in which the active polarizing element group in the Mueller matrix microscopic ellipsometer (1) or (2) can automatically control the azimuth angle. It is characterized by being.

  The Mueller matrix microscopic ellipsometer (4) according to the present invention is the above Mueller matrix microscopic ellipsometer (1) or (2), wherein the active polarizing element group automatically controls the polarizer and the azimuth angle. It is characterized by comprising a phase retarder that can be formed.

  The Mueller matrix microscopic ellipsometer (5) according to the present invention is the above Mueller matrix microscopic ellipsometer (1) or (2), wherein the active polarizing element group includes a polarizer and a variable phase retarder. It is characterized by that.

  The Mueller matrix microscopic ellipsometer (6) according to the present invention is the above Mueller matrix microscopic ellipsometer (1) or (2), wherein the active polarizing element group includes a polarizer and a photoelastic modulator. It is characterized by that.

  According to the Mueller matrix microscopic ellipsometer according to the present invention, the active element included in the apparatus may be either the incident optical system side or the exit optical system side, so that the number of necessary active elements is reduced and the cost of the apparatus is reduced. Can be made.

It is a schematic diagram for demonstrating the property of the back side focal plane of an objective lens, and is the figure which looked at the objective lens from the horizontal direction. It is a schematic diagram for explaining the property of the rear focal plane of the objective lens, and is a view of the rear focal plane along incident light traveling perpendicularly to the front side of the drawing. It is a schematic diagram which shows the measuring system of the Mueller matrix microscopic ellipsometer concerning this invention. FIG. 4 is an incident angle dependence of ellipsometric parameters Ψ of samples measured and calculated at different wavelengths in one embodiment of the present invention. FIG. FIG. 4 is an incident angle dependence of ellipsometric parameters Δ of samples measured and calculated at different wavelengths in one embodiment of the present invention. FIG.

  In the following, first, a theoretical description of the measurement principle and the like will be given, and then specific measurement procedures and calculation procedures will be described as examples.

1. Configuration of Apparatus The Mueller matrix microscopic ellipsometer according to the present invention uses an active element for either the irradiation optical system or the detection optical system, and vertically installs a high NA objective lens. With this configuration, among the 16 elements of the Mueller matrix, 9 or more and 12 elements at the maximum can be obtained. If the sample has the property of not disturbing the polarization, various optical effects on the polarization such as the amplitude ratio and phase difference between the p-polarized light and the s-polarized light can be calculated from the nine elements of the Mueller matrix. From twelve elements, it is possible to calculate all complex optical effects on polarized light, such as birefringence, circular dichroism, and circular birefringence. It is also possible to analyze the arrangement of the liquid crystal, the shape of the periodic nanostructure, etc. by the least square fitting of the Mueller matrix elements obtained by the measurement and the theoretically calculated values.

  A Mueller matrix microscopic ellipsometer (hereinafter also simply referred to as an apparatus of the present invention) according to an embodiment of the present invention includes an objective lens 1, an unpolarized beam splitter 5, and an optical fiber as a light source, as shown in FIG. The exit 6, the entrance optical system 7, the exit optical system 8, and the two-dimensional detector 9 are configured. The objective lens 1 is an infinity correction system, and a sample 10 is installed on the front focal plane. The incident optical system 7 includes a lens system 11 that enters parallel light into the objective lens 1 and a polarizing element group 12. The exit optical system 8 includes a polarizing element group 13 and a lens system 14 that forms an image of the rear focal plane 4 of the objective lens on the two-dimensional detector 9. Furthermore, the control / arithmetic apparatus is connected to the polarizing element group 12 or 13 and the two-dimensional detector 9 via an interface, controls the polarizing element group, and receives and calculates image data from the two-dimensional detector 9. 15.

  Here, in the Mueller matrix microscopic ellipsometer according to the embodiment of the present invention, any one of the polarization element group 12 of the incident optical system 7 and the polarization element group 13 of the emission optical system 8 may include an active element. In the present invention, the active element is set to a plurality of conditions by the control / arithmetic unit 15, the two-dimensional detector 9 captures a plurality of images of the rear focal plane, and the control / arithmetic unit is connected to the objective lens. The Stokes vector image of the emitted light or the vector image of the optical effect from the objective lens to the detector is obtained, the incident angle and azimuth angle dependence of these vector images is extracted, and the elements of the Mueller matrix of the sample are calculated.

2. Measurement Principle In the following, the measurement principle when measuring the Mueller matrix in the Mueller matrix microscopic ellipsometer according to the present invention will be described in two embodiments. In the first embodiment, a polarizing element group including an active element is provided on the exit optical system side, and in the second embodiment, a polarizing element group including an active element is provided on the incident optical system side. Hereinafter, a polarizing element group including an active element is simply referred to as an active polarizing element group or an active polarizing element group.

1) In the case where an active polarizing element group is provided on the exit optical system side The Mueller matrix microscopic ellipsometer according to the first embodiment of the present invention includes the polarizing element group of the incident optical system as a polarizer, The polarizing element group is an active polarizing element group capable of independently measuring at least two elements of the first to third elements of the Stokes vector. Unpolarized light from the light source is converted into a Stokes vector via a polarizer. The light incident on the objective lens is modulated by the optical effect of the sample and the objective lens, and then emitted through the rear focal plane of the objective lens. The Stokes vector of the emitted light is distributed on the polar coordinates with the center of the objective lens as the origin on the back focal plane of the objective lens, as well as the intensity of the light, and after receiving the action of the active polarizing element group, Measured with a two-dimensional detector.

  The Stokes vector of the light emitted from the objective lens is converted into linearly polarized light by modulating and combining polarized components (p and s polarized light) orthogonal to each other by the active polarization element group of the emission optical system. According to a certain algorithm, the Stokes vector of the emitted light is modulated, an image is taken with a two-dimensional measuring device each time, and the captured image is analyzed, so that at least 3 of the Stokes vector of the emitted light from the objective lens is analyzed. Individual elements can be calculated. In this way, at least nine elements of the Mueller matrix of the sample can be calculated from any azimuth angle dependency of the Stokes vector distribution at any of a plurality of incident angles that reach the maximum incident angle determined by the numerical aperture of the objective lens. .

  An exit optical system having an active polarization element group has a function of analyzing the polarization state of incident light, and is called a polarization state analyzer or a polarimeter. There is a lot of research on the configuration and function of polarimeters. For example, Non-Patent Document 8 describes in detail the relationship between the type of active polarizing element group and the Stokes vector element that can be measured. Table 1 shows the relationship between the types of active polarizing element groups and the Stokes vector elements that can be measured.

If the Stokes vector of light incident on the active polarization element group G is S _i , the light intensity I measured by the detector is as follows.

Here, f is a vector representing the optical effect of the detector, and f = [1 0 0 0]. I ₀ represents the product of the intensity of light incident on the optical system and the transmittance of the entire optical system. T _G and F _G are Mueller matrices and vectors representing the optical effects of the active polarizing element group G, respectively. F _G is equal to the first row of T _G and F _i is its element. By appropriately setting a plurality of active polarization element groups G and changing the elements of the optical effect vector, linearly independent equations that give the light intensity I can be obtained. The elements of the Stokes vector S can be calculated by solving these equations. In other words, whether or not the Stokes vector element S _i can be measured is defined by whether or not a linearly independent contribution to the light intensity I can be controlled by the active polarization element group G. Incidentally, elements of the Stokes vector S can be measured contains factors I _0/2. F ₀ represents the transmittance of the active polarizing element group, and the contribution of S ₀ cannot be controlled independently. Therefore, what has been described above applies to the first to third elements of the Stokes vector elements of the incident light.

  Further, the Stokes vector of the light emitted from the objective lens is expressed by the following equation when P is the azimuth angle of the polarizer existing in the incident side optical system and P = 0 °.

Here, m _ij represents the element in the i-th row and j-th column of the Mueller matrix, φ represents the azimuth angle of the incident light, and S and C represent the sin function and the cos function, respectively (for example, S _2P is sin _2P ). If an image corresponding to each of these elements is measured, the element of the Mueller matrix of the sample can be obtained from the azimuth angle dependency of the value.

  Regarding the procedure for obtaining the elements of the Mueller matrix of the sample, the case where the active polarizing element group existing in the emission optical system is the rotating polarizer shown in “1” in Table 1 will be specifically described. The light intensity measured by the two-dimensional detector is expressed as follows, where A is the azimuth angle of the rotating polarizer.

Here, a ₀ , a ₂ , and b ₂ are Fourier coefficients. Therefore, by changing A over 180 ° for each constant angle, each time an image of the rear focal plane is captured with a two-dimensional detector, and the light intensity of the captured image is Fourier analyzed based on equation (5), the DC component I ₀ a _0/2, 2 harmonic coefficients of the coefficient I ₀ sine component of a _2/2 and the second harmonic of the cosine component I ₀ b _2/2 is obtained.

The Fourier coefficients a ₀ , a ₂ , and b ₂ have the following relationship with the elements of the Stokes vector.

On the other hand, S ₀ is represented by the following equation when P = 0 ° from Equation (4).

When P = 90 °, the following equation is obtained.

That performs a measurement of P as 0 ° and 90 °, when obtaining the average seek the direct-current component, its value is equal to I ₀ m _00/2. Therefore, the direct current component by Equation (5), by dividing the coefficients of the coefficient and the sine component of the cosine component of the second harmonic at I ₀ m _00/2, was normalized by the elements m ₀₀ of the Mueller matrix, the objective lens The second through second elements of the Stokes vector of the emitted light are obtained. Furthermore, using the equation (4), nine elements of the Mueller matrix of the sample are obtained from the azimuth angle dependency of these values.

2) When an active polarizing element group is provided on the incident optical system side In the Mueller matrix microscopic ellipsometer according to the second embodiment of the present invention, the polarizing element group of the incident optical system has first to third Stokes vectors. This is an active polarizing element group capable of independently controlling and modulating at least two of the elements, and the polarizing element group of the exit optical system is a polarizer. Unpolarized light from the light source is converted into a Stokes vector via the active polarizing element group. The light incident on the objective lens is modulated by the optical effect of the sample and the objective lens, and then emitted through the rear focal plane of the objective lens. The Stokes vector of the emitted light is distributed on the polar coordinates with the center of the objective lens as the origin on the back focal plane of the objective lens, as well as the intensity of the light. Measured in

  The measured Stokes vector is represented by the product of the Stokes vector of light incident on the objective lens and the vector of the optical effect from the objective lens to the detector. The Stokes vector of the incident light to the objective lens can be controlled and modulated by the active polarizing element group of the incident optical system. According to a certain algorithm, the Stokes vector of incident light is changed, an image is taken with a two-dimensional measuring device each time, and the picked-up image is analyzed, so that at least 3 of the optical effect vectors from the objective lens to the detector are obtained. Individual elements can be calculated. In this way, at least nine elements of the Mueller matrix of the sample can be calculated from an azimuth angle dependency of the distribution of the optical effect vector at an arbitrary plurality of incident angles that reach the maximum incident angle determined by the numerical aperture of the objective lens. it can.

  In contrast to the polarimeter described above, the incident optical system having an active polarization element group has a function of emitting light having a necessary polarization state, and is called a polarization state generation device. It is known that the configuration and function of the polarization state generation device are almost the same as the polarimeter described above except that the traveling direction of light is reversed. That is, the plurality of types of elements included in the polarization element group are reversed in order, and the Stokes vector elements that can be measured by the polarimeter can be controlled by the polarization state generation device. Table 2 shows the relationship between the types of active polarizing element groups and the Stokes vector elements that can be controlled.

If the Stokes vector of light incident on the objective lens is S _i , the light intensity I measured by the detector is as follows.

Here, f is a vector representing the optical effect of the detector, and T _Ob-D and F _Ob-D are a Mueller matrix and a vector representing the optical effect from the objective lens to the detector, respectively. F _Ob-D is equal to the first row of _Tob-D , and F _i is its element. By appropriately setting a plurality of active polarizing element groups and changing the Stokes vector elements of the light incident on the objective lens, linearly independent equations that give the light intensity I can be obtained. By solving these equations, the elements of the optical effect vector F _Ob-D can be calculated. In other words, if the Stokes vector element S _i can be controlled independently by the active polarizing element group, the element of the corresponding optical effect vector F _Ob-D can be measured. Incidentally, elements of the optical effect vector F _Ob-D that can be measured contains factors I _0/2. S ₀ represents the intensity of light incident on the objective lens and cannot be independently controlled using the active polarizing element group. Therefore, the contribution of F _{0 to} the light intensity I cannot be controlled independently. Therefore, what has been described above applies to the first to third elements among the elements of the optical effect vector F _Ob-D .

  Further, the vector of the optical effect from the objective lens to the detector is as follows when the azimuth angle of the polarizer is A and A = 0 °.

If an image corresponding to each of these elements is measured, the element of the Mueller matrix of the sample can be obtained from the azimuth angle dependency of the value.

  Regarding the procedure for obtaining the elements of the Mueller matrix of the sample, the case where the active polarizing element group existing in the incident optical system is a polarizer (fixed) -rotating phase retarder indicated by “3” in Table 2 explain. The light intensity measured by the two-dimensional detector is expressed as follows, where R is the azimuth angle of the phase retarder.

Here, a ₀ , a ₂ , b ₂ , a ₄ and b ₄ are Fourier coefficients. Therefore, by rotating R over 180 ° for every fixed angle, each time a two-dimensional detector captures an image of the rear focal plane, and by performing Fourier analysis on the light intensity of the captured image based on Equation (11), DC component I ₀ F ₀ a ₀ / 2,2 harmonic coefficients of the cosine component I ₀ F ₀ a ₂ / 2,2 harmonic coefficients of the sine component I ₀ F ₀ b ₂ / 2,4 harmonic cosine of factor I ₀ F ₀ b _4/2 coefficients I ₀ F ₀ sine component of a _4/2 and the second harmonic components are obtained.

The Fourier coefficients a ₀ , a ₂ , a ₄ , b ₂ , and b ₄ have the following relationship with the elements of the optical effect vector F _Ob-D .

Here, P is the azimuth angle of the incident side polarizer. Also,

V and Q are optical characteristics of the phase retarder and are expressed by the following equations.

Here, T _f and T _s represent complex transmittances in the fast axis and slow axis directions of the phase retarder, respectively.

From equation (10), when A = 0 °, F ₀ is as follows:

When A = 90 °, the following equation is obtained.

Therefore, when A is measured at 0 ° and 90 °, the above-mentioned DC component is obtained and the average is calculated, F ₀ is equal to m ₀₀ . In addition, we measured the P from equation (12) is 0 ° and 90 °, when obtaining the average of the direct current component, its value is equal to I ₀ m _00/2. Therefore, the direct current component by Equation (11), dividing factor and the coefficient of the sine component of the cosine component of the second harmonic wave, and the coefficients and the coefficient of the sine component of the cosine component of the fourth harmonic at I ₀ m _00/2 Thus, the Fourier coefficient represented by the equation (12) can be calculated, and all four elements of the optical effect vector F _Ob-D normalized by the element m ₀₀ of the Mueller matrix are obtained. Further, 12 elements of the Mueller matrix of the sample are obtained from the azimuth angle dependency of these values using Equation (10).

  As can be seen from the equations (4) and (10), the maximum number of elements of the Mueller matrix obtained by the apparatus of the present invention is 12 out of the 16 elements constituting the matrix. If the sample hardly disturbs polarization, such as a transmission sample that does not cause light scattering or a reflection sample having a smooth surface, the amplitude ratio between p-polarized light and s-polarized light Various optical effects on polarization such as phase difference can be calculated. If the above-described 12 elements of the Mueller matrix are known, all complicated optical effects on polarization such as birefringence, circular dichroism, and circular birefringence can be calculated. It is also possible to analyze the arrangement of the liquid crystal, the shape of the periodic nanostructure, etc. by the least square fitting of the Mueller matrix elements obtained by the measurement and the theoretically calculated values.

  In the apparatus according to an embodiment of the present invention, in the configuration shown in FIG. 3, the polarization element group 12 of the incident optical system 7 is an active element including a first polarizer and a phase retarder having a rotation mechanism. A polarizing element group, and the polarizing element group 13 of the exit optical system 8 is a second polarizer. The light from the xenon lamp was dispersed with a monochromator, and the monochromatic light was guided to the device using an optical fiber with a core diameter of 0.6 mm. In addition, a sharp cut filter is installed in the entrance lens system to remove higher-order scattered light and a neutral density filter (ND) is installed to reduce the light intensity incident on the objective lens. Adjustments were made. The beam splitter was a broadband non-polarizing cube type. The objective lens used was a plan apochromat with a magnification of 60x and a NA1.42 curvature of field and chromatic aberration corrected. In addition, a 1/2 type CCD with 640 × 486 pixels was used for the two-dimensional detector. A cover glass having a 85 nm thick tantalum oxide film deposited on the surface was used as a measurement sample. This cover glass was set upside down on the front side of the objective lens, and the space between them was filled with a refracting liquid and focused.

First, measurement is performed with the azimuth angle of the first polarizer set to 0 ° and 90 °, the average of the direct current components described above is obtained, and the measurement is performed with the azimuth angle of the second polarizer set to 0 ° and 90 °, respectively. The obtained DC component was further averaged to obtain a background image of the light intensity distribution corresponding to I ₀ m _00/2 . Using this, the center and radius of the emitted light were obtained and used as a reference for polar coordinates on the rear focal plane.

Next, the azimuth angles of the first and second polarizers were both set to 0 °, the phase retarder was rotated as described above, and an image of the emitted light was obtained with the CCD each time. From the acquired image, a Fourier coefficient for the azimuth angle of the phase retarder was obtained, and four elements of the optical effect vector F _Ob-D were calculated and normalized with the above-described background image.

In accordance with the polar standard described above on the rear focal plane, the range of incident angles is divided every 0.5 ° over 30-40 °, and the azimuth ranges are equally spaced over 0-180 ° and 180 ° -360 °, respectively. And divided into 16 sections to define concentric sections or sectors. For each sector, and calculating the average value of the normalized optical effects vector F _Ob-D elements, and taking into consideration the nature of the definite integral of the sine and cosine functions, with respect to the elements of F _Ob-D, the azimuth The Fourier coefficient of was calculated. Furthermore, Mueller matrix elements were calculated from Fourier coefficients. Table 3 shows experimental results and calculated values of the Mueller matrix at a wavelength of 600 nm and an incident angle of 39 °. The measurement error is 0.02 or less.

  Next, in order to check whether the measured Mueller matrix was accurate, ellipsometric parameters were calculated from the elements of the Mueller matrix, and the optical constant and thickness of the tantalum oxide film of the cover glass used as a measurement sample were obtained. The following relationship exists between the elements of the Mueller matrix and the ellipsometric parameters Ψ and Δ of the isotropic sample.

The calculated values a, b and c shown in Table 3 are C _2Ψ , S _2Ψ C _Δ and S _2Ψ S _Δ , respectively. From these relationships, the ellipsometric parameters Ψ and Δ of the sample were obtained. Ψ is an arctangent function of the amplitude ratio of p-polarized light and s-polarized light, and Δ is a phase difference between p-polarized light and s-polarized light. On the other hand, in order to correct the influence of the objective lens, the ellipsometric parameters are ψ _Ob and Δ _Ob, and the following formulas are respectively used as a function of the incident angle θ.

The material of the cover glass is equivalent to a glass type called D263T, which is a Schott standard, and its refractive index was used in the calculation.

  Various assumptions were made for the film thickness and refractive index of the tantalum oxide film, and theoretical values were fitted to the measured values. The ellipsometric parameters Ψ and Δ in the incident angle range of 30 to 40 ° measured at wavelengths of 580, 590, 600 and 610 nm are shown in FIGS. 4 and 5, respectively. The result obtained by the measurement is indicated by a symbol, and the calculated value obtained by the fitting is indicated by a line.

  As a result of the fitting, the refractive index and film thickness of tantalum oxide formed on the surface of the cover glass were determined as follows.

Refractive index: 1.975 + 0.1066 / λ ² , film thickness (nm): 93.7
Here, λ is a wavelength (unit: μm). Further, the following values were obtained as constants of the equations (4) and (5) for calculating the ellipsometric parameters of the objective lens.

a _Ψ : 0.31, b _Ψ : 45.5
a _Δ : 0.055, b _Δ : 2.0
Here, the unit of the constant is degrees.

  The optical constant of the tantalum oxide film obtained by measurement was not significantly different from the known value, and the thickness was close to the value set during film formation. The correction formula for the objective lens was also consistent with the known behavior. Therefore, it was concluded that an accurate Mueller matrix could be measured using the apparatus of the present invention.

DESCRIPTION OF SYMBOLS 1 Objective lens 2 Parallel light 3 Sample surface 4 Rear side focal plane 5 Unpolarized beam splitter 6 Optical fiber exit 7 Incident optical system 8 Ejecting optical system 9 Two-dimensional detector 10 Sample 11 Lens system 12 Polarizing element group 13 Polarizing element Group 14 Lens system 15 Control / arithmetic unit

Claims (6)

An infinity correction system objective lens, a non-polarizing beam splitter, a light source, an incident optical system, an exit optical system, a two-dimensional detector, and an arithmetic unit,
A sample to be measured is placed on the front focal plane of the objective lens,
The incident optical system independently controls at least two elements among a first lens system that enters parallel light into the objective lens and first to third elements of a Stokes vector of the parallel light. A polarizing element group,
The exit optical system includes a polarizer and a second lens system that forms an image of a rear focal plane of the objective lens on the two-dimensional detector,
The two-dimensional detector captures a plurality of images of the back focal plane in a plurality of settings of the active polarizing element group for changing elements of the Stokes vector;
The arithmetic unit calculates at least three elements of a vector representing an optical effect from the objective lens to the two-dimensional detector from the plurality of images;
The Mueller matrix microscopic ellipsometer, wherein the arithmetic device calculates at least nine elements of the Mueller matrix of the sample from the image corresponding to each element of the optical effect vector. An infinity correction system objective lens, a non-polarizing beam splitter, a light source, an incident optical system, an exit optical system, a two-dimensional detector, and an arithmetic unit,
A sample to be measured is placed on the front focal plane of the objective lens,
The incident optical system includes a first lens system for entering parallel light into the objective lens, and a polarizer.
The exit optical system controls a linearly independent contribution to the light intensity measured by the two-dimensional detector for at least two elements among the first to third elements of the Stokes vector of the exit light of the objective lens. An active polarizing element group; and a second lens system that forms an image of a rear focal plane of the objective lens on the two-dimensional detector;
The two-dimensional detector captures a plurality of images of the back focal plane in a plurality of settings of the active polarizing element group for changing elements of the Stokes vector;
The arithmetic unit calculates at least three elements of a Stokes vector of light emitted from the objective lens from a plurality of the images,
The Mueller matrix microscopic ellipsometer, wherein the arithmetic device calculates at least nine elements of the Mueller matrix of the sample from the image corresponding to each element of the Stokes vector.   The Mueller matrix microscopic ellipsometer according to claim 1 or 2, wherein the active polarizing element group is a polarizer capable of automatically controlling an azimuth angle.   3. The Mueller matrix microscopic ellipsometer according to claim 1, wherein the active polarizing element group includes a polarizer and a phase retarder capable of automatically controlling an azimuth angle.   3. The Mueller matrix microscopic ellipsometer according to claim 1, wherein the active polarizing element group includes a polarizer and a variable phase retarder. 4.   3. The Mueller matrix microscopic ellipsometer according to claim 1, wherein the active polarizing element group includes a polarizer and a photoelastic modulator. 4.

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