JP2014035254A - Back focal plane microscopic ellipsometer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a back focal plane microscopic ellipsometer which obtains a further accurate optical constant and a film thickness of a sample in consideration of contribution of an objective lens by determining accurate polar coordinates of a back focal plane to correct non-uniformity of a light intensity due to a device.SOLUTION: An incident optical system 6 includes a first lens system 10 which makes parallel light impinge on an object lens 1, and a first polarizer 11, and an emission optical system 7 includes a second polarizer 12 and a second lens system 14 which forms an image of a back focal plane 3 of the objective lens 1 on a two-dimensional detector 13. A background image of the back focal plane is acquired and is used to discriminate an outline of emitted light, polar coordinates of the back focal plane are determined, and a measurement image is standardized by the background image, whereby unevenness of the light intensity due to a device is corrected. An incident angle and an azimuthal angle dependence which reflect characteristics of a sample and the objective lens are detected, a plurality of polarization analysis parameters different by incident angles are calculated, simultaneous fitting at a plurality of incident angles is performed in consideration of contribution of the objective lens, and an optical constant and a film thickness of the sample are obtained.

Description

  The present invention relates to a rear focal plane microscopic ellipsometer, and more specifically, obtains a background image of the rear focal plane, uses this to identify the contour of the emitted light, determines polar coordinates of the rear focal plane, and measures an image. Is normalized with the background image, the non-uniformity of the light intensity caused by the device is corrected, the incidence angle and azimuth angle dependence due to the characteristics of the sample and objective lens are detected, and multiple ellipsometric parameters with different incidence angles are detected. The present invention relates to a back focal plane microscopic ellipsometer that calculates the optical constant and the film thickness of a sample by simultaneously fitting at a plurality of incident angles in consideration of the contribution of the objective lens used for calculation and measurement.

  Various measurement techniques related to the physical properties and thickness of thin films, such as thin films of inorganic substances such as inorganic compounds and metals, and thin films of organic substances such as biological substances and organic compounds, have been developed and used in many technical fields. . In addition, with the advancement of technological development such as miniaturization of electronic devices, display elements, and sensors, the necessity of measuring physical properties and thickness of thin films in finer regions is increasing.

  In recent years, in the field of biotechnology, in order to measure biomolecules present in sample solutions with high sensitivity and high speed, devices having surface structures on the order of several tens of nm to μm have been actively produced. What is needed is a technique for examining the actual surface structure of a device. 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, proteins are more difficult to label with dyes than DNA, so the optical properties and thickness of materials can be examined with sub-μm-scale horizontal resolution and nm-scale depth resolution without using fluorescence from the sample. Measurement technology that can be used is necessary.

  An ellipsometer irradiates a thin film sample formed on a substrate with light and analyzes the polarization state of the reflected or transmitted light. Changes in the intensity ratio and phase difference between the component (p-polarized light) and the component perpendicular to the plane (incident surface) where light enters the sample and is reflected or transmitted (incident surface) and reflected (transmitted). Is a device that measures the optical properties, film thickness, etc. of the thin film. It consists of an incident optical system that makes light incident on the sample and an emission optical system that detects and analyzes the light reflected or transmitted by the sample. The incident optical system includes a light source, a lens system that collimates the light from the light source, and a polarizing element group that adjusts the polarization state. The exit optical system includes a polarizing element group that analyzes the polarization state, and light detection. It comprises a lens system for entering light into the device and the photodetector.

  In a reflective ellipsometer that uses reflection on a sample, an incident optical system is installed obliquely above the sample, and an emission optical system is installed obliquely above the opposite side of the sample. In this manner, the sample is irradiated with light at a constant incident angle, and light reflected at an angle equal to the incident angle is detected. In such an apparatus, the horizontal resolution is about several tens of μm. An apparatus that improves resolution by installing an objective lens between the sample and the injection optical system to collect reflected light from a minute area for use in measuring the surface structure of devices and cells. Has been proposed (Non-Patent Documents 1 to 3). By manipulating the sample stage in the XY directions, it is possible to measure the thickness of the sample thin film and the two-dimensional distribution of optical constants.

  On the other hand, in ellipsometry, there is an optimum incident angle (Brewster angle) that maximizes the sensitivity of measurement. The Brewster angle is, for example, about 74 degrees when the sample is a silicon substrate, and is generally in a large incident angle range of 60 degrees or more. Therefore, it is necessary to tilt the objective lens at a large angle with respect to the sample, and in order to avoid contact with the sample, there is a problem that only a low-power objective lens with a long working distance that can be observed away from the sample can be used. . For this reason, the resolution of an ellipsometer in which the objective lens is installed at an angle is limited to several μm.

  On the other hand, in order to solve this problem, an ellipsometer that realizes high resolution by installing a high-magnification objective lens perpendicular to the sample has been developed. In this type of ellipsometer, light converged by a lens is vertically incident and condensed on the rear focal plane of the objective lens. Parallel light is emitted from the front surface of the objective lens at an angle determined by the incident position of the rear focal plane, and is irradiated onto the sample placed on the front focal plane. This is a technique called epi-irradiation in the field of microscopes. In this way, a microscopic ellipsometer was realized by irradiating the sample with parallel light at a constant incident angle from a fixed azimuth and measuring the reflected light from the sample through the same objective lens (Non-Patent Documents 4 to 6). And Patent Document 1).

  However, in this method, when light generated from a normal light source is used, the light cannot be converged with a sufficiently small spot on the rear focal plane, and the width of the incident angle of the light applied to the sample becomes wide. There is a problem that accurate measurement is difficult. On the other hand, if a coherent laser beam is used to narrow the width of the incident angle, diffraction fringes are generated due to scratches and dust on the surface of the optical element, thereby reducing the image quality and limiting the measurement wavelength. There is a problem that. In addition, if the incident angle is to be changed, the position where the convergent light is incident on the front focal plane of the objective lens must be moved with high accuracy. For this reason, the relative position between the incident optical system and the exit optical system is required. Need to change. In order to do this without reassembling the optical system, a large moving stage carrying the optical system is required. Further, it is difficult to move a large stage with high accuracy, and there is a problem that the incident angle cannot be adjusted with high accuracy. As described above, the methods described in Non-Patent Documents 1 to 6 and Patent Document 1 have various problems. In ellipsometry, in order to obtain a more accurate value of the optical properties and film thickness of a thin film, it is common to measure at multiple incident angles, and it is not easy to change and control the incident angle. It is a considerable disadvantage.

  Here, before describing the methods described in Non-Patent Documents 7 to 10 and Patent Documents 2 and 3, the 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 passes through the rear focal plane 3, is focused on the sample surface 4, and the reflected light is emitted as parallel light through the objective lens. At this time, as shown in FIG. 2, the intensity I 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 3. 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.

sinθ = d / f
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. By measuring the light intensity distribution I (θ, φ) in the rear focal plane, the ellipsometry parameters can be measured. Since the measurement resolution is equal to the objective lens resolution ε,
ε ≒ λ / NA
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, several methods have been developed for measuring ellipsometry using the properties of the back focal plane of the objective lens. Using a two-dimensional detector, ellipsometric parameters were obtained from the azimuth angle dependence of light intensity at a plurality of incident angles, and the optical characteristics of the substrate and thin film and the thin film thickness were calculated (Patent Document 2). Further, a one-dimensional distribution of light intensity in the x direction and the y direction was measured with a linear image sensor, and the optical characteristics and thickness of the thin film were measured from the dependence of the reflectance on the incident angle (Non-Patent Documents 7 and 8) ). 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. the phase difference [delta] ₀ when entering the determined further complex refractive index of the sample was determined (non-Patent Document 9). The rear focal plane is divided into four zones with respect to the azimuth angle. The influence of the objective lens is made uniform in each zone regardless of the incident angle, the influence of the objective lens is obtained, and the ellipsometric parameters are corrected (Patent Document 3). ). At multiple incident angles, the measured value of the Fourier coefficient for the azimuth angle is obtained from the azimuth angle dependency of the light intensity, the influence of the objective lens is considered as a function of the incident angle, and the least square method is used with the theoretical value of the Fourier coefficient. Fitting was performed to determine the thickness of the sample (Non-patent Document 10).

JP 2009-192331 A US Pat. No. 5,042,951 US Pat. No. 7,054,006 US Pat. No. 6,064,388

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  In the conventional method that uses the properties of the back focal plane of the objective lens, the distribution of light intensity at the back focal plane is measured, the ellipsometric parameters of the sample are obtained from the incident angle and azimuth angle dependence, and the substrate or thin film The optical characteristics and the thickness of the thin film are calculated.

  However, although it is not clearly described in the prior literature, the center and radius of the circle of the emitted light are obtained by using the raw image measured by the two-dimensional detector. In the measured image as it is, the light intensity depends strongly on the azimuth angle of the emitted light, so when identifying the outline of the emitted light as a circle, the light intensity threshold varies depending on the location, so accurate circle identification There is a problem that the center and radius cannot be obtained accurately.

  Although not clearly described in the prior art, the intensity distribution along a specific direction is obtained using the intensity of the pixel of the two-dimensional detector as it is. However, since the pixels of the two-dimensional detector are arranged along the axial direction of the orthogonal coordinates, it is difficult to obtain an accurate intensity distribution directly from the intensity of the pixel in the other directions. In addition, it is more difficult to obtain an accurate azimuth angle dependency of the intensity distribution along the same radius.

  Further, in order to accurately read the intensity distribution of the emitted light, it is indispensable to correct the intensity unevenness caused by the apparatus, which is present in the raw image measured by the two-dimensional detector. However, the prior art does not describe such a method.

  Further, in Non-Patent Document 10, in order to obtain the thickness of a sample, fitting is performed by a least square method between a measured value of a Fourier coefficient and a theoretical value. However, since Fourier coefficients do not correspond to physical properties, there is a problem that it is difficult to model a sample.

  Further, in Patent Document 3, it is assumed that the same zone is constant regardless of the incident angle, and an attempt to correct the influence on the measurement value of the objective lens is made. However, the refraction at the objective lens becomes large at a high incident angle. Therefore, that assumption is impossible. In Non-Patent Document 10, an attempt is made to correct the influence on the measurement value of the objective lens. However, different values of film thickness are required at different incident angles, and the correction is not successful.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to acquire a background image of the rear focal plane, identify the outline of the emitted light using this, and accurately determine the rear focal plane. Polar coordinates, normalization of the measurement image with the background image, correction of non-uniformity of the light intensity caused by the device, accurate detection of the incident angle and azimuth angle dependency reflecting the characteristics of the sample and objective lens, and incidence After calculating multiple ellipsometric parameters with different angles, taking into account the contribution of the objective lens, and performing fitting at multiple incident angles simultaneously, the optical constant and film thickness of the sample can be determined accurately and with little error It is to provide a side focal plane microscopic ellipsometer.

In order to achieve the above object, a rear focal plane microscopic ellipsometer (1) according to the present invention comprises:
An infinity correction system objective lens, a non-polarizing beam splitter, an incident optical system, an exit optical system, and an analysis device,
The incident optical system includes a light source, a first lens system that enters parallel light into the objective lens, and a first polarizer,
The exit optical system includes a second polarizer, a second lens system that forms an image of a rear focal plane of the objective lens on a two-dimensional detector, and the two-dimensional detector.
A sample to be measured is placed on the front focal plane of the objective lens,
The first polarizer and the second polarizer are each set to an arbitrary azimuth angle,
The two-dimensional detector measures an image of the back focal plane;
The analysis device is
From the image measured by the two-dimensional detector, the outline of the emitted light is identified as a circle, the center and radius of the circle are determined, the determined center and radius are the center and radius of the rear focal plane, and Determine polar coordinates according to the incident angle and azimuth of the irradiation light of
Based on the polar coordinates defined on the back focal plane, to determine the incident angle and azimuth angle dependence of the light intensity distribution of the back focal plane,
A polarization analysis parameter of the sample is calculated from the azimuth angles of the first and second polarizers and the incident angle and azimuth angle dependence of the light intensity distribution.

The rear focal plane microscopic ellipsometer (2) according to the present invention is the above-described rear focal plane microscopic ellipsometer (1).
The azimuth angle of one of the first polarizer and the second polarizer is set to two or more, and each time the setting is performed, the image of the rear focal plane is measured with the two-dimensional detector, Obtain an image corresponding to a direct current component independent of the azimuth angle of the polarizer,
By averaging the image corresponding to the DC component obtained by setting two or more azimuth angles of the other polarizer of the first polarizer or the second polarizer with respect to the light intensity at each pixel. , Obtaining a background image in which the intensity distribution depending on the incident angle and azimuth angle of the irradiation light to the sample is erased,
The analysis device identifies the outline of the emitted light as a circle from the background image, determines the center and radius of the circle, sets the determined center and radius as the center and radius of the rear focal plane, Polar coordinates according to the incident angle and azimuth angle of the irradiation light can be determined.

Further, the rear focal plane microscopic ellipsometer (3) according to the present invention is the above-described rear focal plane microscopic ellipsometer (1) or (2),
By dividing the image of the rear focal plane measured by the two-dimensional detector by the background image, a normalized light intensity distribution in the rear focal plane is obtained by removing non-uniformity of light intensity caused by the apparatus. ,
Based on the polar coordinates defined on the back focal plane, to determine the azimuth and incidence angle dependence of the normalized light intensity distribution,
The ellipsometric parameters of the sample can be calculated from the azimuth angles of the first and second polarizers and the dependence of the normalized light intensity distribution on the incident angle and azimuth angle.

  A rear focal plane microscopic ellipsometer (4) according to the present invention is a rear stage of the first polarizer in the incident optical system according to any one of the rear focal plane microscopic ellipsometers (1) to (3). Alternatively, a phase retarder can be provided in either one of the stages preceding the second polarizer in the emission optical system.

The rear focal plane microscopic ellipsometer (5) according to the present invention is the above-described rear focal plane microscopic ellipsometer (4).
The azimuth angle of the phase retarder is changed to four or more. Each time the azimuth angle is changed, the image of the rear focal plane is measured by the two-dimensional detector, and the direct current component does not depend on the azimuth angle of the phase retarder. Find the corresponding image,
Irradiation light to the sample is obtained by averaging the images corresponding to the direct current components obtained by combinations of four or more azimuth angles of the first polarizer and the second polarizer with respect to the light intensity at each pixel. The background image from which the intensity distribution depending on the incident angle and azimuth angle of the image is eliminated can be acquired.

Further, the rear focal plane microscopic ellipsometer (6) according to the present invention is the above-mentioned rear focal plane microscopic ellipsometer (4) or (5),
The first polarizer, the second polarizer, and the phase retarder are set to arbitrary azimuth angles, the image of the rear focal plane is measured by the detector, and the image is divided by the background image. By obtaining a normalized light intensity distribution in the rear focal plane, excluding non-uniformity of light intensity caused by the device,
Based on the polar coordinates defined on the back focal plane, to determine the azimuth and incidence angle dependence of the normalized light intensity distribution,
The ellipsometric parameters of the sample are calculated from the azimuth angles of the first polarizer, the second polarizer, and the phase retarder, and the incident angle and azimuth angle dependence of the normalized light intensity distribution. be able to.

Further, the rear focal plane microscopic ellipsometer (7) according to the present invention is any one of the above-mentioned rear focal plane microscopic ellipsometers (1) to (6),
The number of pixels of the two-dimensional detector is H × V (H and V are both natural numbers), and one pixel is divided into n × n (n is a natural number) small pixels. Consider a high-density plane consisting of the number of pixels on which an image is drawn nH x nV,
On the high-density plane, the center and radius of the circle of the emitted light are obtained. Can be determined.

Further, the rear focal plane microscopic ellipsometer (8) according to the present invention is any one of the above-described rear focal plane microscopic ellipsometers (1) to (7),
Defining concentric sectors defined by an incident angle range (θ ₁ , θ ₂ ) and an azimuth angle range (φ ₁ , φ ₂ ) in the rear focal plane on the high-density plane;
The number of pixels at least part of which belongs to a sector is n (n is a natural number), the number of small pixels belonging to the i-th pixel P _i is q _i, and the light intensity of the pixel P _i is I _i . When
Average light intensity I _av of the sector

Can be obtained.

In addition, the rear focal plane microscopic ellipsometer (9) according to the present invention is any one of the above-described rear focal plane microscopic ellipsometers (1) to (8),
The incident angle is between 0 ° and the maximum angle determined by the numerical aperture of the objective lens, the width is in the range of 0.5-2 °, and the azimuth is any angle φ _a to φ _a + 180 ° and φ _a In 2n sectors on the back focal plane defined by dividing each by n equal intervals from + 180 ° to φ _a + 360 °, the average of the normalized light intensity is obtained,
Using the azimuth angle dependence of the light intensity distribution on the rear focal plane, and assuming that the number of ellipsometric parameters obtained by one calculation is k, from the average of the light intensity of 2n sectors, the DC component, and The cosine component or sine component of the second or fourth harmonic of the azimuth change can be calculated, and k ellipsometric parameters can be obtained.

Further, the rear focal plane microscopic ellipsometer (10) according to the present invention is any one of the rear focal plane microscopic ellipsometers (1) to (9) described above.
The incident angle is an arbitrary region between 0 ° and the maximum angle determined by the numerical aperture of the objective lens, and is divided into m ranges at intervals of 0.5 to 2 °.
In each incident angle range, divide the azimuth angle to define 2n sectors and obtain k ellipsometric parameters,
Based on the ellipsometric parameters of a total of km with different incident angles, i is a number indicating the incident angle, j is a number indicating the type of ellipsometric parameter, and y _ij is the (i, j) th polarization. And y ' _ij is the (i, j) ellipsometric parameter obtained by calculation from the optical constant and film thickness of the sample, and σ _ij is the standard deviation of the (i, j) th ellipsometric parameter and when,

The optical constant and film thickness of the sample can be obtained so that the parameter χ ² represented by

Further, the rear focal plane microscopic ellipsometer (11) according to the present invention is any one of the rear focal plane microscopic ellipsometers (1) to (10) described above.
Divide the incident angle and azimuth angle to define 2mn sectors and obtain km ellipsometric parameters,
Based on the measured values of a total of km ellipsometric parameters with different incident angles, i is a number indicating the incident angle, j is a number indicating the type of ellipsometric parameter, and y _ij is (i, j) The measured value of the ellipsometric parameter, _y'ij is the (i, j) th ellipsometric parameter obtained from the optical constant and film thickness of the sample, and _σij is the (i, j) th polarized light the standard deviation of the analysis parameters, y _'j is the calculated value of the j-th type of ellipsometric parameters, the y _"j is the calculated value in consideration of the influence of the j-th type of objective lens of ellipsometric parameters, f _j Is a function specific to the eleventh type of ellipsometric parameters representing the influence of the objective lens, θ is the incident angle,

further,

The optical constant, the film thickness, and k functions of the sample can be obtained so that the parameter χ ² represented by

  According to the rear focal plane microscopic ellipsometer according to the present invention, the background image of the rear focal plane is obtained and the outline of the emitted light is identified using this, so that it is necessary for extraction of the incident angle and azimuth angle dependency. Accurate polar coordinates of the back focal plane can be determined.

  In addition, since the intensity irregularity caused by the device cause is used instead of the original image measured by the two-dimensional detector, the light intensity data at a specific incident angle and azimuth angle can be read accurately and accurately. Can do.

  In addition, since the pixels of the two-dimensional detector have a certain area and use an algorithm that takes into account the difference between orthogonal coordinates and polar coordinates, light intensity data can be read more accurately and with high accuracy. Therefore, it is possible to obtain ellipsometric parameters that are accurate and have good reproducibility.

  In addition, in order to obtain the thickness of the sample, fitting is performed by the least square method between the measured value of the ellipsometric parameter and the theoretical value. Since the ellipsometric parameters correspond to the physical properties of the sample, it is easy to model the sample.

  In addition, since the theoretical value is fitted to the measured value simultaneously at different incident angles, the influence of the objective lens as a function of the incident angle can be obtained in addition to the optical constant and film thickness of the sample.

It is a schematic diagram for demonstrating the property of the back focal plane of a general objective lens, and is the figure which looked at the objective lens from the horizontal direction. It is a schematic diagram for demonstrating the property of the back focal plane of a general objective lens, and is the figure which looked at the back focal plane along the incident light which advances perpendicularly | vertically to the paper front side direction. It is a schematic diagram which shows the measuring system of the back side focal plane microscopic ellipsometer which concerns on this invention. It is the image as it was measured with CCD in one Example of this invention. It is the background image measured by CCD in one Example of this invention. 3 is a CCD image normalized with a background image in an embodiment of the present 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 A back focal plane microscopic ellipsometer (hereinafter simply referred to as an apparatus of the present invention) according to an embodiment of the present invention includes an objective lens 1, a non-polarizing beam splitter 5, An incident optical system 6 and an emission optical system 7 are included. The objective lens 1 is an infinity correction system, and a sample 8 is installed on the front focal plane. The incident optical system 6 includes an optical fiber exit 9 serving as a light source, a lens system 10 for entering parallel light into the objective lens 1, and a first polarizer 11. The exit optical system 7 includes a second polarizer 12, a lens system 14 that forms an image of the rear focal plane 3 of the objective lens on the two-dimensional detector 13, and a two-dimensional detector 13. Furthermore, an analysis device 15 that receives image data from the two-dimensional detector via the interface and calculates the ellipsometric parameters of the sample 8 from the light intensity distribution on the rear focal plane 3 of the objective lens 1 is provided.

  In addition, the apparatus of the present invention can include a phase retarder 15 that converts linearly polarized light into elliptically polarized light, and is subsequent to the first polarizer 11 in the incident optical system 6 or the second polarizer 12 in the exit optical system 7. It can be installed in the previous stage. The phase retarder may be a variable phase retarder as long as it can change linearly polarized light into elliptically polarized light.

  In the apparatus of the present invention, the arrangement of the incident optical system 6 and the emission optical system 7 may be interchanged.

2. Measurement Principle The apparatus of the present invention uses the property of the rear focal plane 3 of the objective lens 1 to determine the ellipsometric parameters from the light intensity distribution on the rear focal plane 3. More specifically, the light intensity distribution on the rear focal plane 3 is measured by forming an image of the rear focal plane 3 on the objective lens 1 on the two-dimensional detector 13, and the azimuth angle dependence at different incident angles. The ellipsometric parameters are obtained from The incident angle that can be measured is from 0 ° to the maximum angle determined by the numerical aperture of the objective lens 1. To be precise, the intensity distribution measured by the two-dimensional detector 13 is not the light intensity distribution itself on the rear focal plane 3, but the light after being modulated by the second polarizer 12 of the exit optical system 7. Intensity distribution. Since the rear focal plane 3 and the two-dimensional detector 13 are in an imaging relationship, the light intensity distribution after being modulated by the second polarizer 12 is measured in the same distribution manner as the rear focal plane 3. Can do. However, for the sake of simplicity, this will be referred to as “light intensity distribution in the rear focal plane”.

1) When there is no phase retarder Polarized light is represented by a four-dimensional vector called a Stokes vector, and optical effects due to polarization elements and coordinate axis operations can be represented by a four-dimensional square matrix called a Mueller matrix. Stokes vector S _o of the light emitted from the objective lens,

It is represented by Here, T _P represents the optical effect of the first polarizer, and R _P represents coordinate conversion when light is emitted from the first polarizer. R _-φ T _S R _φ represents the optical effect of the objective lens including reflection on the sample surface as a whole, T _S represents reflection on the sample surface, and R _φ and R _-φ represent light on the objective lens. Represents coordinate transformation when entering and exiting. E _i is a Stokes vector representing the incident light to the optical system. When non-polarized light from the light source is incident, e _i = [1, 0, 0, 0] ^T , and the light vector S ₀ emitted from the objective lens is calculated as follows.

Here, P represents the azimuth angle of the first polarizer. Ψ and Δ represent the ellipsometric parameters of the sample, Ψ is the arctangent function of the amplitude ratio of P-polarized light and S-polarized light, and Δ is the phase difference between P-polarized light and S-polarized light. φ represents the incident angle on the sample surface. Further, each of the S and C represents the sin function and cos function (e.g., S _2P is sin2P).

  The intensity of the output light is expressed as follows.

Here, T _A represents the optical effect of the second polarizer (also referred to as an analyzer), and R _A represents coordinate conversion when light is incident on the second polarizer. f is an output vector representing the action of the detector and is written as f = [1, 0, 0, 0]. The factor excluding _So in the equation is a vector F representing the optical effect from the objective lens to the detector, and is calculated as follows.

Here, A represents the azimuth angle of the second polarizer.

  Since the apparatus of the present invention uses a two-dimensional detector, the intensity of the output light is a value for each pixel. The light intensity at the rear focal plane has an azimuth angle dependency represented by Expression (2). The ellipsometric parameters of the sample depend on the incident angle, and the incident angle dependency does not appear directly in the equation.

  The measurement is performed by setting the first polarizer and the second polarizer to arbitrary azimuth angles, and the light intensity distribution in the rear focal plane measured by the two-dimensional detector is expressed by using the equations (2) to (4). The ellipsometric parameters of the sample are obtained from the azimuth angle dependence at different incident angles.

2) In the case where the incident optical system has a phase retarder The symbols indicating the optical effect of the polarizing element and the azimuth angle thereof are as described above. The vector S _{i of} polarized light incident on the objective lens is

It is represented by Here, T _R represents the optical effect of the phase retarder, and R _R and R _−R represent coordinate transformations when light enters and exits the phase retarder, respectively. When unpolarized light from the light source is incident, a vector S _{i of} polarized light incident on the objective lens is calculated as follows.

Here, R represents the azimuth angle of the phase retarder. Also,

Where 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.
The intensity of the output light is expressed as follows.

Factors except the expression of the S _i is a vector F that represents the optical effects leading to the detector from the objective lens, is calculated as follows.

The measurement is performed by setting the first polarizer, the second polarizer, and the phase retarder to arbitrary azimuth angles, and the light intensity distribution in the rear focal plane measured by the two-dimensional detector is expressed by equations (6) to (6) 10) and obtain the ellipsometric parameters of the sample from the azimuthal dependence at different incident angles.

3) In the case where there is a phase retarder in the emission optical system The optical effect of the polarizing element and the symbols representing the azimuth angle are as described above. The intensity of the output light is expressed as follows.

Here, S ₀ is as shown in Equation (2), and the factor excluding S ₀ is a vector F representing the optical effect from the objective lens to the detector, and is calculated as follows.

The measurement is performed by setting the first polarizer, the second polarizer, and the phase retarder to arbitrary azimuth angles, and the light intensity distribution in the rear focal plane measured by the two-dimensional detector is expressed by the equations (2), ( 7), (8), (11) and (12) are used for analysis, and the ellipsometric parameters of the sample are obtained from the azimuth dependence at different angles of incidence.

3. Acquisition of background image In order to accurately measure the light intensity distribution in the rear focal plane, the outline of the emitted light is accurately identified, polar coordinates of the rear focal plane are determined, and intensity unevenness due to equipment causes is corrected. There is a need to. For that purpose, first, it is necessary to obtain a background image in which the intensity distribution depending on the incident angle and the azimuth angle is eliminated.
1) When there is no phase retarder The light intensity I measured at each pixel of the two-dimensional detector is expressed by the following equation as a function of the azimuth angle P of the first polarizer.

Here, I ₀ is the intensity of light incident on the optical system, F ₀ , F ₁ and F ₂ are the 0th vector of the vector representing the optical effect from the objective lens to the detector, represented by equation (12), First and second elements. I ₀ F _0/2 term in this equation is equivalent to a direct current component which does not depend on the azimuth angle of the first polarizer. At this time, by changing the azimuth angle P of the first polarizer, for example, in 0 ° and 90 ° and are two, on average the intensity of the measured light, the value is equal to the DC component I ₀ F _0/2. As can be seen from Equation (12), F ₀ is a function of the azimuth angle A of the second polarizer. For example, when A is measured at 0 ° and 90 ° and the average of the DC components is obtained, the value is equal to I _0/2.

  In addition, the same result can be obtained when the measurement is performed in the same procedure while paying attention to the second polarizer. In that case, equation (13) is replaced by equation (14).

Here, S ₀ , S _1, and S ₂ are the 0th, 1st, and 2nd elements of the vector that represent the polarized light exiting from the objective lens, represented by Expression (2). The second was measured azimuth A of the polarizer, for example, as 0 ° and 90 °, averaging the intensity of the measured light, the value is equal to the DC component I ₀ S _0/2. Furthermore, for example, a P was measured as 0 ° and 90 °, when determining the average of the DC component, its value is equal to I _0/2.

  To summarize the above results, the azimuth angle of the first or second polarizer is set to two or more, and each time the image of the rear focal plane is measured by the two-dimensional detector, the azimuth angle of the polarizer. By obtaining an image corresponding to the direct current component independent of, and averaging the image corresponding to the direct current component obtained by setting two or more azimuth angles of another polarizer with respect to the intensity of light at each pixel, A background image from which factors depending on the incident angle and the azimuth angle are eliminated can be acquired.

2) When there is a phase retarder (I)
When the incident optical system has a phase retarder, the intensity I of light measured at each pixel of the two-dimensional detector is expressed by the following equation as a function of the azimuth angle P of the first polarizer.

Here, B ₁ and B ₂ are optical characteristics and azimuth angles of the phase retarder, and functions of F ₀ , F _1, and F ₂ . Usually, V≈45 °, so s≈0, and the second term can be ignored. Therefore, when the azimuth angle P of the first polarizer is changed in two ways, for example, 0 ° and 90 °, and the measured light intensity is averaged, the value is a DC component I ₀ that does not depend on the azimuth angle of the first polarizer. equal to F _0/2. Further, F ₀ is a function of the azimuth angle A of the second polarizer, such as A was measured as 0 ° and 90 °, when determining the average of the DC component, its value is equal to I _0/2.

  Further, when the emission optical system includes a phase retarder, the same result can be obtained by performing measurement in the same procedure while paying attention to the second polarizer. Since this procedure is the same as the case where there is no phase retarder, the description thereof is omitted.

  Therefore, even when the apparatus has a phase retarder, the azimuth angle of the first or second polarizer is set to two or more as in the case where there is no phase retarder, and the two-dimensional detector each time An image of a side focal plane is measured, an image corresponding to a direct current component independent of the azimuth angle of the polarizer is obtained, and the direct current component obtained by setting two or more azimuth angles of the other polarizer is obtained. By averaging the image with respect to the light intensity at each pixel, a background image from which factors depending on the incident angle and the azimuth angle are eliminated can be obtained.

3) When there is a phase retarder (II)
When the device has a phase retarder, a more accurate background image can be obtained by changing the azimuth angle of the phase retarder. That is, the light intensity I measured at each pixel of the two-dimensional detector is expressed by the following equation as a function of the azimuth angle R of the phase retarder.

Here, a _k and b _k are Fourier coefficients. This section of the I ₀ F ₀ a _0/2 in the expression is equivalent to a direct current component which does not depend on the azimuth angle of the phase delay element. At this time, when the azimuth angle R of the phase retarder is changed in four ways, for example, −45 °, 0 °, 45 °, and 90 °, and the average is calculated, the value is the DC component I ₀ F ₀ a _0. Equal to / 2. Here, F ₀ is given by Expression (10), and a ₀ is expressed by the following expression.

F ₀ is a function of the azimuth angle A of the second polarizer. For example, when A is measured in two ways, 0 ° and 90 °, the direct current component is obtained, and the average is calculated, F ₀ is Equal to 1. Further, as can be seen from the equation (17), a ₀ is a function of the azimuth angle P of the first polarizer, and P is measured by changing P in two ways, for example, 0 ° and 90 °, and similarly the direct current When the average of the components is obtained, a ₀ is equal to 1. Therefore, the azimuth angles {φ ₁ , φ ₂ } of the first polarizer and the second polarizer are set to {0 °, 0 °}, {0 °, 90 °}, {90 °, 0 °} and {90 °, was measured by setting the four ways of 90 °}, seek an image corresponding to the DC component, when averaged them in pixel units, it is possible to obtain an image corresponding to the I _0/2.

  In addition, when the phase retarder is installed in the emission optical system, an equivalent result can be obtained. In that case, equation (17) is replaced by equation (18).

Here, S ₀ is given by equation (2). The azimuth angles {φ ₁ , φ ₂ } of the first polarizer and the second polarizer are set to {0 °, 0 °}, {0 °, 90 °}, {90 °, 0 °} and {90 °, 90 ° was measured by setting the four ways of}, when treated in the same manner as described above, it is possible to obtain an image corresponding to the I _0/2.

Thus the average intensity image I _0/2 as measured are erased factor which depends on the incident angle and azimuth, to identify the outline of the emitted light, as a background image to correct the uneven intensity by the device causes Can be used.

4). Definition of polar coordinates in the rear focal plane In the present invention, polar coordinates based on the incident angle and azimuth angle are accurately determined on the rear focal plane in order to obtain the ellipsometric parameters of the sample with higher accuracy from the intensity distribution of the rear focal plane. Defined in In the present invention, since parallel light is incident on the objective lens at the time of measurement, it is considered that the diameter of the exit light is equal to the diameter of the exit pupil when the sample is placed in front of the objective lens and focused accurately. Can do. In the present invention, the background image is acquired by eliminating the incident angle and azimuth angle dependency appearing in the image as it is measured by the two-dimensional detector. By using this background image to identify the outline of the emitted light as a circle and measuring its center and radius, polar coordinates can be accurately determined.

  In order to identify the outline of the emitted light, first, the gradient of pixel values (luminance values) between adjacent pixels is calculated by a known filtering technique. There is a large difference in light intensity between the emitted light and the outside, and the light intensity is discontinuous at the boundary. As a result of calculation, pixels with high luminance are distributed along the contour of the emitted light. An image is obtained. Since the background image is used as the calculation target, the bright line forming the contour is clear. Next, in order to determine the center and radius of the emitted light, the contour is identified as a circle. For this purpose, the circle is fitted so that the overlap between the bright line and the circle is maximized, that is, the total luminance of the pixels through which the circumference passes is maximized. Thus, the center and radius of the emitted light can be determined with high accuracy.

  Furthermore, in order to improve the identification accuracy, it is possible to use a method of dividing the pixel of the two-dimensional detector into small pixels. The resolution of an industrial two-dimensional detector is usually about 640 × 486 pixels. Assuming that the accuracy with which the bright line can be identified is 0.5 pixel (half pixel), the accuracy of determining the center and radius is about 0.2% of the radius even if the diameter of the emitted light is projected to fill the screen of the two-dimensional detector. Therefore, a small pixel obtained by dividing each pixel of the two-dimensional detector into n × n (n is an integer) is considered. If the number of pixels of the two-dimensional detector is H × V, a high-density plane having the number of pixels nH × nV can be obtained. Since the image of the two-dimensional detector is drawn on a highly densified plane, the accuracy of determining the center and radius is improved to 1 / n times. As described in the next section, in the present invention, in order to define polar coordinates on the high-density screen, the center and radius of the rear focal plane serving as the reference are determined in advance on the same high-density screen. This is advantageous in terms of measurement accuracy.

5. Calculation of light intensity in a sector defined by polar coordinates In the present invention, light intensity is defined by polar coordinates, and an intensity distribution I (θ, φ) is measured as a function of an incident angle θ and an azimuth angle φ. Therefore, the light intensity is integrated in concentric sections (hereinafter referred to as sectors) defined by the incident angle range (θ ₁ , θ ₂ ) and the azimuth angle range (φ ₁ , φ ₂ ). On the other hand, since the light intensity of the two-dimensional detector is measured by orthogonal coordinates, it is necessary to convert the coordinates in order to integrate the light intensity. The unit of polar coordinates corresponding to the pixels of the two-dimensional detector is the sector. However, since the polar coordinate has a different axial direction depending on the location, the pixel of the two-dimensional detector and the sector of the polar coordinate cannot be made to correspond one-to-one. There are not a few 2D detector pixels that span multiple sectors. In such a case, the present invention introduces an algorithm that distributes the light intensity of the pixels of the two-dimensional detector to a plurality of sectors (Patent Document 4).

Therefore, as described in the previous section, each pixel of the two-dimensional detector is divided into n × n (n is a natural number) small pixels. If the number of pixels of the two-dimensional detector is H × V (H and V are both natural numbers), a high-density plane consisting of the number of pixels nH × nV is obtained. A sector is defined in the rear focal plane on this densified plane. If the number of all pixels partially belonging to a sector is n, the number of small pixels belonging to the i-th pixel P _i is q _i, and the light intensity of the pixel P _i is I _i , the sector The average value I _av of the light intensity can be calculated by the following equation.

By such a method, in the present invention, even when the number of pixels of the two-dimensional detector is not as large as about 300,000, the average value of the light intensity of the sector from the light intensity distribution measured by the two-dimensional detector, It can be calculated more accurately.

6). Reading the light intensity and calculating the ellipsometric parameters The ellipsometric parameters are calculated from the light intensity distribution in the rear focal plane. The intensity distribution of light on the rear focal plane measured by the two-dimensional detector is expressed by the following equation as a function of the azimuth angle when the incident angle is constant.

Here, α _k and β _k are Fourier coefficients. By dividing the measured intensity distribution of the rear focal plane by the background image, a normalized intensity distribution in which the background signal I ₀ is eliminated is obtained, and all coefficients including α ₀ can be extracted.

Next, in order to obtain the Fourier coefficient from the normalized intensity distribution of the rear focal plane, a narrow sector is defined along the same radius of the rear focal plane. That is, the incident angle is between 0 ° and the maximum angle determined by the numerical aperture of the objective lens, the width is in the range of 0.5 to 2 °, and the azimuth is any angle φ _a to φ _a + 180 ° and 2n sectors are defined on the rear focal plane by dividing each by n equal intervals from φ _a + 180 ° to φ _a + 360 °. As described above, the average of the normalized light intensity in the sector is obtained from the normalized intensity in the pixel of the two-dimensional detector.

  Next, according to the equation (20), the DC component and the cosine component or sine component of the second or fourth harmonic of the azimuth change are calculated from the average of the light intensity of 2n sectors, and the Fourier coefficient is obtained. Ellipsometric parameters are calculated. The number of parameters obtained by one calculation varies depending on the type of ellipsometry parameters and the calculation method in the middle. For example, the parameters Ψ and Δ are usually obtained both in one calculation. On the other hand, the parameters cos2Ψ, sin2ΨcosΔ, and sin2ΨsinΔ can all be obtained by one calculation depending on the calculation method, but only two of them may be obtained.

  It is also possible to simultaneously obtain ellipsometric parameters at a plurality of incident angles by setting a range of a plurality of incident angles. The incident angle is divided into m ranges at an interval of 0.5 to 2 ° in an arbitrary region between 0 ° and the maximum angle determined by the numerical aperture of the objective lens, and is described above for each incident angle range. Thus, 2n sectors are defined by dividing the azimuth angle. As described above, the Fourier coefficient is obtained from the average of the light intensity of 2n sectors, and the ellipsometric parameters are calculated.

If ellipsometric parameters at a plurality of incident angles are obtained, the optical constant and film thickness of the sample can be obtained by fitting values obtained by theoretical calculation. Based on a total of km ellipsometric parameters with different incident angles, i is a number indicating the incident angle, j is a number indicating the type of ellipsometric parameter, and y _ij is the (i, j) th ellipsometric parameter. Y ' _ij is the (i, j) ellipsometric parameter obtained by calculation from the optical constant and film thickness of the sample, and σ _ij is the standard deviation of the (i, j) ellipsometric parameter ,

The optical constant and film thickness of the sample are obtained so that the parameter χ ² represented by

7). Influence of the objective lens In the present invention, the influence of the measurement value of the objective lens on the measurement value of the ellipsometry parameter can be incorporated into the calculation. According to Non-Patent Document 5, the influence of the objective lens is expressed by the following equation.

Here, T ′ _S is a Mueller matrix that represents the apparent optical effect of the sample, T _S is a Mueller matrix that represents the true optical effect, and T _Ob is a Mueller matrix that represents the optical effect of the objective lens. The light passes through the objective lens twice in the opposite direction before and after being reflected by the sample, but the optical effect at that time is considered to be equal. If the scattering of light inside the objective lens can be ignored, _Tob is commutative and can be expressed as follows.

Therefore, the influence of the objective lens can be expressed as follows.

Here, ρ ′ is a complex reflectance that represents the apparent optical effect of the sample, ρ is a complex reflectance that represents the true optical effect of the sample, and ρ _Ob is a complex transmittance that represents the optical effect of the objective lens. is there. Accordingly, the ellipsometric parameters Ψ and Δ are expressed as follows.

and

Where Ψ ′ _S and Δ ′ _S represent the apparent ellipsometric parameters of the sample, Ψ _S and Δ _S represent the true ellipsometric parameters of the sample, and Ψ _Ob and Δ _Ob represent the ellipsometric parameters of the objective lens. Represent.
In addition, the influence of the objective lens is considered to vary depending on the incident angle. Therefore, the ellipsometric parameters Ψ _Ob and Δ _Ob are expressed as a function of the incident angle θ as follows.

Here, g _Ψ and g _Δ are functions specific to the ellipsometric parameters Ψ and Δ, respectively.

  Alternatively, in the case of the ellipsometric parameter Ψ, the expressions (25) and (27) can be collectively expressed as one expression as follows.

The same applies to the ellipsometric parameter Δ. Here, j is a number indicating the type of ellipsometry parameter. Y ′ _j represents the j-th apparent ellipsometric parameter, and y _j represents the j-th true ellipsometric parameter. F _j is a function specific to the j-th type ellipsometric parameter. For example, in the case of the ellipsometric parameter Ψ, if k = 1, the function f ₁ is a composite function of the equations (25) and (27). However, f _j is not always expressed analytically by one expression.

Next, fitting is performed in consideration of the influence of the objective lens, and the optical constant, film thickness, and function f _k of the sample are _obtained . For that purpose, the equation (29) can be rewritten as follows.

Here, y ' _j represents the jth ellipsometric parameter calculated from the optical constant and film thickness of the sample, and y " _j represents the calculated value of the jth ellipsometric parameter taking into account the influence of the objective lens. Show.

  The formula for fitting is written as follows.

The meaning of the symbols is the same as in equation (21).

  The apparatus according to the present invention has the configuration shown in FIG. 3, and a phase retarder having a rotation mechanism is installed in the incident optical system. The light from the xenon lamp was dispersed with a monochromator, and the monochromatic light was guided to the device through an optical fiber having 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. The cover glass was set upside down on the front side of the objective lens, and the space between the covers was filled with a refractive liquid, and the focal position was adjusted.

  First, the light incident on the front of the CCD was blocked and the dark signal was measured. The dark image was subtracted from the CCD image before proceeding to the next processing. A measurement wavelength was selected using a monochromator. A background image was obtained according to the procedure described above. Next, the first polarizer, the second polarizer, and the phase retarder were set to 0 °, 0 °, and 22.5 °, respectively, and an image was acquired by CCD.

  The raw image and background image measured by the CCD are shown in FIGS. 4 and 5, respectively. The measurement wavelength is 600 nm. It can be seen that the intensity distribution depending on the incident angle and azimuth angle seen in the measured image is not seen in the background image. FIG. 6 shows an image normalized with the background image. Only the intensity distribution depending on the incident angle and azimuth required for obtaining ellipsometric parameters is observed.

  Next, as in the above procedure, the center and radius of the emitted light were determined using the background image. In addition, the range of incident angles was divided every 0.5 ° over 30-40 °, the range of azimuths was divided into 16 sections at equal intervals over 0-180 ° and 180 ° -360 °, and sectors were defined. .

  The light intensity measured by the two-dimensional detector is as shown in Equation (23). Here, if the normalized light intensity in each sector is integrated over the range of azimuth angles, the following equation is obtained.

In consideration of the integral value of the trigonometric function, the value of the Fourier coefficient is obtained as follows using the integral value S _i of each sector.

Here, the subscript indicates the sector number in the azimuth angle range of 0 to 180 °. Similar calculations can be performed in the azimuth range of 180-360 °.

On the other hand, the average value I _av normalized for each sector was calculated. Based on the equation (22), averaging the image intensities means dividing the integrated value of the pixel intensities by the integration range. Furthermore, considering the definite integral nature of the trigonometric function, the following relationship exists between the average value I _av of the intensity in each sector and the integral value S.

Here, L is an integration range, and in this embodiment, L = π / 16.

  Now, when the first polarizer and the phase retarder are set to 0 ° and 22.5 °, respectively, the vector of light incident on the objective lens is derived from the equation (6) as follows.

Here, f is obtained by Expression (7). When the second polarizer is set to 0 °, the vector of the optical effect from the objective lens to the two-dimensional detector is derived from Equation (10) as follows.

The intensity I of light measured at each pixel of the two-dimensional detector is as follows:

The relationship between the ellipsometric parameters of the sample and the Fourier coefficient is as follows.

The ellipsometric parameters Ψ and Δ can be calculated by calculating using the equation (38) and further calculating the inverse function of the trigonometric function.

Next, according to the above-mentioned method, the result obtained by measurement and the calculated value were fitted. In order to correct the influence of the objective lens, the following equations were used for the ellipsometric parameters Ψ _Ob and Δ _Ob 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.

  The ellipsometric parameters Ψ and Δ in the incident angle range of 30 to 40 ° measured at wavelengths 590, 600, 610 and 620 nm are shown in FIGS. 7 and 8, 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: 2.036 + 0.055 / λ ² , film thickness (nm): 96.66
Here, λ is a wavelength (unit: μm). Further, the following values were obtained as constants of the equations (39) and (40) for calculating the ellipsometric parameters of the objective lens.

a _Ψ : 0.27, b _Ψ : 47.08
_aΔ : 0.11, _bΔ : 1.97
Here, the unit of the constant is degrees.

DESCRIPTION OF SYMBOLS 1 Objective lens 2 Parallel light 3 Back side focal plane 4 Sample surface 5 Non-polarizing beam splitter 6 Incident optical system 7 Ejection optical system 8 Sample 9 Optical fiber exit port 10 Lens system 11 First polarizer 12 Second polarizer 13 Second Dimensional detector 14 Lens system 15 Phase retarder

Claims (11)

An infinity correction system objective lens, a non-polarizing beam splitter, an incident optical system, an exit optical system, and an analysis device,
The incident optical system includes a light source, a first lens system that enters parallel light into the objective lens, and a first polarizer,
The exit optical system includes a second polarizer, a second lens system that forms an image of a rear focal plane of the objective lens on a two-dimensional detector, and the two-dimensional detector.
A sample to be measured is placed on the front focal plane of the objective lens,
The first polarizer and the second polarizer are each set to an arbitrary azimuth angle,
The two-dimensional detector measures an image of the back focal plane;
The analysis device is
From the image measured by the two-dimensional detector, the outline of the emitted light is identified as a circle, the center and radius of the circle are determined, the determined center and radius are the center and radius of the rear focal plane, and Determine polar coordinates according to the incident angle and azimuth of the irradiation light of
Based on the polar coordinates defined on the back focal plane, to determine the incident angle and azimuth angle dependence of the light intensity distribution of the back focal plane,
A back focal plane microscopic ellipsometer, wherein the ellipsometric parameters of the sample are calculated from the azimuth angles of the first and second polarizers and the incident angle and azimuth angle dependence of the light intensity distribution. The azimuth angle of one of the first polarizer and the second polarizer is set to two or more, and each time the setting is performed, the image of the rear focal plane is measured with the two-dimensional detector, Obtain an image corresponding to a direct current component independent of the azimuth angle of the polarizer,
By averaging the image corresponding to the DC component obtained by setting two or more azimuth angles of the other polarizer of the first polarizer or the second polarizer with respect to the light intensity at each pixel. , Obtaining a background image in which the intensity distribution depending on the incident angle and azimuth angle of the irradiation light to the sample is erased,
The analysis device identifies the outline of the emitted light as a circle from the background image, determines the center and radius of the circle, sets the determined center and radius as the center and radius of the rear focal plane, 2. The back focal plane microscopic ellipsometer according to claim 1, wherein polar coordinates are determined by an incident angle and an azimuth angle of irradiation light. By dividing the image of the rear focal plane measured by the two-dimensional detector by the background image, a normalized light intensity distribution in the rear focal plane is obtained by removing non-uniformity of light intensity caused by the apparatus. ,
Based on the polar coordinates defined on the back focal plane, to determine the azimuth and incidence angle dependence of the normalized light intensity distribution,
The ellipsometric parameters of the sample are calculated from the azimuth angles of the first and second polarizers and the incident angle and azimuth angle dependence of the normalized light intensity distribution. Rear focal plane microscopic ellipsometer described.   4. The phase retarder is provided in either one of the rear stage of the first polarizer in the incident optical system and the front stage of the second polarizer in the emission optical system. 5. The back focal plane microscopic ellipsometer described in any one of the above. The azimuth angle of the phase retarder is changed to four or more. Each time the azimuth angle is changed, the image of the rear focal plane is measured by the two-dimensional detector, and the direct current component does not depend on the azimuth angle of the phase retarder. Find the corresponding image,
Irradiation light to the sample is obtained by averaging the images corresponding to the direct current components obtained by combinations of four or more azimuth angles of the first polarizer and the second polarizer with respect to the light intensity at each pixel. The back focal plane microscopic ellipsometer according to claim 4, wherein the background image from which the intensity distribution depending on the incident angle and the azimuth angle is eliminated. The first polarizer, the second polarizer, and the phase retarder are set to arbitrary azimuth angles, the image of the rear focal plane is measured by the detector, and the image is divided by the background image. By obtaining a normalized light intensity distribution in the rear focal plane, excluding non-uniformity of light intensity caused by the device,
Based on the polar coordinates defined on the back focal plane, to determine the azimuth and incidence angle dependence of the normalized light intensity distribution,
The ellipsometric parameters of the sample are calculated from the azimuth angles of the first polarizer, the second polarizer, and the phase retarder, and the incident angle and azimuth angle dependence of the normalized light intensity distribution. 6. A back focal plane microscopic ellipsometer according to claim 4 or 5, wherein: The number of pixels of the two-dimensional detector is H × V (H and V are both natural numbers), and one pixel is divided into n × n (n is a natural number) small pixels. Consider a high-density plane consisting of the number of pixels on which an image is drawn nH x nV,
On the high-density plane, the center and radius of the circle of the emitted light are obtained. The rear focal plane microscopic ellipsometer according to any one of claims 1 to 6, wherein: Defining concentric sectors defined by an incident angle range (θ ₁ , θ ₂ ) and an azimuth angle range (φ ₁ , φ ₂ ) in the rear focal plane on the high-density plane;
The number of pixels at least part of which belongs to a sector is n (n is a natural number), the number of small pixels belonging to the i-th pixel P _i is q _i, and the light intensity of the pixel P _i is I _i . When
Average light intensity I _av of the sector
The rear focal plane microscopic ellipsometer according to any one of claims 1 to 7, characterized in that: The incident angle is between 0 ° and the maximum angle determined by the numerical aperture of the objective lens, the width is in the range of 0.5-2 °, and the azimuth is any angle φ _a to φ _a + 180 ° and φ _a In 2n sectors on the back focal plane defined by dividing each by n equal intervals from + 180 ° to φ _a + 360 °, the average of the normalized light intensity is obtained,
Using the azimuth angle dependence of the light intensity distribution on the rear focal plane, and assuming that the number of ellipsometric parameters obtained by one calculation is k, from the average of the light intensity of 2n sectors, the DC component, and 9. The back focal plane according to claim 1, wherein a cosine component or a sine component of the second or fourth harmonic of the azimuth change is calculated, and k ellipsometric parameters are obtained. Microscopic ellipsometer. The incident angle is an arbitrary region between 0 ° and the maximum angle determined by the numerical aperture of the objective lens, and is divided into m ranges at intervals of 0.5 to 2 °.
In each incident angle range, divide the azimuth angle to define 2n sectors and obtain k ellipsometric parameters,
Based on the ellipsometric parameters of a total of km with different incident angles, i is a number indicating the incident angle, j is a number indicating the type of ellipsometric parameter, and y _ij is the (i, j) th polarization. And y ' _ij is the (i, j) ellipsometric parameter obtained by calculation from the optical constant and film thickness of the sample, and σ _ij is the standard deviation of the (i, j) th ellipsometric parameter and when,
10. The back focal plane microscopic ellipsometer according to claim 1, wherein the optical constant and the film thickness of the sample are determined so that the parameter χ ² represented by Divide the incident angle and azimuth angle to define 2mn sectors and obtain km ellipsometric parameters,
Based on the measured values of a total of km ellipsometric parameters with different incident angles, i is a number indicating the incident angle, j is a number indicating the type of ellipsometric parameter, and y _ij is (i, j) The measured value of the ellipsometric parameter, _y'ij is the (i, j) th ellipsometric parameter obtained from the optical constant and film thickness of the sample, and _σij is the (i, j) th polarized light the standard deviation of the analysis parameters, y _'j is the calculated value of the j-th type of ellipsometric parameters, the y _"j is the calculated value in consideration of the influence of the j-th type of objective lens of ellipsometric parameters, f _j Is a function specific to the eleventh type of ellipsometric parameters representing the influence of the objective lens, θ is the incident angle,
further,
The back focal plane microscopic ellipsometer according to any one of claims 1 to 10, wherein the optical constant, the film thickness, and k functions of the sample are obtained so that the parameter χ ² represented by