JP2018132467A - Error correction method and two-dimensional polarization analysis method, as well as error correction device and two-dimensional polarization analysis device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an error correction method and two-dimensional polarization analysis method, as well as an error correction device and two-dimensional polarization analysis device for quickly and highly accurately measuring a change in polarization state of reflection light of a measurement object by a single time two-dimensional measurement.SOLUTION: An error correction method includes: a light intensity measurement step of irradiating a measurement object with optically modulated light with respective conditions of a polarizer and phase element changed, receiving, by light reception means, a two-dimensional image of the light reflected from the measurement object and passing through an analyzer, and obtaining light intensity for each pixel of the two-dimensional image; and an error calculation step of, when a manufacturing error of retardation of the phase element, an initial error of a principal-axis azimuth of the phase element, and an initial error of a transmission-axis azimuth of the polarizer are present, obtaining light intensity for each pixel of the two-dimensional image in a state corrected based on these errors, and obtaining, from results of these light intensity, a manufacturing error of the retardation of the phase element, an initial error of the principal-axis azimuth of the phase element, and an initial error of the transmission-axis azimuth of the polarizer.SELECTED DRAWING: Figure 2

Description

  The present invention relates to an error correction method, a two-dimensional ellipsometry, an error correction device, and a two-dimensional ellipsometer.

  Ellipsometry is applied in a wide range of fields from semiconductor measurement to biotechnology. For example, HORIBA, Ltd. (see Non-Patent Document 1), SENTTECH (Germany) (see Non-Patent Document 2), ACCURION (Germany) (See Non-Patent Document 3), J. A. Domestic and foreign companies such as WOOLAM (see Non-Patent Document 4) are actively developing and marketing ellipsometers.

  Most of the ellipsometers currently on the market are for point measurement. In this point measurement, only one point of the measurement object can be measured in one measurement. For this reason, in order to obtain two-dimensional information, a mapping method is used in which point measurement is performed while scanning a measurement object, and then measurement results are mapped. However, the mapping method takes time to measure and the resolution is limited by the beam diameter of the probe light, so the maximum resolution is about 50 μm.

  The only imaging ellipsometer that is currently in practical use is the Null method of the German company Accurion. In the Null method, it is necessary to rotate the phase shifter and the polarizer little by little to obtain the position where the light intensity becomes zero or the minimum value. For this reason, the highest resolution of the Null method is as high as 1 μm, but it takes a very long time to measure, so it is not used for point measurement. Even when the Null method is used for an imaging ellipsometer, two-dimensional information cannot be obtained by one measurement, and it is necessary to perform a huge number of measurements depending on the surface state of the measurement object.

One of the main reasons for limiting the practical application of the imaging ellipsometer is that there are manufacturing errors and alignment errors in the polarizing element used in the ellipsometer. In the case of point measurement, since the probe light always passes through the center of the polarizing element, the manufacturing error of the retardation of the phase shifter may be considered to be constant, but in the case of two-dimensional measurement, the manufacturing error of the retardation of the phase shifter is Present for each location. Therefore, in order to realize highly accurate and quantitative two-dimensional measurement, it is necessary to correct all errors.
Furthermore, in the case of two-dimensional measurement, the signal processing for each pixel of the two-dimensional image received by the light receiving means requires calculation processing several hundred thousand to several million times that in the case of point measurement. However, it is very difficult to put an imaging ellipsometer into practical use.

http://www.horiba.com/jp/thin-film-metrology/ http://www.sentech.com/en/Home__2235/ http://www.accurion.com/solutions-for-science https://www.jawoollam.com/

  An object of the present invention is to solve the above-described problems and achieve the following objects. That is, the present invention provides an error correction method, a two-dimensional ellipsometry method, an error correction apparatus, two An object is to provide a two-dimensional ellipsometer.

The error correction method of the present invention as a means for solving the above-described problems is to irradiate a measurement object with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and reflect the light from the measurement object to detect it. A light intensity measuring step of receiving a two-dimensional image of the light that has passed through the photon by a light receiving means and obtaining a light intensity for each pixel of the two-dimensional image;
When there is a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, each pixel of the two-dimensional image is corrected with these errors. An error calculation step for obtaining a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, from the results of these light intensities, including.

The error correction method irradiates a measurement object with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and receives a two-dimensional image of light reflected from the measurement object and passed through the analyzer. A light intensity measurement step for obtaining a light intensity I for each pixel of the two-dimensional image represented by the following mathematical formula (1):
When there is a manufacturing error ε _δ of retardation of the phaser, an initial error ε _Q of the main axis direction of the phaser, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ , the ε _Q , and by the epsilon _P, equation (1) is corrected by the following equation (2), preferably contains, said epsilon _[delta], the error calculation step of obtaining the epsilon _Q, and the epsilon _P from the equation (2) .

[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).

[Formula (2)]
However, in said Numerical formula (2), a, b, (delta), (theta) _Q , (theta) _P , N, C, and S represent the same meaning as the said Numerical formula (1). epsilon _[delta] represents a manufacturing error of retardation of retarder. ε _Q represents the initial error of the principal axis orientation of the phaser. ε _P represents the initial error of the transmission axis orientation of the polarizer.

The error correction apparatus according to the present invention irradiates a measurement object with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and reflects a two-dimensional image of the light reflected from the measurement object and passed through the analyzer. A light intensity measuring means that receives light by a light receiving means and obtains a light intensity for each pixel of the two-dimensional image;
When there is a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, each pixel of the two-dimensional image is corrected with these errors. An error calculating means for obtaining a retardation error of the phase shifter, an initial error of the main axis direction of the phase shifter, and an initial error of the transmission axis direction of the polarizer from the results of the light intensity; Have

The error correction device irradiates a measurement object with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and receives a two-dimensional image of light reflected from the measurement object and passed through the analyzer. A light intensity measuring means for obtaining a light intensity I for each pixel of the two-dimensional image represented by the mathematical formula (1);
When there is a manufacturing error ε _δ of retardation of the phaser, an initial error ε _Q of the main axis direction of the phaser, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ , the ε _Q , and by the epsilon _P, the corrected equation (1) into equation (2) preferably has, with the epsilon _[delta], error calculating means for obtaining the epsilon _Q, and the epsilon _P from said equation (2) .

  According to the present invention, the above-described problems can be solved and the above-described object can be achieved, and the change in the polarization state of the reflected light of the measurement object can be measured quickly and accurately by a single two-dimensional measurement. Error correction method and two-dimensional ellipsometry, error correction apparatus and two-dimensional ellipsometry apparatus can be provided.

FIG. 1 is a schematic diagram showing the polarization state of light. FIG. 2 is a schematic view showing an example of a reflection type two-dimensional ellipsometer used in the present invention. FIG. 3 is a schematic diagram showing an example of a transmission type two-dimensional ellipsometer used in the present invention. FIG. 4 is a flowchart of the error correction method according to the first embodiment. FIG. 5 is a flowchart of the error correction method according to the second embodiment. FIG. 6 is a flowchart in the two-dimensional ellipsometry of the first embodiment. FIG. 7 is a flowchart in the two-dimensional ellipsometry of the second embodiment. FIG. 8 is a flowchart in the two-dimensional ellipsometry of the third embodiment. FIG. 9 is a flowchart in the two-dimensional ellipsometry of the fourth embodiment. FIG. 10 is a flowchart in the two-dimensional ellipsometry of the fifth embodiment. FIG. 11 is a diagram illustrating the results of measuring the PSI (Ψ) and the phase difference DEL (Δ) of Example 4. FIG. 12 is a diagram illustrating the results of measuring the PSI (Ψ) and the phase difference DEL (Δ) of Example 5.

(Error correction method and error correction apparatus)
The error correction method of the present invention includes a light intensity measurement step and an error calculation step, and further includes other steps as necessary.

  The error correction apparatus of the present invention includes a light intensity measurement unit and an error calculation unit, and further includes other units as necessary.

  The error correction method of the present invention can be suitably implemented by the error correction apparatus of the present invention, the light intensity measurement step can be performed by the light intensity measurement means, and the error calculation step is performed by the error calculation means. The other steps can be performed by the other means.

<Light intensity measuring step and light intensity measuring means>
The light intensity measurement step irradiates a measurement object with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and receives a two-dimensional image of light reflected from the measurement object and passed through the analyzer. This is a step of receiving light by the means and obtaining the light intensity for each pixel of the two-dimensional image, and can be carried out by the light intensity measuring means.
The light intensity measurement step irradiates a measurement object with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and receives a two-dimensional image of light reflected from the measurement object and passed through the analyzer. Preferably, the step of receiving light by the means and obtaining the light intensity I for each pixel of the two-dimensional image represented by the following mathematical formula (1).

[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).

-Measurement object-
The measurement object is not particularly limited as long as it has a small surface roughness and can be measured by oblique incidence, and is used in a wide range of fields from semiconductor measurement to biotechnology, for example, semiconductor substrates, thin films, and gate insulation. Films, lithography films, etc .; polymer films in the chemical field, self-assembled films, proteins, DNA; TFT films for displays, transparent conductive films, organic LEDs, etc .; various dielectric films for antireflection, phase changes such as CD and DVD Materials, magneto-optic films; real-time observation of chemical vapor deposition (CVD), plasma CVD, molecular beam epitaxy (MBE), etching, oxidation / heat treatment, solution processing, thin film formation process, and the like.
The standard sample as the measurement object is a stable substance with known N, C, and S, and examples thereof include a silicon substrate and a silicon substrate with a uniform silicon oxide (SiO ₂ ) film.

-Two-dimensional ellipsometer-
The two-dimensional measurement of the light intensity is performed using a two-dimensional ellipsometer. The reflection type two-dimensional ellipsometer that measures the change in the polarization state (DEL (Δ), PSI (Ψ)) of the measurement object is also called an imaging ellipsometer, and includes a light source, a polarizer, , A phaser, an analyzer, and a light receiving means, and other means as necessary.
In the transmission type two-dimensional ellipsometer, there is no object to be measured (air), and the light source, the polarizing element, and the light receiving means are arranged in parallel.

-Light source-
The light source is preferably a parallel light source, and examples thereof include lasers, deuterium (D ₂ ) lamps, xenon (Xe) lamps, halogen lamps, global lamps, and combinations thereof.

-Polarizer (analyzer)-
The polarizer is usually installed in front of a light source and used to extract linearly polarized light from a non-polarized light source.
The analyzer is placed in front of the light receiving means, and the polarization state is determined from the light intensity passing through the analyzer.
The polarizer and the analyzer are the same polarizing element, but are called differently because they have different roles.
As the polarizer (or analyzer), a CaCO ₃ crystal prism (Grant Taylor prism) called calcite is used. The calcite is a uniaxial crystal because it exhibits optical anisotropy only in the vertical direction.
The Grand Taylor prism has a structure in which two prisms are combined, and only linearly polarized light is extracted from non-polarized light from a light source. When only linearly polarized light in the x-axis direction passes, this x-axis is called the transmission axis. That is, the transmission axis direction of the polarizer means the direction of the transmission axis.

--- Phaser--
The phaser is also called a compensator or a phase shifter, and is installed behind the polarizer or in front of the analyzer, and is used to convert linearly polarized light into elliptically polarized light. Similar to the polarizer, the phase shifter utilizes the anisotropy of the refractive index, and is basically composed only of a cubic birefringent crystal.
When the 45 ° linearly polarized light is converted into counterclockwise circularly polarized light by the phaser, if the refractive index is anisotropic, the fast axis light travels relatively fast and the slow axis travels slowly. . Therefore, when 45-degree linearly polarized light is incident on the phase shifter, a phase difference (retardation) δ is generated in the x and y components of the light emitted from the phase shifter. This phase difference (retardation) δ is expressed by the following equation.
δ = 2π / λ | n _e −n ₀ | d (where, d represents the thickness of the retarder)
As can be seen from the above equation, δ changes as the wavelength of the incident light changes. When the phase is shifted by λ / 4 with respect to the wavelength as in the case of δ = π / 2, the phaser is also called a λ / 4 wavelength plate.
The main axis direction of the phaser is the direction of the fast axis of the phaser in the s, p coordinate system (there is a slow axis perpendicular to the fast axis).
As the phase shifter, for example, MgF ₂ or mica is used.

--Reception means--
The light receiving means is capable of receiving the intensity of light that has passed through the analyzer, and an element having a plurality of light receiving units is used. Among these, an imaging element that can acquire a two-dimensional image composed of a plurality of pixels is preferably used. . Examples of the image pickup device include a charge coupled device (CCD), a complementary metal oxide semiconductor (CMOS), and a gate CCD.

-Other means-
There is no restriction | limiting in particular as said other means, According to the objective, it can select suitably, For example, a control means etc. are mentioned.

Ellipsometry (polarimetric analysis) is a method for obtaining the thickness, refractive index, etc. of the thin film of the measurement object from the phenomenon that the polarization state of incident light changes due to the reflection of the surface of the measurement object. A measurement system using ellipsometry is called an ellipsometer.
Light is an electromagnetic wave, and its electric field vector oscillates perpendicular to the traveling direction of the light. Light is classified into non-polarized light whose field vector oscillation is random and regular polarized light. In polarized light, the locus of the tip of the electric field vector draws a straight line, a circle, and an ellipse in a plane perpendicular to the light traveling direction, and such light is called linearly polarized light, circularly polarized light, and elliptically polarized light, respectively. ing.

  As shown in FIG. 1, linearly polarized light whose electric field oscillates parallel to the incident surface is called p-polarized light, and linearly polarized light whose electric field oscillates perpendicularly to the incident surface is called s-polarized light. p-polarized light and s-polarized light have different amplitude reflection coefficients. Therefore, the amplitude and phase of each of the p and s polarized components change greatly due to reflection on the surface of the measurement object. In ellipsometry, DEL (Δ) and PSI (Ψ), which represent the phase difference and amplitude ratio of p and s-polarized light after reflection in terms of angle, are determined.

  The change in the polarization state of the reflected light is represented by the Stokes vector S in the following mathematical formula (a). When the Stokes vector S is used, all polarization states can be displayed.

[Formula (a)]
However, in the mathematical formula (a), S ₀ represents the incident light intensity. S ₁ represents the light intensity I _x indicated by the linearly polarized light in the x direction minus the light intensity I _y in the y direction. S ₂ represents the light intensity I _{+ 45 °} of linearly polarized light in the + 45 ° direction minus the light intensity I _{−45 °} in the −45 ° direction. S ₃ shows what the intensity I _R of the right-handed circularly polarized light by subtracting the light intensity I _L of the left-handed circularly polarized light. T represents a transposed matrix.

The Stokes vector S _in of incident light (natural light, non-polarized light) from the light source is expressed by the following mathematical formula (b).

[Formula (b)]
In the mathematical formula (b), T represents a transposed matrix.

Here, there is a Mueller matrix as a quantity indicating the interaction between light and a measurement object (object or substance).
The Mueller matrix is a 4 × 4 matrix, and its 16 elements differ depending on the measurement object.
In the following, the Mueller matrix of the polarizer (or analyzer) is represented by the following formula (c), the Mueller matrix of the phase shifter (compensator) is represented by the following formula (d), and the Mueller matrix of the measurement object is represented by the following formula (e). Each is shown.

[Formula (c): Mueller matrix of polarizer (or analyzer): M _P (θ _P )]
However, in the mathematical formula (c), θ _p is the transmission axis direction of the polarizer.

[Formula (d): Mueller matrix of phaser: M _R (δ, θ)]
In the mathematical formula (d), δ is retardation of the retarder, and θ is the principal axis direction of the retarder.

[Formula (e): Mueller matrix of measurement object: M _S ]
In Equation (e), Ψ represents a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ represents a phase difference between s-polarized light and p-polarized light.

  Therefore, in the ellipsometry, N (= cos 2 Ψ), C (= sin 2 Ψ cos Δ), and S (= sin 2 Ψ sin Δ) are measured to obtain the PSI (Ψ) and DEL (Δ) of the measurement object. Can do.

In the reflection-type two-dimensional polarization analyzer 100 shown in FIG. 2, the incident light L _in the light source 2 passes through the polarizer 3, and the phase shifter 4 is reflected by the measuring object 1 surface, the reflected light L _out is After passing through the analyzer 5, the light is received by the light receiving means 6.
In the present invention, in order to measure N (= cos 2 Ψ), C (= sin 2 Ψ cos Δ), and S (= sin 2 Ψ sin Δ) of the measurement object 1, the transmission axis direction of the analyzer 5 is set to 45 ° (π / 4). The Stokes vector S _out of the light (reflected light) reflected from the measurement object 1 by irradiating the measurement object 1 with light that is fixed and light-modulated by changing the respective conditions of the polarizer 3 and the phase shifter 4 is as follows. It is expressed by the formula (f).
Examples of the conditions include rotation and alignment of polarizing elements (polarizers and phase shifters).

[Formula (f)]
In the equation (f), M _P (45 °) is the Mueller matrix of the analyzer with the transmission axis direction fixed at 45 °, M _S is the Mueller matrix of the measurement object, and M _R (δ, θ _Q ) Is the Mueller matrix of the phase shifter, M _P (θ _P ) is the Mueller matrix of the polarizer, and (1, 0, 0, 0) is the Stokes vector S _in of the incident light from the light source. T represents a transposed matrix.

In Stokes vector S _out of the reflected light of the equation (f), is only S ₀ component of the Stokes vector S _out of the emitted light can be detected from the light receiving means 6. Therefore, the light intensity I for each pixel of the two-dimensional image received by the light receiving means 6 is expressed by the following formula (1).

[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).

Here, the retardation δ of the phase shifter in the formula (1) is ideally 90 °, but the retardation δ of the phase shifter always has a manufacturing error that occurs when the phase shifter is manufactured. The manufacturing error of the retardation of the phase shifter varies depending on the location of the phase shifter.
Further, the polarizer and the retarder when rotating respectively, the initial error of the principal axis directions theta _Q retarder as alignment errors, initial error of the transmission axis azimuth theta _P of the polarizer necessarily occur.
Therefore, if the manufacturing error of retardation of the phaser is ε _δ , the initial error of the main axis direction of the phaser is ε _Q , and the initial error of the transmission axis direction of the polarizer is ε _P , the equation (1) is It becomes complicated as shown in the following formula (2).

[Formula (2)]
However, in said Numerical formula (2), a, b, (delta), (theta) _Q , (theta) _P , N, C, and S represent the same meaning as the said Numerical formula (1). epsilon _[delta] represents a manufacturing error of retardation of retarder. ε _Q represents the initial error of the principal axis orientation of the phaser. ε _P represents the initial error of the transmission axis orientation of the polarizer.

<Error calculation process and error calculation means>
In the error calculation step, when there is a retardation manufacturing error, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, the error is corrected with these errors. The light intensity for each pixel of the two-dimensional image is obtained, and from the results of these light intensities, the production error of the retardation of the phaser, the initial error of the main axis direction of the phaser, and the initial error of the transmission axis direction of the polarizer are calculated. This is a step of obtaining, and can be performed by error calculation means.
In the error calculation step, when there is a manufacturing error ε _δ of retardation of the phase shifter, an initial error ε _Q of the main axis direction of the phase shifter, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ the epsilon _Q and, by the epsilon _P, equation (1) is corrected to the equation (2), the epsilon _[delta], the epsilon _Q, and it is preferable to obtain the epsilon _P.

In Equation (2), there are eight unknown parameters, a, b, N, C, S, ε _δ , ε _Q , and ε _P , and these eight unknown parameters are at least eight simultaneous equations. Can be obtained by solving
Therefore, as will be described in detail below, when the main axis azimuth θ _{Q of the} retarder is 0 and π / 4, the polarizer is transmitted through the transmission axis azimuth θ _P = 0, π / 2, π / 4 of the polarizer. Or by rotating each to −π / 4, and receiving the eight two-dimensional images at the respective rotation angles by the light receiving means, and solving eight simultaneous equations corresponding to the obtained eight two-dimensional images. All of the eight unknown parameters can be obtained.

(A) When the main axis azimuth θ _{Q of the} retarder is 0, when the polarizer is rotated to the transmission axis azimuth θ _P = 0 or π / 2 of the polarizer, the formula (2) is expressed by the following formula: (3)

[Formula (3)]
However, in said Numerical formula (3), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (3), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.

(B) When the main axis azimuth θ _{Q of the} retarder is 0, when the polarizer is rotated to the transmission axis azimuth θ _P = π / 4 or −π / 4 of the polarizer, the equation (2) is The following formula (4) is obtained.

[Formula (4)]
However, in said Numerical formula (4), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (4), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.

(C) When the main axis azimuth θ _{Q of the} retarder is π / 4, when the polarizer is rotated to the transmission axis azimuth θ _P = 0 or π / 2 of the polarizer, The following formula (5) is obtained. In the above formula (5), since the phase shifter rotates from 0 to π / 4, the production error ε _δ of retardation of the phase shifter becomes ε ′ _δ .

[Formula (5)]
However, in the formula (5), a, b, ε _Q , ε _P , N, C, and S have the same meaning as the formula (1) and the formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said Equation (5), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.

(D) When the main axis azimuth θ _{Q of the} phase shifter is π / 4, when the polarizer is rotated to the transmission axis azimuth θ _P = π / 4 or −π / 4 of the polarizer, ) Becomes the following formula (6). In the equation (6), since the phase shifter rotates from 0 to π / 4, the retardation production error ε _δ becomes ε ′ _δ .

[Formula (6)]
However, in said Numerical formula (6), a, b, (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said equation (6), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.

Next, in the above formula (3), the following formula (7) can be derived by taking the difference when the transmission axis direction θ _P of the polarizer is 0 and π / 2. In the mathematical formula (7), the unknown parameter b is removed, and the influence of the dark current of the light receiving means (imaging device) can be removed.

[Formula (7)]
However, in said Numerical formula (7), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).

In Equation (7), when the retardation retardation production error ε _δ , the phaser principal axis orientation initial error ε _Q , and the polarizer transmission axis orientation initial error ε _P are known (for example, the second time At the time of subsequent measurement, etc., the ε _δ , the ε _Q , and the ε _P are substituted into the equation (7) to obtain the following equation (7 ′).

[Formula (7 ')]
However, e ₁₁ to e ₁₃ of the formula (7 ') in are as follows.

Next, in Equation (4), the following equation (8) is obtained by taking the difference when the transmission axis direction θ _P of the polarizer is π / 4 and −π / 4. In the formula (8), the unknown parameter b is removed, and the influence of the dark current of the light receiving means (imaging device) can be removed.

[Formula (8)]
However, in said Numerical formula (8), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).

In the equation (6), the retardation error manufacturing error ε _δ , the phaser principal axis orientation initial error ε _Q , and the polarizer transmission axis orientation initial error ε _P are known (for example, the second and subsequent measurements). by the time when, or the like), the epsilon _[delta], the epsilon _Q, and by substituting the epsilon _P in equation (8), the following equation (8 ').

[Formula (8 ')]
However, e ₂₁ to e ₂₃ of the formula (8 ') in are as follows.

Next, in Equation (5), the following equation (9) is obtained by taking the difference when the transmission axis direction θ _P of the polarizer is 0 and π / 2. According to the equation (9), the unknown parameter b is removed, and the influence of the dark current of the light receiving means (imaging device) can be removed.

[Formula (9)]
However, in the formula (9), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).

In the above formula (9), the retardation retardation manufacturing error ε ′ _δ , the phaser principal axis orientation initial error ε _Q , and the polarizer transmission axis orientation initial error ε _P are known (for example, the second and subsequent times). (When measuring, etc.), the ε _δ , the ε _Q , and the ε _P are substituted into the equation (9) to obtain the following equation (9 ′).

[Formula (9 ')]
However, e ₃₁ to e ₃₃ of the formula (9 ') in are as follows.

Next, when the difference between the image signals when the transmission axis direction θ _P of the polarizer is π / 4 and −π / 4 in the equation (6), the following equation (10) is obtained. In the formula (10), the unknown parameter b is removed, and the influence of the dark current of the light receiving means (imaging device) can be removed.

[Formula (10)]
However, in the formula (10), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).

In the above formula (10), the retardation retardation manufacturing error ε ′ _δ , the phaser principal axis orientation initial error ε _Q , and the polarizer transmission axis orientation initial error ε _P are known (for example, the second and subsequent times). (When measuring, etc.), the ε _δ , the ε _Q , and the ε _P are substituted into the equation (10) to obtain the following equation (10 ′).

[Formula (10 ')]
However, e ₄₁ to e ₄₃ in said formula (10 ') are as follows.

As described above, in the mathematical formulas (7) to (10) derived from the mathematical formula (2), when the principal axis orientation θ _Q of the phase shifter is 0 and π / 4, the central portion of the two-dimensional image is the optical axis (phase The manufacturing error ε _δ and ε ′ _δ of the retardation of the phase shifter do not change before and after the rotation of the phase shifter. However, in the portions other than the central portion of the two-dimensional image, the retardation of the phase shifter varies depending on the location of the phase shifter. Therefore, the retardation manufacturing errors ε _δ and ε ′ _δ before and after the rotation of the phase shifter are different. Although different, the initial error ε _Q of the main axis orientation of the retarder and the initial error ε _P of the transmission axis orientation of the polarizer are the same.
Therefore, in the above formulas (7) to (10), the parameters that need to be corrected are retardation retardation manufacturing errors ε _δ , ε ′ _δ , phase shift principal axis orientation initial error ε _Q , and polarizer transmission. This is the initial error ε _P of the axial direction.

<Other processes and other means>
There is no restriction | limiting in particular as said other process, According to the objective, it can select suitably, For example, a control process, a memory | storage process, etc. are mentioned.
There is no restriction | limiting in particular as said other means, According to the objective, it can select suitably, For example, a control means, a memory | storage means, etc. are mentioned.

  The control means includes, for example, a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), a main memory, etc., and a control program for controlling the operation of the entire error correction apparatus. Various processes are executed based on this.

  The storage means is not particularly limited as long as various kinds of information can be stored, and can be appropriately selected according to the purpose. For example, the storage means may be a solid state drive, a hard disk drive, a CD (Compact Disc) drive, a DVD (Digital Versatile). Disc) drive, BD (Blu-ray (registered trademark) Disc) drive, and the like. The storage unit may be a part of a cloud that is a group of computers on the network.

  Here, the first and second embodiments of the error correction method of the present invention will be described in detail with reference to flowcharts.

[Error Correction Method of First Embodiment]
The error correction method according to the first embodiment obtains the ε _δ , ε ′ _δ , the ε _Q , and the ε _P in the equations (7) to (10) according to the flowchart shown in FIG. is there.

First, in step S101, the transmission type two-dimensional ellipsometer 101 as shown in FIG. 3 is used, and when the principal axis orientation θ _Q of the phase shifter is 0 and π / 4 by measurement in the air, the polarizer is moved. By rotating the polarizer to the transmission axis orientation θ _P = 0, π / 2, π / 4, or −π / 4, and receiving eight two-dimensional images at the respective rotation angles by the light receiving means. When the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10) that are the differences between them are obtained, the process proceeds to step S102. Note that N, C, and S of air are 0, 1, and 0, respectively.

Next, in step S102, using the mathematical formulas (7) to (10), from the signal of the pixel at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , An initial error ε _Q of the main axis direction and an initial error ε _P of the transmission axis direction of the polarizer are obtained. The portions other than the central portion of the two-dimensional image are different from the central portion of the two-dimensional image in ε _δ and ε ′ _δ, but ε _Q and ε _P are the same. Therefore, by substituting ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image into the equations (7) to (10), the retardation of the portion other than the center of the image is manufactured. When the errors ε _δ and ε ′ _δ are obtained, this processing is terminated.
As described above, ε _δ , ε ′ _δ , ε _Q , and ε _P in the formulas (7) to (10) can all be obtained.

[Error Correction Method of Second Embodiment]
The error correction method of the second embodiment is to obtain the ε _δ , ε ′ _δ , the ε _Q , and the ε _P in the equations (7) to (10) according to the flowchart shown in FIG. is there.

First, in step S201, a reflective two-dimensional ellipsometer 100 as shown in FIG. 2 is used. When the main axis orientation θ _Q of the phase shifter is 0 and π / 4 with respect to a standard sample, the polarizer is moved to the polarizer. By rotating the transmission axis azimuth θ _P = 0, π / 2, π / 4, or −π / 4, and receiving the two-dimensional images of the eight standard samples at the respective rotation angles, When the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10) which are the differences between them are obtained, the process proceeds to step 202. The standard samples N, C, and S are known.

Next, in step S202, using the equations (7) to (10), from the signal of the pixel in the center of the two-dimensional image, the retardation error of the phase shifter ε _δ = ε ′ _δ , An initial error ε _Q of the main axis direction and an initial error ε _P of the transmission axis direction of the polarizer are obtained. The portions other than the central portion of the two-dimensional image are different from the central portion of the two-dimensional image in ε _δ and ε ′ _δ, but ε _Q and ε _P are the same. Therefore, by substituting ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image into the equations (7) to (10), ε _δ of the portion other than the center of the two-dimensional image, When obtaining the epsilon _'[delta], this processing is completed.
As described above, ε _δ , ε ′ _δ , ε _Q , and ε _P in the formulas (7) to (10) can all be obtained.

  As described above, the error correction method and the error correction apparatus of the present invention are for measuring the change in the polarization state of the reflected light of the measurement object quickly and accurately by one two-dimensional measurement, For example, it is used for ellipsometry for point measurement, two-dimensional ellipsometry, and the like, but is particularly preferably used for the following two-dimensional ellipsometry and two-dimensional ellipsometer of the present invention.

(Two-dimensional ellipsometry and two-dimensional ellipsometer)
The two-dimensional ellipsometry of the present invention is characterized by using the error correction method of the present invention.
The two-dimensional ellipsometer of the present invention has the error correction apparatus of the present invention.

  The control performed by each means in the two-dimensional ellipsometry apparatus of the present invention is synonymous with the implementation of the two-dimensional ellipsometry method of the present invention, and the two-dimensional ellipsometry method of the present invention is the two-dimensional ellipsometry method of the present invention. Since the apparatus can be suitably implemented, the details of the two-dimensional ellipsometer of the present invention will be clarified through the description of the two-dimensional ellipsometry of the present invention.

The two-dimensional ellipsometry of the present invention is a two-dimensional ellipsometry using the error correction method of the present invention in the 1-1 form,
According to the measurement in air in the transmission mode, when the main axis orientation θ _{Q of the} phase shifter is 0 and π / 4, the polarizer is set to the transmission axis orientation θ _P = 0, π / 2, π / 4 of the polarizer. Or by rotating each to −π / 4, and receiving the two two-dimensional images at the respective rotation angles by the light receiving means, the following mathematical formulas (3) to (6) are obtained, and these are the differences between them. Steps for obtaining the following mathematical formulas (7) to (10) (where N, C, and S of air are 0, 1, and 0, respectively);
Using the equations (7) to (10), from the pixel signal at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , the initial error of the principal axis orientation of the phaser ε _Q and an initial error ε _P of the transmission axis direction of the polarizer are obtained, and the ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image are expressed by the equations (7) to (7) 10) to obtain ε _δ and ε ′ _δ of the portion other than the central portion of the two-dimensional image, and the ε _δ , ε ′ _δ , ε _Q , And obtaining ε _P ;
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Alternatively, by rotating each to −π / 4 and receiving eight two-dimensional images at the respective rotation angles, the following mathematical formulas (3) to (6) are obtained, and the following mathematical formula (7) that is the difference between them is obtained. A process for obtaining (10);
The mathematical expressions (7) to (10) obtained from the measurement object include the production errors ε _δ and ε ′ _δ of the retardation of the phaser obtained by the error correction method of the present invention, and the principal axis orientation of the phaser. Substituting the initial error ε _Q and the initial error ε _P of the transmission axis direction of the polarizer to obtain N, C, and S of the measurement object, and further including other steps as necessary Including.

The two-dimensional ellipsometry of the present invention is a two-dimensional ellipsometry using the error correction method of the present invention in the 1-2 type,
When the main axis azimuth θ _{Q of the} phase shifter is 0 and π / 4 by measurement of a standard sample in the reflection mode, the polarizer is transmitted through the transmission axis azimuth θ _P = 0, π / 2, π / 4 of the polarizer. , Or by rotating each to −π / 4, and receiving the two-dimensional images of the eight standard samples at the respective rotation angles to obtain the following formulas (3) to (6), which are the differences between them. Steps for obtaining the following mathematical formulas (7) to (10) (N, C, and S of the standard sample are known);
Using the equations (7) to (10), from the pixel signal at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , the initial error of the principal axis orientation of the phaser ε _Q and an initial error ε _P of the transmission axis direction of the polarizer are obtained, and the ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image are expressed by the equations (7) to (10). ) To obtain ε _δ , ε ′ _δ of the portion other than the center portion of the two-dimensional image, and the ε _δ , ε ′ _δ , ε _Q , and obtaining ε _P ;
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Alternatively, by rotating each to −π / 4 and receiving eight two-dimensional images at the respective rotation angles, the following mathematical formulas (3) to (6) are obtained, and the following mathematical formula (7) that is the difference between them is obtained. A process for obtaining (10);
The mathematical expressions (7) to (10) obtained from the measurement object include the production errors ε _δ and ε ′ _δ of the retardation of the phaser obtained by the error correction method of the present invention, and the principal axis orientation of the phaser. Substituting the initial error ε _Q and the initial error ε _P of the transmission axis direction of the polarizer to obtain N, C, and S of the measurement object, and further including other steps as necessary Including.

In the second embodiment, the two-dimensional ellipsometry of the present invention is a two-dimensional ellipsometry using the error correction method of the present invention,
According to the measurement in air in the transmission mode, when the main axis orientation θ _{Q of the} phase shifter is 0 and π / 4, the polarizer is set to the transmission axis orientation θ _P = 0, π / 2, π / 4 of the polarizer. Or by rotating each to −π / 4, and receiving the two two-dimensional images at the respective rotation angles by the light receiving means, the following mathematical formulas (3) to (6) are obtained, and these are the differences between them. Steps for obtaining the following mathematical formulas (7) to (10) (where N, C, and S of air are 0, 1, and 0, respectively);
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Alternatively, by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the following mathematical formulas (3) to (6) are obtained, and these are the differences. Obtaining the following mathematical formulas (7) to (10);
Using the mathematical formulas (7) to (10) in the air and the mathematical formulas (7) to (10) in the measurement object, the retardation production error ε _δ , ε ′ _δ , An initial error ε _Q of the main axis direction of the phase shifter, an initial error ε _P of the transmission axis direction of the polarizer, and N, C, and S of the measurement object, and further, if necessary Including other processes.

In the third embodiment, the two-dimensional ellipsometry of the present invention is a two-dimensional ellipsometry using the error correction method of the present invention,
According to the measurement of the standard sample in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is transmitted through the transmission axis direction θ _P = 0, π / 2, π / 4, or The following mathematical formulas (3) to (6) are obtained by rotating each to −π / 4 and receiving the two-dimensional images of the eight standard samples at the respective rotational angles, and the following mathematical formula that is the difference between them. (7) to (10) steps for obtaining (note that N, C, and S of the standard sample are known);
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Alternatively, by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the following mathematical formulas (3) to (6) are obtained, and these are the differences. Obtaining the following mathematical formulas (7) to (10);
Using the mathematical formulas (7) to (10) in the standard sample and the mathematical formulas (7) to (10) in the measurement object, the manufacturing error ε _δ , ε ′ _δ of retardation of the phase shifter, An initial error ε _Q of the main axis direction of the phase shifter, an initial error ε _P of the transmission axis direction of the polarizer, and N, C, and S of the measurement object, and further, if necessary Including other processes.

  In the two-dimensional ellipsometry of the first to third embodiments, the mathematical formulas (3) to (10) are as follows, and these are the methods described in the error correction method of the present invention. Can be derived.

[Formula (3)]
However, in said Numerical formula (3), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (3), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.

[Formula (4)]
However, in said Numerical formula (4), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (4), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.

[Formula (5)]
However, in the formula (5), a, b, ε _Q , ε _P , N, C, and S have the same meaning as the formula (1) and the formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said Equation (5), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.

[Formula (6)]
However, in said Numerical formula (6), a, b, (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said equation (6), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.

[Formula (7)]
However, in said Numerical formula (7), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).

[Formula (8)]
However, in said Numerical formula (8), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).

[Formula (9)]
However, in the formula (9), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).

[Formula (10)]
However, in the formula (10), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).

  In the two-dimensional ellipsometry of the first to third aspects of the present invention, N, C, and S of the obtained measurement object are substituted into the following mathematical formulas (11) and (12), and It is preferable to include a step of obtaining Ψ and a phase difference Δ representing the amplitude ratio of the p and s components of the emitted light for each pixel of the two-dimensional image of the measurement object as an angle. Thereby, PSI (Ψ) and DEL (Δ) of the measurement object can be obtained from N, C, and S of the measurement object obtained in each form.

[Formula (11)]

[Formula (12)]

In the fourth embodiment, the two-dimensional ellipsometry of the present invention, in the fourth embodiment, is a manufacturing error ε _δ , ε of retardation of the retardation obtained by the error correction method of the present invention or the two-dimensional ellipsometry of the present invention. ' _δ , the initial error ε _Q of the main axis direction of the phase shifter, and the initial error ε _P of the transmission axis direction of the polarizer are substituted into the formulas (7) to (10), and the following formulas (7 ′) to ( 10 ′), and
The following mathematical formula (13) or (13 ′), mathematical formula (14) or (14 ′), and mathematical formula (15) or (15 ′) are derived from the mathematical formulas (7 ′) to (10 ′), and the measurement target Determining the aN, aC, and aS of the object, and further including other steps as necessary.
The formulas (13) to (15) are derived from I ₁ (the formula (7)), I ₂ (the formula (8)), and I ₄ (the formula (10)).
The equations (13 ′) to (15 ′) are equations derived from I ₁ (the equation (7)), I ₃ (the equation (9)), and I ₄ (the equation (10)).

As described above, according to the two-dimensional ellipsometry of the fourth embodiment, the retardation retardation manufacturing errors ε _δ , ε ′ _δ , the initial error ε _Q of the principal axis direction of the retarder, and the transmission axis of the polarizer When the initial error ε _{P of the} azimuth is known (for example, in the case of the second and subsequent measurements), the ε _δ , ε ′ _δ , the ε _Q , and the From ε _P , aN, aC, and aS can be obtained.

[Formula (7 ')]
However, e ₁₁ to e ₁₃ of the formula (7 ') in are as follows.

[Formula (8 ')]
However, e ₂₁ to e ₂₃ of the formula (8 ') in are as follows.

[Formula (9 ')]
However, e ₃₁ to e ₃₃ of the formula (9 ') in are as follows.

[Formula (10 ')]
However, e ₄₁ to e ₄₃ in said formula (10 ') are as follows.

[Formula (13)]
[Formula (13 ')]
However, e _{11 to} e ₄₃ in the formulas (13) and (13 ′) have the same meaning as the formulas (7 ′) to (10 ′).

[Formula (14)]
[Formula (14 ')]
However, e _{11 to} e ₄₃ in the formulas (14) and (14 ′) have the same meaning as the formulas (7 ′) to (10 ′).

[Formula (15)]
[Formula (15 ')]
However, e _{11 to} e ₄₃ in the formulas (15) and (15 ′) represent the same meanings as the formulas (7 ′) to (10 ′).

  In the four-dimensional ellipsometry of the fourth embodiment, the obtained aN, aC, and aS of the measurement object are substituted into the following mathematical formulas (16) and (17), and the two-dimensional analysis of the measurement object is performed. It is preferable to include a step of obtaining Ψ and a phase difference Δ that express the amplitude ratio of the p and s components of the emitted light for each pixel of the image as an angle.

[Formula (16)]

[Formula (17)]

  Here, the two-dimensional ellipsometry of the first to fifth embodiments will be described in detail with reference to the flowcharts shown in FIGS.

[Two-dimensional ellipsometry of the first embodiment]
In the two-dimensional ellipsometry of the first embodiment, the polarization state change of the measurement object is measured according to the flowchart shown in FIG.

First, in step S301, when the transmission type two-dimensional ellipsometer 101 as shown in FIG. 3 is used and the principal axis direction θ _Q of the phase shifter is 0 and π / 4 by measurement in the air, the polarizer is moved. By rotating the polarizer to the transmission axis orientation θ _P = 0, π / 2, π / 4, or −π / 4, and receiving eight two-dimensional images at the respective rotation angles by the light receiving means. When the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10) which are the differences between them are obtained, the process proceeds to step S302. Note that N, C, and S of air are 0, 1, and 0, respectively.

Next, in step S302, using the mathematical formulas (7) to (10), from the signal of the pixel at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , An initial error ε _Q of the main axis direction and an initial error ε _P of the transmission axis direction of the polarizer are obtained. The portions other than the central portion of the two-dimensional image are different from the central portion of the two-dimensional image in ε _δ and ε ′ _δ, but ε _Q and ε _P are the same. Therefore, by substituting ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image into the equations (7) to (10), the retardation of the portion other than the center of the image is manufactured. Errors ε _δ and ε ′ _δ are obtained. As described above, when ε _δ , ε ′ _δ , ε _Q , and ε _P in the equations (7) to (10) are obtained, the process proceeds to step S303. Steps S301 to S302 are the same as the error correction method of the first embodiment shown in the flowchart of FIG.

Next, in step S303, the reflection type two-dimensional ellipsometer 100 as shown in FIG. 2 is used. When the main axis orientation θ _Q of the phase shifter is 0 and π / 4, Rotating the transmission axis direction of the polarizer θ _P = 0, π / 2, π / 4, or −π / 4, respectively, and receiving two-dimensional images of the eight measurement objects at the respective rotation angles Thus, when the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10) that are the differences between them are obtained, the process proceeds to step S304.

Next, in step (S3-4), the equations (7) to (10) for the measurement object are changed to the equations ε _δ and ε determined by the equations (7) to (10) in the air. 'After substituting _δ , ε _Q , and ε _P to determine N, C, and S of the measurement object, the process proceeds to step S305.

  Next, in step S305, from the obtained N, C, and S of the measurement object, p, of the emitted light for each pixel of the two-dimensional image of the measurement object, according to the equations (11) and (12). When the PSI (ψ) and the phase difference DEL (Δ), which represent the amplitude ratio of the s component as an angle, are obtained, this processing is terminated.

[Two-dimensional ellipsometry of the second embodiment]
In the two-dimensional ellipsometry of the second embodiment, the change in the polarization state of the measurement object is measured according to the flowchart shown in FIG. This second embodiment is an effective method because it can be used for point measurement by a simple reflection type using a standard sample without having to perform measurement with a transmission type.

First, in step S401, the reflection type two-dimensional ellipsometer 100 as shown in FIG. 2 is used. When the main axis orientation θ _Q of the phase shifter is 0 and π / 4 with respect to the standard sample, the polarizer is moved to the polarizer. The transmission axis direction θ _{P is} rotated to 0, π / 2, π / 4, or −π / 4, respectively, and two-dimensional images of the eight standard samples at the respective rotation angles are received. When the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10), which are the differences between them, are obtained, the process proceeds to step S402. The standard samples N, C, and S are known.

Next, in step S402, using the mathematical formulas (7) to (10), from the signal of the pixel at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , An initial error ε _Q of the main axis direction and an initial error ε _P of the transmission axis direction of the polarizer are obtained. The portions other than the central portion of the two-dimensional image are different from the central portion of the two-dimensional image in ε _δ and ε ′ _δ, but ε _Q and ε _P are the same. Therefore, by substituting ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image into the equations (7) to (10), ε _δ of the portion other than the center of the two-dimensional image, When obtaining the epsilon _'[delta], the flow goes to step S403.
As described above, ε _δ , ε ′ _δ , ε _Q , and ε _{P in the} equations (7) to (10) are obtained. Steps S401 to S402 are the same as the error correction method of the second embodiment shown in the flowchart of FIG.

Next, in step S403, when the reflection type two-dimensional ellipsometry apparatus 100 shown in FIG. 2 is used and the main axis direction θ _Q of the phase shifter is 0 and π / 4 with respect to the measurement object, the polarizer is the polarizer. By rotating the transmission axis directions θ _P = 0, π / 2, π / 4, or −π / 4, respectively, and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, When the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10) which are the differences between them are obtained, the process proceeds to step S404.

Next, in step S404, the equations (7) to (10) obtained from the measurement object are replaced with the ε _δ , ε ′ _δ obtained by the equations (7) to (10) in the air, When ε _Q and ε _P are substituted to determine N, C, and S of the measurement object, the process proceeds to step S405.

  Next, in step S405, from the obtained N, C, and S of the measurement object, in the same manner as in the first embodiment of the two-dimensional ellipsometry, for each pixel of the two-dimensional image of the measurement object. When the PSI (Ψ) and the phase difference DEL (Δ) that express the amplitude ratio of the p and s components of the emitted light in terms of angle are obtained, this processing is terminated.

[Two-dimensional ellipsometry of the third embodiment]
In the two-dimensional ellipsometry of the third embodiment, the change in the polarization state of the measurement object is measured according to the flowchart shown in FIG.

First, in step S501, a transmission type two-dimensional ellipsometer 101 as shown in FIG. 3 is used. When the principal axis orientation θ _Q of the phase shifter is 0 and π / 4 in the air, the polarizer is moved to the polarizer. The transmission axis direction θ _{P is} rotated to 0, π / 2, π / 4, or −π / 4, respectively, and eight image signals are received, and the equations (3) to (6) are obtained. When the mathematical expressions (7) to (10) that are the differences are obtained, the process proceeds to step S502. Note that N, C, and S of air are 0, 1, and 0, respectively.

  Next, in step S502, the reflection type two-dimensional ellipsometer 100 as shown in FIG. 2 is used to receive eight image signals of the measurement object in the same manner as in the air, and the mathematical expression (3) After obtaining (6) and obtaining the mathematical expressions (7) to (10) which are the differences between them, the process proceeds to step S503.

Next, in step S503, the retardation of the phase shifter is produced using the equations (7) to (10) in the air and the equations (7) to (10) in the measurement object. When ε _δ , ε ′ _δ , the initial error ε _Q of the principal axis direction of the phase shifter, the initial error ε _P of the transmission axis direction of the polarizer, and N, C, and S of the measurement object are determined, Goes to step S504. Steps S501 to S503 can be the error correction method according to the third embodiment of the present invention.

  Next, in step S504, from the obtained measurement object N, C, and S, in the same manner as in the first embodiment of the two-dimensional ellipsometry, according to the equations (11) and (12), When the PSI (Ψ) and the phase difference DEL (Δ) that represent the amplitude ratio of the p and s components of the emitted light for each pixel of the two-dimensional image of the measurement object as an angle are obtained, this process ends.

[Two-dimensional ellipsometry of the fourth embodiment]
In the two-dimensional ellipsometry of the fourth embodiment, the change in the polarization state of the measurement object is measured according to the flowchart shown in FIG. In the fourth embodiment, the transmission type does not need to be measured and is a simple reflection type using a standard sample. The retardation retardation manufacturing errors ε _δ , ε ′ _δ , and the initial axis orientation of the phase shifter Since the error ε _Q , the initial error ε _P of the transmission axis direction of the polarizer, and the N, C, and S of the measurement object can be quickly determined at once, it is extremely practical.

First, in step S601, a reflective two-dimensional ellipsometer 100 as shown in FIG. 2 is used, and with respect to a standard sample, when the main axis orientation of the phase shifter is θ _Q = 0 and π / 4, the polarizer is the polarizer. The transmission axis direction θ _{P is} rotated to 0, π / 2, π / 4, or −π / 4, respectively, and two-dimensional images of the eight standard samples at the respective rotation angles are received. When the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10), which are the differences between them, are obtained, the process proceeds to step S602. The standard samples N, C, and S are known.

Next, in step S602, the reflection type two-dimensional ellipsometry apparatus 100 as shown in FIG. 2 is used, and when the measurement object is the main axis orientation of the phase shifter θ _Q = 0 and π / 4, Rotating the transmission axis direction of the polarizer θ _P = 0, π / 2, π / 4, or −π / 4, respectively, and receiving two-dimensional images of the eight measurement objects at the respective rotation angles Thus, when the mathematical formulas (3) to (6) are obtained and the mathematical formulas (7) to (10) which are the differences between them are obtained, the process proceeds to step S603.

Next, in step S603, using the mathematical formulas (7) to (10) in the standard sample and the mathematical formulas (7) to (10) in the measurement object, a manufacturing error of retardation of the phase shifter. When ε _δ , ε ′ _δ , the initial error ε _Q of the principal axis direction of the phase shifter, the initial error ε _P of the transmission axis direction of the polarizer, and N, C, and S of the measurement object are determined, Goes to step S604. Steps S601 to S603 can be the fourth embodiment of the error correction method of the present invention.

  Next, in step S604, the two-dimensional image of the measurement object is obtained from the obtained measurement object N, C, and S according to the mathematical expressions (11) and (12) in the same manner as in the first embodiment. When the PSI (Ψ) and the phase difference DEL (Δ) that express the amplitude ratio of the p and s components of the emitted light for each pixel in terms of angle are obtained, this processing is completed.

[Two-dimensional ellipsometry of the fifth embodiment]
In the two-dimensional ellipsometry of the fifth embodiment, the change in the polarization state of the measurement object is measured according to the flowchart shown in FIG. In this fifth embodiment, when the retardation retardation manufacturing errors ε _δ , ε ′ _δ , the phaser principal axis orientation initial error ε _Q , and the polarizer transmission axis orientation initial error ε _P are known. In (for example, the second and subsequent measurements), the aN, aC, and aS of the measurement object can be obtained more simply.

First, in step S701, the retardation error manufacturing error ε _δ , ε ′ _δ , and the initial error ε _Q of the main axis direction of the phase shifter by the error correction method of the present invention or the two-dimensional ellipsometry of the present invention. When the initial error ε _P of the transmission axis direction of the polarizer is obtained, the process proceeds to step S702.
The error correction method of the present invention includes the error correction method of the first embodiment described above or the error correction method of the second embodiment.
The two-dimensional ellipsometry of the present invention includes the two-dimensional ellipsometry of the first to fourth embodiments described above.

Next, in step S702, the ε _δ , ε ′ _δ , the ε _Q , and the ε _P are substituted into the equations (7) to (10), and the equations (7 ′) to (10 ′). ), The process proceeds to step S703.

  Next, in step S703, the following formula (13) or (13 '), formula (14) or (14'), and formula (15) or (15 ') are calculated from the formulas (7') to (10 '). ) To obtain the aN, aC, and aS of the measurement object, the process proceeds to step S704.

  Next, in step S704, the obtained aN, aC, and aS of the measurement object are substituted into the equations (16) and (17), and the output of each two-dimensional image of the measurement object is output for each pixel. When the PSI (ψ) and the phase difference DEL (Δ), which represent the amplitude ratio of the p and s components of the incident light as an angle, are obtained, this processing is terminated.

  The error correction method, the two-dimensional ellipsometry, the error correction device, and the two-dimensional ellipsometry of the present invention measure the change in the polarization state of the reflected light of the measurement object quickly and accurately by one-time two-dimensional measurement. For example, it is possible to accurately measure two-dimensional information such as the surface of the measurement object and the film thickness and refractive index of the thin film on the surface. In-situ observation in the manufacturing process such as film formation and etching is possible, and it can be used for manufacturing management and real-time measurement data collection in the manufacturing process of electronic equipment and optical equipment such as semiconductor elements and display devices. .

  Examples of the present invention will be described below, but the present invention is not limited to these examples.

(Examples 1-3)
-Simulation measurement-
As shown in Table 1, in the case where there are a retardation retardation production error ε _δ , ε ′ _δ , an initial error ε _Q of the main axis orientation of the phase retarder, and an initial error ε _P of the transmission axis orientation of the polarizer, Based on the simulation conditions, the simulation results before and after the error correction of PSI (Ψ) and DEL (Δ) of Examples 1 to 3 were obtained. The results are shown in Table 1.

-Simulation conditions-
Assuming that the value of a is 1 for the values of PSI (Ψ) and DEL (Δ) of the measurement object of 20 ° and 170 °, the errors ε _δ , ε ′ _δ , ε _Q , and ε _P are respectively In the case of the values shown in Examples 1 to 3 in Table 1, these values are substituted into the formulas (7) to (10), and the formulas (13) to (15) or the formulas are obtained from the obtained signals. Using (13 ′) to (15 ′), N, C, and S of the measurement object before and after performing error correction are obtained, and the PSI of the measurement object (16) or (17) is used. Ψ) and DEL (Δ) were obtained.
In addition, in the case before performing error correction, the results calculated using the equations (13) to (15) and the equations (13 ′) to (15 ′) are different. In the analysis results before error correction in Table 1, the values outside the parentheses are the results calculated using the equations (13) to (15), and the values in parentheses are the equations (13 ′) to (15 ′). It is the result calculated using.
In the case of error correction, the calculation results using the equations (13) to (15) and the equations (13 ′) to (15 ′) are the same.

From the results shown in Table 1, even when the measurement object is the same and the error is different, by performing error correction, accurate PSI (Ψ) and DEL (Δ) closer to the theoretical values can be obtained than before error correction. I understood it.

Example 4
-Actual measurement-
Using the two-dimensional ellipsometer 100 shown in FIG. Measurement of PSI (Ψ) and phase difference DEL (Δ), which expresses the amplitude ratio of p and s components of each pixel before and after error correction of 1 (silicon wafer with thermal oxide film, manufactured by Filtech) as an angle. did. Measurement object No. The results of PSI (Ψ) and phase difference DEL (Δ) before and after error correction of 1 are shown in FIG.

-Device contents-
・ Device name: Imaging ellipsometer (self-made)
-Light source: LED (wavelength 532 nm)
-Polarizer: manufactured by Edmund Optics-Phaser: manufactured by Edmund Optics-Analyzer: manufactured by Edmund Optics-Light receiving means: CMOS (manufactured by Edmund Optics)
Measurement area: 6.4 × 4.8 (X × Y) mm ²

-Measurement method-
Standard sample (silicon substrate) and measurement object No. 1 (a silicon wafer with a thermal oxide film, manufactured by Filtech Co., Ltd.) 8 images are captured using the CMOS, and the measurement target is measured from these images using the two-dimensional ellipsometry of the fourth embodiment. N, C, and S of the object were obtained (before error correction).

Next, in the same manner as in the flowchart of FIG. 9 (two-dimensional ellipsometry of the fourth embodiment), PSI (Ψ) and the level representing the amplitude ratio of the p and s components of the output light after error correction in angle. The phase difference DEL (Δ) was measured.
That is, when the reflection type two-dimensional ellipsometer 100 shown in FIG. 2 is used and the main axis direction θ _{Q of the} phase shifter is 0 and p / 4, the polarizer is set to have a transmission axis direction θ _P of 0, π / 2, π / 4, or −π / 4, respectively, and eight standard samples and eight measurement objects No. 1 to receive the two-dimensional image, the standard sample and the measurement object No. 1 is obtained, and the standard sample and the measurement object No. The above-mentioned mathematical formulas (7) to (10) of 1 were obtained.
A silicon substrate was used as a standard sample. N, C, and S of this standard sample were 0.653, −0.757, and 0.037.

Next, the mathematical formulas (7) to (10) in the standard sample and the measurement object No. Using the mathematical formulas (7) to (10) in FIG. 1, retardation retardation manufacturing errors ε _δ , ε ′ _δ , phaser principal axis orientation initial error ε _Q , and polarizer transmission axis orientation initial The error ε _P and the measurement object No. N, C, and S of 1 were obtained (after error correction).
The obtained measurement object No. 1 of N, C, and S, the measurement object No. The PSI (Ψ) and the phase difference DEL (Δ) in which the amplitude ratio of the p and s components of the emitted light for each pixel of one two-dimensional image is expressed as an angle.
The values of PSI (Ψ) and DEL (Δ) after error correction are around 67 ° and 175 °, respectively, and a commercially available point measurement ellipsometer (RC2 ellipsometer, JA Woollam, Co. (USA)). It was close to the value measured in.

(Example 5)
-Actual measurement-
In Example 4, the measurement object No. 1 to the measurement object No. 2 (silicon substrate), the measurement object No. for each pixel is obtained using ε _δ , ε ′ _δ , ε _Q , and ε _P obtained in Example 4 and the equations (13) to (15). The PSI (Ψ) and the phase difference DEL (Δ), in which the amplitude ratio of the p and s components of the emitted light 2 was expressed as an angle, were measured. Measurement object No. The results of PSI (Ψ) and phase difference DEL (Δ) before and after error correction of 2 are shown in FIG.
The values of PSI (Ψ) and DEL (Δ) after error correction were around 24 ° and 177 °, respectively, and were close to the values measured with the same commercially available point measuring ellipsometer as in Example 4.

Aspects of the present invention are as follows, for example.
<1> Light that is light-modulated by changing the conditions of the polarizer and the phase shifter is applied to the measurement object, and a two-dimensional image of the light reflected from the measurement object and passed through the analyzer is received by the light receiving means. A light intensity measuring step for obtaining a light intensity for each pixel of the two-dimensional image;
When there is a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, each pixel of the two-dimensional image is corrected with these errors. An error calculation step for obtaining a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, from the results of these light intensities,
It is an error correction method characterized by including this.
<2> Light that is light-modulated by changing the conditions of the polarizer and the phase shifter is applied to the object to be measured, and a two-dimensional image of the light reflected from the object to be measured and passed through the analyzer is received by the light receiving means. A light intensity measuring step for obtaining a light intensity I for each pixel of the two-dimensional image represented by the following formula (1):
When there is a manufacturing error ε _δ of retardation of the phaser, an initial error ε _Q of the main axis direction of the phaser, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ , the ε _Q , and by the epsilon _P, equation (1) is corrected by the following equation (2), an error calculation step of obtaining the epsilon _[delta], the epsilon _Q, and the epsilon _P from the equation (2),
The error correction method according to <1>, including:
[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).
[Formula (2)]
However, in said Numerical formula (2), a, b, (delta), (theta) _Q , (theta) _P , N, C, and S represent the same meaning as the said Numerical formula (1). epsilon _[delta] represents a manufacturing error of retardation of retarder. ε _Q represents the initial error of the principal axis orientation of the phaser. ε _P represents the initial error of the transmission axis orientation of the polarizer.
<3> In an error calculation step of obtaining the ε _δ , the ε _Q , and the ε _P from the mathematical formula (2),
When the main axis azimuth θ _{Q of the} retarder is 0 and π / 4, the polarizer is rotated to the transmission axis azimuth θ _P = 0, π / 2, π / 4, or −π / 4 of the polarizer, respectively. The error correction method according to <2>, in which the following two equations (3) to (6) are obtained from the equation (2) by receiving eight two-dimensional images at respective rotation angles with the light receiving unit. It is.
[Formula (3)]
However, in said Numerical formula (3), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (3), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.
[Formula (4)]
However, in said Numerical formula (4), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (4), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.
[Formula (5)]
However, in the formula (5), a, b, ε _Q , ε _P , N, C, and S have the same meaning as the formula (1) and the formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said Equation (5), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.
[Formula (6)]
However, in said Numerical formula (6), a, b, (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said equation (6), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.
<4> In the equations (3) and (5), the difference between the transmission axis azimuth θ _P of the polarizer being 0 and π / 2 is taken, and the following equations (7) and (9) are derived,
In the equations (4) and (6), the following equations (8) and (10) are derived by taking the difference when the transmission axis direction θ _P of the polarizer is π / 4 and −π / 4. The error correction method according to <3>.
[Formula (7)]
However, in said Numerical formula (7), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).
[Formula (8)]
However, in said Numerical formula (8), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).
[Formula (9)]
However, in the formula (9), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).
[Formula (10)]
However, in the formula (10), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).
<5> A process for obtaining ε _δ , ε ′ _δ , ε _Q , and ε _P from the equations (7) to (10),
According to the measurement in air in the transmission mode, when the main axis orientation θ _{Q of the} phase shifter is 0 and π / 4, the polarizer is set to the transmission axis orientation θ _P = 0, π / 2, π / 4 of the polarizer. , Or −π / 4, and the two light images at the respective rotation angles are received by the light receiving means to obtain the equations (3) to (6), which are the differences between them. Processing for obtaining the mathematical formulas (7) to (10);
Using the equations (7) to (10), from the pixel signal at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , the initial error of the principal axis orientation of the phaser ε _Q and an initial error ε _P of the transmission axis direction of the polarizer are obtained, and the ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image are expressed by the equations (7) to (7) 10) to obtain ε _δ and ε ′ _δ of the portion other than the central portion of the two-dimensional image, and the ε _δ , ε ′ _δ , ε _Q , And obtaining ε _P ;
The error correction method according to <4>, including:
<6> A process for obtaining the ε _δ , ε ′ _δ , the ε _Q , and the ε _P from the mathematical formulas (7) to (10),
When the main axis azimuth θ _{Q of the} phase shifter is 0 and π / 4 by measurement of a standard sample in the reflection mode, the polarizer is transmitted through the transmission axis azimuth θ _P = 0, π / 2, π / 4 of the polarizer. Or π / 4, respectively, and receiving the two-dimensional images of the eight standard samples at the respective rotation angles to obtain the equations (3) to (6), which are the differences between them. Processing for obtaining the mathematical formulas (7) to (10);
Using the equations (7) to (10), from the pixel signal at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , the initial error of the principal axis orientation of the phaser ε _Q and an initial error ε _P of the transmission axis direction of the polarizer are obtained, and the ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image are expressed by the equations (7) to (10). ) To obtain ε _δ , ε ′ _δ of the portion other than the center portion of the two-dimensional image, and the ε _δ , ε ′ _δ , ε _Q , and processing to obtain ε _P ;
The error correction method according to <4>, including:
<7> A two-dimensional ellipsometry method using the error correction method according to any one of <1> to <6>.
<8> A two-dimensional ellipsometry using the error correction method according to any one of <5> to <6>,
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Or by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the equations (3) to (6) are obtained, and these are the differences. Obtaining the mathematical formulas (7) to (10);
The mathematical expressions (7) to (10) obtained from the measurement object include the retardation error ε _δ and ε ′ _δ of the retardation of the phase shifter, the initial error ε _Q of the principal axis direction of the phase shifter, and the polarizer Substituting an initial error ε _P of the transmission axis direction to determine N, C, and S of the measurement object;
It is the two-dimensional ellipsometry as described in said <7> containing.
<9> A two-dimensional ellipsometry using the error correction method according to <4>,
According to the measurement in air in the transmission mode, when the main axis orientation θ _{Q of the} phase shifter is 0 and π / 4, the polarizer is set to the transmission axis orientation θ _P = 0, π / 2, π / 4 of the polarizer. , Or −π / 4, and the two light images at the respective rotation angles are received by the light receiving means to obtain the equations (3) to (6), which are the differences between them. Obtaining the mathematical formulas (7) to (10);
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Or by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the equations (3) to (6) are obtained, and these are the differences. Obtaining the mathematical formulas (7) to (10);
Using the mathematical formulas (7) to (10) in the air and the mathematical formulas (7) to (10) in the measurement object, the retardation production error ε _δ , ε ′ _δ , Obtaining an initial error ε _Q of the main axis orientation of the phaser, an initial error ε _P of the transmission axis orientation of the polarizer, and N, C, and S of the measurement object;
It is the two-dimensional ellipsometry as described in said <7> containing.
<10> A two-dimensional ellipsometry using the error correction method according to <4>,
According to the measurement of the standard sample in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is transmitted through the transmission axis direction θ _P = 0, π / 2, π / 4, or The formulas (3) to (6) are obtained by rotating each to −π / 4 and receiving the two-dimensional images of the eight standard samples at the respective rotation angles. Obtaining (7) to (10);
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Or by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the equations (3) to (6) are obtained, and these are the differences. Obtaining the mathematical formulas (7) to (10);
Using the mathematical formulas (7) to (10) in the standard sample and the mathematical formulas (7) to (10) in the measurement object, the manufacturing error ε _δ , ε ′ _δ of retardation of the phase shifter, Obtaining an initial error ε _Q of the main axis orientation of the phaser, an initial error ε _P of the transmission axis orientation of the polarizer, and N, C, and S of the measurement object;
It is the two-dimensional ellipsometry as described in said <7> containing.
<11> Substituting N, C, and S of the obtained measurement object into the following mathematical formulas (11) and (12), p of the emitted light for each pixel of the two-dimensional image of the measurement object, The two-dimensional ellipsometry method according to any one of <8> to <10>, including a step of obtaining Ψ and a phase difference Δ in which the amplitude ratio of the s component is expressed by an angle.
[Formula (11)]
[Formula (12)]
<12> Retardation of the retardation obtained by the error correction method according to any one of <5> to <6> or the two-dimensional ellipsometry according to any one of <8> to <10> Substituting the production errors ε _δ , ε ′ _δ , the initial error ε _Q of the principal axis direction of the phase shifter, and the initial error ε _P of the transmission axis direction of the polarizer into the formulas (7) to (10), Obtaining formulas (7 ′) to (10 ′);
The following mathematical formula (13) or (13 ′), mathematical formula (14) or (14 ′), and mathematical formula (15) or (15 ′) are derived from the mathematical formulas (7 ′) to (10 ′), and the measurement target Determining aN, aC, and aS of the object;
It is a two-dimensional ellipsometry characterized by including.
[Formula (7 ')]
However, e ₁₁ to e ₁₃ of the formula (7 ') in are as follows.
[Formula (8 ')]
However, e ₂₁ to e ₂₃ of the formula (8 ') in are as follows.
[Formula (9 ')]
However, e ₃₁ to e ₃₃ of the formula (9 ') in are as follows.
[Formula (10 ')]
However, e ₄₁ to e ₄₃ in said formula (10 ') are as follows.
[Formula (13)]
[Formula (13 ')]
However, e _{11 to} e ₄₃ in the formulas (13) and (13 ′) have the same meaning as the formulas (7 ′) to (10 ′).
[Formula (14)]
[Formula (14 ')]
However, e _{11 to} e ₄₃ in the formulas (14) and (14 ′) have the same meaning as the formulas (7 ′) to (10 ′).
[Formula (15)]
[Formula (15 ')]
However, e _{11 to} e ₄₃ in the formulas (15) and (15 ′) represent the same meanings as the formulas (7 ′) to (10 ′).
<13> Substituting the obtained aN, aC, and aS of the measurement object into the following mathematical formulas (16) and (17), p of the emitted light for each pixel of the two-dimensional image of the measurement object, The two-dimensional ellipsometry method according to <12>, including a step of obtaining Ψ and a phase difference Δ in which the amplitude ratio of the s component is expressed as an angle.
[Formula (16)]
[Formula (17)]
<14> Light that is light-modulated by changing the conditions of the polarizer and the phase shifter is applied to the measurement object, and a two-dimensional image of the light reflected from the measurement object and passed through the analyzer is received by the light receiving means. A light intensity measuring means for obtaining a light intensity for each pixel of the two-dimensional image;
When there is a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, each pixel of the two-dimensional image is corrected with these errors. An error calculating means for obtaining a retardation error of the phase shifter, an initial error of the main axis direction of the phase shifter, and an initial error of the transmission axis direction of the polarizer from the results of the light intensity;
It is an error correction apparatus characterized by having.
<15> Light that is light-modulated by changing the conditions of the polarizer and the phase shifter is applied to the measurement object, and a two-dimensional image of the light reflected from the measurement object and passed through the analyzer is received by the light receiving means. A light intensity measuring means for obtaining a light intensity I for each pixel of the two-dimensional image represented by the following formula (1):
When there is a manufacturing error ε _δ of retardation of the phaser, an initial error ε _Q of the main axis direction of the phaser, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ , the ε _Q , and by the epsilon _P, equation (1) is corrected by the following equation (2), an error calculation means for obtaining the epsilon _[delta], the epsilon _Q, and the epsilon _P from said equation (2),
It is an error correction apparatus as described in said <14> which has.
[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).
[Formula (2)]
However, in said Numerical formula (2), a, b, (delta), (theta) _Q , (theta) _P , N, C, and S represent the same meaning as the said Numerical formula (1). epsilon _[delta] represents a manufacturing error of retardation of retarder. ε _Q represents the initial error of the principal axis orientation of the phaser. ε _P represents the initial error of the transmission axis orientation of the polarizer.
<16> A two-dimensional ellipsometer comprising the error correction device according to any one of <14> to <15>.

  The error correction method according to any one of <1> to <6>, the two-dimensional ellipsometry method according to any one of <7> to <13>, and any one of <14> to <15>. According to the error correction apparatus described in the above and the two-dimensional ellipsometric analysis apparatus described in <16>, it is possible to solve the conventional problems and achieve the object of the present invention.

DESCRIPTION OF SYMBOLS 1 Measurement object 2 Light source 3 Polarizer 4 Phaser 5 Analyzer 6 Light-receiving means 100 Reflective type two-dimensional ellipsometer 101 Transmission type two-dimensional ellipsometer L _in incident light L _out outgoing light

Claims (16)

Irradiating the object to be measured with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and receiving a two-dimensional image of the light reflected from the object to be measured and passed through the analyzer by the light receiving means, A light intensity measurement step for determining the light intensity for each pixel of the two-dimensional image;
When there is a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, each pixel of the two-dimensional image is corrected with these errors. An error calculation step for obtaining a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, from the results of these light intensities,
An error correction method comprising: The measurement object is irradiated with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and a two-dimensional image of light reflected from the measurement object and passed through the analyzer is received by the light receiving means. A light intensity measurement step for obtaining a light intensity I for each pixel of the two-dimensional image represented by the mathematical formula (1);
When there is a manufacturing error ε _δ of retardation of the phaser, an initial error ε _Q of the main axis direction of the phaser, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ , the ε _Q , and by the epsilon _P, equation (1) is corrected by the following equation (2), an error calculation step of obtaining the epsilon _[delta], the epsilon _Q, and the epsilon _P from the equation (2),
The error correction method according to claim 1, comprising:
[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).
[Formula (2)]
However, in said Numerical formula (2), a, b, (delta), (theta) _Q , (theta) _P , N, C, and S represent the same meaning as the said Numerical formula (1). epsilon _[delta] represents a manufacturing error of retardation of retarder. ε _Q represents the initial error of the principal axis orientation of the phaser. ε _P represents the initial error of the transmission axis orientation of the polarizer. In the error calculation step of obtaining the ε _δ , the ε _Q , and the ε _P from the formula (2),
When the main axis azimuth θ _{Q of the} retarder is 0 and π / 4, the polarizer is rotated to the transmission axis azimuth θ _P = 0, π / 2, π / 4, or −π / 4 of the polarizer, respectively. The error correction method according to claim 2, wherein the following mathematical formulas (3) to (6) are obtained from the mathematical formula (2) by receiving eight two-dimensional images at respective rotation angles with the light receiving means.
[Formula (3)]
However, in said Numerical formula (3), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (3), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.
[Formula (4)]
However, in said Numerical formula (4), a, b, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ± of the equation (4), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code.
[Formula (5)]
However, in the formula (5), a, b, ε _Q , ε _P , N, C, and S have the same meaning as the formula (1) and the formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said Equation (5), when the transmission axis azimuth theta _P of the polarizer is 0 + code, transmission axes theta _P of the polarizer when the [pi / 2 - a code.
[Formula (6)]
However, in said Numerical formula (6), a, b, (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2). ε ′ _δ represents a manufacturing error of retardation of the retarder when the main axis direction θ _{Q of the} retarder is rotated by π / 4. ± in said equation (6), when the transmission axis azimuth theta _P of the polarizer is [pi / 4 + code, when the transmission axis azimuth theta _P of the polarizer is - [pi] / 4 - a code. In the equations (3) and (5), the difference when the transmission axis direction θ _P of the polarizer is 0 and π / 2 is taken, and the following equations (7) and (9) are derived,
In the equations (4) and (6), the following equations (8) and (10) are derived by taking the difference when the transmission axis direction θ _P of the polarizer is π / 4 and −π / 4. The error correction method according to claim 3.
[Formula (7)]
However, in said Numerical formula (7), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).
[Formula (8)]
However, in said Numerical formula (8), a, (epsilon) _delta , (epsilon) _Q , (epsilon) _P , N, C, and S represent the same meaning as the said Numerical formula (1) and the said Numerical formula (2).
[Formula (9)]
However, in the formula (9), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6).
[Formula (10)]
However, in the formula (10), a, ε ′ _δ , ε _Q , ε _P , N, C, and S are the formula (1), the formula (2), the formula (5), and the formula. It represents the same meaning as (6). From the equations (7) to (10), a process for obtaining the ε _δ , ε ′ _δ , the ε _Q , and the ε _P ,
According to the measurement in air in the transmission mode, when the main axis orientation θ _{Q of the} phase shifter is 0 and π / 4, the polarizer is set to the transmission axis orientation θ _P = 0, π / 2, π / 4 of the polarizer. , Or −π / 4, and the two light images at the respective rotation angles are received by the light receiving means to obtain the equations (3) to (6), which are the differences between them. Processing for obtaining the mathematical formulas (7) to (10);
Using the equations (7) to (10), from the pixel signal at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , the initial error of the principal axis orientation of the phaser ε _Q and an initial error ε _P of the transmission axis direction of the polarizer are obtained, and the ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image are expressed by the equations (7) to (7) 10) to obtain ε _δ and ε ′ _δ of the portion other than the central portion of the two-dimensional image, and the ε _δ , ε ′ _δ , ε _Q , And obtaining ε _P ;
The error correction method according to claim 4, comprising: From the equations (7) to (10), a process for obtaining the ε _δ , ε ′ _δ , the ε _Q , and the ε _P ,
When the main axis azimuth θ _{Q of the} phase shifter is 0 and π / 4 by measurement of a standard sample in the reflection mode, the polarizer is transmitted through the transmission axis azimuth θ _P = 0, π / 2, π / 4 of the polarizer. Or π / 4, respectively, and receiving the two-dimensional images of the eight standard samples at the respective rotation angles to obtain the equations (3) to (6), which are the differences between them. Processing for obtaining the mathematical formulas (7) to (10);
Using the equations (7) to (10), from the pixel signal at the center of the two-dimensional image, the retardation production error ε _δ = ε ′ _δ , the initial error of the principal axis orientation of the phaser ε _Q and an initial error ε _P of the transmission axis direction of the polarizer are obtained, and the ε _Q and ε _P obtained from the signal of the pixel at the center of the two-dimensional image are expressed by the equations (7) to (10). ) To obtain ε _δ , ε ′ _δ of the portion other than the center portion of the two-dimensional image, and the ε _δ , ε ′ _δ , ε _Q , and processing to obtain ε _P ;
The error correction method according to claim 4, comprising:   A two-dimensional ellipsometry using the error correction method according to claim 1. A two-dimensional ellipsometry using the error correction method according to any one of claims 5 to 6,
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Or by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the equations (3) to (6) are obtained, and these are the differences. Obtaining the mathematical formulas (7) to (10);
The mathematical expressions (7) to (10) obtained from the measurement object include the retardation error ε _δ and ε ′ _δ of the retardation of the phase shifter, the initial error ε _Q of the principal axis direction of the phase shifter, and the polarizer Substituting an initial error ε _P of the transmission axis direction to determine N, C, and S of the measurement object;
The two-dimensional ellipsometry method according to claim 7 including: A two-dimensional ellipsometry using the error correction method according to claim 4,
According to the measurement in air in the transmission mode, when the main axis orientation θ _{Q of the} phase shifter is 0 and π / 4, the polarizer is set to the transmission axis orientation θ _P = 0, π / 2, π / 4 of the polarizer. , Or −π / 4, and the two light images at the respective rotation angles are received by the light receiving means to obtain the equations (3) to (6), which are the differences between them. Obtaining the mathematical formulas (7) to (10);
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Or by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the equations (3) to (6) are obtained, and these are the differences. Obtaining the mathematical formulas (7) to (10);
Using the mathematical formulas (7) to (10) in the air and the mathematical formulas (7) to (10) in the measurement object, the retardation production error ε _δ , ε ′ _δ , Obtaining an initial error ε _Q of the main axis orientation of the phaser, an initial error ε _P of the transmission axis orientation of the polarizer, and N, C, and S of the measurement object;
The two-dimensional ellipsometry method according to claim 7 including: A two-dimensional ellipsometry using the error correction method according to claim 4,
According to the measurement of the standard sample in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is transmitted through the transmission axis direction θ _P = 0, π / 2, π / 4, or The formulas (3) to (6) are obtained by rotating each to −π / 4 and receiving the two-dimensional images of the eight standard samples at the respective rotation angles. Obtaining (7) to (10);
By measuring the measurement object in the reflection mode, when the main axis direction θ _Q of the phase shifter is 0 and π / 4, the polarizer is moved to the transmission axis direction θ _P = 0, π / 2, π / 4, Or by rotating each to −π / 4 and receiving the two-dimensional images of the eight measurement objects at the respective rotation angles, the equations (3) to (6) are obtained, and these are the differences. Obtaining the mathematical formulas (7) to (10);
Using the mathematical formulas (7) to (10) in the standard sample and the mathematical formulas (7) to (10) in the measurement object, the manufacturing error ε _δ , ε ′ _δ of retardation of the phase shifter, Obtaining an initial error ε _Q of the main axis orientation of the phaser, an initial error ε _P of the transmission axis orientation of the polarizer, and N, C, and S of the measurement object;
The two-dimensional ellipsometry method according to claim 7 including: By substituting N, C, and S of the obtained measurement object into the following formulas (11) and (12), the p and s components of the emitted light for each pixel of the two-dimensional image of the measurement object The two-dimensional ellipsometry according to any one of claims 8 to 10, further comprising a step of obtaining Ψ and a phase difference Δ in which the amplitude ratio is expressed by an angle.
[Formula (11)]
[Formula (12)]
Manufacturing errors ε _δ , ε ′ _δ of retardation of the obtained phase shifter by the error correction method according to claim 5 or the two-dimensional ellipsometry according to claim 8. Substituting the initial error ε _Q of the main axis direction of the phase shifter and the initial error ε _P of the transmission axis direction of the polarizer into the formulas (7) to (10), the following formulas (7 ′) to (10 ′ )
The following mathematical formula (13) or (13 ′), mathematical formula (14) or (14 ′), and mathematical formula (15) or (15 ′) are derived from the mathematical formulas (7 ′) to (10 ′), and the measurement target Determining aN, aC, and aS of the object;
A two-dimensional ellipsometric method characterized by comprising:
[Formula (7 ')]
However, e ₁₁ to e ₁₃ of the formula (7 ') in are as follows.
[Formula (8 ')]
However, e ₂₁ to e ₂₃ of the formula (8 ') in are as follows.
[Formula (9 ')]
However, e ₃₁ to e ₃₃ of the formula (9 ') in are as follows.
[Formula (10 ')]
However, e ₄₁ to e ₄₃ in said formula (10 ') are as follows.
[Formula (13)]
[Formula (13 ')]
However, e _{11 to} e ₄₃ in the formulas (13) and (13 ′) have the same meaning as the formulas (7 ′) to (10 ′).
[Formula (14)]
[Formula (14 ')]
However, e _{11 to} e ₄₃ in the formulas (14) and (14 ′) have the same meaning as the formulas (7 ′) to (10 ′).
[Formula (15)]
[Formula (15 ')]
However, e _{11 to} e ₄₃ in the formulas (15) and (15 ′) represent the same meanings as the formulas (7 ′) to (10 ′). The obtained aN, aC, and aS of the measurement object are substituted into the following mathematical formulas (16) and (17), and the p and s components of the emitted light for each pixel of the two-dimensional image of the measurement object are calculated. The two-dimensional ellipsometric method according to claim 12, further comprising a step of obtaining Ψ and a phase difference Δ representing an amplitude ratio in angle.
[Formula (16)]
[Formula (17)]
Irradiates the measurement object with light that has been light-modulated by changing the conditions of the polarizer and the phase shifter, receives a two-dimensional image of the light reflected from the measurement object and passed through the analyzer by a light receiving means, A light intensity measuring means for obtaining a light intensity for each pixel of the two-dimensional image;
When there is a manufacturing error of retardation of the phaser, an initial error of the main axis direction of the phaser, and an initial error of the transmission axis direction of the polarizer, each pixel of the two-dimensional image is corrected with these errors. An error calculating means for obtaining a retardation error of the phase shifter, an initial error of the main axis direction of the phase shifter, and an initial error of the transmission axis direction of the polarizer from the results of the light intensity;
An error correction apparatus comprising: The measurement object is irradiated with light that is light-modulated by changing the conditions of the polarizer and the phase shifter, and a two-dimensional image of light reflected from the measurement object and passed through the analyzer is received by the light receiving means. A light intensity measuring means for obtaining a light intensity I for each pixel of the two-dimensional image represented by the mathematical formula (1);
When there is a manufacturing error ε _δ of retardation of the phaser, an initial error ε _Q of the main axis direction of the phaser, and an initial error ε _P of the transmission axis direction of the polarizer, the ε _δ , the ε _Q , and by the epsilon _P, equation (1) is corrected by the following equation (2), an error calculation means for obtaining the epsilon _[delta], the epsilon _Q, and the epsilon _P from said equation (2),
The error correction device according to claim 14, comprising:
[Formula (1)]
In Equation (1), a is an amount related to the incident light intensity, the quantum effect of the light receiving means, and the like. b is an amount indicating the influence of the dark current of the light receiving means. δ is the retardation of the retarder. θ _Q is the principal axis orientation of the phaser. θ _P is the transmission axis direction of the polarizer. N = cos2Ψ, C = sin2ΨcosΔ, S = sin2ΨsinΔ (where Ψ is a reflection amplitude ratio angle between s-polarized light and p-polarized light, and Δ is a phase difference between s-polarized light and p-polarized light).
[Formula (2)]
However, in said Numerical formula (2), a, b, (delta), (theta) _Q , (theta) _P , N, C, and S represent the same meaning as the said Numerical formula (1). epsilon _[delta] represents a manufacturing error of retardation of retarder. ε _Q represents the initial error of the principal axis orientation of the phaser. ε _P represents the initial error of the transmission axis orientation of the polarizer.   A two-dimensional ellipsometer comprising the error correction device according to claim 14.