KR102176199B1 - Ellipsometer - Google Patents

Abstract

The present invention provides an ellipsometer comprising: a short wavelength light source which irradiates incident light toward a sample; a rotating element which includes a polarizer arranged between the sample and the short wavelength light source and polarizing the incident light and an analyzer analyzing the change in a polarization state of the reflected light whose polarization state has changed as the incident light passing through the polarizer is reflected from the sample; a driving unit which rotates the polarizer or analyzer at a predetermined rotation angle; a detector which measures the intensity of the reflected light passing through the analyzer in units of lines or areas on the sample according to the change of the rotation angle; and an operation unit which calculates a characteristic value of the sample by separating the rotation variable for the rotation angle and the position variable for a position on the sample from the light intensity function of the reflected light. According to the present invention, by using a linear sensor or an area sensor as a detector, there is an effect that the characteristic value of the sample can be measured in units of lines or areas on the sample.

Description

Ellipsometer

The present invention relates to a data analysis method of an ellipse measuring instrument, and more particularly, to an ellipse measuring instrument using variable separation.

By analyzing the intensity of light reflected from a measurement specimen having a multilayer film formed on a substrate, there is an increasing demand from the industry for the analysis of the multilayer film structure of the specimen. Currently used methods are largely divided into reflection technology and elliptical polarization technology, and based on 1㎛, a reflected light meter is mainly applied to a thick film, and an ellipse meter is mainly used for a thin film. There is no distinct distinction due to thickness, and the measurement value varies greatly depending on the user's skill level and the production condition of the specimen.Since the measurement method is measured by points, a separate device is required to measure the area of the specimen. It is a situation that needs to be used additionally.

The structure of a multilayer film used in semiconductors, solar cells and LEDs, including displays, is composed of a multilayer film having a thickness of several nm to several μm. Therefore, the use of ellipsometry is prioritized over reflectometry, but the difficulty of calibration to find the initial parameters of the component and the driving error of the rotation angle of the rotating element Due to the decrease in precision due to this, the user's expertise and high analysis ability for measurement results are required.

1 is a diagram schematically showing general ellipse measuring instruments.

Referring to FIG. 1, as a general elliptic meter, a quenching ellipsometer (NE), a spectroscopic ellipsometer (SE), a rotating-polarizer ellipsometer (RPE), an analyzer circuit A typical rotating-analyzer ellipsometer (RAE) and a compensator rotating compensator ellipsomete (RCE).

Meanwhile, the conventional ellipse measurement method calculates the thickness of the thin film based on the amplitude ratio (ψ) and the phase difference (Δ) of reflected light calculated by applying the Fourier analysis method. Specifically, in the case of a polarizer rotation type elliptically polarization meter (RPE), the intensity (I) of reflected light may be defined by the following equation according to the Fourier analysis method.

<Equation>

I=Io(1+αcos(2θ-2P)+βsin(2θ-2P))

Here, the amplitude ratio (ψ) and the phase difference (Δ) of the reflected light can be calculated through the Fourier coefficients (α, β), and the thickness of the thin film can be calculated from this.

However, such a conventional method requires accurate correction of components including the initial installation angle (P) of the polarizer, and the intensity of reflected light (I) must be measured by changing the rotation angle (θ) at least three times. And, there is a problem in that it is difficult to calculate accurate Fourier coefficients (α, β) because a rotation error may occur when the rotation angle θ is changed.

Registered Patent Publication No. 10-1590389

An object of the present invention is to provide an elliptic meter capable of measuring a characteristic value of a sample in units of lines or areas on the sample using a short wavelength light source as a light source and a linear sensor or an area sensor as a detector.

An object of the present invention is to provide an ellipse measuring instrument capable of analyzing the structure of a specimen that is fast and accurate and insensitive to installation angles and rotational errors by separating variables for a rotational variable and a positional variable constituting a reflected light function.

The technical problems to be achieved in the present invention are not limited to the technical problems mentioned above, and other technical problems that are not mentioned can be clearly understood by those of ordinary skill in the technical field to which the present invention belongs from the following description. There will be.

In order to solve these problems, the present invention is a short-wavelength light source that irradiates incident light toward a sample, and a polarizer that is disposed between the sample and the short-wavelength light source and polarizes the incident light and the incident light that has passed through the polarizer is reflected from the sample. A rotating element including an analyzer that analyzes changes in the polarization state of reflected light, a driving unit that rotates the polarizer or analyzer at a predetermined rotation angle, and the intensity of the reflected light passing through the analyzer in units of lines or areas on the sample according to the change of the rotation angle It provides an ellipse measuring device including a detector to measure by and an operation unit that calculates a characteristic value of a sample by separating a rotation variable for a rotation angle and a position variable for a position on the sample in the light intensity function of reflected light.

Here, the rotating element may further include a polarizer and a compensator disposed between the sample.

In addition, the calculation unit calculates the characteristic value of the specimen in units of lines or areas.

In addition, when the intensity of the reflected light is measured in units of an area on the sample, the position variable is divided into a horizontal position variable for a horizontal position on the sample and a vertical position variable for a vertical position on the sample.

In addition, the calculation unit calculates a characteristic value of the specimen using at least one of a horizontal position variable and a vertical position variable.

In addition, the operation unit defines a light intensity function so that the rotation variable and the position variable are separated, and calculates a characteristic value of the sample based on the intensity of reflected light and the light intensity function.

In addition, the operation unit defines a rotation error function using a rotation variable as a variable based on the intensity of reflected light and the light intensity function, and a position error function using a position variable as a variable.

In addition, the operation unit calculates the rotation angle by applying the least squares method to the position error function according to the position on the sample, and applies the least squares method to the rotation error function, but applies the calculated rotation angle to the rotation variable to determine the Fourier of the light intensity function. Calculate the coefficient.

In addition, the calculation unit may place a limiting condition on the rotation variable.

In addition, the calculation unit may introduce a rotation coefficient for reflecting an effect of rotation of the rotating element on the intensity of the reflected light.

In addition, the operation unit may partially introduce a rotation coefficient for reflecting an influence of the rotation of the rotating element on the intensity of the reflected light.

According to the present invention, a short-wavelength light source is used as a light source, and a linear sensor or an area sensor is used as a detector to measure a characteristic value of a sample in units of lines or areas on the sample.

According to the present invention, by separating the variable that determines the intensity of reflected light into a rotation variable and a position variable, and estimating the rotation angle and Fourier coefficient by applying the binary least squares method by defining each error function, the sample Compared to the conventional analysis method that analyzes the characteristic value of the specimen, it is very fast and accurate, and it is possible to analyze the structure of the specimen, which is insensitive to rotational errors.

The effects obtainable in the present invention are not limited to the above-mentioned effects, and other effects not mentioned can be clearly understood by those of ordinary skill in the art from the following description. will be.

1 is a diagram schematically showing general ellipse measuring instruments.
2 is a block diagram schematically showing an ellipse measuring device according to an embodiment of the present invention.
3 is a diagram illustrating a case in which a detector is a line sensor as an ellipse measuring device according to a first embodiment of the present invention.
4 is a view for explaining a method of calculating Fourier coefficients using a rotation error function and a horizontal position error function with a limiting condition on a rotation variable in the first embodiment of the present invention.
5 is a view for explaining a method of calculating a Fourier coefficient by introducing a rotation coefficient and using a rotation error function and a horizontal position error function in the first embodiment of the present invention.
6 is a diagram illustrating a method of calculating a Fourier coefficient by partially introducing a rotation coefficient and using a rotation error function and a horizontal position error function in the first embodiment of the present invention.
7 is a diagram illustrating a case where a detector is an area sensor as an ellipse measuring device according to a second embodiment of the present invention.
8 is a view for explaining a method of calculating Fourier coefficients using a rotation error function and a vertical position error function with a limiting condition on a rotation variable in the second embodiment of the present invention.
9 is a diagram for explaining a method of calculating a Fourier coefficient by introducing a rotation coefficient and using a rotation error function and a vertical position error function in a second embodiment of the present invention.
10 is a view for explaining a method of calculating a Fourier coefficient by partially introducing a rotation coefficient and using a rotation error function and a vertical position error function in the second embodiment of the present invention.

The terms or words used in this specification and claims should not be construed as being limited to their usual or dictionary meanings, and the inventor may appropriately define the concept of terms in order to describe his own invention in the best way. It should be interpreted as a meaning and concept consistent with the technical idea of the present invention based on the principle that there is.

Therefore, the embodiments described in the present specification and the configurations shown in the drawings are only the most preferred embodiments of the present invention, and do not represent all the technical spirit of the present invention, and various equivalents that can replace them at the time of the present application And it should be understood that there may be variations.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art may easily implement the present invention.

The ellipsometer according to an embodiment of the present invention separates and defines a position variable on a sample and a rotation angle variable of a rotating element in a function of the intensity of reflected light, and introduces a linearized optimization method for each variable. By doing so, it is possible to improve the accuracy of the measured value by minimizing the influence of the error included in the initial setting value and the rotation angle of the rotation element constituting the ellipse measuring device.

2 is a block diagram schematically showing an ellipse measuring device according to an embodiment of the present invention.

As shown in Fig. 2, the ellipse meter according to the embodiment of the present invention includes a short wavelength light source 110, a polarizer 120, a compensator (not shown), an analyzer 130, and a driving unit. (Not shown), it may be configured to include a detector (Detector) 140 and an operation unit 150.

Meanwhile, conventionally, a short-wavelength light source or a tunable laser is used as a light source, and the detector uses a single pixel photodiode or a linear sensor to obtain a measurement result for a point on a sample, and a 2D scanner Area measurement was performed using (Point By Point). However, in recent years, it is developing in the form of a spectral ellipsometer to which an imaging spectrometer using a multi-wavelength light source and an area imaging sensor is applied. Here, an ellipse measuring instrument using an area sensor as a detector can measure a line on a sample with a single measurement, and a 1D scanner is required for area measurement (Line by Line).

In contrast, the ellipse meter according to an embodiment of the present invention uses a short-wavelength light source 110 as a light source, and a linear sensor or an area sensor as the detector 140 in a line or area unit on the sample 10 ( The characteristic value of 10) can be measured. Here, since the ellipse meter according to the embodiment of the present invention uses the short wavelength light source 110, there is no need to provide a separate image spectrometer.

In addition, an ellipse measuring instrument using a line sensor as the detector 140 can measure a line on a sample with one measurement, and a 1D scanner is required for area measurement (Line by Line).

Referring to FIG. 2, the short wavelength light source 110 irradiates incident light toward the sample 10. Further, the polarizer 120 is disposed between the sample 10 and the short wavelength light source 110 and polarizes the incident light.

The analyzer 130 analyzes a change in the polarization state of the reflected light whose polarization state is changed while the incident light passing through the polarizer 120 is reflected from the sample 10. In addition, the driving unit (not shown) rotates any one of the polarizer 120, the analyzer 130, and the compensator (not shown) at a predetermined rotation angle. Hereinafter, the polarizer 120, the analyzer 130, and the compensator (not shown) will be referred to as rotating elements.

The detector 140 measures the intensity of the reflected light passing through the analyzer 130 in units of lines or areas on the specimen 10 according to a change in the rotation angle of the rotating element. In addition, the calculation unit 150 calculates a characteristic value of the specimen 10 by separating a rotation variable for a rotation angle of the rotating element and a position variable for a position on the specimen 10 from the light intensity function of the reflected light.

Specifically, the ellipse meter according to an embodiment of the present invention rotates the rotating element N times or by N intervals and the intensity of the reflected light obtained from the detector 140 (I _n, where n = 0, 1,..., N -1) is analyzed, and the thickness and refractive index, which are characteristic values of the sample 10, are measured from this.

For example, when the rotating element rotates N times in the ellipse measuring instrument, the intensity of reflected light (I _n ) obtained from the detector 140 is defined as in Equation 1 below.

[Equation 1]

In Equation 1, the total reflection coefficient (R _s , R _p ) reflects the characteristics (refractive index (n), thickness (d)) of the sample 10, for example, a multilayer structure according to the wavelength (λ) of the incident light. The intensity (I _n ) of the reflected light reflected from the initial set values (P, A) of the polarizer 120 and the analyzer 130, including the characteristics of the structure, and the rotation angle of the rotating element (θ _n = 2π/N) Is determined by

The Fourier coefficients (α, β) defined in Equation 1 are elliptical coefficients (ρ) defined as the ratio of the total reflection coefficients corresponding to the characteristics of the sample 10 as shown in Equation 2 below. It is expressed by the magnitude (tanψ) and the phase (Δ) of and, by measuring the Fourier coefficients (α, β) as shown in Equation 3 below, the elliptic coefficients (ψ, Δ) can be calculated.

[Equation 2]

[Equation 3]

That is, the Fourier coefficients (α, β) can be analyzed using the measured intensity of reflected light (I _n ), and the elliptic coefficients (ψ, Δ) can be calculated from this. And, conversely, assuming the incident light incident on the sample 10 and the refractive index and thickness of the multilayer film, the total reflection coefficient is calculated, and the theoretical value of the elliptic coefficient is obtained by equation (2). After all, by applying the optimization technique that minimizes the error between the Fourier coefficients (α, β) measured in Equation 2 and the theoretical value, the refractive index and thickness of the multilayer film can be estimated. Here, the precision of the ellipse measuring instrument is determined by the analysis error of the Fourier coefficient and the precision of the applied optimization technique.

The ellipse measuring instrument according to an embodiment of the present invention minimizes the rotational error of the rotating element by separating the rotational variable and the positional variable from the intensity of reflected light (I _n ) function, and can effectively and quickly analyze the Fourier coefficients (α, β). It is a device that can.

Hereinafter, a case where the detector 140 is a line sensor measuring the intensity of reflected light in units of lines on the sample 10 is described as the first embodiment, and the detector 140 determines the intensity of the reflected light on the sample 10. A case of an area sensor that is measured in area units will be described as a second embodiment.

<First Example>

3 is a diagram illustrating a case in which a detector is a line sensor as an ellipse measuring device according to a first embodiment of the present invention.

As shown in FIG. 3, the horizontal direction (i) of the line sensor as the detector 140 corresponds to the horizontal position (x) on the specimen 10.

Here, the calculation unit 150 may calculate the characteristic value of the specimen 10 in units of lines by using the horizontal position variable i.

Hereinafter, a method of calculating the characteristic value of the specimen 10 by the calculation unit 150 of the ellipse measuring instrument according to the first embodiment of the present invention will be described with reference to FIG. 3.

First, the line sensor detects the intensity of the reflected light reflected from the specimen 10, and the rotation variable (n) for the rotation angle (θ) of the rotating element and the horizontal position variable for the horizontal position (x) on the specimen 10 Define the light intensity function of the reflected light so that (i) is separated.

Specifically, the line sensor measures the light intensity (I _in (x, n)) with respect to the rotation angle (θ). In this process, using that the rotation angle θ is physically separated with respect to the horizontal position (x) on the sample, Equation 1 can be converted as shown in Equation 6 below through Equations 4 and 5 below. I can.

[Equation 4]

[Equation 5]

[Equation 6]

In addition, Equation 6 may be converted into a light intensity function of reflected light separated by a variable as in Equation 9 below through Equation 7 and Equation 8 below.

[Equation 7]

[Equation 8]

[Equation 9]

Here, in Equation 9, there is a limiting condition as shown in Equation 10 below.

[Equation 10]

The ellipse meter according to the first embodiment of the present invention may estimate the rotation angle (θ _n ) and Fourier coefficients (α, β) of the rotating element using the least square method.

Specifically, the ellipse measuring device according to the first embodiment of the present invention includes rotation (n=0, 1,..., N-1) and horizontal direction (i=0, 1, ..., X-1) Each error function for the data is defined, and rotation angle and Fourier coefficients (α, β) are alternately calculated according to the least squares method. Here, the rotation angle θ _n converges to a constant value, and the Fourier coefficients α and β can be optimized.

In this process, the error function of the rotation variable converges very quickly into a linear equation with the Fourier coefficients (α, β) as unknown, and the error function for the horizontal position variable (i) is the rotation angle (θ _n ) as unknown. It is a nonlinear equation that can be easily estimated through the Newton-Raphson Method.

Specifically, based on the intensity of reflected light (I' _in ) measured by the line sensor and the light intensity function (I _in ) defined in Equation 9, a rotation error function (E _n ) using a rotation variable (n) as a variable ) Is defined as in Equation 11 below.

[Equation 11]

And, based on the intensity of reflected light (I' _in ) measured by the line sensor and the light intensity function (I _in ) defined by Equation 9, a position error function (E) using a horizontal position variable (i) as a variable _i ) is defined as in Equation 12 below.

[Equation 12]

4 is a view for explaining a method of calculating Fourier coefficients using a rotation error function and a horizontal position error function with a limiting condition on a rotation variable in the first embodiment of the present invention.

First, as shown in the equation on the right side of FIG. 4, the rotation angle θ _n is calculated by applying the least squares method to the horizontal position error function E _i according to the rotation of the rotating element. That is, for an arbitrary rotation angle, an arbitrary rotation angle is estimated by applying the least squares method for each position on the specimen 10 to the horizontal position error function E _i .

Next, as shown in the left equation of FIG. 4, the least squares method is applied to the rotation error function (E _n ), but the rotation angle (θ _n ) calculated in the previous step is applied to the rotation variable (n), and the light intensity function (I _in ) The Fourier coefficients (α, β) of are calculated, respectively. That is, the optimal Fourier coefficients α and β may be estimated by applying the least squares method for each rotation angle estimated in the previous step to the rotation error function E _n .

5 is a view for explaining a method of calculating a Fourier coefficient by introducing a rotation coefficient and using a rotation error function and a horizontal position error function in the first embodiment of the present invention.

Referring to FIG. 5, a rotating factor (R _n ) is introduced as a method of linearizing an expression in a rotation space for the intensity of reflected light. This rotation coefficient (R _n ) is to reflect the effect of rotation on the intensity of reflected light (I _in ), and has a value of 1 in an ideal case.

With the introduction of the rotation coefficient (R _n ), the expression for the intensity of the reflected light (I _in ) can be expressed by separating it into a horizontal position variable (x _i ) and a rotation variable (R _n , θ _n ) as shown in Equation 13 below. have.

Specifically, when the rotation coefficient R _n is introduced in Equation 6, the light intensity function (I(x _i , θ _n , R _n )) of the reflected light is defined as in Equation 13 below.

[Equation 13]

And, if the following Equations 14 and 15 are applied to Equation 13, the reflected light intensity function (I(x _i , θ _n , R _n )) is a horizontal position variable (x _i ) as shown in Equation 16 below. And rotation variables (R _n , θ _n ).

[Equation 14]

[Equation 15]

[Equation 16]

Here, referring to FIG. 5, rotation using a rotation variable (n) as a variable based on the intensity of reflected light (I' _in ) measured by the line sensor and the light intensity function (I _in ) defined in Equation 16 The error function E _n is defined.

And, based on the intensity of reflected light (I' _in ) measured by the line sensor and the light intensity function (I _in ) defined in Equation 16, a horizontal position error function (E) using a horizontal position variable (i) as a variable _i ) is defined.

By applying the least squares method to the rotation error function (E _n ) and the horizontal position error function (E _i ), you can obtain a linear system of equations that are completely symmetric about the rotation variable (n) and the horizontal position variable (i). Data processing for the rotation variable n and the horizontal position variable i makes it possible to quickly estimate the Fourier coefficient values α and β.

Specifically, as shown in the equation on the right side of FIG. 5, the rotation angle θ _n is calculated by applying the least squares method to the horizontal position error function E _i according to the horizontal position x on the sample 10. That is, for an arbitrary rotation angle, an arbitrary rotation angle is estimated by applying the least squares method for each position on the specimen 10 to the horizontal position error function E _i .

Next, the Fourier coefficient as the left equation of Figure 5, the rotation error function (E _n) optical intensity function (I _in) to apply the rotation angle (θ _n) calculated, but applying the least square method to the rotation parameter (n) the (α, β) is calculated, respectively. That is, the optimal Fourier coefficients α and β may be estimated by applying the least squares method for each estimated rotation angle to the rotation error function E _n .

6 is a diagram illustrating a method of calculating a Fourier coefficient by partially introducing a rotation coefficient and using a rotation error function and a horizontal position error function in the first embodiment of the present invention.

In Equation 13, I _oi means background light according to the wavelength of the light source, and further, the offset value of the electric signal by the line sensor and the binarization process are reflected. Therefore, if I _oi includes the change due to rotation, the intensity function (I(x _i , θ _n , R _n )) of the reflected light by removing the rotation coefficient (R _n ) from the background light (I _oi ) is Equation 17 below. Is defined as

[Equation 17]

And, when the following Equations 18 and 19 are applied to Equation 17, the reflected light intensity function (I _in (x _i , θ _n , R _n )) is a horizontal position variable (x _i ) And rotation variables (R _n , θ _n ).

[Equation 18]

[Equation 19]

[Equation 20]

Here, referring to FIG. 6, rotation using a rotation variable (n) as a variable based on the intensity of reflected light (I' _in ) measured by the line sensor and the light intensity function (I _in ) defined in Equation 20 The error function E _n is defined.

And, based on the intensity of reflected light (I' _in ) measured by the line sensor and the light intensity function (I _in ) defined in Equation 20, a position error function (E _i ) using a horizontal position variable (i) as a variable ) Is defined.

By applying the least squares method to the rotation error function (E _n ) and the horizontal position error function (E _i ), you can obtain a linear system of equations that are completely symmetric about the rotation variable (n) and the horizontal position variable (i). Data processing for the rotation variable n and the horizontal position variable i makes it possible to quickly estimate the Fourier coefficients α and β.

Specifically, as shown in the right equation of FIG. 6, the rotation angle θ _n is calculated by applying the least squares method to the horizontal position error function E _i according to the rotation of the rotating element. That is, for an arbitrary rotation angle, the least squares method is applied for each horizontal position on the specimen 10 to the position error function E _i to estimate an arbitrary rotation angle.

Next, as shown in the equation on the left side of FIG. 6, the fourier coefficient of the light intensity function (I _in ) by applying the least squares method to the rotation error function (E _n ) but applying the calculated rotation angle (θ _n ) to the rotation variable (n) (α, β) is calculated, respectively. That is, the optimal Fourier coefficients α and β may be estimated by applying the least squares method for each estimated rotation angle to the rotation error function E _n .

_n), 회전 계수(R_n))와 수평 위치 변수(x_i)로 분리하고, 각각의 오차 함수(E_n, E_i)를 정의하여 이원화된 최소 제곱법을 적용하여 회전각(

_n) 및 퓨리에 계수(α, β)를 추정함으로써, 기존 분석 방법 대비 매우 빠르고 정확하며, 회전 오차에 둔감한 시료의 구조 분석이 가능하다.As described above, in the ellipse meter according to the first embodiment of the present invention, a variable that determines the intensity of reflected light obtained from the line sensor including the rotation of the rotating element is a rotation variable (rotation angle (

_n), rotation coefficient (R _n)) and separated in a horizontal position parameters (x _i), and applying the least square method is defined for each of the error function (E _n, E _i) to the dual angle of rotation (

By estimating _n ) and Fourier coefficients (α, β), it is possible to analyze the structure of a sample that is very fast and accurate compared to the existing analysis method, and is insensitive to rotation errors.

<Second Example>

7 is a diagram illustrating a case where a detector is an area sensor as an ellipse measuring device according to a second embodiment of the present invention.

In the ellipse measuring device according to the second embodiment of the present invention, when the intensity of reflected light is measured in units of area on the sample 10, the horizontal position variable (i) for the horizontal position (x) on the sample 10 And a vertical position variable (j) with respect to the vertical position (y) on the specimen 10.

Here, as shown in FIG. 7, the horizontal direction (i) of the area sensor, which is the detector 140, corresponds to the horizontal position (x) on the sample 10, and the vertical direction (j) is the vertical direction on the sample 10. Corresponds to position (y).

The calculation unit 150 may calculate a characteristic value of the sample 10 by using at least one of the horizontal position variable i and the vertical position variable j. In particular, when both the horizontal position variable (i) and the vertical position variable (j) are used, the characteristic value of the specimen 10 can be calculated in units of area.

Here, the method of calculating the characteristic value of the sample 10 by separating the rotation variable n for the rotation angle θ and the horizontal position variable i for the horizontal position x on the sample 10 is described above. Since it is the same as the first embodiment of the present invention, a description thereof will be omitted.

Hereinafter, a method of calculating the characteristic value of the specimen 10 by the calculation unit 150 of the ellipse measuring instrument according to the second embodiment of the present invention will be described with reference to FIG. 7.

First, the area sensor detects the intensity of the reflected light reflected from the specimen 10, and the rotation variable (n) for the rotation angle (θ) of the rotating element and the vertical position variable for the vertical position (y) on the specimen 10 Define the light intensity function of the reflected light so that (j) is separated.

Specifically, the area sensor measures the light intensity (I _jn (x, n)) with respect to the rotation angle (θ). In this process, using that the rotation angle θ is physically separated with respect to the vertical position (y) on the sample, Equation 1 can be converted as shown in Equation 23 below through Equations 21 and 22 below. I can.

[Equation 21]

[Equation 22]

[Equation 23]

In addition, Equation 23 may be converted into a light intensity function of reflected light separated by variables as shown in Equation 26 below through Equation 24 and Equation 25 below.

[Equation 24]

[Equation 25]

[Equation 26]

Here, in Equation 26, there is a limiting condition as in Equation 27 below.

[Equation 27]

The ellipse meter according to the second embodiment of the present invention may estimate the rotation angle (θ _n ) and Fourier coefficients (α, β) of the rotating element using the least square method.

Specifically, the ellipse measuring machine according to the second embodiment of the present invention includes rotation (n=0, 1,..., N-1) and a vertical direction (j=0, 1, ..., Y-1) Each error function for the data is defined, and rotation angle and Fourier coefficients (α, β) are alternately calculated according to the least squares method. Here, the rotation angle θ _n converges to a constant value, and the Fourier coefficients α and β can be optimized.

In this process, the error function of the rotation variable (n) converges very quickly into a linear equation with the Fourier coefficients (α, β) as unknowns, and the error function for the vertical position variable (j) is the rotation angle (θ _n ) The rotation angle can be easily estimated through the Newton-Raphson Method with a nonlinear equation that is unknown.

Specifically, based on the intensity of reflected light (I' _jn ) measured by the area sensor and the light intensity function (I _jn ) defined in Equation 26, a rotation error function (E _n ) using a rotation variable (n) as a variable ) Is defined as in Equation 28 below.

[Equation 28]

And, based on the intensity of reflected light (I' _jn ) measured by the area sensor and the light intensity function (I _jn ) defined by Equation 26, a position error function (E) using a vertical position variable (j) as a variable _j ) is defined as in Equation 29 below.

[Equation 29]

8 is a view for explaining a method of calculating Fourier coefficients using a rotation error function and a vertical position error function with a limiting condition on a rotation variable in the second embodiment of the present invention.

First, as shown in the equation on the right side of FIG. 8, the rotation angle θ _n is calculated by applying the least squares method to the vertical position error function E _j according to the rotation of the rotating element. That is, for an arbitrary rotation angle, an arbitrary rotation angle is estimated by applying the least squares method for each position on the specimen 10 to the vertical position error function E _j .

Next, the light intensity function (I _jn ) by applying the least squares method to the rotation error function (E _n ), but applying the rotation angle (θ _n ) calculated in the previous step to the rotation variable (n), as shown in the left equation of FIG. 8 The Fourier coefficients (α, β) of are calculated, respectively. That is, the optimal Fourier coefficients α and β may be estimated by applying the least squares method for each rotation angle estimated in the previous step to the rotation error function E _n .

9 is a diagram for explaining a method of calculating a Fourier coefficient by introducing a rotation coefficient and using a rotation error function and a vertical position error function in a second embodiment of the present invention.

Referring to FIG. 9, a rotating factor (R _n ) is introduced as a method of linearizing an expression in a rotation space for the intensity of reflected light. This rotation coefficient (R _n ) is to reflect the effect of rotation on the intensity of reflected light (I _jn ), and has a value of 1 in an ideal case.

With the introduction of the rotation coefficient (R _n ), the expression for the intensity of the reflected light (I _jn ) can be expressed by separating it into a vertical position variable (y _j ) and a rotation variable (R _n , θ _n ) as shown in Equation 30 below. have.

Specifically, when the rotation coefficient R _n is introduced into Equation 26, the light intensity function (I(y _j , θ _n , R _n )) of the reflected light is defined as in Equation 30 below.

[Equation 30]

And, when the following Equations 31 and 32 are applied to Equation 30, the reflected light intensity function (I(y _j , θ _n , R _n )) is a vertical position variable (y _j ) as shown in Equation 33 below. And rotation variables (R _n , θ _n ).

[Equation 31]

[Equation 32]

[Equation 33]

Here, referring to FIG. 9, rotation using a rotation variable (n) as a variable based on the intensity of reflected light (I' _jn ) measured by the area sensor and the light intensity function (I _jn ) defined in Equation 33 The error function E _n is defined.

And, based on the intensity of reflected light (I' _jn ) measured by the area sensor and the light intensity function (I _jn ) defined in Equation 33, a vertical position error function (E) using a vertical position variable (j) as a variable _j ) is defined.

Applying the least squares method to the rotation error function (E _n ) and the vertical position error function (E _j ) gives a linear system of equations that are completely symmetric about the rotational variable (n) and the vertical positional variable (j). The data processing for the rotation variable n and the vertical position variable j makes it possible to quickly estimate the Fourier coefficient values α and β.

Specifically, as shown in the right equation of FIG. 9, the rotation angle θ _n is calculated by applying the least squares method to the vertical position error function E _j according to the vertical position y on the sample 10. That is, for an arbitrary rotation angle, an arbitrary rotation angle is estimated by applying the least squares method for each position on the specimen 10 to the vertical position error function E _j .

Next, the Fourier coefficient as the left expression of Figure 9, the rotation error function (E _n) optical intensity function (I _jn) by applying the rotation angle (θ _n) calculated, but applying the least square method to the rotation parameter (n) the (α, β) is calculated, respectively. That is, the optimal Fourier coefficients α and β may be estimated by applying the least squares method for each estimated rotation angle to the rotation error function E _n .

10 is a view for explaining a method of calculating a Fourier coefficient by partially introducing a rotation coefficient and using a rotation error function and a vertical position error function in the second embodiment of the present invention.

In Equation 26, I _oj means background light according to the wavelength of the light source, and further, the offset value of the electric signal by the area sensor and the binarization process are reflected. Therefore, when I _oj includes the change due to rotation, the intensity function (I(y _j , θ _n , R _n )) of the reflected light by removing the rotation coefficient (R _n ) from the background light (I _oj ) is Equation 34 below. Is defined as

[Equation 34]

And, if the following Equations 35 and 36 are applied to Equation 34, the reflected light intensity function (I _jn (y _j , θ _n , R _n )) is a vertical position variable (y _j ) as shown in Equation 37 below. ) And rotation variables (R _n , θ _n ).

[Equation 35]

[Equation 36]

[Equation 37]

Here, referring to FIG. 10, rotation using a rotation variable (n) as a variable based on the intensity of reflected light (I' _jn ) measured by the area sensor and the light intensity function (I _jn ) defined in Equation 37 The error function E _n is defined.

And, based on the intensity of reflected light (I' _jn ) measured by the area sensor and the light intensity function (I _jn ) defined in Equation 37, a vertical position error function (E) using a vertical position variable (j) as a variable _j ) is defined.

Applying the least squares method to the rotation error function (E _n ) and the vertical position error function (E _j ) gives a linear system of equations that are completely symmetric about the rotational variable (n) and the vertical positional variable (j). Data processing for the rotation variable n and the vertical position variable j makes it possible to quickly estimate the Fourier coefficients α and β.

Specifically, as shown in the equation on the right side of FIG. 10, the rotation angle θ _n is calculated by applying the least squares method to the vertical position error function E _j according to the rotation of the rotating element. That is, for an arbitrary rotation angle, an arbitrary rotation angle is estimated by applying the least squares method for each vertical position on the specimen 10 to the vertical position error function E _j .

Next, the Fourier coefficient as the left equation of Figure 10, the rotation error function (E _n) optical intensity function (I _jn) by applying the rotation angle (θ _n) calculated, but applying the least square method to the rotation parameter (n) the (α, β) is calculated, respectively. That is, the optimal Fourier coefficients α and β may be estimated by applying the least squares method for each estimated rotation angle to the rotation error function E _n .

As described above, in the ellipse meter according to the second embodiment of the present invention, the variable that determines the intensity of reflected light obtained from the area sensor including the rotation of the rotating element is a rotation variable (rotation angle (θ _n ), rotation coefficient (R _n )). )) and the vertical position variable (y _j ), and by defining each error function (E _n , E _j ) and estimating the rotation angle and Fourier coefficients by applying the binary least squares method, It is possible to analyze the structure of a sample that is fast and accurate, and is insensitive to rotational errors.

The detailed description above is illustrative of the present invention. In addition, the above-described content is only for showing and describing preferred embodiments of the present invention, and the present invention can be used in various other combinations, modifications and environments. That is, changes or modifications may be made within the scope of the concept of the invention disclosed in the present specification, the scope equivalent to the disclosed contents, and/or the skill or knowledge of the art. The above-described embodiments are for explaining the best state in carrying out the present invention, and in order to use other inventions such as the present invention, implementation in other states known in the art, and in the specific application fields and uses of the invention Various changes are also possible. Therefore, the detailed description of the invention is not intended to limit the invention to the disclosed embodiment. In addition, the appended claims should be construed as including other embodiments.

110: short wavelength light source
120: polarizer
130: analyzer
140: detector
150: operation unit

Claims (11)

A short wavelength light source that irradiates incident light toward the sample;
A rotating element disposed between the sample and the short-wavelength light source and including a polarizer configured to polarize the incident light, and an analyzer configured to analyze a change in a polarization state of reflected light whose polarization state is changed while the incident light passing through the polarizer is reflected from the sample;
A driving unit that rotates any one of the rotation elements at an arbitrary rotation angle;
A detector for measuring the intensity of the reflected light passing through the analyzer in a line unit or an area unit on the sample according to a change in the rotation angle; And
An operation unit that calculates a characteristic value of the sample by separating a rotation variable for the rotation angle and a position variable for the position on the sample from the light intensity function of the reflected light
Ellipse measuring instrument comprising a.
The method of claim 1,
The rotating element is
Further comprising a compensator disposed between the polarizer and the sample
Elliptic meter.
The method of claim 1,
The operation unit
An ellipse measuring instrument that calculates the characteristic value of the sample in units of lines or areas.
The method of claim 1,
The positional variable is
When the intensity of the reflected light is measured in units of an area on the sample, an ellipse meter is divided into a horizontal position variable for a horizontal position on the sample and a vertical position variable for a vertical position on the sample.
The method of claim 4,
The operation unit
An ellipse measuring instrument that calculates a characteristic value of the specimen using at least one of the horizontal position variable and the vertical position variable.
The method of claim 1,
The operation unit
An ellipse measuring instrument for defining the light intensity function so that the rotation variable and the position variable are separated, and calculating a characteristic value of the specimen based on the intensity of the reflected light and the light intensity function.
The method of claim 6,
The operation unit
An ellipse measuring instrument for defining a rotation error function using the rotation variable as a variable based on the intensity of the reflected light and the light intensity function, and defining a position error function using the position variable as a variable.
The method of claim 7,
The operation unit
Calculate the rotation angle by applying the least squares method to the position error function according to the position on the sample,
An ellipse measuring instrument for calculating a Fourier coefficient of the light intensity function by applying the least squares method to the rotation error function and applying the calculated rotation angle to the rotation variable.
The method of claim 1,
The operation unit
To put a constraint on the rotation variable
Elliptic meter.
The method of claim 2,
The operation unit
An ellipse measuring instrument that introduces a rotation coefficient for reflecting an influence of rotation of the rotating element on the intensity of the reflected light.
The method of claim 2,
The operation unit
An ellipse measuring instrument that partially introduces a rotation coefficient for reflecting an influence of rotation of the rotating element on the intensity of the reflected light.

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