JPH1194733A - Method for measuring ellipsoparameter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve measurement accuracy by changing and measuring a polarization state of a polarized light entering an object to be measured by a plurality of number of times, obtaining an evaluation value for each measurement of the plurality of number of times, and selecting an ellipsoparameter obtained at the measurement whereby the evaluation value is minimum. SOLUTION: A light from a light source 1 is guided sequentially to a polarizer 2a and a phase plate 2b. A polarized light 3 from the phase plate 2b is guided to an object 4 to be measured. A polarized light 5 passing the object 4 to be measured or reflected by the object 4 to be measured is guided to an analyzer 6 arranged to be rotatable about an optical axis 2. An ellipsoparameter of the object 4 to be measured is obtained on the basis of an output of a photodetector 7 measuring an intensity of light from the analyzer 6. At this time, a polarization state of the polarized light 3 entering the object 4 to be measured is changed by a plurality of number of times, and the ellipsoparameter is measured every time the polarization state is changed. An evaluation value is obtained at each measurement of the plurality of number of times with the use of a predetermined calculation formula. The ellipsoparameter obtained at the measurement with the minimum evaluation value among the plurality of measurements is selected.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring ellipsometric parameters (.SIGMA., .DELTA.) Used for calculating, for example, the thickness and refractive index of a thin film.

[0002]

2. Description of the Related Art The ellipsometric parameter is a transmittance ratio or a reflectance ratio Ｐ of P-polarized light and S-polarized light by a test object and a phase difference Δ in transmission or reflection of P-polarized light and S-polarized light by the test object. is there. These Ψ and _{Δ, tanΨ = T S / T} P Δ = Δ S -Δ P T S: transmittance or reflectance for S-polarized light T _P of the object: transmittance or reflectance with respect to P-polarized light of the test object rate delta _S: phase difference delta _P of emitted polarized light with respect to incident S-polarized light: represented by the relationship of the phase difference of the exit polarization relative to the incident P-polarized light.

Next, a conventional method for measuring ellipsometric parameters (Ψ, Δ) will be described. The light from the light source is guided in the order of the polarizer and the phase plate, the polarized light from the phase plate is guided to the test object, and the polarized light transmitted through the test object or reflected by the test object can be rotated about the optical axis. Guide to the analyzer placed. Next, a photodetector for measuring the intensity of light from the analyzer is provided, and ellipsometric parameters (Ψ, Δ) are obtained based on the output of the photodetector. However, in one measurement, the rotation direction of the polarized light incident on the analyzer is not determined, so that the ellipsometric parameter cannot be completely determined. Therefore, the phase plate and the polarizer are set at different angles from those in the first measurement, and the state of polarized light incident on the test object is changed. In this state, a second measurement is performed to obtain a second ellipso parameter. These two measurements completely determine the state of polarization incident on the analyzer. The ellipsometric parameters determined by averaging the ellipsometric parameters obtained by the above two measurements were determined.

[0004]

However, the measured values of the ellipsometric parameters as described above are measured due to factors such as the extinction ratio of the polarizer and the analyzer, the dark output of the detector, and the fluctuation of the light source. Includes the above error. Moreover, the value of the ellipso parameter uses a mere average value of two measured values, and thus cannot always be said to be a highly accurate measurement.
Accordingly, an object of the present invention is to provide a method for measuring ellipso parameters with high measurement accuracy by evaluating an error of each measurement in a plurality of measurements of ellipso parameters.

[0005]

Means for Solving the Problems To solve the above problems,
The present invention guides light from a light source in the order of a polarizer and a phase plate,
The polarized light from the phase plate is guided to the test object and transmitted through the test object or
Rotate the polarized light reflected by the test object around the optical axis
Guides the analyzer to a position where it is possible to reduce the intensity of light from the analyzer.
Provide a photodetector to measure, based on the output of the photodetector,
Ellipsometric parameters for ellipsometric parameters of the specimen
In the measurement method of the
State several times, with each change
The measurement is performed, and the evaluation value A Ask for multiple
Evaluation value A out of measurements Is obtained with a measurement that minimizes
Characteristic ellipso parameters.
This is a method for measuring Lipso parameters. However, evaluation value A
Is A = | Tan^-1｛| Cot (θ_p) ｜ tan (Ψ )｝
−45 ° ｜ θ_p： Polarization measured from the vibration direction of S-polarized light incident on the test object
Direction of photon transmission axis Ψ : Transmittance ratio or reflection of P-polarized light and S-polarized light by the test object
It is the rate ratio.

[0006] The present invention also relates to a method for converting light from a light source into a polarizer.
The polarized light from the phase plate is guided to the test object,
Polarized light transmitted through the specimen or reflected by the specimen
To an analyzer that is rotatable around the
Light detector to measure the intensity of light from
Calculate ellipsometric parameters of test object based on output
In the method of measuring ellipsometric parameters, incident on the test object
The polarization state of the polarized light to be changed multiple times,
Performs measurement of ellipsometric parameters, and every multiple measurements
And evaluation value B Is obtained, and the evaluation value B is obtained from a plurality of measurements.
Ellipso parameters obtained by measurement that minimizes
And a method for measuring ellipsometric parameters
It is. However, the evaluation value B is B = | ｛| (Δ + Γ ): -180 ° | -90 °｝ | Γ: Phase difference between P-polarized light and S-polarized light due to phase plate Δ: For transmission or reflection of P-polarized light and S-polarized light
Phase difference.

[0007]

DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below. FIG. 1 shows a configuration of an ellipsometer, which is a device for obtaining an ellipso parameter first. In the optical path from the light source 1, a polarization optical member 2, which is composed of a polarizer 2a and a phase plate 2b, a test object 4, an analyzer 6, and a photodetector 7, are arranged in that order. The polarizing optical member 2 integrally includes the polarizer 2a and the phase plate 2b and is rotatably disposed at at least two different angular positions about the optical axis z. The analyzer 6 is also arranged rotatably about the optical axis z. Although the example shown in FIG. 1 measures the transmission characteristics of the test object 4, when the reflection characteristics of the test object 4 are to be measured, the analyzer 6 and the photodetector 7 are naturally connected to the reflection optical path. Placed in

Two orthogonal axes x and y are set on a plane orthogonal to the optical axis z, and the vibration direction of the S-polarized light is defined as the x-axis, and the vibration direction of the P-polarized light is defined as the y-axis. As shown in FIG. 2A, θ _{p is} the direction of the transmission axis of the polarizer 2a measured with reference to the x-axis. Also, as shown in FIG. 2B, θ _d : the direction of the slow axis of the phase plate 2b measured with reference to the x axis φ _d : the phase difference between the slow axis and the fast axis of the phase plate 2b Then, the polarization optical member 2 and the test object 4 shown in FIG.
Is expressed by the following equation (1). Here, E _3x and E _3y are the x component and the y component of the electric vector of the polarized light 3.

The polarized light 3 becomes a polarized light 5 having a different polarization state by transmitting or reflecting through the test object 4, and enters the analyzer 6. T _S : transmittance or reflectance of test object 4 for S-polarized light T _P : transmittance or reflectance of test object 4 for P-polarized light Δ: position of transmission or reflection of P-polarized light and S-polarized light by the test object Given a phase difference, the polarization state of the polarized light 5 is expressed by the following equation (2).

The rotation of the analyzer 6 causes the detector 7 to rotate.
Since the amount of light entering the light changes, then the polarization state of the polarized light 5
You can know. The output I (θ) of the detector is expressed by the following equation.
Is done.However, as shown in FIG. 2 (D), θ: in the direction of the transmission axis of the analyzer 6 measured with reference to the x-axis.
is there. FIG. 3 shows the state of the output signal. This is one measurement
And the absolute value of the phase difference of the polarized light 5 by one measurement |
φ_Five| And E _5xAnd E _5yAbsolute value of the ratio | E _5x/ E _5y| And
Is obtained as follows.

That is, first, the equation (3) is modified as follows. However, And φ ₅ represents the phase difference of the polarized light 5.

From equation (4), the signal is transmitted while rotating the analyzer 6.
And Fourier transform this signal with respect to the rotation angle θ.
By doing, a₀, A₁, A_TwoTo find the value of
it can. Then, equations (5a) to (5c) and a₀, A₁, A_Two
From the value of | E _5x| / | E _5y| And φ_FiveAs follows
Can be Where a₁', A_Two′ Is a₀And a₁, A_TwoStandardized
That is, it is defined as follows. a₁'= A₁/ A₀, A_Two'= A_Two/ A₀ Thus, by one measurement, the absolute value of the phase difference of the polarized light 5
| Φ_Five| And E _5xAnd E _5yAbsolute value of the ratio | E _5x/ E _5y| And
Is required.

On the other hand, from equation (2), E _5x, E _5yIs E _3x, E
_3yAnd the following relationship.φ_FiveAlso satisfies the following relationship from equation (2).Where φ_ThreeIs the phase difference of the polarized light 3.

Therefore, from equation (1), | E _3x| / | E _3y
| Can be obtained by one measurement from equation (8)._S/
T_PIs required. However, for the phase difference Δ,
Equation (7) gives φ_FiveInstead of cos (φ_Five)so
Yes, so φ_FiveI can't know the sign of
No. Therefore, when trying to find Δ from equation (9),
The following two solutions exist,I don't know which solution is correct. That is, one measurement
By default, we know whether the direction of rotation of polarized light 5 is clockwise or counterclockwise.
The phase difference φ of the polarized light 5_FiveI do not know the sign of
As a result, transmission or reflection of P-polarized light and S-polarized light by the test object
Cannot be known.

Therefore, in order to specify Δ to be one, the polarization optical member 2 is integrally rotated by approximately 90 °, the polarization 3 is rotated by approximately 90 °, and the measurement is performed again. 1
Times eye during measurement phi ₅ of the value phi _51, phi ₃ of the value and phi _31, likewise the second value of phi ₅ and phi ₃ at the time of measurement phi _52, when the φ _32, (9) formula Thus, the following equation holds. Since the values of φ ₃₁ and φ ₃₂ are correctly obtained from the equation (1), by solving the equation (11a), cos (Δ) and sin
The value of (Δ) can be determined, and thus Δ is determined.

At this time, in order for the solution to exist in the equation (11a), φ ₃₁ and φ ₃₂ must satisfy the following conditions. Therefore, when arranging the polarization optical member 2 shown in FIG. 1, it is important to satisfy the expression (11b).

In order to further improve the measurement accuracy,
The same measurement is performed even when there is no specimen 4, and the position of the polarized light 3 is determined.
Phase difference φ_ThreeAnd E _3xAnd E _3yThe ratio of
It is better to obtain it by measurement. Like this
For example, errors in the direction and phase difference of the polarizer 2a and the phase plate 2b
Can be corrected. However, it enters the analyzer 6
Since the polarity of the polarization phase difference is always unknown,
₃₁, Φ₃₂To know in advance about the sign of
is necessary.

In the prior art, the ellipso parameters obtained by the two measurements as described above are simply averaged, and this value is used as the ellipso parameter. On the other hand, in the present embodiment, the ellipsometric parameters (Ψ, Δ) are determined by the following method.

Originally, the measured values of the ellipsometric parameters include errors such as the extinction ratio of the polarizer 2a and the analyzer 6, the dark output generated by the detector 7, and the fluctuation of the light source. Then, in the measurement of the ellipso parameter, as a result of performing an analysis for reducing the influence of these errors, it was found that the error of the ellipso parameter can be reduced by bringing the polarization state of the polarized light 5 closer to the circularly polarized light.

Therefore, based on the above relationship, ellipsoparameter
To evaluate the magnitude of the error contained in the measured values of
The evaluation value was determined as follows. First, the amplitude ratio of polarized light 5
Is 1, which is the amplitude ratio of circularly polarized light.
I decided. The evaluation value A is A = | Tan^-1｛| Cot (θ_p) ｜ tan (Ψ ) −− 45 ° | (12) Next, the direction of the slow axis with respect to the x-axis of the phase plate 2b
θ_dIs θ_d= 90 °, the phase difference of polarized light 5 is circularly polarized
From the condition of 90 ° or 270 ° which is the phase difference of
Value B was determined. The evaluation value B is B = | ｛| Δ + Γ −180 ° | −90 °｝ | (13) Here, Γ: the phase difference between the P-polarized light and the S-polarized light due to the phase plate. Note that from Equations (12) and (13), the polarization of
The light state becomes circularly polarized because both the evaluation value A and the evaluation value B
It is when 0.

Next, a method for measuring the ellipsometric parameters (Ψ, Δ) using the evaluation values A and B will be described. First, the direction θ _d of the slow axis with respect to the x-axis of the phase plate 2b is _defined as θ _d = 90
Install at °. In this state, the first measurement is performed, and the ellipsometric parameters (Ψ, Δ) and the evaluation values A, B are obtained. Next, the polarizer 2a and the phase plate 2b are integrally rotated by 90 °,
The ellipsometric parameters (Ψ, Δ) and the evaluation values A, B are obtained. And the determination of the ellipso parameters (Ψ, Δ) is 2
The measurement is performed by selecting the ellipso parameters (Ψ, Δ) obtained from the measurement in which the evaluation value A or B is minimized among the measurements.

Next, numerical examples performed using the evaluation value A and the evaluation value B will be described. In this embodiment, the measurement of the ellipsometric parameters (Ψ, Δ) is performed twice. For two measurements, a λ / 8 plate was used as the phase plate 2b. Therefore, the phase difference φ _d between the slow axis and the fast axis of the phase plate 2b is φ _d
= 45 °. Further, as the test object 4, the phase difference Δ = 40
° was used. As the measurement error, an extinction ratio between the polarizer 2a and the analyzer 6 and an error generated by the dark output generated by the detector 7 were considered.

First, in the first measurement, the direction θ _p of the transmission axis of the polarizer 2a = 30 °, and the direction θ _d of the slow axis of the phase plate 2b = θ _d =
The ellipsometric parameters (Ψ, Δ) were determined at 90 °. Since θ _d = 90 °, the phase difference Ｐ between the P-polarized light and the S-polarized light due to the phase plate is Γ = + 45 °. Furthermore, the first measurement error δΨ ₁ of the transmittance ratio (reflectance ratio) of the test objectΨ
When, it was determined and the measurement error .DELTA..delta ₁ of the first phase difference Δ of the object. Next, in the second measurement, the polarizer 2a and the phase plate 2
b was rotated 90 ° integrally, and the state of the polarized light 3 was changed. As a result, θ _p = 120 ° and θ _d = 0 °, and therefore Γ = −45 °. In this state, the second ellipsometric parameters (Ψ, Δ) were obtained. Further, in the same manner as the first measurement, the error [delta] [Psi] ₂ of Ψ transmittance ratio of the test object (reflectance ratio),
It was determined and an error .DELTA..delta ₂ of the phase difference Δ of the object.

The transmittance ratio (reflectance ratio) of the test object and the above
Error δΨ obtained under the condition₁, ΔΨ_Two, ΔΔ₁, ΔΔ_Twoconnection of
Is shown in FIG. The solid line in FIG.₁And the long dashed line is δΨ_Two
Is shown. The short broken line is δΔ₁And the dotted line is δΔ_TwoIs shown. Figure
4, the absolute value of the error of Ψ | δΨ | Is about 4
Below 5 ° | δΨ₁| Is smaller and Ψ is about 45 ° or less
Above | δΨ_Two| Is smaller.

On the other hand, the first and second measurements were evaluated.
The value A was determined. The evaluation value A of the first measurement is A₁As
From equation (12), A₁Is A₁= | Tan^-1｛| Cot (30 °) | ・ tan
(Ψ )｝ − 45 ° |. A₁Is 0 when Ψ = 30 °. Also twice
Evaluation value A of eye measurement is A_TwoFrom equation (12), A
_TwoIs A_Two= | Tan^-1｛| Cot (120 °) | tan
(Ψ )｝ − 45 ° |. A_TwoIs 0 when Ψ = 60 °. More than
From the results, if the evaluation value A becomes smaller, the transmittance ratio of the test object (
The error of the emissivity ratio) is also small, and the result of FIG.
The relationship is in good agreement. Therefore, the evaluation value A
Evaluation indicating the magnitude of the error of the Lipso parameters (Ψ, Δ)
It turns out that it is a value.

The error of the phase difference Δ of the test object is as follows.
Regardless of the value of っ て も from the results in FIG. 4, the error is smaller in the first measurement. On the other hand, the evaluation value B was obtained for the first and second measurements. Assuming that the evaluation value B of the _first measurement is B ₁ , B ₁ is obtained from the equation (13) as follows: B ₁ = | ｛| 40 ° + 45 ° −180 ° | −90 °｝ |
= 5 °. Also, the evaluation value B of the _second measurement is B ₂ ,
From the equation (13), B ₂ is given by: B ₂ = | ｛| 40 ° −45 ° −180 ° | −90 °} |
= 95 °. From the above results, as the evaluation value B decreases, the error of the phase difference Δ of the test object also decreases, and the relationship between the result of FIG. Therefore, the evaluation value B is
It can be seen that the evaluation value indicates the magnitude of the error of the ellipso parameters (Ψ, Δ).

From the results shown in FIG. Is the evaluation value
A Larger error in ellipso parameters (Ψ, Δ) than
The value that contributes. Therefore, ellipsopara with few errors
To obtain the meter (Ψ, Δ), the evaluation value B The value of
Is effective.

[0028]

As described above, the present invention has provided an ellipsometric parameter measuring method for selecting an ellipsometric parameter by using an evaluation value derived from the state of polarization incident on the analyzer. This evaluation value makes it possible to judge a state in which an error due to the measurement is minimized, so that it is possible to improve the measurement accuracy of the ellipsometric parameter.

[Brief description of the drawings]

FIG. 1 is a configuration diagram showing a configuration of an ellipsometer.

FIG. 2 is a view taken along a line (A) AA, a view taken along a line BB (B), a view taken along a line CC (C), and a view taken along a line (D) DD in FIG. FIG.

FIG. 3 is a diagram illustrating an example of a detector output when a rotation angle of an analyzer is changed.

FIG. 4 is an explanatory diagram showing errors in ellipsometric parameters (Ψ, Δ).

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Light source 2 ... Polarizing optical member 2a ... Polarizer 2b ... Phase plate 3, 5 ... Polarized light 4 ... Test object 6 ... Analyzer 7 ... Photodetector z ... Optical axis

Claims (2)

[Claims] The light from a light source is guided in the order of a polarizer and a phase plate.
The polarized light from the phase plate is guided to the test object, and the test object is
Polarized light transmitted or reflected by the specimen is centered on the optical axis.
To the analyzer that is rotatably arranged as
A photodetector for measuring the intensity of the light, and output the photodetector.
The ellipsometric parameters of the test object are determined based on the force.
In the method of measuring ellipsometric parameters, the polarization state of the polarized light incident on the test object is changed a plurality of times.
The ellipsometric parameters are measured for each change.
Evaluation value A for each of the plurality of measurements. The evaluation value A of the plurality of measurements Measurement that minimizes
Selecting the ellipsometric parameters obtained in
How to measure ellipsometric parameters. However, evaluation value A
Is A = | Tan^-1｛| Cot (θ_p) ｜ tan (Ψ )｝
−45 ° ｜ θ_p: Measured from the vibration direction of the S-polarized light incident on the test object
The direction of the transmission axis of the polarizer : Transmittance ratio of P polarized light and S polarized light by the test object or
It is the reflectance ratio. 2. The light from a light source is guided in the order of a polarizer and a phase plate.
The polarized light from the phase plate is guided to the test object, and the test object is
Polarized light transmitted or reflected by the specimen is centered on the optical axis.
To the analyzer that is rotatably arranged as
A photodetector for measuring the intensity of the light, and output the photodetector.
The ellipsometric parameters of the test object are determined based on the force.
In the method of measuring ellipsometric parameters, the polarization state of the polarized light incident on the test object is changed a plurality of times.
The ellipsometric parameters are measured for each change.
Evaluation value B for each of the plurality of measurements. The evaluation value B among the plurality of measurements Measurement that minimizes
Selecting the ellipsometric parameters obtained in
How to measure ellipsometric parameters. However, evaluation value B
Is B = | ｛| (Δ + Γ ): -180 ° | -90 °｝ | Γ: Phase difference between P-polarized light and S-polarized light by the phase plate Δ: Transmission or reflection of P-polarized light and S-polarized light by the test object
Is the phase difference at.