JP2015143618A - Optical characteristics measuring method and optical characteristics measuring apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To solve a problem in which, when optical characteristics of a measuring object in a cell are measured, a photoelastic effect of an entrance window and an emission window as optical windows of the cell reduces accuracy in measuring original optical characteristics of the measuring object.SOLUTION: An optical characteristics measuring method includes the steps of: arranging a measuring object in a cell; measuring a Mueller matrix of a system including a window from deflected incident light and emission light obtained through an emission window by radiating the incident light to the measuring object through an entrance window of the cell; acquiring a birefringence phase difference and a main axis azimuth of the entrance window and the emission window from the measured Mueller matrix of the system including the window; acquiring Mueller matrices of the entrance window and the emission window; acquiring a Mueller matrix of the measuring object; and acquiring Ψ indicating an amplitude ratio of p and s components of the emission light as angle, and a phase difference Δ, of the measuring object.

Description

  The present invention relates to a method for measuring the optical properties (film thickness and refractive index) of a surface of a measurement object and a thin film on the surface using ellipsometry with respect to the measurement object placed in an optical cell. The present invention relates to a method for accurately measuring by eliminating the influence of the photoelastic effect on the cell window.

  Light is an electromagnetic wave and has the property of a transverse wave. Assuming a three-axis (x, y, z) coordinate system orthogonal to each other and the light traveling direction is the z-axis direction, the vibration direction of the electric field vector (or magnetic field vector) of the light is along the xy plane. Can be divided into an x-axis component and a y-axis component. At that time, light in which the phase difference and amplitude ratio of the x-axis component and y-axis component change randomly with time is referred to as non-polarized light, and constant light without change is referred to as polarized light. The polarization state of light is related to the phase difference between the x-axis component and the y-axis component and the value of the amplitude ratio.

  When a transparent measurement object with optical anisotropy or the surface of the measurement object is irradiated with light in a certain polarization state and output light such as transmitted light or reflected light is obtained, the light is between the incident light and the output light. A change in the polarization state is observed. Obtaining information related to the anisotropy of the transparent measurement object or the optical properties of the surface of the measurement object from this change in polarization state is referred to as polarization measurement. The anisotropy of the measurement object is related to the anisotropy of the molecular structure, the presence of stress, and the optical characteristics of the measurement sample surface are related to the refractive index and the film thickness of the thin film.

  A polarization measurement method for measuring a change in polarization state due to reflection on the surface of an object to be measured is called ellipsometry, and a measurement system using ellipsometry is called an ellipsometer. Ellipsometry generally uses s, p, z orthogonal coordinate systems instead of x, y, z coordinate systems. As shown in FIG. 1, the s-axis component and the p-axis component of light are called s-polarized light and p-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, two values are determined: Psi (Ψ) representing the amplitude ratio of the reflected p and s polarized components as an angle and Del (Δ) representing the phase difference.

  Since ellipsometry has high measurement accuracy and can perform in-situ measurement, it is often used for evaluation of a measurement object in a process in a cell such as a vacuum container or a liquid container. The cell has two observation optical windows, an entrance window and an exit window. The ideal observation optical window is optically isotropic, that is, it is desirable that the polarization state of incident light and outgoing light by the optical window does not change during measurement. However, in the actual manufacturing process, installation process, and experimental process, the window has anisotropy due to external stress. The phenomenon in which optical anisotropy appears in a material due to this stress is called a photoelastic effect. There is a birefringence amount as an amount representing the photoelastic effect, and the birefringence amount is determined by the birefringence phase difference (δ) and the principal axis direction (θ). The birefringence phase difference is a phase difference generated between the p-axis component and the s-axis component of light when the light passes through the anisotropic substance. The principal axis direction is s, and the fast axis of the anisotropic material (p This is the orientation of the slow axis perpendicular to the fast axis. The principal axis orientation of the anisotropic material due to the photoelastic effect is determined by the orientation of the principal stress. The measurement of Del and Psi of the measurement object in the cell by ellipsometry includes birefringence amounts of two windows, and it is difficult to accurately measure the optical characteristics of the measurement object.

In order to reduce the influence of the optical window, select a material with as little birefringence as possible according to the experimental conditions, and at the same time approximate a small angle
Non-Patent Document 1 discloses performing window correction using the. However, in this method, a material having a small birefringence is expensive, and a birefringence phase difference that can be approximated by a small angle is limited to about δ <0.1 radians.

  In Patent Document 1, the polarization state of the reflected light from the measurement object in the absence of a window is measured in advance, and subsequently the polarization state of the reflected light from the measurement object in the presence of a window in the cell is measured. It is disclosed that the photoelastic effect of a window is obtained and window correction is performed. In this window correction formula, it is assumed that the birefringence amount due to the photoelastic effect of the entrance window and the exit window is the same in order to avoid complicated calculation. However, in practice, the amount of birefringence generated in the entrance window and the exit window is not always the same.

  In Non-Patent Document 2, it is not necessary to measure the polarization state of the reflected light from the measurement object in the absence of a window in advance, but the incident window-measurement object-exit window system and exit window-measurement object-incident It is disclosed that the polarization state of light from a window system is measured, and the window is corrected by obtaining the photoelastic effect of the window from the difference in polarization state. At this time, both light paths and the input light intensity must match. Therefore, it is necessary to devise such as adding an optical element to be a beam splitter, a reflecting mirror, and a photodetector to the ellipsometer. These conventional methods are troublesome because they perform measurement and window correction, and the birefringence amount of the window material changes due to the influence of the environment in the cell.

JP 2012-52972 A

H. G. Tompkins, E. A. Irene, “Handbook of Ellipsometry,” Chapter 5, pp. 407-425, (2005) N. Nissim, S. Eliezer, L. Bakshi, D. Moreno, L. Perelmutter, “In situ correction of windows’ linear birefringence inellipsometry measurements, ”Optics Communications, 282, 3414-3420 (2009)

  As described above, the conventional measurement method has limitations, and there is a problem that sufficient measurement accuracy cannot be obtained.

  In order to solve the above problems, a method for measuring an optical characteristic according to the present invention includes a step of placing a measurement object in a cell, polarized incident light, and the incident light through the incident window of the cell. A step of measuring the Mueller matrix of the system including the window from the emitted light obtained by irradiating the object and passing through the output window; and the birefringence of the incident window and the output window from the measured Mueller matrix of the system including the window Obtaining a phase difference and a principal axis direction; obtaining a Mueller matrix of the entrance window and the exit window; obtaining a Mueller matrix of the measurement object; and p and s components of the emitted light of the measurement object. And a step of obtaining ψ representing the amplitude ratio in angle and a phase difference Δ.

  An optical property measuring apparatus according to the present invention includes a light source, a polarization generation system, a polarization detection system, a photodetector, a cell having an entrance window and an exit window, and a cell in which a measurement object is contained, and the polarization A calculation unit that calculates a Mueller matrix of a system including a window from incident light irradiated from a generation system and polarization characteristics of outgoing light entering the polarization detection system, and the calculation unit includes a Mueller of the system including the window; The Mueller matrix of the measurement object is further calculated from the matrix.

  There is no restriction, and there is an effect that measurement of optical control with high accuracy is possible.

FIG. 4 is a diagram showing a polarization state of light. These are the schematic diagrams for demonstrating the measuring apparatus of the optical characteristic by this invention. These are the figures for demonstrating the flow of the measuring method of the optical characteristic by this invention. FIG. 5 is a diagram showing a flow of a method for measuring optical characteristics according to Example 1 of the present invention. FIG. 5 is a diagram showing a flow of a method for measuring optical characteristics according to Example 2 of the present invention. These are figures which show the wavelength dependence of the example which measured the optical characteristic by this invention, the optical system at the time of measuring the system containing the window before correction | amendment, the measuring object after correction | amendment, and a measuring object only. It is a figure which shows a characteristic. These are figures which show the wavelength dependence of the example which measured birefringence phase difference and principal axis direction by this invention, and are figures which show the birefringence phase difference and principal axis direction of the incident window which is an optical window, and an output window.

  Embodiments of the present invention will be described below with reference to the drawings.

FIG. 2 is a schematic diagram of an optical characteristic measuring apparatus for carrying out the present invention.
The measuring device includes a white light source 1 for emitting light, a polarization generation system 2 for controlling the polarization state of the probe light received from the light source and irradiated on the measurement object, and the polarization generation system 2 A polarization detection system 7 that detects the polarization state of light obtained by reflection on the surface of the measurement object 4 and a photodetector 8 that measures the intensity of light are provided. Reference numeral 9 denotes a probe light beam. The measurement object 4 is installed in a cell 5, and the cell 5 includes an entrance window 3 and an exit window 6 which are optical windows. Here, the cell 5 may serve not only as the measurement object 4 but also as a processing chamber for performing some processing on the measurement object 4. Reference numeral 10 denotes an arithmetic unit that calculates a Mueller matrix from the polarization state of incident light and the polarization state of outgoing light. Here, the calculation unit may also serve as a control unit for the white light source 1, the polarization generation system 2, the polarization detection system 7, and the photodetector 8.

FIG. 3 is a diagram showing a flow of an optical characteristic measuring method for carrying out the present invention. The method for measuring optical characteristics according to the present invention includes a step of placing a measurement object in a cell, and measuring a Mueller matrix of a system including an entrance window and an exit window (hereinafter referred to as a “system including a window”). Calculating the birefringence phase difference δ _i and the principal axis direction θ _i , which are characteristics indicating the photoelastic effect of the entrance window and the exit window, and obtaining the Mueller matrix of the entrance window and the exit window by the operation unit. A step, a step of obtaining a Mueller matrix of the measurement object by the calculation unit, and a step of measuring Ψ and Δ indicating the optical characteristics of the measurement object by the calculation unit.

  Here, i is 1 or 2, 1 indicates incident light, and 2 indicates outgoing light. Also, Ψ and Δ indicate the optical characteristics of the measurement object, Ψ indicates the amplitude ratio of the p and s components indicating the polarization characteristics of the emitted light, and Δ indicates the phase difference.

The Mueller matrix obtained by this measurement is a spectral Mueller matrix, which is a Mueller matrix for each wavelength. The Mueller matrix is a 4 × 4 matrix indicating the interaction of the measurement object with light, and its 16 elements are determined by the above-described Del (Δ), Psi (Ψ), δ _i , θ _{i and the} like.

  Hereinafter, examples of the present invention will be described in detail.

FIG. 4 is a diagram showing a flow of an optical property measurement method of the present embodiment using the optical property measurement device shown in FIG. In the present example, six arbitrary matrix elements m ₁₂ , m _13, m ₁₄ and m ₂₁ , m ₃₁ , and m ₄₁ of the Mueller matrix of the system including the window are used to represent any two of the photoelastic effects of the entrance window and the exit window. By taking the ratio of the elements, the characteristic birefringence phase difference δ _i and the principal axis direction θ _i are obtained.

Also, the elements of the Mueller matrix of the object to be measured, as shown in FIG. 4 (a), the matrix element m ₂₂ Mueller matrix containing the window, select any two of nine elements ~m ₄₄ simultaneous It is obtained by establishing and solving an equation.

Mueller matrix
Is described.

The Mueller matrices S and W of the object to be measured and the optical window that are the entrance window and the exit window are respectively Ψ and Δ, δ and θ,
When
Can be described.

When the measurement object is evaluated while being placed in the cell, the measured Mueller matrix is not shown in Equation 2, but the following equation including Mueller matrices W1 and W2 of the entrance window and the exit window.
However,
Here, each symbol represents the following formula.

Next, from the Mueller matrix of equations (4) and (5), birefringence (δ _i (0 ≤ δ _i ≤ π), θ _i (-π / 2 ≤ θ _i ≤ π / 2)) of each window and measurement target A procedure for obtaining Del (Δ) and Psi (Ψ) of an object will be described.

First, a simultaneous equation is established by taking an arbitrary ratio of two elements from matrix elements m ₁₂ , m ₁₃ , m ₁₄ and m ₂₁ , m ₃₁ , m ₄₁ . For example, if X _i = cos δ _i and Y _i = sin 2θ _i are defined, the following equations are obtained from the matrix elements m ₁₃ , m ₁₄ , m ₃₁ , and m ₄₁ .
Organizing equation (8)
It becomes.

Similarly, the following expression is obtained from the matrix elements m ₁₂ , m ₁₄ , m ₂₁ , and m ₄₁ .
Substituting equation (9) into equation (10) and rearranging yields Y _i .
Δ _i and θ _i can be obtained from the following equations.

The signs of + and − in equations (11) and (12) are determined by the following steps using matrix elements m ₁₂ , m ₁₃ , m ₁₄ , m ₂₁ , m ₃₁ and m ₄₁ .

Since Ai included in the matrix elements m ₁₂ and m ₂₁ is always a positive number, the sign of N is determined from the values of m ₁₂ and m ₂₁ . For m ₁₂ a product m ₁₂ · m _13> 0 of m ₁₃ (or _{m 21 · m 31> 0)} , the Bi> 0. In addition, when m ₁₂ · m ₁₃ <0 (or m ₂₁ · m ₃₁ <0), Bi <0. Similarly, in the case of m ₁₂ and product m ₁₂ · m ₁₄ of m ₁₄ <0 (or _{m 21 · m 41> 0)} , a Ci> 0. In the case of m ₁₂ · m ₁₄ > 0 (or m ₂₁ · m ₃₁ <0), Ci <0. Next,
It becomes.
Next, the obtained δ _i and θ _i are substituted into the equation (3), and a complete Mueller matrix of the entrance window and the exit window can be obtained. That is, Ai, Bi, Ci, Di, Ei, and Fi of each window are obtained.

Next, N of the measurement object sample is obtained from the following equation.

The SC and SS of the object to be measured are obtained from two simultaneous equations composed of arbitrary two matrix elements among nine matrix elements from m ₂₂ to m ₄₄ . However, the values of m ₂₃ , m ₂₄ , m ₃₂ , and m ₄₂ are generally small, and measurement noise of the measurement system is likely to ride. Therefore, as shown in FIG. 4B, it is desirable to derive the values using m ₃₃ , m ₃₄ , m ₄₃ , and m ₄₄ whose values are mainly determined by SC and SS. For example,
Find SC and SS from simultaneous equations of m ₃₃ and m ₃₄ .

  In the following, another embodiment of the present invention will be described.

  FIG. 5 is a diagram showing a flow of the optical property measuring method of the present embodiment using the optical property measuring apparatus shown in FIG. In this embodiment, as shown in FIG. 5, the elements of the Mueller matrix of the measurement object are obtained by calculating an inverse matrix of the Mueller matrix of the entrance window and the exit window and calculating the Mueller matrix including the window.

When δ _i and θ _i are obtained, Mueller matrices W1 and W2 of the entrance window and the exit window are obtained. Subsequently, inverse matrices W1 ^-1 and W2 ^-1 of each window are obtained, and the Mueller matrix of the measurement object is derived from the following equation.

Del (Δ) and Psi (Ψ) of the measurement object are obtained by the following equations.

  6 and 7 show Del (Δ) and Psi (Ψ) of the measurement object for each wavelength actually measured according to the present invention, and δ and θ of each window. The measurement object (sample) used here is a silicon substrate coated with an oxide film having a thickness of 25 nm, and the entrance window and the exit window use phase shifters.

  FIG. 6 is a graph showing Δ and Ψ of a system including a window before correction, Δ and Ψ of a measurement object after correction, and Δ and Ψ measured without passing through an optical window only with the measurement object. is there. It can be seen that Δ and Ψ of the measurement object after correction, and Δ and Ψ measured without passing through the optical window with only the measurement object have the same value at any wavelength, and the lines overlap. That is, this measurement method shows that optical characteristics can be obtained with high accuracy. FIG. 7 shows δ and θ of the entrance window and the exit window.

  The optical property measuring method and the optical property measuring apparatus according to the present invention can accurately measure a measurement object placed in a cell having an optical window. Observation is possible, and it can be used for manufacturing management and collection of measurement data in real time in the manufacturing process of electronic devices such as semiconductor elements and display devices, and optical devices.

DESCRIPTION OF SYMBOLS 1 Light source 2 Polarization generation system 3 Incident window 4 Measurement object 5 Cell 6 Output window 7 Polarization detection system 8 Photodetector 9 Probe light beam 10 Calculation part

Claims (11)

Placing a measurement object in a cell;
Measuring the Mueller matrix of the system including the window from the polarized incident light, and the exit light obtained by irradiating the object to be measured through the entrance window of the cell and passing through the exit window;
Determining the birefringence phase difference and principal axis orientation of the entrance window and the exit window from the measured Mueller matrix of the system including the window;
Obtaining a Mueller matrix of the entrance window and the exit window;
Obtaining a Mueller matrix of the measurement object;
Obtaining Ψ and phase difference Δ representing the amplitude ratio of the p and s components of the emitted light of the measurement object as an angle;
A method for measuring optical characteristics, comprising:   The step of obtaining the birefringence phase difference and the principal axis direction of the entrance window and the exit window includes a first row k column element (k = 2, 3, 4) of a Mueller matrix of the system including the measured window, and the j th 2. The method for measuring an optical characteristic according to claim 1, wherein the optical characteristic is obtained by solving simultaneous equations obtained from row 1 column elements (j = 2, 3, 4).   The step of obtaining the Mueller matrix of the object to be measured includes the obtained Mueller matrix of the entrance window and the exit window, and the jth row (j = 2, 3, 4) k columns of the Mueller matrix of the system including the window ( 3. The method for measuring optical characteristics according to claim 2, wherein the optical characteristic is obtained by solving simultaneous equations obtained from two elements among nine elements of k = 2, 3, 4).   The step of obtaining the Mueller matrix of the object to be measured includes the obtained Mueller matrices of the entrance window and the exit window, and the j-th row (j = 3, 4) k columns (k =) of the Mueller matrix of the system including the window. 3. The method for measuring optical characteristics according to claim 2, wherein the optical characteristic is obtained by solving simultaneous equations obtained from two of the four elements of (3, 4).   The step of obtaining the Mueller matrix of the measurement object is obtained by calculating the inverse matrix of the obtained Mueller matrix of the entrance window and the exit window and the Mueller matrix of the system including the obtained window. The method for measuring an optical characteristic according to claim 2. A light source;
A polarization generating system;
A polarization detection system;
A photodetector;
A cell having an entrance window and an exit window and containing an object to be measured;
A calculation unit that calculates a Mueller matrix of a system including a window from the polarization characteristics of incident light irradiated from the polarization generation system and emission light entering the polarization detection system,
The apparatus for measuring optical characteristics, wherein the calculation unit further calculates a Mueller matrix of the measurement object from a Mueller matrix of a system including the window.   The computing unit obtains the birefringence phase difference and principal axis direction of the entrance window and the exit window from the measured Mueller matrix of the system including the window, obtains the Mueller matrix of the entrance window and the exit window, and the measurement object 7. The apparatus for measuring optical characteristics according to claim 6, wherein a Mueller matrix of an object is calculated.   The computing unit is obtained from the first row k column element (k = 2, 3, 4) and the j th row 1 column element (j = 2, 3, 4) of the measured Mueller matrix including the window. 8. The apparatus for measuring optical characteristics according to claim 7, wherein a birefringence phase difference and a principal axis direction of the entrance window and the exit window are obtained by solving the simultaneous equations.   The computing unit is obtained Mueller matrix of the entrance window and the exit window, jth row k column (j = 2, 3, 4, k = 2, 3, 4) of the Mueller matrix of the system including the window 9. The optical characteristic measuring apparatus according to claim 7, wherein a Mueller matrix of the measurement object is obtained by solving simultaneous equations obtained from two of the nine elements. .   The calculation unit includes the obtained Mueller matrix of the entrance window and the exit window, and four rows of the j-th row and k-th column (j = 3, 4, k = 3, 4) of the Mueller matrix of the system including the window. 9. The optical characteristic measuring device according to claim 7, wherein a Mueller matrix of the measurement object is obtained by solving simultaneous equations obtained from two elements.   The calculation unit calculates the Mueller matrix of the measurement object by calculating the inverse matrix of the obtained Mueller matrix of the entrance window and the exit window, and the Mueller matrix of the system including the obtained window. 9. The optical characteristic measuring apparatus according to claim 7, wherein the optical characteristic measuring apparatus is obtained.