A method of calibrating a single-rotation ellipsometry system

Abstract

The application relates to a calibration method of a single-rotation ellipsometry system, comprising the following steps: acquiring first system parameters of a double-rotation system, and measuring fitting thicknesses of a plurality of standard samples by using the double-rotation system; switching the double-rotation system into a single-rotation system, measuring light intensity information of the plurality of standard samples, and performing Fourier transform on the light intensity information to obtain second Fourier coefficients; performing one-by-one fitting iteration replacement on the first system parameters by using the second Fourier coefficients, the first system parameters and the fitting thicknesses, until all the first system parameters except thickness and incident angle are updated, and single-rotation system parameters are obtained; measuring light intensity information of a to-be-measured sample by using the updated single-rotation system, performing Fourier transform on the light intensity information of the to-be-measured sample to obtain third Fourier coefficients; and calculating a Mueller matrix of the to-be-measured sample by using the single-rotation system parameters and the third Fourier coefficients. The method can make the measurement result more accurate.

Description

Technical Field

[0001] This invention relates to the field of spectral measurement technology, and specifically to a calibration method for a single rotating ellipsoid system. Background Technology

[0002] In the semiconductor industry, the measurement of optical critical dimensions (OCD) and the measurement of fine structural film thickness are directly related to the accuracy and yield of production samples. Ellipsometry is widely used in semiconductor process monitoring due to its advantages such as non-contact, non-destructive, fast, and high precision.

[0003] The basic configuration of an ellipsometer includes ( Figure 2 The components include: 1. Light source; 2. Polarizer; 3. Rotary motor 1 (slow-speed motor); 4. Compensator; 5. Sample to be tested; 6. Compensator; 7. Rotary motor 2 (fast-speed motor); 8. Analyzer; and 9. Spectrometer. In actual mass production, due to the speed limits of the motors and the required speed ratio between the two motors, the measurement speed is based on the slow-speed motor. To improve the measurement speed, the traditional approach is as follows:

[0004] 1. In a dual-rotation system, the light intensity information of the standard sample in the measurement system is measured, and the light intensity information is processed by Fourier transform to obtain the Fourier coefficients.

[0005] 2. Using the Fourier coefficients from step 1, the system parameters of the double-rotation system are obtained through fitting and iteration.

[0006] 3. Switch to a single rotation system, stop the rotation of motor 2, and increase the speed of motor 1.

[0007] 4. In a single rotation system, the light intensity information of the standard sample in the measurement system is measured, and the light intensity information is processed by Fourier transform to obtain the Fourier coefficients.

[0008] 5. Using the Fourier coefficients from step 4, fit and iterate to obtain the system parameters of the single-rotation system. Only the initial azimuth angles of the two waveplates need to be iterated, and the remaining system parameters are the same as those of the double-rotation system.

[0009] 6. Measure the light intensity of the sample to be tested, and perform a Fourier transform on the measured light intensity to obtain the Fourier coefficients.

[0010] 7. The Mueller matrix of the sample is calculated using the parameters of the single rotation system and the Fourier coefficients of the sample under test.

[0011] Although traditional methods can achieve relatively fast measurement and calibration, their accuracy is insufficient and cannot meet the needs of high-precision measurement scenarios. Summary of the Invention

[0012] This invention addresses the technical problems existing in the prior art by providing a calibration method for a single rotating elliptic system. This method improves upon the original measurement and calibration method, resulting in more accurate measurement results.

[0013] The technical solution of this invention to solve the above-mentioned technical problems is as follows: A calibration method for a single rotating elliptic system, comprising the following steps:

[0014] The first system parameters of the dual rotation system are obtained, and the fitted thickness of multiple standard samples is measured using the dual rotation system.

[0015] The dual-rotation system is switched to a single-rotation system, the light intensity information of multiple standard samples is measured, and the light intensity information is processed by Fourier transform to obtain the second Fourier coefficients.

[0016] Using the second Fourier coefficients, the first system parameters, and the fitted thickness, the first system parameters are iteratively replaced one by one until all the first system parameters except for the thickness and the incident angle are updated, thus obtaining the single rotation system parameters.

[0017] The light intensity information of the sample under test is measured using the updated single rotation system, and the light intensity information of the sample under test is Fourier transformed to obtain the third Fourier coefficient.

[0018] The Mueller matrix of the sample under test is calculated using the single rotation system parameters and the third Fourier coefficients.

[0019] Furthermore, the acquisition of the first system parameters of the dual-rotation system and the measurement of the fitted thickness of multiple standard samples using the dual-rotation system include:

[0020] The light intensity information of the standard sample was measured using a dual rotation system, and the light intensity information of the standard sample was processed by Fourier transform to obtain the first Fourier coefficients;

[0021] The first system parameters of the double-rotation system are obtained by fitting and iterating using the first Fourier coefficients.

[0022] The fitted thickness of multiple standard samples was measured using the updated dual-rotation system.

[0023] Furthermore, the methods for implementing the fitting iteration include traversal methods, global optimization methods, and local optimization algorithms.

[0024] Furthermore, the local optimization algorithms include: Levenberg-Marquardt method, Newton's method, gradient descent method, and conjugate gradient method.

[0025] Furthermore, using the second Fourier coefficients, the first system parameters, and the fitting thickness, the first system parameters are iteratively fitted and replaced one by one, including:

[0026] The system parameters of the dual-rotation system are fixed as the first system parameters, wherein the Mueller matrix of the standard sample is fixed by measuring the thickness and incident angle of multiple standard samples through the dual-rotation system.

[0027] The two parameters in the first system parameters are released sequentially to participate in the fitting, and the parameters obtained after fitting replace the original parameters.

[0028] The beneficial effects of this invention are: after calibration using a dual-rotation system, the thickness of multiple standard samples is measured. Then, the thicknesses of these multiple samples are used for single-rotation system calibration, and all system parameters except for thickness and incident angle are recalibrated. This pairwise calibration substitution method avoids coupling of system parameter calibrations, resulting in more accurate results. Attached Figure Description

[0029] Figure 1 This is a schematic flowchart of a calibration method for a single rotating elliptic deflection system provided in an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of the dual-rotational elliptic deflection system in an embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0032] In the description of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0033] In the description of this application, the term "for example" is used to mean "used as an example, illustration, or description." Any embodiment described as "for example" in this application is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to make and use the invention. Details are set forth in the following description for purposes of explanation. It should be understood that those skilled in the art will recognize that the invention can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid obscuring the description of the invention with unnecessary detail. Therefore, the invention is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed in this application.

[0034] Figure 1 The diagram shown is a flowchart of the method disclosed in this invention.

[0035] In step 1, measurement equipment such as a spectrometer can be used to obtain the light intensity variation information of the standard sample. The light intensity information is then processed by Fourier transform to obtain the Fourier coefficients.

[0036] In step 2, the Fourier coefficients from step 1 are used to iterate and fit with the measured Fourier coefficients of the theoretical sample. This allows us to obtain the phase delay of the analyzer, the azimuth of the analyzer, the phase delay of the polarizing plate, the azimuth of the polarizing plate, the azimuth of the analyzer, and the azimuth of the polarizing plate. Methods for implementing the fitting iteration parameters include, but are not limited to, the Levenberg-Marquardt method, Newton's method, gradient descent, and conjugate gradient method.

[0037] In step 3, the thickness of multiple standard samples is measured using a dual rotation system.

[0038] In step 4, switch to single rotation mode, stop the second rotation motor, and increase the speed of the first rotation motor.

[0039] In step 5, using measuring equipment such as a spectrometer, the light intensity variation information of multiple standard samples under a single rotation system is obtained. The light intensity information is then processed by Fourier transform to obtain Fourier coefficients.

[0040] In step 6, the Fourier coefficients from step 5 are used to perform pairwise fitting and iterative replacement with the measured Fourier coefficients of the theoretical sample to obtain the phase retardation of the analyzer, the azimuth angle of the analyzer, the phase retardation of the polarizing plate, the azimuth angle of the polarizing plate, the azimuth angle of the analyzer, and the azimuth angle of the polarizing plate. The fitting thickness and incident angle are fixed. Methods for implementing the fitting iteration parameters include, but are not limited to, the Levenberg-Marquardt method, Newton's method, gradient descent method, and conjugate gradient method.

[0041] In step 7, the light intensity information of the sample under test in a single rotation system is measured, and the Fourier coefficients are obtained by performing a Fourier transform on the measured light intensity.

[0042] In step 8, the Mueller matrix of the sample under test is calculated using the system parameters from step 6 and the Fourier coefficients from step 7.

[0043] The specific principle is as follows:

[0044] The system model of the double rotation is as follows:

[0045] S out =[M A R(A)]×[R(-ω2t-C2)M(δ2)R(ω2t+C2)]×

[0046] M S ×[R(-ω1t-C1)M(δ1)R(ω1t+C1)]×[R(-P)M P ]×S in

[0047] Where M S M is the Mueller matrix of the sample. P M A Let M(δ1) and M(δ2) be the Mueller matrices of the polarizers of the polarizing arm and the analyzing arm, ω1 and ω2 be the rotational speeds of motor 1 and motor 2, M(δ1) and M(δ2) be the Mueller matrices of the phase delay of the polarizer and the analyzing plate, R be the rotation matrix, P, A, C1, and C2 be the azimuth angles of the polarizer, the analyzing plate, the polarizing waveplate, and the analyzing waveplate, respectively, and S be the polarizer's azimuth angle. in This is the Stokes vector of normalized natural light.

[0048] The system model for a single rotation is:

[0049] S out1 =[M A' R(A')]×[R(-C 02 )M(δ 02 )R(C 02 )]×

[0050] M S ×[R(-ω 01 tC 01 )M(δ 01 )R(ω 01 t+C 01 )]×[R(-P')M P' ]×S in

[0051] Where ω 01 C is the rotational speed of motor number one in a single rotating system. 01 C 02The azimuth angles of the polarizer and analyzer under single rotation.

[0052] First, in dual-rotation mode, the measurement S of the standard sample is used. out The light intensity information S0 is subjected to Fourier transform processing to obtain Fourier coefficients. Then, based on the measured Fourier coefficients and theoretical Fourier coefficients, the phase delay δ2 of the analyzer, the azimuth angle C2 of the analyzer, the phase delay δ1 of the polarizing plate, the azimuth angle C1 of the polarizing plate, the azimuth angle A of the analyzer, and the azimuth angle P of the polarizing plate are obtained. Next, the thickness of multiple standard samples is measured using the rotation system parameters. Then, the system is switched to single rotation mode, the rotation of motor 2 is stopped, and the speed of motor 1 is increased. The light intensity information measured from multiple standard samples is subjected to Fourier transform processing to obtain Fourier coefficients. Then, the measured Fourier coefficients and theoretical Fourier coefficients are iteratively replaced pairwise. For example, the system parameters are first fixed as dual-rotation system parameters, Ms is fixed by measuring the thickness of multiple samples and the incident angle through dual rotation, and then C1 and C2 are released to participate in the fitting. The newly obtained C 01 C 02 Replace C1 and C2; then let δ2 and A participate in the fitting separately, and use the newly obtained δ 02 And A' replaces δ2 and A; finally, δ1 and P are left to participate in the fitting, and the newly obtained δ 01 And P' replaces δ1 and P. Finally, the light intensity information of the sample under test in the single rotation system is subjected to Fourier transform to obtain Fourier coefficients, and the Mueller matrix of the sample is calculated by using the Fourier coefficients and the parameters of the single rotation system.

[0053] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0054] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A calibration method for a single rotating elliptic system, characterized in that, Includes the following steps: The first system parameters of the dual rotation system are obtained, and the fitted thickness of multiple standard samples is measured using the dual rotation system. The dual-rotation system is switched to a single-rotation system, the light intensity information of multiple standard samples is measured, and the light intensity information is processed by Fourier transform to obtain the second Fourier coefficients. Using the second Fourier coefficients, the first system parameters, and the fitted thickness, the first system parameters are iteratively replaced one by one until all the first system parameters except for the thickness and the incident angle are updated, thus obtaining the single rotation system parameters. The light intensity information of the sample under test is measured using the updated single rotation system, and the light intensity information of the sample under test is Fourier transformed to obtain the third Fourier coefficient. The Mueller matrix of the sample under test is calculated using the parameters of the single rotation system and the third Fourier coefficients. Using the second Fourier coefficients, the first system parameters, and the fitting thickness, the first system parameters are iteratively fitted and replaced one by one, including: The system parameters of the dual-rotation system are fixed as the first system parameters, wherein the Mueller matrix of the standard sample is fixed by the fitted thickness and incident angle of multiple standard samples measured by the dual-rotation system. The two parameters in the first system parameters are released sequentially to participate in the fitting, and the parameters obtained after fitting replace the original parameters.

2. The method according to claim 1, characterized in that, The method of obtaining the first system parameters of the dual-rotation system and measuring the fitted thickness of multiple standard samples using the dual-rotation system includes: The light intensity information of the standard sample was measured using a dual rotation system, and the light intensity information of the standard sample was processed by Fourier transform to obtain the first Fourier coefficients; The first system parameters of the double-rotation system are obtained by fitting and iterating using the first Fourier coefficients. The fitted thickness of multiple standard samples was measured using the updated dual-rotation system.

3. The method according to claim 1, characterized in that, The fitting iteration can be implemented using methods such as traversal, global optimization, or local optimization algorithms.

4. The method according to claim 3, characterized in that, The local optimization algorithms include: Levenberg-Marquardt method, Newton's method, gradient descent method, or conjugate gradient method.

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