A calibration method for non-ideal ellipsometric systems

Abstract

The present invention provides a calibration method for a non-ideal ellipsometer system, comprising: obtaining measured light intensity information of a standard sample in a measurement system and normalizing it to obtain measured normalized light intensity information of the standard sample; iteratively fitting system parameters of the measurement system based on the measured normalized light intensity information of the standard sample and theoretical normalized light intensity information; obtaining measured light intensity information of a sample to be measured and normalizing it to obtain measured normalized light intensity information of the sample to be measured; and iteratively fitting parameters of the sample to be measured based on the measured normalized light intensity information of the sample to be measured and theoretical normalized light intensity information according to the system parameters of the measurement system obtained by iterative fitting. When solving the system parameters, the present invention adds fitting parameters of trigonometric functions to the system parameters. When a wave plate is tilted, high-precision wavelength-by-wavelength calibration can still be performed.

Description

Technical Field

[0001] The present invention relates to the field of spectral measurement, and more particularly to a calibration method for a non-ideal ellipsometric system. Background Art

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

[0003] The basic configuration of the ellipsometer can be found in Figure 1 , mainly includes a light source 1, a polarizer 2, a first rotating motor 3, a polarizing composite wave plate 4, a sample to be measured 5, an analyzing composite wave plate 6, a second rotating motor 7, an analyzing composite wave plate 8 and a spectrometer 9.

[0004] The basic principle process of system calibration and measurement of ellipsometer is as follows:

[0005] 1. Natural light passes through a polarizer and a (rotating) wave plate to obtain polarized light;

[0006] 2. New polarized light obtained by reflection or transmission of polarized light through the standard sample material;

[0007] 3. The new polarized light passes through the (rotating) wave plate and analyzer of the analyzer arm to obtain the changed light intensity information;

[0008] 4. Process the measured light intensity change information to obtain system parameters;

[0009] 5. Measure the light intensity information of the sample to be tested;

[0010] 6. Use the system parameters and the light intensity information of the sample to be tested to fit iteratively to obtain the Mueller matrix of the sample.

[0011] Among them, the system parameters obtained in 4 include the phase delay of the analyzer composite wave plate, the azimuth angle of the analyzer composite wave plate, the phase delay of the polarizer composite wave plate, the azimuth angle of the polarizer composite wave plate, the azimuth angle of the analyzer, and the azimuth angle of the polarizer. The entire optical system is calibrated by wavelength-by-wavelength calibration, but there is a wave plate tilt problem in the actual process installation or production process, which reduces the calibration accuracy. Summary of the Invention

[0012] The present invention addresses the technical problems existing in the prior art and provides a calibration method for a non-ideal ellipsometric system, comprising:

[0013] Obtaining the measured light intensity information of the standard sample in the measurement system and normalizing it to obtain the measured normalized light intensity information of the standard sample;

[0014] According to the measured normalized light intensity information and the theoretical normalized light intensity information of the standard sample, the system parameters of the measurement system are fitted and iterated, wherein the system parameters include the phase delay of the analyzer composite wave plate, the azimuth of the analyzer composite wave plate, the phase delay of the polarizing composite wave plate, the azimuth of the polarizing composite wave plate, the azimuth of the analyzer, and the azimuth of the polarizing plate, and the newly added trigonometric function phase and amplitude of the phase delay of the analyzer composite wave plate, the trigonometric function phase and amplitude of the azimuth of the analyzer composite wave plate, the trigonometric function phase and amplitude of the phase delay of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth of the analyzer composite wave plate, and the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate;

[0015] Obtaining the measured light intensity information of the sample to be tested and normalizing it to obtain the measured normalized light intensity information of the sample to be tested;

[0016] According to the system parameters of the measurement system obtained through iterative fitting, the parameters of the sample to be measured are obtained through iterative fitting based on the measured normalized light intensity information and the theoretical normalized light intensity information of the sample to be measured.

[0017] The present invention provides a calibration method for a non-ideal ellipsometric system. When solving the system parameters, fitting parameters of trigonometric functions are added to the system parameters. Even when the wave plate is tilted, high-precision wavelength-by-wavelength calibration can still be performed. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the structure of the optical measurement system;

[0019] Figure 2 Schematic diagram of the fluctuation trend of the equivalent optical rotation angle;

[0020] Figure 3 Schematic diagram of the fluctuation trend of the equivalent phase delay;

[0021] Figure 4 Schematic diagram of the fluctuation trend of the equivalent fast axis azimuth;

[0022] Figure 5 This is a flow chart of a calibration method for a non-ideal ellipsometric system provided by the present invention.

[0023] In the accompanying drawings, the names of the components represented by the reference numbers are as follows:

[0024] 1. Light source, 2. Polarizer, 3. First rotating motor, 4. Polarizer composite wave plate, 5. Sample to be tested, 6. Analyzer composite wave plate, 7. Second rotating motor, 8. Analyzer, 9. Spectrometer. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention can be arbitrarily combined with each other to form a feasible technical solution. This combination is not restricted by the sequence of steps and / or structural composition mode, but must be based on the ability of ordinary technicians in this field to implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0026] based on Figure 1 The optical measurement system in the CMOS is based on the following principles:

[0027] The phase retardation of a single wave plate at any incident angle and azimuth angle can be calculated using the following formula:

[0028]

[0029] Among them, θ tile is the incident angle, β is the fast axis azimuth, d is the thickness of the single wave plate, n e and n o are the e-light and o-light refractive indices of the material, and λ is the wavelength.

[0030] The composite wave plate model has the following formula:

[0031]

[0032] Among them, λ i is the central wavelength of the i-th wave plate of the composite wave plate model, is the angle between the optical axes of the i+1th wave plate and the first wave plate in the composite wave plate model, M wp is the equivalent Mueller matrix of the composite wave plate, δ1 is the equivalent phase delay, ρ1 is the equivalent optical rotation angle, and θ1 is the equivalent fast axis azimuth.

[0033] By selecting the central wavelength, optical axis angle, incident angle and wavelength through formula (2), and changing the fast axis azimuth, the fluctuation trends of the equivalent phase delay, equivalent optical rotation angle and equivalent fast axis azimuth are obtained, respectively. Figure 2 、 Figure 3 and Figure 4 , the variation trend is approximately a trigonometric function, so the present invention can calibrate the tilt measurement system by adding trigonometric functions.

[0034] Figure 5 A flow chart of a calibration method for a non-ideal ellipsometric system provided by the present invention is shown as follows: Figure 5 As shown, the method includes:

[0035] S1, obtaining the measured light intensity information of the standard sample in the measurement system and normalizing it to obtain the measured normalized light intensity information of the standard sample.

[0036] As an embodiment, the method of obtaining the measured light intensity information of the standard sample in the measurement system and normalizing it to obtain the measured normalized light intensity information of the standard sample includes: obtaining multiple different time points t1, t2, t3, ..., t n The measured light intensity information in the measurement system is used to obtain the measured light intensity information sequence of the standard sample within a set time period; the measured light intensity information sequence of the standard sample within the set time period is normalized to obtain the measured normalized light intensity information of the standard sample.

[0037] It is understood that the light intensity variation information of the standard sample is obtained using a measurement system such as a spectrometer. Specifically, the measured light intensity information of the standard sample at multiple different times over a period of time is measured using a measurement system such as a spectrometer to form a measured light intensity information sequence of the standard sample. The measured light intensity information sequence of the standard sample is then normalized to obtain the measured normalized light intensity information of the standard sample.

[0038] S2, based on the measured normalized light intensity information of the standard sample and the theoretical normalized light intensity information, the system parameters of the measurement system are fitted and iterated.

[0039] It is understandable that this step utilizes the measured normalized light intensity information and theoretical normalized light intensity information of the standard sample obtained in S1 to iteratively fit the system parameters of the measurement system, wherein the system parameters here include not only the phase delay of the analyzer composite wave plate, the azimuth of the analyzer composite wave plate, the phase delay of the polarizing composite wave plate, the azimuth of the polarizing composite wave plate, the azimuth of the polarizing composite wave plate, and the azimuth of the polarizing composite wave plate, but also adds the trigonometric function phase and amplitude of the phase delay of the analyzer composite wave plate in the form of trigonometric functions, the trigonometric function phase and amplitude of the azimuth of the analyzer composite wave plate, the trigonometric function phase and amplitude of the phase delay of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate, and the trigonometric function phase and amplitude of the azimuth of the analyzer, as well as the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate. The fitting iterative method includes but is not limited to the Levenberg-Marquardt method, the Newton method, the gradient descent method, the conjugate gradient method, and the like.

[0040] Based on the system parameter factors, a system model of the measurement system is constructed. When no system parameters in the form of trigonometric functions are added, the system model is:

[0041] S out =[M A R(A+ρ2)]×[R(-ω2t-C2-θ2)M(δ2)R(ω2t+C2+θ2)]×Ms×[R(-ω1t-C1-θ1+ρ1)M(δ1)R(ω1t+C1+θ1-ρ1)]×[R(-P+ρ1)M p ]×S in (3).

[0042] After adding the system parameters in the form of trigonometric functions, the system model is:

[0043] S out =[M A R(A+ρ2+A A0 sin(2ω2+φ A0 ))]×[R(-ω2t-C2-θ2-A C20 sin(2ω2+φ C20 ))M(δ2+A δ20 sin(2ω2+φ δ20 ))R(ω2t+C2+θ2+A C20 sin(2ω2+φ C20 ))]×Ms×[R(-ω1t-C1-θ1+ρ1-A C10 sin(2ω1+φ C10 ))M(δ1+A δ10 sin(2ω1+φ δ10 ))R(ω1t+C1+θ1-ρ1+A C10 sin(2ω1+φ C10 ))]×[R(-P+ρ1-A P0 sin(2ω1+φ P0 ))M P ]×S in (4);

[0044] Among them, M s is the sample Mueller matrix, M P 、M Ais the polarizer Mueller matrix of the polarizing arm and the analyzing arm, ρ1 and ρ2 are the optical rotation angles of the polarizing composite wave plate 1 and the analyzing composite wave plate 2, θ1 and θ2 are the optical axis azimuths of the polarizing composite wave plate 1 and the analyzing composite wave plate 2, ω1 and ω2 are the speeds of motor 1 and motor 2, M(δ1) and M(δ2) are the phase delay Mueller matrices of the polarizing composite wave plate and the analyzing composite wave plate, R is the rotation matrix, t is the measurement time, Ms is the measurement sample parameter, P, A, C1, C2 are the initial azimuths of the polarizer, analyzer, polarizing composite wave plate and analyzing composite wave plate, S in is the Stokes vector of normalized natural light, A A0 With φ A0 A is the amplitude and phase of the trigonometric function of the azimuth angle of the analyzer. C20 With φ C20 A is the amplitude and phase of the trigonometric function of the azimuth angle of the composite wave plate. δ20 With φ δ20 A is the amplitude and phase of the trigonometric function of the phase delay of the composite wave plate. C10 With φ C10 A is the amplitude and phase of the trigonometric function of the azimuth angle of the polarizing composite wave plate, δ10 With φ δ10 A is the amplitude and phase of the trigonometric function of the phase retardation of the polarizing composite wave plate. P0 With φ P0 are the amplitude and phase of the trigonometric function of the polarizer azimuth angle.

[0045] It can be understood that the measured normalized light intensity information of the standard sample in S1 is used to iteratively fit the theoretical normalized light intensity information using formula (4), so that the theoretical normalized light intensity information after the fitting iteration is as close as possible to the measured normalized light intensity information of the standard sample, thereby obtaining the system parameters of the measurement system.

[0046] During the fitting iteration process, other parameters are known, but the system parameters are unknown. The system parameters are adjusted, and the theoretical normalized light intensity information is solved based on formula (4). An evaluation function is then used to evaluate the solved theoretical normalized light intensity information and the measured normalized light intensity information of the standard sample. By continuously adjusting the system parameters, the corresponding theoretical normalized light intensity information is solved until the evaluation function value of the solved theoretical normalized light intensity information and the measured normalized light intensity information of the standard sample meets the conditions, and the system parameters at that time are obtained.

[0047] Among them, the initial system parameters are determined, and the corresponding theoretical normalized light intensity information is solved according to formula (4), including: for each time t1, t2, t3, ..., t nAccording to formula (4), based on the determined initial system parameters, the theoretical light intensity information at each moment is solved; the theoretical light intensity information at each moment is normalized to obtain the theoretical normalized light intensity information.

[0048] It can be understood that when using formula (4) to solve the theoretical normalized light intensity information, under a set of adjusted system parameters, the theoretical light intensity information at each moment is solved by formula (4), and then the theoretical light intensity information at all moments is normalized to obtain the theoretical normalized light intensity information.

[0049] S3, obtaining the measured light intensity information of the sample to be tested and normalizing it to obtain the measured normalized light intensity information of the sample to be tested.

[0050] It is understood that the measured light intensity information of the sample to be tested is measured using a measurement system such as a spectrometer and normalized to obtain the measured normalized light intensity information of the sample to be tested. The measurement process is the same as that of measuring the measured normalized light intensity information of the standard sample in S1, and will not be repeated here.

[0051] S4, according to the system parameters of the measurement system obtained by iterative fitting, based on the measured normalized light intensity information and theoretical normalized light intensity information of the sample to be measured, iteratively fitting the parameters of the sample to be measured.

[0052] As an embodiment, the system parameters of the measurement system obtained by fitting iteration are fitted and iterated based on the measured normalized light intensity information and theoretical normalized light intensity information of the sample to be measured, including: determining the initial parameters of the sample to be measured based on the known system parameters of the measurement system obtained by fitting iteration, solving the corresponding theoretical normalized light intensity information through formula (4), and calculating the evaluation value between the theoretical normalized light intensity information and the measured normalized light intensity information of the sample to be measured; continuously adjusting the parameters of the sample to be measured, solving the corresponding theoretical normalized light intensity information through formula (4), until the evaluation value between the theoretical normalized light intensity information and the measured normalized light intensity information of the sample to be measured meets the conditions, and obtaining the parameters of the sample to be measured.

[0053] It is understandable that after obtaining the measured normalized light intensity information of the sample to be tested, the system parameters of the measurement system iteratively obtained by S2 fitting are continuously adjusted, and the theoretical normalized light intensity information is solved based on formula (4) until the evaluation value of the theoretical normalized light intensity information and the measured normalized light intensity information of the sample to be tested meet the conditions, thereby obtaining the parameters of the sample to be tested. Among them, the parameters of the sample to be tested are the parameters of the Mueller matrix.

[0054] An embodiment of the present invention provides a calibration method for a non-ideal ellipsometric system, which involves the problem of two wave plates being tilted. Therefore, new fitting parameters are added, including the trigonometric function phase and amplitude of the phase delay of the analyzing composite wave plate, the trigonometric function phase and amplitude of the azimuth angle of the analyzing composite wave plate, the trigonometric function phase and amplitude of the phase delay of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth angle of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth angle of the analyzing plate, and the trigonometric function phase and amplitude of the azimuth angle of the polarizing plate, to perform wavelength-by-wavelength calibration and improve calibration accuracy.

[0055] It should be noted that, in the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0056] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0057] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0058] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0059] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0060] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0061] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A calibration method for a non-ideal ellipsometric system, characterized in that: include: Obtaining the measured light intensity information of the standard sample in the measurement system and normalizing it to obtain the measured normalized light intensity information of the standard sample; According to the measured normalized light intensity information and the theoretical normalized light intensity information of the standard sample, the system parameters of the measurement system are fitted and iterated, wherein the system parameters include the phase delay of the analyzer composite wave plate, the azimuth of the analyzer composite wave plate, the phase delay of the polarizing composite wave plate, the azimuth of the polarizing composite wave plate, the azimuth of the analyzer, and the azimuth of the polarizing plate, and the newly added trigonometric function phase and amplitude of the phase delay of the analyzer composite wave plate, the trigonometric function phase and amplitude of the azimuth of the analyzer composite wave plate, the trigonometric function phase and amplitude of the phase delay of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate, the trigonometric function phase and amplitude of the azimuth of the analyzer composite wave plate, and the trigonometric function phase and amplitude of the azimuth of the polarizing composite wave plate; Obtaining the measured light intensity information of the sample to be tested and normalizing it to obtain the measured normalized light intensity information of the sample to be tested; According to the system parameters of the measurement system obtained through iterative fitting, the parameters of the sample to be measured are obtained through iterative fitting based on the measured normalized light intensity information and the theoretical normalized light intensity information of the sample to be measured; The method of iteratively fitting the system parameters of the measurement system based on the measured normalized light intensity information and the theoretical normalized light intensity information of the standard sample includes: Construct a system model of the measurement system: （4）； in, is the sample Mueller matrix, is the polarizer Mueller matrix of the polarizing arm and the analyzing arm, is the optical rotation angle of the polarizing composite wave plate and the analyzing composite wave plate, is the azimuth angle of the optical axis of the polarizing composite wave plate and the analyzing composite wave plate, is the speed of motor 1 and motor 2, as well as is the phase delay Mueller matrix of the polarizing composite wave plate and the analyzing composite wave plate, R is the rotation matrix, P, A, C 1、 C2 is the initial azimuth of the polarizer, analyzer, polarizing composite wave plate and analyzer composite wave plate, t is the time, is the Stokes vector of normalized natural light, 、 、 、 、 as well as are the system parameters of the measurement system, where and are the amplitude and phase of the trigonometric function of the analyzer azimuth angle, and are the amplitude and phase of the trigonometric function of the azimuth angle of the composite wave plate, and is the amplitude and phase of the trigonometric function of the phase delay of the composite wave plate, and are the amplitude and phase of the trigonometric function of the azimuth angle of the polarizing composite wave plate, and is the amplitude and phase of the trigonometric function of the phase retardation of the polarizing composite wave plate, and is the amplitude and phase of the trigonometric function of the polarizer azimuth angle; Determine the initial system parameters, solve the corresponding theoretical normalized light intensity information according to formula (4), and calculate the evaluation value between the solved theoretical normalized light intensity information and the measured normalized light intensity information of the standard sample; By continuously adjusting the system parameters, the corresponding theoretical normalized light intensity information is solved based on formula (4) until the evaluation value between the solved theoretical normalized light intensity information and the measured normalized light intensity information of the standard sample meets the conditions, and the system parameters of the measurement system are obtained.

2. The calibration method of a non-ideal ellipsometric system according to claim 1, wherein: The step of obtaining the measured light intensity information of the standard sample in the measurement system and normalizing the information to obtain the measured normalized light intensity information of the standard sample includes: Get multiple different times t1, t2, t3, ..., t within the set time period of the standard sample n The measured light intensity information in the measurement system is used to obtain the measured light intensity information sequence of the standard sample within the set time period; The measured light intensity information sequence of the standard sample within a set time period is normalized to obtain the measured normalized light intensity information of the standard sample.

3. The calibration method of a non-ideal ellipsometric system according to claim 1, wherein: The initial system parameters are determined, and the corresponding theoretical normalized light intensity information is solved according to formula (4), including: For each moment t1, t2, t3, ..., t n , according to formula (4), based on the determined initial system parameters, solve the theoretical light intensity information at each moment; The theoretical light intensity information at each moment is normalized to obtain theoretical normalized light intensity information.

4. The calibration method of a non-ideal ellipsometric system according to claim 1, wherein: The system parameters of the measurement system obtained through iterative fitting are obtained by iteratively fitting the parameters of the sample to be measured based on the measured normalized light intensity information and the theoretical normalized light intensity information of the sample to be measured, including: According to the known system parameters of the measurement system obtained by fitting iteration, the initial parameters of the sample to be tested are determined, the corresponding theoretical normalized light intensity information is solved by formula (4), and the evaluation value between the theoretical normalized light intensity information and the measured normalized light intensity information of the sample to be tested is calculated; The parameters of the sample to be tested are continuously adjusted, and the corresponding theoretical normalized light intensity information is solved by formula (4) until the evaluation value between the theoretical normalized light intensity information and the measured normalized light intensity information of the sample to be tested meets the conditions, and the parameters of the sample to be tested are obtained.

5. The calibration method of a non-ideal ellipsometric system according to claim 1, wherein: The parameters of the sample to be tested are Mueller matrix parameters.

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