System calibration method and device for dual-rotating compensator type mueller matrix ellipsometer

Abstract

The application provides a system calibration method and device of a double-rotating compensator type Mueller matrix ellipsometer, wherein a standard sample with an arbitrary thickness is measured by using a double-rotating compensator type Mueller matrix ellipsometer to be calibrated, a measurement light intensity signal corresponding to the sample is obtained, then a theoretical light intensity signal is simulated by using to-be-calibrated parameters of each optical device in the ellipsometer, a film thickness of the standard sample, an incident angle of polarized light irradiated to the sample surface and an equivalent light source intensity, and the system parameters in a full spectral range are obtained by fitting the measurement light intensity signal and the theoretical light intensity signal. The calibration algorithm of the double-rotating compensator type Mueller matrix ellipsometer system provided by the application can obtain real installation azimuth angle parameters, and is helpful to reduce system differences of instruments in factory.

Description

Technical Field

[0001] This invention relates to the field of elliptic deflection system calibration, and more specifically, to a system calibration method and apparatus for a Mueller matrix elliptic deflector with dual rotating compensators. Background Technology

[0002] In the semiconductor industry, the measurement of optical critical dimension (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 advanced semiconductor process monitoring due to its advantages such as non-contact, non-destructive, low cost, speed, and high precision.

[0003] Taking the Mueller matrix ellipsometer with dual rotating compensators as an example, such as Figure 1 As shown, its basic configuration includes: light source 1, polarizer 2, first rotary motor 3, first compensator 4, sample to be tested 5, second compensator 6, second rotary motor 7, analyzer 8, and spectrometer 9. The ellipsometer works on a model-based measurement principle. The light intensity signal measured by the spectrometer is converted into the required ellipsometric spectrum through the system model. The parameters required as input to the system model include the azimuth angle of the polarizer, the azimuth angle of the analyzer, the azimuth angles of the two rotary compensators, and the phase delay. The specific steps of the ellipsometer operation are as follows:

[0004] 1. The light source emits natural light, which is converted into polarized light after passing through a polarizer;

[0005] 2. Polarized light shines on the sample stage after passing through the first rotary compensator, and is reflected or refracted after passing through the sample surface to become new polarized light;

[0006] 3. The new polarized light passes through another rotating compensator and analyzer, and then the intensity signal of the new polarized light is obtained by the spectrometer.

[0007] 4. The ellipsometric spectrum of the sample is derived using the light intensity signal detected by the spectrometer;

[0008] 5. The thickness of the sample is obtained based on the ellipsoidal spectrum of the sample.

[0009] Among them, the system parameters of the ellipsometer have a great influence on the final measurement results of the sample parameters. Therefore, the calibration of the system parameters of the ellipsometer is particularly important. Summary of the Invention

[0010] This invention addresses the technical problems existing in the prior art by providing a system calibration method and apparatus for a Mueller matrix ellipsometer with dual rotating compensators.

[0011] According to a first aspect of the present invention, a system calibration method for a dual-rotation compensator type Mueller matrix ellipsometer is provided, comprising:

[0012] Step 1, obtaining the measured light intensity signal of the sample to be measured at each wavelength;

[0013] Step 2, simulating the simulated light intensity signal at each wavelength based on the system parameter reference value, equivalent light source intensity, sample thickness and polarization light incident angle at each wavelength;

[0014] Step 3, adjusting the system parameters, equivalent light source intensity, sample thickness and polarization light incident angle at each wavelength based on the regression fitting method to obtain the corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and obtaining the system parameters of the sample to be measured at each wavelength.

[0015] According to the second aspect of the present application, a system calibration device of a double-rotating compensator type Mueller matrix ellipsometer is provided, comprising:

[0016] The acquisition module is configured to obtain the measured light intensity signal of the sample to be measured at each wavelength;

[0017] The simulation calculation module is configured to simulate the simulated light intensity signal at each wavelength based on the system parameter reference value, equivalent light source intensity, sample thickness and polarization light incident angle at each wavelength;

[0018] The calibration module is configured to adjust the system parameters, equivalent light source intensity, sample thickness and polarization light incident angle at each wavelength based on the regression fitting method to obtain the corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and obtain the system parameters of the sample to be measured at each wavelength.

[0019] The present application provides a system calibration method and device of a double-rotating compensator type Mueller matrix ellipsometer, which obtains the system parameters in the full spectral range through the wavelength-by-wavelength calibration method, which helps to reduce the system differences of the instrument out of the factory. The present application is characterized in that the equivalent light source intensity is set as the parameter to be calibrated, and the light intensity signal is used as the target to obtain the system parameters in the full spectral range required for calibration through the regression iteration. After the system parameters of the instrument are obtained, they can be used to measure the thickness and other information of other samples. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 Fig. 1 is a structural schematic diagram of a double-rotating compensator type Mueller matrix ellipsometer;

[0021] Figure 2 Fig. 2 is a flow chart of a system calibration method of a double-rotating compensator type Mueller matrix ellipsometer provided by the present application;

[0022] Figure 3 Fig. 3 is a structural schematic diagram of a system calibration device of a double-rotating compensator type Mueller matrix ellipsometer provided by the present application.

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

[0024] 1, light source, 2, polarizer, 3, first rotary motor, 4, first compensator, 5, sample to be measured, 6, second compensator, 7, second rotary motor, 8, analyzer, 9, spectrometer. DETAILED DESCRIPTION

[0025] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present application. In addition, the technical features in each of the embodiments or in a single embodiment provided by the present application can be combined with each other at will to form a feasible technical solution, and such combination is not restricted by the order of steps and / or structure composition mode, but must be based on the fact that it can be realized by those of ordinary skill in the art. When the combination of technical solutions appears to be contradictory or unfeasible, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection required by the present application.

[0026] Figure 2 A system calibration method for a double-rotating compensator type Mueller matrix ellipsometer provided by the present application, as shown in Figure 2 The method comprises the following steps:

[0027] Step 1: Obtain the measured light intensity signal of the sample to be measured at each wavelength.

[0028] It can be understood that the measured light intensity signal of the sample to be measured at each wavelength λ i (i is the wavelength number) is obtained by using an ellipsometric measuring device such as a spectrometer, that is, each wavelength λ i corresponds to a group of measured light intensity signals, denoted as I meas .

[0029] Step 2: Based on the system parameter reference value, equivalent light source intensity, sample thickness and polarization light incident angle at each wavelength, simulate to obtain the simulated light intensity signal at each wavelength.

[0030] As an embodiment, the step 2 of simulating to obtain the simulated light intensity signal at each wavelength based on the system parameter reference value, equivalent light source intensity, sample thickness and polarization light incident angle at each wavelength comprises: for each wavelength, setting the system parameter reference value, equivalent light source intensity, sample thickness and polarization light incident angle, and calculating the corresponding simulated light intensity signal through the system model of the double-rotating compensator type ellipsometer.

[0031] wherein the system model of the dual-rotating compensator type ellipsometer is obtained by multiplying the Mueller matrix of each optical device, the sample, and the specific expression is as follows: S out = [M A R(A)]

[0032]

[0033] The polarization state of the light beam is described using a Stokes vector, and the Stokes vector has four components, of which the first component is the light intensity signal strength. S in is the Stokes vector describing the polarization state of the light source, and it is generally considered that the light source emits natural light, i.e. S in = [s, 0, 0, 0] T , s is the equivalent light source intensity, and S out represents the Stokes vector of the light beam received by the spectrometer. R(-P)M P is the Mueller matrix describing the polarizer, and P is the equivalent azimuth angle of the polarizer. is the Mueller matrix describing the first rotating compensator, wherein C1=ω1t+C s1 , C s1 is the initial azimuth angle of the first compensator, ω1 is the mechanical frequency of the rotation of the first motor, t is time, and δ1 is the phase retardation of the first compensator. is the Mueller matrix describing the second rotating compensator, wherein C2=ω2t+C s2 , C s2 is the initial azimuth angle of the second compensator, ω2 is the mechanical frequency of the rotation of the second motor, and δ2 is the phase retardation of the second compensator. M A R(A) is the Mueller matrix describing the analyzer, and A is the equivalent azimuth angle of the analyzer. M S (d, θ) is the Mueller matrix of the sample, d is the thickness of the sample, and θ is the incident angle of the polarized light.

[0034] In step 3, based on a regression fitting method, the system parameters, the equivalent light source intensity, the thickness of the sample, and the incident angle of the polarized light at each wavelength are adjusted to obtain a corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and the system parameters of the sample to be measured at each wavelength are obtained.

[0035] As an example, in step 3, based on a regression fitting method, the system parameters, the equivalent light source intensity, the thickness of the sample, and the incident angle of the polarized light at each wavelength are adjusted to obtain a corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and the system parameters of the sample to be measured at each wavelength are obtained, including: adjusting the polarizer azimuth angle P, the analyzer azimuth angle A, and the azimuth angles C s1, Cs2, and phase retardation amounts δ1, δ2, equivalent light source intensity s, sample thickness d, and polarized light incidence angle θ as calibration parameters, and by continuously adjusting the calibration parameters until the calculated simulation light intensity signal is close to the measured light intensity signal of the corresponding wavelength, the calibrated parameters under the corresponding wavelength are obtained.

[0036] It can be understood that for each wavelength, the calibration parameters include: P, C s1 , δ1, C s2 , δ2, A, d, θ, and s. Given all the reference values of the calibration parameters, the simulation light intensity signal received by the spectrometer can be simulated and is denoted as I sim .

[0037] In the calibration process of the ellipsometer device, each wavelength is calibrated one by one. For each wavelength, the corresponding simulation light intensity signal is calculated through the system model of the double-rotating compensator type ellipsometer by setting the calibration parameters, and it is determined whether the calculated simulation light intensity signal is close to the measured light intensity signal. By continuously adjusting the calibration parameters, the calculated simulation light intensity signal is close to the measured light intensity signal of the corresponding wavelength, and the calibrated parameters under the corresponding wavelength are obtained, including: each time the calibration parameters are adjusted, the residual error between the simulation light intensity signal and the measured light intensity signal is calculated, and the calibration parameters are continuously adjusted until the residual error between the simulation light intensity signal and the measured light intensity signal is minimized, and the corresponding calibrated parameters are obtained.

[0038] It can be understood that by adjusting the azimuth angle P of the polarizer, the azimuth angle A of the analyzer, the azimuth angles C s1 , Cs2 of the two rotating compensators, the phase retardation amounts δ1, δ2, the equivalent light source intensity s, and the sample thickness d and the polarized light incidence angle θ, all parameter values that make the residual error ||I sim (P, A, C S1 , C S1 , δ1, δ2, s, d, θ)-I meas ||2 between the sample measured light intensity signal and the simulation light intensity signal minimum are regressed and fitted. The subscript "opt" represents the optimal solution, and ||·||2 represents the two-norm of the vector.

[0039] As an example, the thickness of the sample to be measured and the polarized light incidence angle are: the average value of the calibrated thickness d i of the sample to be measured corresponding to each wavelength is taken as the thickness of the sample to be measured, and the average value of the calibrated polarized light incidence angle θ i of the sample to be measured corresponding to each wavelength is taken as the polarized light incidence angle of the sample to be measured.

[0040] It can be understood that the thickness d and the polarization light incidence angle θ of the sample to be measured are independent of the wavelength, but the d opt and θ opt calibrated at each wavelength are not completely consistent, and the d opt and θ opt at each wavelength are averaged as the thickness and the polarization light incidence angle of the sample to be measured.

[0041] The regression fitting method in the above process includes but is not limited to traversal method, global optimization method (such as genetic algorithm, particle swarm algorithm, ant colony algorithm, etc.) and local optimization algorithm (such as Levenberg-Marquardt method, Newton method, quasi-Newton method, gradient descent method, conjugate gradient method, etc.).

[0042] After obtaining the system parameters by the above calibration method, the ellipsometer can be used to directly measure the thickness and other information of any sample.

[0043] Referring to Figure 3 , a system calibration device of a double-rotating compensator type Mueller matrix ellipsometer provided by the present application, comprising an acquisition module 301, a simulation calculation module 302 and a calibration module 303, wherein:

[0044] The acquisition module 301 is used to acquire the measured light intensity signal of the sample to be measured at each wavelength;

[0045] The simulation calculation module 302 is used to simulate the simulation light intensity signal at each wavelength based on the system parameter reference value, the equivalent light source intensity, the sample thickness and the polarization light incidence angle at each wavelength;

[0046] The calibration module 303 adjusts the system parameter, the equivalent light source intensity, the sample thickness and the polarization light incidence angle at each wavelength based on the regression fitting method, obtains the corresponding simulation light intensity signal, so that the simulation light intensity signal is close to the measured light intensity signal, and acquires the system parameter of the sample to be measured at each wavelength.

[0047] It can be understood that the system calibration device of the double-rotating compensator type Mueller matrix ellipsometer provided by the present application corresponds to the system calibration method of the double-rotating compensator type Mueller matrix ellipsometer provided by the foregoing embodiments, and the related technical features of the system calibration device of the double-rotating compensator type Mueller matrix ellipsometer can refer to the related technical features of the system calibration method of the double-rotating compensator type Mueller matrix ellipsometer, which will not be repeated here.

[0048] The system calibration method and device of the dual-rotating compensator type Mueller matrix ellipsometer provided by the embodiment of the present application can obtain the system parameters in the full spectral range through the wavelength-by-wavelength calibration mode, which helps to reduce the system difference of the instrument when leaving the factory.

[0049] It should be noted that in the above embodiments, the description of each embodiment has its own focus, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0050] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0051] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system), and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows 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 the processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing devices to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices produce a device that implements the flowcharts and / or block diagrams. Figure 1 The function specified in one flow or multiple flows and / or blocks Figure 1 The device that implements the function specified in one block or multiple blocks.

[0052] These computer program instructions can also be stored in a computer readable storage medium that can guide the computer or other programmable data processing devices to work in a specific way, so that the instructions stored in the computer readable storage medium produce a product including instruction devices that implement the flowcharts and / or block diagrams. Figure 1 The function specified in one flow or multiple flows and / or blocks Figure 1 The device that implements the function specified in one block or multiple blocks.

[0053] These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 The flowchart blocks Figure 1 The flowchart blocks

[0054] While the preferred embodiments of the application have been described, additional variations and modifications can be made to the preferred embodiments by those skilled in the art once they learn of the basic inventive concepts. Therefore, the appended claims are intended to cover all such additional variations and modifications as fall within the scope of the present application.

[0055] Obviously, numerous modifications and variations of the present application are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A system calibration method of a dual-rotating compensator Mueller matrix ellipsometer, comprising: Step 1, obtaining a measured light intensity signal of a sample to be measured at each wavelength; Step 2, simulating a simulated light intensity signal at each wavelength based on a system parameter reference value, an equivalent light source intensity, a sample thickness, and a polarized light incident angle at each wavelength; Step 3, adjusting the system parameter, the equivalent light source intensity, the sample thickness, and the polarized light incident angle at each wavelength based on a regression fitting method to obtain a corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and obtaining the system parameter of the sample to be measured at each wavelength; The step 2, simulating the simulated light intensity signal at each wavelength based on the system parameter reference value, the equivalent light source intensity, the sample thickness, and the polarized light incident angle at each wavelength, comprises: For each wavelength, setting the system parameter reference value, the equivalent light source intensity, the sample thickness, and the polarized light incident angle, and calculating a corresponding simulated light intensity signal through a system model of a dual-rotating compensator ellipsometer; the system model of the dual-rotating compensator ellipsometer is expressed as: wherein the polarization state of the light beam is described using a Stokes vector, the Stokes vector having four components, the first component being the light intensity signal strength, S in is the Stokes vector describing the polarization state of the light source, i.e. S in = [s, 0, 0, 0] T , s being the equivalent light source intensity, S out denotes the Stokes vector of the light beam received by the spectrometer, i.e. the light intensity signal, R(-P)M P is the Mueller matrix describing the polarizer, P being the equivalent azimuth angle of the polarizer, To describe the Mueller matrix of the first rotation compensator, where C1= ω1t + C s1 , C s1 is the azimuth angle of the first compensator, ω1is the mechanical frequency of rotation of the first motor, t is time, δ1is the phase delay of the first compensator, where C2= ω2t + C s2 , C s2 is the azimuth angle of the second compensator, ω2is the mechanical frequency of the second motor rotation, δ2is the phase delay of the second compensator, M A R(A) is the Mueller matrix describing the analyzer, A is the equivalent azimuth angle of the analyzer, M S (d, θ) is the Mueller matrix of the sample, d is the sample thickness, and θ is the incident angle of the polarized light.

2. The system calibration method of claim 1, wherein, The step 1, obtaining the measured light intensity signal of the sample to be measured at each wavelength, comprises: Based on the ellipsometric measuring device, the measurement light intensity signals of the sample to be measured at each wavelength λ i are acquired, each wavelength λ i corresponds to a set of measurement light intensity signals, denoted as Imeas, i indicating the number of wavelengths.

3. The system calibration method of claim 1, wherein, The step 3, adjusting the system parameter, the equivalent light source intensity, the sample thickness, and the polarized light incident angle at each wavelength based on the regression fitting method to obtain the corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and obtaining the system parameter of the sample to be measured at each wavelength, comprises: The azimuth angle P of the polarizer, the azimuth angle A of the analyzer, the azimuth angle C of the two rotation compensators s1 , C s2 and the phase retardation δ1, δ2, the equivalent light source intensity s, the thickness d of the sample to be measured and the incident angle θ of the polarized light are taken as the parameters to be calibrated. By continuously adjusting the parameters to be calibrated, until the calculated simulated light intensity signal is close to the measured light intensity signal of the corresponding wavelength, the calibrated parameters under the corresponding wavelength are obtained.

4. The system calibration method of claim 3, wherein, The continuously adjusting the to-be-calibrated parameter until the calculated simulated light intensity signal is close to the measured light intensity signal at the corresponding wavelength to obtain the calibrated parameter at the corresponding wavelength, comprises: Each time the to-be-calibrated parameter is adjusted, the residual error between the simulated light intensity signal and the measured light intensity signal is calculated, and the to-be-calibrated parameter is continuously adjusted until the residual error between the simulated light intensity signal and the measured light intensity signal is minimized, and the corresponding calibrated parameter is obtained. 5.A system calibration device of a dual-rotating compensator Mueller matrix ellipsometer, used for implementing the system calibration method of any one of claims 1-4, comprising: an obtaining module, configured to obtain a measured light intensity signal of a sample to be measured at each wavelength; a simulation calculation module, configured to simulate a simulated light intensity signal at each wavelength based on a system parameter reference value, an equivalent light source intensity, a sample thickness, and a polarized light incident angle at each wavelength; a calibration module, configured to adjust the system parameter, the equivalent light source intensity, the sample thickness, and the polarized light incident angle at each wavelength based on a regression fitting method to obtain a corresponding simulated light intensity signal, so that the simulated light intensity signal is close to the measured light intensity signal, and obtain the system parameter of the sample to be measured at each wavelength.

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