Method for measuring a sample based on ellipsometry and ellipsometry measuring device

Abstract

The present disclosure relates to a method for measuring a sample based on an ellipsometer and an ellipsometric measuring device. The method for measuring a sample based on an ellipsometer comprises: collecting a first measurement Mueller spectrum corresponding to a reference light spot position, and obtaining a first Mueller matrix; moving a cylindrical body along a direction perpendicular to an incident plane by a first preset distance to form a measurement light spot, collecting a second measurement Mueller spectrum corresponding to the measurement light spot position, and obtaining a second Mueller matrix; determining a mathematical relationship between the second Mueller matrix and the first Mueller matrix; representing the second Mueller matrix as a first function of an incident light wavelength, a film thickness, and an included angle based on a Fresnel equation and the mathematical relationship; fitting the second measurement Mueller spectrum based on the first function using a nonlinear regression algorithm to obtain a measured value of the film thickness and the included angle; and calculating a radius of the cylindrical body based on the first preset distance and the measured value of the included angle. The method realizes rapid and non-destructive measurement of the radius of the cylindrical sample.

Description

Technical Field

[0001] This invention relates to the field of optical measurement technology, and in particular to a method and device for measuring samples based on an ellipsometer. Background Technology

[0002] In the semiconductor manufacturing industry, methods for measuring semiconductor dimensions typically include non-contact physical measurement methods and optical scattering measurements.

[0003] Non-contact physical measurement methods include measurements using laser thickness gauges, X-ray thickness gauges, and ultrasonic thickness gauges. However, these methods suffer from drawbacks such as slow measurement speed, easy sample damage, insufficient measurement accuracy, and difficulty in measuring the nanoscale oxide layer thickness on the surface of cylindrical samples.

[0004] Optical scattering measurement offers advantages such as high speed, low cost, non-contact, non-destructive operation, and ease of integration, leading to its widespread application in advanced semiconductor process monitoring and manufacturing. Optical scattering measurement relies on the scattering characteristics of light and model fitting to indirectly obtain structural parameters. Common methods include Optical Critical Dimension (OCD) and Film Thickness Measurement. OCD requires the light spot to completely cover a specific area of ​​the sample to obtain sufficient information for dimensional measurement. Therefore, existing optical dimension measurement methods can only measure the microscopic dimensions of samples, such as morphological parameters, and cannot measure the macroscopic dimensions of cylindrical samples, such as their radius. Similarly, film thickness measurement is typically used to analyze the state of the reflected light from the sample using instruments such as ellipsometers to measure film thickness, and it is not used to determine the radius of cylindrical samples. Summary of the Invention

[0005] To address the aforementioned problems in related technologies, a method and ellipsometric measurement device based on an ellipsometer are proposed.

[0006] A first aspect of the present invention provides a method for measuring a sample based on an ellipsometer. The sample includes a cylindrical body and a film layer covering the side surface of the cylindrical body. The method includes: obliquely incident light onto the side surface of the sample to form a reference spot, and taking a plane tangent to the side surface through the reference spot as a reference sectional plane, wherein the incident plane of the incident light corresponding to the reference spot passes through the axis of the cylindrical body, and the azimuth angle of the incident light on the reference sectional plane is zero; acquiring a first measurement Mueller spectrum corresponding to the position of the reference spot, and obtaining a first Mueller matrix M0 corresponding to the first measurement Mueller spectrum; moving the cylindrical body along a direction perpendicular to the incident plane by a first preset distance L to form a measurement spot located on the side surface, and acquiring a second measurement Mueller spectrum Sm corresponding to the position of the measurement spot, the second measurement Mueller spectrum Sm corresponding to a second Mueller matrix M1; determining the mathematical relationship between the second Mueller matrix M1 and the first Mueller matrix M0: M1 =R(-a)*M0*R(a), where R(-a) and R(a) are rotation matrices, and the included angle α is the angle between the reference section and the measurement section, wherein the measurement section is a plane tangent to the side surface through the measurement spot; based on the Fresnel equation and the mathematical relationship, the second Mueller matrix M1 is expressed as a first function of the incident light wavelength wave, film thickness thk, and the included angle α: M1 = f(wave, thk, α); the initial values ​​of the film thickness thk and the included angle α are obtained, and based on the first function, the second measurement Mueller spectrum Sm is fitted using a nonlinear regression algorithm to obtain the measured value thk_value of the film thickness thk and the measured value a_value of the included angle α; based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L, the radius R of the cylindrical body is calculated.

[0007] In one embodiment, the radius R of the cylindrical body is calculated based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L, including: R = L / sin(a_value).

[0008] In one embodiment, the radius R of the cylindrical body is calculated based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L, including: obtaining a plurality of different second preset distances L_n and the measured value a_n_value of the included angle α corresponding to each second preset distance L_n; obtaining the sine value sin(a_n_value) of the included angle α corresponding to the second preset distance L_n through mathematical transformation based on the measured value a_n_value of the included angle α corresponding to each second preset distance L_n; performing linear fitting based on the sine value sin(a_n_value) of the included angle α corresponding to the second preset distance L_n and obtaining the slope value Slope_value of the obtained linear fitting function; and using the slope value Slope_value as the radius R of the cylindrical body.

[0009] In one embodiment, after obtaining the radius R of the cylindrical body, the method further includes verifying the radius R. The verification of the radius R includes: substituting the sine values ​​sin(a_n_value) of the included angles α corresponding to multiple second preset distances L_n as independent variables into the linear fitting function to obtain the fitted value y_bsl_n corresponding to the offset distance; and based on the fitted value y_bsl_n corresponding to each offset distance and the second preset distance L_n, obtaining a correlation coefficient characterizing the similarity between the fitted value y_bsl_n corresponding to each offset distance and the second preset distance L_n. Determine the correlation coefficient Does it meet the first preset condition? If it does, then the radius R of the cylindrical body is determined to meet the condition. If it does not meet the first preset condition, then the radius R of the cylindrical body is remeasured.

[0010] In one embodiment, the method further includes obtaining the precise value of the film thickness thk, thk_precise_value. The step of obtaining the precise value of the film thickness thk, thk_precise_value, includes: based on a plurality of second preset distances L_n and the slope value Slope_value of the linear fitting function, obtaining the precise value a'_n_value of the included angle α corresponding to each of the second preset distances L_n, wherein the precise value a'_n_value of the included angle α corresponding to the second preset distance L_n satisfies: a'_n_value = arcsin(L_n / Slope_value); and converting the precise values ​​a'_n_value of the plurality of included angles α... Substituting n_value into the first function f(wave,thk,a) respectively, we obtain the second function f(wave,thk,a'_n_value) corresponding to each second preset distance L_n, and determine multiple second functions f(wave,thk,a'_n_value) as a function group; obtain the third measurement Mueller spectrum Sm_n corresponding to each second preset distance L_n, and obtain a measurement spectrum group based on multiple third measurement Mueller spectra Sm_n; obtain the initial value of film thickness thk, and use a nonlinear regression algorithm to fit the measurement spectrum group based on the function group to determine the precise value thk_precise_value of film thickness thk.

[0011] In one embodiment, the method further includes obtaining a precise value of the film thickness, thk_precise_value. The step of obtaining the precise value of the film thickness, thk_precise_value, further includes: obtaining a plurality of measured values ​​of the film thickness thk, thk_n_value; obtaining an average value of the film thickness thk, thk_avg_value, based on the plurality of measured values ​​of the film thickness thk, thk_n_value; and using the average value of the film thickness thk, thk_avg_value, as the precise value of the film thickness thk, thk_precise_value.

[0012] In one embodiment, before obtaining the average value thk_avg_value of the film thickness thk based on the measured values ​​thk_n_value of multiple film thicknesses thk, the method further includes: verifying the measured values ​​thk_n_value of the film thickness thk; the verification of the measured values ​​thk_n_value of the film thickness thk includes: obtaining the standard deviation Sigma of the measured values ​​thk_n_value of multiple film thicknesses thk; determining whether the standard deviation Sigma satisfies a second preset condition; if the standard deviation Sigma satisfies the second preset condition, then the step of obtaining the average value thk_avg_value of the film thickness thk is executed; if the standard deviation Sigma does not satisfy the second preset condition, then the step of obtaining the measured values ​​thk_n_value of multiple film thicknesses thk and verifying the measured values ​​thk_n_value of the film thickness thk is re-executed.

[0013] In one embodiment, after obtaining the first Mueller matrix M1, the method further includes a step of determining whether the current position of the reference spot meets the conditions. The step includes: determining whether the value of the second diagonal element of the first Mueller matrix M1 meets the third preset condition; if the third preset condition is met, determining that the current position of the reference spot meets the conditions; if the third preset condition is not met, readjusting the position of the reference spot on the side of the cylindrical body.

[0014] In one embodiment, after incident light is obliquely incident onto the side of the sample to form a reference light spot, the method further includes a step of determining whether the azimuth angle of the incident light on the reference section is zero. This step includes: moving the sample along the axis of its cylindrical body; during the movement, continuously acquiring the position of the light spot on the detector of the ellipsometer after reflection from the film layer on the side of the cylindrical body; determining whether the position of the light spot remains unchanged during the movement; if the position of the light spot remains unchanged, determining that the azimuth angle of the incident light on the reference section is zero; if the position of the light spot changes, readjusting the position of the sample so that the azimuth angle of the incident light on the reference section is zero.

[0015] A second aspect of the present invention provides an ellipsometric measurement apparatus, comprising: a light source for generating a measurement beam; a polarizing arm for modulating the measurement beam to form incident light and obliquely incident the incident light onto a sample, wherein the sample comprises a cylindrical sample; a stage for placing the sample and being capable of moving the sample; a polarizing arm for polarizing outgoing light reflected from a film layer covering the sample; a detector for receiving the outgoing light polarized by the polarizing arm; and a control device electrically connected to the stage, the control device being capable of controlling the stage to move the sample to a position where the sample... The system is configured to: 1) Position where the axis of the sample coincides with the incident plane of the incident light; 2) Position where the stage moves the sample from the first position a preset distance L along a direction perpendicular to the sample's central axis to a second position; 3) Data acquisition module, electrically connected to the control device and the detector, for acquiring the preset distance L and for acquiring the measured Mueller spectrum of the emitted light reflected from the film layer covering the sample at the second position; and 4) Calculation module, for calculating the size and film thickness thk of the sample based on the measured spectrum and the preset distance L, wherein the size includes the radius R of the cylindrical sample.

[0016] The technical solutions provided by the embodiments of this disclosure can include the following beneficial effects: by moving the sample a set distance, a relationship is established between the sample radius and the set distance; this relationship is determined by analyzing the state of the emitted light before and after moving the set distance, thereby determining the sample radius. This method determines the sample radius through mathematical conversion, eliminating the need for other instruments and enabling convenient and non-destructive measurement of the radius of cylindrical samples, thus improving detection efficiency. Furthermore, it allows the determination of the radius and film thickness of a cylindrical sample in a single measurement process, eliminating the need for separate measurements of the radius and film thickness, and reducing the steps required for measuring cylindrical samples. Attached Figure Description

[0017] The above and other objects, features, and advantages of embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example and not limitation, wherein:

[0018] Figure 1 This is a schematic diagram illustrating the principle of measuring the thickness of a film layer on the surface of a sample using an ellipsometer, according to an exemplary embodiment.

[0019] Figure 2 This is a flowchart illustrating a method for measuring a sample based on an ellipsometer according to an exemplary embodiment.

[0020] Figure 3 This is a schematic diagram illustrating the principle of incident light obliquely incident on the side of a sample to form a reference light spot, according to an exemplary embodiment.

[0021] Figure 4 This is a schematic diagram illustrating the principle of forming a measurement spot by incident light obliquely onto the side of a sample, according to an exemplary embodiment.

[0022] Figure 5 This is a cross-sectional view showing a measurement spot formed by incident light obliquely incident on the side of a sample, according to an exemplary embodiment.

[0023] Figure 6 This is a measured Mueller spectrum shown according to an exemplary embodiment.

[0024] Figure 7 This is a flowchart illustrating, according to an exemplary embodiment, the determination of the radius of the cylindrical body of a sample by solving a right triangle.

[0025] Figure 8 This is a flowchart illustrating, according to an exemplary embodiment, the determination of the precise radius R of a cylindrical body through multiple measurements.

[0026] Figure 9 This is a flowchart illustrating a method for verifying a measured radius R according to an exemplary embodiment.

[0027] Figure 10 This is a flowchart illustrating the process of obtaining the precise film thickness value thk_precise_value according to an exemplary embodiment.

[0028] Figure 11 This is a flowchart illustrating, according to an exemplary embodiment, how to obtain the precise value of film thickness thk, thk_precise_value, by performing multiple measurements on film thickness thk.

[0029] Figure 12 This is a flowchart illustrating the verification of a measured value of film thickness thk according to an exemplary embodiment.

[0030] Figure 13 This is a flowchart illustrating, according to an exemplary embodiment, a method for determining whether the current position of a reference spot meets certain conditions.

[0031] Figure 14 This is a flowchart illustrating, according to an exemplary embodiment, a method for determining whether the azimuth angle of incident light on a reference section is zero.

[0032] Figure 15 This is a structural diagram of an ellipticity measuring device provided according to an exemplary embodiment.

[0033] In the accompanying drawings, the same or corresponding reference numerals indicate the same or corresponding parts. Detailed Implementation

[0034] The principles and spirit of the invention will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement the invention, and are not intended to limit the scope of the invention in any way.

[0035] The method for measuring samples based on an ellipsometer provided in this disclosure is applied to the scenario of measuring semiconductor samples. The semiconductor sample is cylindrical, and its surface is covered by a film layer.

[0036] The samples disclosed herein include a cylindrical body and a film covering the sides of the cylindrical body. The samples can be cylindrical high-precision steel, high-precision instrument parts, cylindrical single-crystal silicon rods, etc. The cross-sectional radius of the samples is on the order of millimeters. The film can be, for example, an etched oxide layer on the sample surface. The thickness of the oxide layer is on the order of nanometers.

[0037] In related technologies, ellipsometers and other spectral thickness gauges are commonly used to measure the thickness of films such as oxide films. An ellipsometer obliquely incidents incident light onto the surface of the film and collects the outgoing light after reflection. The Mueller spectrum of the sample is determined from the outgoing light, and the film thickness is determined based on the principles of ellipsometric optics and the Mueller spectrum of the sample. Figure 1 This is a schematic diagram illustrating the principle of measuring the thickness of a film layer on the surface of a sample using an ellipsometer, according to an exemplary embodiment. Figure 1 As shown, the ellipsometer includes a light source 101, a polarizer 102, a first compensator 103, a second compensator 105, an analyzer 106, and a detector 107. The light source 101 emits incident light towards the sample 104 to be measured. After passing through the polarizer 102 and the first compensator 103, the incident light obliquely enters the film layer of the sample 104 and is reflected by the film layer to generate outgoing light. The outgoing light passes through the second compensator 105 and the analyzer 106 and is collected by the detector 107. After passing through the polarizer 102, the first compensator 103, the film layer, the second compensator 105, and the analyzer 106, the polarization characteristics of the incident light change. By analyzing the polarization characteristics of the outgoing light, the thickness of the film layer can be measured. However, although this method can measure the thickness of the film layer on the sample surface, it cannot measure macroscopic dimensions such as the radius of the sample.

[0038] In view of this, this disclosure provides a method for measuring a sample using an ellipsometer. The method involves moving a preset distance from a reference spot position to a measurement spot position, and acquiring Mueller spectra at both the reference and measurement spot positions. Based on the Mueller spectra corresponding to the reference and measurement spot positions, the measured angle between the reference and measurement cross-sections, resulting from the movement of the preset distance, is determined. The radius of the cylindrical sample body is determined based on the preset distance and the measured angle. In this disclosure, by moving the sample a preset distance, a relationship is established between the radius of the cylindrical sample body and geometric parameters that change with the movement of the preset distance, enabling the ellipsometer to measure the cross-sectional radius of a cylindrical sample without the addition of other measuring devices.

[0039] Figure 2 This is a flowchart illustrating a method for measuring a sample using an ellipsometer, according to an exemplary embodiment. Figure 2 As shown, the method for measuring samples based on an ellipsometer includes the following steps.

[0040] In step S11, the incident light is obliquely incident on the side of the sample to form a reference light spot, and the plane that passes through the reference light spot and is tangent to the side is used as the reference sectional plane.

[0041] The incident plane of the incident light corresponding to the reference spot passes through the axis of the cylindrical body, and the azimuth angle of the incident light on the reference sectional plane is zero.

[0042] In this embodiment of the disclosure, incident light of a set wavelength and intensity is incident on the side surface of the sample. Oblique incidence refers to the light rays entering at an angle that is not perpendicular to the sample surface. The angle of oblique incidence can be, for example, Brewster's angle, or other angles of oblique incidence, and there is no specific limitation thereto.

[0043] Figure 3 This is a schematic diagram illustrating the principle of incident light obliquely incident on the side surface of a sample to form a reference light spot, according to an exemplary embodiment. Figure 3 As shown, when the incident plane of the incident light corresponding to the reference spot passes through the axis of the cylindrical body, it indicates that the position where the incident light illuminates the sample surface is the highest point on the cross-section of the cylindrical body. At this time, the extension of the incident light passes through the center of the cross-section. Figure 3 In this model, a spatial rectangular coordinate system XOY is established with the center of the cross-section of the cylindrical body of the sample as the origin. The reference spot is located at the intersection of the surface of the film and the Z-axis.

[0044] In step S12, the first measured Mueller spectrum corresponding to the reference spot position is acquired, and the first Mueller matrix M0 corresponding to the first measured Mueller spectrum is obtained.

[0045] Specifically, based on the collected emitted light intensity and system parameters, the first measured Mueller spectrum corresponding to the reference spot position is calculated, and the expression for the first Mueller matrix corresponding to this first measured Mueller spectrum is M0:

[0046]

[0047] Where N represents the degree of linear polarization, C represents the circular birefringence parameter, and S represents the circular dichroism parameter.

[0048] In step S13, the cylindrical body is moved a first preset distance L along a direction perpendicular to the incident plane to form a measurement spot on the side, and the second measurement Mueller spectrum Sm corresponding to the position of the measurement spot is collected. The second measurement Mueller spectrum Sm corresponds to the second Mueller matrix M1.

[0049] To establish the relationship between the surface oxide layer thickness, cross-sectional radius, and the measured Mueller spectrum, a cylindrical body can be moved a first preset distance L along a direction perpendicular to the incident plane. This first preset distance L can be actively set or randomly moved, and the value of the randomly moved first preset distance L is collected. However, it must be ensured that the first preset distance L is less than the radius of the cylindrical body. When the cylindrical body is moved to a position perpendicular to the incident plane by the first preset distance L, the light spot formed on the surface of the cylindrical body is the measurement spot. Figure 4 This is a schematic diagram illustrating the principle of forming a measurement spot by incident light obliquely onto the side of a sample, according to an exemplary embodiment. Figure 5 This is a cross-sectional view illustrating, according to an exemplary embodiment, how incident light obliquely strikes the side of a sample to form a measurement spot. For example... Figure 4 and Figure 5 As shown, before the cylindrical body is moved along a direction perpendicular to the incident plane, the position where the incident light obliquely strikes the sample surface is the highest point on the cross-section of the cylindrical sample body, i.e., the intersection of the Z-axis and the sample surface. After the sample is moved a first preset distance L, the incident light forms a measurement spot at position F. Point E on the Z-axis is the projection of F onto the Z-axis, and the length of EF is denoted as the distance L by which the sample is moved along a direction perpendicular to the incident plane. In this embodiment, the light source can also be moved a first preset distance L along a direction perpendicular to the incident plane; this disclosure does not impose a specific limitation. Figure 5 As shown, the plane passing through position F and tangent to the side of the cylindrical sample is the measurement section. Figure 6 This is a measured Mueller spectrum illustrated according to an exemplary embodiment. For example... Figure 6 As shown, the acquired Mueller spectra consist of 16 images, each corresponding to an element in the Mueller matrix. Each Mueller spectrum image includes the values ​​of the corresponding element in the Mueller matrix at different wavelengths.

[0050] In step S14, the mathematical relationship between the second Mueller matrix M1 and the first Mueller matrix M0 is determined: M1 = R(-a) * M0 * R(a), where R(-a) and R(a) are rotation matrices, the included angle a is the angle between the reference tangent plane and the measurement tangent plane, and the measurement tangent plane is the plane that passes through the measurement spot and is tangent to the side surface.

[0051] In this embodiment of the disclosure, the measurement spot formed by the incident light obliquely incident on the side of the sample can be regarded as the reference spot obtained by rotating the reference spot around the center of the cross-section of the cylindrical body of the sample by an included angle α. Combined with Figure 3 , Figure 4 and Figure 5 In this embodiment, the second Mueller matrix M1 can be represented as the component of the first Mueller matrix M0 transformed from the initial coordinate system of the ellipsometer corresponding to the reference section by rotating it around the OY axis by an included angle α to the sample coordinate system corresponding to the measurement section. Since the detector can only receive the emitted light in the YOZ plane of the initial coordinate system, this component is the component of the first Mueller matrix M0 after the coordinate system transformation in the YOZ plane of the initial coordinate system. Therefore, the second Mueller matrix M1 is determined.

[0052] In step S15, based on the Fresnel equation and mathematical relationships, the second Mueller matrix M1 is expressed as a first function of the incident light wavelength wave, film thickness thk, and included angle a: M1 = f(wave, thk, a).

[0053] In this embodiment, ellipticity parameters can be obtained based on the Fresnel equations, where the ellipticity parameters include the amplitude ratio Ψ and the phase difference Δ. The ellipticity parameters are functions related to the film thickness thk, the reflection angle θ, and the refractive index, where the refractive index is a known quantity related to the wavelength Wave. Since the elements of the Mueller matrix can be determined by the ellipticity parameters, the second Mueller matrix M1 can be expressed as M1 = f(wave,thk,a) based on the Fresnel equations and the mathematical relationship between the second Mueller matrix M1 and the first Mueller matrix M0. This first function is a function with the second Mueller matrix M1 as the dependent variable and the wavelength Wave, film thickness thk, and angle α as independent variables.

[0054] In step S16, the initial values ​​of the film thickness thk and the included angle a are obtained, and the second measurement Mueller spectrum Sm is fitted based on the first function using a nonlinear regression algorithm to obtain the measured values ​​of the film thickness thk_value and the included angle a_value.

[0055] In this embodiment, a first function is pre-established, and initial values ​​for the film thickness thk and the included angle α are obtained. The values ​​of film thickness thk and included angle α are iteratively updated based on a nonlinear regression algorithm until the error between the value of the first function at each wavelength Wave, determined based on the current values ​​of film thickness thk and included angle α, and the value of the second measured Mueller spectrum Sm at each corresponding wavelength Wave meets a preset condition, or the number of iterations reaches a preset value, at which point iteration stops. The value of film thickness thk at the time of stopping iteration is taken as the measured value of film thickness thk, and the value of included angle α is taken as the measured value of included angle α. The nonlinear regression algorithm can be, for example, the LM algorithm.

[0056] In step S17, the radius R of the cylindrical body is calculated based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L.

[0057] Through the above embodiments, the sample is moved a first preset distance L from the reference position to obtain the measurement spot. The geometric relationship between the measurement spot and the center of the circle is determined by the mathematical relationship between the first Mueller matrix M0 corresponding to the reference spot position and the second Mueller matrix M1 corresponding to the measurement spot position. This geometric relationship is then used to obtain the radius of the cylindrical sample body, achieving rapid and non-destructive measurement of the radius of the cylindrical sample.

[0058] It is understandable that moving the cylindrical body along a direction perpendicular to the incident plane by a first preset distance L, the resulting measurement spot, the center of the cylindrical body, and the projection of the measurement spot onto the Z-axis, can form a right triangle. Solving for this right triangle simplifies the process of determining the radius of the cylindrical sample body. The following embodiments further illustrate the method for determining the radius R of the cylindrical body.

[0059] In one exemplary embodiment, Figure 7 This is a flowchart illustrating, according to an exemplary embodiment, the determination of the radius of the cylindrical body of a sample by solving a right-angled triangle. For example... Figure 7 As shown, the method of determining the radius of the cylindrical body of the sample by solving a right triangle includes the following steps.

[0060] In step S21, the cylindrical body is moved a first preset distance L in a direction perpendicular to the incident plane to form a measurement spot on the side.

[0061] In step S22, the measured value a_value of the included angle α corresponding to the first preset distance L is determined.

[0062] In step S23, the radius R of the cylindrical body is calculated by R = L / sin(a_value) based on the measured value a_value of the first preset distance L and the included angle α corresponding to the first preset distance L.

[0063] In this embodiment, moving the cylindrical body a first preset distance L along a direction perpendicular to the incident plane is to make the line connecting the measurement spot, the projection of the measurement spot on the Z-axis, and the center point form a right triangle, establishing a connection between the first preset distance L and the radius R of the cylindrical body. The first preset distance L is equal to the length of one of the right-angled sides of the right triangle. The included angle α is the angle between the reference sectional plane and the measurement sectional plane. Since the light spot changes from the reference light spot to the measurement light spot, it is equivalent to rotating the included angle α about the axis of the cylindrical body, therefore the included angle α is equal to an acute angle of the right triangle. Once one right-angled side and one acute angle of the right triangle are determined, the hypotenuse of the right triangle can be obtained using trigonometric functions, and the length of the hypotenuse is the radius R of the cylindrical body.

[0064] In the above embodiments, the cylindrical body is moved a first predetermined distance to construct a right-angled triangle based on the measurement spot, the projection of the measurement spot on the Z-axis, and the position of the center of the circle. One leg of this right-angled triangle is known. An acute angle of this right-angled triangle is determined through mathematical conversion, thereby obtaining the hypotenuse of the right-angled triangle. This achieves rapid and non-destructive measurement of the radius of a cylindrical sample by obtaining parameters that can be measured by an ellipsometer through mathematical conversion.

[0065] It is understandable that, due to the small size of optical measurement devices and samples, the parameters measured each time are usually affected by random errors. Multiple measurements can reduce the impact of random errors and improve measurement accuracy. The following embodiments further illustrate the method of determining the precise radius R of a cylindrical body through multiple measurements.

[0066] In one exemplary embodiment, Figure 8 This is a flowchart illustrating, according to an exemplary embodiment, the determination of the precise radius R of a cylindrical body through multiple measurements. (e.g.) Figure 8 As shown, the method for determining the precise radius R of the cylindrical body through multiple measurements includes the following steps.

[0067] In step S31, the measured values ​​a_n_value of the angle α between multiple different second preset distances L_n and each second preset distance L_n are obtained.

[0068] In step S32, based on the measured value a_n_value of the included angle α corresponding to each second preset distance L_n, the sine value sin(a_n_value) of the included angle α corresponding to the second preset distance L_n is obtained through mathematical transformation.

[0069] In step S33, a linear fit is performed based on the sine value sin(a_n_value) of the angle α between the second preset distance L_n and the second preset distance L_n, and the slope value Slope_value of the obtained linear fit function is obtained.

[0070] In step S34, the slope value Slope_value is used as the radius R of the cylindrical body.

[0071] In this embodiment, multiple second preset distances L_n can be randomly generated or selected according to a set rule, and the measured value a_n_value of the included angle α corresponding to each second preset distance L_n is measured. Based on the relationship between the preset distance L and the included angle α in a right triangle, the second preset distance L_n is determined as the ordinate of the function to be linearly fitted, and the sine value sin(a_n_value) of the included angle α corresponding to the second preset distance L_n is determined as the abscissa of the function to be linearly fitted. Based on the determined ordinate and abscissa, the multiple second preset distances L_n and the measured value a_n_value of the included angle α are linearly fitted to obtain a linear fitting function. The slope value Slope_value of this linear fitting function represents the length of the hypotenuse in the right triangle determined by the second preset distances through trigonometric functions. Therefore, the slope value Slope_value of the linear fitting function is the radius of the cylindrical body. Since random errors exhibit irregular fluctuations in multiple measurements, and linear fitting can find the average trend of these fluctuations, random errors can be effectively eliminated through linear fitting.

[0072] Through the above embodiments, the sine value sin(a_n_value) of the included angle α corresponding to the second preset distance L_n, obtained from multiple measurements, is linearly fitted, eliminating the influence of random errors and thus improving the accuracy of the radius measurement of the cylindrical sample. Furthermore, compared to the method of repeatedly measuring the radius R of the cylindrical body and then averaging it, this method avoids the influence of sampling errors and can obtain the radius R of the cylindrical body more accurately.

[0073] In the embodiments of this disclosure, the measured radius R can be verified to determine the validity of the measurement result, thereby further improving the measurement accuracy. The following embodiments further illustrate the method of verifying the measured radius R in this disclosure.

[0074] In one exemplary embodiment, Figure 9This is a flowchart illustrating a method for verifying a measured radius R according to an exemplary embodiment. For example... Figure 9 As shown, the method for verifying the measured radius R includes the following steps:

[0075] In step S41, the sine value sin(a_n_value) of the included angle α corresponding to the multiple second preset distances L_n is substituted into the linear fitting function as the independent variable to obtain the fitting value y_bsl_n corresponding to the offset distance.

[0076] In step S42, based on the fitted value y_bsl_n corresponding to each offset distance and the second preset distance L_n, the correlation coefficient is obtained to characterize the similarity between the fitted value y_bsl_n corresponding to each offset distance and the second preset distance L_n.

[0077] In step S43, the correlation coefficient is determined. Does it meet the first preset condition?

[0078] In step S44, if the first preset condition is met, it is determined that the radius R of the cylindrical body meets the condition.

[0079] In step S45, if the first preset condition is not met, the radius R of the cylindrical body is remeasured.

[0080] In this embodiment, the linear fitting function is obtained from multiple second preset distances L_n and the sine value sin(a_n_value) of their corresponding included angle α. Therefore, the linear fitting function can be used to characterize the relationship between the second preset distances L_n and their corresponding included angle α. In this embodiment, multiple second preset distances L_n can be randomly determined or determined according to set rules, and the sine value sin(a_n_value) of the included angle α is calculated separately for each second preset distance L_n. The sine value sin(a_n_value) of the actually measured included angle α is substituted into the linear fitting function obtained from the same second preset distance L_n to obtain the fitted value y_bsl_n corresponding to the offset distance. The offset distance characterizes the preset distance obtained by fitting the actually measured included angle α through the linear fitting function; therefore, there should be a correlation between the fitted value y_bsl_n corresponding to the offset distance and the second preset distance L_n. The correlation coefficient between the offset distance and the second preset distance L_n can be calculated. The correlation is verified using the following method. If the correlation coefficient meets the first preset condition, it indicates the existence of the correlation, meaning the linear fitting function meets the condition, and thus the radius R of the cylindrical body determined by the slope value of the linear fitting function is reasonable. If the correlation coefficient does not meet the first preset condition, it means the measured radius of the cylindrical body does not meet the requirements, and the radius of the cylindrical body needs to be remeasured. The first preset condition can be, for example, the correlation coefficient.

[0081] Through the above embodiments, by calculating the correlation coefficient, it is determined whether there is a correlation between the known multiple second preset distances L_n and the offset distance obtained by inverse calculation through the fitting function, thus verifying the accuracy of the fitting function. By confirming the accuracy of the linear fitting function, it is determined that random errors have been effectively eliminated during the measurement process, ensuring the accuracy of the cylindrical body radius R obtained through the linear fitting function, thereby improving the measurement accuracy of the cylindrical body radius R of the sample.

[0082] In the embodiments of this disclosure, since the film thickness is relatively small, typically within the range of 1nm-100nm, random errors have a significant impact on the film thickness thk measurement results. The influence of random errors on the film thickness thk can be reduced by utilizing the precise value a'_n_value of the included angle α, which eliminates random errors, thereby obtaining the precise value thk_precise_value of the film thickness thk. The following embodiments further illustrate the method for obtaining the precise value thk_precise_value of the film thickness.

[0083] In one exemplary embodiment, Figure 10 This is a flowchart illustrating the process of obtaining the precise film thickness value thk_precise_value according to an exemplary embodiment. For example... Figure 10 As shown, the method for obtaining the precise value of the film thickness thk, thk_precise_value, includes the following steps.

[0084] In step S51, based on the slope value Slope_value of the linear fitting function and the multiple second preset distances L_n, the precise value a'_n_value of the included angle α corresponding to each second preset distance L_n is obtained, wherein the precise value a'_n_value of the included angle α corresponding to the second preset distance L_n satisfies: a'_n_value=arcsin(L_n / Slope_value).

[0085] In step S52, the precise values ​​a'_n_value of multiple included angles a are substituted into the first function f(wave,thk,a) to obtain the second function f(wave,thk,a'_n_value) corresponding to each second preset distance L_n, and the multiple second functions f(wave,thk,a'_n_value) are determined as a function group.

[0086] In step S53, the third measurement Mueller spectrum Sm_n corresponding to each second preset distance L_n is obtained, and a measurement spectrum group is obtained based on multiple third measurement Mueller spectra Sm_n.

[0087] In step S54, the initial value of the film thickness thk is obtained, and based on the function group, a nonlinear regression algorithm is used to fit the measurement spectrum group to determine the precise value of the film thickness thk, thk_precise_value.

[0088] In this embodiment, multiple second preset distances L_n can be randomly determined or specified according to a set rule. Each second preset distance L_n determines multiple precise values ​​a'_n_values ​​of the included angle α using a linear fitting function. After determining the first function with the second Mueller matrix M1 as the dependent variable, the incident light wavelength wave, the film thickness thk, and the included angle α as independent variables, it is necessary to determine the two unknown quantities, film thickness thk and included angle α, in the first function using a nonlinear regression algorithm. By using the precise values ​​a'_n_values ​​of the multiple included angles α as known quantities in the first function, multiple second functions f(wave, thk, a'_n_value) can be determined. At this time, the second function contains only one floating unknown quantity, film thickness thk. The method for determining the unknown quantity thk in the second function f(wave,thk,a'_n_value) is as follows: An initial value for the film thickness thk is set. The value of thk is iteratively updated using a nonlinear regression algorithm until the error between the value of the function group at each wavelength (based on the current film thickness value) and the value of the corresponding measured spectrum group at each wavelength meets a preset condition, or the number of iterations reaches a preset value. At this point, iteration stops, and the current value of the film thickness thk is taken as the precise value of thk, thk_precise_value. The preset condition could be, for example, that the mean square error calculated between the value of the function group at each wavelength (based on the current film thickness value) and the value of the measured spectrum group at each wavelength is less than a set threshold.

[0089] Through the above embodiments, by substituting the precise values ​​of multiple angles 'a' (with random errors eliminated) into the first function, one of the two unknowns in the first function is eliminated, resulting in a function set composed of multiple second functions. This embodiment of the disclosure uses multiple measured Mueller spectra to form a spectral set, and further determines the precise value of the film thickness thk in the second function, thk_precise_value, by fitting the spectral set based on the function set. In this way, by utilizing the relationship between the angle 'a' and the second preset distance L_n, the precise value of the angle 'a' (with random errors eliminated), a'_n_value, is used to re-determine the precise value of the film thickness thk, thk_precise_value. This reduces the impact of random errors on the measurement of film thickness thk and improves measurement accuracy.

[0090] In the embodiments of this disclosure, since the components of the optical measurement equipment are easily affected by environmental factors, even multiple measurements of the film thickness at the same location on the side of the sample may result in deviations. The random error introduced during film thickness measurement can be reduced by averaging multiple measurements, thereby improving the accuracy of the film thickness thk_n_value. The following embodiments further illustrate the method of obtaining the precise value thk_precise_value of film thickness thk through multiple measurements.

[0091] In one exemplary embodiment, Figure 11 This is a flowchart illustrating, according to an exemplary embodiment, how to obtain the precise value of film thickness thk (thk_precise_value) by performing multiple measurements on thk. Figure 11 As shown, the method of obtaining the precise value of film thickness thk_precise_value by measuring the film thickness thk multiple times includes the following steps.

[0092] In step S61, the measured values ​​thk_n_value of multiple film thicknesses thk are obtained.

[0093] In step S62, the average value of the film thickness thk, thk_avg_value, is obtained based on the measured values ​​thk_n_value of multiple film thicknesses thk.

[0094] In step S63, the average value of the film thickness thk, thk_avg_value, is used as the precise value of the film thickness thk, thk_precise_value.

[0095] In this embodiment, the error in measuring the film thickness thk is a random error caused by the insufficient precision of the optical measuring equipment components. Furthermore, the film thickness of a qualified sample should yield the same measurement result when measured at different locations. Therefore, measurements can be performed at the same location, either randomly generated or selected according to a set rule, at multiple measurement spots with a second preset distance L_n, to obtain multiple film thickness thk measurement values ​​thk_n_values. Since the random error exhibits irregular fluctuations in multiple measurements, and the film layer at different locations on the same sample is uniform and of equal thickness, obtaining multiple film thickness thk measurement values ​​thk_n_values ​​can offset the influence between multiple measurements.

[0096] Through the above embodiments, by obtaining the film thickness thk_n_value multiple times and averaging the values, the random error caused by the hardware limitations of the equipment components can be reduced, thereby obtaining the accurate value of film thickness thk_precise_value and improving the measurement accuracy.

[0097] In the embodiments of this disclosure, due to the presence of random errors in the optical measurement process and the significant environmental influence on the accuracy of optical component measurement results, outliers may appear in the measurement results during multiple measurements. Therefore, it is necessary to exclude outliers in order to use the data from multiple measurements as valid data. The following embodiments of this disclosure further illustrate the method for verifying the measured value of film thickness thk obtained in this disclosure.

[0098] In one exemplary embodiment, Figure 12 This is a flowchart illustrating the verification of a measured value of film thickness thk according to an exemplary embodiment. Figure 12 As shown, the method for verifying the measured value of film thickness thk includes the following steps.

[0099] In step S71, the standard deviation Sigma of the measured values ​​thk_n_value of multiple film thicknesses thk is obtained.

[0100] In step S72, it is determined whether the standard deviation Sigma satisfies the second preset condition.

[0101] In step S73, if the standard deviation Sigma satisfies the second preset condition, then the step of obtaining the average value thk_avg_value of the film thickness thk is executed.

[0102] In step S74, if the standard deviation Sigma does not meet the second preset condition, the steps of obtaining the measured values ​​thk_n_value of multiple film thicknesses thk and verifying the measured values ​​thk_n_value of film thickness thk are re-executed.

[0103] In this embodiment, since the film thickness thk is the same on all sides of the sample, even under the influence of random errors, the measured values ​​thk_n_value of the film thickness thk obtained multiple times will only fluctuate within a specific range. Therefore, the existence of outliers can be determined by calculating the standard deviation and checking whether the standard deviation meets a second preset condition. After determining that no outliers exist, it is then determined whether the obtained measured values ​​thk_n_value of the film thickness thk can be used to obtain the precise value thk_precise_value of the film thickness. For example, there may be instances where the film thickness thk of multiple surface oxide layers fluctuates within a set range centered at 50 nm. In this case, the standard deviation Sigma of all measured values ​​thk_n_value of the film thickness thk is calculated. If the standard deviation meets the second preset condition, then all measured values ​​thk_n_value of the film thickness thk are considered to be non-outliers, and the average value thk_avg_value of the film thickness thk can be calculated. Otherwise, the measured values ​​of multiple film thicknesses thk (thk_n_value) can be redefined, or the measured value of film thickness thk (thk_n_value) that deviates the most from the average value can be removed, and the calculation can be repeated until the second preset condition is met. The second preset condition can be, for example, the standard deviation Sigma < 0.01.

[0104] In this embodiment, the measured first Mueller spectrum can only determine the mathematical relationship between the second Mueller matrix M1 and the first Mueller matrix M0 as M1 = R(-a)*M0*R(a) if the incident plane of the incident light corresponding to the reference spot passes through the axis of the cylindrical body. Before measurement, it is necessary to determine that the incident plane of the incident light corresponding to the reference spot passes through the axis of the cylindrical body. The incident plane of the incident light corresponding to the reference spot passing through the axis of the cylindrical body requires that the position of the reference spot is directly above the cylindrical body. The following embodiments further illustrate the method by which this disclosure determines whether the current position of the reference spot meets the conditions.

[0105] In one exemplary embodiment, Figure 13 This is a flowchart illustrating, according to an exemplary embodiment, a method for determining whether the current position of a reference spot meets certain conditions. For example... Figure 13 The method for determining whether the current position of the reference spot meets the conditions includes the following steps:

[0106] In step S81, the first Mueller matrix M1 corresponding to the reference spot position is obtained.

[0107] In step S82, it is determined whether the values ​​of the second diagonal elements of the first Mueller matrix M1 satisfy the third preset condition.

[0108] In step S83, if the third preset condition is met, it is determined that the current position of the reference spot meets the condition.

[0109] In step S84, if the third preset condition is not met, the position of the reference spot on the side of the cylindrical body is readjusted.

[0110] In this embodiment, the second diagonal elements of the Mueller matrix are used to characterize the depolarization and phase retardation characteristics of the sample. When the incident light irradiates the sample with the incident plane perpendicular to the sample surface, since there is no depolarization or phase retardation effect caused by the angle between the incident plane and the sample surface, the elements of the Mueller matrix are zero. Therefore, when the value of the second diagonal element of the first Mueller matrix M1 corresponding to the measured reference spot position of the Mueller matrix satisfies the third preset condition, it can be determined that the incident plane is perpendicular to the sample surface. When the incident plane is perpendicular to the sample surface, the current position of the reference spot is determined to meet the condition. The third preset condition may be that all the second diagonal elements of the first Mueller matrix are in the range of [-0.001, 0.001], and ideally all the second diagonal elements are 0. In this embodiment, the incident light can be obliquely incident on any position of the sample, and the first Mueller matrix of the outgoing light reflected from the film layer at that position can be read. If any of the second diagonal elements of the first Mueller matrix has a value outside the range [-0.001, 0.001], it indicates that the position does not meet the requirements, and the sample position needs to be changed to readjust the position of the reference spot. The sample position can be adjusted manually or randomly until all the second diagonal elements of the first Mueller matrix are within the range [-0.001, 0.001].

[0111] Through the above embodiments, the element values ​​in the Mueller matrix can reflect the characteristics of depolarization or phase delay effects, verifying that the current position of the reference spot meets the conditions. This method analyzes the Mueller matrix obtained by measuring the radius R of the cylindrical body to determine the state of the Mueller matrix when the incident plane is perpendicular to the sample surface, thus determining whether the reference position meets the conditions. No additional instrument calibration is required; measurements can be performed directly after calibration, simplifying the measurement steps and improving the efficiency of measuring the radius R and film thickness thk of the cylindrical body.

[0112] In this embodiment, the cylindrical body is moved a first preset distance along a direction perpendicular to the incident plane only when the azimuth angle of the incident light on the reference section is zero. The mathematical relationship between the determined second Mueller matrix M1 and the first Mueller matrix M0 must satisfy M1 = R(-a) * M0 * R(a) to be valid. Before measurement, it is necessary to determine whether the azimuth angle of the incident light on the reference section is zero. The following embodiments further illustrate how this disclosure determines whether the azimuth angle of the incident light on the reference section is zero.

[0113] In one exemplary embodiment, Figure 14 This is a flowchart illustrating, according to an exemplary embodiment, a method for determining whether the azimuth angle of incident light on a reference section is zero. For example... Figure 14 As shown, the method for determining whether the azimuth angle of the incident light on the reference section is zero includes the following steps.

[0114] In step S91, the incident light is obliquely incident onto the side of the sample to form a reference light spot.

[0115] In step S92, the sample is moved along the axis of its cylindrical body.

[0116] In step S93, during the movement, the detector based on the ellipsometer continuously acquires the position of the light spot on the detector after the emitted light is reflected by the film layer on the side of the cylindrical body.

[0117] In step S94, it is determined whether the position of the light spot remains unchanged during the movement.

[0118] In step S95, if the position of the light spot remains unchanged, it is determined that the azimuth angle of the incident light on the reference section is zero.

[0119] In step S96, if the position of the light spot changes, the position of the sample is readjusted so that the azimuth angle of the incident light on the reference section is zero.

[0120] In this embodiment, since the reference light spot is at the highest point of the cylindrical body of the sample, if the azimuth angle of the incident light on the reference section is zero, moving the sample along its cylindrical axis will keep the light spot position on the sample at the highest point of the cylindrical body. Because the incident angle does not change, the position of the light spot on the detector will remain unchanged. In this embodiment, it can be first determined that the incident light is obliquely incident at the highest point of the cylindrical body, and then the sample is moved along the cylindrical axis. If the azimuth angle of the incident light on the reference section is zero, it means that the axis is on the incident plane. No matter how the sample moves along the axis, the axis always remains on the incident plane, i.e., the incident angle remains unchanged. If the azimuth angle of the incident light on the reference section is not zero, then as long as the sample is moved along the axis, the reference light spot will leave the highest point of the cylindrical body, and the incident angle will change. After the incident angle changes, the position and shape of the emitted light on the detector will change accordingly. The position of the emitted light spot on the detector can be obtained by visual observation or image recognition, and this disclosure does not make specific limitations.

[0121] Through the above embodiments, by moving the sample along the axis of the cylindrical body and observing whether the position of the light spot on the detector changes, it is determined whether the azimuth angle of the incident light on the reference section is zero. This method achieves the determination solely through the geometric properties of light, eliminating the need for other measuring instruments, simplifying the determination process, and improving the efficiency of measuring the radius R and film thickness thk of the cylindrical body.

[0122] Based on the same concept, this disclosure also provides an ellipticity measurement device. Figure 15 This is a structural diagram of an ellipticity measuring device provided according to an exemplary embodiment. (e.g.) Figure 15 As shown, the ellipticity measurement device includes:

[0123] Light source 201 is used to generate a measurement beam.

[0124] The polarizing arm 202 is used to modulate the measurement beam to form an incident light and to obliquely incident the incident light onto the sample, wherein the sample includes a cylindrical sample.

[0125] Workbench 203 is used to place samples and allows for sample movement.

[0126] The polarization analyzer 204 is used to analyze the outgoing light reflected from the film layer covering the sample.

[0127] Detector 205 is used to receive the emitted light after it has been polarized by polarizer 204.

[0128] The control device is electrically connected to the worktable 203. The control device can control the worktable 203 to move the sample to a first position so that the axis of the sample coincides with the incident plane of the incident light. It can also control the worktable 203 to move the sample from the first position to a second position along a direction perpendicular to the central axis of the sample.

[0129] The data acquisition module, electrically connected to the control device and detector 205, is used to acquire a preset distance L and to measure the Mueller spectrum of the emitted light reflected from the film layer covering the sample at the second position.

[0130] The calculation module is used to calculate the sample size and film thickness thk based on the measured spectrum and the preset distance L, where the size includes the radius R of the cylindrical sample.

[0131] In this embodiment, a movable sample stage 203 is provided, and a control device controls the movement of the sample to a first position where the sample's axis coincides with the incident plane of the incident light, and then moves the sample from the first position a preset distance L along a direction perpendicular to the sample's central axis to a second position. For example, when measuring a sample, the sample can be fixed on the stage 203. The angle and position of the stage are adjusted to form a reference light spot. When the incident plane of the incident light passes through the axis of the cylindrical body, and the azimuth angle of the incident light on the reference section is zero, it is considered that a reference light spot has been formed. The user can set a specific value for the preset distance L to move the sample, or lock the device's movement direction to be perpendicular to the incident plane and move the sample manually, reading the distance L in real time. The light spot formed by the incident light on the side of the sample after moving the preset distance L is the measurement light spot. The outgoing light corresponding to the measurement light spot position is read by the polarizer 204 and the detector 205. The Mueller spectrum is determined using a data acquisition module and a calculation module, which then calculates the radius R of the cylindrical sample. This device establishes the geometric relationship between the radius of the cylindrical sample, the distance traveled, and the incident light. Once this relationship is established, the data acquisition and calculation modules determine the specific values ​​within this geometric relationship, thereby enabling the measurement of the radius R of the cylindrical sample.

[0132] Through the above embodiments, the ellipsometry measuring device, by setting a worktable 203 capable of moving the sample, establishes the geometric relationship between the radius, moving distance, and incident light of the cylindrical sample. Without adding additional measuring equipment, it can calibrate the sample's reference position and obtain the sample's dimensions and film thickness (thk) in a single measurement process. This improves the accuracy and efficiency of sample size and film thickness measurements.

[0133] It should be noted that although the terms "first," "second," etc., are used herein to describe different modules, steps, and data in the embodiments of the present invention, these terms are only for distinguishing between different modules, steps, and data, and do not indicate a specific order or degree of importance. In fact, the terms "first," "second," etc., can be used interchangeably.

[0134] It is understood that although operations are described in a specific order in the accompanying drawings in the embodiments of the present invention, this should not be construed as requiring these operations to be performed in the specific order or serial order shown, or requiring all of the shown operations to be performed to obtain the desired result. In certain environments, multitasking and parallel processing may be advantageous.

[0135] The methods and apparatuses involved in the embodiments of the present invention can be implemented using standard programming techniques, and various method steps can be implemented using rule-based logic or other logic. It should also be noted that the terms "apparatus" and "module" as used herein and in the claims are intended to include implementations using one or more lines of software code and / or hardware implementations and / or devices for receiving input.

[0136] Any step, operation, or procedure described herein may be performed or implemented using one or more hardware or software modules, either alone or in combination with other devices. In one embodiment, the software module is implemented using a computer program product comprising a computer-readable medium containing computer program code, which is executable by a computer processor to perform any or all of the described steps, operations, or procedures.

[0137] The foregoing description of embodiments of the invention has been provided for purposes of illustration and description. The foregoing description is not exhaustive and is not intended to limit the invention to the exact forms disclosed; various modifications and variations may be made in accordance with the foregoing teachings, or may be derived from the practice of the invention. These embodiments were chosen and described to illustrate the principles of the invention and its practical application, enabling those skilled in the art to utilize the invention in various embodiments and with various modifications to suit the particular purpose of the concept.

Claims

1. A method for measuring samples based on an ellipsometer, characterized in that, The sample comprises a cylindrical body and a film layer covering the side of the cylindrical body, and the method includes: Incident light is obliquely incident onto the side of the sample to form a reference spot, and the plane that passes through the reference spot and is tangent to the side is used as a reference sectional plane. The incident plane of the incident light corresponding to the reference spot passes through the axis of the cylindrical body, and the azimuth angle of the incident light on the reference sectional plane is zero. Acquire the first measured Mueller spectrum corresponding to the reference spot position, and obtain the first Mueller matrix M0 corresponding to the first measured Mueller spectrum; The cylindrical body is moved a first preset distance L along a direction perpendicular to the incident plane to form a measurement spot on the side surface, and the second measurement Mueller spectrum Sm corresponding to the position of the measurement spot is collected. The second measurement Mueller spectrum Sm corresponds to the second Mueller matrix M1. Determine the mathematical relationship between the second Mueller matrix M1 and the first Mueller matrix M0: M1 = R(-a) * M0 * R(a), where R(-a) and R(a) are rotation matrices, and the included angle a is the angle between the reference section and the measurement section, wherein the measurement section is a plane that passes through the measurement spot and is tangent to the side surface; Based on the Fresnel equation and the mathematical relationship, the second Mueller matrix M1 is expressed as a first function of the incident light wavelength wave, film thickness thk, and the included angle a: M1 = f(wave, thk, a); The initial values ​​of the film thickness thk and the included angle a are obtained, and the second measured Mueller spectrum Sm is fitted based on the first function using a nonlinear regression algorithm to obtain the measured value of the film thickness thk_value and the measured value of the included angle a_value. Based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L, the radius R of the cylindrical body is calculated.

2. The method for measuring samples based on an ellipsometer according to claim 1, characterized in that: Based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L, the radius R of the cylindrical body is calculated, including: R = L / sin(a_value).

3. The method for measuring samples based on an ellipsometer according to claim 1, characterized in that: Based on the first preset distance L and the measured value a_value of the included angle α corresponding to the first preset distance L, the radius R of the cylindrical body is calculated, including: Obtain the measured value a_n_value of the angle α between multiple different second preset distances L_n and each second preset distance L_n; Based on the measured value a_n_value of the included angle a corresponding to each second preset distance L_n, the sine value sin(a_n_value) of the included angle a corresponding to the second preset distance L_n is obtained through mathematical transformation. Based on the sine value sin(a_n_value) of the angle a between the second preset distance L_n and the angle a corresponding to the second preset distance L_n, a linear fit is performed to obtain the slope value Slope_value of the obtained linear fit function; The slope value (Slope_value) is used as the radius R of the cylindrical body.

4. The method for measuring samples based on an ellipsometer according to claim 3, characterized in that: After obtaining the radius R of the cylindrical body, the method further includes verifying the radius R, which includes: The sin(a_n_value) of the included angle a corresponding to the multiple second preset distances L_n is substituted into the linear fitting function as the independent variable to obtain the fitting value y_bsl_n corresponding to the offset distance; Based on the fitted value y_bsl_n corresponding to each offset distance and the second preset distance L_n, obtain the correlation coefficient used to characterize the similarity between the fitted value y_bsl_n corresponding to each offset distance and the second preset distance L_n. Determine the correlation coefficient Does it meet the first preset condition? If the first preset condition is met, then the radius R of the cylindrical body is determined to meet the condition; If the first preset condition is not met, the radius R of the cylindrical body is remeasured.

5. The method for measuring samples based on an ellipsometer according to claim 3, characterized in that: The method further includes obtaining the precise value of the film thickness thk, thk_precise_value. The step of obtaining the precise value of the film thickness thk, thk_precise_value, includes: Based on the slope values ​​Slope_value of multiple second preset distances L_n and the linear fitting function, the precise value a'_n_value of the included angle α corresponding to each second preset distance L_n is obtained, wherein the precise value a'_n_value of the included angle α corresponding to the second preset distance L_n satisfies: a'_n_value=arcsin(L_n / Slope_value). Substitute the precise values ​​a'_n_value of the multiple included angles a into the first function f(wave,thk,a) to obtain the second function f(wave,thk,a'_n_value) corresponding to each second preset distance L_n, and determine the multiple second functions f(wave,thk,a'_n_value) as a function group; Obtain the third measurement Mueller spectrum Sm_n corresponding to each of the second preset distances L_n, and obtain a measurement spectrum group based on multiple third measurement Mueller spectra Sm_n; An initial value for the film thickness thk is obtained, and based on the function set, a nonlinear regression algorithm is used to fit the measurement spectrum set to determine the precise value of the film thickness thk, thk_precise_value.

6. The method for measuring samples based on an ellipsometer according to claim 5, characterized in that: The method further includes obtaining the precise value of the film thickness, thk_precise_value, and the step of obtaining the precise value of the film thickness, thk_precise_value, further includes: Obtain multiple measured values ​​of the film thickness thk, thk_n_value; Based on the measured values ​​thk_n_value of multiple film thicknesses thk, the average value thk_avg_value of the film thickness thk is obtained; The average value of the film thickness thk, thk_avg_value, is used as the precise value of the film thickness thk, thk_precise_value.

7. The method for measuring samples based on an ellipsometer according to claim 6, characterized in that: Before obtaining the average value thk_avg_value of the film thickness thk based on multiple measured values ​​thk_n_value of the film thickness thk, the method further includes: verifying the measured value thk_n_value of the film thickness thk. The verification of the measured value thk_n_value of the film thickness thk includes: Obtain the standard deviation Sigma of multiple measured values ​​of the film thickness thk_n_value; Determine whether the standard deviation Sigma satisfies the second preset condition; If the standard deviation Sigma satisfies the second preset condition, then the step of obtaining the average value thk_avg_value of the film thickness thk is executed; If the standard deviation Sigma does not meet the second preset condition, the steps of obtaining multiple measured values ​​thk_n_value of the film thickness thk and verifying the measured values ​​thk_n_value of the film thickness thk are re-executed.

8. The method for measuring samples based on an ellipsometer according to claim 1, characterized in that: After obtaining the first Mueller matrix M1, the method further includes a step of determining whether the current position of the reference spot meets the conditions, the step including: Determine whether the values ​​of the second diagonal elements of the first Mueller matrix M1 satisfy the third preset condition; If the third preset condition is met, then the current position of the reference light spot is determined to meet the condition; If the third preset condition is not met, the position of the reference light spot on the side of the cylindrical body will be readjusted.

9. The method for measuring samples based on an ellipsometer according to claim 1, characterized in that: After incident light is obliquely incident onto the side of the sample to form a reference light spot, the method further includes a step of determining whether the azimuth angle of the incident light on the reference section is zero. This step includes: The sample is moved along the axis of its cylindrical body. During the movement, the detector based on the ellipsometer continuously acquires the position of the light spot on the detector after the emitted light is reflected by the film layer on the side of the cylindrical body. Determine whether the position of the light spot remains unchanged during the movement; If the position of the light spot remains unchanged, it is determined that the azimuth angle of the incident light on the reference section is zero; If the position of the light spot changes, the position of the sample is readjusted so that the azimuth angle of the incident light on the reference section is zero.

10. An ellipticity measuring device, characterized in that: include A light source, used to generate the measurement beam; A polarizing arm is used to modulate the measurement beam to form incident light and to obliquely incident the incident light onto the sample, wherein the sample includes a cylindrical sample; A worktable for placing and moving samples; A polarization detector arm is used to detect the polarization of the emitted light reflected from the film layer covering the sample. A detector is used to receive the emitted light after it has been polarized by the polarizer arm; A control device is electrically connected to the worktable. The control device can control the worktable to move the sample to a first position where the axis of the sample coincides with the incident plane of the incident light. It can also control the worktable to move the sample from the first position to a second position along a direction perpendicular to the central axis of the sample. The data acquisition module is electrically connected to the control device and the detector, and is used to acquire the preset distance L, and to acquire the measured Mueller spectrum of the outgoing light reflected from the film layer covering the sample at the second position. The calculation module is used to calculate the size and film thickness thk of the sample based on the measured Mueller spectrum and the preset distance L, wherein the size includes the radius R of the cylindrical sample.

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