CN114264632B - In-situ calibration method for polarization effect of objective lens in angle-resolved scatterometer - Google Patents
In-situ calibration method for polarization effect of objective lens in angle-resolved scatterometer Download PDFInfo
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Abstract
The invention belongs to the technical field of system parameter calibration, and discloses an in-situ calibration method for an objective polarization effect in an angle-resolved scatterometer, which comprises the following steps: (1) Measuring the standard film by an angle resolution type scattering measurement system to obtain an actual measurement image of the back focal plane of the objective lens; meanwhile, a system simulation model containing the polarization effect of the objective lens is established, the standard film is taken as a sample, and a simulated image of the back focal plane of the objective lens is generated through the system simulation model; (2) Calculating to obtain measured and theoretical multi-incidence angle ellipsometry parameters based on an ellipsometry parameter system equation of the sample, a measured image of the back focal plane of the objective lens and a simulation image of the back focal plane of the objective lens; (3) And determining an objective ellipsometry parameter solving equation based on the objective polarization effect transfer matrix, and further solving to obtain objective ellipsometry parameters with multiple incidence angles so as to complete in-situ calibration of the objective polarization effect in the angle-resolved scatterometry system. The invention can effectively reduce the measurement error caused by the polarization effect error of the objective lens in the instrument.
Description
Technical Field
The invention belongs to the technical field related to system parameter calibration, and particularly relates to an in-situ calibration method for an objective polarization effect in an angle-resolved scatterometer.
Background
Fringe field measurement is an on-line detection technique oriented to integrated circuit fabrication, and is receiving increasing attention as chip nodes continue to shrink. According to the guidance of the international semiconductor technology roadmap, the semiconductor devices with the specification of 4nm and higher are about to be mass-produced, which means that the structure of the semiconductor devices is more complex, and the critical dimensions and the overlay are more and more approaching the resolution limit of optical imaging. Conventional optical critical dimension (optical critical dimension, OCD) measurement often adopts measurement schemes such as an atomic force microscope and a scanning electron microscope, and the schemes have the defects of destructive measurement of samples, low efficiency, high cost, severe use environment and the like. The optical scattering field measurement is a novel model-based optical measurement means, has the advantages of no contact, no damage, high efficiency, low cost, no Abbe diffraction limit and the like, and is an optical critical dimension measurement scheme suitable for manufacturing advanced technology node process semiconductor chips.
As a main device for measuring a scattered field, the scatterometer is also an important instrument in measuring the optical critical dimension, and compared with the traditional optical scatterometer, the scatterometer can only obtain measurement information under single incidence angle and single azimuth angle configuration in single measurement, and each point on the back focal plane of an objective lens of the angle-resolved scatterometer can be regarded as a point light source, and different incidence angles, azimuth angles and polarization states are formed after segregation of the objective lens. Therefore, the single measurement can obtain the reflectivity information under multiple incidence angles (the angle range depends on the numerical aperture of the objective lens) and all azimuth angles, and is more beneficial to the characterization of the morphological structure parameters of the sample. As one of optical scattering measurement instruments, the angle-resolved scatterometer has been increasingly used in the measurement of sub-wavelength nanostructure parameters due to the advantages of non-destructive property, high sensitivity, high efficiency and the like.
A high numerical aperture (Numerical Aperture, NA) objective is typically selected for use in angle-resolved scatterometers to produce a focused illumination spot and collect sample fringe field signals. In order to improve the measurement sensitivity, the probe light is usually modulated into linearly polarized light with a specific polarization state, and the outgoing signal light collected by the objective lens after converging, sample reflecting and objective lens is polarized light. In practical instruments, when the numerical aperture of the objective lens is larger, that is, the exit angle or the incident angle of the objective lens is larger, the non-normal incidence phenomenon is more obvious when the light beam passes through the objective lens, and the polarization effect has larger influence on the light intensity distribution of the emergent signal light, that is, the polarization effect of the objective lens has obvious incident angle dependency. The existence of the polarization effect of the objective lens influences the measurement accuracy of the nanostructure parameters, and when the same sample to be measured is measured by light beams with different polarization states, the measurement result cannot keep good consistency. In addition, the polarization effect of the objective lens is related to the optical characteristics of the objective lens body, and the residual stress generated when the objective lens is fixedly installed in the instrument also affects the polarization effect of the objective lens. Therefore, a fast and accurate in-situ calibration scheme for the polarization effect of an objective lens for an angle-resolved scatterometer is needed.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides an in-situ calibration method for the polarization effect of an objective lens in an angle-resolved scatterometer, which comprises the steps of carrying out simulation and experimental measurement on a standard sample to obtain a back focal plane simulation and experimental image, establishing a Cartesian coordinate system on an image plane, calculating an incidence angle and an azimuth angle corresponding to each pixel, screening the pixels in a certain incidence angle azimuth, arranging corresponding light intensity values according to the azimuth angle from small to large to form a periodic signal, carrying out frequency domain analysis on the periodic signal to obtain amplitude coefficients at all frequencies, substituting the amplitude coefficients into an ellipsometry parameter coefficient equation to obtain theoretical ellipsometry parameters and experimental ellipsometry parameters, carrying out matching analysis on the theoretical ellipsometry parameters and the experimental ellipsometry parameters to obtain objective lens ellipsometry parameters, substituting the calibrated results into a coefficient model containing the polarization effect of the objective lens, and effectively reducing measurement errors caused by the polarization effect errors of the objective lens in the instrument.
To achieve the above object, according to one aspect of the present invention, there is provided an in-situ calibration method of polarization effect of an objective lens in an angle-resolved scatterometer, the calibration method mainly comprising the steps of:
(1) Providing an angle resolution type scattering measurement system, and measuring a standard film through the angle resolution type scattering measurement system to obtain an actual measurement image of a back focal plane of an objective lens; meanwhile, a system simulation model of the angle resolution type scattering measurement system, which comprises an objective lens polarization effect, is established, and the standard film is taken as a sample, and an objective lens back focal plane simulation image is generated through the system simulation model;
(2) Based on an ellipsometry parameter system equation of a sample, an obtained objective lens back focal plane actual measurement image and an objective lens back focal plane simulation image, calculating to obtain an actual measurement multiple-incidence-angle ellipsometry parameter and a theoretical multiple-incidence-angle ellipsometry parameter;
(3) And determining an objective lens ellipsometry parameter solving equation based on the derived objective lens polarization effect transfer matrix, and further solving the objective lens multiple-incidence-angle ellipsometry parameter by utilizing the obtained actually measured multiple-incidence-angle ellipsometry parameter and the theoretical multiple-incidence-angle ellipsometry parameter to complete in-situ calibration of the objective lens polarization effect in the angle-resolved scatterometry system.
Further, the mathematical expression of the system simulation model is:
in the method, in the process of the invention,representing azimuth angle, θ representing incident angle; />Indicating a rotation angle of +.>Is rotated by the coordinate of the agar matrix; p represents the jones matrix of the polarizer; j (J) M Representing a sample reflection coordinate transformation matrix; j (J) S The Jones matrix is a sample to be measured; j (J) obj The objective lens polarization effect quantization description Jones matrix is called as the objective lens Jones matrix for short; e (E) in And E is connected with out The electric field intensity vectors of the incident light and the emergent light are respectively represented, usually E in ＝I 0 ·[1 1] T 。
Further, a polarizer is respectively arranged in an incident light path and an emergent light path of the angle-resolved scatterometry system and is respectively used as a polarizer and an analyzer, and the azimuth angles of the polarizer and the analyzer are respectively 0 DEG and-45 DEG by taking the plane of the angle-resolved scatterometry system as a reference; the expression of the system simulation model containing the polarization effect of the objective lens is as follows:
in the method, in the process of the invention,represents an incident light azimuth angle, θ represents an incident light angle; />Indicating a rotation angle of +.>Is rotated by the coordinate of the agar matrix; p represents a polarizer jones matrix; j (J) M Representing a sample reflection coordinate transformation matrix; j (J) S The Jones matrix is a sample to be measured; j (J) obj The objective lens polarization effect quantization description Jones matrix is called as the objective lens Jones matrix for short; e (E) in And E is connected with out Representing the intensity vectors of the incident light and the emergent light electric field respectively, usually E in ＝I 0 ·[1,1] T 。
Further, a Cartesian coordinate system is established by taking the center of the back focal plane image as an origin, the corresponding incidence angle and azimuth angle of each pixel point are calculated, the pixel points in a specific incidence angle range are screened, the pixel points are ordered from small to large according to azimuth angles, a triangular periodic signal is obtained, and a theoretical expression of the triangular periodic signal is deduced as follows:
wherein I represents the intensity of emergent light; alpha 0 、α 2 、α 4 Respectively representing the amplitude coefficients at the frequency multiplication positions of 0, 2 and 4;indicating the azimuth angle of the incident light; θ represents the incident angle of the incident light.
Further, frequency domain analysis is carried out on the periodic signal through Fourier change or least square fitting is carried out according to a theoretical expression to obtain amplitude coefficients corresponding to different frequencies, then an azimuth angle combination of two polaroid sheets is used for determining a sample ellipsometry parameter coefficient equation, actual measurement ellipsometry parameters and theoretical ellipsometry parameters of the sample under the incident angle are calculated, the selected incident angle range is changed, and then the actual measurement ellipsometry parameters and the theoretical ellipsometry parameters of the sample corresponding to a plurality of incident angles can be calculated.
Further, the ellipsometry parameter psi and delta at any incident angle can be obtained by the amplitude coefficient alpha at each frequency 0 、α 2 、α 4 Expressed as the following ellipsometric parameter coefficient equation:
furthermore, the angle-resolved scatterometry system adopts the same objective lens to illuminate and measure the sample, and the polarization effect transfer matrix of the objective lens is not changed along with the configuration change of the system, so that the polarization effect transfer matrix of the objective lens can be deduced according to the light beam propagation rule in the system.
Further, according to the deduced objective ellipsometry parameter and the sample ellipsometry parameter coupling transfer matrix, the objective ellipsometry parameter expression can be obtained through variable transformation.
Further, the system simulation model is regarded as that the light beam is converged through the objective lens, reflected by the sample and then collected by the objective lens, and expressed as follows by using the jones matrix:
wherein J is S Representing a sample theoretical jones matrix; psi represents the theoretical amplitude ratio angle; delta represents the theoretical phase difference angle; j (J) obj Representing an objective lens jones matrix; psi obj Indicating the amplitude ratio angle of the objective lens; delta obj Representing the phase angle of the objective lens; j (J) S ' represents the measured sample jones matrix.
Further, the objective ellipsometry parameter solving equation is:
wherein, the subscript i represents different incident angles; psi phi type i Represents the amplitude ratio angle, delta, of the objective lens at an incident angle i i An objective phase difference angle when the incident angle is i; psi phi type obj Indicating the amplitude ratio angle of the objective lens; delta obj Representing the phase angle of the objective lens; continuously adjusting the ellipsometry parameter psi of the objective lens obj And delta obj And when the value of the objective lens ellipsometry parameter solving equation is minimum, the parameter value used is the objective lens ellipsometry parameter.
In general, compared with the prior art, the in-situ calibration method for the polarization effect of the objective lens in the angle-resolved scatterometer mainly has the following beneficial effects:
1. the polarization effect of the objective lens actually has angle dependence, which is the optical characteristic of the objective lens, especially for the objective lens with high numerical aperture, the polarization effect of the objective lens tends to be greatly increased at the edge of the back focal plane, which is the larger incidence angle, and the measurement accuracy can be improved by considering the incidence angle dependence of the polarization effect of the objective lens, so that the dependence of the measurement result on the incidence angle can be effectively reduced.
2. The in-situ calibration has the advantages that the time efficiency of measurement and calibration can be improved, the calibration result can be more approximate to a true value, other calibration methods can be used for adding a complex mechanical or electric control modulation structure into the system, or the objective lens is taken down and placed in a special calibration system, the calibration process is complex, the time consumption is long, the requirement of the integrated circuit manufacturing industry on the time efficiency cannot be met, the polarization effect of the objective lens is closely related to the residual stress during installation besides being related to the optical structure of the objective lens and the material, so that the in-situ calibration method can obtain the calibration value which is more approximate to the true ellipsometry parameter of the objective lens in the system, the corresponding measurement result can be more accurate, the whole system is calibrated without independently dismantling the objective lens, and the process is simpler.
3. The method is easy to implement, has strong applicability and is beneficial to popularization and application.
Drawings
FIG. 1 is a flow chart of an in situ calibration method for polarization effects of an objective lens in an angle resolved scatterometer according to the present invention;
FIG. 2 is a schematic diagram of an angle-resolved scatterometry system provided by the present invention;
FIG. 3 is a graph showing the variation of the theoretical ellipsometry parameter of a standard sample provided by the invention with the incident angle at the measurement wavelength;
fig. 4 (a) and (b) are respectively a back focal plane measured image and a theoretical image of the calibration sample at the measurement wavelength in example 1 of the present invention;
fig. 5 (a), (b), (c), and (d) are schematic diagrams of actual measurement periodic signals and simulation periodic signals at a specific incident angle according to an embodiment of the present invention;
FIG. 6 is a diagram showing the measured ellipsometry parameters, the simulated ellipsometry parameters, and the differences between the two in the calibration samples according to the embodiment of the invention;
FIG. 7 is a diagram showing a comparison between the ellipsometry parameters of a calibration objective lens and the ellipsometry parameters of a theoretical objective lens in an embodiment of the present invention;
FIG. 8 is a graph showing the comparison of film thickness measurements of standard film samples at various angles of incidence, before and after calibration, with nominal reference values in an embodiment of the present invention;
fig. 9 is a schematic diagram of a back focal plane actual measurement image and a simulation image, and an actual measurement periodic signal and a simulation periodic signal at a specific incident angle according to another embodiment of the present invention;
FIG. 10 is a diagram showing the comparison of the corrected objective lens ellipsometry parameters and the theoretical objective lens ellipsometry parameters according to another embodiment of the present invention.
The same reference numbers are used throughout the drawings to reference like elements or structures, wherein: 210-light source, 220-modulator, 221-filter, 222-polarizer, 230-probe light shaping mechanism, 240-probe and reference mechanism, 241-objective lens, 242-reflector, 250-demodulation and spatial filter, 251-analyzer, 260-outgoing signal light collecting mechanism, 270-data processing mechanism.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Referring to fig. 1 and 2, the in-situ calibration method for polarization effect of an objective lens in an angle-resolved scatterometer according to the present invention mainly includes the following steps:
step S1, an angle resolution type scattering measurement system is built according to preset system configuration, and a standard film is measured through the angle resolution type scattering measurement system so as to obtain an actual measurement image of a back focal plane of an objective lens.
Specifically, the provided angle-resolved scatterometry system includes a light source 210, a modulator 220, a probe light shaping mechanism 230, and a probe and reference mechanism 240, which are sequentially disposed along a horizontal direction, and further includes a data processing mechanism 270, an outgoing signal light collecting mechanism 260, and a demodulation and spatial filter 250, which are disposed along a vertical direction from top to bottom, wherein the demodulation and spatial filter 250 is disposed between the outgoing signal light collecting mechanism 260 and the probe and reference mechanism 240. The modulator 220 includes a filter 221 and a polarizer 222 arranged at intervals; the detecting and referencing mechanism 240 includes an objective lens 241 and a reflecting mirror 242 arranged along a horizontal direction; the demodulation and spatial filter 250 includes an analyzer 251. In the angle-resolved scatterometry system, a polarizer is respectively disposed in the incident light path and the exit light path as a polarizer 222 and an analyzer 251, and the azimuth angles of the polarizer 222 and the analyzer 252 are respectively 0 ° and-45 ° with respect to the plane of the system. The azimuth angles of the alternative polarizer 222 and analyzer 251 may be set to 0 ° and 0 °, 90 ° and 90 °, 0 ° and 45 °, and other combinations.
The analyzer 251 is only disposed in the outgoing light path when the polarization effect of the objective lens is calibrated, the analyzer 251 is removed when the nanostructure scattered field is measured, the reflected light generated by the mirror 242 may overlap with the outgoing signal light, but the beam splitter may be removed or the reference beam may be isolated by a light shielding device when the reference light has an influence on the measurement. To eliminate the dispersion effect of the system, the probe beam is set to monochromatic light using a filter 221.
In this embodiment, referring to fig. 3 and 4, the specific standard sample is a silicon substrate silicon dioxide thin film sample with a nominal thickness of 54 nm; the measurement wavelength was chosen to be 532nm; an objective lens with a numerical aperture of 0.95 is selected, and according to the Abbe imaging principle, the corresponding incidence angle range of-71.8 degrees can be calculated, and the theoretical ellipsometry parameters of the standard sample are shown in figure 3. In this embodiment a set of objective polarization effects are input that are linearly dependent on the angle of incidence:. Psi obj-input ＝45.5°+0.5°×θ×π/180，Δ obj-input ＝-2°-1.5°×θ×π/180。
And S2, constructing a system simulation model of the angle-resolved scatterometry system comprising the polarization effect of the objective lens according to a preset system configuration, taking a standard film as a sample, and generating a back focal plane simulation image of the objective lens through the system simulation model.
Specifically, in the angle-resolved scatterometry system, the expression of the system model including the objective polarization effect is:
in the method, in the process of the invention,representing azimuth angle, θ representing incident angle; />Indicating a rotation angle of +.>Is rotated by the coordinate of the agar matrix; p represents the jones matrix of the polarizer; j (J) M Representing a sample reflection coordinate transformation matrix; j (J) S The Jones matrix is a sample to be measured; j (J) obj The objective lens polarization effect quantization description Jones matrix is called as the objective lens Jones matrix for short; e (E) in And E is connected with out The electric field intensity vectors of the incident light and the emergent light are respectively represented, usually E in ＝I 0 ·[1 1] T 。
When the azimuth angles of the polarizer 222 and the analyzer 251 are set to 0 ° and-45 °, the expression of the system model including the polarization effect of the objective lens is:
in the method, in the process of the invention,represents an incident light azimuth angle, θ represents an incident light angle; />Indicating a rotation angle of +.>Is rotated by the coordinate of the agar matrix; p represents a polarizer jones matrix; j (J) M Representing a sample reflection coordinate transformation matrix; j (J) S The Jones matrix is a sample to be measured; j (J) obj The objective lens polarization effect quantization description Jones matrix is called as the objective lens Jones matrix for short; e (E) in And E is connected with out Representing the intensity vectors of the incident light and the emergent light electric field respectively, usually E in ＝I 0 ·[1,1] T 。
In one embodiment, the objective lens 251 is made to be an ideal objective lens, i.e., an objective lens Jones matrix J obj The main diagonal elements are all 1, and the auxiliary diagonal elements are all 0; the intensity of the emergent light can be calculated by the intensity vector of the emergent photoelectric fieldAt a certain angle of incidence and azimuth, the intensity of the outgoing light can be expressed as:
wherein I represents the intensity of emergent light, alpha 0 、α 2 、α 4 Represents the amplitude coefficient at the frequency multiplication of 0, 2, 4, and α 0 、α 2 、α 4 The ellipsometry parameters of the sample can be uniquely expressed as:
wherein psi is the amplitude ratio angle and delta phase difference angle; the ellipsometry parameters ψ, Δ are related to the reflection coefficient or transmission coefficient, which can be expressed as:
wherein R is p And R is R s Belonging to complex domain, respectively representing reflection coefficients of p light and s light, delta p And delta s Respectively representing p-light and s-lightPhase angle of reflection coefficient.
Compared with the actually measured back focal plane image containing the polarization effect of the objective lens, the light intensity distribution has obvious difference and the center of the image has no sharp fluctuation; nanostructure parameter extraction is typically a model-based measurement, where the accuracy of the objective polarization parameters will affect the accuracy of nanostructure parameter extraction.
And S3, deducing a sample ellipsometry parameter coefficient equation according to a preset system configuration, and further calculating the measured multiple-incidence-angle ellipsometry parameter and the theoretical multiple-incidence-angle ellipsometry parameter of the sample by using the obtained objective lens back focal plane measured image and the objective lens back focal plane simulation image.
After obtaining a back focal plane simulation image and an actual measurement image, establishing a Cartesian coordinate system by taking the center of the back focal plane image as an origin, calculating the corresponding incidence angle and azimuth angle of each pixel point, screening the pixel points in a specific incidence angle range, sorting the pixel points from small to large according to azimuth angles to obtain a triangular periodic signal, and deducing the theoretical expression of the triangular periodic signal according to system configuration as follows:
the method comprises the steps of carrying out frequency domain analysis on a periodic signal through Fourier change or carrying out least square fitting according to a theoretical expression to obtain amplitude coefficients corresponding to different frequencies, determining a sample ellipsometry parameter coefficient equation through azimuth angle combination of two polaroid sheets, calculating actual measurement ellipsometry parameters and theoretical ellipsometry parameters of a sample under the incident angle, and calculating the actual measurement ellipsometry parameters and the theoretical ellipsometry parameters of the sample corresponding to a plurality of incident angles by changing the selected incident angle range.
Specifically, the azimuth angles of the polarizer 222 and the analyzer 251 are respectively 0 ° and-45 °, and the ellipsometry parameters ψ, Δ at any incident angle can be determined by the amplitude coefficient α at each frequency 0 、α 2 、α 4 Expressed as the following ellipsometric parameter coefficient equation:
by amplitude coefficient alpha 0 、α 2 、α 4 The form of representing the ellipsometric parameters psi and delta is not unique, the back focal plane light intensity calculation can be directly adopted in consideration of the complex measuring process of the reflectivity, and the coefficient equation ensures that the frequency of the numerator and the amplitude coefficient in the denominator are consistent, for example, the frequency of the numerator and the amplitude coefficient in the denominator is 1.
Referring to fig. 5, a standard cartesian coordinate system is established on a plane on which a back focal plane image is located, a maximum radius of a circle in the back focal plane is taken as a unit length, an incident angle and an azimuth angle corresponding to each pixel point are calculated, and light intensity information of the pixel points in a certain selected azimuth angle range is screened; generally, the azimuth angle range depends on the resolution of the image, so that the acquired pixel points can form a continuous uninterrupted circle, and the light intensity is arranged from small to large according to the corresponding azimuth angle to obtain a sine periodic signal; as can be seen from fig. 5, the actual periodic signal and the theoretical periodic signal have distinct waveforms at the same incident angle.
Frequency domain analysis is carried out on the periodic signal through Fourier transformation to obtain amplitude coefficient alpha at each frequency 0 、α 2 、α 4 Or performing least square fitting on the periodic signal according to the theoretical light intensity expression, and also obtaining the amplitude coefficient alpha at each frequency 0 、α 2 、α 4 The method comprises the steps of carrying out a first treatment on the surface of the Substituting the amplitude coefficient into an ellipsometry parameter coefficient equation to obtain an ellipsometry parameter under a selected incident angle; the measured ellipsometry parameters and the theoretical ellipsometry parameters corresponding to each discrete incident angle can be obtained by continuously changing the selected incident angle range, as shown in fig. 6.
And S4, deriving an objective polarization effect transfer matrix according to a preset system configuration to determine an objective ellipsometry parameter solving equation, and further solving the objective multiple-incidence-angle ellipsometry parameter by utilizing the obtained actually measured multiple-incidence-angle ellipsometry parameter and the theoretical multiple-incidence-angle ellipsometry parameter to complete in-situ calibration of the objective polarization effect in the angle-resolved scatterometry system.
The angle resolution type scattering measurement system adopts the same objective lens to illuminate and measure the sample, the polarization effect transfer matrix of the objective lens is not changed along with the configuration change of the system, and the polarization effect transfer matrix of the objective lens can be deduced according to the light beam propagation rule in the system. According to the deduced coupling transfer matrix of the objective lens ellipsometry parameters and the sample ellipsometry parameters, an objective lens ellipsometry parameter expression can be obtained through variable transformation, and then the multi-incidence angle ellipsometry parameters of the objective lens can be solved by utilizing the actually measured multi-incidence angle ellipsometry parameters and the theoretical multi-incidence angle ellipsometry parameters.
In this embodiment, the system model is considered that the light beam is collected by the objective lens 241, reflected by the sample, and collected by the objective lens 241, and can be described as follows by using the jones matrix:
wherein J is S Represents a sample theoretical Jones matrix, ψ represents a theoretical amplitude ratio angle, Δ represents a theoretical phase difference angle, J obj Representing the objective Jones matrix, ψ obj Indicating the amplitude ratio angle delta of the objective lens obj Indicating the phase angle of the objective lens, J S ' represents the measured sample jones matrix.
The ellipsometry parameters extracted by the experiment can be expressed as a combination of theoretical ellipsometry parameters and objective ellipsometry parameters:
tanΨ'(θ)＝tanΨ(θ)·tan 2 Ψ obj (θ)
Δ'(θ)＝Δ(θ)+2Δ obj (θ)
ψ 'represents the measured amplitude ratio angle, and Δ' represents the measured phase difference angle.
Taking the actually measured ellipsometry parameters and the theoretical ellipsometry parameters as original data, and determining an expression of the ellipsometry parameters of the objective along with the incident angle according to an objective ellipsometry parameter transfer equation:
Δ obj (θ)＝(Δ'(θ)-Δ(θ))/2。
the extracted objective lens is subjected to multi-incidence angle ellipsometry parameter psi obj And delta obj Substituting into the established system model, specifically, the ellipsometry parameters of the objective lens extracted in this embodiment are shown in fig. 7, and in this embodiment, the ellipsometry parameters obtained by experiment under each incident angle are consistent with the ellipsometry parameters of the input objective lens, so as to illustrate the effectiveness of the objective lens polarization effect calibration method provided by the invention. The extracted objective ellipsometry parameters are substituted into a system model, so that measurement errors caused by objective polarization effects can be corrected, and the nanostructure parameter extraction precision is improved.
In order to further verify the effectiveness of the calibration, a simulated measurement experiment was performed according to the above-described polarization effect calibration results. The method comprises the following steps: substituting the multi-incidence-angle ellipsometry parameters of the objective lens extracted in the step S4 into a system model of the step S2 to serve as fixed parameters, and correcting measurement errors caused by the polarization effect of the objective lens; when sample parameter fitting is carried out, only pixel points in a specific incident angle range are selected as fitting initial data, a sample measurement result under the selected incident angle can be obtained, and a measurement result under multiple incident angles can be obtained by continuously changing the incident angle range.
In the embodiment, the simulation sample is a 54nm silicon substrate silicon dioxide film, and an analyzer on an emergent light path is removed in the simulation measurement process. And (3) establishing a standard Cartesian coordinate system on a back focal plane image generated by the sample in accordance with the analysis process, and calculating the corresponding incidence angle and azimuth angle of each point. Pixel points within a certain incident angle range are selected and used as raw data to perform sample parameter fitting, and a group of measurement results are shown in fig. 8. Before correction, a large deviation exists between the fitting value of the film thickness under different incidence angles and the reference value, and the measurement results under different incidence angles are not consistent; after correction, the film thickness at each incident angle is kept consistent with the reference value, and the extracted value can be considered to be strictly consistent with the reference value in consideration of the calculated rounding error, so that the effectiveness of the calibration method is further verified.
The order of step S1 and step S2 may be changed or may be performed in parallel.
The present invention will be described in further detail with reference to the following examples.
Examples
To further verify that the correction method of the present invention is effective, another set of embodiments is presented herein, namely that the polarizer 222 and analyzer 251 are azimuthally set to 0 ° and 0 °, and that the objective polarization effect is considered uniform across the focal plane.
In view of the different system configurations, the basic flow of measuring system model and objective polarization effect calibration is not changed, so the processing and calculation procedures of each step are not detailed in this embodiment, and only different calculation methods due to different combinations of polarizer azimuth angles are given.
In step S1, an angle-resolved scatterometry system is built according to a system configuration in which the azimuth angles of the polarizer 222 and the analyzer 251 are 0 ° and 0 °, respectively.
In step S2, a system simulation model is built according to the system configurations in which the azimuth angles of the polarizer 222 and the analyzer 251 are 0 ° and 0 °, respectively.
Specifically, when the azimuth angles of the polarizer 222 and the analyzer 251 are set to 0 ° and 0 °, the expression of the system model including the polarization effect of the objective lens is:
specifically, let the objective lens 241 be an ideal objective lens, the light intensity of the outgoing light can be expressed as:
wherein I represents the intensity of emergent light, alpha 0 、α 2 、α 4 Represents the amplitude coefficient at the frequency multiplication of 0, 2, 4, and α 0 、α 2 、α 4 The ellipsometry parameters of the sample can be uniquely expressed as:
the back focal plane measured image is shown in FIG. 9, in this embodiment the input objective polarization effect is ψ obj-input ＝46.3°，Δ obj-input ＝-3.8°。
And (3) modeling the back focal plane image of the standard sample according to the system model established in the step S2. Compared with the actual measurement back focal plane image containing the polarization effect of the objective lens, the specific back focal plane theoretical image has obvious difference in light intensity distribution and does not have severe fluctuation in the center of the image.
And deducing a sample ellipsometry parameter coefficient equation according to a preset system configuration.
Specifically, the azimuth angles of the polarizer 222 and the analyzer 251 are 0 ° and 0 °, respectively, and the ellipsometry parameters ψ, Δ at any incident angle can be determined by the amplitude coefficient α at each frequency 0 、α 2 、α 4 Expressed as the following ellipsometric parameter coefficient equation:
in the formula, the number of times of the amplitude coefficient of the numerator and denominator is 1.
Based on the obtained back focal plane actual measurement and simulation images, actual measurement ellipsometry parameters and theoretical ellipsometry parameters corresponding to each incident angle are calculated, as shown in fig. 10. Specifically, the ellipsometry parameter calculation procedure is the same as that of embodiment 1, and it is noted that the updated magnitude coefficient expression and the updated ellipsometry parameter coefficient expression are required to be used.
In this embodiment, an objective ellipsometry parameter extraction method with strong noise immunity and good stability is provided, specifically, actually measured ellipsometry parameters and theoretical ellipsometry parameters are taken as raw data, and the following fitting form is determined according to an objective ellipsometry parameter transfer equation:
wherein, the subscript i represents different incident angles; continuously adjusting the ellipsometry parameter ψ of the objective lens obj And delta obj And when the summation type sub-value is minimum, the parameter value used is the objective ellipsometry parameter.
In this embodiment the extraction objective ellipsometry parameter is ψ obj ＝46.3002°、Δ obj The = -3.7885 ° can be considered as a strict agreement of the input objective ellipsometry parameters, considering the calculation errors, and also agree with the objective ellipsometry parameters extracted in the previous embodiment, which illustrates that the configuration selected in this embodiment can correctly extract the objective polarization effect. The validity of the calibration method is further verified, the universality of the calibration method is also demonstrated, and the calibration method can be used for calibrating the polarization effect of the objective lens in an angle-resolved scattering system under the azimuth angle combination of various polarizers and analyzers.
And performing simulation measurement experiments on the polarization effect calibration results. The simulation samples used, in addition to the 54nm thick silicon-based silicon dioxide films described above, used silicon-based silicon dioxide films of 19nm and 115nm thickness. Simulation measurements were performed on the two orthogonal polarizations TM, TE, and the measurement results are shown in the following table. As can be seen from the table, before the objective lens polarization effect calibration is performed, the film thickness measurement result is completely deviated from the true value, the 19nm standard film sample cannot be measured, and the measurement results of different polarization states of the same sample are different; the difference between the calibrated film measurement result and the nominal value is extremely small, the calculated rounding error is considered, the extracted value is considered to be strictly consistent with the input value, the measurement results among different polarization states have good consistency, the effectiveness of the calibration method is further verified, the universality of the calibration method is also demonstrated, and the method can be used for calibrating the polarization effect of the objective lens in an angle-resolved scattering system with various polarizer and analyzer azimuth combinations, various measurement polarization states and various objective lens polarization effect distributions.
Table 1: standard film simulation measurement results before and after calibration
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (5)
1. An in-situ calibration method for polarization effects of an objective lens in an angle-resolved scatterometer, comprising the steps of:
(1) Providing an angle resolution type scattering measurement system, and measuring a standard film through the angle resolution type scattering measurement system to obtain an actual measurement image of a back focal plane of an objective lens; meanwhile, a system simulation model of the angle resolution type scattering measurement system, which comprises an objective lens polarization effect, is established, and the standard film is taken as a sample, and an objective lens back focal plane simulation image is generated through the system simulation model;
(2) Based on an ellipsometry parameter system equation of a sample, an obtained objective lens back focal plane actual measurement image and an objective lens back focal plane simulation image, calculating to obtain an actual measurement multiple-incidence-angle ellipsometry parameter and a theoretical multiple-incidence-angle ellipsometry parameter;
(3) Determining an objective lens ellipsometry parameter solving equation based on the derived objective lens polarization effect transfer matrix, and further solving the objective lens multiple-incidence-angle ellipsometry parameter by utilizing the obtained actually measured multiple-incidence-angle ellipsometry parameter and the theoretical multiple-incidence-angle ellipsometry parameter to complete in-situ calibration of the objective lens polarization effect in the angle-resolved scatterometry system;
a polarizer is respectively arranged in an incident light path and an emergent light path of the angle-resolved scatterometry system and is respectively used as a polarizer and an analyzer, and the azimuth angles of the polarizer and the analyzer are respectively 0 DEG and-45 DEG by taking the plane of the angle-resolved scatterometry system as a reference; the expression of the system simulation model containing the polarization effect of the objective lens is as follows:
in the method, in the process of the invention,represents an incident light azimuth angle, θ represents an incident light angle; />Indicating a rotation angle of +.>Is rotated by the coordinate of the agar matrix; p represents a polarizer jones matrix; j (J) M Representing a sample reflection coordinate transformation matrix; j (J) S The Jones matrix is a sample to be measured; j (J) obj The objective lens polarization effect quantization description Jones matrix is called as the objective lens Jones matrix for short; e (E) in And E is connected with out Representing the intensity vectors of the incident light and the emergent light electric field respectively, usually E in ＝I 0 ·[1,1] T ；
A Cartesian coordinate system is established by taking the center of a back focal plane image as an origin, the corresponding incidence angle and azimuth angle of each pixel point are calculated, the pixel points in a specific incidence angle range are screened, the pixel points are ordered from small to large according to azimuth angles, a triangular periodic signal is obtained, and a theoretical expression of the triangular periodic signal is deduced as follows:
wherein I represents the intensity of emergent light; alpha 0 、α 2 、α 4 Respectively representing the amplitude coefficients at the frequency multiplication positions of 0, 2 and 4;indicating the azimuth angle of the incident light; θ represents an incident angle of incident light;
carrying out frequency domain analysis on a periodic signal through Fourier change or carrying out least square fitting according to a theoretical expression to obtain amplitude coefficients corresponding to different frequencies, then determining a sample ellipsometry parameter coefficient equation by combining azimuth angles of two polaroids, calculating actual measurement ellipsometry parameters and theoretical ellipsometry parameters of the sample under the incident angle, and changing the selected incident angle range, so that the actual measurement ellipsometry parameters and the theoretical ellipsometry parameters of the sample corresponding to a plurality of incident angles can be calculated;
the ellipsometry parameters psi and delta at any incidence angle can be obtained by the amplitude coefficient alpha at each frequency 0 、α 2 、α 4 Expressed as the following ellipsometric parameter coefficient equation:
2. the method for in-situ calibration of the polarization effect of an objective lens in an angle resolved scatterometer of claim 1, wherein: the angle-resolved scatterometry system adopts the same objective lens to illuminate and measure the sample, and the polarization effect transfer matrix of the objective lens is not changed along with the change of system configuration, so that the polarization effect transfer matrix of the objective lens can be deduced according to the light beam propagation rule in the system.
3. The method for in-situ calibration of the polarization effect of an objective lens in an angle-resolved scatterometer of claim 2, wherein: and coupling the transmission matrix according to the deduced objective ellipsometry parameters and the sample ellipsometry parameters, and obtaining an objective ellipsometry parameter expression through variable transformation.
4. The method for in-situ calibration of the polarization effect of an objective lens in an angle resolved scatterometer of claim 1, wherein: in the system simulation model, the light beam is regarded as being converged through the objective lens, reflected by the sample, collected by the objective lens and expressed as follows by using the Jones matrix:
wherein J is S Representing a sample theoretical jones matrix; psi represents the theoretical amplitude ratio angle; delta represents the theoretical phase difference angle; j (J) obj Representing an objective lens jones matrix; psi obj Indicating the amplitude ratio angle of the objective lens; delta obj Representing the phase angle of the objective lens; j (J) S ' represents the measured sample jones matrix.
5. The method for in-situ calibration of the polarization effect of an objective lens in an angle resolved scatterometer of claim 1, wherein: the objective ellipsometry parameter solving equation is:
wherein, the subscript i represents different incident angles; psi phi type i Represents the amplitude ratio angle, delta, of the objective lens at an incident angle i i An objective phase difference angle when the incident angle is i; psi obj Indicating the amplitude ratio angle of the objective lens; delta obj Representing the phase angle of the objective lens; continuously adjusting the ellipsometry parameter ψ of the objective lens obj And delta obj And when the value of the objective lens ellipsometry parameter solving equation is minimum, the parameter value used is the objective lens ellipsometry parameter.
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