CN117030623A - Ellipsometry system calibration method based on bandwidth deconvolution - Google Patents
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- 238000005457 optimization Methods 0.000 claims abstract description 5
- 238000005259 measurement Methods 0.000 claims description 44
- 238000004364 calculation method Methods 0.000 claims description 2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/21—Polarisation-affecting properties
- G01N21/211—Ellipsometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/21—Polarisation-affecting properties
- G01N21/211—Ellipsometry
- G01N2021/213—Spectrometric ellipsometry
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Abstract
The invention provides a calibration method of an ellipsometry system based on bandwidth deconvolution, which comprises the steps of using an ellipsometry system to be calibrated to measure standard samples with any thickness, obtaining measured light intensity signals corresponding to the samples, performing bandwidth deconvolution on the measured light intensity signals, then performing system calibration by using the measured light intensity signals after bandwidth deconvolution, obtaining a Mueller matrix of the measured samples after system parameters, and selecting optimal system parameters by taking the optimization of the precision of the Mueller matrix as a standard. The ellipsometer system calibration method based on bandwidth deconvolution provided by the invention carries out bandwidth deconvolution processing on the measured light intensity signals, and the obtained system parameters are more accurate, thereby being beneficial to improving the precision of measuring the sample parameters by the instrument.
Description
Technical Field
The invention relates to the field of ellipsometry system calibration, in particular to an ellipsometry system calibration method based on bandwidth deconvolution.
Background
In the semiconductor industry, the measurement of optical critical dimensions (optical critical dimension, OCD) and the measurement of fine structure film thickness directly relate to the precision and yield of the production samples. Ellipsometers are widely used in advanced semiconductor process monitoring because of their advantages of non-contact, non-damage, low cost, rapidness, high precision, etc.
Taking a dual rotation compensator type mueller matrix ellipsometer as an example, as shown in fig. 1, the basic configuration includes: the device comprises a light source 1, a polarizer 2, a first rotating motor 3, a first compensator 4, a sample to be tested 5, a second compensator 6, a second rotating motor 7, an analyzer 8 and a spectrometer 9. The working principle of the ellipsometer is based on the measurement of a model, and a light intensity signal measured by the spectrometer is converted into a required ellipsometry spectrum through a system model, wherein parameters required to be input in the system model comprise an azimuth angle of a polarizer, an azimuth angle of an analyzer, azimuth angles of two rotation compensators and phase delay amounts. The ellipsometer works as follows:
1. the light source emits natural light, and the natural light is converted into polarized light after passing through the polarizer;
2. the polarized light irradiates the sample stage through the first rotary compensator and is reflected or refracted to become new polarized light after passing through the surface of the sample;
3. detecting the new polarized light by a spectrometer after passing through another rotary compensator and a polarization analyzer to obtain a light intensity signal of the new polarized light;
4. deducing by utilizing the light intensity signal detected by the spectrometer to obtain an ellipsometry spectrum of the sample;
5. and obtaining the thickness of the sample piece based on the ellipsometry spectrum of the sample piece.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides an ellipsometry test system calibration method based on bandwidth deconvolution, which comprises the following steps:
step 1, obtaining an initial measurement light intensity signal of a sample;
step 2, performing bandwidth deconvolution processing on the initial measured light intensity signals, recording measured light intensity signals obtained by repeated recursion, and executing step 3 on a group of measured light intensity signals obtained by each recursion;
step 3, calculating a sample measurement Mueller matrix based on each group of measurement light intensity signals and initial values of system parameters; calculating a sample theoretical Mueller matrix based on the sample thickness and the initial value of the polarized light incident angle;
step 4, continuously adjusting system parameters, sample thickness and polarized light incidence angle based on a regression fitting method, so that the calculated sample measurement Mueller matrix is close to the sample theoretical Mueller matrix, and calibrated system parameters corresponding to each group of measured light intensity signals are obtained;
and 5, calculating a sample measurement Mueller matrix based on each group of measured light intensity signals and the corresponding calibrated system parameters, and selecting the calibrated system parameters corresponding to the sample measurement Mueller matrix with highest precision in the plurality of sample measurement Mueller matrices as optimal system parameters.
According to the bandwidth deconvolution-based ellipsometry system calibration method, bandwidth deconvolution processing is carried out on the measured light intensity signals, the obtained system parameters are more accurate, and the accuracy of measuring the sample parameters by the instrument is improved.
Drawings
FIG. 1 is a schematic diagram of a dual rotation compensator type Mueller matrix ellipsometer;
fig. 2 is a flow chart of a calibration method of an ellipsometry system based on bandwidth deconvolution.
In the drawings, the names of the components represented by the reference numerals are as follows:
1. the device comprises a light source, a polarizer, a first rotating motor, a first compensator, a sample to be tested, a second compensator, a second rotating motor, an analyzer, a spectrometer and a spectrometer, wherein the light source, the polarizer, the first rotating motor, the first compensator, the sample to be tested, the second compensator, the second rotating motor, the light source, the polarizer, the first rotating motor, the first compensator, the sample to be tested, the first compensator, the second compensator, the light source, the polarizer, the first rotating motor, the polarizer and the optical spectrometer.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. In addition, the technical features of each embodiment or the single embodiment provided by the invention can be combined with each other at will to form a feasible technical scheme, and the combination is not limited by the sequence of steps and/or the structural composition mode, but is necessarily based on the fact that a person of ordinary skill in the art can realize the combination, and when the technical scheme is contradictory or can not realize, the combination of the technical scheme is not considered to exist and is not within the protection scope of the invention claimed.
The ellipsometry system obtains a measured light intensity signal through the spectrometer, and due to the structural characteristics of the spectrometer, the measured light intensity signal has a bandwidth convolution effect instead of a real signal, and errors introduced by the bandwidth convolution in the light intensity signal can be transmitted to system parameters obtained through calibration, so that the accuracy of the ellipsometry for measuring the sample parameters is affected. Common bandwidth deconvolution methods include, but are not limited to, the Levenberg-Marquardt method, the regularized LM method, the Richardson-Lucy method, and the like. The Levenberg-Marquardt method and the regularized LM method are difficult to solve the noise problem in the light intensity signals, and the noise in the light intensity signals can be amplified to influence the quality of an ellipsometry spectrum, and finally the repeatability, the measurement accuracy and the like of the machine are influenced. The Richardson-Lucy method is a display recurrence method and generally requires defining a suitable stopping iteration criterion to find the optimal bandwidth deconvoluted light intensity signal.
Based on this, fig. 1 provides a calibration method of an ellipsometry system based on bandwidth deconvolution according to the present invention, the calibration method comprising:
and step 1, obtaining an initial measured light intensity signal of the sample.
It can be understood that the ellipsometry system such as a spectrometer is utilized to obtain the sample to be measuredThe initial measured light intensity signal is recorded as
And step 2, performing bandwidth deconvolution processing on the initial measured light intensity signals, recording measured light intensity signals obtained by repeated recursions, and executing step 3 on a group of measured light intensity signals obtained by each recursion.
It is understood that the measured light intensity signal is subjected to a Richardson-Lucy bandwidth deconvolution process. The Richardson-Lucy bandwidth deconvolution formula is:
where B is a bandwidth function, commonly used bandwidth functions include, but are not limited to Gauss functions, triangle functions, etc., operators "×" representing convolutions; n is the recurrence times, and the numerical value of N is set according to specific conditions. Obtaining a plurality of groups of measured light intensity signals through a formula (1)
Deconvolving each set of bandwidths to measure the intensity signalAnd (5) repeating the step 3 and the step 4.
Step 3, calculating a sample measurement Mueller matrix based on each group of measurement light intensity signals and initial values of system parameters; and calculating a sample theoretical muller matrix based on the sample thickness and the initial value of the incident angle of polarized light.
As an embodiment, the step 3 is based on each set of measured light intensity signalsAnd initial system parameters, calculating a sample measurement mueller matrix,comprising the following steps: performing Fourier transform on each group of measured light intensity signals to obtain corresponding Fourier coefficients; and calculating the sample measurement Mueller matrix based on a calculation function formula of the sample measurement Mueller matrix according to the Fourier coefficient and the initial value of the system parameter of the ellipsometry system.
It can be appreciated that for measuring light intensity informationPerforming Fourier transformation to obtain Fourier coefficients, measuring the conversion relation of the Mueller matrix by using the Fourier coefficients and the sample, and giving the azimuth angle P of the polarizer, the azimuth angle A of the analyzer and the azimuth angles C of the two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 Initial values of system parameters are calculated, and a sample measurement Mueller matrix M is calculated meas (P,A,C 1 ,C 2 ,δ 1 ,δ 2 ) Wherein, the sample measures the Mueller matrix and polarizer azimuth P, the azimuth A of the analyzer, the azimuth C of the two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 And the like.
As an embodiment, in the step 3, calculating a sample theoretical muller matrix based on the sample thickness and the reference value of the incident angle of polarized light includes: giving the thickness d of the sample and the incident angle theta of polarized light, and calculating a sample theoretical Mueller matrix M by using a sample theoretical Mueller matrix model sim (d,θ)。
And 4, continuously adjusting system parameters, sample thickness and polarized light incident angle based on a regression fitting method, so that the calculated sample measurement Mueller matrix is close to the sample theoretical Mueller matrix, and acquiring calibrated system parameters corresponding to each group of measured light intensity signals.
As an embodiment, based on a regression fitting method, continuously adjusting system parameters, sample thickness and polarized light incident angle, so that the calculated sample measurement muller matrix is close to the sample theoretical muller matrix, and obtaining calibrated system parameters corresponding to each group of measurement light intensity signals includes: polarizer azimuth angle P and analyzer based on ellipsometry systemAzimuth angle a of (2), azimuth angle C of two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 Calculating a sample measurement Mueller matrix; calculating a sample theoretical Mueller matrix based on the thickness d of the sample and the incident angle theta of the polarized light; continuously adjusting the azimuth angle P of the polarizer, the azimuth angle A of the analyzer and the azimuth angles C of the two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 Calculating a sample measurement Mueller matrix, continuously adjusting the thickness d of the sample and the polarized light incident angle theta, calculating a sample theoretical Mueller matrix until the residual error between the sample measurement Mueller matrix and the sample theoretical Mueller matrix is minimum, and acquiring the calibrated system parameters, the sample thickness and the polarized light incident angle.
It can be understood that by adjusting the polarizer azimuth angle P, the analyzer azimuth angle A, and the two rotation compensators azimuth angle C in the ellipsometry system 1 、C 2 And a phase delay amount delta 1 、δ 2 And adjusting the thickness d of the sample and the incident angle theta of polarized light, and adopting regression fitting to enable the sample to measure residual error II M between the Mueller matrix and the theoretical Mueller matrix of the sample meas (P,A,C 1 ,C 1 ,δ 1 ,δ 2 )-M sim (d,θ)‖ 2 Minimum all parameter values, i.e The subscript "opt" indicates the optimal solution, II.|II 2 Representing the two norms of the vector, expanding the Mueller matrix into a vector form according to columns, and then performing operation to obtain calibrated system parameters
The regression fit implementation method in the above process includes, but is not limited to, a traversal method, a global optimization method (such as a genetic algorithm, a particle swarm algorithm, an ant swarm algorithm, etc.), and a local optimization algorithm (such as a Levenberg-Marquardt method, a Newton method, a quasi-Newton method, a gradient descent method, a conjugate gradient method, etc.).
And carrying out the processing on each group of measured light intensity signals subjected to the bandwidth deconvolution processing to obtain calibrated system parameters corresponding to each group of measured light intensity signals.
And 5, calculating a sample measurement Mueller matrix based on each group of measured light intensity signals and the corresponding calibrated system parameters, and selecting the calibrated system parameters corresponding to the sample measurement Mueller matrix with highest precision in the plurality of sample measurement Mueller matrices as optimal system parameters.
It will be appreciated that based on step 4, each set of light intensity signalsCorrespondingly obtaining a set of calibrated system parametersBy means of system parameters and measuring the light intensity signal +.>Measurement Mueller matrix of available samples>
The mueller matrix is a fourth order matrix with 8 auxiliary diagonal elements m 13 ,m 14 ,m 23 ,m 24 ,m 31 ,m 32 ,m 42 ,m 42 The theoretical value should be 0, and the closer the 8 auxiliary diagonal elements are to 0, the higher the accuracy of the muller matrix is considered. Comparison ofFinding the measurement Mueller matrix with highest precision, wherein the corresponding system parameter is the final system parameter after calibration. After the system parameters are obtained in the above calibration mode, the ellipsometer can be directly used for measuring the thickness and other information of any sample.
According to the method for calibrating the ellipsometry measurement system based on the bandwidth deconvolution, which is provided by the embodiment of the invention, the Richardson-Lucy bandwidth deconvolution method is combined with the system calibration method, the system calibration is performed after the bandwidth deconvolution is performed on the measured light intensity signals, the precision of the measured Mueller matrix is taken as an index, and the group of system parameters corresponding to the highest precision of the measured Mueller matrix is selected, so that the measurement precision of an instrument is improved.
In the foregoing embodiments, the descriptions of the embodiments are focused on, and for those portions of one embodiment that are not described in detail, reference may be made to the related descriptions of other embodiments.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (6)
1. An ellipsometry system calibration method based on bandwidth deconvolution, comprising:
step 1, obtaining an initial measurement light intensity signal of a sample;
step 2, performing bandwidth deconvolution processing on the initial measured light intensity signals, recording measured light intensity signals obtained by repeated recursion, and executing step 3 on a group of measured light intensity signals obtained by each recursion;
step 3, calculating a sample measurement Mueller matrix based on each group of measurement light intensity signals and initial values of system parameters; calculating a sample theoretical Mueller matrix based on the sample thickness and the initial value of the polarized light incident angle;
step 4, continuously adjusting system parameters, sample thickness and polarized light incidence angle based on a regression fitting method, so that the calculated sample measurement Mueller matrix is close to the sample theoretical Mueller matrix, and calibrated system parameters corresponding to each group of measured light intensity signals are obtained;
and 5, calculating a sample measurement Mueller matrix based on each group of measured light intensity signals and the corresponding calibrated system parameters, and selecting the calibrated system parameters corresponding to the sample measurement Mueller matrix with highest precision in the plurality of sample measurement Mueller matrices as optimal system parameters.
2. The method according to claim 1, wherein said step 2, for said initial measured light intensity signalPerforming bandwidth deconvolution processing, including:
wherein B is a bandwidth function, operator "×" represents convolution; n is the recurrence times, and the numerical value of N is set according to specific conditions;
obtaining a plurality of groups of measured light intensity signals according to the formula (1)k and N are positive integers.
3. The method of calibrating an ellipsometry system according to claim 1, wherein the step 3 of calculating a sample measurement muller matrix based on each set of measured light intensity signals and initial system parameters comprises:
performing Fourier transform on each group of measured light intensity signals to obtain corresponding Fourier coefficients;
calculating a sample measurement Mueller matrix M based on a calculation function of the sample measurement Mueller matrix according to the Fourier coefficient and an initial value of a system parameter of an ellipsometry system meas (P,A,C 1 ,C 2 ,δ 1 ,δ 2 ) The system comprises a polarizer azimuth angle P, an azimuth angle A of an analyzer and an azimuth angle C of two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 。
4. A method of calibrating an ellipsometry system according to claim 3, wherein the calculating a sample theoretical muller matrix based on the sample thickness and initial values of polarized light incidence angle comprises:
given the sample thickness d and the polarized light incident angle theta, a sample theoretical Mueller matrix M calculated by using a sample theoretical Mueller matrix model is obtained sim (d,θ)。
5. The method for calibrating an ellipsometry system according to claim 4, wherein step 4, based on a regression fitting method, continuously adjusts system parameters, sample thickness and polarized light incident angle, so that the calculated sample measurement mueller matrix is close to the sample theoretical mueller matrix, and obtaining calibrated system parameters corresponding to each set of measured light intensity signals includes:
based on polarizer azimuth P, analyzer azimuth A, azimuth C of two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 Calculating a sample measurement Mueller matrix; calculating a sample theoretical Mueller matrix based on the thickness d of the sample and the incident angle theta of the polarized light;
continuously adjusting the azimuth angle P of the polarizer, the azimuth angle A of the analyzer and the azimuth angles C of the two rotation compensators 1 、C 2 And a phase delay amount delta 1 、δ 2 Calculating a sample measurement Mueller matrix, continuously adjusting the thickness d of the sample and the polarized light incident angle theta, calculating a sample theoretical Mueller matrix until the residual error between the sample measurement Mueller matrix and the sample theoretical Mueller matrix is minimum, and acquiring the calibrated system parameters, the sample thickness and the polarized light incident angle.
6. The ellipsometry system calibration method of claim 5, wherein the regression fitting method comprises a traversal method, a global optimization method comprising a genetic algorithm, a particle swarm algorithm, and an ant swarm algorithm, and a local optimization method comprising a Levenberg-Marquardt method, a newton method, a quasi-newton method, a gradient descent method, and a conjugate gradient method.
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