CN111473742A - Morphology simulation and compensation method for batwing effect of white light scanning interferometry - Google Patents
Morphology simulation and compensation method for batwing effect of white light scanning interferometry Download PDFInfo
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- CN111473742A CN111473742A CN202010443270.5A CN202010443270A CN111473742A CN 111473742 A CN111473742 A CN 111473742A CN 202010443270 A CN202010443270 A CN 202010443270A CN 111473742 A CN111473742 A CN 111473742A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/30—Measuring arrangements characterised by the use of optical techniques for measuring roughness or irregularity of surfaces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/02055—Reduction or prevention of errors; Testing; Calibration
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/0209—Low-coherence interferometers
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/02—Preprocessing
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/08—Feature extraction
- G06F2218/10—Feature extraction by analysing the shape of a waveform, e.g. extracting parameters relating to peaks
Abstract
The invention provides a morphology simulation and compensation method for batwing effect of white light scanning interferometry, which comprises the following steps: s1: giving a simulation appearance; s2: generating a light intensity signal of a measurement result of the white light scanning interferometer; s3: obtaining a new interference light intensity signal by using a convolution theorem; s4: extracting phases from the interference light intensity signals obtained in the step S3 by adopting a peak value extraction algorithm and reconstructing the interferometer measurement morphology; s5: and (3) compensating the batwing effect, namely generating a simulated interference light intensity signal by using the simulated morphology containing the batwing effect obtained in the step S4 according to a formula (1), then obtaining the compensated interference light intensity signal by using a deconvolution theorem, and obtaining the compensated height information of the compensated interference light intensity signal by using a peak value extraction algorithm, so as to obtain the compensated morphology. The invention solves the problem that the existing white light scanning interferometry technique is influenced by batwing effect errors and limits the measurement precision and accuracy of a white light interferometer.
Description
Technical Field
The invention relates to the field of white light scanning interferometry, in particular to a morphology simulation and compensation method for batwing effect in white light scanning interferometry.
Background
The optical measurement method is a main means for detecting and metering the appearance of the ultra-precision machining technology due to the advantages of non-contact measurement, simple operation process, high efficiency and the like. The white light scanning interferometry measurement technology has the measurement precision as high as nanoscale or even sub-nanoscale, can not damage the surface of a workpiece, can measure the three-dimensional morphology, has the measurement range from nanoscale to millimeter level, and is widely applied to the morphology measurement of various ultra-precision machined surfaces such as grinding and polishing.
However, because the surface topography information is obtained by analyzing the optical interference fringe image, errors introduced by the interference image have great influence on the result, such as Rayleigh diffraction limit, light intensity loss caused by diffuse reflection, background light noise and the like, so that various measurement errors, such as batwing effect, 2 pi error, chromatic dispersion and chromatic aberration, multiple reflection and the like, are caused. The existence of numerous errors limits the measurement accuracy and precision of the white light interferometer.
When white light interferometry of a given morphology is performed, interference light intensity signals are as follows:
the above formula does not take into account the effects of light diffraction effects. The point source forms an enlarged image point due to diffraction after passing through any optical system, and image information can be accurately extracted by combining a point spread function of a measurement system. Any complex object is composed of numerous point sources, the intensity of which is the convolution of the object intensity with the point spread function, which is expressed as:
In,image(x,y)＝In(x,y)*psf(x,y)
interference signals obtained by the measurement process of the white light scanning interferometry system are affected by diffraction effects. Xie et al think through experimental measurement that the shape and size of the interference light intensity signal are influenced by the numerical aperture of the objective lens and the spectral bandwidth of the light source; in addition, local surface features of the measurement object itself, such as step height, slope, or curvature, also affect the shape of the interference light intensity signal.
The zero optical path difference position of each sampling point is found by carrying out algorithm processing on the interference light intensity signal of each frame, and then height information can be extracted from the light intensity information to obtain surface morphology information. The peak value extraction algorithm includes a gravity center method, a polynomial fitting method, an envelope line method, a spatial frequency domain method, a white light phase shift method and the like. And different extraction algorithms have different positioning accuracy, interference resistance, calculation speed and sampling intervals.
The practical measurement result of white light scanning interferometer shows that when the height of the step smaller than the coherent length is measured, the step edge affected by diffraction effect will produce batwing artifact called batwing effect.
The batwing effect is generally believed to be due to system diffraction effects. When the top of the step is measured, incident light is emitted by the interference objective lens, diffraction is generated when the light passes through the edge of a steep step, diffracted light enters the bottom of the step, light intensity information of the bottom part and light intensity information of the top part return to the objective lens at the same time to form light intensity information of the top part, so that the light intensity of the top part is changed, and the height information of the top part is raised; conversely, the bottom height information decreases, thereby forming a distinct shape as the height information of the batwing at the step edge. The batwing effect limits the measurement precision and accuracy of the white light interferometer when measuring the hundred-nanometer step, and further limits the application of the white light interferometer in the field of microstructures in ultra-precision machining.
Disclosure of Invention
According to the technical problem that the conventional white light scanning interferometer is influenced by various measurement errors and limits the measurement precision and accuracy, the morphology simulation method for the batwing effect of the white light scanning interferometer measurement process is provided by the invention through a white light scanning interferometry light intensity simulation program and a peak value extraction program. The batwing measurement error generated during measurement of the hundred-nanometer steps is compensated by the deconvolution algorithm, and the measurement precision and accuracy of the white light scanning interference morphology are improved.
The technical means adopted by the invention are as follows:
a morphology simulation and compensation method for batwing effect of white light scanning interferometry comprises the following steps:
s1: giving a simulation appearance;
s2: generating a light intensity signal of a measurement result of the white light scanning interferometer:
when the spatial coherence is neglected, assuming that the spectral characteristics of the light source obey gaussian distribution, the white light interference intensity signal of a given simulated morphology is as follows:
wherein h (x, y) is a height value of the morphology to be detected; lcIs the coherence length of the light source spectrum; λ is the central wavelength of the light source spectrum; z is a radical of0When h is 0, the position where the difference between the measurement optical path length and the reference optical path length is zero, and z is assumed in the simulation0＝0；
The phase angle of the interference signal at equal optical path length; Δ z is the scanning distance between two consecutive frames of interferograms; the interference intensity I of different scanning positions z-n.DELTA z under white light irradiation can be obtained by simulationn(x, y), n represents the number of selected scanning positions;
s3: obtaining a new interference light intensity signal by using a convolution theorem;
s4: extracting phase positions from the interference light intensity signal obtained in the step S3 by adopting a peak value extraction algorithm and reconstructing the interferometer measurement morphology:
extracting height information from the interference light intensity signal obtained in the step S3 by adopting a peak value extraction algorithm, and reconstructing a morphology result of the interferometer measurement sample to obtain a simulated morphology containing the batwing effect;
s5: morphology compensation of the batwing effect:
and (2) generating a simulated interference light intensity signal by using the simulated morphology containing the batwing effect obtained in the step (S4) according to a formula (1), eliminating the influence of point source diffraction of the white light scanning interferometry system by using a deconvolution theorem to obtain a compensated interference light intensity signal, and obtaining the compensated height information of the compensated interference light intensity signal by using a peak value extraction algorithm to obtain the compensated morphology.
Further, step S3 specifically includes:
respectively carrying out Fourier transform on a white light interference light intensity signal with a given simulation morphology and a point spread function to obtain a frequency spectrum;
multiplying the interference light intensity signal spectrum by a point spread function spectrum to obtain a new light intensity spectrum;
and carrying out inverse Fourier transform on the new light intensity frequency spectrum to obtain a new interference light intensity signal.
Further, the peak extraction algorithm used in steps S3 and S5 includes an envelope method, a spatial frequency domain method, and a seven-step phase shift method.
Compared with the prior art, the invention has the following advantages:
1. in the morphology simulation and compensation method for batwing effect of white light scanning interferometry provided by the invention, a light intensity simulation program for white light scanning interferometry is utilized, corresponding light intensity information can be directly simulated for specific morphology, the diffraction influence of a point source on light intensity is considered, a diffraction light intensity model based on a point spread function is simulated, and the influence result of system diffraction effect on light intensity can be directly contrastingly considered.
2. In the morphology simulation and compensation method for batwing effect of white light scanning interferometry provided by the invention, the peak value extraction program of white light scanning interferometry is utilized to extract several different peak values of an envelope method, a space frequency domain method, a seven-step phase shift method and the like from the light intensity information after diffraction processing, so as to obtain simulated height information, and the height information can be directly extracted from the light intensity signal.
3. The appearance simulation and compensation method for batwing effect of white light scanning interferometry provided by the invention directly compensates the measured appearance without changing the software and hardware of the measuring instrument, and the compensation method is simple and effective; meanwhile, the precision and accuracy of the ultra-precise grinding surface appearance of the white light scanning interferometry are improved, especially the appearance profile and the appearance roughness, and a foundation is laid for the on-site measurement of the ultra-precise machining.
In conclusion, the technical scheme of the invention is applied to compensate the measured morphology by deconvolution aiming at the error of the batwing effect, and the measurement precision and accuracy of the white light scanning interferometric morphology are improved. Therefore, the technical scheme of the invention solves the problem that the white light scanning interferometer is limited in measurement precision and accuracy by batwing errors generated by diffraction effect.
Based on the reason, the invention can be widely popularized in the fields of white light interferometry and the like.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a morphology compensation method for batwing effect of white light scanning interferometry according to the present invention.
Fig. 2 is a fringe pattern for a given simulated topography.
FIG. 3 is a topographical map of a given simulated topography.
FIG. 4 is a graphical representation of the results of a batwing compensated simulated topography incorporating the batwing effect.
FIG. 5 is a block diagram of a simulation flow for white light scanning interferometry batwing effect as described in example 1.
FIG. 6 is a surface topography measurement of a standard reticle sample of example 1.
Fig. 7 is a fringe pattern of the surface topography of the grating sample simulated in example 1.
Fig. 8 is a surface topography of a simulated grating sample in example 1.
FIG. 9 is a graphical representation of the results of the batwing compensated surface topography of the standard grating sample of example 1.
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in FIGS. 1-4, the present invention provides a morphology simulation and compensation method for batwing effect of white light scanning interferometry, which comprises the following steps:
s1: giving a simulation appearance, and performing simulation of a measurement process by adopting software: the software-simulated light source has a central wavelength of 600nm, a shape of 200nm height value and a period of 8 μm; the point spread function employed in this embodiment is:
wherein the content of the first and second substances,
x and y are coordinate points in a Cartesian coordinate system; j. the design is a square1Is a Bessel function of a first type; u (ρ) ═ k · NA · ρ, and k ═ 2 π/λ denotes the wave number vector associated with the center wavelength, λ denotes the center wavelength of the white light interferometer light source, NA denotes the numerical aperture of the white light interferometer, NA ═ 0.9 and λ ═ 600nm in this embodiment;
s2: generating a light intensity signal of a measurement result of the white light scanning interferometer:
when the spatial coherence is neglected, assuming that the spectral characteristics of the light source obey gaussian distribution, the white light interference intensity signal of a given simulated morphology is as follows:
wherein h (x, y) is a height value of the morphology to be detected; lcIs the coherence length of the light source spectrum; λ is the central wavelength of the light source spectrum; z is a radical of0When h is 0, the position where the difference between the measurement optical path length and the reference optical path length is zero, and z is assumed in the simulation0＝0；
The phase angle of the interference signal at equal optical path length; Δ z is the scanning distance between two consecutive frames of interferograms; the interference intensity I of different scanning positions z-n.DELTA z under white light irradiation can be obtained by simulationn(x, y), n represents the number of selected scanning positions;
s3: obtaining a new interference light intensity signal by using convolution theorem:
respectively carrying out Fourier transform on a white light interference light intensity signal with a given simulation morphology and a point spread function to obtain a frequency spectrum;
multiplying the interference light intensity signal spectrum by a point spread function spectrum to obtain a new light intensity spectrum;
carrying out inverse Fourier transform on the new light intensity spectrum to obtain a new interference light intensity signal;
s4: extracting phase positions from the interference light intensity signal obtained in the step S3 by adopting a peak value extraction algorithm and reconstructing the interferometer measurement morphology:
extracting height information from the interference light intensity signal obtained in the step S3 by adopting a peak value extraction algorithm, and reconstructing a morphology result of the interferometer measurement sample to obtain a simulated morphology containing the batwing effect;
comparing the simulation morphology given in the step S1 with the morphology containing the batwing effect obtained in the step S4, so as to illustrate the rationality of the simulation of the batwing effect morphology in the measuring process of the invention;
s5: morphology compensation of the batwing effect:
generating a simulated interference light intensity signal by using the simulated morphology containing the batwing effect obtained in the step S4 according to a formula (1), eliminating the influence of point source diffraction of the white light scanning interference measurement system by using a deconvolution theorem to obtain a compensated interference light intensity signal, and obtaining compensated height information of the compensated interference light intensity signal by using a peak value extraction algorithm to obtain a compensated morphology;
as shown in fig. 4, 7 and 8, the compensated interference light intensity signal is subjected to a peak extraction algorithm to obtain the compensated height information, which can be consistent with the simulated feature given in S1, thereby illustrating the rationality of the feature compensation method of the present invention.
Further, the peak extraction algorithms adopted in step S3 and step S5 are gravity center method, envelope method, spatial frequency domain method and seven-step phase shift method.
The shape compensation method for batwing effect of white light scanning interferometry according to the invention is described in the following by specific examples:
in the embodiment, a white light interferometer is adopted to measure the appearance of a rectangular grating standard sample piece, wherein the measuring sample piece is a standard grating sample piece, and the height of the standard grating sample piece is 200 nm;
as shown in fig. 5, the specific steps include:
s1: and (3) measuring the appearance of the sample by adopting a white light interferometer:
(1-1) marking the contour line of the sample piece to be detected;
(1-2) obtaining the appearance of a sample piece to be detected: measuring the surface profile morphology of a sample by adopting a white light interferometer, wherein as shown in FIG. 6, the measuring sample piece is a standard grating sample piece with the height of 200 nm;
(1-3) extracting profile morphology: extracting the contour of the same area near the mark contour line by using interferometer related software, and carrying out numerical processing;
s2: generating a light intensity signal of a measurement result of the white light scanning interferometer by adopting a mathematical tool;
s3: carrying out Fourier transform on the white light interference light intensity signal at each pixel point of the appearance of the sample by adopting a mathematical tool to obtain an amplitude-frequency curve and a phase-frequency curve so as to obtain an amplitude spectrum and a phase spectrum;
s4: performing Fourier transform on the point spread function to obtain an amplitude-frequency curve and a phase-frequency curve of the point spread function, expanding the amplitude-frequency curve to two dimensions to obtain an amplitude-frequency spectrogram, and dividing the interference light intensity spectrum and the point spread function spectrum by using the deconvolution theorem to obtain a new light intensity spectrum;
s5: carrying out inverse Fourier transform on the amplitude-frequency information at each pixel point obtained after deconvolution processing by adopting a mathematical tool to obtain a compensated interference light intensity signal;
s6: the method for extracting the phase and reconstructing the initial morphology of the sample piece to be detected of the interferometer by adopting the peak value extraction algorithm from the interference light intensity signal after deconvolution processing comprises the following steps: and extracting height information from the compensated light intensity signal by adopting a peak value extraction algorithm to an interference light intensity signal equal peak value extraction algorithm, thereby reconstructing the real appearance of the sample to be measured of the interferometer.
As shown in fig. 6 and 9, the topography findings before and after compensation of the interferometer measurements were compared: compared with the profile morphology before compensation, the coincidence degree of the compensated measured morphology and the ideal morphology curve is higher, and the comparison verifies the effectiveness of the morphology compensation method.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (3)
1. A morphology simulation and compensation method for batwing effect of white light scanning interferometry is characterized by comprising the following steps:
s1: giving a simulation appearance;
s2: generating a light intensity signal of a measurement result of the white light scanning interferometer:
when the spatial coherence is neglected, assuming that the spectral characteristics of the light source obey gaussian distribution, the white light interference intensity signal of a given simulated morphology is as follows:
wherein h (x, y) is a height value of the morphology to be detected; lcIs the coherence length of the light source spectrum; λ is the central wavelength of the light source spectrum; z is a radical of0When h is 0, the position where the difference between the measurement optical path length and the reference optical path length is zero, and z is assumed in the simulation0＝0；
The phase angle of the interference signal at equal optical path length; Δ z is the scanning distance between two consecutive frames of interferograms; the interference intensity I of different scanning positions z-n.DELTA z under white light irradiation can be obtained by simulationn(x, y), n represents the number of selected scanning positions;
s3: obtaining a new interference light intensity signal by using a convolution theorem;
s4: extracting phase positions from the interference light intensity signal obtained in the step S3 by adopting a peak value extraction algorithm and reconstructing the interferometer measurement morphology:
extracting height information from the interference light intensity signal obtained in the step S3 by adopting a peak value extraction algorithm, and reconstructing a morphology result of the interferometer measurement sample to obtain a simulated morphology containing the batwing effect;
s5: morphology compensation of the batwing effect:
and (2) generating a simulated interference light intensity signal by using the simulated morphology containing the batwing effect obtained in the step (S4) according to a formula (1), eliminating the influence of point source diffraction of the white light scanning interferometry system by using a deconvolution theorem to obtain a compensated interference light intensity signal, and obtaining the compensated height information of the compensated interference light intensity signal by using a peak value extraction algorithm to obtain the compensated morphology.
2. The method for morphological simulation and compensation of batwing effect of white light scanning interferometry according to claim 1, wherein step S3 specifically comprises:
respectively carrying out Fourier transform on a white light interference light intensity signal with a given simulation morphology and a point spread function to obtain a frequency spectrum;
multiplying the interference light intensity signal spectrum by a point spread function spectrum to obtain a new light intensity spectrum;
and carrying out inverse Fourier transform on the new light intensity frequency spectrum to obtain a new interference light intensity signal.
3. The topography simulation and compensation method for batwing effect of white light scanning interferometry according to claim 1, wherein the peak extraction algorithm envelope method, the spatial frequency domain method and the seven-step phase shift method are adopted in steps S3 and S5.
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