CN105806236A - Nonlinear phase compensation method for Linnik type interference spectrum thin film measurement - Google Patents
Nonlinear phase compensation method for Linnik type interference spectrum thin film measurement Download PDFInfo
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- CN105806236A CN105806236A CN201610312995.4A CN201610312995A CN105806236A CN 105806236 A CN105806236 A CN 105806236A CN 201610312995 A CN201610312995 A CN 201610312995A CN 105806236 A CN105806236 A CN 105806236A
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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
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
Abstract
A nonlinear phase compensation method for Linnik type interference spectrum thin film measurement comprises the steps that the surface of a reflector is measured aiming at a Michelson interference structure, the influence of the changes of equivalent thickness on the current non-linear phase of a system is analyzed, and a wavelength calibration method is used for correcting the equivalent thickness to enable the equivalent thickness to be constant; under the condition that other elements and parameters are not changed and only a reference mirror and a sample are adjusted, the same reflector surface is measured aiming at a Linnik interference structure, and the non-linear phases of two reference measuring systems are compared after the equivalent thickness is constant; the thin film sample is measured under the linnik interference structure, an initial value is estimated through the non-linear phase frequency of a thin film, non-linear phase signals caused by the equivalent thickness and two objectives are considered, correction compensation is carried out on extracted thin film nonlinearity, and high-precision thin film thickness information is obtained through fitting by means of a local optimization algorithm.Thin film non-linear phase information can be acquired more accurately, and measuring frequency and measuring accuracy are improved.
Description
Technical field
The present invention relates to a kind of nonlinear phase compensation method measuring film thickness.Particularly relate to a kind of Linnik type interference spectrum and measure the nonlinear phase compensation method of thin film.
Background technology
White light interference spectrum as an important research direction of white light interference, processing the measurement of striped is changed into the measurement to spectral density function by spectrogrph, obtain the metrical information of requirement by analyzing the phase characteristic of spectrum.White light interference spectrometry combines the precision of white light interference and the speed of spectrum analysis, it is achieved that high-precision rapid survey, can not only measure absolute distance, moreover it can be used to measure film characteristics.
White light interference spectrographic method mainly utilizes interference of light principle and spectrum principle, utilizes the light interference light intensity at different wave length place to solve.The light of light source outgoing is divided into two bundles through Amici prism, wherein a branch of incides reference mirror, and another bundle incides measuring samples surface, and two-beam reflection all occurs and incides Amici prism, and now this two-beam can interfere.Interference light obtains white-light spectrum interference signal through spectrometer collection, by being analyzed drawing film characteristics to its interference signal.Its test process is simple, and precision is high, can not only measure the thickness of thin film, refractive index, and can measure phase characteristic.At present, abroad having the Institute of Technology of India M.P.Kothiyal et al., technical college Y.S.Ghim and S.K.Debnath such as Korea S is high et al., Stuttgart University, Germany W.Osten team etc. is carrying out the research of this respect.Domestic mainly University Of Tianjin, Taiwan Univ., Zhejiang University is all in the research carrying out related fields.
Under some complicated test environments, sample needs to apply external signal when need to pass through transparent enclosure measurement or test, it is thus desirable to measurement system has longer operating distance, and Michaelson and Mirau type micro-interference object lens are due to the restriction of self structure, long reach cannot be realized measure, thus the measurement system of Linnik type interference structure must be adopted.
Summary of the invention
The technical problem to be solved is to provide one can obtain thin film nonlinear phase information more accurately, improves the Linnik type interference spectrum measuring efficiency and measurement accuracy and measures the nonlinear phase compensation method of thin film.
The technical solution adopted in the present invention is: a kind of nonlinear phase compensation method measuring thin film based on Linnik type interference spectrum, comprises the steps:
1) nonlinear phase of Linnik type white light interference spectral measurement system equivalent thickness is obtained, including:
(1) equivalent thickness model is set up when known first Amici prism refractive indexWhereinFor equivalent thickness phase place, n1K () is Amici prism refractive index, et is equivalent thickness, and k is wave number；
(2) nonlinear phase of the emulation equivalent thickness by equivalence thickness model linear fit is obtained；
(3) measure the sample mirror surface as sample when objective lens in removing Linnik type white light interference spectral measurement system, obtain measurement system nonlinear phase under different optical path differences；
(4) nonlinear phase of emulation equivalent thickness is utilized, carry out linear fit from actually measured Linnik type white light interference spectral measurement system nonlinear phase under different optical path differences respectively, obtain Linnik type white light interference spectral measurement system equivalent thickness value under different optical path differences；
(5) constant equivalent thickness value is obtained by tuning wavelength；
(6) by equivalence thickness model linear fit being obtained the nonlinear phase of constant equivalent thickness value；
2) nonlinear phase of Linnik type white light interference spectral measurement system objective lens is obtained, including:
(1) the sample mirror surface as sample is measured when Linnik type white light interference spectral measurement system rejoins objective lens, measurement system entirety phase place when asking interference spectrum visibility more than 0.1；
(2) linear fitting is utilized to obtain measurement system entirety nonlinear phase；
(3) isolate in Linnik type white light interference spectral measurement system and do not mated the nonlinear phase caused by objective lens；
3) nonlinear phase of film sample is obtained, including:
(1) film sample, measurement system entirety phase place when asking interference spectrum visibility more than 0.1 are measured when Linnik type white light interference spectral measurement system rejoins objective lens；
(2) linear fitting is utilized to obtain measurement system entirety nonlinear phase；
(3) nonlinear phase of thin film is extracted.
The Linnik type interference spectrum of the present invention measures the nonlinear phase compensation method of thin film, when thin film is thicker, relative to traditional film thickness method for solving, obtain the thin film nonlinear phase measured and it is compensated and corrected can obtain thin film initial estimate value more accurately, and then obtain the film thickness of more high accuracy, improve certainty of measurement and the measurement scope of system.The present invention, when based thin film nonlinear phase frequency carries out initial estimate, can obtain thin film nonlinear phase information more accurately, improves and measures efficiency and measurement accuracy.
Accompanying drawing explanation
Fig. 1 is the interference structure figure removing objective lens in measurement system；
Fig. 2 is the interference structure figure rejoining objective lens in measurement system；
Fig. 3 is tuning wavelength process；
Fig. 4 isolates objective lens nonlinear phase process；
Fig. 5 is that film thickness solves flow process；
Fig. 6 is the interference signal entirety nonlinear phase measuring systematic survey film sample and boundary-layer theory nonlinear phase；
Fig. 7 is interference signal nonlinear phase and the boundary-layer theory nonlinear phase of removing equivalent thickness impact；
Fig. 8 is measurement thin film nonlinear phase and the boundary-layer theory nonlinear phase of removing objective lens impact again.
In figure
1: white light source 2: collimating lens
3: sample reflecting mirror 4: the first Amici prism
5: the second Amici prisms 6: lens
7: optical fiber 8: spectrogrph
9: pipe mirror 10:CCD
11: reference mirror 12: piezo-ceramic micro displacement unit
13: computer 14: the first object lens
15: the second object lens 16: sample
Detailed description of the invention
The nonlinear phase compensation method Linnik type interference spectrum of the present invention being measured thin film below in conjunction with embodiment and accompanying drawing is described in detail.
As shown in Figure 1 and Figure 2, compared with Michelson interference structure, the difference in Linnik type interference system structure mainly respectively with the addition of a microcobjective in reference path and optical path.Although the pair of lens of same company, same model, same batch of production and processing can be selected in the process of system constructing, but the effect that two camera lenses required in principle mate completely can not be fully achieved.The source not mating phenomenon of objective lens includes mismachining tolerance and the rigging error of objective lenses, and these errors are unavoidable in actual production.According to Linnik interference structure and basic principle of interference, not mating of objective lens will cause that the situation interfering two-arm optical path difference becomes complex so that the phase information of interference signal changes.Additionally, in practice, the center Amici prism that white light interference system uses does not ensure that the light path coupling of its two-beam separated, namely in chromatic dispersion material propagate geometric path and differ, therefore Amici prism can be decomposed into desirable Amici prism and the flat board made by identical material, and this slab-thickness is defined as equivalent thickness.When Amici prism does not mate, two-beam phase contrast because equivalent thickness produces nonlinear change, can affect measuring accuracy.Therefore, when selecting based thin film nonlinear phase frequency estimation initial value, in order to obtain thin film nonlinear phase information more accurately when measuring, the present invention proposes the nonlinear phase compensation method being applied to Linnik type white light interference spectral measurement film thickness system.
The Linnik type interference spectrum of the present invention measures the nonlinear phase compensation method of thin film, comprises the steps:
1) nonlinear phase of Linnik type white light interference spectral measurement system equivalent thickness is obtained, including:
(1) equivalent thickness model is set up when known first Amici prism refractive indexWhereinFor equivalent thickness phase place, n1K () is Amici prism refractive index, et is equivalent thickness, and k is wave number；
(2) nonlinear phase of the emulation equivalent thickness by equivalence thickness model linear fit is obtained；
(3) such as Fig. 1, measure the sample mirror surface as sample when objective lens in removing Linnik type white light interference spectral measurement system, obtain measurement system nonlinear phase under different optical path differences；
(4) nonlinear phase of emulation equivalent thickness is utilized, carry out linear fit from actually measured Linnik type white light interference spectral measurement system nonlinear phase under different optical path differences respectively, obtain Linnik type white light interference spectral measurement system equivalent thickness value under different optical path differences；
(5) constant equivalent thickness value is obtained by tuning wavelength；Tuning wavelength as described in Figure 3 includes:
() utilizes the piezo-ceramic micro displacement unit of nano grade positioning precision to move reference mirror, gathers the white-light spectrum interference signal under different optical path difference, and calculating optical path difference is h1Time phase contrastIt is h with optical path difference2Time phase contrastWherein φ1、φ2For Phase Unwrapping Algorithm, m1、m2For order of interference；
() utilizes the piezo-ceramic micro displacement unit of nano grade positioning precision to move the amount of movement of reference mirror, and calculating optical path difference is h1Time phase contrastAnd optical path difference is h2Time phase contrastWherein k is wave number；
() calculates the difference of the phase contrast under two groups of difference optical path differences of correspondence respectivelyWith
() passes through linear fitWithObtain preliminary corrections formula Y=0.9897X+0.001, make under different optical path differenceWithThe most identical, wherein X is original wavelength, and Y is the wavelength after correction；
() repeats () step～the () step, the correction parameter of preliminary corrections formula is finely tuned, it is determined that final updating formula Y=0.9887X+0.0032.
(6) by equivalence thickness model linear fit being obtained the nonlinear phase of constant equivalent thickness value；
2) nonlinear phase of Linnik type white light interference spectral measurement system objective lens is obtained, as shown in Figure 4, including:
(1) such as Fig. 2, the sample mirror surface as sample is measured when Linnik type white light interference spectral measurement system rejoins objective lens, system entirety phase place when asking interference spectrum visibility more than 0.1；Described ask for interference spectrum visibility more than 0.1 time system entirety phase place include:
() utilizes the piezo-ceramic micro displacement unit of nano grade positioning precision that reference mirror carries out five step phase shifts, spectroscopic data when collection interference spectrum visibility is more than 0.1；
() utilizes the five step phase shift algorithm spectroscopic data to collecting to carry out phase extraction, tries to achieve Phase Unwrapping Algorithm φ；
() utilizes cyclic iterative method to solve order of interference m, obtain interference spectrum visibility more than 0.1 time overall phase place.
(2) linear fitting is utilized to obtain system entirety nonlinear phase；
(3) isolate in innik type white light interference spectral measurement system and do not mated the nonlinear phase caused by objective lens；Described separation is to adopt: system objective lens nonlinear phase=system entirety nonlinear phase-constant equivalent thickness value nonlinear phase.
3) nonlinear phase of film sample is obtained, including:
(1) such as Fig. 2, film sample, system entirety phase place when asking interference spectrum visibility more than 0.1 are measured when Linnik type white light interference spectral measurement system rejoins objective lens；Described ask for interference spectrum visibility more than 0.1 time system entirety phase place include:
Reference mirror is carried out five step phase shifts by the piezo-ceramic micro displacement unit of nano grade positioning precision by (), gather interference spectrum visibility more than 0.1 time spectroscopic data；
() utilizes the five step phase shift algorithm spectroscopic data to collecting to carry out phase extraction, tries to achieve Phase Unwrapping Algorithm φ；
() utilizes cyclic iterative method to solve order of interference m, obtain interference spectrum visibility more than 0.1 time overall phase place.
(2) linear fitting is utilized to obtain system entirety nonlinear phase；
(3) extracting the nonlinear phase of thin film, the described nonlinear phase extracting thin film is to adopt: thin film nonlinear phase=system entirety nonlinear phase-constant equivalent thickness nonlinear phase-objective lens nonlinear phase.
Object lesson is given below:
This example is to realize the fast accurate to film thickness information under Linnik type white light interference spectral measurement system as shown in Figure 2 to measure, and this measurement system is using piezo-ceramic micro displacement unit (PZT) (model: PI Corp. S303 or PI Corp. N-216.2A) as system motion parts；Optical interference system uses Linnik microcobjective group；Acquisition system includes spectrogrph, ccd video camera and image pick-up card；Use optical fiber type Halogen light as light source lighting, and utilize air flotation vibration isolation to reduce the low-frequency vibration impact in experiment.The software of system includes controlling program and the data processor based on MATLAB based on the hardware integration of LABVIEW.The step that the fast accurate of film thickness information is measured is:
(1) the measuring samples mirror surface when removing Linnik type white light interference spectral measurement system objective lens, analyze the source of equivalent thickness and the change of situation of change and equivalent thickness to the impact that now mission nonlinear phase place causes, wavelength is corrected and makes equivalent thickness constant.The wavelength calibration formula that native system is finally determined is Y=0.9887X+0.0032, and constant equivalent thickness value is 30.86 μm.
(2) at other elements and parameter constant, when only regulating reference mirror and sample, Linnik type white light interference spectral measurement system rejoins objective lens, measure identical sample mirror surface, contrasting the nonlinear phase of the two interferometer measuration system after constant equivalent thickness, what the latter was considered as objective lens with the former difference does not mate the nonlinear phase distortion caused.The objective lens nonlinear phase thus separated is less with absolute distance change, can ignore this change.
(3) sample reflecting mirror in step (2) is changed to the silicon base silica membrane sample of 953nm thickness, consider the nonlinear phase signal caused by equivalent thickness and objective lens, the thin film nonlinear phase extracted is modified, i.e. thin film nonlinear phase=system entirety nonlinear phase-constant equivalent thickness nonlinear phase-objective lens nonlinear phase.
(4) as it is shown in figure 5, utilize the nonlinear phase frequency of thin film to realize initial estimate, carry out local optimum matching by Levenberg-Marquardt Nonlinear Quasi hop algorithm and obtain high-precision film thickness information.The phase place extracted in Fig. 6, Fig. 7, Fig. 8 respectively actual measurement process and boundary-layer theory nonlinear phase contrast situation, initial estimate result respectively 877.7nm, 965.1nm, the 949.6nm obtained, film thickness result respectively 943.5nm, 949.nm, 953.8nm that local optimum matching obtains.Removing the film thickness after equivalent thickness and objective lens nonlinear phase and calculate result (i.e. 953.8nm) closer to actual value, this result demonstrates the feasibility of the inventive method.
(5) same point of measuring being measured in triplicate, the film thickness obtained respectively 953.6nm, 953.8nm, 953.8nm, average is 953.7nm.Additionally change sample is along the position of optical axis direction, and the result that twice measurement obtains respectively 954.3nm and 952.7nm is all less with the deviation of actual value.Measurement result demonstrates the repeatability of the inventive method.
Claims (5)
1. the nonlinear phase compensation method measuring thin film based on Linnik type interference spectrum, it is characterised in that comprise the steps:
1) nonlinear phase of Linnik type white light interference spectral measurement system equivalent thickness is obtained, including:
(1) equivalent thickness model is set up when known first Amici prism refractive indexWhereinFor equivalent thickness phase place, n1K () is Amici prism refractive index, et is equivalent thickness, and k is wave number；
(2) nonlinear phase of the emulation equivalent thickness by equivalence thickness model linear fit is obtained；
(3) measure the sample mirror surface as sample when objective lens in removing Linnik type white light interference spectral measurement system, obtain measurement system nonlinear phase under different optical path differences；
(4) nonlinear phase of emulation equivalent thickness is utilized, carry out linear fit from actually measured Linnik type white light interference spectral measurement system nonlinear phase under different optical path differences respectively, obtain Linnik type white light interference spectral measurement system equivalent thickness value under different optical path differences；
(5) constant equivalent thickness value is obtained by tuning wavelength；
(6) by equivalence thickness model linear fit being obtained the nonlinear phase of constant equivalent thickness value；
2) nonlinear phase of Linnik type white light interference spectral measurement system objective lens is obtained, including:
(1) the sample mirror surface as sample is measured when Linnik type white light interference spectral measurement system rejoins objective lens, measurement system entirety phase place when asking interference spectrum visibility more than 0.1；
(2) linear fitting is utilized to obtain measurement system entirety nonlinear phase；
(3) isolate in Linnik type white light interference spectral measurement system and do not mated the nonlinear phase caused by objective lens；
3) nonlinear phase of film sample is obtained, including:
(1) film sample, measurement system entirety phase place when asking interference spectrum visibility more than 0.1 are measured when Linnik type white light interference spectral measurement system rejoins objective lens；
(2) linear fitting is utilized to obtain measurement system entirety nonlinear phase；
(3) nonlinear phase of thin film is extracted.
2. Linnik type interference spectrum according to claim 1 measure thin film nonlinear phase compensation method, it is characterised in that step 1) in the tuning wavelength described in (5th) step include:
() utilizes the piezo-ceramic micro displacement unit of nano grade positioning precision to move reference mirror, gathers the white-light spectrum interference signal under different optical path difference, and calculating optical path difference is h1Time phase contrastIt is h with optical path difference2Time phase contrastWherein φ1、φ2For Phase Unwrapping Algorithm, m1、m2For order of interference；
() utilizes the piezo-ceramic micro displacement unit of nano grade positioning precision to move the amount of movement of reference mirror, and calculating optical path difference is h1Time phase contrastAnd optical path difference is h2Time phase contrastWherein k is wave number；
() calculates the difference of the phase contrast under two groups of difference optical path differences of correspondence respectivelyWith
() passes through linear fitWithObtain preliminary corrections formula Y=0.9897X+0.001, make under different optical path differenceWithThe most identical, wherein X is original wavelength, and Y is the wavelength after correction；
() repeats () step～the () step, the correction parameter of preliminary corrections formula is finely tuned, it is determined that final updating formula Y=0.9887X+0.0032.
3. Linnik type interference spectrum according to claim 1 measures the nonlinear phase compensation method of thin film, it is characterized in that, step 2) in (1st) step and step 3) in (1st) step described in ask for interference spectrum visibility more than 0.1 time system entirety phase place include:
Reference mirror is carried out five step phase shifts by the piezo-ceramic micro displacement unit of nano grade positioning precision by (), gather interference spectrum visibility more than 0.1 time spectroscopic data；
() utilizes the five step phase shift algorithm spectroscopic data to collecting to carry out phase extraction, tries to achieve Phase Unwrapping Algorithm φ；
() utilizes cyclic iterative method to solve order of interference m, obtain interference spectrum visibility more than 0.1 time overall phase place.
4. Linnik type interference spectrum according to claim 1 measures the nonlinear phase compensation method of thin film, it is characterized in that, step 2) in the separation described in (3rd) step be adopt: system objective lens nonlinear phase=system entirety nonlinear phase-constant equivalent thickness value nonlinear phase.
5. Linnik type interference spectrum according to claim 1 measures the nonlinear phase compensation method of thin film, it is characterized in that, step 3) in the nonlinear phase taking thin film described in (3rd) step be adopt: thin film nonlinear phase=system entirety nonlinear phase-constant equivalent thickness nonlinear phase-objective lens nonlinear phase.
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| CN113834430A (en) * | 2021-09-24 | 2021-12-24 | 天津大学 | Method for measuring thickness and refractive index of film |
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