CN105911015B - Broadband dielectric parameter acquisition methods based on multiple-beam interference effect - Google Patents
Broadband dielectric parameter acquisition methods based on multiple-beam interference effect Download PDFInfo
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- 229910052710 silicon Inorganic materials 0.000 description 16
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- G—PHYSICS
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- 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
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
- G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
- G01N21/3581—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using far infrared light; using Terahertz radiation
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- G—PHYSICS
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- 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
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
- G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
- G01N21/3581—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using far infrared light; using Terahertz radiation
- G01N21/3586—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using far infrared light; using Terahertz radiation by Terahertz time domain spectroscopy [THz-TDS]
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- G01N22/00—Investigating or analysing materials by the use of microwaves or radio waves, i.e. electromagnetic waves with a wavelength of one millimetre or more
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- G—PHYSICS
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- 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
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
- G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
- G01N2021/3595—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using FTIR
Abstract
The present invention relates to broadband range material dielectric parameters to obtain field, to provide the new method that can be used for obtaining from the dielectric parameter of microwave, Terahertz to infrared band.The technical solution adopted by the present invention is, broadband dielectric parameter acquisition methods based on multiple-beam interference effect, including data acquisition and two processes of data processing, data acquisition includes background data and the signal data acquisition that is put into after sample, acquisition interference pattern is measured using Fourier spectrometer, the abscissa of interference pattern is the position of spectrometer interfere arm index glass, and ordinate is response voltage of the detector to interference signal;Data processing contains Inversion Calculation two parts of preliminary treatment and optical parameter to initial data;The Inversion Calculation of optical parameter is subdivided into order of interference solution, real refractive index calculates, extinction coefficient calculates, absorption coefficient calculates, dielectric parameter calculating;It is final to obtain dielectric parameter.Present invention is mainly applied to broadband range material dielectric parameters to obtain occasion.
Description
Technical field
The present invention relates to broadband range material dielectric parameter acquisition fields to be specifically related to a kind of birefringence of material
Rate, absorption coefficient, the measurement of dielectric parameter and inversion method.
Background technology
The optical parameter of material specifically contains the refractive index of material, absorption coefficient, extinction coefficient and is obtained by inverting
The dielectric parameter arrived can be used for characterizing a kind of optical characteristics of material, be set using material progress engineering calculation, product
The indispensable parameter of meter, analogue simulation.For any material, they are in various wave bands such as ultraviolet, visible light, infrared and microwaves
Spectral characteristic and the measurement of optical parameter are always the problem of people extremely pay close attention to.In recent years with the continuous hair of Terahertz Technology
Exhibition, material are calculated in the dielectric parameter of terahertz wave band and are also paid more and more attention with measurement.Accurate dielectric parameter data are in thunder
Up to playing very important effect in the systems such as scattering section calculating, objective optics identification, optic communication, spectrometer, radar.Due to
The dielectric parameter of different materials is different, and the physical characteristic on surface has prodigious difference, and same material is in different-waveband dielectric
Parameter also differs greatly.
In existing measuring system, infrared band is more for the research of materials optical and physical characteristic, and with compared with
For the ripe practical measurement material of equipment and condition the wave band part dielectric parameter.Do not having measuring condition and means
In the case of, it is also effective side to carry out inverting to the dielectric parameter of unknown wave band and wavelength material by mathematical model method
Method.Kramers-Kronig (K-K) relations act is a kind of important method in numerous inversion methods, can be with using K-K relations acts
It is finally inversed by the reflection, transmission and absorption coefficient etc. of various different materials, to obtain the dielectric parameter of material.However, this method
Model foundation process need to assume various preconditions, it is assumed that the dielectric parameter that can make of uncertainty deposit
In certain error, therefore K-K relations acts are not a kind of high-precision measurement and computational methods.
In terahertz wave band, more currently used for measurement materials optical parameter is terahertz time-domain spectroscopy system, the party
Method combination Fresnel reflection law can measure and calculate the absorption coefficient of sample, refractive index, to be finally inversed by dielectric parameter
Deng.But it is limited to the wavelength band and terahertz sources power of terahertz time-domain spectroscopy system, there are larger noises for high band
Lead to systemtatic uncertainty, therefore the data within the scope of accurate broadband can not be obtained.Meanwhile terahertz time-domain spectroscopy system exists
When carrying out data processing, the multiple reflections signal (the multistage interference spectrum i.e. in time-domain signal) of sample surfaces will be carried out suitably
Interception, which can lead to lost part useful information, increase so as to cause error.Research in conjunction with current optical parameter is existing
Shape is badly in need of a kind of method that can accurately obtain dielectric material parameter in broadband range.
Invention content
It in order to overcome the deficiencies of the prior art, can the present invention is intended to provide a kind of novel dielectric material parameter acquiring method
For being obtained from the dielectric parameter of microwave, Terahertz to infrared band.The technical solution adopted by the present invention is, dry based on multiple beam
The broadband dielectric parameter acquisition methods of effect are related to, including data acquisition and two processes of data processing, data acquisition includes the back of the body
Scape data and the signal data acquisition being put into after sample measure acquisition interference pattern using Fourier spectrometer, interference pattern
Abscissa is the position of spectrometer interfere arm index glass, and ordinate is response voltage of the detector to interference signal;Data processing packet
Inversion Calculation two parts for having contained the preliminary treatment and optical parameter to initial data, when the preliminary treatment of initial data is subdivided into
Domain interference pattern conversion obtains frequency-domain spectrum figure, obtains Transmittance spectrum step;The Inversion Calculation of optical parameter is subdivided into order of interference
It solves, real refractive index calculates, extinction coefficient calculates, absorption coefficient calculates, dielectric parameter calculates;It is final to obtain dielectric parameter.
Described comprises the concrete steps that the preliminary treatment of initial data:
1. time-domain background signal obtains and the processing of sample signal interference pattern
The voltage signal obtained using detector is set as ordinate, using step motor position as abscissa, stepper motor
Movement is linear corresponding, the correspondence of applications distances and time with the time, and range information is converted to temporal information, is applied
Formula is as follows
T is the time for completing single pass process, s2For the secondary end of scan when stepper motor where position, s1For
Position when this time scanning starts where stepper motor, c are the light velocity in vacuum, and Δ s is the single stepping-in amount of stepper motor, will
Each parameter obtains t after bringing above-mentioned formula into, to which the interference pattern that abscissa is position is converted to time domain interferogram;
2. carrying out Fourier transformation to time domain interference signal figure obtains corresponding frequency-domain spectrum figure;
3. to background and being put into two kinds of situations of sample and carrying out processing 1. and 2. respectively, then by two groups of frequency domain numbers of acquisition
According to being divided by, obtains sample signal and the relative permeability of background signal is composed, apply formula as described below here
Wherein I1And I2Light intensity when indicating background respectively and being put into sample, E1And E2Background is indicated respectively and is put into sample
When electric field strength.
The Inversion Calculation part of the optical parameter includes the following steps:
1. the transmitance or reflectance curves that handled by preliminary data, for the parallel sample in two surfaces, light beam
It will appear multiple-beam interference effect in sample interior, the phase difference that adjacent two-stage interference generates in flat samples is
Wherein d is thickness of sample, and n is refractive index, and λ is wavelength;For approximate normal incidence transmission-type measurement pattern, incidence angle
θ is considered θ=1 zero, cos, and the order of interference that one of interference is greatly located is m1, corresponding frequency, wavelength relationship υ1=c/
λ1, it is m to be spaced the order of interference that x is interfered greatly to locate2, corresponding frequency, wavelength relationship υ2=c/ λ2, then:
m2=m1+(x+1) (4)
Wherein m1And m2For the integer more than or equal to 1, take two adjacent interference very big or several adjacent interference poles
At big peak value, solved using multiple-beam interference theory, then
Combinatorial formula (4)-(6), acquire order of interference m1And m2Value, reapply interference formula (3) and acquire frequency point m1And m2
Locate corresponding refractive index real part n1And n2Value, and then acquire the refractive index value of real part of the substance in entire wavelength band;
For there are the Reflection measurement modes of certain incident angle cannot ignore incidence angle, at this time by the law of refraction:
n1sinθ1=n2sinθ2 (7)
Think sample outer surface air refraction n1=1, if incidence angle is θ, have
The process for solving order of interference is identical as transmission mode, but formula should be used when solving refractive index real part
(8) it is calculated;
2. the solution of the substance extinction coefficient, absorption coefficient and the dielectric parameter that are related to, detailed process is as follows:
Parallel flat sample with certain transmitance is by measuring the multiple beam that obtained transmitance is periodic swinging
Interference pattern carries out multistage Savitzky-Golay smoothing processings to transmittance curve first, will transmit through rate curve and obtained folding
Penetrate that rate real part is corresponding to obtain corresponding transmitance T (ν) at each frequency point, then the following formula of the extinction coefficient of sample
The absorption coefficient of sample
The real part ε of complex permittivity can be obtained according to the relationship of dielectric parameter and complex refractivity indexr(ν) and imaginary part εi(ν)
εr(ν)=n2(ν)-κ2(ν), εi(ν)=2n (ν) κ (ν) (12)
ν represents frequency.
The features of the present invention and advantageous effect are:
Method involved in the present invention is to carry out data acquisition and data processing using multiple-beam interference mechanism, can be fast
Speed is effectively obtained various optical parameters of the substance within the scope of broadband and ensure that without the interception of time domain interference signal
The accuracy of optical parameter.Applicable wavelength band is wide, can cover the measurement from microwave, Terahertz until infrared band and meter
It calculates, data processing method is equally applicable when handling time domain results of spectral measurements and Fourier spectrometer measurement result.
Description of the drawings:
Fig. 1 flow chart of data processing figure.Fig. 2 transmission-type measuring system structure charts.
The reflective measuring system structure charts of Fig. 3.Fig. 4 transmission-types background and sample signal interference pattern.
Fig. 5 silicon sample transmission measurement spectrograms.Fig. 6 silicon sample transmission measurement transmitance figures.
Fig. 7 silicon sample transmission measurement index of refraction diagram.Fig. 8 silicon sample transmission measurement extinction coefficients.
Fig. 9 silicon sample transmission measurement absorption coefficients.Figure 10 silicon sample transmission measurement dielectric parameters.
Figure is released:1 radiating light source, 2 diaphragm, 3 chopper, 4 off-axis parabolic mirror, 5 stepper motor, 6 plane mirror
7 beam splitter, 8 object, 9 plane mirror, 10 off-axis parabolic mirror, 11 plane mirror, 12 detector.
Specific implementation mode
Measurement and calculating present situation for optical parameter in background technology and existing deficiency, it is proposed that in following invention
Hold.
Main contents of the present invention are directed to the material with certain transmitance, and Fourier spectrometer base is utilized in broadband range
The acquisition of substance optical parameter such as complex refractivity index, absorption coefficient etc. is carried out in multiple-beam interference mechanism, and is finally inversed by its multiple dielectric
Parameter.
Optical parameter acquisition methods of the present invention specifically contain data acquisition and two processes of data processing.
Data acquisition in the optical parameter acquisition methods, including background data and the signal number that is put into after sample
According to acquisition, acquisition interference pattern is measured using Fourier spectrometer, the abscissa of interference pattern is spectrometer interfere arm index glass
Position, ordinate are response voltage of the detector to interference signal.
Data handling procedure in the optical parameter acquisition methods, specifically contain preliminary treatment to initial data and
Inversion Calculation two parts of optical parameter, specific flow chart of data processing are as shown in Figure 1.
Described has following steps to the preliminary treatment of initial data:
1. time-domain background signal obtains and the processing of sample signal interference pattern.
The initial data that the present invention is handled is the interference pattern of Fourier spectrometer acquisition, the voltage signal obtained with detector
For ordinate, using step motor position as abscissa.The movement of stepper motor and time be it is linear corresponding, applications distances and when
Between correspondence, range information can be converted to temporal information, it is as follows using formula
T is the time for completing single pass process, and position when s2 is the secondary end of scan where stepper motor, s1 is
Position when this time scanning starts where stepper motor, c are the light velocity in vacuum, and Δ s is the single stepping-in amount of stepper motor.It will
Each parameter obtains t after bringing above-mentioned formula into, to which the interference pattern that abscissa is position is converted to time domain interferogram.
2. carrying out Fourier transformation to time domain interference signal figure obtains corresponding frequency-domain spectrum figure.The process is not to multistage
Interference signal is intercepted, therefore remains all information of sample, and obtained data are more accurate.
3. to background and being put into two kinds of situations of sample and carrying out processing 1. and 2. respectively, then by two groups of frequency domain numbers of acquisition
According to being divided by, sample signal can be obtained, the relative permeability of background signal is composed, apply formula as described below here
Wherein I1And I2Light intensity when indicating background respectively and being put into sample, E1And E2Background is indicated respectively and is put into sample
When electric field strength.
The Inversion Calculation part of data handling procedure in the optical parameter acquisition methods, optical parameter includes following step
Suddenly:
1. the transmitance or reflectance curves that handled by preliminary data, for the parallel sample in two surfaces, light beam
It will appear multiple-beam interference effect in sample interior, the phase difference that adjacent two-stage interference generates in flat samples is
Wherein d is thickness of sample, and n is refractive index, and λ is wavelength.For approximate normal incidence transmission-type measurement pattern, incidence angle
θ is considered θ=1 zero, cos, and the order of interference that one of interference is greatly located is m1, and corresponding frequency is υ1=c/ λ1, it is spaced x
(x is generally the integer of 0-5) is a to interfere the order of interference greatly located to be m2, corresponding frequency is υ2=c/ λ2, then:
m2=m1+(x+1) (4)
Wherein m1 and m2 is the integer more than or equal to 1.Take two adjacent interference very big or several adjacent interference
At maximal peak (phase difference δ is the integral multiple of 2 π), solved using multiple-beam interference theory, then
Combinatorial formula (4)-(6) can reapply interference formula (3) and acquire frequency point in the hope of the value of order of interference m1 and m2
The value of corresponding refractive index real part n1 and n2 at m1 and m2, and then can be real in the hope of the refractive index of the substance in entire wavelength band
Portion's value.
For there are the Reflection measurement modes of certain incident angle cannot ignore incidence angle, at this time by the law of refraction
n1sinθ1=n2sinθ2 (7)
Think sample outer surface (air) refractive index n1=1, if incidence angle is θ, have
The process for solving order of interference is identical as transmission mode, but formula should be used when solving refractive index real part
(8) it is calculated.
2. the solution of the substance extinction coefficient, absorption coefficient and the dielectric parameter that are related to, detailed process is as follows:
Parallel flat sample with certain transmitance is by measuring the multiple beam that obtained transmitance is periodic swinging
Interference pattern carries out multistage Savitzky-Golay smoothing processings to transmittance curve first, will transmit through rate curve and obtained folding
Penetrate that rate real part is corresponding to obtain corresponding transmitance T (ν) at each frequency point, then the following formula of the extinction coefficient of sample
The absorption coefficient of sample
The real and imaginary parts of complex permittivity (ε=ε r+i ε i) can be obtained according to the relationship of dielectric parameter and complex refractivity index
εr(ν)=n2(ν)-κ2(ν), εi(ν)=2n (ν) κ (ν) (12)
It below will be by specific implementation mode come invention is further explained.
It is mainly handled using spectrometer measurement fused data in the existing method for obtaining substance dielectric parameter, Yi Jili
With terahertz time-domain spectroscopy systematic survey and data processing.But conventional spectrometers can not directly measure comprehensive optical parameter,
There are causal it is assumed that therefore can also there is certain error for the calculating of traditional K-K relationships.And for terahertz time-domain light
Spectra system, may be implemented the measurement of low frequency terahertz wave band, frequency coverage in 0.1THz~3THz, 3THz or more frequency range by
In the limitation of terahertz time-domain spectroscopy system radiant power, and the time domain letter to repeatedly interfering is needed in data processing
It number is intercepted, is lost part raw information.Method involved in the present invention is using multiple-beam interference mechanism come into line number
According to acquisition and data processing, calculating process remains whole initial data, therefore result is more accurate.
Dielectric material parameter acquiring method of the present invention, specifically contains the preliminary treatment to initial data and dielectric
Inversion Calculation two parts of parameter.
The interference pattern for obtaining background and sample respectively by measuring system first, obtains initial data.Then dry to time domain
It relates to pattern progress Fourier transformation and obtains frequency domain spectra figure, carry out corresponding data processing inverting again to spectrum and obtain the light of substance
Learn parameter and dielectric parameter.Method of the present invention can quickly and effectively obtain various light of the substance within the scope of broadband
It learns parameter and ensure that the accuracy of optical parameter without the interception of time domain interference signal.Applicable wavelength band is wide, can contain
The measurement and calculating of lid terahertz wave band and infrared band, data processing method is to time domain results of spectral measurements and other are infrared
Fourier spectrometer measurement result is equally applicable when being handled.
Embodiment 1:It is that laboratory sample has carried out practical measurement and calculating to select the silicon chip of polishing, and the thickness of sample is
0.38mm, a diameter of 50mm.
Far infrared Fourier spectrometer transmission-type measuring system, a whole set of measuring system structure chart are as shown in Figure 2.
It is radiating light source using high-pressure sodium lamp, emits continuous wide band spectrum, terahertz wave band and far infrared wave can be covered
Section, it is 65W that measurement process, which adjusts high-pressure sodium lamp to stablize output power,;
The effective clear aperature of aperture of application is 2mm;
The effective focal length of the off-axis parabolic mirror of application is 250mm, a diameter of 100mm, uses surface plating oxidation
Property golden film processing;
It is 10 times, scanning resolution 0.6cm-1, cutoff wavelength 260cm-1 that initialization system, which scans number of repetition,;
The plane mirror size of actual measurement application is 100mm × 100mm, and oxidisability golden film is plated on surface;
The detector of actual measurement application is low temperature (4.2K) Bolometer detectors.
Step 1:Measure no sample when vacuum background interference pattern and record corresponding data file.
1. light path has been debugged, it is vacant inside sample cell, vacuum degree is evacuated to about 102Pa;
2. setting parameters in embodiment, vacuum background scans and data acquisition, obtained background interference figure are carried out
Sample is as shown in Fig. 4 backgrounds;
Step 2:It measures the interference pattern after placing sample and automatically saves data.
1. having debugged light path, silicon chip to be tested is placed in vertical optical path direction in sample cell, is evacuated to vacuum degree to about
102Pa;
2. setting parameters in embodiment, the scanning of sample and data acquisition under vacuum environment are carried out, signal is obtained
Interference pattern is as shown in Fig. 4 signals;
Step 3:The background and sample data of acquisition are calculated and analyzed, corresponding optical parameter and dielectric are obtained
Parameter.
What is changed over time in measurement process is the linear motion step number of stepper motor, and applications distances are corresponding with the time
Relationship,
Range information is converted into temporal information, it is as follows using formula
T is the time of single sweep operation process, and s2=4902960 is the position where stepper motor at the end of single sweep operation
It sets, position when s1=4417150 starts for single sweep operation where stepper motor, c=3.0 × 108m/s is the light in vacuum
Speed, s=0.02 μm of Δ are the single stepping-in amount of stepper motor.T=64.8ps is obtained after bringing each parameter into above-mentioned formula.Pass through
Step 1 and step 2 respectively obtain the time domain interference signal figure of background and sample.To the time domain interference signal figure changed over time
It carries out Fourier transformation and obtains corresponding frequency-domain spectrum figure, as shown in Figure 5.
2. asking silicon sample in the transmitance of test wave band by the two groups of frequency domain datas obtained in 1., i.e.,
Obtained transmitance is as shown in Figure 6.
3. silicon sample has higher transmitance and low absorption in the terahertz wave band of actual measurement, can from transmitance
Go out, 0.38mm thickness will appear multistage interference peak, first with formula
m2=m1+(x+1)
The order of interference that all peak values go out has been acquired, has then been acquired according to the order of interference and multiple-beam interference formula acquired
The refractive index real part of silicon sample, as shown in Figure 7.
4. the solution procedure of the extinction coefficient of silicon sample, absorption coefficient and dielectric parameter is as follows:
Multistage Savitzky-Golay smoothing processings are carried out to transmittance curve, will transmit through rate curve and obtained refractive index
Real part is corresponding to obtain corresponding transmitance T (ν) at each frequency point, and the thickness of test sample is d=0.38mm, is brought into delustring
It is as shown in Figure 8 that extinction coefficient curve is obtained in coefficient solution formula.
It is equally as shown in Figure 9 by the absorption coefficient calculation formula of the sample coefficient curve that is absorbed.
With the dielectric parameter that the frequency of incident light changes, the results of calculation of real and imaginary parts is as shown in Figure 10.
Embodiment 2:It is that laboratory sample has carried out practical measurement and calculating to select the silicon sample of polishing, and the thickness of sample is
0.38mm, a diameter of 50mm.
The optical interference circuit system of reflective measuring system, spectrometer is identical as transmission-type, the placement of reflective sample cell and
Sample puts the known angle of needs, and the placement of sample is as shown in Figure 2.
Measuring environment and external condition are identical as transmission-type measurement.
Step 1:Measure no sample when vacuum background interference pattern and record corresponding data file, obtain background interference
Figure;
Step 2:It measures the interference pattern after placing sample and preserves data, obtain signal interference figure;
Step 3:The background and sample data of acquisition are calculated and analyzed, corresponding optical parameter and dielectric are obtained
Parameter.
1. what is changed over time in measurement process is the linear motion step number of stepper motor, pair of applications distances and time
It should be related to, range information is converted into temporal information, it is as follows using formula
T is the time of single sweep operation process, and s2=4855570 is the position where stepper motor at the end of single sweep operation
It sets, position when s1=4369760 starts for single sweep operation where stepper motor, c=3.0 × 108m/s is the light in vacuum
Speed, Δ s=0.02um are the single stepping-in amount of stepper motor.T=64.8ps is obtained after bringing each parameter into above-mentioned formula.Step
One and step 2 respectively obtained the time domain interference signal figure of background and sample.To the time domain interference signal figure that changes over time into
Row Fourier transformation obtains corresponding frequency-domain spectrum figure.
2. by the two groups of frequency domain datas obtained in 1. solve silicon sample test wave band transmitance.
3. Reflection measurement mode can cause the variation of relative thickness, which is used to ask the calculation formula of refractive index real part such as
Under:
The refractive index real part of silicon sample is acquired using order of interference and multiple-beam interference formula.
4. utilizing above-mentioned formula and refractive index real part, the extinction coefficient, absorption coefficient and Jie of Reflective mode silicon sample are calculated
Electrical parameter.
Claims (2)
1. a kind of broadband dielectric parameter acquisition methods based on multiple-beam interference effect, characterized in that comprising data acquisition and
Two processes of data processing, data acquisition includes background data and the signal data acquisition that is put into after sample, utilizes Fourier's light
Spectrometer measures acquisition interference pattern, and the abscissa of interference pattern is the position of spectrometer interfere arm index glass, and ordinate is detector
To the response voltage of interference signal;Data processing contains the Inversion Calculation two of preliminary treatment and optical parameter to initial data
The preliminary treatment of part, initial data is subdivided into time domain interferogram conversion, obtains frequency-domain spectrum figure, obtains Transmittance spectrum step;
The Inversion Calculation of optical parameter is subdivided into order of interference solution, real refractive index calculates, extinction coefficient calculates, absorption coefficient calculates,
Dielectric parameter calculates;Final to obtain dielectric parameter, the preliminary treatment to initial data comprises the concrete steps that:
1. time-domain background signal obtains and the processing of sample signal interference pattern
The voltage signal obtained using detector is set as ordinate, using step motor position as abscissa, the movement of stepper motor
It is linear corresponding with the time, range information is converted to temporal information, using formula by the correspondence of applications distances and time
It is as follows
T is the time for completing single pass process, s2For the secondary end of scan when stepper motor where position, s1For this time
Position when scanning starts where stepper motor, c are the light velocity in vacuum, and Δ s is the single stepping-in amount of stepper motor, by each ginseng
Amount obtains t after bringing above-mentioned formula into, to which the interference pattern that abscissa is position is converted to time domain interferogram;
2. carrying out Fourier transformation to time domain interference signal figure obtains corresponding frequency-domain spectrum figure;
3. to background and being put into two kinds of situations of sample and carrying out processing 1. and 2. respectively, then by two groups of frequency domain data phases of acquisition
It removes, obtains sample signal and the relative permeability of background signal is composed, apply formula as described below here
Wherein I1And I2Light intensity when indicating background respectively and being put into sample, E1And E2Electricity when indicating background respectively and being put into sample
Field intensity.
2. the broadband dielectric parameter acquisition methods based on multiple-beam interference effect as described in claim 1, characterized in that institute
The Inversion Calculation part for the optical parameter stated includes the following steps:
1. the transmitance or reflectance curves that handled by preliminary data, for the parallel sample in two surfaces, light beam is in sample
It will appear multiple-beam interference effect inside product, the phase difference that adjacent two-stage interference generates in flat samples is
Wherein d is thickness of sample, and n is refractive index, and λ is wavelength;For approximate normal incidence transmission-type measurement pattern, incidence angle θ is recognized
To be θ=1 zero, cos, the order of interference that one of interference is greatly located is m1, corresponding frequency, wavelength relationship υ1=c/ λ1,
The order of interference greatly located is interfered to be m in x, interval2, corresponding frequency, wavelength relationship υ2=c/ λ2, then:
m2=m1+(x+1) (4)
Wherein m1And m2For the integer more than or equal to 1, take two adjacent interference very big or several very big peaks of adjacent interference
At value, solved using multiple-beam interference theory, then
Combinatorial formula (4)-(6), acquire order of interference m1And m2Value, reapply interference formula (3) and acquire frequency point m1And m2Place pair
The refractive index real part n answered1And n2Value, and then acquire the refractive index value of real part of the substance in entire wavelength band;
For there are the Reflection measurement modes of certain incident angle cannot ignore incidence angle, at this time by the law of refraction:
n1sinθ1=n2sinθ2 (7)
Think sample outer surface air refraction n1=1, if incidence angle is θ, have
Solve order of interference process it is identical as transmission mode, but when solving refractive index real part should using formula (8) come
It is calculated;
2. the solution of the substance extinction coefficient, absorption coefficient and the dielectric parameter that are related to, detailed process is as follows:
Parallel flat sample with certain transmitance is by measuring the multiple-beam interference that obtained transmitance is periodic swinging
Figure carries out multistage Savitzky-Golay smoothing processings to transmittance curve first, will transmit through rate curve and obtained refractive index
Real part is corresponding to obtain corresponding transmitance T (ν) at each frequency point, then the following formula of the extinction coefficient of sample
The absorption coefficient of sample
The real part ε of complex permittivity can be obtained according to the relationship of dielectric parameter and complex refractivity indexr(ν) and imaginary part εi(ν)
εr(ν)=n2(ν)-κ2(ν), εi(ν)=2n (ν) κ (ν) (12)
ν represents frequency.
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