CN110057401A - A kind of transparent ultrathin membrane refractive index and method for measuring thickness - Google Patents
A kind of transparent ultrathin membrane refractive index and method for measuring thickness Download PDFInfo
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Abstract
The invention belongs to measured thin film representational fields, and specifically disclose a kind of transparent ultrathin membrane refractive index and method for measuring thickness, include the following steps: S1 with 2 π dT/ λ is that variable is ellipse to transparent ultrathin membrane compares ρ partially1Carry out the second Taylor series and obtain power series form: S2 isolates parameter T relevant to transparent ultrathin membrane in power series form1And T2, and obtainExpression formula；S3 calculates the real part of power series form and the slope R of imaginary part square, is calculated according to slope ROccurrence；S4 is by calculatingOccurrence brings in the expression formula of step S2 the refractive index n for solving transparent ultrathin membrane intoT, and calculate according to refractive index the thickness of transparent ultrathin membrane.The refractive index of transparent ultrathin membrane and quick, direct, the accurate measurement of thickness can be achieved in the present invention, has applied widely, and measurement is accurate, the advantages that without complicated analytic process.
Description
Technical field
The invention belongs to measured thin film representational fields, survey more particularly, to a kind of transparent ultrathin membrane refractive index and thickness
Amount method, the quick precise measurement suitable for ultrathin membrane refractive index and thickness transparent in a variety of substrates.
Background technique
Transparent ultrathin membrane refers to the ultrathin membrane that extinction coefficient is zero, including organic film, thin polymer film, metal oxide
Deng in anti-reflection plated film, biosensor, solar battery etc. is all widely used.The thickness of transparent ultrathin membrane is to it
Optical property has a significant impact, its optical constant of the transparent ultrathin membrane of different-thickness is different.And thickness, the optics of transparent ultrathin membrane
Constant determines the optical properties such as its transmission, reflection, also determines their part physical characteristics, it is therefore desirable to transparent ultrathin membrane
Thickness and its optical constant measure.
Currently, the measurement & characterization method of ultrathin membrane mainly include quartz crystal microbalance, surface phasmon, photometry,
Ellipsometer etc..For thin layer ganoine thin film, Sauerbrey formula is can be used in quartz crystal microbalance, according to sensor vibration
The quality for calculating adsorption layer obtains the thickness of film layer.But the film softer for opposed substrate or submergence in a liquid thin
Film, membrane molecular and liquid therein all have an impact to quality increase, and quartz crystal microbalance can not determine film thickness.Surface
Phasmon is that collective occurs in metal surface under the driving of electromagnetic field due to the free electron near fermi level on conduction band
Concussion generates, and meets wave vector matching condition by modes such as prism-coupleds, and being combined using fresnel formula and phasmon can be with
Film thickness is calculated, but this method is generally used for measurement metal film or requires film substrate to need for metal material.Photometry base
The thickness of film is determined in the transmissivity and reflectivity of spectrophotometer measurement film, is divided into envelope method, full spectrum simulation
Method etc., wherein envelope method is the most commonly used one kind, but generally requires film thicker, for ultrathin membrane and improper；Entirely
Fitting process is composed to need to select different oscillators to have larger impact to fitting result by dispersive model.Ellipsometry measurement has nothing
The advantages that non-contact, sensitivity accuracy is high is damaged, 0.01nm can achieve to the sensitivity of thickness, but ellipsometry is a kind of non-
Direct measuring method needs just acquire thickness and optical constant (including refractive index and the delustring of film by computer fitting
Coefficient).Ellipsometer, due to having very strong coupled relation between thickness and optical constant, is hardly resulted in when measuring ultrathin membrane
Unique fitting result.For this difficulty, Multi-example method, on-line measurement, a variety of surrounding medium conditioned measurements etc. can be used
Method solves.But all there is respective limitation in the above method, Multi-example analysis this assumes that the optical constant of film
Not with thickness change, and in fact, can change for ultrathin membrane its optical constant with thickness change；On-line measurement there is also
Defect as Multi-example method；A variety of surrounding medium conditions introduce complicated liquid measure environment, film need not with Jie
Matter reacts, and cannot be porous material.
(the Method for determination of the parameters such as Andriy Kostruba of Ukraine
of transparent ultrathin films deposited on transparent substrates under
Conditions of low optical contrast, Applied optics, 2015,54 (20): 6208-6216) it is directed to
Transparent membrane in transparent substrates proposes a kind of measurement method, and this method finds specific incidence by multiple angles of incidence measurement
Angle, under the angle, ellipsometric parameter Amplitude Ration (Ψ) will not change, ellipsometric parameter phase difference (Δ) with the variation of film thickness
It is linear with film thickness.The disadvantages of this method is that use scope is limited to, and is only used for measurement and substrate refractive index very
Close transparent ultrathin membrane and base material needs absolutely not to absorb.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of transparent ultrathin membrane refractive index and thickness
Measurement method is spent, by ellipse inclined than carrying out the second Taylor series and by transformation and calculating the refraction of the transparent ultrathin membrane of realization
Rate and thickness it is quick, direct, accurately measure and calculate, have applied widely, measurement is accurate, excellent without complicated analytic process etc.
Point.
To achieve the above object, the invention proposes a kind of transparent ultrathin membrane refractive index and method for measuring thickness comprising
Following steps:
S1 is with 2 π dT/ λ is that variable is ellipse to transparent ultrathin membrane to be measured compares ρ partially1It carries out the second Taylor series and obtains power level number form
Formula, wherein dTFor the thickness of transparent ultrathin membrane to be measured, λ is the wavelength of incident light:
S2 isolates parameter T relevant to transparent membrane thickness in power series form1And T2, and obtain following formula:
Wherein, n0For the refractive index of surrounding medium, nsFor substrate refractive index, nTFor the refractive index of transparent ultrathin membrane to be measured, base
Bottom is transparent or similar transparent；
S3 calculates the real part of power series form and the slope R of imaginary part square, is calculated according to slope ROccurrence；
S4 calculates step S3Occurrence brings in the expression formula of step S2 the refractive index for solving transparent ultrathin membrane into
nT, and according to the refractive index n of transparent ultrathin membraneTCalculate the thickness d for obtaining transparent ultrathin membraneT。
As it is further preferred that power series form in step S1 specifically:
Wherein, ρ0For the ellipse inclined ratio of substrate used in transparent ultrathin membrane, dTFor the thickness of transparent ultrathin membrane to be measured, λ is incident light
Wavelength, ρ1'、ρ″aWith ρ "bIt is coefficient.
As it is further preferred that parameter T in step S21And T2Specifically:
As it is further preferred that the slope R in step S3 is specifically calculated using following formula:
Wherein, Re ρ0With Re ρ1Respectively substrate is ellipse compares ρ partially0Real part and transparent ultrathin membrane is ellipse compares ρ partially1Real part, Im ρ0
With Im ρ1Respectively substrate is ellipse compares ρ partially0Imaginary part and transparent ultrathin membrane is ellipse compares ρ partially1Imaginary part.
As it is further preferred that in step S3Occurrence using following formula calculate:
Wherein, n0For the refractive index of surrounding medium, nsFor substrate refractive index, θ0For the incidence angle of incident light, θ1For incident light
At the refraction angle of substrate, R is slope.
As it is further preferred that n in step S4TAnd dTSpecifically determine in the following way:
S41 judges that the transparent ultrathin membrane of measured in advance is ellipse and compares ρ partially1With substrate is ellipse compares ρ partially0It is whether equal, if so, nT=
ns, then according to the refractive index n of transparent ultrathin membraneTCalculate ρ1', and utilize formulaCalculate the thickness of transparent ultrathin membrane
Spend dT, wherein Im ρ1Compare ρ partially for transparent ultrathin membrane is ellipse1Imaginary part, λ be incident light wavelength；If it is not, being then transferred to step S42；
S42 is calculate by the following formula out two refractive index of transparent ultrathin membrane:
S43 utilizes formula according to two refractive index of transparent ultrathin membraneTwo thickness are calculated separately out, so
Correct refractive index is judged using the physical condition that thickness need to be positive afterwards.
As it is further preferred that ρ1' calculated using following formula:
Wherein, n0For the refractive index of surrounding medium, nsFor substrate refractive index, θ0For the incidence angle of incident light, θ1For incident light
At the refraction angle of substrate, nTFor the refractive index of the step S4 transparent ultrathin membrane solved.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, mainly have below
Technological merit:
The present invention obtains power series form by carrying out the second Taylor series to ellipse inclined ratio, and passes through a series of conversions and meter
The refractive index of transparent ultrathin membrane (thickness is within the scope of 5nm-20nm) can be achieved in calculation and the rapid survey of thickness calculates, and existing
Bright ultrathin membrane measurement & characterization method is compared, and inventive process avoids the thickness nonuniqueness in modeling fit procedure, operation letters
Just, without complicated analytic process, and to transparent ultrathin membrane and substrate without particular/special requirement, it is applicable in transparent or similar transparent substrate
On any transparent ultrathin membrane, applied widely, measurement is accurate.The present invention, which directly leads to too small amount of formula calculating, can be obtained
The refractive index of bright ultrathin membrane, and the thickness of transparent ultrathin membrane is calculated in the refractive index based on transparent ultrathin membrane, measures quickly quasi-
Really, have wide practical use in transparent ultrathin membrane measurement & characterization field.
Detailed description of the invention
Fig. 1 is the refractive index of transparent ultrathin membrane provided in an embodiment of the present invention and the flow chart of THICKNESS CALCULATION method；
Fig. 2 is that substrate of glass provided in an embodiment of the present invention is bent in the optical constant spectrum of 600~1000nm wavelength band
Line；
Fig. 3 is substrate of glass aluminum oxide film membrane sample optical model schematic diagram provided in an embodiment of the present invention；
Fig. 4 is that utilization spectroscopic ellipsometers measurement substrate of glass aluminum oxide film ellipsometric parameter provided in an embodiment of the present invention shows
It is intended to；
Fig. 5 is the calculating provided in an embodiment of the present invention when 60 ° of incidence angle, lambda1-wavelength are within the scope of 600-1000nm
The refractive index of aluminium oxide ultrathin membrane in obtained substrate of glass；
Fig. 6 is the calculating provided in an embodiment of the present invention when 60 ° of incidence angle, lambda1-wavelength are within the scope of 600-1000nm
The thickness of aluminium oxide ultrathin membrane in obtained substrate of glass.
In all the appended drawings, identical appended drawing reference is used to denote the same element or structure, in which:
1- light source, 2- are polarized arm, 3- sample stage, 4- analyzing arm, 5- detector, 6- sample to be tested.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
As shown in Figure 1, the refractive index and method for measuring thickness of a kind of transparent ultrathin membrane provided in an embodiment of the present invention, are used for
It realizes the quick and precisely measurement of transparent ultrathin membrane refractive index and thickness, every measurement parameter, including incidence is first obtained before measurement
The incidence angle θ of light wavelength lambda range Γ, incident light0, substrate refractive index ns, surrounding medium refractive index n0, incident light enter substrate
Refraction angle θ1, the ellipse of transparent ultrathin membrane compare ρ partially1Ellipse with substrate compares ρ partially0.Specifically, real according to material property, instrument etc.
Border situation, selection measurement wave-length coverage Γ and incidence angle θ0；By approach such as experiment measurement, consulting literatures or databases, obtain
Optical constant (the substrate refraction of associated materials (including base material, surrounding dielectric material etc.) in selected wave-length coverage Γ
Rate nsWith surrounding medium refractive index n0), need to meet transparent or similar transparent condition according to the requirement base material of calculation method
(extinction coefficient is less than 0.01)；Incident light enters the refraction angle θ of substrate1Pass through n0sin(θ0)=nssin(θ1) calculate；By ellipse
Inclined instrument or imaging ellipsometer etc. measure the ellipsometric parameter Amplitude Ration Ψ of transparent ultrathin membrane1And phase difference1, the ellipsometric parameter of substrate
Amplitude Ration Ψ0And phase difference0, the transparent ultrathin membrane of calculating acquisition is ellipse to compare ρ partially1=tan ψ1×exp(iΔ1) and substrate it is ellipse partially
Compare ρ0=tan ψ0×exp(iΔ0)。
For any transparent ultrathin membrane, measurement method of the invention the following steps are included:
S1 is with 2 π dT/ λ is that variable is ellipse to transparent ultrathin membrane compares ρ partially1It carries out the second Taylor series and obtains power series form (two
Rank approximate form):
Firstly, it is ellipse to express transparent ultrathin membrane using the ratio between the p luminous reflectivity of incident light and s luminous reflectivity of incident light
Compare ρ partially1, relationship is as follows:
Wherein, rpFor the reflection coefficient of the p light of incident light, specific formula for calculation is as follows:
Wherein, nsFor substrate refractive index, n0For the refractive index of surrounding medium, λ is lambda1-wavelength, dTIt is to be measured transparent super
The thickness of film, θ1Enter the refraction angle of substrate, n for incident lightTFor the refractive index of transparent ultrathin membrane to be measured；
rsFor the s luminous reflectivity of incident light, specific formula for calculation is as follows:
Then, formula described in formula (1)-(3) is surrounded into 2 π dT/ λ is launched into power series form, and saves second order or more
Higher order term obtains:
Wherein, coefficient entry is respectively as follows:
S2 isolate in power series form with transparent membrane thickness dTRelevant parameter T1And T2:
S3 calculates the real part of power series form and the slope R of imaginary part square, is calculated according to slope ROccurrence:
Assuming that constant term and cubic term are real in formula (4) in the case that surrounding medium, ultrathin membrane and substrate are all transparent
Number, linear term is imaginary number, separates real part Re ρ to formula (4)1With imaginary part Im ρ1It obtains:
It is obtained according to formula (11):It willAnd formula (5)~(7) substitute into abbreviation in formula (10)
:
From above-mentioned formula (12) it can be seen that Re ρ1(Im ρ1)2Between there are linear relationship, R indicates slope.
Wherein:
It is obtained according to formula (8) and (9):
Specifically, slope R is calculated using following formula:
Wherein, Re ρ0With Re ρ1The substrate respectively measured in advance is ellipse to compare ρ partially0Real part and transparent ultrathin membrane is ellipse compares ρ partially1
Real part, Im ρ0With Im ρ1Respectively substrate is ellipse compares ρ partially0Imaginary part and transparent ultrathin membrane is ellipse compares ρ partially1Imaginary part.
It can be obtained by formula (13):
By the substrate refractive index n that formula (15) calculate the R obtained and measurement obtains in advances, surrounding medium refractive index n0, it is incident
The incidence angle θ of light0Enter the refraction angle θ of substrate with incident light1It calculates and obtains in substitution formula (16)
S4 calculates step S3Occurrence substitutes into the refractive index n that transparent ultrathin membrane is solved in formula (14)T, further according to
The refractive index n of transparent ultrathin membraneTCalculate the thickness of transparent ultrathin membrane.
Under normal circumstances, to specific transparent ultra-thin membrane material, the approximate range of refractive index can tentatively be estimated by document,
Then judge that the relationship of itself and substrate refractive index, reselection correspond to calculation formula and accurately calculated, wherein when transparent ultrathin membrane
When refractive index is less than substrate refractive index:
When transparent ultrathin membrane refractive index is greater than substrate refractive index:
In addition, comparing ρ partially when the transparent ultrathin membrane obtained is ellipse1With substrate is ellipse compares ρ partially0When equal, that is, illustrate transparent ultrathin membrane folding
Rate is penetrated equal to substrate refractive index, due to substrate refractive index it is known that then without calculating transparent ultrathin membrane refractive index.
Certainly, the sometimes bad relationship for judging refractive index of transparent films with double-prisms and substrate refractive index, because of the transparent membrane estimated
Refractive index is a range, and substrate refractive index may be difficult to determine relationship between the two within the scope of this, at this time can be same
When calculate two groups of refractive index and thickness, then solve calculated thickness using mistake and do not meet physical condition (as negative) to two
Group solution is excluded.
Specifically, calculating separately out two refractive index using formula (17a) and (17b), utilized further according to two refractive index
Formula (18) calculates separately out two thickness, and wherein corresponding refractive index of the thickness greater than zero is correct solution, and thickness is minus right
The refractive index answered is mistake solution, is excluded.
Specifically, according to the refractive index n of transparent ultrathin membraneTThe thickness of transparent ultrathin membrane is calculated using following formula:
Wherein, ρ1Ellipse inclined ratio for the transparent ultrathin membrane measured in advance, Im ρ1It refers to that transparent ultrathin membrane is ellipse and compares ρ partially1Void
Portion, ρ1' calculation formula are as follows:The transparent of acquisition will be calculated
The refractive index n of ultrathin membraneTAnd the substrate refractive index n that measurement obtains in advances, surrounding medium refractive index n0, incident light incidence angle θ0
Enter the refraction angle θ of substrate with incident light1It is calculated in substitution formula (5) and obtains ρ1'.If the refractive index n of transparent ultrathin membraneTWith substrate
Refractive index is equal, then the thickness of transparent ultrathin membrane can not be found out by above-mentioned formula, other replaceable substrates measure point
Analysis, but such case seldom occurs, and the refractive index of few materials is identical in nature, and refractive index can be with the variation of wavelength
And change, the refractive index of two kinds of materials will not be identical in entire wave band.
The following are specific embodiments, illustrate that transparent ultrathin membrane refractive index of the present invention and thickness are quick in order to clearer
The implementation process of measurement method, in the present embodiment preferably using spectroscopic ellipsometer to the aluminium oxide ultrathin membrane in substrate of glass into
Row measurement calculates the refractive index and thickness of aluminium oxide by formula (17a), (17b) and formula (18), specific as follows:
(1) wave-length coverage of selection measurement, the wave-length coverage for choosing measurement is Γ=[600,1000] nm；
(2) measurement incidence angle is selected, incidence angle selection does not have particular/special requirement, and the angle that general ellipsometer can measure is equal
Can, this incidence angle selection θ0=60 °；
(3) optical constant of substrate of glass and surrounding medium used is determined, the accurate optical constant for determining substrate is subsequent
The premise for accurately calculating aluminium oxide membrane thickness, the base material more stable for optical constant can directly use document
Reference value is fitted to guarantee that the ellipsometric parameter of ellipsometer measurement substrate of glass also can be used in the accuracy of calculated result
To its optical constant.Transparent substrates can have the incoherent light of backside of substrate reflection, and interference measurement results are general using to substrate
It carries out grinding process or carrying out index matching makes measurement light enter matching materials to eliminate the interference of incoherent light, at 60 °
Ellipsometry is carried out to substrate of glass under incidence angle, the refractive index of substrate of glass can be obtained using Cauchy (Cauchy) models fitting
It arrives, surrounding medium is air, refractive index n0=1, the refractive index n of substrate of glasss(λ) is as shown in Figure 2；
(4) ellipsometric parameter of ellipsometer measurement ultrathin alumina film and blank substrate is utilized:
Light measures the ellipsometric parameter of sample to be tested with 60 ° of selected angle incidences(λ) and blank substrate it is ellipse partially
Parameter ρsubstrate(λ)；Measuring device schematic diagram as shown in figure 4, ellipsometer used by light source 1, be polarized arm 2, sample stage 3, analyzing
The composition such as arm 4, detector 5, sample to be tested 6 are placed on sample stage 3；Light, which is polarized arm 2 from the outgoing of light source 1, becomes polarised light,
It is irradiated on sample to be tested 6, polarised light and sample to be tested 6 act on, and polarization state changes, reflected light quilt after analyzing arm 4
Detector 5 receives, the above-mentioned basic process to detect ellipsometric parameter by ellipsometer；
(5) refractive index of ultrathin alumina to be measured is calculated(λ):
Using (4) step measurement data, it is calculated using the following equation:
Check online optical constant data library, the refractive index of substrate of glass is near 1.5, and the refractive index of aluminium oxide is 1.7
Near, since the aluminium oxide ultrathin membrane refractive index under corresponding wavelength is greater than substrate refractive index, therefore(λ) uses following formula meter
It calculates:
Wherein, into the refraction angle θ of substrate1Pass throughIt calculates.
Fig. 5 is when 60 ° of incidence angle, lambda1-wavelength are within the scope of 600-1000nm, in the substrate of glass that is calculated
Aoxidize the refractive index of ultrathin membrane；
(6) thickness d of ultrathin alumina to be measured is calculated:
Due to having selected spectroscopic ellipsometry, a thickness value d can be calculated under each wavelength points
(λ):
Fig. 6 is when 60 ° of incidence angle, lambda1-wavelength are within the scope of 600-1000nm, in the substrate of glass that is calculated
Aoxidize the thickness of ultrathin membrane.As can be seen from Figure 6 acquired results have certain variation at different wavelengths, this is because second order
The inaccuracy of result caused by formula is approximate, but the error is in sub-nanometer magnitude, by taking mean value to obtain aluminium oxide thickness
Final thickness d be 10.23nm, the present invention is that basic data calculate and can measure lower survey to avoid Single wavelength with ellipsometric parameter
Measuring result error caused by amount system random error.
Above-described embodiment is only by taking the aluminum oxide film in substrate of glass as an example, for the transparent ultra-thin membrane material of remaining type
Or different transparent substrates types can also carry out refractive index and thickness measure according to method of the same race.
Transparent ultrathin membrane refractive index provided by the present invention and thickness method for fast measuring avoid tradition modeling fitting feelings
Transparent ultrathin membrane refractive index is unknown so that thickness and refractive index intercouple under condition, can not accurately uniquely determine transparent ultrathin membrane folding
Penetrate the problem of rate and thickness, it can be achieved that transparent ultrathin membrane refractive index and thickness quick and precisely measurement and calculating, principle is simple, easily
In operation.
The method of the present invention is not limited to above-mentioned specific embodiment, and persons skilled in the art disclose according to the present invention
Content, the present invention can be implemented using other a variety of specific embodiments, the instrument of polarization information can be measured by such as using other instead
Device uses other substrates transparent or that absorption is seldom instead, therefore, all using design method principle of the invention and thinking, does
The design of some simple variations or change, both falls within the scope of protection of the invention.
Claims (7)
1. a kind of transparent ultrathin membrane refractive index and method for measuring thickness, which comprises the steps of:
S1 is with 2 π dT/ λ is that variable is ellipse to transparent ultrathin membrane to be measured compares ρ partially1It carries out the second Taylor series and obtains power series form,
In, dTFor the thickness of transparent ultrathin membrane to be measured, λ is the wavelength of incident light:
S2 isolates parameter T relevant to transparent membrane thickness in power series form1And T2, and obtain following formula:
Wherein, n0For the refractive index of surrounding medium, nsFor substrate refractive index, nTFor the refractive index of transparent ultrathin membrane to be measured, substrate is
Transparent or similar transparent；
S3 calculates the real part of power series form and the slope R of imaginary part square, is calculated according to slope ROccurrence；
S4 calculates step S3Occurrence brings in the expression formula of step S2 the refractive index n for solving transparent ultrathin membrane intoT, and
According to the refractive index n of transparent ultrathin membraneTCalculate the thickness d for obtaining transparent ultrathin membraneT。
2. transparent ultrathin membrane refractive index as described in claim 1 and method for measuring thickness, which is characterized in that the power in step S1
Progression form specifically:
Wherein, ρ0For the ellipse inclined ratio of substrate used in transparent ultrathin membrane, dTFor the thickness of transparent ultrathin membrane to be measured, λ is the wave of incident light
It is long, ρ1'、ρ”aAnd ρ "bIt is coefficient.
3. transparent ultrathin membrane refractive index as described in claim 1 and method for measuring thickness, which is characterized in that the ginseng in step S2
Measure T1And T2Specifically:
4. transparent ultrathin membrane refractive index as described in claim 1 and method for measuring thickness, which is characterized in that oblique in step S3
Rate R is specifically calculated using following formula:
Wherein, Re ρ0With Re ρ1Respectively substrate is ellipse compares ρ partially0Real part and transparent ultrathin membrane is ellipse compares ρ partially1Real part, Im ρ0And Im
ρ1Respectively substrate is ellipse compares ρ partially0Imaginary part and transparent ultrathin membrane is ellipse compares ρ partially1Imaginary part.
5. transparent ultrathin membrane refractive index as described in claim 1 and method for measuring thickness, which is characterized in that in step S3's
Occurrence is calculated using following formula:
Wherein, n0For the refractive index of surrounding medium, nsFor substrate refractive index, θ0For the incidence angle of incident light, θ1It is incident light in base
The refraction angle at bottom, R are slope.
6. transparent ultrathin membrane refractive index as described in any one in claim 1-5 and method for measuring thickness, which is characterized in that step
N in S4TAnd dTSpecifically determine in the following way:
S41 judges that the transparent ultrathin membrane of measured in advance is ellipse and compares ρ partially1With substrate is ellipse compares ρ partially0It is whether equal, if so, nT=ns, so
Afterwards according to the refractive index n of transparent ultrathin membraneTCalculate ρ1', and utilize formulaCalculate the thickness d of transparent ultrathin membraneT,
Wherein, Im ρ1Compare ρ partially for transparent ultrathin membrane is ellipse1Imaginary part, λ be incident light wavelength；If it is not, being then transferred to step S42；
S42 is calculate by the following formula out two refractive index of transparent ultrathin membrane:
S43 utilizes formula according to two refractive index of transparent ultrathin membraneTwo thickness are calculated separately out, it is then sharp
Correct refractive index is judged with the physical condition that thickness need to be positive.
7. transparent ultrathin membrane refractive index as claimed in claim 6 and method for measuring thickness, which is characterized in that ρ1' using following public
Formula calculates:
Wherein, n0For the refractive index of surrounding medium, nsFor substrate refractive index, θ0For the incidence angle of incident light, θ1It is incident light in base
The refraction angle at bottom, nTFor the refractive index of the step S4 transparent ultrathin membrane solved.
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| CN113433077A (en) * | 2021-06-11 | 2021-09-24 | 大连海事大学 | Method for obtaining oil film attenuation coefficient based on relative thickness of oil film |
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