CN110057401A - A kind of transparent ultrathin membrane refractive index and method for measuring thickness - Google Patents

Abstract

The invention belongs to the field of thin film measurement and characterization, and specifically discloses a method for measuring the refractive index and thickness of _a transparent ultra-thin film _. Obtain the power series form: S2 separates out the parameters T ₁ and T ₂ related to the transparent ultrathin film in the power series form, and obtains Expression; S3 calculates the slope R of the square of the real part and the imaginary part in the form of a power series, calculated according to the slope R The specific value of ; S4 will calculate the The specific value is brought into the expression of step S2 to solve the refractive index n _T of the transparent ultra-thin film, and the thickness of the transparent ultra-thin film is calculated according to the refractive index. The invention can realize fast, direct and accurate measurement of the refractive index and thickness of the transparent ultra-thin film, and has the advantages of wide application range, accurate measurement, and no complicated analysis process.

Description

A kind of transparent ultra-thin film refractive index and thickness measurement method

technical field

The invention belongs to the field of thin film measurement and characterization, and more particularly relates to a method for measuring the refractive index and thickness of transparent ultra-thin films, which is suitable for fast and accurate measurement of the refractive index and thickness of transparent ultra-thin films on various substrates.

Background technique

Transparent ultra-thin films refer to ultra-thin films with zero extinction coefficient, including organic films, polymer films, metal oxides, etc., and are widely used in anti-reflection coatings, biosensors, solar cells, etc. The thickness of the transparent ultra-thin film has a great influence on its optical properties, and the optical constants of the transparent ultra-thin film with different thickness are different. The thickness and optical constants of transparent ultra-thin films determine their optical properties such as transmission and reflection, and also determine some of their physical properties. Therefore, it is necessary to measure the thickness and optical constants of transparent ultra-thin films.

At present, the measurement and characterization methods of ultra-thin films mainly include quartz crystal microbalance, surface plasmon, photometry, ellipsometer and so on. For thin hard films, the quartz crystal microbalance can use the Sauerbrey formula to calculate the mass of the adsorption layer according to the vibration of the sensor to obtain the thickness of the film. However, for films that are relatively soft to the substrate or immersed in liquid, both the film molecules and the liquid in them have an effect on the mass increase, and the quartz crystal microbalance cannot determine the film thickness. Surface plasmon is generated due to the collective oscillation of free electrons in the conduction band near the Fermi level on the metal surface driven by an electromagnetic field. The wave vector matching conditions are satisfied by means of prism coupling. The excimer combination can calculate the film thickness, but this method is generally used to measure metal films or require that the film substrate needs to be a metal material. The photometric method is based on measuring the transmittance and reflectance of the film to determine the thickness of the film. It can be divided into envelope method and full spectrum fitting method. It is not suitable for ultra-thin films; the full spectrum fitting method needs to rely on the dispersion model, and the selection of different oscillators has a great influence on the fitting results. Ellipsometry measurement has the advantages of non-destructive and non-contact, high sensitivity and precision, and its sensitivity to thickness can reach 0.01nm, but ellipsometry is an indirect measurement method, which requires computer fitting to obtain the thickness and optical constant of the film (including refractive index and extinction coefficient). When an ellipsometer is used to measure ultrathin films, it is difficult to obtain a unique fitting result due to the strong coupling relationship between thickness and optical constants. In view of this difficulty, methods such as multi-sample method, online measurement, and measurement of various surrounding medium conditions can be used. However, the above methods all have their own limitations. The premise of multi-sample analysis is to assume that the optical constant of the thin film does not change with the thickness. In fact, the optical constant of the ultra-thin film will change with the thickness. There are also online measurement methods and multi-sample methods. The same drawbacks; multiple ambient media conditions introduce a complex liquid measurement environment, the membrane needs to be non-reactive with the media and cannot be a porous material.

Ukraine's Andriy Kostruba et al. (Method for determination of the parameters of transparent ultrathin films deposited on transparent substrates underconditions of low optical contrast, Applied optics, 2015, 54(20): 6208-6216) proposed a method for transparent films on transparent substrates Measurement method, this method finds a specific incident angle by measuring multiple incident angles, at this angle, the ellipsometry parameter amplitude ratio (Ψ) does not change with the change of the film thickness, and the ellipsometry parameter phase difference (Δ) is related to the film thickness. The thickness is linear. The disadvantage of this method is that the scope of application is limited, and it can only be used to measure transparent ultra-thin films with a refractive index very close to that of the substrate, and the substrate material needs to have no absorption at all.

SUMMARY OF THE INVENTION

In view of the above defects or improvement requirements of the prior art, the present invention provides a method for measuring the refractive index and thickness of a transparent ultra-thin film, which realizes the refractive index of the transparent ultra-thin film by performing second-order Taylor expansion on the ellipsometric ratio and transforming and calculating. It has the advantages of fast, direct and accurate calculation and measurement of thickness and thickness, and has the advantages of wide application range, accurate measurement and no complicated analysis process.

To achieve the above object, the present invention proposes a transparent ultra-thin film refractive index and a thickness measurement method, which comprises the following steps:

S1 takes 2πd _T /λ as the variable to perform the second-order Taylor expansion of the ellipsometry ratio ρ ₁ of the transparent ultra-thin film to be measured to obtain a power series form, where d _T is the thickness of the transparent ultra-thin film to be measured, and λ is the wavelength of the incident light:

S2 separates out the parameters T ₁ and T ₂ related to the thickness of transparent ultrathin films in power series form and obtains the following expressions:

Wherein, n ₀ is the refractive index of the surrounding medium, n _s is the refractive index of the substrate, n _T is the refractive index of the transparent ultra-thin film to be measured, and the substrate is transparent or approximately transparent;

S3 calculates the slope R of the square of the real part and the imaginary part in the form of a power series, and calculates according to the slope R the specific value of ;

S4 will be calculated in step S3 The specific value is brought into the expression of step S2 to solve the refractive index n _T of the transparent ultra-thin film, and the thickness d _T of the transparent ultra-thin film is obtained by calculating according to the refractive index n _T of the transparent ultra-thin film.

As a further preference, the power series form in step S1 is specifically:

Wherein, ρ ₀ is the ellipsometry ratio of the substrate used for the transparent ultra-thin film, d _T is the thickness of the transparent ultra-thin film to be measured, λ is the wavelength of the incident light, and ρ ₁ ′, ρ″ _a and ρ″ _b are coefficients.

As a further preference, the parameters T ₁ and T ₂ in step S2 are specifically:

As a further preference, the slope R in step S3 is calculated by the following formula:

where Reρ ₀ and Reρ ₁ are the real part of the substrate ellipsometry ratio ρ ₀ and the real part of the transparent ultra-thin film ellipsometry ratio ρ ₁ , respectively, and Imρ ₀ and Imρ ₁ are the imaginary part of the substrate ellipsometry ratio ρ ₀ and the transparent ultra-thin film ellipsometry ratio ρ 1, respectively. _The imaginary part of the film ellipsometry ratio ρ1.

As a further preference, in step S3 The specific value of is calculated using the following formula:

Among them, n ₀ is the refractive index of the surrounding medium, _ns is the refractive index of the substrate, θ ₀ is the incident angle of the incident light, θ ₁ is the refraction angle of the incident light on the substrate, and R is the slope.

As a further preference, in step S4, n _T and d _T are specifically determined in the following manner:

S41 judges whether the pre-measured transparent ultra-thin film ellipsometric ratio ρ ₁ and substrate ellipsometric ratio ρ ₀ are equal, if so, n _T = _ns , then calculate ρ ₁ ' according to the refractive index n _T of the transparent ultra-thin film, and use the formula Calculate the thickness d _T of the transparent ultra-thin film, wherein, Imρ ₁ is the imaginary part of the ellipsometry ratio ρ ₁ of the transparent ultra-thin film, and λ is the wavelength of the incident light; if not, then go to step S42;

S42 calculates the two refractive indices of the transparent ultra-thin film by the following equations:

S43 utilizes the formula according to the two refractive indices of the transparent ultra-thin film Calculate the two thicknesses separately, and then use the physical condition that the thickness needs to be positive to determine the correct refractive index.

As a further preference, ρ ₁ ' is calculated by the following formula:

Among them, n ₀ is the refractive index of the surrounding medium, n _s is the refractive index of the substrate, θ ₀ is the incident angle of the incident light, θ ₁ is the refraction angle of the incident light at the substrate, and n _T is the transparent ultra-thin film calculated in step S4. refractive index.

In general, compared with the prior art, the above technical solutions conceived by the present invention mainly have the following technical advantages:

The present invention obtains the power series form by performing second-order Taylor expansion on the ellipsometry ratio, and can realize the rapid measurement and calculation of the refractive index and thickness of the transparent ultra-thin film (thickness in the range of 5nm-20nm) through a series of conversions and calculations. Compared with the existing transparent ultra-thin film measurement and characterization methods, the method of the present invention avoids the thickness non-uniqueness in the modeling and fitting process, is easy to operate, has no complicated analysis process, and has no special requirements for the transparent ultra-thin film and the substrate, and can be applied to Any transparent ultra-thin film on a transparent or nearly transparent substrate has a wide range of applications and accurate measurement. The method can directly obtain the refractive index of the transparent ultra-thin film through a small amount of formula calculation, and calculate the thickness of the transparent ultra-thin film based on the refractive index of the transparent ultra-thin film, the measurement is fast and accurate, and has wide application prospects in the field of measurement and characterization of the transparent ultra-thin film .

Description of drawings

Fig. 1 is the flow chart of the refractive index and the thickness calculation method of the transparent ultra-thin film that the embodiment of the present invention provides;

Fig. 2 is the optical constant spectral curve of the glass substrate provided in the embodiment of the present invention in the wavelength range of 600-1000 nm;

3 is a schematic diagram of an optical model of a glass-substrate alumina film sample provided in an embodiment of the present invention;

4 is a schematic diagram of measuring ellipsometry parameters of glass-substrate alumina thin films using a spectral ellipsometer provided by an embodiment of the present invention;

5 is the refractive index of the alumina ultra-thin film on the glass substrate calculated when the incident angle is 60° and the incident light wavelength is in the range of 600-1000nm according to the embodiment of the present invention;

FIG. 6 is the thickness of the ultra-thin aluminum oxide film on the glass substrate calculated and obtained when the incident angle is 60° and the incident light wavelength is in the range of 600-1000 nm according to the embodiment of the present invention.

Throughout the drawings, the same reference numbers are used to refer to the same elements or structures, wherein:

1-light source, 2-polarizing arm, 3-sample stage, 4-analyzing arm, 5-detector, 6-sample to be tested.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

As shown in FIG. 1, a method for measuring the refractive index and thickness of a transparent ultra-thin film provided by an embodiment of the present invention is used to realize the fast and accurate measurement of the refractive index and thickness of the transparent ultra-thin film. Before the measurement, various measurement parameters are obtained, including The wavelength λ range Γ of the incident light, the incident angle θ ₀ of the incident light, the refractive index of the substrate _ns , the refractive index of the surrounding medium n ₀ , the refraction angle θ ₁ of the incident light entering the substrate, the ellipsometry ratio ρ ₁ of the transparent ultra-thin film and the Ellipsometry ratio ρ ₀ . Specifically, according to the actual conditions such as material characteristics and instruments used, the measurement wavelength range Γ and the incident angle θ ₀ are selected; through experimental measurement, reference to literature or databases, etc., obtain the selected wavelength range Γ. Related materials (including substrate materials, The optical constants (substrate refractive index n _s and surrounding medium refractive index n ₀ ) of surrounding medium materials, etc., according to the requirements of the calculation method, the substrate material needs to meet the transparent or nearly transparent conditions (extinction coefficient is less than 0.01); the refraction of incident light entering the substrate The angle θ ₁ is calculated by n ₀ sin(θ ₀ )= _ns sin(θ ₁ ); the ellipsometry parameter amplitude ratio Ψ ₁ and phase difference Δ ₁ of the transparent ultra-thin film are measured by ellipsometer or imaging ellipsometer, etc. , the ellipsometry parameter amplitude ratio Ψ ₀ and the phase difference Δ ₀ of the substrate, the transparent ultra-thin film ellipsometry ratio ρ ₁ =tanΨ ₁ ×exp(iΔ ₁ ) and the substrate ellipsometry ratio ρ ₀ =tanΨ ₀ ×exp( iΔ ₀ ).

For any transparent ultra-thin film, the measuring method of the present invention comprises the following steps:

S1 takes 2πd _T /λ as the variable to perform the second-order Taylor expansion of the ellipsometry ratio ρ ₁ of the transparent ultra-thin film to obtain the power series form (second-order approximate form):

First, the ratio of the p light reflection coefficient of the incident light to the s light reflection coefficient of the incident light is used to express the ellipsometry ratio ρ ₁ of the transparent ultra-thin film, and the relationship is as follows:

Among them, r _p is the reflection coefficient of the p light of the incident light, and its specific calculation formula is as follows:

where n _s is the refractive index of the substrate, n ₀ is the refractive index of the surrounding medium, λ is the wavelength of the incident light, d _T is the thickness of the transparent ultra-thin film to be measured, θ ₁ is the refraction angle of the incident light entering the substrate, and n _T is the Measuring the refractive index of transparent ultra-thin films;

rs is the _s light reflection coefficient of the incident light, and its specific calculation formula is as follows:

Then, expand the formula described by equations (1)-(3) into a power series form around 2πd _T /λ, and omit the higher-order terms above the second order:

Among them, the coefficient terms are:

S2 separates out the parameters T ₁ and T ₂ related to the thickness d _T of the transparent ultrathin film in the form of a power series:

S3 calculates the slope R of the square of the real part and the imaginary part in the form of a power series, and calculates according to the slope R The specific value of:

Assuming that the surrounding medium, ultra-thin film and substrate are all transparent, the constant term and the cubic term in equation (4) are real numbers, and the linear term is an imaginary number. For equation (4), the real part Reρ ₁ and the imaginary part Imρ ₁ are separated to obtain:

According to formula (11), we get: Will And formulas (5)-(7) are substituted into formula (10) and simplified to get:

From the above formula (12), it can be seen that there is a linear relationship between Reρ ₁ and (Imρ ₁ ) ² , and R represents the slope.

in:

According to formulas (8) and (9), we get:

Specifically, the slope R is calculated by the following formula:

Wherein, Reρ ₀ and Reρ ₁ are respectively the real part of the substrate ellipsometry ratio ρ ₀ and the real part of the transparent ultra-thin film ellipsometry ratio ρ ₁ , respectively, and Imρ ₀ and Imρ ₁ are respectively the imaginary base ellipsometry ratio ρ ₀ part and the imaginary part of the ellipsometry ratio ρ1 _of the transparent ultrathin film.

By formula (13), it can be obtained:

Substitute the R calculated from the formula (15) and the refractive index _ns of the substrate, the refractive index n ₀ of the surrounding medium, the incident angle θ ₀ of the incident light and the refraction angle θ ₁ of the incident light entering the substrate into the formula (16). Calculated

S4 will be calculated in step S3 The specific value is substituted into the formula (14) to obtain the refractive index n _T of the transparent ultra-thin film, and then the thickness of the transparent ultra-thin film is calculated according to the refractive index n _T of the transparent ultra-thin film.

In general, for a specific transparent ultra-thin film material, the approximate range of its refractive index can be preliminarily estimated from the literature, and then determine the relationship between it and the refractive index of the substrate, and then select the corresponding calculation formula for accurate calculation. When the ratio is less than the substrate refractive index:

When the refractive index of the transparent ultra-thin film is greater than that of the substrate:

In addition, when the obtained transparent ultra-thin film ellipsometry ratio ρ ₁ and substrate ellipsometry ratio ρ ₀ are equal, that is to say that the transparent ultra-thin film refractive index is equal to the substrate refractive index, because the substrate refractive index is known, then there is no need to calculate the transparent ultra-thin film refractive index .

Of course, sometimes it is not easy to judge the relationship between the refractive index of the transparent film and the refractive index of the substrate, because the estimated refractive index of the transparent film is within a range, and the refractive index of the substrate may be within this range, so it is difficult to determine the relationship between the two. Two sets of refractive indices and thicknesses can be calculated at the same time, and then the two sets of solutions can be excluded by using the thickness calculated by the wrong solution that does not meet the physical conditions (ie, a negative number).

Specifically, two indices of refraction are calculated using equations (17a) and (17b), respectively, and two thicknesses are calculated using equation (18) according to the two indices of refraction, where the corresponding indices of refraction whose thickness is greater than zero are correct. solution, the corresponding refractive index with thickness less than zero is an incorrect solution and is excluded.

Specifically, according to the refractive index n _T of the transparent ultra-thin film, the thickness of the transparent ultra-thin film is calculated by the following formula:

Wherein, ρ ₁ is the ellipsometry ratio of the transparent ultra-thin film measured in advance, Imρ ₁ refers to the imaginary part of the ellipsometry ratio ρ ₁ of the transparent ultra-thin film, and the calculation formula of ρ ₁ ' is: The refractive index n _T of the transparent ultra-thin film to be calculated and the refractive index n _s of the substrate obtained by the previous measurement, the refractive index n ₀ of the surrounding medium, the incident angle θ ₀ of the incident light and the refraction angle θ ₁ of the incident light entering the substrate are substituted into the formula ( 5) to obtain ρ ₁ '. If the refractive index n _T of the transparent ultra-thin film is equal to the refractive index of the substrate, the thickness of the transparent ultra-thin film cannot be calculated by the above formula, and other substrates can be replaced for measurement and analysis, but this situation rarely occurs, and rarely occurs in nature. Materials have the same index of refraction, and the index of refraction varies with wavelength, and the index of refraction of two materials will not be exactly the same over the entire wavelength band.

The following are specific examples. In order to more clearly describe the implementation process of the method for rapidly measuring the refractive index and thickness of the transparent ultra-thin film of the present invention, in this embodiment, a spectral ellipsometer is preferably used to conduct the ultra-thin alumina film on the glass substrate. Measure, calculate the refractive index and thickness of alumina by formula (17a), (17b) and formula (18), as follows:

(1) Select the wavelength range for measurement, and select the wavelength range for measurement as Γ=[600,1000] nm;

(2) Select the incident angle for measurement. There is no special requirement for the selection of the incident angle. Generally, any angle that can be measured by the ellipsometer can be used. This time, the incident angle is selected as θ ₀ =60°;

(3) Determine the optical constants of the glass substrate and the surrounding medium. Accurate determination of the optical constants of the substrate is the premise for the subsequent accurate calculation of the thickness of the ultra-alumina ultra-thin film. For the substrate materials with relatively stable optical constants, the reference value of literature can be used directly. The accuracy of the results can also be measured by using an ellipsometer to measure the ellipsometry parameters of the glass substrate, and its optical constants can be obtained by fitting. The transparent substrate will have incoherent light reflected from the back of the substrate, which will interfere with the measurement results. Generally, the substrate is polished or the index of refraction is matched to make the measurement light enter the matching material to eliminate the interference of the incoherent light. The substrate is measured by ellipsometry. The refractive index of the glass substrate can be obtained by fitting the Cauchy model. The surrounding medium is air, and its refractive index n ₀ =1. The refractive index of the glass substrate _ns (λ) is shown in Figure 2. Show;

(4) Using an ellipsometer to measure the ellipsometric parameters of the ultra-thin alumina thin film and blank substrate:

The light is incident at a selected angle of 60°, and the ellipsometry parameters of the sample to be measured are measured (λ) and the ellipsometry parameter ρ _substrate (λ) of the blank substrate; the schematic diagram of the measurement device is shown in Figure 4. The ellipsometer used consists of a light source 1, a polarizing arm 2, a sample stage 3, an analyzer arm 4, and a detector 5 The sample 6 to be tested is placed on the sample stage 3; the light emitted from the light source 1 is transformed into polarized light through the polarizing arm 2, and irradiated on the sample to be tested 6, the polarized light interacts with the sample to be tested 6, and the polarization state changes , the reflected light is received by the detector 5 after passing through the analyzer arm 4, and the above is the basic process of detecting the ellipsometric parameters by the ellipsometer;

(5) Calculate the refractive index of the ultra-thin alumina to be measured (λ):

Using the measured data in step (4), use the following formula to calculate:

Looking at the online optical constant database, the refractive index of the glass substrate is around 1.5, and the refractive index of alumina is around 1.7. (λ) is calculated using the following formula:

where the angle of refraction θ ₁ entering the substrate passes through calculate.

Figure 5 is the calculated refractive index of the ultra-thin oxide film on the glass substrate when the incident angle is 60° and the incident light wavelength is in the range of 600-1000nm;

(6) Calculate the thickness d of the ultra-thin alumina to be tested:

Since spectral ellipsometry is selected, a thickness value d(λ) can be calculated at each wavelength point:

Figure 6 shows the calculated thickness of the ultra-thin oxide film on the glass substrate when the incident angle is 60° and the incident light wavelength is in the range of 600-1000 nm. It can be seen from Figure 6 that the obtained results will vary at different wavelengths. This is due to the inaccuracy of the results caused by the approximation of the second-order formula, but the error is in the sub-nanometer level. The final thickness d is 10.23 nm, and the present invention calculates based on the ellipsometry parameter, which can avoid the measurement result error caused by the random error of the measurement system under single-wavelength measurement.

The above embodiment only takes the aluminum oxide film on the glass substrate as an example, and the refractive index and thickness measurement can also be performed according to the same method for other types of transparent ultra-thin film materials or different types of transparent substrates.

The method for fast measurement of the refractive index and thickness of the transparent ultra-thin film provided by the invention avoids the fact that the refractive index of the transparent ultra-thin film is unknown in the traditional modeling fitting situation, which makes the thickness and the refractive index coupled with each other, and cannot accurately and uniquely determine the refractive index and thickness of the transparent ultra-thin film. It can realize fast and accurate measurement and calculation of the refractive index and thickness of transparent ultra-thin films. The principle is simple and easy to operate.

The method of the present invention is not limited to the above-mentioned specific embodiments. Those skilled in the art can use other specific embodiments to implement the present invention according to the content disclosed in the present invention, such as using other instruments capable of measuring polarization information or using other The substrate is transparent or absorbs little. Therefore, any simple change or modification of the design using the principles and ideas of the design method of the present invention falls within the protection scope of the present 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 d_T/ 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, d_TFor 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, n_sFor substrate refractive index, n_TFor 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 into_T, and According to the refractive index n of transparent ultrathin membrane_TCalculate the thickness d for obtaining transparent ultrathin membrane_T。

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, d_TFor 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, n_sFor 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 S4_TAnd d_TSpecifically 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, n_T=n_s, so Afterwards according to the refractive index n of transparent ultrathin membrane_TCalculate ρ₁', and utilize formulaCalculate the thickness d of transparent ultrathin membrane_T, 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, n_sFor substrate refractive index, θ₀For the incidence angle of incident light, θ₁It is incident light in base The refraction angle at bottom, n_TFor the refractive index of the step S4 transparent ultrathin membrane solved.