A method for calculating the refractive index, extinction coefficient and thickness of micron-sized single crystals through transmission spectrum

Abstract

The present invention provides a method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal through a transmission spectrum, the method comprising: testing the micro-area transmission spectrum of the sample, obtaining the relevant parameters of the extreme points by reading the spectrum, and then respectively solving the interference median of the extreme points; respectively calculating the refractive index, extinction coefficient and absorption coefficient of the even extreme points and the odd extreme points through algorithms such as iteration, drawing a refractive index dispersion curve through the above parameters, and finally drawing an extinction coefficient dispersion curve through iterative calculation. The method can obtain information of micron-sized samples, and is simpler, faster and cheaper than the existing ellipsometer test.

Description

Technical Field

[0001] The present invention belongs to the field of computational optics, and relates to a method for calculating optical parameters of a micron-sized single crystal through a transmission spectrum, and in particular to a method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal through a transmission spectrum. Background Art

[0002] In recent years, with the rapid development of micro-nano processing technology, the size of microelectronic devices has been reduced day by day. More and more new micro-nano materials have been designed and prepared. At the same time, many traditional materials have been developed new micro-nano preparation paths. However, there is a lack of understanding of their basic optical parameters (refractive index, extinction coefficient) for these new materials. Due to the limitation of material size, it is difficult to measure their optical parameters through existing technical means such as ellipsometers. The study of various physical phenomena on these new materials is inseparable from basic optical parameters. Therefore, how to obtain reliable optical parameters of micro-nano materials is one of the urgent problems to be solved in the field of new material characterization. Summary of the invention

[0003] In order to solve the technical problems existing in the prior art, the present invention provides a method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal through a transmission spectrum. The method can obtain information of micron-sized samples and is simpler, faster and cheaper than the existing ellipsometer test.

[0004] In order to achieve the above technical effects, the present invention adopts the following technical solutions:

[0005] The present invention provides a method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal by transmission spectrum, the method comprising the following steps:

[0006] (1) Micro-area transmission spectrum of the test sample;

[0007] (2) Read the wavelength λ of the extreme point of the micro-area transmission spectrum m and transmittance T m ;

[0008] (3) The wavelength λ passing through the extreme point and its adjacent extreme point m Calculate the interference order m of the extreme point;

[0009] (4) Using the transmittance T of the odd extreme point odd Calculate the approximate refractive index at odd extreme points;

[0010] (5) At the even-numbered extreme value point, the approximate refractive index average of the two neighboring odd-numbered extreme value points is taken as an approximate value, and is brought into the transmittance model, and the extinction coefficient and the absorption coefficient of the even-numbered extreme value point are iteratively calculated;

[0011] (6) At the odd-numbered extreme value point, the average value of the absorption coefficients of the two neighboring even-numbered extreme value points is used as an approximate value and substituted into the transmittance model to calculate the refractive index of the odd-numbered extreme value point;

[0012] (7) using the refractive index and optical path length of the odd-numbered extreme points, calculating the sample thickness corresponding to a series of odd-numbered extreme points, and taking the average value to obtain the sample thickness d;

[0013] (8) Using the optical path of the even-numbered extreme value points and the determined thickness d, calculate the refractive index of a series of even-numbered extreme value points;

[0014] (9) Using the single oscillator dispersion model, a series of wavelengths and refractive indices corresponding to the odd and even extreme points are input to calculate the E of the sample. d Dispersion energy and E0 single oscillator energy, and the refractive index dispersion curve of the sample is plotted at the same time;

[0015] (10) Substituting the obtained refractive index dispersion curve and sample thickness d into the transmittance model to obtain the extinction coefficient dispersion curve.

[0016] As a preferred technical solution of the present invention, the method for testing the micro-area transmission spectrum of the sample in step (1) is: according to the transmission intensity spectrum (I sam , I sub , I air ), the transmission light intensity of the sample to be tested and the transmission light intensity of the transparent substrate are divided by the transmission light intensity of the air to obtain the transmission spectrum (T sam =I sam / I air , T sub =I sub / I air ).

[0017] In the present invention, the testing device and method of the micro-area transmission spectrum refer to patent CN112964655A.

[0018] In the present invention, the thickness of the sample for which the optical constants can be calculated by transmission spectrum must meet certain conditions, similar to Figure 2 Several extreme points (about ten is more appropriate) appear to facilitate calculation.

[0019] In the present invention, if the transmittance spectrum of the substrate is enveloping above the transmittance spectrum of the sample, it means that the refractive index of the sample is greater than that of the substrate. Conversely, if the transmittance spectrum of the substrate is enveloping at the lower edge of the transmittance spectrum of the sample, it means that the refractive index of the sample is smaller than that of the substrate.

[0020] As a preferred technical solution of the present invention, the calculation of the interference order m in step (3) uses the formula 4πn satisfied at the extreme point sam d / λ m =mπ, where n sam is the refractive index of the sample.

[0021] In the present invention, the interference order can be expressed as 4πn sam d / λ m =mπ, that is By deduction, we can conclude When the interference point interval is small, m is not easy to determine. We can consider that the difference between adjacent interference points m is 1, and m gradually decreases along the direction of increasing wavelength. The parity rule of m is that the extreme point tangent to the substrate transmittance is an even-order interference point to help determine the sequence of m.

[0022] In the present invention, the formula 4πn sam d / λ m Although =mπ is only valid for dispersion-free films, small dispersion will not cause large errors.

[0023] In the present invention, at the extreme value, the phase angle is Applying this formula to the expression of transmittance, the transmittance of odd interference order and even interference order is obtained as follows:

[0024]

[0025]

[0026] Comparing the expressions of even-order transmittance and substrate transmittance, it can be found that when the substrate absorption is 0 or very small in the long-wave region, the even-order transmittance is equal to the substrate transmittance. Therefore, the extreme point tangent to the substrate transmittance is the even-order interference point, and it can be proved that when n sam >n sub When T odd <T even , that is, the overall transmission curve is below the transmission curve of the substrate. sam <n sub The opposite is true.

[0027] As a preferred technical solution of the present invention, step (4) is based on the formula Solving for n sam 2 The quadratic equation gives the approximate refractive index n of the odd extreme points sam =[β±(β 2 -n air 2 n sub 2 )1 / 2 ] 1 / 2 ,in Where n air is the refractive index of air, n sub Refractive index for the substrate.

[0028] In the present invention, when the sample refractive index is greater than the substrate refractive index, only one root satisfies this condition. After determining the refractive index of the odd-numbered interference point, the formula 4πn sam d / λ m =mπ to calculate a series of thickness values, and then determine the refractive index of the even-numbered interference points through the average value of the thickness values ​​and the optical path length of the even-numbered points. Here we get a preliminary approximation of the refractive index.

[0029] As a preferred technical solution of the present invention, the approximate refractive index of the odd-numbered extreme point obtained in step (4) is substituted into the formula 4πn sam d / λ m =mπ to obtain a series of thickness values ​​d, and then determine the approximate refractive index of the even-numbered extreme points through the average value of the thickness values ​​and the optical path length of the even-numbered points.

[0030] As a preferred technical solution of the present invention, step (5) is based on the approximate refractive index of the even-numbered extreme point, and the expression of the transmittance modulated by the sample optical constant and thickness is introduced: The extinction coefficient and the absorption coefficient of the even-numbered extreme value points are calculated using an iterative method.

[0031] In the present invention, the transmittance is modulated by the sample optical constant and thickness by The derivation principle is as follows:

[0032] like Figure 1 As shown, the amplitudes of the reflected electric field and the transmitted electric field at each dielectric interface ij relative to the incident field are given by the corresponding Fresnel coefficients:

[0033]

[0034] Complex refractive index

[0035] For the calculation of the system of finite thickness sample on finite thickness transparent substrate, it is necessary to first calculate the system of finite thickness film bounded by two semi-infinite media. For the incident medium, sample and substrate medium, the electric field amplitude of the wave transmitted and reflected by the film is given by the following coefficients. For different incident directions (air-sample-substrate or substrate-sample-air), the reflection and transmission directions are opposite.

[0036] When the incident direction is air-sample-substrate:

[0037]

[0038]

[0039] Where, t air-sam represents the amplitude of the transmitted electric field at the air-sample interface, t sam-sub represents the amplitude of the transmitted electric field at the sample-substrate interface, r air-sam represents the amplitude of the reflected electric field at the air-sample interface, r sam-sub Represents the amplitude of the reflected electric field at the sample-substrate interface.

[0040] When the incident direction is substrate-sample-air:

[0041]

[0042]

[0043] Where, t sub-sam represents the amplitude of the transmitted electric field at the substrate-sample interface, t sam-air represents the amplitude of the transmitted electric field at the sample-air interface, r sub-sam represents the amplitude of the reflected electric field at the substrate-sample interface, r sam-air Represents the amplitude of the reflected electric field at the sample-air interface.

[0044] Ψ / 2 is the phase difference of the wave between the upper and lower interfaces of the sample

[0045]

[0046] The real and imaginary parts of Ψ are

[0047]

[0048] Im(Ψ)=4πk sam d / λ=αd

[0049] α=4πk / λ is usually called the absorption coefficient, It is called the phase angle.

[0050] According to electromagnetic theory, for a system where a finite-thickness film is bounded by two semi-infinite media, the reflectivity and transmittance of the film are defined as:

[0051] R=r·r *

[0052] R′=r′·r ′*

[0053]

[0054] Where R and T are the reflectivity and transmittance when the incident direction is air-sample-substrate, respectively, and R' represents the reflectivity when the incident direction is substrate-sample-air.

[0055] According to the thin film optics of Knittl et al. (Knittl, Zdenek.Optics of thin films: an optical multilayer theory [M]. Wiley, 1976.), the transmittance and reflectance of a finite substrate (when the incident direction is air-sample-substrate) are given by the following expressions, which are applicable to transparent and weakly absorbing substrates:

[0056]

[0057]

[0058]

[0059] The factor U is the result of taking into account the weak absorption in the substrate, T s is the transmittance of the bare substrate. ρ is the reflectivity of the air-substrate interface.

[0060] Generally, the absorption of the substrate used in transmission experiments is close to zero or very small. In order to simplify the calculation, a substrate with very small absorption can be selected for the experiment. In this way, K9 glass is used in this example. After reorganizing the expression of transmittance, we get the expression of transmittance modulated by the sample optical constant and thickness, as shown below:

[0061]

[0062] A, B, C, and D are algebraic functions of the optical constants and thickness of the sample and adjacent medium.

[0063] The weak absorption U of the substrate and the reflectivity ρ of the substrate are both needed in subsequent calculations, so U and ρ are first calculated through the transmission spectrum and reflection spectrum of the substrate.

[0064] In the present invention, the transmittance value at the even-numbered extreme value depends largely on k2, but weakly on n2. Therefore, by using the approximate value of the refractive index n2, the expression of the transmittance modulated by the sample optical constants and thickness obtained above is An iterative method can be used to determine a more accurate value of the extinction coefficient k2 at the even extreme value. The approximate value of the refractive index required for calculation is given by the approximate calculation of the odd points in the previous step. The refractive index of the even interference point is determined by the average value of the thickness value and the optical path of the even point. The average value of the refractive index of the two neighboring odd points of the even point can also be used as the approximate value of the refractive index of the even point.

[0065] In the present invention, the iterative method of step (5) can be:

[0066] Will Arrange as And note that the extreme points also satisfy relationship, and 4πk sam d / λ=αd, then αd*n sam =mπ*k sam , which can be used as the judgment condition for the end of iteration, specifically written as |log(expαd)*n sam / (m*π*k sam )-1|>10 -9 , before entering the loop, give the initial value of expαd. Since the wavelength range where interference occurs is the low absorption region and the absorption coefficient is close to 0, the initial value can be set to a number slightly greater than 1. In the loop, let k sam =log(expαd)*n sam / (m*π), and then use the obtained k sam Substitute into the algebraic expression of u, v, s, t, Y, Z, A, B, C, D, and notice that because it satisfies m is an even number, so C = -4*Z*Y. Substitute the obtained A, B, C, and D into the expression expαd can be obtained. If the iteration end condition is not met at this time, the loop will be entered again until the condition is met. In this way, the approximate absorption coefficient and extinction coefficient values ​​of the even extreme value points are obtained.

[0067] As a preferred technical solution of the present invention, step (6) brings the extinction coefficient and absorption coefficient of the two neighboring even-numbered extreme points obtained in step (5) into the expression of transmittance modulated by the optical constant and thickness of the sample: The refractive index of the odd-numbered extreme points is iteratively obtained.

[0068] In the present invention, the iterative method of step (6) may be:

[0069] The iteration end judgment condition can be set to |T / T odd -1|>10 -5 , give the refractive index an initial value greater than 0 and less than the refractive index of CsPbBr3, for example 1, and set the growth step size to 10 -5 , and then the refractive index n sam Substitute into the algebraic expression of u, v, s, t, Y, Z, A, B, C, D, and notice that because it satisfies So C = -2*(4*n sub *k sam 2 -Z*Y+p*U 2 *(Z*Y+4*nsub *k sam 2 ), substitute into the transmittance expression T can be obtained. If the iteration end condition is not met at this time, the loop will be entered again until the condition is met.

[0070] Preferably, step (7) substitutes the refractive index of the odd-numbered extreme point in step (6) into the formula 4πn sam d / λ m =mπ to obtain the sample thickness d.

[0071] As a preferred technical solution of the present invention, the single oscillator dispersion model in step (9) is:

[0072] As a preferred technical solution of the present invention, the obtained refractive index dispersion curve and the sample thickness d are substituted into a transmittance model to obtain an extinction coefficient dispersion curve.

[0073] In the present invention, the extinction coefficient dispersion curve can be obtained by substituting the obtained refractive index dispersion curve and sample thickness into the transmittance model. Specifically, the extinction coefficient dispersion curve can be obtained by: the refractive index, sample thickness and transmittance are known, and the iteration condition is set to |log(expαd)*λ / (4*π*d*k sam )-1|>10 -9 , before entering the loop, set k sam and the initial value of α. The absorption coefficient in the absorption zone is large, so the initial value can be appropriately set to a larger number, such as k sam =1, α=10, after entering the iteration loop, k sam =log(expαd)*λ / (4*π*d), The obtained k sam and Substitute the obtained A, B, C, D into the algebraic expression of u, v, s, t, Y, Z, A, B, C, D expαd can be obtained. If the iteration end condition is not met at this time, the loop will be entered again until the condition is met.

[0074] In the present invention, the formula required for calculation also includes:

[0075]

[0076]

[0077] A=16n sub (1-ρ)(n sam 2 +k sam 2 )

[0078] B=st-Usvρ

[0079]

[0080] D=uv-U 2 tuρ

[0081] u=(n air -n sam ) 2 +k sam 2

[0082] v=(n sam -n sub ) 2 +k sam 2

[0083] s=(n air +n sam ) 2 +k sam 2

[0084] t=(n sam +n sub ) 2 +k sam 2

[0085] Y=n sam 2 -n air 2 +k sam 2

[0086] Z=n sam 2 -n sub 2 +k sam 2

[0087] The transmittance, reflectance, and absorption of the substrate are defined by the following equations:

[0088]

[0089]

[0090]

[0091]

[0092] When the substrate absorption is 0 or very small, the transmittance, T s =(1-ρ) / (1+ρ)=(2nair n sub ) / (n air 2 +n sub 2 ).

[0093] Compared with the prior art, the present invention has at least the following beneficial effects:

[0094] The present invention provides a method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal through a transmission spectrum. The method can obtain information of a micron-sized sample and is simpler, faster and cheaper than the existing ellipsometer test. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 A system schematic diagram of the calculation method provided by the present invention;

[0096] Figure 2 Transmission spectra of the transparent substrate and the sample to be tested provided in the embodiments of the present invention;

[0097] Figure 3 A refractive index-photon energy relationship diagram of a sample provided in an embodiment of the present invention;

[0098] Figure 4 A refractive index dispersion curve diagram of a sample provided in an embodiment of the present invention;

[0099] Figure 5 This is an extinction coefficient dispersion diagram of the sample provided in the embodiment of the present invention.

[0100] The present invention is further described in detail below. However, the following examples are only simplified examples of the present invention and do not represent or limit the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims. DETAILED DESCRIPTION

[0101] The technical solution of the present invention is further described below by specific implementation methods. It should be understood by those skilled in the art that the embodiments are only to help understand the present invention and should not be regarded as specific limitations of the present invention.

[0102] Example 1

[0103] This embodiment provides a method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal by using a transmission spectrum, the method comprising the following steps:

[0104] (1) Testing the micro-area transmission spectrum of the sample. The testing method of the micro-area transmission spectrum of the sample is as follows: according to the transmission intensity spectra of the sample to be tested, the transparent substrate and the air obtained by the test, the transmission light intensity of the sample to be tested and the transmission light intensity of the transparent substrate are divided by the transmission light intensity of the air to obtain the transmission spectra of the sample to be tested and the transparent substrate, such as Figure 2 As shown;

[0105] The test device and method of step (1) refer to patent CN112964655A;

[0106] In the entire visible spectrum, the experimentally measured transmittance and reflectance of the substrate are basically constant, 0.773 and 0.05 respectively. U=exp(-α s d s ) It is easy to calculate that the refractive index n of the substrate is 1.424, p is 0.0306, and U is 0.8235. The specific calculation method is to rearrange the above formula to get Let exp(-α s d s ) is a number slightly greater than 0, such as 0.1, ρ is set to 0, and the loop end condition is set to |exp(-α s d s )-2*exp(-α s d s )*ρ+(1-T s )*(1-ρ 2 *[exp(-α s d s )] 2 )|, within the loop, the increment step of ρ is 10 -6 ,Then Then we can get the results of p and U. Solution The equation can be used to obtain n as 1.424;

[0107] (2) Read the wavelength λ of the extreme point of the micro-area transmission spectrum m and transmittance T m , as shown in Table 1;

[0108] (3) The wavelength λ passing through the extreme point and its adjacent extreme point m , substitute into the formula 4πn sam d / λ m =mπ, calculate the interference order m of the extreme point, the results are shown in Table 1;

[0109] The interference order can be expressed as 4πn sam d / λ m =mπ, that is By deduction, we can conclude

[0110] (4) According to the formula Solving for n sam 2 The quadratic equation gives the approximate refractive index n of the odd extreme points sam =[β±(β 2 -n air 2 n sub 2 ) 1 / 2 ] 1 / 2 ,in

[0111] (5) Substitute the approximate refractive index of the odd-numbered extreme point obtained in step (4) into the formula 4πn sam d / λ m = mπ to obtain a series of thickness values ​​d, the results are shown in Table 2, and then the approximate refractive index of the even-numbered extreme points is determined by the average value of the thickness value and the optical path length of the even-numbered points;

[0112] According to the formula Solving for n sam 2 The quadratic equation gives the approximate refractive index n of the odd extreme points sam =[β±(β 2 -n air 2 n sub 2 ) 1 / 2 ] 1 / 2 ,in

[0113] After determining the refractive index of the odd interference point, the formula 4πn sam d / λ m =mπ to calculate a series of thickness values;

[0114] According to the approximate refractive index of the even-numbered extreme points, the expression of transmittance modulated by the sample optical constants and thickness is substituted into The extinction coefficient and absorption coefficient of the even-numbered extreme point are calculated using an iterative method, and the results are shown in Table 3;

[0115] The specific iterative method is to rearrange the above transmittance expression into And note that the extreme points also satisfy relationship, and 4πk sam d / λ=αd, then αd*n sam=mπ*k sam , which can be used as the judgment condition for the end of iteration, specifically written as |log(expαd)*n sam / (m*π*k sam )-1|>10 -9 , before entering the loop, give the initial value of expαd. Since the wavelength range where interference occurs is the low absorption region and the absorption coefficient is close to 0, the initial value can be set to a number slightly greater than 1. In the loop, let k sam =log(expαd)*n sam / (m*π), and then use the obtained k sam Substitute into the algebraic expression of u, v, s, t, Y, Z, A, B, C, D, and notice that because it satisfies m is an even number, so C = -4*Z*Y. Substitute the obtained A, B, C, and D into the expression expαd can be obtained. If the iteration end condition is not met at this time, the loop will be entered again until the condition is met;

[0116] (6) Substitute the extinction coefficient and absorption coefficient of the two neighboring even-numbered extreme points obtained in step (5) into the expression of transmittance modulated by the sample optical constant and thickness: Iteratively calculating the refractive index of the odd-numbered extreme value points;

[0117] The specific iteration method is: The iteration end judgment condition can be set to |T / T odd -1|>10 -5 , give the refractive index an initial value greater than 0 and less than the refractive index of CsPbBr3, for example 1, and set the growth step size to 10 -5 , and then the refractive index n sam Substitute into the algebraic expression of u, v, s, t, Y, Z, A, B, C, D, and notice that because it satisfies So C = -2*(4*n sub *k sam 2 -Z*Y+p*U 2 *(Z*Y+4*n sub *k sam 2 ), substitute into the transmittance expression T can be obtained. If the iteration end condition is not met at this time, the loop will be entered again until the condition is met;

[0118] (7) Substitute the refractive index of the odd-numbered extreme point in step (6) into the formula 4πn sam d / λ m=mπ to obtain the sample thickness d. The results are shown in Table 4. The average value is 3135.60nm. The result of AFM measurement is 3164nm, indicating that the error between the calculated result of this scheme and the true value is less than 1%;

[0119] (8) Using the optical path of the even-numbered extreme value points and the determined thickness d, the refractive index of a series of even-numbered extreme value points is calculated. The results are shown in Table 5.

[0120] (9) Using the single-oscillator dispersion model Substitute a series of wavelengths and refractive indices corresponding to the odd and even extreme points to calculate the E of the sample. d The dispersion energy and E0 single oscillator energy are shown in Table 5. At the same time, the refractive index dispersion curve of the sample is plotted as Figure 4 As shown;

[0121] (10) Substitute the refractive index dispersion curve and sample thickness obtained in step (9) into the expression of transmittance modulated by the sample optical constant and thickness: The extinction coefficient dispersion curve is obtained by iterative calculation, such as Figure 5 As shown;

[0122] The specific iteration method is that the refractive index, sample thickness and transmittance are known, and the iteration condition is set to |log(expαd)*λ / (4*π*d*k sam )-1|>10 -9 , before entering the loop, set k sam and the initial value of α. The absorption coefficient in the absorption zone is large, so the initial value can be appropriately set to a larger number, such as k sam =1, α=10, after entering the iteration loop, k sam =log(expαd)*λ / (4*π*d), The obtained k sam and Substitute the obtained A, B, C, D into the algebraic expression of u, v, s, t, Y, Z, A, B, C, D expαd can be obtained. If the iteration end condition is not met at this time, the loop will be entered again until the condition is met.

[0123] Table 1

[0124]

[0125]

[0126] Table 2

[0127] λ(nm) 709.13 676.16 648.2 622.6 600.8 581.8 565.5 552.4 542 m 41 43 45 47 49 51 53 55 57 T 0.65 0.652 0.647 0.64 0.636 0.629 0.62 0.613 0.58 n 2.304 2.298 2.313 2.335 2.348 2.370 2.399 2.422 2.534 d(nm) 3154.7 3163.3 3152.2 3132.5 3134.4 3129.5 3122.8 3135.7 3048.5

[0128] Table 3

[0129]

[0130] Table 4

[0131]

[0132]

[0133] Table 5

[0134]

[0135] The applicant declares that the above is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention are within the protection scope and disclosure scope of the present invention.

Claims

1. A method for calculating the refractive index, extinction coefficient and thickness of a micron-sized single crystal by transmission spectrum, characterized in that: The method comprises the following steps: (1) Micro-area transmission spectrum of the test sample; (2) Read the wavelength λ at the extreme point of the micro-area transmission spectrum m and transmittance T m ; (3) The wavelength λ passing through the extreme point and its adjacent extreme point m Calculate the interference order m of the extreme point; (4) Using the transmittance T of the odd extreme point odd Calculate the approximate refractive index at odd extreme points; (5) At the even-numbered extreme value point, the approximate refractive index of the two neighboring odd-numbered extreme value points is averaged as an approximate value, and is substituted into the expression of the transmittance modulated by the optical constant and thickness of the sample, and the extinction coefficient and absorption coefficient of the even-numbered extreme value point are iteratively calculated; (6) At the odd-numbered extreme value point, the average value of the absorption coefficient of the two neighboring even-numbered extreme value points is used as an approximate value, and substituted into the expression of the transmittance modulated by the optical constant and thickness of the sample, and the refractive index of the odd-numbered extreme value point is calculated by iterative calculation; (7) using the refractive index and optical path length of the odd-numbered extreme points, calculating the sample thickness corresponding to a series of odd-numbered extreme points, and taking the average value to obtain the sample thickness d; (8) Using the optical path of the even-numbered extreme value points and the determined thickness d, calculate the refractive index of a series of even-numbered extreme value points; (9) Using the single oscillator dispersion model, substituting the wavelengths and refractive indices corresponding to a series of odd-numbered extreme points and even-numbered extreme points, the E of the sample is calculated. d Dispersion energy and E0 single oscillator energy, and the refractive index dispersion curve of the sample is plotted at the same time; (10) using the obtained refractive index dispersion curve and the sample thickness d to substitute into the expression of transmittance modulated by the sample optical constant and thickness to obtain the extinction coefficient dispersion curve; Step (4) According to the formula Solving for n sam 2 The quadratic equation gives the approximate refractive index n of the odd extreme points sam =[β±(β 2 -n air 2 n sub 2 ) 1 / 2 ] 1 / 2 ,in Where n air is the refractive index of air, n sub is the refractive index of the substrate; Step (5) Substitute the approximate refractive index of the even-numbered extreme point into the expression of the transmittance modulated by the sample optical constant and thickness: The extinction coefficient and the absorption coefficient of the even-numbered extreme value points are calculated by an iterative method, wherein A, B, C and D are algebraic functions of the optical constants and thicknesses of the sample and the adjacent medium.

2. The method according to claim 1, characterized in that The testing method of the micro-area transmission spectrum of the sample in step (1) is: according to the transmission intensity spectra of the sample to be tested, the transparent substrate and the air obtained by the test, the transmission light intensity of the sample to be tested and the transmission light intensity of the transparent substrate are divided by the transmission light intensity of the air to obtain the transmission spectrum of the sample to be tested and the transparent substrate.

3. The method according to claim 1, characterized in that: Step (3) The interference order m is calculated using the formula 4πn satisfied at the extreme point sam d / λ m =mπ, where n sam is the refractive index of the sample.

4. The method according to claim 1, characterized in that Substitute the approximate refractive index of the odd-numbered extreme point obtained in step (4) into the formula 4πn sam d / λ m =mπ to obtain a series of thickness values ​​d, and then determine the approximate refractive index of the even-numbered extreme points through the average value of the thickness values ​​and the optical path length of the even-numbered points.

5. The method according to claim 1, characterized in that Step (6) Substitute the extinction coefficient and absorption coefficient of the two neighboring even-numbered extreme points obtained in step (5) into the expression of transmittance modulated by the sample optical constant and thickness: The refractive index of the odd-numbered extreme points is iteratively obtained.

6. The method according to claim 1, characterized in that Step (7) Substitute the refractive index of the odd-numbered extreme point in step (6) into the formula 4πn sam d / λ m =mπ to obtain the sample thickness d.

7. The method according to claim 1, characterized in that The single oscillator dispersion model in step (9) is:

8. The method according to claim 1, characterized in that Step (10) Substitute the refractive index dispersion curve and sample thickness obtained in step (9) into the expression of transmittance modulated by the sample optical constant and thickness: The extinction coefficient dispersion curve is obtained by iterative calculation.

9. The method according to any one of claims 1 to 8, characterized in that: The method comprises the following steps: (1) testing a micro-area transmission spectrum of a sample, wherein the testing method of the micro-area transmission spectrum of the sample is as follows: according to the transmission intensity spectra of the sample to be tested, the transparent substrate and the air obtained by the test, the transmission light intensity of the sample to be tested and the transmission light intensity of the transparent substrate are divided by the transmission light intensity of the air to obtain the transmission spectra of the sample to be tested and the transparent substrate; (2) Read the wavelength λ at the extreme point of the micro-area transmission spectrum m and transmittance T m ; (3) The wavelength λ passing through the extreme point and its adjacent extreme point m , substitute into the formula 4πn sam d / λ m =mπ, calculate the interference order m of the extreme point; (4) According to the formula Solving for n sam 2 The quadratic equation gives the approximate refractive index n of the odd extreme points sam =[β±(β 2 -n air 2 n sub 2 ) 1 / 2 ] 1 / 2 ,in (5) Substitute the approximate refractive index of the odd-numbered extreme point obtained in step (4) into the formula 4πn sam d / λ m =mπ to obtain a series of thickness values ​​d, and then determine the approximate refractive index of the even-numbered extreme points through the average value of the thickness value and the optical path length of the even-numbered points; According to the approximate refractive index of the even-numbered extreme points, the expression of transmittance modulated by the sample optical constants and thickness is substituted into The extinction coefficient and the absorption coefficient of the even-numbered extreme value points are calculated using an iterative method; (6) Substitute the extinction coefficient and absorption coefficient of the two neighboring even-numbered extreme points obtained in step (5) into the expression of transmittance modulated by the sample optical constant and thickness: Iteratively calculating the refractive index of the odd-numbered extreme value points; (7) Substitute the refractive index of the odd-numbered extreme point in step (6) into the formula 4πn sam d / λ m =mπ to obtain the sample thickness d; (8) Using the optical path of the even-numbered extreme value points and the determined thickness d, calculate the refractive index of a series of even-numbered extreme value points; (9) Using the single-oscillator dispersion model Substitute the wavelengths and refractive indices corresponding to a series of odd-numbered extreme points and even-numbered extreme points to calculate the E of the sample. d Dispersion energy and E0 single oscillator energy, and the refractive index dispersion curve of the sample is plotted at the same time; (10) Substitute the refractive index dispersion curve and sample thickness obtained in step (9) into the expression of transmittance modulated by the sample optical constant and thickness: The extinction coefficient dispersion curve is obtained by iterative calculation.

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