Parameter fitting calculation method and system of composite material layer
By using the effective medium EMA general model and iterative parameter adjustment method, the problem of poor fitting accuracy of composite material layers in the prior art is solved, and the parameters of composite material layers are obtained efficiently and flexibly.
Patent Information
- Application Number
- CN202210583699.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-05-25
- Publication Date
- 2025-12-05
- Estimated Expiration
- 2042-05-25
AI Technical Summary
Existing multi-component effective medium models have poor accuracy and high complexity when fitting parameters of composite material layers, and cannot be applied to composite material layers with complex structures.
The effective medium EMA general model is adopted, and the parameters of the composite material layer are adjusted iteratively, including the amount of material components, dielectric constant, volume fraction, thickness and depolarization factor, until the fitted spectrum meets the accuracy requirements of the measured spectrum.
It improves the accuracy and flexibility of parameter fitting for composite material layers, is applicable to parameter acquisition for any composite material layer, and reduces the limitations of the model.
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Figure CN115060661B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the effective medium theory calculation field in the optical / material field, and more particularly, to a parameter fitting calculation method and system for a composite material layer. BACKGROUND
[0002] In the field of spectral measurement, the basic principle process of material parameter measurement mainly includes the following steps:
[0003] 1. Natural light passes through a polarizer or a polarizer and a (rotating) wave plate to obtain polarized light.
[0004] 2. The new polarized light obtained by the reflection or transmission of the sample material.
[0005] 3. The new polarized light passes through the (rotating) wave plate and the analyzer of the polarizer to obtain the change of light intensity information.
[0006] 4. The light intensity change information is processed to obtain the thickness of the material and the complex refractive index (or dielectric constant) of the material, wherein the complex refractive index and the dielectric constant have a specific conversion relationship expression.
[0007] In the process of processing light intensity information, the complex refractive index of the material needs to be fitted, that is, the dielectric constant of the material needs to be calculated. In actual situations, each layer of film may be a composite material containing multiple components, so the effective medium (EMA) of the material needs to be calculated. The basic idea is to regard the mixed medium as an effective medium with a single effective dielectric constant tensor in a specific spectral range, that is, to calculate the effective dielectric constant.
[0008] The effective medium (EMA) theory of the material contains many different models, of which the five most common are: linear model, inverse proportional model, Maxwell-Garnett model, Lorentz-Lorentz model and Bruggeman model. In the past research, in order to facilitate the expression and calculation of the five models, a general formula for binary EMA has been proposed. However, as the complexity of materials increases, more and more different materials are mixed together, and the formula of binary EMA cannot meet the current needs, so the model of multi-EMA needs to be added to the fitting process of the effective medium of the material, but the existing multi-EMA model is complex and can only be applied to a fixed number of models, and the fitting accuracy is poor. SUMMARY
[0009] The present application aims at the technical problems existing in the prior art, and in order to effectively improve the fitting accuracy, a general formula for multi-EMA is proposed, and a parameter fitting calculation method and system for a composite material layer are provided.
[0010] According to a first aspect of the present application, a parameter fitting calculation method of a composite material layer is provided, comprising:
[0011] a. obtaining a measured spectrum of a sample to be measured, the sample to be measured comprising a composite material layer;
[0012] b. fitting calculating a fitting spectrum of the sample to be measured based on an effective medium approximation (EMA) general model according to parameters of the composite material layer;
[0013] c. if the fitting spectrum meets the accuracy requirement of the measured spectrum, obtaining the parameters of the composite material layer; if the fitting spectrum does not meet the accuracy requirement of the measured spectrum, adjusting the parameters of the composite material layer, repeating b and c for iteration until the fitting spectrum meets the accuracy requirement of the measured spectrum, and obtaining the parameters of the composite material layer;
[0014] wherein the parameters of the composite material layer at least include the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer, the depolarization factor representing the shape of the composite material layer.
[0015] According to a second aspect of the present application, a parameter fitting calculation system of a composite material layer is provided, comprising:
[0016] an obtaining module configured to obtain a measured spectrum of a sample to be measured, the sample to be measured comprising a composite material layer;
[0017] a fitting calculation module configured to fitting calculate a fitting spectrum of the sample to be measured based on an effective medium approximation (EMA) general model according to parameters of the composite material layer;
[0018] an iteration module configured to, if the fitting spectrum meets the accuracy requirement of the measured spectrum, obtain the parameters of the fitting composite material layer; if the fitting spectrum does not meet the accuracy requirement of the measured spectrum, adjust the parameters of the composite material layer, repeat the fitting calculation module and the iteration module until the fitting spectrum meets the accuracy requirement of the measured spectrum, and obtain the parameters of the composite material layer;
[0019] wherein the parameters of the composite material layer at least include the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer, the depolarization factor representing the shape of the composite material layer.
[0020] The application provides a parameter fitting calculation method and system of a composite material layer, constructs an effective medium EMA general model, is not limited to a certain model or a limited number of models, and iteratively calculates a fitting spectrum of a to-be-measured sample by adjusting any parameter of the composite material layer. When the parameter is adjusted, the method is not limited by a certain specific model or a few specific models, and can be applied to acquisition of parameters of a to-be-measured sample containing any composite material layer. BRIEF DESCRIPTION OF DRAWINGS
[0021] Figure 1 A parameter fitting calculation method of a composite material layer provided by the application is shown in the flowchart.
[0022] Figure 2-1 A structure diagram of a composite material layer suitable for a Maxwell-Garnett model is shown in the figure.
[0023] Figure 2-2 A structure diagram of a composite material layer suitable for a Bruggeman model is shown in the figure.
[0024] Figure 2-3 A structure diagram of a composite material layer suitable for a linear model is shown in the figure.
[0025] Figure 2-4 A structure diagram of a composite material layer suitable for an inverse proportional model is shown in the figure.
[0026] Figure 3 A structure diagram of a composite material layer suitable for an inverse proportional model is shown in the figure.
[0027] Figure 4 A structure diagram of a parameter fitting calculation system of a composite material layer provided by the application is shown in the figure. DETAILED DESCRIPTION
[0028] The specific embodiments of the application are described in further detail below in combination with the drawings and examples. The following examples are used to illustrate the application, but are not used to limit the scope of the application.
[0029] Example 1
[0030] A parameter fitting calculation method of a composite material layer, as shown in Figure 1 The parameter fitting calculation method mainly includes the following steps:
[0031] a. Obtain a measurement spectrum of a to-be-measured sample, wherein the to-be-measured sample includes a composite material layer.
[0032] It can be understood that the optical measuring instrument such as a reflectometer, a transmission instrument and an ellipsometer can be used to obtain the light intensity change information of the sample to be measured. The Mueller matrix of the sample to be measured can be calculated through the Fourier transform of the light intensity change information, so that the spectral information of the sample, that is, the measurement spectrum of the sample to be measured, is obtained. The sample to be measured in the embodiment of the present application includes a composite material layer, and the composite material layer includes a plurality of different material components, and the thickness, volume ratio, dielectric constant and distribution structure of each material component are different, so that the overall structure of the composite material layer is relatively complex.
[0033] b. According to the parameters of the composite material layer, the fitting spectrum of the sample to be measured is fitted based on the effective medium EMA general model.
[0034] As an embodiment, the fitting spectrum of the sample to be measured is fitted based on the effective medium EMA general model according to the parameters of the composite material layer in b, including: fitting the effective dielectric constant of the composite material layer based on the effective medium EMA general model according to the number of material components of the composite material, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component and the depolarization factor of the composite material, to obtain the fitting effective dielectric constant of the composite material layer; and calculating the fitting spectrum of the sample to be measured according to the fitting effective dielectric constant of the composite material layer and the fitting thickness of the composite material layer.
[0035] It can be understood that the traditional effective medium EMA model of the composite material layer is a specific model or a few specific models, which is only applicable to simulate relatively simple composite material layers and has great limitations.
[0036] The embodiment of the present application proposes a general effective medium EMA model to fit the effective dielectric constant of the composite material layer, which is referred to as the fitting effective dielectric constant below, in the face of a complex composite material layer. Specifically, the effective dielectric constant of the composite material layer is fitted based on the effective medium EMA general model according to the number of material components of the composite material layer, the dielectric constant of the main component, the dielectric constant of each material component, the volume ratio of each material component and the depolarization factor of the composite material, to obtain the fitting effective dielectric constant. The fitting spectrum of the sample to be measured is also related to the thickness of the composite material layer, so when fitting the spectrum of the sample to be measured, the thickness of the composite material layer needs to be fitted, and then the fitting spectrum of the composite material layer is calculated according to the fitting effective dielectric constant and the fitting thickness of the composite material layer.
[0037] c. if the fitting spectrum reaches the accuracy requirement of the measured spectrum, obtaining the parameters of the composite material layer; if the fitting spectrum does not reach the accuracy requirement of the measured spectrum, adjusting the parameters of the composite material layer, repeating steps b and c for iteration until the fitting spectrum reaches the accuracy requirement of the measured spectrum, and obtaining the parameters of the composite material layer; wherein the parameters of the composite material layer at least include the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer.
[0038] It can be understood that, in the above a, the measured spectrum of the sample to be measured is measured by the instrument, in b, the fitting spectrum of the composite material layer is calculated by the effective medium EMA general model fitting, the fitting spectrum and the measured spectrum are compared, if the fitting spectrum reaches the accuracy requirement of the measured spectrum, it can be considered that the dielectric constant of the main component of the fitting composite material layer, the dielectric constant of each material component, the volume ratio of each material component and the thickness of the composite material are the actual parameters of the composite material layer of the sample to be measured, and the fitting process is ended. If the fitting spectrum does not reach the accuracy requirement of the measured spectrum, the parameters of the composite material layer need to be adjusted, that is, one or more of the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer and the depolarization factor of the composite material layer are adjusted, and the effective dielectric constant of the composite material layer is fitted and calculated again by the effective medium EMA general model, the fitting spectrum of the sample to be measured is iteratively fitted by repeatedly adjusting the parameters of the composite material layer, until the fitting spectrum reaches the accuracy requirement of the measured spectrum, or the iteration number reaches the maximum iteration number set, and the parameters of the composite material layer at this time are obtained, mainly including the effective dielectric constant of the composite material of the sample to be measured and the thickness of the composite material layer.
[0039] As an embodiment, adjusting one or more of the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer and the depolarization factor includes: based on the provided parameters of the composite material layer of the sample to be measured, adjusting one or more of the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer and the depolarization factor, and the parameters of the composite material layer include the number of material components contained in the composite material layer and the material properties of each material component.
[0040] It can be understood that, in the process of iteratively fitting the fitting spectrum of the sample to be tested, how to adjust the parameters of the composite material layer of the sample to be tested will affect the iteration efficiency and accuracy of the effective medium EMA general model. Since the provider of the sample to be tested will provide a set of reference parameters of the sample to be tested in advance, mainly including the composition parameters of the composite material layer, the composition parameters of the composite material layer including the number of material components of the composite material layer and the material properties of each material component. The embodiment of the present application can adjust the parameters of the composite material layer based on the set of reference parameters of the sample to be tested provided by the provider in advance. Thus, adjusting the parameters of the composite material layer within a reference range will be more optimal, making the iteration process more efficient and the iteration result more accurate.
[0041] As an embodiment, according to the number of material components of the composite material layer, the dielectric constant of the main material component, the depolarization factor, the volume ratio of each material component, and the dielectric constant of each material component, the effective medium EMA general model of the composite material layer is constructed.
[0042] wherein the expression of the effective medium EMA general model is:
[0043]
[0044] wherein,
[0045] wherein m1≠m2;
[0046] wherein m1≠m2≠m3, at the (n-1)th order, wherein m1≠m2≠...≠mn-1;
[0047]
[0048] wherein m1≠m2;
[0049] wherein m1≠m2≠m3, at the (n-1)th order,
[0050]
[0051] wherein, N≥2 and is the number of material components of the composite material layer, m1, m2...m n-1 represent the m1, m2...m n-1 material components, respectively, the value range is 1 to N, (n-1) is the order, the value range of n is 2 to N, and m1≠m2≠...≠m n-1 , ε hwherein, κ is the depolarization factor, q is the depolarization factor, and ε is the permittivity of the main material component. wherein, Vm1 represents the volume fraction of the m1th material component, wherein, εm1 represents the permittivity of the m1th material component.
[0052] According to the expression of the effective medium approximation (EMA) general model, the effective medium approximation (EMA) general model is related to the permittivity of each material component of the composite layer, the permittivity of the main material component, the volume fraction of each material component, and the set depolarization factor, so when the effective permittivity of the composite layer of the sample under test is iteratively solved based on the effective medium approximation (EMA) general model, these parameters need to be adjusted.
[0053] wherein, it is to be noted that according to the structure of the composite layer of the sample under test and the set depolarization factor, the effective medium approximation (EMA) general model can be simplified, for example, according to the permittivity of the main material component of the composite layer and the depolarization factor, the effective medium approximation (EMA) general model can be simplified into a Maxwell-Garnett model, a Bruggeman model, a linear model, an inverse proportion model, or a Lorentz-Lorenz model.
[0054] wherein, specifically, when only one material component in the composite layer is the main material component (see Figure 2-1 , the b material component is the main material component of the composite layer), and the depolarization factor q = 1 / 3, the effective medium approximation (EMA) general model is a Maxwell-Garnett model, and the expression thereof is:
[0055]
[0056] wherein, ε h = ε m1 , and ε m1 is the permittivity of the main material component, and this model is suitable for the case where only one material component is dominant in the composite material.
[0057] When there is no dominant main material component in the composite layer (see Figure 2-2 , neither the a material component nor the b material component of the composite material is dominant), and the depolarization factor q = 1 / 3, the effective medium approximation (EMA) general model is a Bruggeman model, and the expression thereof is:
[0058]
[0059] wherein, ε h= ε represents the medium constant of the main material component as the effective medium constant of the composite material layer, and this model is suitable for the case where there is no dominant material component in the composite material layer.
[0060] When the multiple material components of the composite material layer are arranged in left-right layers, and each layer of material components is independent (see Figure 2-3 , the material component a and the material component b are arranged in left-right layers, and the material component a and the material component b are completely independent without overlapping), this case represents that the depolarization factor q tends to 0, but is not equal to 0, and is often recorded as q = 0, including q = 0 + and q = 0 - , which respectively represent that q is greater than zero and tends to 0, and q is less than zero and tends to 0, and the effective medium EMA general model is a linear model, and the expression is:
[0061] ε = f m1 ε m1 + f m2 ε m2 +... + f mN ε mN .
[0062] When the multiple material components of the composite material layer are arranged in top-bottom layers, and each layer of material components is independent (see Figure 2-4 , the material component a and the material component b are arranged in top-bottom layers, and the material component a and the material component b are completely independent without overlapping), this case represents that the depolarization factor q = 1, and the effective medium EMA general model is an inverse proportional model, and the expression is:
[0063]
[0064] When the dielectric constant of the main material component of the composite material layer is the dielectric constant of air, and the depolarization factor q = 1 / 3, the effective medium EMA general model is the Lorentz-Lorenz model, and the expression is:
[0065]
[0066] , where ε h = 1 represents that the medium constant of the main material component is the dielectric constant of air.
[0067] It can be understood that when the main material component of the composite material layer of the sample to be measured satisfies one of the above several cases, the effective dielectric constant of the composite material layer of the sample to be measured can be fitted and calculated based on the above one of the simplified models. In addition, the above only provides five simplified models, and in practice, the effective medium EMA general model can also be simplified into more models according to the composition of the composite material layer and the depolarization factor.
[0068] In addition, when using the effective medium approximation (EMA) general model, the depolarization factor q value can be changed to calculate the dielectric constant of Maxwell-Garnett, Lorentz-Lorenz, and Bruggeman models in non-1 / 3 cases, and the effective dielectric constant ε h , i.e. the dielectric constant of the main material component of the composite layer, so that the calculation is a pure mathematical solution.
[0069] As an example, based on the parameters of the composite layer, the fitting spectrum of the sample to be measured is calculated by fitting based on the effective medium approximation (EMA) general model, including: by adjusting the dielectric constant of the main component of the composite layer and the depolarization factor, determining the specific model corresponding to the effective medium approximation (EMA) general model; based on the specific model, the fitting spectrum of the sample to be measured is calculated by fitting based on the parameters of the composite layer.
[0070] If the composition of the composite layer and the depolarization factor cannot meet any of the simplified models provided above, the effective dielectric constant of the composite layer is fitted based on the original effective medium approximation (EMA) general model. In the fitting process, the number of material components of the composite layer, the dielectric constant of the main material component, and the depolarization factor can be mainly adjusted, and the dielectric constant of each material component of the composite layer and the volume fraction of each material component can be appropriately adjusted, as well as the thickness of the composite layer. Through the adjustment of multiple parameters, the fitting spectrum of the sample to be measured is iteratively calculated until the fitting spectrum of the sample to be measured meets the accuracy requirement of the measured spectrum. In the process of iteratively fitting the spectrum of the sample to be measured based on the provided effective medium approximation (EMA) general model, any of the above parameters can be adjusted, not limited to the adjustment parameters of the above certain model. The specific wide universality can be applied to the fitting calculation of the fitting spectrum of any different composite layer.
[0071] Example Two
[0072] A parameter fitting calculation method of a composite layer, referring to Figure 3 , the overall flowchart of the parameter fitting calculation method mainly includes the following steps:
[0073] Step 1, the light intensity change information of the sample to be measured can be obtained by using a reflectometer, a transmission instrument, and an ellipsometer, etc. The Mueller matrix of the sample to be measured can be calculated by Fourier transform of the light intensity information, so as to obtain the spectrum information of the sample, i.e. the measured spectrum of the sample to be measured.
[0074] Step 2, the number of layers of the composite material layer of the sample to be measured and the material properties of each layer of material component are required.
[0075] Wherein, the sample includes a composite material layer, the number of the composite material layer can be one or more layers, and the material properties of the composite material layer include the type of the material and the number of the material. For each layer of the composite material layer, the parameters of the corresponding composite material layer are finally obtained based on the effective medium average (EMA) general formula model provided in the embodiment.
[0076] In some embodiments, the sample further includes a single material layer, and the calculation of the thickness and the dielectric constant (or complex refractive index) of the single material layer is the prior art, which is not described here.
[0077] Step 3, the thickness of each layer of the sample to be measured and the dielectric constant or complex refractive index of the material are fitting target values, wherein the dielectric constant or complex refractive index of each material component can be provided by an experimental measurement table, a vibrator model or an EMA model. When the effective medium average (EMA) general formula model is used, the depolarization factor q and the dielectric constant ε h of the main component can be iterated to obtain different EMA model results, i.e. different fitting spectra of the sample to be measured. In the iteration process, the adjustable parameters include one or more of the number of material components of the composite material layer, the dielectric constant of each material component, the volume ratio of each material component, the dielectric constant of the main material component, the thickness of the composite material and the depolarization factor. The implementation method of the fitting iteration parameters includes but is not limited to the Levenberg-Marquardt method, the Newton method, the gradient descent method and the conjugate gradient method.
[0078] Step 4, the difference between the simulated spectrum and the measured spectrum is calculated, and if the accuracy requirement is met, it is considered that the thickness of each layer and the dielectric constant or complex refractive index of the composite material layer of the sample to be measured fitted in the EMA model are the actual values of the sample to be measured, and the fitted thickness of the composite material layer and the dielectric constant or complex refractive index of the composite material layer are output, and the measurement is completed; otherwise, the thickness of each layer, the component composition of the material, the vibrator model and the fitting parameter initial value of the EMA model are adjusted until the difference between the fitting spectrum and the measured spectrum meets the accuracy requirement or the iteration number reaches the maximum iteration number.
[0079] Step 5, after the iteration is stopped, the thickness of the composite material layer of the sample to be measured and the effective dielectric constant of the composite material layer are output.
[0080] The general effective medium average (EMA) model provided in the embodiment is compared with the conventional EMA fixed mode or binary EMA general formula calculation, the multi-element EMA can be compatible with the fixed mode of the multi-element EMA and the binary EMA general formula, and the depolarization factor q and the dielectric constant ε h of the main component can be more flexibly adjusted to calculate the effective dielectric constant ε of the composite material layer.
[0081] Embodiment three
[0082] A parameter fitting calculation system of a composite material layer, referring to Figure 4 The parameter fitting calculation system comprises an acquisition module 41, a fitting calculation module 42 and an iteration module 43, wherein:
[0083] The acquisition module 41 is used for acquiring a measured spectrum of a sample to be measured, the sample to be measured comprising a composite material layer; the fitting calculation module 42 is used for fitting and calculating a fitting spectrum of the sample to be measured based on an effective medium approximation (EMA) general model according to parameters of the composite material layer; the iteration module 43 is used for acquiring the parameters of the fitted composite material layer if the fitting spectrum reaches an accuracy requirement of the measured spectrum; if the fitting spectrum does not reach the accuracy requirement of the measured spectrum, the parameters of the composite material layer are adjusted, the fitting calculation module 42 and the iteration module 43 are repeatedly executed until the fitting spectrum reaches the accuracy requirement of the measured spectrum, and the parameters of the composite material layer are acquired; wherein the parameters of the composite material layer at least comprise a number of material components of the composite material layer, a dielectric constant of a main material component, a dielectric constant of each material component, a volume ratio of each material component, a thickness of the composite material and a depolarization factor of the composite material, the depolarization factor representing a shape of the composite material layer.
[0084] It can be understood that the parameter fitting calculation system of the composite material layer provided by the present application corresponds to the parameter fitting calculation method of the composite material layer provided by the foregoing embodiments, and the related technical features of the parameter fitting calculation system of the composite material layer can refer to the related technical features of the parameter fitting calculation method of the composite material layer, which will not be described here.
[0085] The parameter fitting calculation method and system of the composite material layer provided by the embodiments of the present application construct an effective medium approximation (EMA) general model, are not limited to a certain model or a limited number of models, and can iteratively calculate a fitting spectrum of a sample to be measured by adjusting any parameter of a composite material layer. The parameter fitting calculation method and system are not limited by a certain model or a few specific models when adjusting the parameters, and can be applied to the acquisition of parameters of any composite material layer sample to be measured.
[0086] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.
[0087] Those skilled in the art will appreciate that embodiments of the present application can be devised for a variety of applications. It is intended that the present application be limited only by the scope of the appended claims, and it is intended that various modifications and alterations made by those skilled in the art be considered as within the scope of the present application. The embodiments of the present application will be described with reference to the attached drawings, wherein:
[0088] The present application is described in reference to the drawings using a flowchart and / or a block diagram of the method, apparatus (system) and computer program product according to embodiments of the application. It will be understood that each block of the flowchart and / or block diagram, and combinations of blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.
[0089] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.
[0090] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.
[0091] While the preferred embodiments of the application have been described, additional variations and modifications can be made to the embodiments by those skilled in the art once they learn of the basic inventive concepts. Therefore, the appended claims are intended to cover all such modifications and variations as fall within the scope of the present application.
[0092] Obviously, many modifications and variations of the present application are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.
Claims
1. A method of parameter fitting calculation of a composite material layer, characterized in that, The method comprises the following steps: a. acquiring a measured spectrum of a sample to be measured, the sample to be measured comprising a composite material layer; b. fitting a fitting spectrum of the sample to be measured based on an effective medium approximation (EMA) general model according to parameters of the composite material layer; c. if the fitting spectrum meets the accuracy requirement of the measured spectrum, acquiring the parameters of the composite material layer; if the fitting spectrum does not meet the accuracy requirement of the measured spectrum, adjusting the parameters of the composite material layer, repeating steps b and c for iteration until the fitting spectrum meets the accuracy requirement of the measured spectrum, and acquiring the parameters of the composite material layer; wherein the parameters of the composite material layer at least include the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer, the depolarization factor representing the shape of the composite material layer; in step b, fitting the fitting spectrum of the sample to be measured based on the effective medium approximation (EMA) general model according to the parameters of the composite material layer, comprising: fitting the effective dielectric constant of the composite material layer based on the effective medium approximation (EMA) general model according to the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, and the depolarization factor of the composite material layer, to obtain the fitting effective dielectric constant of the composite material layer; calculating the fitting spectrum of the sample to be measured according to the fitting effective dielectric constant of the composite material layer and the fitting thickness of the composite material layer.
2. The parameter fitting calculation method according to claim 1, characterized in that, in step c, if the fitting spectrum does not meet the accuracy requirement of the measured spectrum, adjusting the parameters of the composite material layer, repeating steps b and c until the fitting spectrum meets the accuracy requirement of the measured spectrum, and acquiring the parameters of the composite material layer, comprising: if the fitting spectrum does not meet the accuracy requirement of the measured spectrum, adjusting one or more of the number of material components of the composite material, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer, repeating steps b and c until the fitting spectrum meets the accuracy requirement of the measured spectrum, and acquiring the thickness and the fitting effective dielectric constant of the composite material layer.
3. The parameter fitting calculation method according to claim 2, characterized in that, the adjustment of one or more of the number of material components of the composite material, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer, comprises: Adjust one or more of the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, the thickness of the composite material layer, and the depolarization factor of the composite material layer, based on the constitutive parameters of the composite material layer of the pre-provided to-be-measured sample, the constitutive parameters of the composite material layer including the number of material components included in the composite material layer and the material properties of each material component.
4. The parameter fitting calculation method of claim 1, wherein, Also includes: According to the number of material components of the composite material layer, the dielectric constant of the main material component, the depolarization factor, the volume ratio of each material component, and the dielectric constant of each material component, the effective medium EMA general model of the composite material layer is constructed.
5. The parameter fitting calculation method according to claim 4, characterized in that, The expression of the effective medium EMA general model is: wherein wherein ml ≠ m2; wherein ml≠m2≠m3, at the (n-1)th order, wherein ml≠m2≠...≠m n-1 ; wherein ml ≠ m2; where m1≠m2≠m3, at the (n-1)th order, wherein, N≥2 and is the number of material components of the composite layer, m1, m2...m n-1 respectively represent the m1, m2...m n-1 material components, the value range is 1 to N, (n-1) is the order, the value range of n is 2 to N, and m1≠m2≠...≠m n-1 , ε h is the dielectric constant of the main material component, the depolarization coefficient q is the depolarization factor; represents the volume fraction of the m1 material component, the dielectric constant of the m1 6. The parameter fitting calculation method according to claim 5, characterized in that, According to the dielectric constant of the main material component and the depolarization factor of the composite material layer, the effective medium EMA general model can be converted into Maxwell-Garnett model, Bruggeman model, linear model, inverse proportional model or Lorentz-Lorenz model.
7. The parameter fitting calculation method according to claim 6, characterized in that, According to the dielectric constant of the main material component and the depolarization factor of the composite material layer, the effective medium EMA general model can be converted into Maxwell-Garnett model, Bruggeman model, linear model, inverse proportional model or Lorentz-Lorenz model, including: When only one material component in the composite material layer is the main material component, and the depolarization factor q=1 / 3, the effective medium EMA general model is Maxwell-Garnett model, and its expression is: where ε h = ε m1 , ε m1 is the dielectric constant of the main material component; When there is no dominant main material component in the composite material layer, and the depolarization factor q=1 / 3, the effective medium EMA general model is Bruggeman model, and its expression is: wherein ε h = ε represents the medium constant of the main material component as the effective medium constant of the composite material layer; When the multi-layer material components of the composite material layer are arranged in left and right layers, and each layer of material components is independent, it means that the depolarization factor q tends to 0, and the effective medium EMA general model is linear model, and its expression is: e = f m1 e m1 + f m2 e m2 +... + f mN e mN ; When the multi-layer material components of the composite material layer are arranged in upper and lower layers, and each layer of material components is independent, it means that the depolarization factor q=1, and the effective medium EMA general model is inverse proportional model, and its expression is: When the dielectric constant of the main material component of the composite material layer is the dielectric constant of air, and the depolarization factor q=1 / 3, the effective medium EMA general model is Lorentz-Lorenz model, and its expression is: wherein ε h = 1 means that the main material component dielectric constant is air dielectric constant.
8. The parameter fitting calculation method of claim 6, wherein, According to the parameters of the composite material layer, the fitting spectrum of the to-be-measured sample is fitted and calculated based on the effective medium EMA general model in the b, including: By adjusting the dielectric constant of the main material component and the depolarization factor of the composite material layer, the specific model corresponding to the effective medium EMA general model is determined; Based on the specific model, the fitting spectrum of the to-be-measured sample is fitted and calculated according to the parameters of the composite material layer.
9. A parameter fitting computing system for composite material layers, characterized by, Including: An acquisition module is configured to acquire a measurement spectrum of a sample to be measured, the sample to be measured comprising a composite material layer; A fitting calculation module is configured to calculate a fitting spectrum of the sample to be measured based on an effective medium approximation (EMA) general model according to parameters of the composite material layer; An iteration module is configured to obtain the parameters of the composite material layer if the fitting spectrum reaches an accuracy requirement of the measurement spectrum, and to adjust the parameters of the composite material layer, and repeatedly execute the fitting calculation module and the iteration module until the fitting spectrum reaches the accuracy requirement of the measurement spectrum, and obtain the parameters of the composite material layer if the fitting spectrum does not reach the accuracy requirement of the measurement spectrum; The parameters of the composite material layer at least include a number of material components of the composite material layer, a dielectric constant of a main material component, a dielectric constant of each material component, a volume ratio of each material component, a thickness of the composite material, and a depolarization factor of the composite material, the depolarization factor representing a shape of the composite material layer. In the b, the fitting calculation module is configured to calculate the fitting spectrum of the sample to be measured based on the EMA general model according to the parameters of the composite material layer, including: The fitting calculation module is configured to calculate an effective dielectric constant of the composite material layer based on the EMA general model according to the number of material components of the composite material layer, the dielectric constant of the main material component, the dielectric constant of each material component, the volume ratio of each material component, and the depolarization factor of the composite material layer, to obtain a fitting effective dielectric constant of the composite material layer, and to calculate the fitting spectrum of the sample to be measured according to the fitting effective dielectric constant of the composite material layer and a fitting thickness of the composite material layer.
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Thin-flim characteristic measuring method using spectroellipsometer
US20040207844A1