Method and apparatus for analyzing multilayer thin film characteristics through algebraic analysis of ellipsometric signals

Abstract

The present invention relates to a method and an apparatus for analyzing multilayer thin film characteristics through algebraic analysis of ellipsometric signals and, more specifically, to a method and an apparatus for analyzing multilayer thin film characteristics through algebraic analysis of ellipsometric signals, whereby the refractive index and thickness of a multilayer thin film can be simultaneously analyzed through algebraic equation analysis of reflection or transmission signals of light obtained through ellipsometry measurement.

Description

Method and apparatus for characterizing multilayer thin films through algebraic analysis of ellipsometry signals

[0001] The present invention relates to a method and apparatus for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal, and more specifically, to a method and apparatus for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal, which simultaneously analyzes the refractive index and thickness of the multilayer thin film through the analysis of algebraic equations using a light reflection or transmission signal obtained through ellipsometry measurement.

[0002] Determining the refractive index and thickness of each thin film layer forming a multilayer thin film by measuring the change in polarization of transmitted or reflected light is called ellipsometry.

[0003] In the ellipsometry method, it is usually the ratio of the reflection coefficients of the incident s-polarized and p-polarized light. It measures and is a complex number The real part of the amplitude ratio Let it be denoted as such, and let the phase part be the phase difference Δ, It is written as.

[0004] In the analysis step to determine the refractive index and thickness of each thin film layer constituting the multilayer thin film, experimental values ​​measured by the ellipsometry and theoretical model values ​​obtained through optical theory By comparing, the theoretical model value experimental value from The combination of refractive index and thickness of each thin film layer that best reproduces it is obtained through regression analysis methods such as the least-square fit.

[0005] In this case, if the refractive index and thickness of each thin film layer are unknowns to be determined by ellipsometry analysis, then a theoretical model that reproduces the measured values, i.e., This is the equation that needs to be solved.

[0006] In many cases, the number of measurements is limited, so the number of equations is small compared to the number of unknowns to be solved.

[0007] To solve these problems, spectroscopic ellipsometry (SE), a type of ellipsometry, is widely used.

[0008] In SE, various wavelengths ( The ratio of the reflection coefficient of ) to light Measure the spectrum, and the theoretical model value Complex refractive index spectrum entering Using a specific dispersion model for at different wavelengths By introducing correlations between values, the problem of discrepancy between the number of unknowns and the number of equations is partially overcome, thereby improving the accuracy of regression analysis processes such as the least squares method.

[0009] However, the regression analysis process based on the dispersion model of materials requires prior knowledge of the material properties, and the difference between experimental and theoretical model values ​​depending on the combination of refractive index and thickness of the thin film layer It has several local minima.

[0010] In this case, the correct minimum value for the refractive index and thickness of the thin film layer depends heavily on the initial guess of the regression analysis.

[0011] Therefore, regression analysis of ellipsometry measurements can yield erroneous results depending on prior knowledge of the material.

[0012] This acts as a limitation in accurately measuring the refractive index and thickness of thin films through ellipsometry analysis.

[0013] [Prior Art Literature]

[0014] (Patent Document 1) Korean Registered Patent 10-2504761 (Registered on Feb. 23, 2023)

[0015] (Patent Document 2) Korean Registered Patent 10-1655096 (Registered Sep 1, 2016)

[0016] The present invention has been devised to solve the problems of the prior art as described above. The objective of the present invention is to provide a method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal and an ellipsometry measurement device, which can simultaneously analyze the refractive index and thickness of a multilayer thin film through the analysis of algebraic equations using light reflection or transmission signals obtained through ellipsometry measurement.

[0017] The present invention for achieving the above objectives is,

[0018] A method for analyzing the characteristics of a multilayer thin film sample composed of multiple thin films stacked between an incident medium and a substrate may include: a first step of storing measurement result data of the ratio of reflection coefficients for multiple incident angles in the incident medium; a second step of deriving an algebraic polynomial equation for complex refractive index and thickness by applying an expansion function for thin film thickness to a theoretical model of reflection coefficients composed of a system of transcendental equations; and a third step of calculating approximate values ​​of the complex refractive index and thickness of each of the multiple thin films as a solution to the algebraic polynomial equation of the second step.

[0019] Additionally, it may further include a 3-1 step for eliminating non-physical solutions among the solutions derived in the above 3rd step that do not satisfy the passivity condition, the optical magnetic absence condition, and the physical thickness condition.

[0020] Additionally, it may further include a fourth step of calculating the complex refractive index and thickness as the solution of the reflection coefficient theory model composed of a system of transcendental equations, using the approximate values ​​of the complex refractive index and thickness derived in the third step as the initial values ​​for regression analysis, depending on the magnitude of the error obtained by comparing the reflection coefficient theory model composed of the system of transcendental equations with the solution of the algebraic polynomial equation of the third step.

[0021] Additionally, it may further include a 4-1 step for eliminating non-physical solutions among the derived solutions of the above 4th step that do not satisfy the passivity condition, the optical magnetic absence condition, and the physical thickness condition.

[0022] In addition, the theoretical model of reflection coefficients composed of the above system of transcendental equations is obtained using the transfer matrix method, a type of optical theory, and is expressed by the following equation.

[0023]

[0024] (step, is the m-th specific angle of incidence, is for the m-th specific angle of incidence Measured value, is the refractive index of the p-th thin film, is the thickness of the p-th thin film.)

[0025] In addition, the expansion function for the thin film thickness of the second step is the following equation

[0026]

[0027] And,

[0028] The derived algebraic polynomial equation is the following equation

[0029]

[0030] am.

[0031] (step, The ratio of the reflection coefficient of the substrate, is the ratio of the reflection coefficient of the entire sample Thickness among the contribution of the p-thin film to primary term component of, is the ratio of the reflection coefficient of the entire sample Thickness among the contribution of the p-thin film to secondary component of, The ratio of the reflection coefficient of the entire sample The second-order term contribution to the interference components of the q-th thin film and the r-th thin film.)

[0032] Meanwhile, in a multilayer thin film characteristic analysis device through algebraic analysis of an ellipsometry signal, the device includes a memory for storing at least one program and a processor for executing said at least one program, wherein the processor stores reflection coefficient ratio data for a plurality of incident angles of a multilayer thin film sample composed of a plurality of thin films stacked between an incident medium and a substrate in said memory, and the processor derives a system of transcendental equations of a theoretical model corresponding to the reflection coefficient ratio for each incident angle of said stored data, thereby calculating an approximation of the complex refractive index and thickness of each thin film layer of the multilayer thin film sample.

[0033] According to the present invention, it has an excellent effect of simultaneously analyzing the refractive index and thickness of a multilayer thin film through the analysis of algebraic equations using light reflection or transmission signals obtained through ellipsometry measurement.

[0034] Figure 1 shows the complex refractive index Incident medium and complex refractive index A drawing illustrating a multilayer thin film sample composed of N thin films stacked between substrates.

[0035] FIG. 2 is a flowchart of a method for analyzing multilayer thin film characteristics through algebraic analysis of an ellipsometry signal according to the present invention.

[0036] FIG. 3 is a drawing illustrating an example of measurement according to a known micro-ellipsometer.

[0037] Figure 4 is an example of incident angle-reflection coefficient ratio data measured according to Figure 3.

[0038] Figure 5 shows the complex refractive index Incident medium and complex refractive index A drawing illustrating a thin film sample consisting of one thin film stacked between substrates.

[0039] FIG. 6 is a diagram of the device configuration of the present invention.

[0040] The embodiments of the present disclosure are illustrative for the purpose of explaining the technical concept of the present disclosure. The scope of rights according to the present disclosure is not limited to the embodiments presented below or the specific description thereof.

[0041] All technical and scientific terms used in this disclosure, unless otherwise defined, have the meaning generally understood by those skilled in the art to which this disclosure pertains. All terms used in this disclosure are selected for the purpose of further clarifying this disclosure and are not selected to limit the scope of the rights under this disclosure.

[0042] Expressions such as “comprising,” “comprising,” “having,” etc. used in this disclosure should be understood as open-ended terms implying the possibility of including other embodiments, unless otherwise stated in the phrase or sentence containing such expressions.

[0043] Unless otherwise stated, singular expressions described in this disclosure may include a plural meaning, and this applies likewise to singular expressions described in the claims.

[0044] Hereinafter, preferred embodiments of the method and apparatus for analyzing multilayer thin film characteristics through algebraic analysis of ellipsometry signals according to the present invention will be described in detail with reference to the attached drawings.

[0045]

[0046] Figure 1 shows the complex refractive index Incident medium and complex refractive index FIG. 1 is a drawing illustrating a multilayer thin film sample composed of N thin films stacked between substrates, FIG. 2 is a flowchart of a method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal according to the present invention, FIG. 3 is a drawing illustrating an example of measurement according to a known micro-ellipsometer, FIG. 4 is an example of incident angle-reflection coefficient ratio data measured according to FIG. 3, and FIG. 5 is a complex refractive index Incident medium and complex refractive index Figure 6 is a diagram illustrating a thin film sample consisting of one thin film stacked between substrates, and is a diagram of the apparatus configuration of the present invention.

[0047]

[0048] The present invention relates to a method and apparatus for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal, which can simultaneously analyze the refractive index and thickness of the multilayer thin film through the analysis of algebraic equations of a light reflection or transmission signal obtained through ellipsometry measurement. The method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal (hereinafter referred to as the "multilayer thin film characteristic analysis method") is a method for analyzing the characteristics of a multilayer thin film sample composed of a plurality of thin films stacked between an incident medium and a substrate, as shown in FIG. 2, and comprises: a first step of storing data obtained by measuring the ratio of reflection coefficients for a plurality of incident angles in the incident medium; and a second step of comparing the measured data with a system of transcendental equations of a theoretical model corresponding to the ratio of reflection coefficients for each incident angle, thereby enabling the calculation of approximate values ​​for the complex refractive index and thickness of each thin film layer of the multilayer thin film sample.

[0049]

[0050] The multilayer thin film sample as shown in Fig. 1 has a refractive index Incident medium and refractive index It consists of N thin films stacked between substrates.

[0051] If the order of the thin films relative to the incident medium is denoted as p, the thin film located after the incident medium can be referred to as the first thin film (p=1), the next thin film as the second thin film (p=2), and similarly, the thin film located directly above the substrate as the Nth thin film (p=N).

[0052] At this time, the refractive index of the p-th film forming the multilayer thin film is and the corresponding permittivity is and the thickness is (In this specification, a tilde above a variable indicates that the variable is a complex number. For example, if n and k are the real and imaginary parts of the complex refractive index, respectively, the complex refractive index It is expressed as.)

[0053] In order to analytically determine the complex refractive index and thickness of each thin film layer constituting a multilayer thin film sample, the present invention relates to the reflection coefficient ratio for a multilayer thin film sample as shown in FIG. 1. Measurement data measured for M different angles is stored. (Step 1)

[0054] m-th specific angle of incidence in the incident medium Reflection coefficient ratio for The measured value When deciding to express it as, That is, the reflection coefficient ratio can be measured using various ellipsometric techniques such as a variable angle spectroscopic ellipsometer (VASE), a multiple angle of incidence ellipsometer (MAI), and a micro-ellipsometer (ME), and examples of such measurement methods will be described later.

[0055] On the other hand, a specific angle of incidence Regarding, reflection coefficient ratio The theoretical model of the reflection coefficient corresponding to Generally, the full-wave equation can be theoretically obtained through the transfer matrix method.

[0056] Then, the exact refractive index and thickness of each thin film layer are the solutions to a system of transcendental equations such as Equation 1 am.

[0057]

[0058] However, since the system of equations in Equation 1 consists of transcendental equations, generally and A closed-form solution for cannot be found.

[0059] Therefore, in the present invention, the warm-wave theory model It can be derived by expanding it for each thin film thickness as in mathematical formula 2.

[0060]

[0061] Interference term between thin films in a multilayer thin film structure, i.e., was considered.

[0062] At this time, the second-order expansion function for the thin film thickness as follows If defined as such, it is equal to mathematical formula 3.

[0063]

[0064] At this time, in mathematical formulas 2 and 3 is the ratio of the reflection coefficients occurring between the incident medium and the substrate, that is, the ratio of the substrate's reflection coefficients, and is the ratio of the reflection coefficient of the entire sample Thickness among the contribution of the p-thin film to It corresponds to the primary term component of, and is the ratio of the reflection coefficient of the entire sample Thickness among the contribution of the p-thin film to It corresponds to the secondary term component of, and The ratio of the reflection coefficient of the entire sample It corresponds to the second-order contribution to the interference components of the q-th thin film and the r-th thin film.

[0065] Since Equation 3 has been expanded to a second-order term with respect to the thin film thickness, an algebraic polynomial equation that can be solved by analytical methods is derived, rather than a transcendental equation for the complex refractive index and thickness of each thin film layer. (Step 2)

[0066] As explained above, instead of solving the system of transcendental equations in Equation 1, a system of polynomial equations such as Equation 4 is solved using the approximation in Equation 3 for the complex refractive index and thickness of N thin films Can solve for. (Stage 3)

[0067]

[0068] In this case, the system of polynomial equations in Equation 4 can be solved through various different analytical or numerical methods when the number of different angle measurements M is greater than or equal to the number of unknowns N (M≥N).

[0069] The equation forming mathematical formula 3 is the refractive index It is a higher-order polynomial equation for (p = 1, 2, …, N).

[0070] Analytical or numerical solution methods become easier as the degree of the polynomial equation decreases.

[0071] Therefore, the refractive index Instead, permittivity If we solve for it, the degree of the polynomial equation can be significantly reduced.

[0072] In addition, since mathematical equations 3 and 4 are higher-order polynomial equations, the solutions to mathematical equations 3 and 4 There can be multiple.

[0073] At this point, the non-physical solutions among the solutions to mathematical equations 3 and 4 can be eliminated through the following conditions. (Step 3-1)

[0074] First, the solutions to mathematical equations 3 and 4 are that the imaginary part of the thin film refractive index is positive, i.e., It must satisfy the passivity condition (p = 1, 2, …, N).

[0075] Next, regarding the solutions to mathematical equations 3 and 4, since natural materials do not have magnetism at optical frequencies, when measuring materials in that frequency range, the real part of the refractive index is positive, i.e., It must satisfy the no optical magnetism condition (p = 1, 2, …, N).

[0076] Next, the solutions to mathematical equations 3 and 4 are that the thin film thickness is a real number and a positive number greater than 0, i.e., and It must satisfy the physical thickness condition (p = 1, 2, …, N).

[0077] The solution obtained by solving mathematical equation 4 If so, depending on the case, this solution Although it is a solution obtained through approximation, depending on the magnitude of the error when comparing the system of transcendental equations of Equation 1 and the system of polynomial equations of Equation 4, if the error is smaller than a predetermined standard, the solution of Equation 4 can be derived as the complex refractive index and thickness.

[0078]

[0079] The solution obtained by solving mathematical equation 4 If so, depending on the case (for example, when the thin film is thick or the refractive index of the thin film is high), this solution Since is a solution obtained through approximation, it is the solution to Equation 1 , that is, it may not be equal to the exact refractive index and thickness of the thin film.

[0080] The goal of the present invention is to obtain the refractive index and thickness of each thin film layer with high precision. You must obtain it.

[0081] To solve the transcendental equation in Equation 1, regression analysis such as a root-finding algorithm or the least squares method must be performed, and the solution to Equation 4 is used as the initial value for the regression analysis. If used, the refractive index and thickness of the actual thin film layer among several local minima satisfying Equation 1 can be accurately determined.

[0082] That is, the present invention can accurately derive the complex refractive index and thickness as the solution to the system of transcendental equations of Equation 1, wherein, depending on the magnitude of the error when comparing the system of transcendental equations of Equation 1 and the system of polynomial equations of Equation 4, if the error is greater than a predetermined standard, the approximate value of the complex refractive index and thickness, which is the solution of Equation 4, is used as the initial value for regression analysis. (Step 4)

[0083] At this time, non-physical solutions among the solutions of the system of transcendental equations of Equation 1, which use the approximate values ​​of the complex refractive index and thickness that are solutions of Equation 4 as the initial values ​​for regression analysis, can be eliminated through the above conditions. (Step 4-1)

[0084]

[0085] Meanwhile, the above mathematical formula 3 is explained in detail as follows.

[0086] The first-order term of mathematical formula 3 is given as in mathematical formula 5.

[0087]

[0088] The quadratic term of mathematical formula 3 is equal to mathematical formulas 6 and 7.

[0089]

[0090]

[0091] Each term of mathematical formulas 6 and 7 is given as follows.

[0092]

[0093]

[0094]

[0095]

[0096] At this time, is the angle of incidence at the m-th measurement, is the angle of light traveling inside the substrate for the corresponding angle of incidence. silver Given this, it is determined according to Snell's Law.

[0097]

[0098] Next, we will explain how to find an approximate solution using the system of polynomial equations (Equation 4).

[0099] To implement the present invention, a method for obtaining a numerical solution to a system of polynomial equations of Equation 3, consisting of Equation 3 and Equations 5 to 11, may be used.

[0100] Methods for finding numerical solutions generally belong to global equation solvers and do not require an initial guess to find the solution.

[0101] Examples of such methods include the general solution of higher-order polynomial equations, the endomorphism matrix method, the homotopy continuation method, the monodromy method, and the Gröbner basis method. Various methods such as ) can be used.

[0102] If it is difficult to find an approximate solution to mathematical equation 3, it is also possible to solve the minimization problem of the equation instead.

[0103]

[0104] Next, we will explain how to improve accuracy using a root-finding algorithm.

[0105] Most root-finding algorithms are local equation solvers that use iterative techniques, so they require initial estimates for the roots.

[0106] Various methods, such as Newton's method, affine covariant Newton method, Brent's method, and secant method, can be used as examples of such root-finding algorithms for implementing the present invention.

[0107] If the solution of the system of polynomial equations (Equation 4) of the present invention described above is used as the initial estimate for this root-finding algorithm, the problem of false local solutions experienced by the root-finding algorithm can be successfully avoided.

[0108]

[0109] Meanwhile, the m-th specific angle of incidence in the incident medium for Measured value The various methods for measuring it are explained as follows.

[0110] First, here is an explanation of the measurement method using a micro-ellipsometer (ME).

[0111] The present invention can be carried out using a microellipsometer (hereinafter referred to as "ME measuring instrument").

[0112] The ME measuring instrument is a device that measures the Fourier plane (FP) image of the sample reflectance formed on the back-focal plane (BFP) of the objective lens, as shown in FIG. 3. In FIG. 3, L represents the lens, F represents the filter, P represents the polarizer, OBJ represents the objective lens, and BS represents the beam splitter.

[0113] The Fourier image of the sample reflectance measured by the ME instrument is the ratio of the reflection coefficients at various angles of incidence It contains information.

[0114] Figure 4 is one example of data obtainable through an ME measuring instrument, as shown in Figure 5. = 10 nm thick SiN thin film (refractive index) ) A single layer is a Si substrate (refractive index This is an ME image that can be obtained using a red light source with a wavelength of 660 nm when deposited on top.

[0115] ME images are in polar coordinate systems It is expressed as, the distance from the origin, i.e., the radius component is the angle of incidence It represents information about, and each component It has information about polarization.

[0116] In other words, the intensity of a point on a 2D ME image Ratio of reflection coefficient for a specific angle of incidence from You can find out information about it.

[0117] Thus, the ratio of reflection coefficients for various incident angles required in the present invention It can be obtained through a single measurement of the sample.

[0118] Experimental values ​​obtained through the ME measuring instrument Based on this, the complex refractive index and thickness of each thin film layer can be measured by implementing the present invention through the process of Equation 2 and Equations 4 to 10 (polynomial approximation) and Fig. 2.

[0119] Next, there is a description of measurement methods using the Variable Angle Elliptical Spectrometer (VASE) and the Multi-Angle Elliptical Spectrometer (MAI).

[0120] The present invention can be carried out using various commercially available VASE or MAI devices.

[0121] Since VASE or MAI instruments can measure by varying the angle of incidence, the reflection coefficient ratios for various angles of incidence required in this invention It can be obtained by taking multiple measurements as needed for the sample.

[0122] Based on experimental values ​​obtained through a VASE or MAI instrument, the complex refractive index and thickness of each thin film layer can be measured by implementing the present invention through the process of Equation 2 and Equations 4 to 10 (polynomial approximation) and Fig. 2.

[0123] Next, there is a description of a method for measuring a sample using a limited number of angle of incidence measurements.

[0124] The simplest embodiment is a substrate (refractive index) as shown in FIG. 5 The refractive index of a single thin film when a single thin film layer is placed on top of ) , thickness It is to measure it through the method presented in the present invention.

[0125] Since there are two unknowns to be measured, the two angles of incidence are obtained through an ellipsometer , The ratio of the reflection coefficient for, respectively , Let's assume it was measured as...

[0126] Then, mathematical equation 3, which must be solved analytically, becomes a system of equations consisting of two polynomial equations as follows.

[0127]

[0128] for example, = 10 nm thick SiN thin film (refractive index) =2.0074) Monolayer on a Si substrate (refractive index) Let's assume that it is deposited on ) and a light source with a wavelength of 660 nm is used. In this case, in the ideal scenario where there is no instrument error, and The ratio of the reflection coefficient measured at the angle of incidence is, respectively , is. Using the measured value class By solving Equation 12 for and eliminating non-physical solutions among the obtained solutions, the approximate solution for the refractive index and thickness of the corresponding thin film is =2.0158 and It can be seen that =9.9407.

[0129] This value is the actual refractive index of the thin film. =2.0074 and actual thickness There is a slight error with =10 nm.

[0130] Therefore, the solution to mathematical equation 12 =2.0162, With =9.9409 as the initial estimate, a root-finding algorithm can be applied to Equation 1, i.e., the following system of transcendental equations.

[0131]

[0132] The result of the root-finding algorithm for Equation 13 is the actual refractive index of the thin film =2.0074 and actual thickness Since it is exactly equal to 10 nm, the refractive index and thickness of the thin film were measured accurately.

[0133] The above example measured the reflection ratio for two different angles of incidence for the measurement of a single-layer thin film.

[0134] Generalizing this to the case of multilayer thin films, it is as follows.

[0135] If the number of unknowns to be measured and the number of measurements are the same, the system of polynomial equations in Equation 4 can be solved.

[0136] That is, in the case of N multilayer thin films, the total number of unknowns to be measured is 2N, since the refractive index and thickness of each thin film layer must be measured.

[0137] Therefore, to fully measure N multilayer thin films, at least 2N measurements must be performed.

[0138]

[0139] At this time, as described above, at least 2N measurements must be performed to achieve complete measurement of N multilayer thin films, but if measurements can be performed more than 2N times, the measurement error can be reduced.

[0140] While there are various methods to reduce error in situations where the number of measurements exceeds the number of unknowns, the example below explains the method using the Moore-Penrose pseudoinverse.

[0141] From the form of mathematical equations 5 to 11, it can be seen that it is expressed as the product of the refractive index function, the angle function, and the thickness function.

[0142] Specifically, mathematical formula 5 can be expressed as mathematical formula 14.

[0143]

[0144] Each term of mathematical formulas 6 and 7, namely mathematical formulas 8 to 11, can be expressed as mathematical formulas 15 to 18.

[0145]

[0146]

[0147]

[0148]

[0149] Assuming that a total of M measurements were taken for different angles of incidence, ( , N is the number of layers of the multilayer thin film) Equation 4 It can be expressed as a determinant of the form, and each matrix is ​​given as in mathematical equation 19.

[0150]

[0151] Each term of mathematical formula 19 is It is defined as.

[0152]

[0153]

[0154] procession Since (Equation 20) is a system of polynomial equations with the refractive index and thickness of each thin film as unknowns, the Moore-Penrose pseudo-inverse matrix through It can be decided that...

[0155] At this time, The matrix is ​​a matrix in which measurement error has been reduced by the Moore-Penrose pseudo-inverse operation.

[0156] The i-th row element of the matrix When saying, Three equations, Equations 22 to 24, can be obtained by this.

[0157]

[0158]

[0159]

[0160] Through mathematical formulas 23 and 24 It can be seen that, specifically, this can be expressed as in mathematical formula 25.

[0161]

[0162] Equation 25 is the refractive index of the thin film. A fourth-order equation for, or permittivity It is an equation that can be easily solved as a quadratic equation.

[0163] By eliminating the non-physical solutions among the solutions of mathematical equation 25 as described above, the refractive index Once this is determined, the thickness of the thin film can be obtained as in Equation 26 through Equation 22.

[0164]

[0165] Meanwhile, the apparatus (100) for performing the method of analyzing multilayer thin film characteristics through algebraic analysis of an ellipsometry signal according to the present invention may include a memory (110), a processor (120), and a communication module (130).

[0166] That is, the multilayer thin film characteristic analysis device through algebraic analysis of an ellipsometry signal according to the present invention includes a memory (110) that stores at least one program and a processor (120) that executes said at least one program, and said processor (120) stores reflection coefficient ratio data for a plurality of incident angles of a multilayer thin film sample composed of a plurality of thin films stacked between an incident medium and a substrate in said memory (110), and said processor (120) executes said program to compare said stored data with a system of transcendental equations of a theoretical model corresponding to the reflection coefficient ratio for each incident angle, thereby obtaining an approximation of the complex refractive index and thickness of each thin film layer of the multilayer thin film sample.

[0167] The memory (110) may be implemented as a DRAM (dynamic random access memory), SRAM (static random access memory), ROM (read-only memory), EEPROM (electrically erasable programmable read-only memory), CD-ROM, Blu-ray or other optical disc storage, HDD (hard disk drive), SSD (solid state drive), or flash memory, but is not limited thereto. Additionally, program code for controlling the analysis device (100) or calculating the analysis steps of the present invention may be temporarily or permanently stored in the memory (110).

[0168] At least one program stored in memory (110) can be executed by the processor (120).

[0169] The processor (120) and the components of the processor (120) can control the device (100) of the present invention to perform the steps of the multilayer thin film characteristic analysis method. For example, the processor (120) and the components of the processor (120) may be implemented to execute instructions according to the code of an operating system included in the memory (110) and the code of at least one program. Here, the components of the processor (120) may be representations of different functions of the processor (120) that are performed by the processor (120) according to instructions provided by the program code stored in the analysis device (100).

[0170] The communication module (130) can provide a function for communicating with an external server or external device through a network.

[0171]

[0172] Accordingly, the method and apparatus (100) for analyzing multilayer thin film characteristics through algebraic analysis of an ellipsometry signal according to the present invention as described above has various advantages, such as the ability to simultaneously analyze the refractive index and thickness of a multilayer thin film through algebraic equation analysis of a light reflection or transmission signal obtained through ellipsometry measurement.

[0173]

[0174] The methods and devices described above may be implemented as hardware components, software components, and / or combinations of hardware and software components. For example, the devices and components described in the embodiments may be implemented using one or more general-purpose or special-purpose computers, such as, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable array (FPA), a programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. The processing unit may execute an operating system (OS) and one or more software applications executed on said operating system. Additionally, the processing unit may access, store, manipulate, process, and generate data in response to the execution of the software. The processing unit may include multiple processors or one processor and one controller. Additionally, other processing configurations, such as parallel processors, are also possible.

[0175] Software may include computer programs, code, instructions, or a combination of one or more of these, and may configure a processing unit to operate as desired or command the processing unit independently or collectively. Software and / or data may be permanently or temporarily embodied in any type of machine, component, physical device, virtual equipment, computer storage medium or device, or transmitted signal wave in order to be interpreted by the processing unit or to provide instructions or data to the processing unit. Software may be distributed over networked computer systems and may be stored or executed in a distributed manner. Software and data may be stored on one or more computer-readable recording media.

[0176] The method and apparatus according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and may be recorded on a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc., either alone or in combination. The program instructions recorded on the medium may be those specifically designed and configured for the embodiment, or they may be those known and available to those skilled in the art of computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes; optical recording media such as CD-ROMs and DVDs; magneto-optical media such as floptical disks; and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, and flash memory.

[0177] Although the embodiments have been described above with reference to limited examples and drawings, those skilled in the art can make various modifications and variations from the description above. For example, suitable results can be achieved even if the described techniques are performed in a different order than described, and / or the components of the described system, structure, device, circuit, etc. are combined or assembled in a form different from described, or replaced or substituted by other components or equivalents.

[0178]

[0179] The above-described embodiments are explained with respect to the most preferred examples of the present invention, but are not limited to the above embodiments, and it is obvious to those skilled in the art that various modifications are possible within the scope of the technical spirit of the present invention.

Claims

1. A method for analyzing the characteristics of a multilayer thin film sample composed of a plurality of thin films stacked between an incident medium and a substrate, A first step of storing measurement result data of the ratio of reflection coefficients for multiple angles of incidence in an incident medium, and A second step of deriving algebraic polynomial equations for complex refractive index and thickness by applying an expansion function for thin film thickness to a theoretical model of reflection coefficients consisting of a system of transcendental equations, and A method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal, comprising: a third step of calculating approximate values ​​of the complex refractive index and thickness of each of the plurality of thin films as the solution to the algebraic polynomial equation of the second step above.

2. In Paragraph 1, A method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometric signal, further comprising a 3-1 step of eliminating non-physical solutions among the solutions derived in the above 3rd step that do not satisfy the passivity condition, the optical magnetic absence condition, and the physical thickness condition.

3. In Paragraph 1, A method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal, further comprising: a fourth step of calculating the complex refractive index and thickness as the solution of a reflection coefficient theory model composed of a system of transcendental equations, wherein the approximate values ​​of the complex refractive index and thickness derived in the third step are used as the initial values ​​for regression analysis, depending on the magnitude of the error obtained by comparing the reflection coefficient theory model composed of the system of transcendental equations and the solution of the algebraic polynomial equation of the third step.

4. In Paragraph 3, A method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometric signal, further comprising a 4-1 step of eliminating non-physical solutions among the solutions derived in the above 4th step that do not satisfy the passivity condition, the optical magnetic absence condition, and the physical thickness condition.

5. In Paragraph 1, A theoretical model of reflection coefficients composed of the above system of transcendental equations is obtained using the transfer matrix method, a type of optical theory, and is a method for analyzing the characteristics of a multilayer thin film through algebraic analysis of an ellipsometry signal, expressed by the following equation. (step, is the m-th specific angle of incidence, is for the m-th specific angle of incidence Measured value, is the refractive index of the p-th thin film, is the thickness of the p-th thin film.) 6. In Paragraph 1, The expansion function for the thin film thickness of the second stage above is the following equation And, The derived algebraic polynomial equation is the following equation Method for characterizing multilayer thin films through algebraic analysis of ellipsometry signals. (step, The ratio of the reflection coefficient of the substrate, is the ratio of the reflection coefficient of the entire sample Thickness among the contribution of the p-thin film to primary term component of, is the ratio of the reflection coefficient of the entire sample Thickness among the contribution of the p-thin film to secondary component of, The ratio of the reflection coefficient of the entire sample The second-order term contribution to the interference components of the q-th thin film and the r-th thin film.) 7. In a multilayer thin film characterization apparatus through algebraic analysis of ellipsometry signals, It includes a memory for storing at least one program and a processor for executing said at least one program, The above processor stores reflection coefficient ratio data for multiple incident angles of a multilayer thin film sample composed of multiple thin films stacked between an incident medium and a substrate in the memory, and A multilayer thin film characteristic analysis device through algebraic analysis of ellipsometry signals, wherein the processor derives a system of transcendental equations of a theoretical model corresponding to the ratio of reflection coefficients for each incident angle of the stored data, and calculates approximate values ​​of the complex refractive index and thickness of each thin film layer of a multilayer thin film sample.

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