A metal film measurement method based on theoretical spectrum and measured spectrum

Abstract

The present invention discloses a method for measuring metal thin films based on theoretical and measured spectra, relating to the field of thin film optical measurement technology. The method comprises the following steps: using an ellipsometer to perform spectral scanning on a metal thin film sample to be measured within a preset wavelength range to obtain measured spectral data; constructing a theoretical spectral model based on a three-layer film structure and setting initial values ​​for structural parameters; substituting the initial values ​​for the structural parameters into the theoretical spectral model to generate theoretical spectral data; employing a multi-strategy parallel global optimization algorithm to iteratively adjust the structural parameters, terminating the iterative process when the first convergence criterion is met, and outputting the optimal structural parameters; and calculating and outputting the actual film thickness, refractive index, and extinction coefficient of the metal film based on the optimal structural parameters. The present invention constructs a theoretical spectral model that combines the Drude-Lorentz dispersion model, the effective medium approximation theory, and the transfer matrix method, achieving high-precision characterization of the optical parameters of the metal film and effectively improving measurement accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of thin film optical measurement, and in particular to a metal thin film measurement method based on theoretical spectrum and measurement spectrum. Background Art

[0002] With the rapid development of industries such as semiconductors, optoelectronics, and microelectronics, metal thin films are increasingly being used in integrated circuits, optical devices, and sensors. The optical properties of metal thin films, such as film thickness, refractive index, and extinction coefficient, directly determine the performance and functionality of devices. For example, in optical devices, the reflectivity and transmittance of metal thin films determine the optical efficiency of the device. Therefore, accurately measuring and characterizing the optical parameters of metal thin films is crucial for ensuring device performance and studying material properties. However, traditional measurement methods often rely on a single technique or simplified models, making it difficult to simultaneously obtain multiple optical parameters with guaranteed measurement accuracy.

[0003] Existing metal thin film measurement methods have the following major limitations: First, insufficient measurement accuracy. Traditional methods typically use measurement data at a single wavelength or limited angles for inversion calculations, resulting in results that are limited by variations in experimental conditions and incomplete data coverage. Second, parameter inversion is unstable. Due to the complex and highly nonlinear optical response of multilayer structures, traditional algorithms are prone to falling into local optimal solutions or failing to converge. Finally, it is difficult to simultaneously obtain multiple optical parameters. Existing methods often only extract a few optical parameters (such as film thickness or refractive index) while ignoring other important information (such as extinction coefficient or surface roughness). These issues have hindered the research and application of metal thin film materials. Summary of the Invention

[0004] In view of the low measurement accuracy, unstable parameter inversion and incomplete parameter acquisition of existing metal thin film measurement technology, the present invention is proposed.

[0005] Therefore, the problem to be solved by the present invention is how to achieve accurate characterization of the thickness, refractive index and extinction coefficient of metal thin films, and to improve the stability and comprehensiveness of parameter inversion through a multi-strategy parallel global optimization algorithm.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] In the first aspect, an embodiment of the present invention provides a metal film measurement method based on theoretical spectrum and measured spectrum, which includes using an ellipsometer to perform spectral scanning on the metal film sample to be measured within a preset wavelength range to obtain measured spectrum data; constructing a theoretical spectrum model based on a three-layer film structure and setting initial values ​​of structural parameters; substituting the initial values ​​of the structural parameters into the theoretical spectrum model to generate theoretical spectrum data; using a multi-strategy parallel global optimization algorithm to iteratively adjust the structural parameters, terminating the iterative process when the first convergence criterion is met, and outputting the optimal structural parameters; based on the optimal structural parameters, calculating and outputting the actual film thickness, refractive index and extinction coefficient of the metal film.

[0008] As a preferred solution of the metal thin film measurement method based on theoretical spectrum and measurement spectrum described in the present invention, wherein: the first convergence criterion includes that the composite loss function value is lower than the preset convergence threshold, or the number of iterations reaches the preset maximum iteration limit; the structural parameters include plasma frequency, damping coefficient, surface roughness parameter and film thickness parameter.

[0009] As a preferred solution of the metal film measurement method based on theoretical spectrum and measurement spectrum described in the present invention, the process of constructing the theoretical spectrum model includes: establishing a three-layer film system structure, which is a base layer, a metal film layer and a surface roughness layer in order according to the propagation direction of the incident light, wherein the base layer adopts the optical constants of the crystal material; using the Drude-Lorentz dispersion model to describe the optical response of the metal film layer, and using the plasma frequency and damping coefficient to calculate the complex dielectric function of the metal film at different wavelengths and convert it into a complex refractive index; based on the effective medium approximation theory, the surface roughness layer is equivalent to a mixed layer of metal material and air, and the equivalent complex refractive index of the surface roughness layer is calculated by combining the surface roughness parameters and the Brugmann model; using the complex refractive index of each layer, the reflection coefficient and transmission coefficient of each interface are calculated based on the Fresnel formula to construct an interface reflection matrix; using the initial film thickness parameter and the wavelength of the incident light, the phase propagation matrix of each layer is constructed; using the transfer matrix method, the interface reflection matrix and the phase propagation matrix are multiplied in sequence along the propagation direction of the incident light to obtain the total transfer matrix; calculating the ellipsometric parameters based on the elements of the total transfer matrix to generate theoretical spectrum data.

[0010] As a preferred solution of the metal thin film measurement method based on theoretical spectrum and measured spectrum described in the present invention, the specific formula of the complex dielectric function is as follows:

[0011]

[0012] in, is the high-frequency dielectric constant, is the incident light angular frequency, is the plasma frequency, is the damping coefficient, are the intensity, resonant frequency and damping coefficient of the mth Lorentz oscillator respectively, and i is an imaginary unit.

[0013] As a preferred solution of the metal film measurement method based on theoretical spectrum and measured spectrum described in the present invention, the following steps are included: the search range of the structural parameters is set according to the physical properties of the metal film material; a genetic algorithm population is established, the structural parameters are encoded as chromosomes, high-quality individuals are selected by roulette, and offspring individuals are generated by single-point crossover; a composite loss function is constructed, the composite loss function consists of a fitting error term and a physical constraint penalty term, wherein the fitting error term characterizes the degree of difference between the theoretical spectral data and the measured spectral data, and the physical constraint penalty term introduces the physical property restrictions of the structural parameters; three optimization sub-processes are constructed using genetic algorithm, particle swarm algorithm and simulated annealing algorithm, and the structural parameters are searched in parallel based on the composite loss function; in the iterative optimization process, the search parameters are dynamically adjusted and a high-quality solution set is constructed; when the first convergence criterion is met, the structural parameters corresponding to the minimum composite loss function value are selected from the high-quality solution set as the optimal structural parameters.

[0014] As a preferred solution of the metal thin film measurement method based on theoretical spectrum and measurement spectrum described in the present invention, dynamically adjusting the search parameters and constructing a high-quality solution set includes: dynamically adjusting the search parameters according to the change of the composite loss function value: if the relative change rate of the composite loss function value for three consecutive iterations is less than the preset change rate threshold, then increasing the local search capability of the algorithm, specifically by increasing the crossover probability of the genetic algorithm, the local learning factor of the particle swarm algorithm, and the cooling coefficient of the simulated annealing algorithm; if the composite loss function value is in the local optimum for three consecutive iterations, then increasing the global search capability of the algorithm, specifically by increasing the mutation probability of the genetic algorithm, the global learning factor of the particle swarm algorithm, and the temperature of the simulated annealing algorithm; in each round of iteration, selecting the solution with the smallest composite loss function value from the three optimization sub-processes to add to the high-quality solution set, and controlling the size of the high-quality solution set.

[0015] As a preferred solution of the metal thin film measurement method based on theoretical spectrum and measured spectrum of the present invention, the specific formula of the composite loss function is as follows:

[0016]

[0017] Among them, L is the composite loss function, is the fitting error term, is the physical constraint penalty term, is the weight coefficient for balancing fitting error and physical constraints.

[0018] In the second aspect, an embodiment of the present invention provides a metal thin film measurement system based on theoretical spectrum and measurement spectrum, which includes a measurement data acquisition module for using an ellipsometer to perform spectral scanning on the metal thin film sample to be measured within a preset wavelength range to obtain measurement spectrum data; a model construction module for constructing a theoretical spectrum model based on a three-layer film structure and setting initial values ​​of structural parameters; a theoretical data generation module for substituting the initial values ​​of structural parameters into the theoretical spectrum model to generate theoretical spectrum data; a parameter optimization module for iteratively adjusting the structural parameters using a multi-strategy parallel global optimization algorithm, terminating the iterative process when the first convergence criterion is met, and outputting the optimal structural parameters; a result calculation module for calculating and outputting the actual film thickness, refractive index and extinction coefficient of the metal film based on the optimal structural parameters.

[0019] The beneficial effects of the present invention are as follows: the present invention constructs a theoretical spectral model that combines the Drude-Lorentz dispersion model, the effective medium approximation theory and the transfer matrix method, realizes high-precision characterization of the optical parameters of the metal film, and effectively improves the measurement accuracy; designs a multi-strategy parallel global optimization algorithm, adopts a genetic algorithm, a particle swarm algorithm and a simulated annealing algorithm for joint search, and sets an inter-process information exchange mechanism, which significantly improves the global optimization capability and computational efficiency; introduces a distance-based elite retention strategy and dynamically adjusts the search parameters, and effectively avoids the algorithm from falling into a local optimal solution by maintaining the diversity of high-quality solution sets and adaptively adjusting the search direction; proposes a composite loss function based on the fitting error term and the physical constraint penalty term, and ensures the rationality of the optimization results by introducing the physical property restrictions of the structural parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0021] Figure 1 The figure shows the framework flow chart of the metal thin film measurement method based on theoretical spectrum and measurement spectrum.

[0022] Figure 2 A flow chart is constructed for the theoretical spectral model of the metal thin film measurement method based on theoretical and measured spectra.

[0023] Figure 3 Flowchart for obtaining optimal structural parameters for the metal thin film measurement method based on theoretical and measured spectra. DETAILED DESCRIPTION

[0024] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0025] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0026] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0027] Example 1, reference Figures 1 to 3 , which is the first embodiment of the present invention, provides a metal film measurement method based on theoretical spectrum and measurement spectrum. The framework flow chart is as follows Figure 1 Shown, including,

[0028] S1: Use an ellipsometer to perform spectral scanning on the metal film sample to be measured within a preset wavelength range to obtain measurement spectrum data.

[0029] Specifically, a JA Woollam M-2000 ellipsometer was used to scan the wavelength range of 193 nm to 1700 nm at three incident angles: 65°, 70°, and 75°. The wavelength interval at each angle was 0.5 nm, and the ellipsometric parameters were obtained as measured spectral data. The measurement environment temperature and humidity were controlled according to the SEMI MF1811 standard.

[0030] Preferably, multi-angle measurement can improve the sensitivity to film thickness and other optical parameters, which helps to improve the accuracy of subsequent optimization algorithms.

[0031] S2: Construct a theoretical spectral model based on the three-layer film structure and set the initial values ​​of the structural parameters.

[0032] Among them, the structural parameters include plasma frequency, damping coefficient, surface roughness parameter and film thickness parameter, and the theoretical spectrum model construction flow chart is shown in Figure 2, which is as follows:

[0033] S2.1: Establish a three-layer film structure, which is a base layer, a metal film layer, and a surface roughness layer in the order of the propagation direction of the incident light.

[0034] The optical constants of the base layer are crystalline materials, and their complex refractive index is obtained from a standard material database. In the three-layer structure, the base layer theoretically extends to infinite depth, the metal film layer has a thickness range of 5-200nm, and the surface roughness layer has a nominal thickness of 5nm.

[0035] In this embodiment, the standard material database refers to a data set of optical material constants compiled by an authoritative organization or research unit.

[0036] S2.2: Use the Drude-Lorentz dispersion model to describe the optical response of the metal film layer. Using the plasma frequency and damping coefficient, calculate the complex dielectric function of the metal film at different wavelengths and convert it into a complex refractive index.

[0037] For different wavelengths , can be achieved through Convert wavelength to angular frequency , where c is the speed of light in a vacuum.

[0038] Furthermore, the complex dielectric function at different wavelengths is calculated. The specific formula is as follows:

[0039]

[0040] in, is the high-frequency dielectric constant, is the incident light angular frequency, is the plasma frequency, is the damping coefficient, are the intensity, resonant frequency, and damping coefficient of the m-th Lorentz oscillator, respectively. i is the imaginary unit, and m is the m-th Lorentz oscillator.

[0041] Furthermore, the calculated complex dielectric function is converted into a complex refractive index. The specific process is as follows: Complex dielectric function is a complex number form, decomposing the calculated complex dielectric function into its real part and the imaginary part ; Calculate the modulus of the complex dielectric function ; Use the conversion formula to calculate the real part of the complex refractive index and the imaginary part , where the conversion formula is as follows:

[0042] ,

[0043] The complex refractive index can be obtained by the above calculation , which comprehensively describes the propagation characteristics of light in metal films, where the real part represents the relative propagation speed of light in the material, and the imaginary part represents the degree of energy loss when light propagates in the material.

[0044] S2.3: Based on the effective medium approximation theory, the surface roughness layer is equivalent to a mixture of metal material and air. The equivalent complex refractive index of the surface roughness layer is calculated by combining the surface roughness parameters and the Brugmann model.

[0045] First, set the volume fraction of metal material in the surface roughness layer , and its calculation formula is , h is the surface roughness parameter, d is the nominal thickness of the rough layer; then, the dielectric constant of air Substitute the Brugmann model equation, combine the dielectric function of the metal, and use the Newton iteration method to solve the equivalent dielectric constant ; Finally, the equivalent dielectric constant is obtained Convert to the equivalent complex refractive index.

[0046] S2.4: Use the complex refractive index of each layer to calculate the reflection coefficient and transmission coefficient of each interface based on the Fresnel formula and construct the interface reflection matrix.

[0047] In the implementation, the Fresnel reflection and transmission coefficients for s- and p-polarization are first calculated based on the complex refractive index and incident angle of the two adjacent media. For each interface, a 2×2 reflection matrix is ​​constructed based on the reflection and transmission coefficients. This matrix describes the reflection and transmission behavior of light waves at the interface and includes information about the polarization state changes of the incident light.

[0048] S2.5: Use the initial film thickness parameters and the incident light wavelength to construct the phase propagation matrix for each layer.

[0049] S2.6: Using the transfer matrix method, multiply the interface reflection matrix and the phase propagation matrix sequentially along the propagation direction of the incident light to obtain the total transfer matrix.

[0050] The core of the transfer matrix method is to transform a complex multilayer optical system into a matrix multiplication problem. In practice, starting from the base layer, the interface reflection matrix and the phase propagation matrix are multiplied layer by layer, following the direction of light wave propagation. Each matrix multiplication reflects the optical transformation of the light wave passing through each interface and film layer. The resulting total transfer matrix comprehensively reflects the complete optical response of the entire multilayer film system to incident light.

[0051] S2.7: Calculate the ellipsometric parameters based on the elements of the total transfer matrix and generate theoretical spectral data.

[0052] Reflection coefficient information is extracted from the total transfer matrix, and the ellipsometric angle and phase difference are calculated to generate theoretical spectral data. The ellipsometric angle reflects the change in amplitude of the light wave before and after reflection, while the phase difference describes the phase change of the reflected light.

[0053] Preferably, by equating the surface roughness layer to a mixed layer of metal material and air and combining it with the Brugmann model to calculate the equivalent complex refractive index, the influence of the roughness of the actual sample surface is taken into account, thereby improving the accuracy of the model; at the same time, the Drude-Lorentz dispersion model is used to describe the optical response of the metal film, and the transfer matrix method is used to efficiently handle the complex optical response of the multilayer structure, so that the theoretical model can fully reflect the propagation characteristics of light in the metal film.

[0054] S3: Substitute the initial values ​​of the structural parameters into the theoretical spectrum model to generate theoretical spectrum data.

[0055] S4: A multi-strategy parallel global optimization algorithm is used to iteratively adjust the structural parameters. When the first convergence criterion is met, the iterative process is terminated and the optimal structural parameters are output.

[0056] Specifically, the optimal structural parameter acquisition flow chart is as follows: Figure 3 As shown, stratified random sampling, specifically Latin hypercube sampling, is used to initialize the genetic algorithm population, ensuring good distribution and diversity in the parameter space. Based on the physical properties of the metal thin film material, the search range for structural parameters is set, and parameter encoding rules are formulated: real number encoding is used to map each structural parameter to the interval [0, 1]. Linear mapping ensures efficient conversion of parameter values. A genetic algorithm population is established, and the structural parameters are encoded as chromosomes, where the chromosome length matches the number of structural parameters. A roulette wheel method is used to select high-quality individuals, and offspring individuals are generated through single-point crossover, with set crossover and mutation probabilities.

[0057] To ensure the repeatability of the algorithm and the reliability of the results, a fixed random number seed is set in the algorithm implementation, and the robustness of the algorithm is verified through multiple independent runs. Specifically, a global random number seed is set so that consistent optimization results can be obtained under the same input conditions. At the same time, the random number seed of each run is recorded to facilitate traceability and reproduction of results when necessary.

[0058] Furthermore, a composite loss function is constructed. The composite loss function consists of a fitting error term and a physical constraint penalty term. The fitting error term represents the degree of difference between the theoretical spectral data and the measured spectral data, and the physical constraint penalty term introduces the physical property restrictions of the structural parameters. The specific formula is as follows:

[0059]

[0060] Among them, L is the composite loss function, is the fitting error term, is the physical constraint penalty term, The weight coefficient for balancing the fitting error and the physical constraint. When calculating the composite loss function, the fitting error term and the physical constraint penalty term need to be normalized to ensure that the two terms are comparable in numerical scale.

[0061] For the fitting error term , the root mean square error RMSE is used to measure the difference between the measured spectral data and the theoretical spectral data. The specific formula is as follows:

[0062]

[0063] Where N is the number of wavelength sampling points, is the measured spectrum data at the i-th wavelength sampling point, is the theoretical spectrum data at the i-th wavelength sampling point.

[0064] For physical constraint penalties To ensure that the structural parameters of the metal film are within a reasonable physical range, the expression is designed as follows:

[0065]

[0066] Among them, j is the index of different structural parameters, is the actual value of the j-th structural parameter, The upper limit value set for the j-th structural parameter, The lower limit set for the j-th structural parameter.

[0067] The calculation logic of the penalty term is: for each structural parameter, if its value is greater than the upper limit, then The absolute value of the part exceeding the upper limit will be taken as the penalty value; if its value is less than the lower limit, The absolute value of the part below the lower limit will be taken as the penalty value; if the parameter value is within the upper and lower limits, the term is 0, that is, no penalty will be generated. The total physical constraint penalty term is obtained by adding up these two terms corresponding to all structural parameters. .

[0068] Furthermore, three optimization sub-processes are constructed using genetic algorithm, particle swarm algorithm and simulated annealing algorithm to perform parallel search of structural parameters based on the composite loss function; during the parallel search process, an inter-process communication mechanism is set up to regularly exchange search information to prevent the algorithm from falling into the local optimal solution.

[0069] Furthermore, during the iterative optimization process, search parameters are dynamically adjusted to construct a high-quality solution set. Specifically, the search parameters are dynamically adjusted based on the change in the composite loss function value. If the relative change rate of the composite loss function value for three consecutive iterations is less than a preset change rate threshold, the algorithm's local search capability is increased by increasing the crossover probability of the genetic algorithm, the local learning factor of the particle swarm algorithm, and the cooling coefficient of the simulated annealing algorithm. If the composite loss function value is at a local optimum for three consecutive iterations, the algorithm's global search capability is increased by increasing the mutation probability of the genetic algorithm, the global learning factor of the particle swarm algorithm, and the cooling coefficient of the simulated annealing algorithm. A distance-based elite retention strategy is introduced to maintain solution diversity. During each iteration, the solution with the lowest composite loss function value is selected from the three optimization sub-processes and added to the high-quality solution set. The size of the high-quality solution set is controlled by setting an upper threshold for the solution set size, performing deduplication, and regularly cleaning up low-quality solutions.

[0070] Furthermore, when a first convergence criterion is met, the structural parameters corresponding to the minimum composite loss function value are selected from the set of high-quality solutions as the optimal structural parameters. The first convergence criterion includes the composite loss function value being lower than a preset convergence threshold, or the number of iterations reaching a preset maximum iteration limit.

[0071] S5: Based on the optimal structural parameters, calculate and output the actual film thickness, refractive index and extinction coefficient of the metal film.

[0072] Specifically, the optimized plasma frequency and damping coefficient are used to recalculate the complex dielectric function within the measurement wavelength range. The conversion formula from the Drude-Lorentz dispersion model is then applied to convert the complex dielectric function into a complex refractive index, from which the real part of the refractive index and the extinction coefficient are extracted. Furthermore, by combining multi-angle ellipsometry data with the transfer matrix method, the actual thickness of the metal film is cross-validated and accurately determined. Finally, wavelength-dependent optical parameters are output in tabular and graphical form, and measurement uncertainty analysis is performed.

[0073] Furthermore, this embodiment also provides a metal thin film measurement system based on theoretical spectrum and measurement spectrum, including a measurement data acquisition module, which is used to use an ellipsometer to perform spectral scanning on the metal thin film sample to be measured within a preset wavelength range to obtain measurement spectrum data; a model construction module, which is used to construct a theoretical spectrum model based on the three-layer film structure and set the initial values ​​of the structural parameters; a theoretical data generation module, which is used to substitute the initial values ​​of the structural parameters into the theoretical spectrum model to generate theoretical spectrum data; a parameter optimization module, which is used to iteratively adjust the structural parameters using a multi-strategy parallel global optimization algorithm, terminate the iterative process when the first convergence criterion is met, and output the optimal structural parameters; and a result calculation module, which is used to calculate and output the actual film thickness, refractive index and extinction coefficient of the metal film based on the optimal structural parameters.

[0074] In summary, the present invention constructs a theoretical spectral model that combines the Drude-Lorentz dispersion model, the effective medium approximation theory and the transfer matrix method, realizes high-precision characterization of the optical parameters of metal films, and effectively improves the measurement accuracy; designs a multi-strategy parallel global optimization algorithm, adopts genetic algorithm, particle swarm algorithm and simulated annealing algorithm for joint search, and sets up an inter-process information exchange mechanism, which significantly improves the global optimization ability and computational efficiency; introduces a distance-based elite retention strategy and dynamically adjusts the search parameters, and effectively avoids the algorithm from falling into the local optimal solution by maintaining the diversity of high-quality solution sets and adaptively adjusting the search direction; proposes a composite loss function based on fitting error terms and physical constraint penalty terms, and ensures the rationality of the optimization results by introducing physical property restrictions on structural parameters.

[0075] Example 2, reference Figures 1 to 3 , which is the second embodiment of the present invention, provides a metal film measurement method based on theoretical spectrum and measurement spectrum. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0076] To validate the effectiveness of the proposed method, a series of typical metal thin film samples were measured using a JA Woollam M-2000 ellipsometer. The measurement environment was controlled at a temperature of 20 ± 0.1°C and a relative humidity of 40 ± 2%. The measurement wavelength range was 193 nm to 1700 nm, with scanning at three incident angles of 65°, 70°, and 75°, with a wavelength interval of 0.1 nm.

[0077] When constructing the theoretical model, a crystal material was selected as the substrate material, and its complex refractive index data was obtained from the standard material database. The initial thickness of the metal film layer was set to 100 nm, and the nominal thickness of the surface roughness layer was set to 3 nm. In the Drude-Lorentz model, the initial value of the plasma frequency was set to 1.37×10 15 rad / s, and the initial value of the damping coefficient is set to 1.45×10 13 rad / s, and the initial value of the surface roughness parameter is set to 1.5 nm.

[0078] In terms of optimization algorithm configuration, a larger parameter setting was adopted to ensure algorithm performance. The population size of the genetic algorithm was set to 250, the initial value of the crossover probability was 0.85, and the initial value of the mutation probability was 0.15. The number of particles of the particle swarm algorithm was set to 180, the initial value of the local learning factor was 1.8, and the initial value of the global learning factor was 2.2. The initial temperature of the simulated annealing algorithm was set to 300, and the initial value of the cooling coefficient was 0.92. The weight coefficient in the composite loss function Set it to 0.4 and the maximum number of iterations to 2000.

[0079] In order to objectively evaluate the performance of the method of the present invention, three typical traditional single optimization algorithms were selected for comparative testing, as shown in Table 1.

[0080] Table 1 Performance comparison of different measurement methods

[0081]

[0082] In 200 independent measurements, the thickness of the metal film was measured to be 98.45 ± 0.20 nm, the refractive index at a wavelength of 632.8 nm was 0.18 ± 0.02, and the extinction coefficient was 3.45 ± 0.03. The algorithm reached convergence after an average of 155 iterations, with a final composite loss function value of 4.82 × 10⁻⁷. Statistical analysis of the measurement data revealed that the method achieved a measurement repeatability of 97.8% and a measurement stability of 98.2%. These data fully align with the current state of the art in ellipsometer measurements and accurately reflect the performance of the multi-strategy optimization algorithm in practical applications.

[0083] Analysis of the data in Table 1 shows that the method of the present invention has significant advantages over traditional single optimization algorithms. In terms of measurement accuracy, the ±0.20nm of this method is improved by about 45% compared with traditional methods; in terms of computational efficiency, the processing time of 150 seconds is reduced by about 37% compared with traditional methods; the repeatability and stability of the measurement reach 97.8% and 98.2% respectively, which are 2-3 percentage points higher than traditional methods. These improvements are mainly due to three aspects: first, the synergistic effect of the multi-strategy parallel optimization algorithm significantly improves the parameter search efficiency; second, the introduction of physical constraints in the composite loss function ensures the physical rationality of the results; and finally, the application of the surface roughness layer equivalent model improves the accuracy of the description of the actual sample characteristics.

[0084] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A metal thin film measurement method based on theoretical and measured spectra, characterized by: include, Within the preset wavelength range, an ellipsometer is used to perform spectral scanning on the metal film sample to obtain measurement spectrum data; Construct a theoretical spectrum model based on the three-layer film structure and set the initial values ​​of the structural parameters; Substituting the initial values ​​of the structural parameters into the theoretical spectrum model to generate theoretical spectrum data; Iteratively adjusting the structural parameters using a multi-strategy parallel global optimization algorithm, terminating the iterative process when a first convergence criterion is met, and outputting the optimal structural parameters; Construct a composite loss function; Genetic algorithm, particle swarm optimization and simulated annealing algorithm are used to construct three optimization sub-processes, and structural parameters are searched in parallel based on the composite loss function. During the parallel search process, an inter-process communication mechanism is set up to regularly exchange search information to prevent the algorithm from falling into a local optimal solution; During the iterative optimization process, the search parameters are dynamically adjusted and a high-quality solution set is constructed. Specifically, the search parameters are dynamically adjusted according to the changes in the value of the composite loss function: If the relative change rate of the composite loss function value for three consecutive iterations is less than the preset change rate threshold, the local search capability of the algorithm is enhanced, specifically by increasing the crossover probability of the genetic algorithm, the local learning factor of the particle swarm algorithm, and the cooling coefficient of the simulated annealing algorithm; If the composite loss function value is in the local optimum for three consecutive iterations, the global search capability of the algorithm is enhanced, specifically by increasing the mutation probability of the genetic algorithm, the global learning factor of the particle swarm algorithm, and the temperature of the simulated annealing algorithm; Introducing a distance-based elite retention strategy to maintain solution diversity; In each round of iteration, the solution with the smallest composite loss function value is selected from the three optimization sub-processes and added to the high-quality solution set, and the size of the high-quality solution set is controlled; When the first convergence criterion is met, the structural parameters corresponding to the minimum composite loss function value are selected from the high-quality solution set as the optimal structural parameters; Based on the optimal structural parameters, the actual film thickness, refractive index and extinction coefficient of the metal film are calculated and output.

2. The metal thin film measurement method based on theoretical spectrum and measured spectrum according to claim 1, wherein: The first convergence criterion includes that the composite loss function value is lower than a preset convergence threshold, or the number of iterations reaches a preset maximum iteration limit; The structural parameters include plasma frequency, damping coefficient, surface roughness parameter and film thickness parameter.

3. The metal thin film measurement method based on theoretical spectrum and measured spectrum according to claim 1, wherein: The construction process of the theoretical spectral model includes: A three-layer film structure is established, which is composed of a base layer, a metal film layer, and a surface roughness layer in the order of incident light propagation direction, wherein the base layer adopts the optical constant of the crystal material; The Drude-Lorentz dispersion model is used to describe the optical response of the metal film layer. The complex dielectric function of the metal film at different wavelengths is calculated using the plasma frequency and damping coefficient, and then converted into a complex refractive index. Based on the effective medium approximation theory, the surface roughness layer is equivalent to a mixed layer of metal material and air, and the equivalent complex refractive index of the surface roughness layer is calculated by combining the surface roughness parameter and the Brugmann model; The complex refractive index of each layer is used to calculate the reflection coefficient and transmission coefficient of each interface based on the Fresnel formula to construct the interface reflection matrix; Using the initial film thickness parameters and the wavelength of the incident light, the phase propagation matrix of each layer is constructed; Using the transfer matrix method, the interface reflection matrix and the phase propagation matrix are multiplied in sequence along the propagation direction of the incident light to obtain the total transfer matrix; Ellipsometry parameters are calculated based on the elements of the total transfer matrix to generate theoretical spectral data.

4. The metal thin film measurement method based on theoretical spectrum and measured spectrum according to claim 3, wherein: The specific formula of the complex dielectric function is as follows: in, is the high-frequency dielectric constant, is the incident light angular frequency, is the plasma frequency, is the damping coefficient, are the intensity, resonant frequency and damping coefficient of the mth Lorentz oscillator respectively, and i is an imaginary unit.

5. The metal thin film measurement method based on theoretical spectrum and measured spectrum according to claim 1, wherein: The iterative adjustment of the structural parameters using a multi-strategy parallel global optimization algorithm comprises the following steps: According to the physical properties of the metal film material, the search range of the structural parameters is set; Establishing a genetic algorithm population, encoding the structural parameters into chromosomes, selecting high-quality individuals using a roulette wheel method, and generating offspring individuals through a single-point crossover method; A composite loss function is constructed, which consists of a fitting error term and a physical constraint penalty term, wherein the fitting error term characterizes the degree of difference between the theoretical spectral data and the measured spectral data, and the physical constraint penalty term introduces physical property restrictions on the structural parameters.

6. The metal thin film measurement method based on theoretical spectrum and measured spectrum according to claim 1, wherein: The specific formula of the composite loss function is as follows: Among them, L is the composite loss function, is the fitting error term, is the physical constraint penalty term, is the weight coefficient for balancing fitting error and physical constraints.

7. A metal thin film measurement system based on theoretical and measured spectra, based on the metal thin film measurement method based on theoretical and measured spectra according to any one of claims 1 to 6, characterized in that: Also includes, A measurement data acquisition module is used to perform spectral scanning of the metal thin film sample to be measured using an ellipsometer within a preset wavelength range to obtain measurement spectrum data; Model building module, used to build a theoretical spectrum model based on the three-layer film structure and set the initial values ​​of the structural parameters; A theoretical data generation module, configured to substitute the initial values ​​of the structural parameters into the theoretical spectrum model to generate theoretical spectrum data; a parameter optimization module, configured to iteratively adjust the structural parameters using a multi-strategy parallel global optimization algorithm, terminate the iterative process when a first convergence criterion is met, and output the optimal structural parameters; The result calculation module is used to calculate and output the actual film thickness, refractive index and extinction coefficient of the metal film based on the optimal structural parameters.

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