Method for synchronously acquiring hardness and thickness of thin film in thin film substrate system

Abstract

The invention discloses a method for synchronously acquiring hardness and thickness of a film in a film substrate system, which relates to the technical field of surface coating, and comprises the following steps: carrying out indentation test on a first film substrate system with known film thickness to obtain a plurality of groups of first data; inputting the multiple groups of first data into a hardness-depth model for fitting to obtain a first curve and returning the first curve to infinity to obtain the hardness of the substrate and a calibration value of a hardness distribution parameter; performing indentation test on a second film substrate system which is unknown in film thickness and adopts the same material to obtain multiple groups of second data; the hardness of the substrate, the calibration value and the multiple sets of second data are input into a hardness-depth model for fitting, and the film thickness is obtained; and the film thickness, the substrate hardness and the multiple sets of second data are input into the hardness-depth model for fitting, a second curve is obtained, the second curve is regressed to the depth of 0, and the hardness of the film is obtained. According to the invention, the dependence of fitting quality on data in a wide range is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of surface coating, in particular to a method for synchronously obtaining the hardness and thickness of a thin film in a thin film-substrate system. BACKGROUND

[0002] Thin film-substrate systems are widely used in many industrial fields. Thin films play an important role in these fields because they can endow substrates with excellent properties such as thermal insulation, corrosion resistance and oxidation resistance. The mechanical properties of thin films play a decisive role in their use effect. With the continuous progress of surface engineering technology, the mechanical behavior of thin film-substrate systems has attracted widespread attention from academia and industry. Among many characterization techniques, micro-indentation testing has become an important tool for studying the mechanical response of thin films due to its simple operation, low cost and small invasiveness. As a simple, non-destructive and efficient indicator for evaluating the mechanical properties of materials, hardness measurement has a history of nearly a hundred years and is widely used in the performance evaluation of various thin film-substrate systems. Similarly, the thickness of the thin film is another key physical parameter. For example, the coating on the cladding of nuclear fuel is usually very thin, but it plays a crucial protective role. Therefore, accurate evaluation of the hardness and thickness of the thin film is crucial for evaluating the reliability of engineering materials.

[0003] In hardness measurement, when the thickness of the thin film is extremely thin, the substrate material inevitably participates in the deformation process during indentation, and partial plastic deformation occurs. This leads to the measured hardness value reflecting not the true hardness of the thin film, but the composite hardness of the thin film-substrate system. Therefore, how to effectively separate the true hardness of the thin film from the thin film-substrate system has become a key issue in the research field. Scholars have thoroughly explored the relationship between the relative indentation depth (RID) and the composite hardness, and generally believe that the indentation depth should be controlled below 10% of the thickness of the thin film to accurately reflect the true hardness. A large number of experimental and numerical simulation studies have shown that this empirical rule lacks universality. In order to improve the measurement accuracy, sometimes a deeper indentation is used to reduce the influence of surface roughness and probe defects. However, as the indentation depth increases, the influence of the substrate on the hardness measurement result becomes more and more obvious. In the industrial scene, the main method for extracting the thickness of the thin film mainly relies on optical measurement and probe technology. This requires the simultaneous determination of the thickness and hardness of the thin film through independent testing. More difficultly, the extremely thin nature of the thin film makes accurate measurement even more difficult. Therefore, to reliably obtain the thickness and hardness data of the thin film at the same time, there are still major challenges. Therefore, there is an urgent need for a method that can simultaneously and accurately measure the true hardness and thickness of the thin film.

[0004] To break the bottleneck, reduce the influence of the substrate on the measurement results, and obtain the real hardness of the thin film, Korsunsky et al. proposed a hardness-depth model for characterizing the relationship between the composite hardness and the relative indentation depth based on the energy consumed by the deformation of the thin film and the substrate during the indentation process, which provides a new understanding and analysis method for the hardness value of the thin film substrate system from the perspective of energy. The model has been applied to a series of indentation processes of thin film systems with known film thickness and indentation experiments with various depth ranges, and the fitting quality is good, but the fitting quality is still largely dependent on the indentation data obtained in a large amount of data. For unknown film thickness and smaller range of data, the quality of model fitting is poor. SUMMARY

[0005] Based on the defects existing in the prior art, the present application provides a method for simultaneously obtaining the hardness and thickness of a thin film in a thin film substrate system, which solves the problem that the fitting quality of the existing model is largely dependent on the indentation data obtained in a large amount of data. For unknown film thickness and smaller range of data, the quality of model fitting is poor.

[0006] The present application adopts the following technical solutions: The present application provides a method for simultaneously obtaining the hardness and thickness of a thin film in a thin film substrate system, comprising the following steps: Performing indentation testing on a first thin film substrate system with known thin film thickness to obtain a plurality of first data, each of which includes a relative indentation depth and a corresponding system composite hardness value; Inputting the plurality of first data into a hardness-depth model for fitting to obtain a first curve, and regressing the first curve to infinity to obtain the calibration value of the hardness of the substrate and the hardness distribution parameter in the hardness-depth model in the first thin film substrate system. The hardness-depth model is used to characterize the relationship between the composite hardness and the relative indentation depth in the thin film substrate system. The hardness distribution parameter is used to quantify the behavior transition process from the thin film dominance to the substrate dominance; Performing indentation testing on a second thin film substrate system with unknown thin film thickness but using the same material to obtain a plurality of second data, each of which includes an absolute indentation depth and a corresponding system composite hardness value. The absolute indentation depth is the depth value of the indenter pressed into the thin film, and the relative indentation depth is the ratio of the absolute indentation depth to the thickness of the thin film; Inputting the hardness of the substrate, the calibration value of the hardness distribution parameter, and the plurality of second data into the hardness-depth model for fitting to obtain the thickness of the thin film in the second thin film substrate system. Inputting the thickness of the thin film, the hardness of the substrate, and the plurality of second data into the hardness-depth model for fitting to obtain a second curve, and regressing the second curve to a depth of 0 to obtain the hardness of the thin film in the second thin film substrate system.

[0007] Preferably, the hardness-depth model is specified as follows: ; wherein, H is the composite hardness of the film-substrate system, Hs is the hardness of the substrate, Hf is the hardness of the film, h is the relative indentation depth, is the hardness distribution parameter.

[0008] Preferably, the input of the plurality of sets of first data to the hardness-depth model is fitted by a least squares method.

[0009] Preferably, the same size and shape of indenter is used for the indentation tests of different film-substrate systems.

[0010] Compared with the prior art, the above at least one technical solution adopted by the present application can achieve the following beneficial effects: The present application firstly performs an indentation test on a first film-substrate system with a known film thickness to obtain a plurality of sets of first data, inputs the plurality of sets of first data to a hardness-depth model for fitting to obtain a first curve, and regresses the first curve to infinity to obtain the hardness of the substrate in the first film-substrate system and the calibrated value of the hardness distribution parameter in the hardness-depth model. The present application proposes a new numerical regression method, which calibrates the parameters of a film-substrate system with a known material property and film thickness once, does not need to use indentation data in a large range for fitting, avoids fitting the data in the entire indentation depth range, and reduces the dependence of the fitting quality on the data in a wide range.

[0011] Then, an indentation test is performed on a second film-substrate system with an unknown film thickness but using the same material to obtain a plurality of sets of second data, inputs the hardness of the substrate, the calibrated value of the hardness distribution parameter, and the plurality of sets of second data to the hardness-depth model for fitting to obtain the film thickness in the second film-substrate system, inputs the film thickness, the hardness of the substrate, and the plurality of sets of second data to the hardness-depth model for fitting to obtain a second curve, and regresses the second curve to a depth of 0 to obtain the hardness of the film. The present application only needs to calibrate the hardness distribution parameter of a film-substrate system with a known film thickness once, and then the film hardness, the film thickness, and the hardness of the substrate of a film-substrate system with an unknown film thickness but using the same material can be obtained by one fitting of the numerical method. BRIEF DESCRIPTION OF DRAWINGS

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 The curve showing the variation of composite hardness of the entire membrane-based system; Figure 2 This is a flowchart of a method for simultaneously obtaining the hardness and thickness of a thin film in a thin film substrate system according to the present invention; Figure 3 This is a schematic diagram of the nanoindentation simulation of the present invention; Figure 4 This is a diagram showing the boundary conditions of the model in this invention. Figure 5 This is a load-displacement curve of a 100nm film thickness according to the present invention; Figure 6 This is a load-displacement curve of a 300nm film thickness according to the present invention; Figure 7 This is a load-displacement curve of a 300nm film thickness according to the present invention; Figure 8 This is a hardness-depth curve of the substrate material of the present invention; Figure 9 This is a hardness-depth curve of the thin film of the present invention; Figure 10 For different film thicknesses of the present invention curve; in, Figure 10 (a): film thickness curve, Figure 10 (b): Enlarged view of a portion; Figure 11 This is a schematic diagram of the load-relative indentation depth curves for films of different thicknesses according to the present invention; Figure 12 The substrate hardness and parameters are fitted when the film thickness of the present invention is 0.1 μm. x A schematic diagram; Figure 13 The substrate hardness and parameters are fitted when the film thickness of the present invention is 0.2 μm. x A schematic diagram; Figure 14 The substrate hardness and parameters are fitted when the film thickness of the present invention is 0.3 μm. x A schematic diagram; Figure 15 This is a schematic diagram of fitting a 0.1 μm film thickness using parameter x according to the present invention; Figure 16 Graph of film thickness of 0.2 μm fitted by parameter x for the present invention; Figure 17 Graph of film thickness of 0.3 μm fitted by parameter x for the present invention; Figure 18 Graph of film thickness of 0.5 μm fitted by parameter x for the present invention; Figure 19 Graph of film hardness regression of 0.2 μm fitted for the present invention; Figure 20 Graph of film hardness regression of 0.3 μm fitted for the present invention; Figure 21 Graph of film hardness regression of 0.5 μm fitted for the present invention; Figure 22 Graph of hardness of the modified material backing for the present invention; Figure 23 Graph of H-RID of the same film material different backing for the present invention; Figure 24 Graph of film thickness of 0.1 μm fitted backing hardness and parameter x for the present invention; Figure 25 Graph of film thickness of 0.2 μm fitted backing hardness and parameter x for the present invention; Figure 26 Graph of film thickness of 0.3 μm fitted backing hardness and parameter x for the present invention; Figure 27 Graph of film thickness of 0.1 μm fitted by parameter x for the present invention; Figure 28 Graph of film thickness of 0.2 μm fitted by parameter x for the present invention; Figure 29 Graph of film thickness of 0.3 μm fitted by parameter x for the present invention; Figure 30 Graph of film thickness of 0.5 μm fitted by parameter x for the present invention; Figure 31 Graph of film hardness regression of 0.2 μm fitted for the present invention; Figure 32 Graph of film hardness regression of 0.3 μm fitted for the present invention; Figure 33 Graph of film hardness regression of 0.5 μm fitted for the present invention. DETAILED DESCRIPTION

[0014] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort are within the scope of the present application.

[0015] Embodiment 1 Relevant background: The existing model usually estimates the composite hardness at different indentation depths by changing the indentation load, while assuming that the film thickness is fixed. However, B.D. and Korsunsky et al. found that as the indentation depth increases, the response of the film-substrate system will undergo different mechanical states: first, the pure elastic response stage, and the material mechanical process can be divided into four stages: the film dominant stage, the mixed transition stage, the substrate dominant stage, and the final complete substrate dominant stage. When the indentation test is carried out with a pointed indenter or a conical indenter, it is found that the highest load P applied almost always corresponds to the maximum indentation depth delta . The highest load P applied and the maximum indentation depth delta may also be chosen to describe the indentation, and for a given hardness value, there is a one-to-one relationship between the highest load P applied and the maximum indentation depth delta , which is given by the following equation: (1); where H is the hardness, is a parameter describing the indenter geometry. For a Vickers indenter, , where is the diagonal of the indentation. It is implicitly assumed here that there is no significant elastic recovery of the diagonal length of the indentation during unloading, so the measured unloading value can be used to infer the depth. If the sample hardness is assumed to be constant, equation (2) can be re-expressed in terms of load-displacement relationship as follows: (2); The energy required by the loading system to produce the maximum indentation depth is calculated by the work done during the entire indentation process: (3); This quantity is called the "total work of indentation" and can be measured by using the continuous indentation technique.

[0016] The hardness H in equation (4) is expressed in terms of the total work : (4); In the thin film substrate hardness test, the total energy consumption is composed of two parts: the energy consumed by the plastic deformation of the substrate material consumption and the energy consumed by the crack and deformation of the thin film The total energy consumed is: (5); Substitute equation (6) into equation (5) and consider the energy distribution of the substrate and the film to obtain: (6); (7); The relationship allows the hardness of the film and the substrate to be determined by fitting experimental data obtained at a series of contact scales, the quality of the fitting depends on the range of indentation data, and multiple tests combined with different indentation data are required. During the entire indentation test, as the indenter continuously penetrates the film-base system, the initial stage reflects the hardness of the film, and the composite hardness value of the entire system gradually transitions from the hardness value of the film to the hardness value of the substrate as the indentation depth increases. When the penetration depth is large enough, the composite hardness value of the entire system will eventually tend to the hardness value of the substrate, and the change of the composite hardness of the entire film-base system presents a type, and equation (7) reflects this change trend, as shown in Figure 1 Through numerical calculation and analysis of the entire equation, it is found that the error of the composite hardness described by the formula is small, and the composite hardness is determined by the film hardness and the substrate hardness. Since hardness is an inherent property of an object, for the same kind of film and substrate, even if the thickness of the film is different, their hardness will not change. The relationship between the composite hardness of the film-base system with different film thickness and the relative indentation depth is the same. The dimensionless factor , also known as the hardness distribution parameter, describes the range of the entire composite hardness from the film hardness to the substrate hardness.

[0017] Based on the above problems and related background, the present application proposes a method for simultaneously obtaining the hardness and thickness of a thin film in a film-substrate system. The hardness-depth model is used to calibrate the dimensionless parameter in the model using a film-substrate system with known film thickness. The hardness, thickness and hardness of the substrate of the film in the film-substrate system with unknown film thickness but the same material properties are simultaneously extracted using the segmented fitting strategy under the condition of only a small amount of indentation experiment. The method can separate the film thickness, hardness and substrate hardness from the indentation data, and the method is verified by finite element simulation. The method aims to avoid the limitations of traditional methods, improve test efficiency, and provide method guidance for subsequent application in experimental testing. Referring to Figure 2 , the method specifically includes the following steps:​​ S1: Perform indentation test on a first film-substrate system with known film thickness, to obtain a plurality of first data, each of which includes relative indentation depth and corresponding system composite hardness value.

[0018] When extracting hardness by indentation method, the surface of the sample must be smooth and flat, because the surface topography of the sample will significantly affect the measurement results, resulting in a large deviation in the measurement results. For thinner films, polishing may not meet the requirements and may introduce mechanical stress during polishing, further causing deviation in the measurement results, so a larger indentation depth is selected to reduce the influence of surface topography, and a suitable numerical method is used for fitting.

[0019] S2: Input the plurality of first data into the hardness-depth model for fitting to obtain a first curve, and regress the first curve to infinity to obtain the hardness of the substrate in the first film-substrate system and the calibrated value of the hardness distribution parameter in the hardness-depth model.

[0020] Select all the composite hardness and relative indentation depth data from the transition region data to the maximum indentation depth data of the first curve, and input the plurality of data into the hardness-depth model for fitting by using the least squares method. The equation curve obtained by fitting can be extrapolated to infinity to obtain the substrate hardness value, and the hardness distribution parameter is also obtained.

[0021] The composite hardness value of the entire system during the indentation process of the film-substrate system is constantly changing with the indentation depth, and for the same material and different film thickness of the film-substrate system, their relative indentation depth hardness is the same. The parameter in formula (7) reflects the entire transition region. Since the indentation depth is constantly increasing, the final composite hardness will tend to the hardness value of the substrate, and to calibrate the parameter , the fitting data range only needs to include part of the transition region data.

[0022] S3: Perform indentation test on a second film-substrate system with unknown film thickness but using the same material, to obtain a plurality of second data, each of which includes absolute indentation depth and corresponding system composite hardness value.

[0023] In actual industrial applications, the film thickness is usually unknown, so it is necessary to extract the relationship between composite hardness and absolute depth by indentation technology. The absolute indentation depth is the depth value of the indenter pressed into the film, and the relative indentation depth is the ratio of the absolute indentation depth to the film thickness.

[0024] S4: inputting the calibration value of the hardness and hardness distribution parameter of the substrate and the plurality of second data into the hardness-depth model to perform fitting to obtain the film thickness in the second film-substrate system; inputting the film thickness, the hardness of the substrate and the plurality of second data into the hardness-depth model to perform fitting to obtain the second curve, and regressing the second curve to the depth of 0 to obtain the film hardness in the second film-substrate system.

[0025] The calibration value of the hardness and hardness distribution parameter of the substrate is inputted into the hardness-depth model to perform fitting in combination with the data of the hardness and absolute indentation depth at different depths obtained through experiments, the film thickness is fitted through the least square method by fitting a plurality of hardness and absolute indentation depth. The film thickness and the hardness of the substrate are inputted into the hardness-depth model to perform fitting by using the same processing method, and the hardness value corresponding to the depth of 0 when the fitted data curve is regressed to the depth of 0 is the hardness of the film.

[0026] Example 2 Elastic-plastic deformation under the action of the indenter is a highly nonlinear contact problem with variable geometry boundary conditions.

[0027] In order to simulate the indentation process of the film-substrate system, the present embodiment uses a commercial finite element program Abaqus (Advanced Simulation for Engineering and Sciences) for modeling and analysis. In addition to being able to simulate contact problems, it can also simulate large deformation and elastic-plastic strain related to indentation. The indenter used for nanoindentation testing is usually a Berkovich indenter and a cube corner indenter, because they can be more easily manufactured with a sharp tip than a Vickers and Knoop indenter. The research of Dao et al. shows that the Berkovich indenter and the conical indenter have the same depth-area relationship, so in the finite element analysis, the Vickers indenter is usually approximated as a movable rigid cone with a half-cone angle of 70.32°, and a reference point is established for the indenter to facilitate the application of load. In view of the fact that a two-dimensional model can significantly speed up the finite element analysis and save computing resources, in order to reduce the computing resources of the finite element simulation, the present invention establishes a two-dimensional nanoindentation axisymmetric geometric model, as shown in Figure 3 The size of the nanoindentation geometric model is 10m x 10m, and the film thickness is set to 0.1m-0.3m. The nanoindentation geometric model includes the pressed material and the indenter, and the maximum indentation depth is 1.5 times the film thickness to ensure sufficient excitation of the plastic deformation of the substrate. The model size is more than 10 times the maximum indentation depth, according to the Saint-Venant principle, plastic deformation only occurs in the local part of the material being pressed, and the material far away is not much affected, and the size effect has little effect on the simulation results.

[0028] The indenter and the pressed material are designed for surface-to-surface contact, with the indenter as the principal surface and the pressed material as the secondary surface. It is assumed that the film and substrate are perfectly bonded, and the contact between the rigid indenter and the film is defined as frictionless. Both the film and the substrate are considered stress-free and in perfect contact. The contact properties are set as tangential frictionless contact and normal hard contact, meaning that no delamination or slippage will occur at the interface or the contact point between the indenter and the film during the indentation process. The material is assumed to be an isotropic, homogeneous, elastoplastic material that obeys the von Mises yield criterion.

[0029] (8); In the formula, S ij For the deviatoric stress tensor, sigma ij For equivalent compressive stress, It is the Kronecker symbol. p It is stress. q This is the yield stress.

[0030] Boundary conditions are a crucial step in the finite element simulation process. Their correct setting determines the accuracy and convergence of the calculation results. The boundary conditions for a nanoindentation geometric model are as follows: Figure 4 As shown. The material being indented is far from the indentation location, so it does not generate significant stress and strain. Therefore, the right side of the model can be set as a free surface, the bottom of the model as completely fixed, and the left side of the model as axisymmetric constraint. The degree of freedom in the x-direction is fixed, and a load in the y-direction is applied to the reference point of the indenter. The degrees of freedom in the x-displacement direction and z-rotation direction are fixed, meaning the reference point only moves along the y-direction. There are two loading methods in the nanoindentation finite element simulation process: displacement loading and force loading. The load-displacement curves obtained by displacement loading and force loading are the same. Considering the convergence of the simulation calculation, displacement loading is used. In the finite element program, a downward displacement is applied to the indenter, causing the indenter to press into the material surface. When a given indenter displacement is reached, an upward displacement is then given to the indenter until it no longer contacts the sample. For each indenter displacement, the corresponding load is determined by the sum of the reaction forces at the indenter contact node, obtained by solving the nonlinear equation: (9); In the formula, K It is the stiffness matrix. It is nodal displacement. It is an increase in force.

[0031] In finite element simulation, meshing strategy has important influence on calculation accuracy and efficiency, mainly involving the selection of element type and the reasonable design of element size and shape. Based on the assumption of axisymmetry, the finite element model of nanoindentation is established, and the four-node axisymmetric reduced integration element CAX4R is used for discretization. This element type shows good numerical stability and calculation efficiency when dealing with complex problems such as geometric nonlinearity, large deformation and material nonlinearity, and is especially suitable for capturing local strong nonlinear response. In order to improve the simulation accuracy and consider the consumption of calculation resources, a progressive meshing strategy is adopted, that is, fine mesh is applied in the contact area, and the element size gradually increases in the area away from the contact area. The minimum element size in the contact area between the indenter and the material is refined to 0.005 microns. It is worth noting that the element size in the contact area needs to be determined through multiple iterative calculations to ensure the stability and accuracy of the simulation results. If the mesh in the contact area is too coarse, although the calculation time is significantly reduced, it will lead to a decrease in the accuracy of the load-displacement curve, and the curve in the loading stage will fluctuate obviously. On the contrary, refining the mesh can effectively improve the smoothness and accuracy of the curve, but it will significantly increase the calculation amount. Therefore, the minimum element size in the contact area needs to be reasonably determined by balancing the calculation efficiency and the result accuracy, so as to ensure the reliability and representativeness of the finite element simulation results. The constitutive model of the material is assumed to be ideal elastic-plastic, the Poisson's ratio of the material is 0.3, the yield strength of the film is 5000 MPa, the yield strength of the substrate is 500 MPa, the film thickness is set to 0.1 microns-0.3 microns, and table 1 shows the values of the elastic modulus (Es) of the film and the elastic modulus (Ef) of the substrate.

[0032] Table 1 input parameters in finite element simulation

[0033] Figures 5-7 The load-displacement curves obtained by simulation calculation are drawn respectively when the elastic modulus of the substrate is 100 GPa, the elastic modulus of the film is 150 GPa, and the film thickness is 0.1 microns, 0.2 microns and 0.3 microns respectively. The three groups of curves are smooth and continuous curves, and there is no obvious fluctuation in the loading stage and unloading stage. When the indentation depth of the indenter reaches the maximum, the stress is mainly concentrated in the tip of the indenter, and presents a semicircular shape outward, and the stress value in the tip of the indenter reaches the maximum, and the stress nephogram is not affected by the boundary, which shows the rationality of the model.

[0034] According to the method of Oliver-Pharr, the hardness is usually defined as the average contact stress: (10); In the formula, The maximum load is A, the contact area is H, and the hardness is H. ​

[0035] It reflects the sample material's ability to withstand contact loads, and the contact area is a measure of that ability. It is usually not measured directly, but rather through an area function. This is sometimes referred to as the indenter shape function. Table 2 shows the characteristic parameters of commonly used indenters.

[0036] Table 2 Characteristic parameters of commonly used indenters

[0037] The contact area of ​​the two-dimensional nanoindentation axisymmetric geometric model is , This represents the indentation depth at maximum load. The hardness of the bulk material was calculated first, followed by the hardness of the thin-film substrate composite material. Figure 8 and Figure 9 This is a hardness-depth curve for a pure bulk material. For pure bulk materials, the substrate does not affect the hardness. The graph shows varying degrees of oscillation in the initial stage, which is due to the convergence of the initial finite element calculation. As the calculation progresses and the indentation depth increases, the curve gradually stabilizes. The average hardness of the pure bulk material substrate is calculated. The average hardness of the thin film of a pure bulk material is calculated to be: .

[0038] Figure 10 and Figure 11 The thin film-substrate system was plotted separately. (Relative indentation depth) curve and thin film substrate system The curves show that for thin-film-substrate systems of the same material, even with different film thicknesses, their relative indentation depth-hardness curves are the same. Relative indentation depth is calculated by dividing the indentation depth by the film thickness. This is because for film-substrate systems of the same material but different film thicknesses, the load they experience when indented to the same depth is the same, and the contact area under the indenter is also the same. The curves also show that initially, the hardness is close to that of a bulk film. As the indentation depth increases, the hardness gradually transitions from the hardness of a film to that of a bulk substrate. Then, with further increases in indentation depth, the hardness value gradually approaches that of a bulk substrate. Therefore, it can be concluded that the hardness of the film-substrate system changes with the indentation depth. As shown in the figure, for different film thicknesses, when the relative indentation depth is the same, the thicker the film, the greater the load it bears. This is because when the relative indentation depth is the same, the absolute indentation depth of films of different thicknesses is different. The thicker the film, the deeper the absolute indentation depth. This will result in a larger contact area between the indenter and the material when the indenter is pressed into a thicker film, and the reaction force borne by the indenter will be greater.

[0039] Figure 10 This shows that the composite hardness value of the entire system changes continuously with the indentation depth during the indentation process of the thin film-substrate system. Furthermore, for thin film-substrate systems of the same material but different film thicknesses, their relative indentation depth hardness is the same. The parameters in equation (7) are as follows. This reflects the entire transition zone, Figure 10 The transition region of (a) after magnification is as follows: Figure 10 As shown in (b), they still exhibit the same pattern. Due to the continuous increase in indentation depth, the final composite hardness will tend to the hardness value of the substrate, requiring parameter calibration. The fitted data only needs to include data from a portion of the transition region. In this embodiment, data from half the film thickness to the deepest point is selected. By pushing the fitted curve to infinity, the substrate hardness can be obtained and calibrated simultaneously. The value of . Select the data from the transition region to the deepest point and fit it using the least squares method (7), and extrapolate it to infinity. Figures 12-14 The hardness values ​​of the fitted substrate were plotted using logarithmic coordinates, and the values ​​at that time were also plotted. The values ​​shown in the figure are 1.732 GPa, 1.727 GPa, and 1.727 GPa, respectively. The relative errors of the fitted substrate hardness are all less than 1%. At this point, the corresponding fitted values ​​are... The values ​​were 10.62, 10.57, and 10.52, respectively. The value fluctuates within a very small range and tends to a constant, which is calculated to be... The average value is 10.57.

[0040] The results were obtained through fitting and calibration. The value is then used, and the same data range is selected. However, the thickness of the film is fitted using an absolute indentation depth hardness curve. The hardness of the substrate obtained from the fitting is then used to determine the hardness of the substrate. The average value is substituted into equation (7) as a known parameter to fit the film thickness using the least squares method. Figures 15-17 It can be seen that the fitted film thicknesses t are 0.1008 μm, 0.1987 μm and 0.298 μm, respectively. The results show that the error of the film thickness obtained by this method is within 1%.

[0041] Then, the thickness of the film is changed to 0.5 μm, and other conditions remain unchanged. The data of absolute indentation depth and composite hardness are obtained by simulation, and the data of relative indentation depth and hardness calibrated before are used to fit the value of the film thickness and the hardness value of the substrate using the same method, as shown in .The fitted thickness of the film is 0.498 μm, and the relative error is only 0.4%. Figure 18

[0042] Next, the data of absolute indentation depth and composite hardness in the range of 15% of the film thickness of 0.2 μm, 0.3 μm and 0.5 μm are selected, and the film thickness and the hardness of the substrate are substituted into formula (7) to perform numerical fitting using the least square method. The hardness value corresponding to the depth of 0 of the fitted curve is the hardness of the film. The range of the fitting data of the film thickness is selected because it is generally believed that the indentation depth within one-tenth is not affected by the hardness of the substrate. Since this principle is not universal and the fitting data needs to use the hardness of the substrate, the range of the data is expanded to highlight the influence of the substrate, and through this operation, it is not necessary to strictly distinguish whether the hardness of the film will be affected by the substrate, because the influence of the substrate has been included in the fitting data. From Figures 19-21 , it can be seen that the hardness values of the three groups of films are 8 GPa, 7.98 GPa and 7.99 GPa, respectively, and the relative errors are 0.5%, 0.74% and 0.62%, respectively. The relative error values of the three groups are less than 1%, indicating the feasibility of the method.

[0043] In order to further verify whether the method is feasible, the following conditions remain unchanged, only the material properties of the substrate are changed and , and the indentation experiments of different film thicknesses are simulated. The hardness value of the substrate after changing the material properties is shown in Figure 22 , and the hardness value remains constant as the indentation depth increases, that is, the accurate hardness value of the simulation material is . Figure 23 The composite hardness value after changing the material of the substrate and the composite hardness value of the substrate without changing are shown, it can be seen that since the film material properties do not change, the trends are consistent, the hardness value of the substrate gradually changes, the transition in the middle also changes, and the hardness finally tends to be stable.

[0044] Next, the hardness of the substrate is fitted using the same method, and , Figures 24-26 The fitted hardness value of the substrate and the The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained

[0045] The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained Figures 27-29 The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained Figure 30 The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained

[0046] The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained Figures 31-33 The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained

[0047] The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained

[0048] The values of the three groups of fitting base hardness are 3.641 GPa, 3.65 GPa and 3.651 GPa respectively, and the relative errors of the calculated fitting base hardness are all less than 1%, and the fitting obtained The calibration of the hardness-depth model is shown in the following. Through one-time calibration, subsequent thin film substrate systems with unknown film thickness of the same material can be fitted by the numerical method to obtain the film hardness, film thickness and substrate hardness. Since the segmented fitting avoids fitting data in the entire indentation range, the dependence of the fitting quality on the data in a wide range is reduced. The feasibility of the method is verified by finite element simulation, which reduces the measurement workload and provides a theoretical reference for subsequent experimental tests. The method is only applicable to low load action or when the film does not crack during indentation.

[0049] To solve these problems, a segmented numerical fitting method based on the indentation energy theory is proposed. The innovations are as follows: (1) key parameters (dimensionless factor ) are calibrated through single calibration, realizing rapid analysis of unknown film thickness systems; (2) the segmented fitting strategy is used to avoid the dependence of the traditional model on wide range data; (3) the film hardness, thickness and substrate hardness are extracted simultaneously, providing an efficient solution for quantitative performance evaluation of ultra-thin coatings. The feasibility of the method is verified by finite element simulation, which reduces the measurement workload and provides a theoretical reference for subsequent experimental tests.

[0050] Example 3 The hardness-depth model is slightly modified as follows: (11); In the formula, is the composite hardness of the film and substrate, is the substrate hardness, is the film hardness, is the relative indentation depth, is the film thickness, is the indentation depth, is the hardness distribution parameter. The meaning expressed by the model is consistent with the previous hardness-depth model, and the same method can be used to obtain the film thickness, hardness and substrate hardness.

[0051] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to include the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0052] Obviously, those skilled in the art can make various modifications and changes to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and changes of the present application fall within the scope of the claims of the present application and their equivalents, the present application also intends to include these modifications and changes.

Claims

1. A method for synchronously obtaining the hardness and thickness of a film in a film substrate system, characterized in that, The method comprises the following steps: indentation test is performed on a first film-substrate system with a known film thickness to obtain a plurality of first data sets, each of which comprises a relative indentation depth and a corresponding system composite hardness value; the plurality of first data sets are input into a hardness-depth model for fitting to obtain a first curve, and the first curve is regressed to infinity to obtain a calibration value of a substrate hardness in the first film-substrate system and a hardness distribution parameter in the hardness-depth model, the hardness-depth model being used to represent a relationship between a composite hardness and a relative indentation depth in a film-substrate system, and the hardness distribution parameter being used to quantify a behavior transition process of the composite hardness from film-dominant to substrate-dominant; indentation test is performed on a second film-substrate system with an unknown film thickness but using the same material to obtain a plurality of second data sets, each of which comprises an absolute indentation depth and a corresponding system composite hardness value, the absolute indentation depth being a depth value of a pressure head pressed into the film, and the relative indentation depth being a ratio of the absolute indentation depth to the film thickness; the calibration value of the substrate hardness and the hardness distribution parameter and the plurality of second data sets are input into the hardness-depth model for fitting to obtain a film thickness in the second film-substrate system, and the film thickness, the substrate hardness and the plurality of second data sets are input into the hardness-depth model for fitting to obtain a second curve, and the second curve is regressed to a depth of 0 to obtain a film hardness in the second film-substrate system.

2. The method of claim 1, wherein the film thickness and the film hardness are simultaneously measured. The hardness-depth model is specifically as follows: ； wherein is the composite hardness of the thin film substrate system, is the hardness of the substrate, is the hardness of the thin film, is the relative indentation depth, is the hardness assignment parameter.

3. The method of claim 1, wherein the film thickness and the film hardness are simultaneously measured. The plurality of first data sets are input into the hardness-depth model for fitting by a least square method.

4. The method of claim 1, wherein the film thickness and the film hardness are simultaneously measured. When performing indentation test on different film-substrate systems, a pressure head with the same size and shape needs to be used.

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