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

Abstract

The application discloses a kind of synchronous acquisition method of film hardness and thickness in film substrate system, it is related to surface coating technical field, comprising the following steps: first film substrate system of known film thickness is carried out indentation test, obtains multiple first data;Multiple first data is input to hardness-depth model and is fitted, obtains first curve and regression to infinity, obtains the hardness of substrate and the calibration value of hardness distribution parameter;Second film substrate system of unknown film thickness but using same material is carried out indentation test, obtains multiple second data;The hardness of substrate, calibration value and multiple second data are input to hardness-depth model and are fitted, obtain film thickness;Film thickness, substrate hardness and multiple second data are input to hardness-depth model and are fitted, obtain second curve, second curve is regression to depth 0, obtain the hardness of film.The application reduces the dependence of fitting quality on data in wider range.

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 energy perspective. 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 of the model is largely dependent on the indentation data obtained in a large amount of data. For unknown film thickness and small range data, the quality of the model fitting is poor. SUMMARY

[0005] Based on the defects of the existing 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 of poor fitting quality of the existing model, which is largely dependent on indentation data obtained in a large amount of data. For unknown film thickness and small range data, the quality of the model fitting is poor.

[0006] The present application adopts the following technical solutions:

[0007] 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:

[0008] Performing indentation testing on a first thin film-substrate system with known film thickness to obtain a plurality of first data sets, each first data set including a relative indentation depth and a corresponding system composite hardness value;

[0009] Inputting the plurality of first data sets into a hardness-depth model for fitting to obtain a first curve, and regressing the first curve to infinity to obtain the calibration values of the substrate hardness in the first thin film-substrate system and the hardness allocation parameter in the hardness-depth model, the hardness-depth model being used to characterize the relationship between the composite hardness and the relative indentation depth in the thin film-substrate system, and the hardness allocation parameter being used to quantify the behavior transition process of the composite hardness from thin film dominance to substrate dominance;

[0010] Performing indentation testing on a second thin film-substrate system with unknown film thickness but using the same material to obtain a plurality of second data sets, each second data set including an absolute indentation depth and a corresponding system composite hardness value; the absolute indentation depth being the depth value of the indenter pressed into the thin film, and the relative indentation depth being the ratio of the absolute indentation depth to the film thickness;

[0011] The calibration value of the hardness distribution parameter and the plurality of second data are input into the hardness-depth model to be fitted to obtain the film thickness in the second film-substrate system; the film thickness, the substrate hardness and the plurality of second data are input into the hardness-depth model to be fitted to obtain a second curve, and the second curve is regressed to the depth of 0 to obtain the film hardness in the second film-substrate system.

[0012] Preferably, the hardness-depth model is specifically as follows:

[0013] ;

[0014] In the formula, is the composite hardness of the film-substrate system, is the hardness of the substrate, is the hardness of the film, is the relative indentation depth, is the hardness distribution parameter.

[0015] Preferably, the plurality of first data are input into the hardness-depth model to be fitted by the least square method.

[0016] Preferably, the same size and shape of the indenter are used when the indentation tests are performed on different film-substrate systems.

[0017] Compared with the prior art, the above at least one technical scheme of the present application can achieve the following beneficial effects:

[0018] The present application firstly performs the indentation test on the first film-substrate system with the known film thickness to obtain the plurality of first data, inputs the plurality of first data into the hardness-depth model to be fitted to obtain a first curve, regresses the first curve to infinity to obtain the hardness of the substrate in the first film-substrate system and the calibration 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 the film-substrate system with the known material properties and film thickness once, does not need to use the indentation data in a wide range to be fitted, avoids the fitting of the data in the whole indentation depth range, and reduces the dependence of the fitting quality on the data in a wide range.

[0019] Then, the indentation test is performed on a second film-substrate system with unknown film thickness but same material as the first film-substrate system, to obtain a plurality of second data, and the hardness of the substrate, the calibrated value of the hardness distribution parameter, and the plurality of second data are input into the hardness-depth model for fitting, to obtain the film thickness in the second film-substrate system; the film thickness, the hardness of the substrate, and the plurality of second data are input into the hardness-depth model for fitting, to obtain a second curve, and the second curve is regressed to the depth of 0, to obtain the hardness of the film. The present application only needs to calibrate the hardness distribution parameter of the film-substrate system with known film thickness once, and then the film hardness, the film thickness, and the hardness of the substrate of the film-substrate system with unknown film thickness and same material can be obtained by the numerical method once. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0021] Figure 1 is the change curve of the composite hardness of the whole film-substrate system;

[0022] Figure 2 is a flow chart of a method for synchronously obtaining the hardness and thickness of a film in a film-substrate system according to the present application;

[0023] Figure 3 is a nanoindentation simulation diagram according to the present application;

[0024] Figure 4 is a model boundary condition diagram according to the present application;

[0025] Figure 5 is a load-displacement curve diagram of a 100 nm film thickness according to the present application;

[0026] Figure 6 is a load-displacement curve diagram of a 300 nm film thickness according to the present application;

[0027] Figure 7 is a load-displacement curve diagram of a 300 nm film thickness according to the present application;

[0028] Figure 8 is a hardness-depth curve diagram of a substrate material according to the present application;

[0029] Figure 9 is a hardness-depth curve diagram of a film according to the present application;

[0030] Figure 10 is a load-displacement curve diagram of different film thicknesses according to the present application; Curve;

[0031] wherein, Figure 10 (a) of Figure 1 : Load vs. Relative Indentation Depth curves for different film thicknesses Curve, Figure 10 (b) of Figure 1 : Close-up view;

[0032] Figure 11 Figure 2 is a schematic representation of Load vs. Relative Indentation Depth curves for different thickness films of the present invention;

[0033] Figure 12 Figure 3 is a schematic representation of the fitted substrate hardness and parameters of Equation 1 for a film thickness of 0.1 μm of the present invention; x

[0034] Figure 13 Figure 4 is a schematic representation of the fitted substrate hardness and parameters of Equation 1 for a film thickness of 0.2 μm of the present invention; x

[0035] Figure 14 Figure 5 is a schematic representation of the fitted substrate hardness and parameters of Equation 1 for a film thickness of 0.3 μm of the present invention; x

[0036] Figure 15 Figure 6 is a schematic representation of the fitted 0.1 μm film thickness by parameter x of the present invention;

[0037] Figure 16 Figure 7 is a schematic representation of the fitted 0.2 μm film thickness by parameter x of the present invention;

[0038] Figure 17 Figure 8 is a schematic representation of the fitted 0.3 μm film thickness by parameter x of the present invention;

[0039] Figure 18 Figure 9 is a schematic representation of the fitted 0.5 μm film thickness by parameter x of the present invention;

[0040] Figure 19 Figure 10 is a schematic representation of the fitted 0.2 μm film hardness regression of the present invention;

[0041] Figure 20 Figure 11 is a schematic representation of the fitted 0.3 μm film hardness regression of the present invention;

[0042] Figure 21 Figure 12 is a schematic representation of the fitted 0.5 μm film hardness regression of the present invention;

[0043] Figure 22 Figure 13 is a schematic representation of the hardness of the substrate after changing the material of the present invention;

[0044] Figure 23 Figure 14 is a schematic representation of the H-RID of the same film material on different substrates of the present invention; ​​​

[0045] Figure 24 Fitting of substrate hardness and parameter x for 0.1 μm film thickness of the present application;

[0046] Figure 25 Fitting of substrate hardness and parameter x for 0.2 μm film thickness of the present application;

[0047] Figure 26 Fitting of substrate hardness and parameter x for 0.3 μm film thickness of the present application;

[0048] Figure 27 Fitting of 0.1 μm film thickness by parameter x for the present application;

[0049] Figure 28 Fitting of 0.2 μm film thickness by parameter x for the present application;

[0050] Figure 29 Fitting of 0.3 μm film thickness by parameter x for the present application;

[0051] Figure 30 Fitting of 0.5 μm film thickness by parameter x for the present application;

[0052] Figure 31 Fitting of 0.2 μm film hardness regression for the present application;

[0053] Figure 32 Fitting of 0.3 μm film hardness regression for the present application;

[0054] Figure 33 Fitting of 0.5 μm film hardness regression for the present application. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those of ordinary skill in the art without any creative work fall within the protection scope of the present application.

[0056] Embodiment 1

[0057] Related background:

[0058] Existing models typically estimate the composite hardness at different indentation depths by varying the indentation load, while assuming a constant film thickness. However, BD and Korsunsky et al. found that the response of the film-substrate system undergoes different mechanical states with increasing indentation depth: first, a purely elastic response stage; then, the material mechanics process can be divided into four stages: a film-dominated stage, a mixed transition stage, a substrate-dominated stage, and finally, a completely substrate-dominated stage. When conducting indentation tests using pointed or conical indenters, the highest applied load was found to be... P Almost always with the maximum indentation depth delta Regarding this, the highest load that can be applied can also be selected. P and maximum indentation depth delta To describe the indentation, for a given hardness value, the highest load... P and maximum indentation depth delta There exists a one-to-one relationship, given by the following formula:

[0059] (1);

[0060] in, H It's hardness. These are parameters describing the geometry of the indenter. For Vickers indenters, ,in It is the diagonal of the indentation. Here, it is implicitly assumed that the diagonal length of the indentation does not undergo significant elastic recovery during unloading, so the depth can be inferred using the measured unloading value. If the specimen hardness is assumed to be constant, equation (2) can be reformulated using the load-displacement relationship as follows:

[0061] (2);

[0062] The energy required for the loading system to generate the maximum indentation depth is the power generated during the entire indentation process. The calculation shows that:

[0063] (3);

[0064] This quantity is called the "total work done by indentation" and can be measured using continuous indentation techniques.

[0065] The hardness in equation (4) H Total work express:

[0066] (4);

[0067] In thin film substrate hardness testing, the total energy consumption consists of two parts: when the substrate material undergoes plastic deformation... consumption energy and the energy consumed when the film cracks and deforms , the total energy consumed is:

[0068] (5);

[0069] Substituting equation (6) into equation (5) and considering the energy distribution between the substrate and the film, we obtain:

[0070] (6);

[0071] (7);

[0072] This relationship allows the hardness of the film and the substrate to be determined by fitting experimental data obtained at a range of contact scales, and the quality of the fit depends on the range of indentation data and requires multiple tests with different indentation data. During the entire indentation test, as the indenter continuously penetrates the film-substrate 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 depth of penetration is large enough, the composite hardness value of the entire system will eventually tend to the hardness value of the substrate, and the change in the composite hardness of the entire film-substrate system exhibits a type, and equation (7) reflects this trend, as shown in Figure 1 . Through numerical calculation and analysis of the entire equation, it is found that the error in the description of the composite hardness is very small, and the composite hardness is determined by the hardness of the film and the substrate. Since hardness is an inherent property of an object, for the same material 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-substrate system with different film thicknesses 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 transition from the film hardness to the substrate hardness.

[0073] Based on the above problems and related background, the present application proposes a method for simultaneously obtaining the hardness and thickness of a film in a film-substrate system. The method uses a hardness-depth model, calibrates the dimensionless parameter in the model using a film-substrate system with a known film thickness, and uses a piecewise fitting strategy to simultaneously extract the hardness, thickness, and hardness of the substrate in a film-substrate system with unknown film thickness but the same material properties under the condition of only a small amount of indentation experiments. This method can separate the film thickness, hardness, and substrate hardness from the indentation data, and the method is verified by finite element simulation. This method aims to avoid the limitations of traditional methods, improve testing efficiency, and provide method guidance for subsequent application in experimental testing. Referring to Figure 2 , the method specifically includes the following steps:

[0074] 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.

[0075] When extracting hardness by indentation method, the surface of the sample must be smooth, 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.

[0076] 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.

[0077] 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 in depth to obtain the substrate hardness value, and the hardness distribution parameter is also obtained.

[0078] 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.

[0079] 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.

[0080] 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.

[0081] 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.

[0082] 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.

[0083] Example 2

[0084] Elastic-plastic deformation under the action of the indenter is a highly nonlinear contact problem with variable geometry boundary conditions.

[0085] 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 10m10m, 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.

[0086] The contact between the indenter and the material is assumed to be face-to-face, the indenter is the master face and the material is the slave face. The contact between the rigid indenter and the film is assumed to be frictionless. The film and the substrate are assumed to be stress free and perfectly bonded. The contact behavior is assumed to be tangential frictionless and normal hard, which means that no delamination or slip occurs at the interface and the contact location between the indenter and the film during the indentation process. The material is assumed to be isotropic, homogeneous, elastic-plastic and obey the von Mises yield criterion.

[0087] (8);

[0088] wherein, S ij is the deviatoric stress tensor, sigma ij is the equivalent pressure stress, is the Kronecker symbol, p is the stress, q is the yield stress.

[0089] The boundary conditions are one of the important steps in the finite element simulation process, and the correctness of the setting determines the correctness and convergence of the calculation results. The boundary conditions of the nanoindentation geometric model are shown in FIG. 1. The right side of the model is set as a free surface, the bottom of the model is set as a complete fixation, and the left side of the model is set as an axisymmetric constraint, fixing the freedom in the x direction. The reference point of the indenter is subjected to a load in the y direction, and the freedom in the x displacement direction and the z rotation direction is fixed, that is, the reference point only moves in the y direction. Figure 4 The loading method in the nanoindentation finite element simulation process includes 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 adopted, and a downward displacement is applied to the indenter in the finite element program, and the indenter is pressed into the material surface. When the given indenter displacement is reached, a upward displacement is then applied to the indenter until it is not in contact with the sample. For each indenter displacement, the corresponding load is determined by the sum of the reaction forces at the contact nodes of the indenter, by solving the nonlinear equation:

[0090] (9);

[0091] wherein, K is the stiffness matrix, is the node displacement, is the force increment.

[0092] 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. The present application establishes a nanoindentation finite element model based on the assumption of axisymmetry, and uses four-node axisymmetric reduced integration element CAX4R 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 μm. 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 μm-0.3 μm, and table 1 shows the values of the elastic modulus (Es) of the film and the elastic modulus (Ef) of the substrate.

[0093] Table 1 Input parameters in finite element simulation

[0094]

[0095] Figures 5-7 The load-displacement curves obtained by simulation calculation are drawn respectively when the elastic modulus of the substrate is 100 GPa and 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.

[0096] According to the method of Oliver-Pharr, the hardness is usually defined as the average contact stress:

[0097] (10);

[0098] In the formula,​ Maximum load, A is the contact area, and H is the hardness.

[0099] 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.

[0100] Table 2 Characteristic parameters of commonly used indenters

[0101]

[0102] 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 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: .

[0103] 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.

[0104] Figure 10 This shows that the composite hardness value of the entire thin film-substrate system changes continuously with the indentation depth during the indentation process. 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... 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.

[0105] 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%.

[0106] 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

[0107] 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 values of the relative errors of the three groups are less than 1%, which indicates the feasibility of the method.

[0108] In order to further verify whether the method is feasible, next, other conditions remain unchanged, only the material properties of the substrate are changed and , and 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 of the substrate after changing the material is shown, and the composite hardness value of the substrate without changing the material is shown. It can be seen that since the material properties of the film 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.

[0109] Next, the hardness of the substrate is fitted using the same method, and the , 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 average value of the three groups of fitting base hardness is 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

[0110] 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

[0111] 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

[0112] 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

[0113] 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 calibration, the subsequent thin film substrate system 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 the data in the entire indentation depth 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.

[0114] To solve these problems, a segmented numerical fitting method based on the indentation energy theory is proposed. The innovations of the method are as follows: (1) key parameters (dimensionless factor ) are calibrated at one time to realize the 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 synchronously to provide an efficient solution for the 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.

[0115] Example 3

[0116] The hardness-depth model is slightly modified as follows:

[0117] (11);

[0118] 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 film thickness, hardness and substrate hardness can be obtained by using the same method in combination with the model.

[0119] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all changes and modifications falling within the scope of the present application.

[0120] 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 is also intended 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 hardness and thickness 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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