Optical characteristic modeling method, photoacoustic measurement method and related equipment

Abstract

The embodiment of the invention discloses an optical characteristic modeling method, a photoacoustic measurement method and related equipment, which are used for realizing more accurate optical modeling so as to measure more accurate sample thickness based on a more accurate optical modeling result. The method provided by the embodiment of the invention comprises the following steps: based on film layer parameters of film layers in a sample and optical system parameters of photoacoustic measurement equipment, constructing a temperature field function of the sample when the photoacoustic measurement equipment measures the sample, the temperature field function is used for describing the temperature distribution condition of the surface of the sample and the temperature distribution condition in the sample; based on the temperature field function, a strain field function of the sample when the photoacoustic measurement equipment measures the sample is constructed, and the strain field function is used for describing the strain distribution condition of the surface of the sample and the strain distribution condition in the sample.

Description

Technical Field

[0001] Embodiments of the present application relate to the field of optical measurement, and in particular to an optical property modeling method, a photoacoustic measurement method, and related devices. Background Art

[0002] In the semiconductor field, the photoacoustic effect principle is widely used to measure a series of film layer parameters such as the film thickness, sound velocity, and Young's modulus of metal and dielectric films.

[0003] In most of the existing technical solutions, the optical properties of the sample are modeled and calculated to simulate signals based on the film layer parameters, and the simulated signals are fitted with the measured photoacoustic signals. Finally, the sample thickness is determined according to the fitting result. However, when performing optical property modeling in the existing solutions, only the temperature distribution of the film layer on the sample surface is considered. For a thin film layer, it is not accurate enough to calculate the strain through the top layer temperature distribution, which leads to inaccurate results of optical property modeling and finally inaccurate sample thickness determined according to the fitting result. Summary of the Invention

[0004] Embodiments of the present application provide an optical property modeling method, a photoacoustic measurement method, and related devices, which are used to achieve more accurate optical modeling, and then measure a more accurate sample thickness based on the more accurate optical modeling result.

[0005] A first aspect of the embodiments of the present application provides an optical property modeling method, including:

[0006] Based on the film layer parameters of the film layers in the sample and the optical system parameters of the photoacoustic measurement device, construct a temperature field function of the sample when the photoacoustic measurement device measures the sample. The sample includes multiple film layers, and the temperature field function is used to describe the temperature distribution on the sample surface and the temperature distribution inside the sample;

[0007] Based on the temperature field function, construct a strain field function of the sample when the photoacoustic measurement device measures the sample. The strain field function is used to describe the strain distribution on the sample surface and the strain distribution inside the sample.

[0008] In a specific implementation manner, the constructing a temperature field function of the sample when the photoacoustic measurement device measures the sample based on the film layer parameters of the film layers in the sample and the optical system parameters includes:

[0009] Based on the optical system parameters and the film layer parameters of the first film layer, determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample from front to back. The first film layer is the first film layer arranged in sequence along the direction from the sample surface to the inside of the sample;

[0010] Based on the temperature distribution of the i-th film layer, the film layer parameters of the (i + 1)-th film layer, and the optical system parameters, determine the temperature distribution function of the (i + 1)-th film layer when the photoacoustic measurement device measures the sample, where i is a positive integer;

[0011] Based on the temperature distribution function of each film layer, determine the temperature field function.

[0012] In a specific implementation manner, the constructing the strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function includes:

[0013] Based on the temperature field function and the acoustic wave equation, construct the displacement field function of the sample, where the independent variable of the displacement field function includes the film layer thickness of each film layer in the sample;

[0014] Derive the displacement field function along the film layer thickness direction to obtain the strain field function.

[0015] In a specific implementation manner, the constructing the strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function of the sample when the photoacoustic measurement device measures the sample includes:

[0016] Discretize the first equation included in the temperature field function into a preset format according to a preset discretization accuracy to obtain a discrete temperature field function, and discretize the second equation included in the acoustic wave equation into the preset format according to the preset discretization accuracy to obtain a discrete acoustic wave equation, where the independent variable of the temperature field function includes the film layer thickness of each film layer in the sample;

[0017] Based on the discrete temperature field function and the discrete acoustic wave equation, construct the displacement field function;

[0018] Derive the displacement field function along the film layer thickness direction to obtain the strain field function.

[0019] The second aspect of the embodiments of the present application provides a photoacoustic measurement method, including:

[0020] Obtain the strain field function of the sample when the photoacoustic measurement device measures the sample, where the strain field function is determined according to any method in the first aspect;

[0021] According to the strain field function of the sample when the photoacoustic measurement device measures the sample, calculate the simulation signal function of the sample when the photoacoustic measurement device measures the sample, where the independent variable of the simulation signal function includes the film layer thickness of each film layer in the sample;

[0022] Based on the different predicted film thicknesses of the sample and the simulation signal function, determine the simulation signals of the sample for each film layer at different predicted film thicknesses;

[0023] Based on the fitting degree between the measured signal of the sample when the photoacoustic measurement device measures the sample and each simulation signal of the sample, determine the actual film thickness of each film layer in the sample.

[0024] In a specific implementation manner, the determining the actual film thickness of each film layer in the sample based on the fitting degree between the measured signal of the sample when the photoacoustic measurement device measures the sample and each simulation signal of the sample includes:

[0025] Adopt the polynomial fitting method to remove the base trend of the measured signal;

[0026] Perform local filtering on the measured signal after removing the base trend to obtain the target measured signal;

[0027] Based on the fitting degree between the target measured signal and each simulation signal of the sample, determine the actual film thickness of each film layer in the sample.

[0028] The third aspect of the embodiments of the present application provides a computer device, including:

[0029] A construction unit, configured to construct a temperature field function of the sample when the photoacoustic measurement device measures the sample based on the film layer parameters of the film layers in the sample and the optical system parameters of the photoacoustic measurement device. The sample includes multiple film layers, and the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample;

[0030] The construction unit is further configured to construct a strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function. The strain field function is used to describe the strain distribution on the surface of the sample and the strain distribution inside the sample.

[0031] In a specific implementation manner, the construction unit is specifically configured to determine, from first to last, the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample based on the optical system parameters and the film layer parameters of the first film layer. The first film layer is the first film layer arranged in sequence along the direction from the surface of the sample to the inside of the sample; based on the temperature distribution of the i-th film layer, the film layer parameters of the (i + 1)-th film layer, and the optical system parameters, determine the temperature distribution function of the (i + 1)-th film layer when the photoacoustic measurement device measures the sample, where i is a positive integer;

[0032] Based on the temperature distribution function of each film layer, determine the temperature field function.

[0033] In a specific implementation manner, the building unit is specifically configured to construct the displacement field function of the sample based on the temperature field function and the acoustic wave equation, where the independent variable of the displacement field function includes the film thickness of each film layer in the sample; and take the derivative of the displacement field function along the film thickness direction to obtain the strain field function.

[0034] In a specific implementation manner, the building unit is specifically configured to discretize the first equation included in the temperature field function into a preset format according to a preset discretization accuracy to obtain a discrete temperature field function, and discretize the second equation included in the acoustic wave equation into the preset format according to the preset discretization accuracy to obtain a discrete acoustic wave equation, where the independent variable of the temperature field function includes the film thickness of each film layer in the sample; construct the displacement field function based on the discrete temperature field function and the discrete acoustic wave equation; and take the derivative of the displacement field function along the film thickness direction to obtain the strain field function.

[0035] A fourth aspect of the embodiments of the present application provides a computer device, including:

[0036] An acquisition unit, configured to acquire the strain field function of the sample when the photoacoustic measurement device measures the sample, where the strain field function is determined according to any one of the methods in the first aspect;

[0037] A calculation unit, configured to calculate the simulation signal function of the sample when the photoacoustic measurement device measures the sample according to the strain field function of the sample when the photoacoustic measurement device measures the sample, where the independent variable of the simulation signal function includes the film thickness of each film layer in the sample;

[0038] A determination unit, configured to determine the simulation signal of the sample for each film layer at different predicted film thicknesses based on the different predicted film thicknesses of the sample and the simulation signal function;

[0039] The determination unit is further configured to determine the actual film thickness of each film layer in the sample based on the fitting degree between the measured signal of the sample when the photoacoustic measurement device measures the sample and each simulation signal of the sample.

[0040] In a specific implementation manner, the determination unit is specifically configured to use the polynomial fitting method to remove the base trend of the measured signal; perform local filtering processing on the measured signal after removing the base trend to obtain a target measured signal; and determine the actual film thickness of each film layer in the sample based on the fitting degree between the target measured signal and each simulation signal of the sample.

[0041] The fifth aspect of the embodiments of the present application provides a computer device, including:

[0042] A central processing unit, a memory, and an input / output interface;

[0043] The memory is a transient storage memory or a persistent storage memory;

[0044] The central processing unit is configured to communicate with the memory and execute the instruction operations in the memory to execute the method described in the first aspect or the second aspect.

[0045] The sixth aspect of the embodiments of the present application provides a computer program product including instructions, which, when the computer program product runs on a computer, cause the computer to execute the method described in the first aspect or the second aspect.

[0046] The seventh aspect of the embodiments of the present application provides a computer storage medium, in which instructions are stored, and when the instructions are executed on a computer, the computer is caused to execute the method described in the first aspect or the second aspect.

[0047] As can be seen from the above technical solutions, the embodiments of the present application have the following advantages: In the process of constructing the temperature field function, the film layer parameters of each film layer in the sample are fully considered, and the obtained temperature field function can be used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample. Furthermore, the strain field function constructed based on this temperature field function can also be used for the strain distribution on the surface of the sample and the strain distribution inside the sample. The influence of temperature changes on the surface and inside of the sample on the strain of the sample is fully considered, realizing more accurate optical modeling, and then obtaining a more accurate sample thickness after fitting. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic flowchart of an optical property modeling method disclosed in the embodiments of the present application;

[0049] Figure 2 It is a schematic diagram of the temperature distribution in a sample disclosed in the embodiments of the present application;

[0050] Figure 3 It is a schematic diagram of the displacement distribution in a sample disclosed in the embodiments of the present application;

[0051] Figure 4 It is a schematic diagram of the strain distribution in a sample disclosed in the embodiments of the present application;

[0052] Figure 5 It is a schematic diagram of the fitting of the measured signal and the simulation signal disclosed in the embodiments of the present application;

[0053] Figure 6 A schematic structural diagram of a computer device disclosed in an embodiment of the present application;

[0054] Figure 7 Another schematic structural diagram of a computer device disclosed in an embodiment of the present application;

[0055] Figure 8 Another schematic structural diagram of a computer device disclosed in an embodiment of the present application. Detailed implementation manners

[0056] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0057] The embodiments of the present application provide an optical property modeling method, a photoacoustic measurement method, and related devices, which are used to achieve more accurate optical modeling, and then measure a more accurate sample thickness based on more accurate optical modeling results.

[0058] To better illustrate the optical feature modeling method in the embodiments of the present application, the photoacoustic effect principle for realizing the measurement is first described. The measurement principle is as follows: A beam of ultrashort pulsed laser (excitation light) is incident on the surface of the sample. A part of the light energy is absorbed to generate instantaneous thermal expansion, and then an ultrasonic pulse signal is excited. The generated ultrasonic pulse signal starts to transmit in the sample and reflects and transmits at the interfaces of different film layers in the sample. The reflected sound wave (i.e., the ultrasonic pulse signal) transmits back to the sample surface again. If the film layer on the sample surface is a metal film layer, then the sound wave reflected back to the sample surface will change the optical property of the film layer on the sample surface, that is, the reflectivity. Therefore, when the ultrasonic pulse signal transmits back to the sample surface and changes the reflectivity of the film layer on the sample surface, if a beam of probe light is incident on the point where the reflectivity changes for measurement, the reflected light intensity of the probe light will change due to the change in reflectivity. Considering that the probe light is incident on the sample surface when the reflectivity of the film layer on the sample surface changes, there is a certain time delay relative to the incident time of the excitation light. The time for the ultrasonic pulse signal to transmit inside the metal material (i.e., the metal film layer on the sample surface) can be inferred according to the time when the reflected light intensity of the probe light changes. Then, combined with the sound velocity of the metal film layer, the thickness of the film layer on the sample surface can be obtained, that is, film thickness = probe light intensity change time point * sound velocity / 2.

[0059] However, for the measurement of film thickness when there are multiple film layers on the sample to be measured, there will be signal aliasing of different film layers in the returned echo signal. That is to say, it is difficult to distinguish the echo signals returned by each film layer, which brings difficulties to film thickness calculation and makes it impossible to accurately obtain the thickness of each film layer.

[0060] Therefore, the existing technical solution further proposes a film thickness measurement method based on optical property modeling. The optical properties of the sample are modeled and simulated signals are calculated according to the film layer parameters, and the simulated signals are fitted with the measured photoacoustic signals. Finally, the sample thickness is determined according to the fitting result. However, in the existing solution, only the temperature distribution of the film layer on the sample surface is considered when performing optical property modeling. For thin film layers, it is not accurate enough to calculate the strain through the top layer temperature distribution, which in turn leads to inaccurate results of optical property modeling and finally inaccurate sample thickness determined according to the fitting result.

[0061] To solve the above problems, please refer to Figure 1 , an embodiment of the present application provides an optical property modeling method, including the following steps:

[0062] 101. Based on the film layer parameters of the film layers in the sample and the optical system parameters of the photoacoustic measurement device, construct a temperature field function of the sample when the photoacoustic measurement device measures the sample. The sample includes multiple film layers, and the temperature field function is used to describe the temperature distribution on the sample surface and the temperature distribution inside the sample.

[0063] In the embodiment of the present application, first, based on the film layer parameters of each film layer in the sample, the optical system parameters of the photoacoustic measurement device, and the heat equation, the temperature distribution on the sample surface and the temperature distribution inside the sample are simulated. The temperature distribution on the sample surface and inside the sample can be represented by the temperature field function. Among them, the heat equation can be a heat equation constructed based on, but not limited to, a heat diffusion model, a heat conduction model, and a two-temperature model.

[0064] Specifically, the change in the temperature distribution of the sample is caused by the excitation light emitted by the photoacoustic measurement device. Therefore, it is necessary to obtain the optical system parameters related to the photoacoustic measurement device, such as the wavelength of the excitation light, the power of the excitation light, and the spot area of the light spot formed when the excitation light irradiates the object surface. In addition, the same excitation light will cause different temperature changes in the film layers of different materials. Therefore, it is also necessary to know the film layer parameters of each film layer in the sample, such as the sound velocity of the material of each film layer, the refractive index of each film layer, and the extinction coefficient of each film layer, etc., specifically depending on the parameters required by the heat equation. It should be noted that after substituting all the known film layer parameters and the known optical system parameters into the heat equation, the variable in the formula is the film layer thickness of each film layer. That is, the temperature field function constructed in this application can describe the temperature distribution on the surface of the sample and inside the sample after the excitation light irradiates the surface of the sample when the film layer thicknesses of each film layer in the sample are different.

[0065] 102. Based on the temperature field function, construct a strain field function of the sample when the photoacoustic measurement device measures the sample. The strain field function is used to describe the strain distribution on the surface of the sample and the strain distribution inside the sample.

[0066] As mentioned in the photoacoustic effect principle described above, the reason for the appearance of a bulge (i.e., strain) on the surface of the sample is the excitation light emitted by the photoacoustic measurement device. Specifically, the excitation light emitted by the photoacoustic measurement device irradiates the surface of the sample, causing the temperature of the surface film layer and the internal film layer of the sample to change, and then causing the corresponding film layers of the sample to undergo strain. Therefore, after obtaining the temperature distribution of each film layer in the sample, the strain distribution of each film layer in the sample, that is, the strain field function, can be further deduced.

[0067] It can be understood that when the surface film layer and the internal film layer of the sample undergo strain, the reflectivity of the surface film layer and the internal film layer of the sample will also change, and the change in the reflectivity can be reflected by the echo signal (or the measured signal) received by the photoacoustic measurement device. Therefore, after obtaining the strain field function, the embodiments of the present application can determine the film layer thickness of each film layer from the strain field function with the highest fitting degree to the measured signal.

[0068] In the embodiments of the present application, during the construction of the temperature field function, the film layer parameters of each film layer in the sample are fully considered. The obtained temperature field function can be used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample. Furthermore, the strain field function constructed based on the temperature field function can also be used for the strain distribution on the surface of the sample and the strain distribution inside the sample. The influence of temperature changes on the surface and inside of the sample on the strain of the sample is fully considered, realizing more accurate optical modeling, and then obtaining a more accurate sample thickness after fitting.

[0069] In some specific implementation manners, the foregoing step 101 may be implemented in the following manner: Based on the optical system parameters and the film layer parameters of the first film layer, determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample from front to back. The first film layer is the first film layer sequentially arranged along the direction from the sample surface to the inside of the sample; Based on the temperature distribution of the i-th film layer, the film layer parameters of the (i + 1)-th film layer, and the optical system parameters, determine the temperature distribution function of the (i + 1)-th film layer when the photoacoustic measurement device measures the sample, where i is a positive integer; Based on the temperature distribution function of each film layer, determine the temperature field function.

[0070] To better illustrate the technical solution of the embodiments of the present application, in the embodiments of the present application, according to the distance from the substrate, multiple film layers of the sample are sequentially determined as the first film layer (i.e., the film layer farthest from the substrate among the multiple film layers of the sample), the second film layer,..., the n-th film layer. Thus, it can be seen that the first film layer is the surface film layer of the sample, and the n-th film layer is the film layer adjacent to the substrate.

[0071] Specifically, since the excitation light is irradiated onto the surface film layer of the sample, in actual applications, the temperature of the surface film layer (i.e., the first film layer) of the sample should be affected first, followed by the second film layer. The second film layer will be affected by the temperature change of the first film layer and then undergo a temperature change, and so on. The (i + 1)-th film layer will be affected by the temperature of the i-th film layer. Therefore, in the embodiments of the present application, from front to back (from the first film layer to the n-th film layer), the temperature distribution function of the (i + 1)-th film layer is calculated according to the temperature distribution function of the previous film layer (i.e., the i-th film layer) of the (i + 1)-th film layer. Finally, by synthesizing the temperature distribution functions of each film layer, the temperature field function can be determined.

[0072] In some other specific implementation manners, the foregoing step 102 may be implemented in the following manner: Based on the temperature field function and the acoustic wave equation, construct the displacement field function of the sample. The independent variable of the displacement field function includes the film layer thickness of each film layer in the sample; Take the derivative of the displacement field function along the film layer thickness direction to obtain the strain field function.

[0073] It should be noted that the temperature difference at different thicknesses of the sample will cause thermal expansion, which is the cause of sound wave generation, or in other words, the strain generated by thermal expansion is the initial condition of the sound wave equation. Specifically, the temperature difference at different thicknesses of the sample will cause thermal expansion, which generates thermal stress, and the thermal stress generates sound waves (i.e., thermal strain) and starts to propagate. Therefore, the sound wave equation represents the process of sound wave transmission, and the sound wave at the initial moment is calculated according to the thermal expansion formula. Based on the above content, it can be known that there is a mathematical relationship between the sound wave equation and the temperature field function. Therefore, by substituting the temperature field function into the sound wave equation, the displacement field change of each film layer after the sample is irradiated by the excited light can be obtained. Among them, since the independent variable of the temperature field function is the film layer thickness of each film layer, the independent variable of the displacement field function obtained after substituting the temperature field function is also the film layer thickness of each film layer. Then, by taking the derivative of the displacement field function along the film layer thickness direction, the strain field function can be obtained.

[0074] Based on the foregoing embodiments, in some specific implementation manners, in order to improve the modeling accuracy, the equations that cannot be discretized in the temperature field function or the strain field function can also be converted into a preset form that can be discretized. The specific steps can be referred to as follows: discretize the first equation included in the temperature field function into a preset format according to a preset discretization accuracy to obtain a discretized temperature field function, and discretize the second equation included in the sound wave equation into a preset format according to a preset discretization accuracy to obtain a discretized sound wave equation. The independent variable of the temperature field function includes the film layer thickness of each film layer in the sample; based on the discretized temperature field function and the discretized sound wave equation, construct a displacement field function; take the derivative of the displacement field function along the film layer thickness direction to obtain a strain field function.

[0075] Among them, the embodiments of the present application conceive of converting the non-discretizable first equation in the temperature field function into a discretizable preset format, and converting the non-discretizable second equation in the sound wave equation into a discretizable preset format; in this way, both the sound wave equation and the temperature field function can be discretized with any preset discretization accuracy, and the accuracy of the obtained strain field function can also change with the preset discretization accuracy, improving the feasibility of the solution. It should be noted that since the independent variable of the temperature field function includes the film layer thickness of each film layer in the sample, based on the discretized temperature field function and the discretized sound wave equation, the constructed displacement field function also has an independent variable that includes the film layer thickness of each film layer in the sample. Therefore, by taking the derivative of the independent variable of the displacement field function, a strain field function is obtained.

[0076] In another implementation, before constructing the temperature field function, the third equation in the heat equation that cannot be discretized, the known parameters required to be substituted into the heat equation (including but not limited to known film layer parameters and known optical system parameters), the second equation in the acoustic wave equation that cannot be discretized, and the known parameters required to be substituted into the acoustic wave equation (including but not limited to known film layer parameters and known optical system parameters) can be discretized first, and then the temperature field function and the displacement field function are calculated. Then, the displacement field function is differentiated along the film layer thickness direction to obtain the strain field function. No steps are defined for the function of the strain field obtained by discretization to a preset discretization accuracy.

[0077] It can be understood that since the discrete temperature field function and the discrete displacement field function are discrete, the corresponding known parameters also need to be discretized. Additionally, generally, the equations that cannot be discretized (such as the first equation, the second equation, and the third equation) can be differential equations in the respective equations, and the preset format can be an implicit difference format that allows discretization.

[0078] The foregoing content describes various embodiments of the optical property modeling method of the present application. Based on the optical property modeling method of the present application, the following photoacoustic measurement method for measuring the film layer thickness is provided, including the following steps: obtaining the strain field function of the sample when the photoacoustic measurement device measures the sample, where the strain field function is determined according to the optical property modeling method of the present application; calculating the simulation signal function of the sample when the photoacoustic measurement device measures the sample according to the strain field function of the sample when the photoacoustic measurement device measures the sample, where the independent variable of the simulation signal function includes the film layer thickness of each film layer in the sample; determining the simulation signal of the sample at different predicted film layer thicknesses for each film layer based on the different predicted film layer thicknesses of the sample and the simulation signal function; and determining the actual film layer thickness of each film layer in the sample based on the fitting degree between the measured signal of the sample when the photoacoustic measurement device measures the sample and each simulation signal of the sample.

[0079] Specifically, since the strain field function and the displacement field function of the sample when the photoacoustic measurement device measures the sample can be determined according to the optical property modeling method of the present application, but the independent variables in the strain field function and the displacement field function are the film layer thicknesses of each film layer in the sample, the simulation signal function with the independent variable being the film layer thickness of each film layer in the sample can be determined. Then, by substituting the film layer thickness values of each film layer in the sample at different predicted film layer thicknesses into the simulation signal function, the simulation signal of the sample at different predicted film layer thicknesses can be obtained.

[0080] Generally, if the simulation signal function is y = f(x1, x2, x3), where x1, x2, and x3 are the film thicknesses of the first film layer, the second film layer, and the third film layer respectively. If the film thicknesses of the first film layer, the second film layer, and the third film layer are a, b, and c respectively, then the simulation signal when the predicted film thickness is (a, b, c) is y = f(a, b, c). Specifically, any two of (a, b, c), (a, b, d), and (e, f, g) are different film thicknesses. If the predicted film thickness of the sample is (a, b, c), then the expected film thickness of the first film layer at this predicted film thickness is a, the expected film thickness of the second film layer at this predicted film thickness is b, and the expected film thickness of the third film layer at this predicted film thickness is c.

[0081] Finally, the measured signal obtained by the optical measurement device is fitted with the simulation signals of the sample at different predicted film thicknesses to obtain the fitting degree between each measured signal and the simulation signals of the sample at different predicted film thicknesses. The higher the fitting degree between the measured signal and the simulation signal (or the greater the fitting degree), it indicates that the expected film thicknesses of each film layer in the sample corresponding to the simulation signal are closer to the true film thicknesses of each film layer in the sample. Therefore, the predicted film thickness corresponding to the simulation signal with the highest fitting degree with the measured signal is determined as the actual film thickness of each film layer in the sample.

[0082] In fact, in order to improve the fitting efficiency and the efficiency of determining the simulation signal with the highest fitting degree, the embodiments of this application use the film layer parameters of each film layer in the sample as variables to construct an optimization model, and obtain the film thickness of each film layer corresponding to the simulation signal when the fitting degree between the simulation signal and the preprocessed target measured signal is the highest, as the actual film thickness of each film layer. Specifically, first, an optimization mathematical model is established by constructing an objective function (the optimization objective is as shown in the foregoing content). Then, according to the Levenberg-Marquardt algorithm (i.e., the optimization algorithm), the film thicknesses of each film layer are iterated to obtain a series of fitting degrees between the simulation signals and the preprocessed measured signals and finally converge. Finally, the film thicknesses of each film layer when the fitting degree is the largest are obtained to complete the measurement of the film thickness. Among them, the optimization algorithm can also be the Newton method or the Gauss-Newton method, which is not limited here.

[0083] Further, to improve the fitting accuracy, before fitting the measured signal and the simulation signal, the embodiment of the present application can also use the polynomial fitting method to remove the baseline trend of the measured signal, and perform local filtering on the measured signal after removing the baseline trend to obtain the target measured signal. Then, use the preprocessed target measured signal to replace the measured signal and fit it with each simulation signal to obtain the corresponding fitting degree, and then determine the predicted film thickness corresponding to the simulation signal with the highest fitting degree as the actual film thickness of each film layer in the sample.

[0084] Taking the heat equation constructed based on the heat diffusion model as an example, in a specific scenario, the optical property modeling and photoacoustic measurement method of the present application will be described below.

[0085] Taking the heat diffusion formula as an example, the temperature field function is constructed as shown in the following formula:

[0086]

[0087] Among them, C is the unit volume heat capacity, T is the temperature, t is the time, k is the thermal conductivity, z is the thickness, a is the reciprocal of the incident depth of the excitation light, R is the reflectivity of the film layer on the sample surface, I is the light intensity, and f(t) is the normalized function of the change of the excitation light intensity with time. Then, using the Crank-Nicolson method, the differential equation in the foregoing formula (1) is discretized to obtain the following formula:

[0088]

[0089] Further, the above formula (2) is written in the following matrix form:

[0090]

[0091] Among them, the u matrix is the temperature at different thicknesses of the sample at a certain time point, and the coefficient matrix is composed of a, b, and c. The coefficients are known quantities composed of Δt, Δx, and α. Then, according to the loop and the algorithm, the temperature at different thicknesses of the sample at this time point is solved, and further the temperature distribution at the next time point (after the excitation light is incident on the sample) is solved until the temperature at all thicknesses of the sample at all times is obtained.

[0092] When specific film thicknesses, film layer parameters, and optical system parameters are substituted, through the above temperature field function and method, the temperature distribution of the sample as shown in Figure 2 can be obtained. Among them, the horizontal axis is the time, the vertical axis is the sample thickness (the thickness of the sample surface is 0, and the thickness starts to increase as it goes deeper), and a certain point is the temperature value at the corresponding thickness position in the sample at the corresponding time. It should be noted that, actually, the independent variables of the temperature field function include not only the film thickness of each film layer in the sample, but also the time when the excitation light is incident on the sample.

[0093] Further, for the calculation of the displacement field function, in the same way, after writing the acoustic wave equation in implicit difference format and rewriting it in the form of matrix (multiplication), all displacements at all thicknesses for all time samples can be obtained through iterative solution. By substituting specific film thicknesses, film parameters, and optical system parameters, the displacement distribution of the sample as shown in Figure 3 can be obtained. The horizontal axis represents time, and the vertical axis represents the sample thickness (the thickness at the sample surface is 0, and the thickness increases as it goes deeper). A certain point represents the displacement value at the corresponding thickness position in the sample at the corresponding time. It should be noted that, in fact, the independent variables of the displacement field function include not only the film thickness of each film layer in the sample but also the time when the excitation light is incident on the sample.

[0094] Similarly, by substituting specific film thicknesses, film parameters, and optical system parameters, Figure 4 the strain distribution of the sample as shown is obtained. The horizontal axis represents time, and the vertical axis represents the sample thickness (the thickness at the sample surface is 0, and the thickness increases as it goes deeper). A certain point represents the strain value at the corresponding thickness position in the sample at the corresponding time. It should be noted that, in fact, the independent variables of the strain field function include not only the film thickness of each film layer in the sample but also the time when the excitation light is incident on the sample.

[0095] Next, after obtaining the strain field function, by substituting specific predicted film thicknesses, film parameters, and optical system parameters, the simulation signal as shown in Figure 5 can be obtained. And multiple measured signals (i.e., multiple echo signals returned to the sample surface) can be acquired through a photoacoustic measurement device. Then, after preprocessing steps such as removing the baseline trend of the measured signal (the effect after processing can be referred to as the measured signal after removing the baseline trend) and local filtering (the effect after processing can be referred to as the target measured signal), the measured signal is fitted with the simulation signal, and the fitting schematic effect is as shown in Figure 5 removing the baseline trend of the measured signal) and local filtering processing (the effect after processing can be referred to as the target measured signal), etc., and then fitting with the simulation signal, where the fitting schematic effect is as shown in Figure 5 the target measured signal), etc., and then fitting with the simulation signal, where the fitting schematic effect is as shown in Figure 5 shown.

[0096] In the embodiment of the present application, according to the change of the surface film reflectivity with temperature and the change of the surface temperature of the sample to be measured in the simulation signal, the measured signal is preprocessed to remove the signal baseline caused by the heat generated by the laser; and the signal-to-noise ratio of the measured signal is improved through signal processing means such as filtering. The preprocessing of the measured signal improves the accuracy of the fitting result between the simulation signal and the measured signal.

[0097] Please refer to Figure 6 , the embodiment of the present application provides a computer device, including:

[0098] A construction unit 601, configured to construct a temperature field function of a sample when a photoacoustic measurement device measures the sample based on the film layer parameters of the film layers in the sample and the optical system parameters of the photoacoustic measurement device. The sample includes multiple film layers, and the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample;

[0099] The construction unit 601 is further configured to construct a strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function. The strain field function is used to describe the strain distribution on the surface of the sample and the strain distribution inside the sample.

[0100] In a specific implementation manner, the construction unit 601 is specifically configured to determine, from the first to the last, the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample based on the optical system parameters and the film layer parameters of the first film layer. The first film layer is the first film layer sequentially arranged along the direction from the surface of the sample to the inside of the sample; determine the temperature distribution function of the (i + 1)-th film layer when the photoacoustic measurement device measures the sample based on the temperature distribution of the i-th film layer, the film layer parameters of the (i + 1)-th film layer, and the optical system parameters, where i is a positive integer;

[0101] Determine the temperature field function based on the temperature distribution function of each film layer.

[0102] In a specific implementation manner, the construction unit 601 is specifically configured to construct a displacement field function of the sample based on the temperature field function and the acoustic wave equation. The independent variable of the displacement field function includes the film layer thickness of each film layer in the sample; perform a derivative of the displacement field function along the film layer thickness direction to obtain the strain field function.

[0103] In a specific implementation manner, the construction unit 601 is specifically configured to discretize a first equation included in the temperature field function into a preset format according to a preset discretization accuracy to obtain a discrete temperature field function, and discretize a second equation included in the acoustic wave equation into a preset format according to the preset discretization accuracy to obtain a discrete acoustic wave equation. The independent variable of the temperature field function includes the film layer thickness of each film layer in the sample; construct the displacement field function based on the discrete temperature field function and the discrete acoustic wave equation; perform a derivative of the displacement field function along the film layer thickness direction to obtain the strain field function.

[0104] Please refer to Figure 7 , this application embodiment provides a computer device, including:

[0105] An acquisition unit 701, configured to acquire the strain field function of the sample when the photoacoustic measurement device measures the sample. The strain field function is determined according to any one of the optical characteristic modeling methods of this application;

[0106] A calculation unit 702, configured to calculate a simulation signal function of a sample when the photoacoustic measurement device measures the sample according to a strain field function of the sample when the photoacoustic measurement device measures the sample, where the independent variable of the simulation signal function includes the film thickness of each film layer in the sample;

[0107] A determination unit 703, configured to determine the simulation signal of the sample for each film layer at different predicted film thicknesses of the sample based on the different predicted film thicknesses of the sample and the simulation signal function;

[0108] The determination unit 703 is further configured to determine the actual film thickness of each film layer in the sample based on the fitting degree between the measured signal of the sample when the photoacoustic measurement device measures the sample and each simulation signal of the sample.

[0109] In a specific implementation manner, the determination unit 703 is specifically configured to use a polynomial fitting method to remove the baseline trend of the measured signal; perform local filtering processing on the measured signal after removing the baseline trend to obtain a target measured signal; and determine the actual film thickness of each film layer in the sample based on the fitting degree between the target measured signal and each simulation signal of the sample.

[0110] Figure 8 It is a schematic structural diagram of a computer device provided by an embodiment of the present application. The computer device 800 may include one or more central processing units (CPUs) 801 and a memory 805, and one or more application programs or data are stored in the memory 805.

[0111] Among them, the memory 805 may be volatile storage or persistent storage. The program stored in the memory 805 may include one or more modules, and each module may include a series of instruction operations on the computer device. Further, the central processor 801 may be configured to communicate with the memory 805 and execute a series of instruction operations in the memory 805 on the computer device 800.

[0112] The computer device 800 may further include one or more power supplies 802, one or more wired or wireless network interfaces 803, one or more input / output interfaces 804, and / or one or more operating systems, such as Windows ServerTM, Mac OS XTM, UnixTM, LinuxTM, FreeBSDTM, etc.

[0113] The central processor 801 may execute the operations performed by the computer device in the foregoing Figures 1 to 7 illustrated embodiment, which will not be elaborated here specifically.

[0114] It should be noted that although the steps in the flowcharts involved in the embodiments are drawn in sequence according to the arrows, unless otherwise clearly stated in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or steps or stages in other steps.

[0115] Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes of the above-described systems, devices, and units can refer to the corresponding processes in the foregoing method embodiments, and will not be described herein again.

[0116] In several embodiments provided in the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces, indirect couplings or communication connections of devices or units, and can be in electrical, mechanical or other forms.

[0117] The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they can be located in one place, or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0118] In addition, the functional units in each embodiment of the present application can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.

[0119] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, read-only memory), random access memories (RAM, random access memory), magnetic disks, or optical discs that can store program codes.

[0120] Embodiments of this application also provide a computer program product containing instructions. When the computer program product runs on a computer, it causes the computer to execute the optical property modeling method and the photoacoustic measurement method as described above.

Claims

1. An optical property modeling method, characterized in that, Comprising: Based on the film layer parameters of the film layers in the sample and the optical system parameters of the photoacoustic measurement device, construct a temperature field function of the sample when the photoacoustic measurement device measures the sample. The sample includes multiple film layers, and the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample; Based on the temperature field function, construct a strain field function of the sample when the photoacoustic measurement device measures the sample. The strain field function is used to describe the strain distribution on the surface of the sample and the strain distribution inside the sample.

2. The method according to claim 1, characterized in that, The constructing the temperature field function of the sample when the photoacoustic measurement device measures the sample based on the film layer parameters of the film layers in the sample and the optical system parameters includes: Based on the optical system parameters and the film layer parameters of the first film layer, determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample from front to back. The first film layer is the first film layer arranged in sequence along the direction from the surface of the sample to the inside of the sample; Based on the temperature distribution of the i-th film layer, the film layer parameters of the (i + 1)-th film layer, and the optical system parameters, determine the temperature distribution function of the (i + 1)-th film layer when the photoacoustic measurement device measures the sample, where i is a positive integer; Based on the temperature distribution function of each film layer, determine the temperature field function.

3. The method according to claim 1, wherein The constructing the strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function includes: Based on the temperature field function and the acoustic wave equation, construct a displacement field function of the sample. The independent variable of the displacement field function includes the film layer thickness of each film layer in the sample; Derive the displacement field function along the film layer thickness direction to obtain the strain field function.

4. The method according to claim 1, wherein The constructing the strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function of the sample when the photoacoustic measurement device measures the sample includes: Discretize the first equation included in the temperature field function into a preset format according to a preset discretization accuracy to obtain a discrete temperature field function, and discretize the second equation included in the acoustic wave equation into the preset format according to the preset discretization accuracy to obtain a discrete acoustic wave equation. The independent variable of the temperature field function includes the film layer thickness of each film layer in the sample; Based on the discrete temperature field function and the discrete acoustic wave equation, construct a displacement field function; Derive the displacement field function along the film layer thickness direction to obtain the strain field function.

5. A photoacoustic measurement method, characterized in that, Comprising: Obtain the strain field function of the sample when the photoacoustic measurement device measures the sample. The strain field function is determined by the method according to any one of claims 1 to 4; According to the strain field function of the sample when the photoacoustic measurement device measures the sample, calculate the simulation signal function of the sample when the photoacoustic measurement device measures the sample. The independent variable of the simulation signal function includes the film layer thickness of each film layer in the sample; Based on the different predicted film layer thicknesses of the sample and the simulation signal function, determine the simulation signals of the sample for each film layer at different predicted film layer thicknesses; Based on the fitting degree between the measured signal of the sample and each simulation signal of the sample when the photoacoustic measurement device measures the sample, determine the actual film thickness of each film layer in the sample.

6. The method according to claim 5, wherein The determining the actual film thickness of each film layer in the sample based on the fitting degree between the measured signal of the sample and each simulation signal of the sample when the photoacoustic measurement device measures the sample includes: Use the polynomial fitting method to remove the base trend of the measured signal; Perform local filtering on the measured signal after removing the base trend to obtain a target measured signal; Based on the fitting degree between the target measured signal and each simulation signal of the sample, determine the actual film thickness of each film layer in the sample.

7. A computer device, characterized in that, Include: A construction unit configured to construct a temperature field function of the sample when the photoacoustic measurement device measures the sample based on the film parameters of the film layers in the sample and the optical system parameters of the photoacoustic measurement device, where the sample includes a plurality of film layers, and the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample; The construction unit is further configured to construct a strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function, and the strain field function is used to describe the strain distribution on the surface of the sample and the strain distribution inside the sample.

8. A computer device, characterized in that, Include: An acquisition unit configured to acquire a strain field function of the sample when the photoacoustic measurement device measures the sample, and the strain field function is determined according to the method of any one of claims 1 to 4; A calculation unit configured to calculate a simulation signal function of the sample when the photoacoustic measurement device measures the sample according to the strain field function of the sample when the photoacoustic measurement device measures the sample, and the independent variable of the simulation signal function includes the film thickness of each film layer in the sample; A determination unit configured to determine the simulation signal of the sample at different predicted film thicknesses of each film layer based on the different predicted film thicknesses of the sample and the simulation signal function; The determination unit is further configured to determine the actual film thickness of each film layer in the sample based on the fitting degree between the measured signal of the sample and each simulation signal of the sample when the photoacoustic measurement device measures the sample.

9. A computer device, characterized in that, Include: A central processing unit, a memory, and an input / output interface; The memory is a transient storage memory or a persistent storage memory; The central processing unit is configured to communicate with the memory and execute the instruction operations in the memory to execute the method of any one of claims 1 to 4 or 5 to 6.

10. A computer storage medium, characterized in that, Instructions are stored in the computer storage medium, and when the instructions are executed on a computer, the computer is caused to execute the method of any one of claims 1 to 4 or 5 to 6.

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