Optical characteristic modeling method, photoacoustic measurement method and related equipment

Abstract

The embodiment of the invention discloses an optical property modeling method, a photoacoustic measurement method and related equipment, which are used for adapting to the precision requirements of samples with different thicknesses on optical property modeling and better meeting the actual modeling requirements. The method provided by the embodiment of the invention comprises the following steps: discretizing a first equation contained in a thermal equation into a preset format according to preset discretization precision to obtain a discrete thermal equation, and processing film layer parameters of a sample according to the preset discretization precision to obtain discrete film layer parameters, processing optical system parameters of the photoacoustic measurement equipment according to the preset discrete precision to obtain discrete optical system parameters; constructing a temperature field function of the sample based on the discrete thermal equation, the discrete film layer parameters and the discrete optical system parameters; and based on the temperature field function, constructing a strain field function of the sample when the photoacoustic measurement equipment measures 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 a 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, the method of performing optical property modeling in the existing solutions only allows calculation of all samples according to a specific discrete accuracy, and the specific discrete accuracy cannot well meet the accuracy requirements of different thickness samples for optical property modeling, resulting in poor flexibility. 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 meet the accuracy requirements of different thickness samples for optical property modeling and better conform to the actual modeling needs.

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

[0006] Discretize a first equation included in the heat equation into a preset format according to a preset discrete accuracy to obtain a discrete heat equation, process the film layer parameters of the sample according to the preset discrete accuracy to obtain discrete film layer parameters, and process the optical system parameters of the photoacoustic measurement device according to the preset discrete accuracy to obtain discrete optical system parameters;

[0007] Based on the discrete heat equation, the discrete film layer parameters, and the discrete optical system parameters, construct a temperature field function of the sample;

[0008] Based on the temperature field function, construct a strain field function of the sample when the photoacoustic measurement device measures the sample.

[0009] In a specific implementation manner, the sample includes multiple film layers, the film layer parameters of the sample include the film layer parameters of each film layer in the sample, the discrete film layer parameters of the sample include the discrete film layer parameters of each film layer in the sample, the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample, 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.

[0010] In a specific implementation manner, constructing the temperature field function of the sample when the photoacoustic measurement device measures the sample based on the discrete heat equation, the discrete film layer parameters, and the discrete optical system parameters includes:

[0011] Based on the discrete heat equation, the discrete film layer parameters of the first film layer, and the discrete optical system parameters, determining the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample, where 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;

[0012] Based on the discrete heat equation, the discrete film layer parameters of the (i + 1)-th film layer, the discrete optical system parameters, and the temperature distribution function of the i-th film layer, determining 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;

[0013] Based on the temperature distribution function of each film layer, determining the temperature field function.

[0014] In a specific implementation manner, constructing the strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function includes:

[0015] Discretizing the second equation included in the acoustic wave equation into a preset format according to the preset discrete precision to obtain a discrete acoustic wave equation;

[0016] Based on the temperature field function and the discrete acoustic wave equation, constructing the displacement field function of the sample when the photoacoustic measurement device measures the sample, where the independent variable of the displacement field function includes the film layer thickness of each film layer in the sample;

[0017] Taking the derivative of the displacement field function along the film layer thickness direction to obtain the strain field function.

[0018] A second aspect of the embodiments of the present application provides a photoacoustic measurement method, including:

[0019] 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 any one of the methods in the first aspect;

[0020] According to the strain field function of the sample when the photoacoustic measurement device measures the sample, calculating 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;

[0021] Based on the different predicted film layer thicknesses of the sample and the simulation signal function, determining the simulation signals of the sample at different predicted film layer thicknesses;

[0022] 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 the sample.

[0023] In a specific implementation manner, the determining the actual film thickness of 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:

[0024] Adopt the polynomial fitting method to remove the base trend of the measured signal;

[0025] Perform local filtering on the measured signal after removing the base trend to obtain a target measured signal;

[0026] The determining the actual film thickness of 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:

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

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

[0029] A discrete unit, configured to discretize the first equation included in the heat equation into a preset format according to a preset discretization accuracy to obtain a discrete heat equation, process the film parameters of the sample according to the preset discretization accuracy to obtain discrete film parameters, and process the optical system parameters of the photoacoustic measurement device according to the preset discretization accuracy to obtain discrete optical system parameters;

[0030] A construction unit, configured to construct a temperature field function of the sample based on the discrete heat equation, the discrete film parameters, and the discrete optical system parameters;

[0031] 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.

[0032] In a specific implementation manner, the sample includes multiple film layers, the film parameters of the sample include the film parameters of each film layer in the sample, the discrete film parameters of the sample include the discrete film parameters of each film layer in the sample, the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample, 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.

[0033] In a specific implementation manner, the construction unit is specifically configured to determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample based on the discrete heat equation, the discrete film layer parameters of the first film layer, and the discrete optical system parameters, where the first film layer is the first film layer sequentially arranged in 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 discrete heat equation, the discrete film layer parameters of the (i + 1)-th film layer, the discrete optical system parameters, and the temperature distribution function of the i-th film layer, where i is a positive integer; and determine the temperature field function based on the temperature distribution function of each film layer.

[0034] In a specific implementation manner, the construction unit is specifically configured to discretize the second equation included in the acoustic wave equation into a preset format according to the preset discrete precision to obtain a discrete acoustic wave equation; construct the displacement field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function and the discrete acoustic wave equation, where the independent variable of the displacement field function includes the film layer thickness of each film layer in the sample; and take the derivative of the displacement field function along the film layer 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 by the method according to any one of 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 layer thickness of each film layer in the sample;

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

[0039] The determination unit is further configured to determine the actual film layer thickness of 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 baseline trend of the measured signal; perform local filtering on the measured signal after removing the baseline trend to obtain a target measured signal;

[0041] A determination unit, specifically configured to determine the actual film thickness of the sample based on the fitting degree between the target measured signal and each simulation signal of the sample.

[0042] A fifth aspect of the embodiments of the present application provides a computer device, including:

[0043] A central processing unit, a memory, and an input / output interface;

[0044] The memory is a transient storage memory or a persistent storage memory;

[0045] 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.

[0046] A sixth aspect of the embodiments of the present application provides a computer program product containing instructions. When the computer program product runs on a computer, it causes the computer to execute the method described in the first aspect or the second aspect.

[0047] A seventh aspect of the embodiments of the present application provides a computer storage medium. Instructions are stored in the computer storage medium. When the instructions are executed on a computer, they cause the computer to execute the method described in the first aspect or the second aspect.

[0048] It can be seen from the above technical solutions that the embodiments of the present application have the following advantages: The finite difference method is used to discretize the heat equation, film layer parameters, and optical system parameters, and at the same time, any preset discretization accuracy is allowed for processing. On the premise of ensuring the modeling accuracy of optical characteristics, any preset discretization accuracy can well adapt to the accuracy requirements of different thickness samples for optical characteristics modeling, and is more in line with the actual modeling needs. Description of the Drawings

[0049] Figure 1 It is a schematic flow chart of an optical characteristics modeling method disclosed in the embodiments of the present application;

[0050] Figure 2 It is a schematic diagram of the temperature distribution in a sample disclosed in the embodiments of the present application;

[0051] Figure 3 It is a schematic diagram of the displacement distribution in a sample disclosed in the embodiments of the present application;

[0052] Figure 4 It is a schematic diagram of the strain distribution in a sample disclosed in the embodiments of the present application;

[0053] Figure 5 It is a schematic diagram of the fitting between the measured signal and the simulation signal disclosed in the embodiments of the present application;

[0054] Figure 6 A schematic structural diagram of a computer device disclosed in an embodiment of the present application;

[0055] Figure 7 Another schematic structural diagram of a computer device disclosed in an embodiment of the present application;

[0056] Figure 8 Another schematic structural diagram of a computer device disclosed in an embodiment of the present application. Detailed implementation manners

[0057] Next, in combination with the accompanying drawings in the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. 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.

[0058] The embodiments of the present application provide an optical property modeling method, a photoacoustic measurement method, and related devices, which are used to meet the accuracy requirements of optical property modeling for samples with different thicknesses and better conform to the actual modeling needs.

[0059] To better illustrate the optical feature modeling method in the embodiments of the present application, the photoacoustic action 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 and there is a certain time delay relative to the incident time of the excitation light, the transmission time of the ultrasonic pulse signal in 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 speed 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 speed / 2.

[0060] Please refer to Figure 1 , the embodiments of the present application provide an optical property modeling method, including the following steps:

[0061] 101. Discretize the first equation included in the heat equation into a preset format according to a preset discrete precision to obtain a discrete heat equation, process the film layer parameters of the sample according to the preset discrete precision to obtain discrete film layer parameters, and process the optical system parameters of the photoacoustic measurement device according to the preset discrete precision to obtain discrete optical system parameters.

[0062] The embodiments of the present application come up with converting the non-discretizable first equation in the heat equation into a discretizable preset format, where the heat equation can be, including but not limited to, a heat equation constructed based on a heat diffusion model, a heat equation constructed based on a heat conduction model, and a heat equation constructed based on a two-temperature model.

[0063] 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 spot formed when the excitation light irradiates the object surface. In addition, the same excitation light will cause different temperature changes in different materials. Therefore, the film layer parameters of the sample, such as material sound velocity, refractive index, and extinction coefficient, etc., are also required, specifically depending on the parameters required by the heat equation. At the same time, since the heat equation is in a discrete form, each known parameter substituted into the heat equation needs to be discretized for calculation.

[0064] 102. Based on the discrete heat equation, discrete film layer parameters, and discrete optical system parameters, construct the temperature field function of the sample.

[0065] Specifically, the optical property modeling method of the present application first simulates the temperature distribution of the sample based on the film layer parameters of the sample, the optical system parameters of the photoacoustic measurement device, and the heat equation, and the temperature distribution of the sample can be represented by the temperature field function.

[0066] Since the discrete heat equation, discrete film layer parameters, and discrete optical system parameters are all in a discrete state, the constructed temperature field function of the sample is also in a discrete state. And since the discrete heat equation, discrete film layer parameters, and discrete optical system parameters can all be discretized with any preset discrete precision, the precision of the obtained temperature field function can also change with the preset discrete precision, improving the feasibility of the solution.

[0067] It should be noted that after substituting all known film layer parameters and known optical system parameters into the heat equation, the variable in the formula is the film layer thickness of the sample. That is, the temperature field function constructed in the present application can describe the temperature distribution of the sample after the excitation light irradiates the sample surface when the film layer thickness of the sample is different.

[0068] 103. Based on the temperature field function, construct the strain field function of the sample when the photoacoustic measurement device measures the sample.

[0069] As mentioned in the foregoing photoacoustic effect principle, the cause of the bulge (i.e., strain) appearing 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 sample to change, and then causing the sample to undergo strain. Therefore, after obtaining the temperature distribution of the sample, the strain distribution occurring in the sample, i.e., the strain field function, can be further deduced.

[0070] It can be understood that while the sample undergoes strain, the reflectivity of the sample also changes, and the change in 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 embodiment of the present application can determine the film thickness of the sample from the strain field function when the fitting degree with the measured signal is the highest.

[0071] In some specific implementation manners, this step can be implemented in the following manner: discretize the second equation included in the acoustic wave equation into a preset format according to a preset discretization accuracy to obtain a discrete acoustic wave equation; based on the temperature field function and the discrete acoustic wave equation, construct a displacement field function of the sample when the photoacoustic measurement device measures the sample, and the independent variable of the displacement field function includes the film thickness of each film layer in the sample; take the derivative of the displacement field function along the film thickness direction to obtain the strain field function.

[0072] It should be noted that the temperature difference at different thicknesses of the sample will cause thermal expansion, and thermal expansion is the cause of the generation of sound waves, or the strain generated by thermal expansion is the initial condition of the acoustic wave equation. Specifically, the temperature difference at different thicknesses of the sample will cause thermal expansion, thermal expansion generates thermal stress, and thermal stress generates sound waves (i.e., thermal strain) and starts to propagate. Therefore, the acoustic 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 acoustic wave equation and the temperature field function. Therefore, by substituting the temperature field function into the acoustic wave equation, the change in the displacement field of each film layer of the sample after being irradiated by the excitation light can be obtained. Among them, since the independent variable of the temperature field function is the film thickness of each film layer, the independent variable of the displacement field function obtained after substituting the temperature field function is also the film thickness of each film layer. Then, take the derivative of the displacement field function along the film thickness direction to obtain the strain field function.

[0073] Specifically, based on step 101, it is also necessary to convert the second equation in the acoustic wave equation that cannot be discretized into a preset format that can be discretized. In this way, both the acoustic 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 vary 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 thickness of each film layer in the sample, therefore, based on the discretized temperature field function and the discretized acoustic wave equation, the constructed displacement field function also has the film thickness of each film layer in the sample (i.e., the film thickness of the sample) as its independent variable. Therefore, by taking the derivative of the independent variable of the displacement field function, the strain field function is obtained.

[0074] In the embodiments of the present application, the finite difference method is used to discretize the heat equation, the film layer parameters, and the optical system parameters, and at the same time, any preset discretization accuracy is allowed for processing. On the premise of ensuring the accuracy of the optical property modeling, any preset discretization accuracy can well adapt to the accuracy requirements of different thickness samples for optical property modeling, and is more in line with the actual modeling needs.

[0075] In some specific implementation manners, the sample includes multiple film layers, the film layer parameters of the sample include the film layer parameters of each film layer in the sample, the discretized film layer parameters of the sample include the discretized film layer parameters of each film layer in the sample, the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample, 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.

[0076] It can be understood that since the discretized temperature field function and the discretized displacement field function are discrete, therefore, the corresponding known parameters (the discretized film layer parameters of each film layer in the sample and the discretized optical system parameters) also need to be discretized. In addition, generally, the non-discretizable equations (such as the first equation, the second equation, and the third equation) can be differential equations in the corresponding equations, and the preset format can be an implicit difference format that allows discretization.

[0077] It should be noted that the same excitation light will cause different temperature changes in the film layers of different materials. Therefore, if the sample includes multiple film layers, then the film layer parameters of each film layer in the sample are also required, such as the sound speed of each film layer material, 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 thickness of each film layer. That is, the temperature field function constructed in the present 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 thickness of each film layer in the sample is different.

[0078] In some specific implementation manners, the foregoing step 102 may be implemented in the following manner: based on the discrete heat equation, the discrete film layer parameters of the first film layer, and the discrete optical system parameters, determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample, where the first film layer is the first film layer sequentially arranged along the direction from the sample surface to the interior of the sample; based on the discrete heat equation, the discrete film layer parameters of the (i + 1)-th film layer, the discrete optical system parameters, and the temperature distribution function of the i-th film layer, 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.

[0079] To better illustrate the technical solution of the embodiments of the present application, in the embodiments of the present application, 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 according to the distance from the substrate. 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.

[0080] Specifically, since the excitation light irradiates the surface film layer of the sample, in practical 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. By analogy, 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 the first to the last (from the first film layer to the n-th film layer), the temperature distribution function of the (i + 1)-th film layer is calculated successively 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, the discrete film layer parameters of the (i + 1)-th film layer, and the discrete optical system parameters. Finally, by integrating the temperature distribution function of each film layer, the temperature field function can be determined.

[0081] The foregoing content describes multiple 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 signals of the sample at different predicted film layer thicknesses based on different predicted film layer thicknesses of the sample and the simulation signal function; determining the actual film layer thickness of 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.

[0082] Specifically, since the optical property modeling method according to the present application can determine the strain field function and displacement field function of the sample when the photoacoustic measurement device measures the sample, but the independent variables in the strain field function and displacement field function are the film thicknesses of each film layer in the sample, therefore, a simulation signal function with the independent variables being the film thicknesses of each film layer in the sample can be determined. Then, by substituting the film thickness values of each film layer in the sample at different predicted film thicknesses into the simulation signal function, the simulation signals of the sample at different predicted film thicknesses can be obtained.

[0083] 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 at the predicted film thickness (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.

[0084] 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 (or the greater the fitting degree) between the measured signal and the simulation signal, the closer the expected film thicknesses of each film layer in the sample corresponding to the simulation signal are 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.

[0085] In fact, in order to improve the fitting efficiency and the efficiency of determining the simulation signal with the highest fitting degree, in the embodiments of the present application, the film layer parameters of each film layer in the sample are used as variables to construct an optimization model, and when the fitting degree between the simulation signal and the preprocessed target measured signal is the highest, the film layer thickness of each film layer corresponding to the simulation signal is obtained as the actual film layer 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 layer thickness of each film layer is iterated to obtain a series of fitting degrees between the simulation signal and the preprocessed measured signal and finally converge. Finally, the film layer thickness of each film layer when the fitting degree is the largest is 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.

[0086] Furthermore, in order to improve the fitting accuracy, in the embodiments of the present application, before fitting the measured signal and the simulation signal, the polynomial fitting method can also be used to remove the base trend of the measured signal, and local filtering processing is performed on the measured signal after removing the base trend to obtain the target measured signal. Then, the preprocessed target measured signal is used to replace the measured signal to fit with each simulation signal to obtain the corresponding fitting degree, and then the predicted film layer thickness corresponding to the simulation signal with the highest fitting degree is determined as the actual film layer thickness of each film layer in the sample.

[0087] Next, 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 are described.

[0088] Next, taking the heat diffusion formula as an example, a temperature field function as shown in the following formula is constructed:

[0089]

[0090] 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:

[0091]

[0092] Furthermore, the above formula (2) is written in the following matrix form:

[0093]

[0094] Among them, the u matrix is the temperature at different thicknesses of the sample at a certain time point, and a, b, and c form a coefficient matrix. The coefficients are known quantities composed of Δt, Δx, and α. Then, according to the loop and 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 temperatures at all thicknesses of all samples at all times are obtained.

[0095] When specific film thicknesses, film parameters, and optical system parameters are substituted, through the above temperature field function and method, it is possible to obtain as Figure 2 shown in the temperature distribution of the sample. Among them, the horizontal axis is time, and 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). A certain point among them is the temperature 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 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.

[0096] Furthermore, the calculation of the displacement field function is the same. After writing the acoustic wave equation in implicit difference format and rewriting it in the form of matrix (multiplication), through loop solving, the displacements at all thicknesses of all samples at all times can be obtained. When specific film thicknesses, film parameters, and optical system parameters are substituted, through the above displacement field function and method, it is possible to obtain as Figure 3 shown in the displacement distribution of the sample. Among them, the horizontal axis is time, and 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). A certain point among them is 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.

[0097] Similarly, when specific film thicknesses, film parameters, and optical system parameters are substituted, Figure 4 it is the strain distribution of the sample shown. Among them, the horizontal axis is time, and 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). A certain point among them is 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.

[0098] Next, after obtaining the strain field function, when specific predicted film thicknesses, film parameters, and optical system parameters are substituted, a 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, the base trend is removed from the measured signals (the processed effect can be referred to Figure 5The measured signal after removing the base trend) and local filtering processing (the effect after processing can be referred to Figure 5 the target measured signal), etc. After preprocessing steps such as Figure 5 , the fitting is carried out with the simulation signal, and the fitting schematic effect is as

[0099] shown. In the embodiment of the present application, according to the change of the surface film layer 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 base caused by the heat generated by the laser; and, the signal-to-noise ratio of the measured signal is improved by 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.

[0100] Please refer to Figure 6 , the embodiment of the present application provides a computer device, including:

[0101] A discrete unit 601, configured to discretize the first equation included in the heat equation into a preset format according to a preset discretization accuracy to obtain a discrete heat equation, process the film layer parameters of the sample according to a preset discretization accuracy to obtain discrete film layer parameters, and process the optical system parameters of the photoacoustic measurement device according to a preset discretization accuracy to obtain discrete optical system parameters;

[0102] A construction unit 602, configured to construct a temperature field function of the sample based on the discrete heat equation, the discrete film layer parameters, and the discrete optical system parameters;

[0103] The construction unit 602 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.

[0104] In a specific implementation manner, the sample includes multiple film layers, the film layer parameters of the sample include the film layer parameters of each film layer in the sample, the discrete film layer parameters of the sample include the discrete film layer parameters of each film layer in the sample, the temperature field function is used to describe the temperature distribution on the surface of the sample and the temperature distribution inside the sample, 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.

[0105] In a specific implementation manner, the construction unit 602 is specifically configured to determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample based on the discrete heat equation, the discrete film layer parameters of the first film layer, and the discrete optical system parameters, where 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; determine the temperature distribution function of the (i + 1)-th film layer when the photoacoustic measurement device measures the sample based on the discrete heat equation, the discrete film layer parameters of the (i + 1)-th film layer, the discrete optical system parameters, and the temperature distribution function of the i-th film layer, where i is a positive integer; determine the temperature field function based on the temperature distribution function of each film layer.

[0106] In a specific implementation manner, the construction unit 602 is specifically configured to discretize the second equation included in the acoustic wave equation into a preset format according to a preset discrete precision to obtain a discrete acoustic wave equation; based on the temperature field function and the discrete acoustic wave equation, construct a displacement field function of the sample when the photoacoustic measurement device measures the sample, and the independent variable of the displacement field function includes the film thickness of each film layer in the sample; take the derivative of the displacement field function along the film thickness direction to obtain a strain field function.

[0107] Please refer to Figure 7 , an embodiment of the present application provides a computer device, including:

[0108] An acquisition unit 701, 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 any optical property modeling method of the present application;

[0109] A calculation unit 702, 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;

[0110] A determination unit 703, configured to determine the simulation signals of the sample at different predicted film thicknesses based on different predicted film thicknesses of the sample and the simulation signal function;

[0111] The determination unit 703 is further configured to determine the actual film thickness of 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.

[0112] In a specific implementation manner, the determination unit 703 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;

[0113] The determination unit 703 is specifically configured to determine the actual film thickness of the sample based on the fitting degree between the target measured signal and each simulation signal of the sample.

[0114] Figure 8 FIG. 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.

[0115] Among them, the memory 805 can be volatile storage or persistent storage. The programs 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 processing unit 801 can be configured to communicate with the memory 805 and execute a series of instruction operations in the memory 805 on the computer device 800.

[0116] 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.

[0117] The central processing unit 801 can perform the operations executed by the computer device in the foregoing Figures 1 to 7 illustrated embodiments, and details are not described herein again.

[0118] It should be noted that although the steps in the flowcharts involved in the embodiments are sequentially drawn according to the indication of the arrows, unless there is a clear description 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 some 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 moment, but can be executed at different moments. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or alternately with at least some of the steps or stages in other steps or other steps.

[0119] Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments, and details are not described herein again.

[0120] In several embodiments provided in this 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. In actual implementation, there may be other division methods. 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, direct couplings, or communication connections to each other can be indirect couplings or communication connections through some interfaces, devices, or units, and can be in electrical, mechanical, or other forms.

[0121] The unit described as a separation component may or may not be physically separated. The component shown as a unit may or may not be a physical unit, that is, it may 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.

[0122] In addition, each functional unit in various embodiments of the present application may be integrated in a processing unit, may exist separately as individual physical units, or two or more units may be integrated in one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of a software functional unit.

[0123] If 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 such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The 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 various embodiments of the present application. The foregoing 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.

[0124] The embodiments of the present 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 Including: Discretize the first equation included in the heat equation into a preset format according to a preset discrete precision to obtain a discrete heat equation, process the film layer parameters of the sample according to the preset discrete precision to obtain discrete film layer parameters, and process the optical system parameters of the photoacoustic measurement device according to the preset discrete precision to obtain discrete optical system parameters; Construct a temperature field function of the sample based on the discrete heat equation, the discrete film layer parameters, and the discrete optical system parameters; Construct a strain field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function.

2. The method according to claim 1, characterized in that, The sample includes multiple film layers. The film layer parameters of the sample include the film layer parameters of each film layer in the sample. The discrete film layer parameters of the sample include the discrete film layer parameters of each film layer in the sample. 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 strain field function is used to describe the strain distribution on the surface of the sample and the strain distribution inside the sample.

3. The method according to claim 2, wherein The constructing the temperature field function of the sample when the photoacoustic measurement device measures the sample based on the discrete heat equation, the discrete film layer parameters, and the discrete optical system parameters includes: Based on the discrete heat equation, the discrete film layer parameters of the first film layer, and the discrete optical system parameters, determine the temperature distribution function of the first film layer when the photoacoustic measurement device measures the sample. 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 discrete heat equation, the discrete film layer parameters of the (i + 1)-th film layer, the discrete optical system parameters, and the temperature distribution function of the i-th film layer, 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.

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 includes: Discretize the second equation included in the acoustic wave equation into a preset format according to the preset discrete precision to obtain a discrete acoustic wave equation; Construct a displacement field function of the sample when the photoacoustic measurement device measures the sample based on the temperature field function and the discrete acoustic wave equation. 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.

5. A photoacoustic measurement method, characterized in that, Including: 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 at different predicted film layer thicknesses. Determine the actual film thickness of 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.

6. The method according to claim 5, wherein The determining the actual film thickness of 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 baseline trend of the measured signal; Perform local filtering on the measured signal after removing the baseline trend to obtain a target measured signal; Determine the actual film thickness of the sample based on the fitting degree between the target measured signal and each simulation signal of the sample.

7. A computer device, characterized in that, Includes: A discrete unit for discretizing the first equation included in the heat equation into a preset format according to a preset discretization accuracy to obtain a discrete heat equation, processing the film layer parameters of the sample according to the preset discretization accuracy to obtain discrete film layer parameters, and processing the optical system parameters of the photoacoustic measurement device according to the preset discretization accuracy to obtain discrete optical system parameters; A construction unit for constructing a temperature field function of the sample based on the discrete heat equation, the discrete film layer parameters, and the discrete optical system parameters; 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.

8. A computer device, characterized in that, Includes: An acquisition unit for acquiring 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 described in any one of claims 1 to 4; A calculation unit for calculating 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 for determining the simulation signals of the sample at different predicted film thicknesses 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 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, Includes: 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 described in 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 described in any one of claims 1 to 4 or 5 to 6.

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