Method and equipment for acquiring thermal conductivity distribution of material in depth direction based on frequency domain heat reflection

Abstract

The invention belongs to the related technical field of thermophysical property measurement, and discloses a method and equipment for obtaining thermal conductivity distribution in the depth direction of a material based on frequency domain heat reflection, and the method comprises the following steps: (1) representing a mapping relation between the thermal conductivity and the depth of the material by adopting a prior thermal conductivity distribution function; (2) dividing the material into a plurality of thin layers with equal thickness along the depth direction, and deriving a heat transfer matrix of each thin layer based on the heat conductivity of the material; (3) calculating through the heat transfer matrix to obtain theoretical phase signals of the material under different heating frequencies, and performing iterative optimization on unknown parameters in the prior heat conductivity distribution function by using a quasi-Newton method to obtain the unknown parameters in the prior heat conductivity distribution function; and (4) obtaining thermal conductivity distribution in the depth direction of the material based on the prior thermal conductivity distribution function. According to the invention, the thermophysical property change of the material in a near-micron range is extracted from heat reflection signals with different frequencies.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field related to thermophysical property measurement, and more particularly, relates to a method and device for obtaining material deep direction thermal conductivity distribution based on frequency domain thermal reflectance. BACKGROUND

[0002] The material in the preparation and use process due to the change of micro-nano structure or component has influence on the physical property, the detection of the thermal conductivity distribution in the depth direction of the material in the micron range can construct the material structure-physical property relationship, which is very important for the preparation and application of the material. For example, diamond has the highest thermal conductivity in the material, which can reach 2000 W m -1 K -1 , and has broad application potential in high-power device heat dissipation substrate. However, in the process of vapor deposition method (CVD) growth, the polycrystalline diamond film in the area far away from the growth surface will form smaller grains, and the boundary scattering caused by the grain boundary will increase, which will cause the thermal conductivity of the corresponding area to decrease significantly. It is of great significance to detect the thermal conductivity distribution of CVD diamond film in the depth direction for the development of CVD diamond and its application in thermal management. In addition, in nuclear power plants and outer space, high-energy ion irradiation will cause damage to the lattice of the material surface when the material is exposed to high radiation environment for a long time, which will further cause the thermal conductivity in the micron range of the material surface to decrease significantly, which may lead to material failure. Characterizing the influence of irradiation damage on the thermal conductivity of the material is helpful for the safe application of the material in the irradiation environment.

[0003] However, it is still very difficult to analyze the thermal physical property distribution of the material along the depth direction in the micron scale. Most of the existing characterization methods can only give the overall equivalent thermal conductivity of the sample, and the spatial resolution is difficult to be reduced to the micron level. The frequency domain thermal reflectance (FDTR) technology is a method for obtaining the thermal physical property of the material by periodically heating the sample surface with a modulated light beam and detecting the phase or amplitude change of the reflected probe light. In the frequency domain thermal reflectance experiment, the depth range of the heating effect of the laser is usually evaluated by the thermal penetration depth (κ, C are the thermal conductivity and volumetric specific heat of the material, and f is the modulation frequency). Since the pump laser can reach a high heating frequency, the frequency domain thermal reflectance method can detect the thermal conductivity of the material in the micron range. However, the existing FDTR method mainly obtains the overall equivalent thermal conductivity of the material in the micron range from the probe light signals at different frequencies, and lacks the resolution in the depth direction. The phase signals at different heating frequencies correspond to the thermal conductivity distribution at different depths, but the phase signal and the distribution of the thermal conductivity in the depth direction are nonlinear functions. It is a complex inverse problem to extract the thermal physical property from the phase at different frequencies, and there is currently no method to extract the thermal conductivity distribution of the material in the depth direction from the signals at different frequencies. SUMMARY

[0004] To address the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a method and apparatus for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection. The aim is to provide a method that can extract the changes in thermal properties of a material in the near-micrometer range from thermal reflection signals of different frequencies.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for obtaining the thermal conductivity distribution of a material along its depth direction based on frequency domain thermal reflection is provided, the method comprising the following steps:

[0006] (1) The mapping relationship between the thermal conductivity of a material and its depth is represented by a prior thermal conductivity distribution function, which contains unknown parameters.

[0007] (2) Divide the material into multiple thin layers of equal thickness along the depth direction, and derive the heat transfer matrix of each thin layer based on the thermal conductivity of the material.

[0008] (3) The theoretical phase signal of the material at different heating frequencies is obtained by calculating the heat transfer matrix. The unknown parameters in the prior thermal conductivity distribution function are iteratively optimized by using the quasi-Newton method so that the error between the collected experimental phase signal and the theoretical phase signal is less than the set threshold, thereby obtaining the unknown parameters in the prior thermal conductivity distribution function.

[0009] (4) The thermal conductivity distribution in the depth direction of the material is obtained based on the prior thermal conductivity distribution function.

[0010] Furthermore, the thickness of the thin layer is set to approximately 10 nm to 50 nm, and the total depth of the thin layer is determined by the thermal penetration depth at the lowest frequency.

[0011] Furthermore, by setting initial values ​​for the unknown parameters in the prior thermal conductivity distribution function, the thermal conductivity corresponding to thin layers of different thicknesses is calculated, and then the heat transfer matrix corresponding to each thin layer is calculated.

[0012] Furthermore, based on the heat transfer matrix of multiple thin layers, the theoretical phase signal at different heating frequencies is calculated through integral operations.

[0013] Furthermore, the sensitivity of different parameters to phase signals at different heating frequencies is calculated, and the measurement error of the unknown parameters of the prior thermal conductivity distribution function is calculated using the error propagation matrix based on the obtained sensitivity.

[0014] The present invention also provides a system for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the method described above for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection.

[0015] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method described above for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection.

[0016] In summary, compared with the prior art, the method and equipment for obtaining the thermal conductivity distribution of materials in the depth direction based on frequency domain thermal reflection provided by the present invention have the following advantages:

[0017] 1. First, a priori thermal conductivity distribution function with unknown parameters is introduced. The material is divided into multiple thin layers of equal thickness along the depth direction. Initial values ​​for the unknown parameters are set, and the heat transfer matrix corresponding to each thin layer is calculated. The theoretical phase signal is then calculated based on the heat transfer matrix. Finally, the unknown parameters in the priori thermal conductivity distribution function are fitted using a quasi-Newton method, ensuring that the error between the experimental and theoretical phase signals reaches a threshold, thus obtaining the thermal conductivity distribution function of the material along the depth direction. Therefore, through the method of this invention, by leveraging the established prior distribution function, the thermal property distribution along the depth direction of the material can be conveniently reconstructed from frequency-domain thermal reflection signals of different frequencies. This method has the potential to be applied to in-situ, non-contact, and non-destructive testing of thermal conductivity changes caused by structural and compositional variations within the near-micron range during material processing.

[0018] 2. This invention also provides a method for evaluating the fitting error of the thermal conductivity depth distribution. This method first provides a calculation method for the sensitivity of the phase signal to each parameter to determine the fitting frequency range and the value range of the known parameters. Then, using the error propagation matrix, the reconstruction error of the thermal conductivity distribution in the depth direction is calculated, thereby quantifying the influence of signal noise and the uncertainty of known parameters on the thermal conductivity reconstruction result. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of a method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection provided by the present invention;

[0020] Figure 2 This is a flowchart of a method for reconstructing the thermal property distribution in the depth direction using a frequency domain thermal reflection method, as provided in an embodiment of the present invention.

[0021] Figure 3 This is a comparison diagram of frequency domain thermal reflection phase signals of a sample before and after irradiation, provided by an embodiment of the present invention;

[0022] Figure 4 This is a schematic diagram of a method for discretizing and calculating a multilayer heat transfer matrix based on prior thermal conductivity, provided by an embodiment of the present invention.

[0023] Figure 5(a) and (b) in the figure are schematic diagrams of sample thermal conductivity fitting and depth direction thermal conductivity reconstruction provided by the embodiments of the present invention;

[0024] Figure 6 This is a schematic diagram illustrating the sensitivity of parameters in a priori thermal property distribution and interfacial thermal conductivity provided by an embodiment of the present invention.

[0025] Figure 7 This is a schematic diagram illustrating the distribution of calculated thermal conductivity error with depth, provided by an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] Research on related technologies has revealed that in frequency-based thermal reflection experiments, the phase of different heating frequencies corresponds to thermal property information at different depths of the sample. Previous methods typically involve fitting phase signals across different frequency bands to obtain a uniform thermal conductivity of the material, failing to capture thermal property information along the depth direction and lacking a method to directly extract the non-uniform thermal property distribution along the depth direction from frequency-domain thermal reflection signals.

[0028] Based on this, this invention proposes a method for obtaining the thermal conductivity distribution of materials along the depth direction based on frequency-domain thermal reflection. It assumes that the thermal properties satisfy a prior distribution function containing unknown parameters along the depth direction. In a layered heat transfer model, the depth direction is discretized, the corresponding heat transfer matrix is ​​calculated, and the theoretical phase signal is obtained. Iterative optimization using a quasi-Newton method is employed to achieve optimal fitting between the experimental phase signal and the theoretical signal at different frequencies, thus determining the unknown parameters in the prior distribution function. Furthermore, this invention also provides a method for calculating the thermal conductivity reconstruction error along the depth direction using an error propagation matrix.

[0029] Please see Figure 1 The method mainly includes the following steps:

[0030] Step 1: The mapping relationship between the thermal conductivity of the material and the depth is represented by the prior thermal conductivity distribution function, which contains unknown parameters.

[0031] Step 2: Divide the material into multiple thin layers of equal thickness along the depth direction, and derive the heat transfer matrix of each thin layer based on the thermal conductivity of the material.

[0032] Specifically, it includes the following sub-steps:

[0033] Define the thickness and number of thin layers in the depth direction;

[0034] Typically, the thickness of the thin layer can be set to around 10nm to 50nm. The total depth of the thin layer is determined by the thermal penetration depth at the lowest frequency. When the depth is greater than the thermal penetration depth, the thermal properties of the material have almost no effect on the signal. Therefore, the thickness of the last thin layer can be set to be sufficiently large.

[0035] Set initial values ​​for the unknown parameters in the prior thermal conductivity distribution function, and calculate the thermal conductivity corresponding to thin layers of different thicknesses;

[0036] Calculate the heat transfer matrix for each thin layer.

[0037] Step 3: The theoretical phase signal of the material at different heating frequencies is obtained by calculating the heat transfer matrix. The unknown parameters in the prior thermal conductivity distribution function are iteratively optimized using the quasi-Newton method so that the error between the collected experimental phase signal and the theoretical phase signal is less than a set threshold, thereby obtaining the unknown parameters in the prior thermal conductivity distribution function.

[0038] Specifically, it includes the following sub-steps:

[0039] Based on the heat transfer matrices of the above-mentioned multiple thin layers, the theoretical phase signals at different heating frequencies are calculated by integral operation.

[0040] The unknown parameters in the prior thermal conductivity distribution function are iteratively optimized using the quasi-Newton method (LBFGS) to ensure that the error between the acquired experimental phase signal and the theoretical phase signal is less than a set threshold.

[0041] Step 4: Obtain the thermal conductivity distribution along the depth direction of the material based on the prior thermal conductivity distribution function.

[0042] The mapping relationship between the thermal conductivity of a material and its depth is represented by a prior thermal conductivity distribution function. This prior thermal conductivity distribution function contains unknown parameters, and its form is determined by the characteristics of the material. For example, in irradiated materials, the thermal conductivity distribution of the sample in the depth direction is a Gaussian distribution function.

[0043] This invention provides a method for calculating the fitting error of thermal conductivity in the depth direction, specifically including the following steps:

[0044] The measurement error of the unknown parameters of the prior thermal conductivity distribution function is calculated using the error propagation matrix based on the aforementioned sensitivity.

[0045] The error in the distribution of thermal conductivity with depth is calculated based on the error of the above fitting parameters.

[0046] The sensitivity of different parameters to phase signals at different heating frequencies is calculated. These different parameters include: unknown parameters to be fitted, including unknown parameters of the prior thermal conductivity distribution and the interfacial thermal conductivity between the gold film and the material; and known parameters in the model, such as the thickness, thermal conductivity, and specific heat of the gold film, and the specific heat of the material.

[0047] The measurement error used to calculate the unknown parameters of the prior thermal conductivity distribution function using the above sensitivity and error propagation matrix specifically refers to:

[0048] The Jacobian matrix of the phase signal is calculated using the sensitivity described above for both known and unknown parameters in the model.

[0049] Based on the Jacobian matrix obtained above, the uncertainty of other known parameters and the error of the noise of the phase signal on the unknown parameters of the prior thermal conductivity distribution function are calculated through the error propagation matrix.

[0050] In one embodiment, a priori depth distribution of thermal conductivity with unknown parameters is first introduced. The material is divided into multiple thin layers of equal thickness along the depth direction. Initial values ​​for the unknown parameters are set, and the heat transfer matrix corresponding to each thin layer is calculated. The theoretical phase signal is then calculated based on the heat transfer matrix. Finally, the unknown parameters in the priori thermal conductivity distribution are fitted using a quasi-Newton method, ensuring that the error between the experimental and theoretical phase signals reaches a threshold, thus obtaining the thermal conductivity distribution of the material along the depth direction. Therefore, by using the method of this invention and by setting the form of the prior function distribution, the thermal property distribution of the material along the depth direction can be conveniently reconstructed from frequency-domain thermal reflection signals of different frequencies. This method has the potential to be applied to in-situ, non-contact, and non-destructive testing of thermal conductivity changes caused by structural and compositional variations within the near-micrometer range during material processing.

[0051] The present invention will be further described in detail below with reference to specific embodiments.

[0052] Figure 2 A flowchart of the method for reconstructing the thermal property distribution in the depth direction using the frequency domain thermal reflection method provided in this embodiment of the invention is shown below. Figure 2 As shown, the method for extracting the thermal conductivity distribution in the depth direction within a micrometer range based on a frequency domain thermal reflection system provided by this embodiment of the invention includes the following steps:

[0053] S11: Measure the thermal phase signal of the sample at different heating frequencies using a frequency domain thermal reflection system.

[0054] The frequency-domain thermal reflection system mainly includes a pump laser, a probe laser, an optical isolator, a photoelectric balance detector, a lock-in amplifier, etc. The system uses a pump light beam that can be modulated at different frequencies to heat the surface of a sample. Typically, a metal sensing film is deposited on the sample surface. Periodically heating the pump heat wave causes a periodic temperature response in the metal sensing film, which in turn causes a periodic thermal reflection response. A separate probe light beam detects the thermal reflection signal from the sample surface.

[0055] The specific implementation of the "phase signal under different heating frequencies" is as follows: First, a gold film of about 100 nm is deposited on the sample surface. Then, the pump light (usually a biased sine wave) is modulated by a lock-in amplifier, and the thermal phase signal of the probe light under different heating frequencies is extracted by the lock-in amplifier.

[0056] When pump light of different frequencies heats the sample surface, the amplitude of the internal temperature change attenuates with depth. The range of heat transfer influence at that heating frequency, i.e., the heat penetration depth, is typically determined by finding the point where the temperature change amplitude is 1 / e of the surface temperature change amplitude.

[0057]

[0058] In the formula, κ represents the thermal conductivity of the sample, f represents the pump light heating frequency, and C represents the volumetric specific heat of the sample. The pump heating light has a modulated wide frequency range of 100Hz-20MHz, corresponding to a thermal penetration depth range from hundreds of nanometers to tens of micrometers. Information at different depths can be detected by heating light signals of different frequencies.

[0059] Figure 3 The frequency domain thermal reflectance signal diagrams of bulk SiC and irradiated bulk silicon carbide provided in this embodiment are shown. The bulk silicon carbide can be fitted with a uniform thermal conductivity.

[0060] Previous methods for processing frequency domain thermal reflectance data assumed that the sample had uniform thermal conductivity, and determined the overall equivalent thermal conductivity at different frequency bands by fitting phase signals from different frequency bands. In this embodiment, the thermal conductivity is assumed to be a priori distribution function containing unknown parameters, and phase signals from a wide frequency band are fitted to determine the thermal conductivity distribution information in the depth direction, thereby enabling the detection of the thermal property distribution of the sample surface in the micrometer range.

[0061] S21: Assume that the thermal conductivity distribution along the depth direction is a priori function containing unknown parameters.

[0062] Assume that the thermal conductivity follows a certain distribution pattern with respect to depth, including unknown parameters, such as... Figure 4As shown, in one possible implementation, for He ion-irradiated SiC samples, it is generally assumed that the irradiation damage follows a near-Gaussian distribution along the depth direction, and the thermal conductivity is set to satisfy a priori distribution function along the depth direction as follows:

[0063]

[0064] In the formula, κ is the thermal conductivity value at a depth h from the surface, and B, C, h c p is an unknown Gaussian distribution parameter.

[0065] Alternatively, for other samples with prior structural distribution information, it can be assumed that the thermal conductivity satisfies other prior distribution functions, such as linear distribution, exponential distribution, or superposition of other distributions, etc.

[0066] S22: Divide the material into multiple thin layers of equal thickness along the depth direction and calculate the heat transfer matrix and theoretical phase signal.

[0067] The heat transfer matrix refers to the matrix used to calculate the heat flux density and temperature between the top and bottom of each layer. When calculating the theoretical phase signal of frequency-domain thermal reflection, the heat transfer matrices of each layer need to be superimposed to calculate the theoretical signal. Specifically, the heat transfer equation can be reduced to a one-dimensional form after Fourier transform and Hankel transform:

[0068]

[0069] In the formula, κ r κ z Let be the in-plane and out-of-plane thermal conductivity of the material, respectively; ω be the heating frequency; C be the volumetric specific heat of the material; k be the Hankel transform coefficient; and T be the Fourier transform of the temperature. Solving this heat transfer equation yields the following heat transfer matrix for materials with homogeneous thermophysical properties, where the temperature and heat flux density between the top and bottom of the material satisfy the following condition:

[0070]

[0071] In the formula, T b f b T corresponds to the temperature change and heat flux density at the bottom, respectively. t f t These correspond to the temperature change and heat flux density at the top, respectively; d is the thickness between the top and bottom; and M is the thickness between the top and bottom. i Let this be denoted as the heat transfer matrix of the i-th layer. For the interface, it can be considered as a thinner layer; in the interface layer heat transfer matrix, the specific heat C = 0, and the interface thermal conductivity...

[0072] Dividing the material into multiple thin layers of equal thickness along the depth direction is necessary because the thermal properties in the heat transfer matrix must remain uniform. This requires discretizing the material along the depth direction and dividing it into multiple thin layers of sufficiently small thickness. The heat transfer matrix of each thin layer is calculated using an initial value given by a priori thermal conductivity function. Specifically, in this embodiment, the material is divided into 200 thin layers along the depth, each with a thickness of d0 = 25 nm. For the i-th thin layer, its thermal conductivity is calculated as follows: And the heat transfer matrix M under these parameters is obtained. i For the last layer, its thickness is considered sufficiently large, and the thickness d of the last layer is taken as a sufficiently large value.

[0073] By multiplying the multilayer heat transfer matrices, the following relationship can be obtained between the surface temperature and heat flux density at a sufficiently far distance:

[0074]

[0075] In the formula, M i (i = 1, 2, ..., n) is the heat transfer matrix of the i-th layer of the material, M Au With M G These represent the heat transfer matrices at the interface between the gold film and the material, respectively. A, B, C, and D are the numerical results of the matrices after multiplying the layered heat transfer models. Since the bottom layer is sufficiently large, its heat flux density [f] is... b ] n =0, and the following relationship between surface heat flux density and temperature change can be obtained: Further derivation yields the expression for the frequency domain response H(ω) of the theoretical phase difference signal:

[0076]

[0077] In the formula, w0 and w1 are the Gaussian spot radii of the heating light and the probe light, respectively, and k is the Hankel variable parameter. The theoretical phase signal φ of the target sampling point... model (ω) is:

[0078]

[0079] S23: The unknown parameters in the prior thermal conductivity distribution function are obtained by fitting the experimental phase and the theoretical phase through an iterative method.

[0080] Specifically, in one possible implementation, the loss function is defined as follows:

[0081]

[0082] In the formula, ω i (i = 1, ..., M) represent different heating frequencies, φ exLet φ be the phase signal obtained from the frequency domain thermal reflection experiment. model To obtain the theoretical phase signal, the quasi-Newton algorithm in the scipy.minimize package of Python is used to iteratively optimize the above loss function, and to find the unknown parameters in the thermal conductivity distribution function in the depth direction when the loss function converges to the set threshold.

[0083] During the iteration process, boundary settings can be added based on the unknown parameters in the prior thermal conductivity distribution function along the depth direction to reduce iteration time and prevent the fitted parameters from getting trapped in local optima.

[0084] S24: Based on the above results, the thermal property distribution of the material in the depth direction is obtained.

[0085] After determining the unknown parameters in the prior thermal conductivity distribution function through S23 fitting, the thermal property distribution of the material in the depth direction is calculated. When the depth exceeds the maximum depth of the divided thin layers, the thermal conductivity of the material remains at the bulk value of the material. In this embodiment, as... Figure 5 The figures show the experimental signal of silicon carbide irradiation, the fitted experimental phase signal, and the distribution of thermal conductivity of silicon carbide after He ion irradiation in the depth direction.

[0086] S31: Reconstruction error of thermal conductivity distribution in the depth direction.

[0087] The process of calculating the depth-direction thermal conductivity distribution error is as follows: calculate the sensitivity of different functions to the phase signal, calculate the uncertainty of other known parameters and the error of signal noise on the unknown parameters in the thermal conductivity distribution based on the error transfer matrix, and calculate the depth-direction thermal conductivity distribution error based on the error of the parameters in the above thermal conductivity distribution.

[0088] Alternatively, the sensitivity of different parameters can be calculated using the following formula:

[0089]

[0090] In the formula, S x The sensitivity of parameter s. In this embodiment, Figure 6 Sensitivity analysis is used to assess the influence of parameters on the signal in different frequency ranges, in order to verify the reliability of the fitting of unknown parameters of the prior thermal conductivity distribution function and to select the frequency range with the highest sensitivity.

[0091] The error propagation matrix is ​​an important method for analyzing error propagation in multivariable functions. In the frequency domain thermal reflection experiment, the error in reconstructing the thermal conductivity distribution originates from errors caused by other known parameters such as the thermal conductivity and thickness of the gold film, as well as uncertainties caused by signal noise.

[0092] Specifically, in this embodiment, the error propagation matrix is ​​calculated as follows:

[0093]

[0094] In the formula, X U These are the parameters to be fitted in the theoretical phase signal model calculation, including unknown parameters in the interfacial thermal conductivity between the gold film and the material, and the prior thermal conductivity distribution. Known parameter X C These are known parameters used in the theoretical phase signal model calculations, including gold film thickness, specific heat, thermal conductivity, the material's thermal conductivity, and the radius of the light spot. Var represents the covariance matrix, where the matrix Var[X]... C Let be a diagonal matrix, where the diagonal terms are the variances of the known parameters. Var[Φ] is also a diagonal matrix, where the diagonal terms are the variances of the phase signals at different frequencies. U [ ] is the covariance matrix of the unknown parameters, with the diagonal terms representing the variance of the unknown parameters and the off-diagonal terms representing the covariance of the two parameters. The uncertainty of the known parameters calculated in this embodiment is shown in Table 1 below. The standard deviation of the known parameters can be determined by multiplying the uncertainty by the value of the material itself.

[0095] Table 1 Uncertainty of known parameters in error propagation

[0096]

[0097] Calculated using the following formula:

[0098]

[0099]

[0100] In the formula, x1, x2, ..., x p x is an unknown parameter in the model. p ,x p+1 ,…,x N The known parameters in the model are ω1, ω2, ..., ω. M For different heating frequencies, after obtaining the error of the parameters to be fitted, the distribution error of thermal conductivity in the depth direction can be calculated by the following formula:

[0101]

[0102] In the formula, y j (j=1,…,l) are the unknown parameters in the thermal conductivity distribution function. Its standard deviation. In this embodiment, the calculated distribution error of thermal conductivity in the depth direction is as follows: Figure 7 As shown.

[0103] The present invention also provides a system for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the method described above for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection.

[0104] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method described above for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection.

[0105] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for obtaining the thermal conductivity distribution of a material along its depth direction based on frequency domain thermal reflection, characterized in that, The method includes the following steps: (1) The mapping relationship between the thermal conductivity of a material and its depth is represented by a prior thermal conductivity distribution function, which contains unknown parameters. (2) Divide the material into multiple thin layers of equal thickness along the depth direction, and derive the heat transfer matrix of each thin layer based on the thermal conductivity of the material. (3) The theoretical phase signal of the material at different heating frequencies is obtained by calculating the heat transfer matrix. The unknown parameters in the prior thermal conductivity distribution function are iteratively optimized by using the quasi-Newton method so that the error between the collected experimental phase signal and the theoretical phase signal is less than the set threshold, thereby obtaining the unknown parameters in the prior thermal conductivity distribution function. (4) The thermal conductivity distribution in the depth direction of the material is obtained based on the prior thermal conductivity distribution function.

2. The method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection as described in claim 1, characterized in that: The thickness of the thin layer is set to be around 10nm to 50nm, and the total depth of the thin layer is determined by the thermal penetration depth at the lowest frequency.

3. The method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection as described in claim 2, characterized in that: We set initial values ​​for the unknown parameters in the prior thermal conductivity distribution function, calculate the thermal conductivity corresponding to thin layers of different thicknesses, and then calculate the heat transfer matrix corresponding to each thin layer.

4. The method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection as described in claim 1, characterized in that: Based on the heat transfer matrix of multiple thin layers, the theoretical phase signal at different heating frequencies is calculated by integral operation.

5. The method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection as described in claim 1, characterized in that: The sensitivity of different parameters to phase signals at different heating frequencies is calculated, and the measurement error of the unknown parameters of the prior thermal conductivity distribution function is calculated using the error propagation matrix based on the obtained sensitivity.

6. A system for obtaining the thermal conductivity distribution of a material along its depth direction based on frequency domain thermal reflection, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method for obtaining the thermal conductivity distribution of a material in the depth direction based on frequency domain thermal reflection as described in any one of claims 1-5.

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