Method and device for measuring interface thermal resistance

Abstract

The present invention belongs to the technical field related to interface thermal resistance measurement, and discloses an interface thermal resistance measurement method and device, which comprises the following steps: (1) using heating light and detection light to move from one side of the interface to be measured to the other side of the interface to be measured, while performing frequency domain thermal reflection measurement on the sample to be measured to obtain a measurement signal; (2) inputting the initial parameter value and the estimated interface thermal resistance value of the sample to be measured into a vertical interface heat transfer model to obtain a simulation signal, and then based on the best fit, with the goal of minimizing the deviation between the measurement signal and the simulation signal, comparing the measurement signal and the simulation signal to obtain the interface thermal resistance value of the interface to be measured; the vertical interface heat transfer model is obtained by integrating and summing the thermal response functions of the media on both sides of the interface to be measured and the thermal response functions generated by the mutual heat transfer between the media on both sides. The present invention enables the interface thermal resistance value of the interface to be measured to be accurately fitted even if the interface to be measured is perpendicular to the heating interface.

Description

Technical Field

[0001] The present invention belongs to the technical field related to interface thermal resistance measurement, and more specifically, relates to a method and device for measuring interface thermal resistance. Background Art

[0002] The interfacial thermal resistance of micro-nano devices plays a vital role in the device's heat dissipation, stability, efficiency and other performance aspects. Therefore, it is necessary to accurately measure the interfacial thermal resistance of micro-nano devices. Currently, the common method for measuring the interfacial thermal resistance of micro-nano devices is to use frequency domain thermoreflectometry (FDTR) and time domain thermoreflectometry (TDTR) techniques to perform non-contact heating and detection of micro-nano device samples with lasers, and then obtain the interfacial thermal resistance of the micro-nano device sample by fitting the detection signal with the calculated signal of the heat conduction model. Figure 1 As shown, it is a schematic diagram of a multi-layer micro-nano device sample, where Layer 1, Layer 2, etc. are made of different materials. There is an interface 12 to be measured between the layers. Currently, laser heating and detection are performed at the center position of the dotted line of the heating interface 11 with the z direction as the heating and detection direction.

[0003] Since the thermal conduction models of TDTR and FDTR both rely on the transfer matrix method, which expresses the heat flow transfer process between sample layers by calculating the matrix, it requires that the layers are regular parallel layers. This limits the method to only measuring the interfacial thermal resistance between layers parallel to the sample surface, that is, the heating interface 11 needs to be parallel to the interface to be measured 12.

[0004] However, for polycrystalline materials, composite materials, heterojunctions, etc., where there is an interface to be measured perpendicular to the heated interface, e.g. Figure 2 , two different materials (medium 1 on the left and medium 2 on the right) are separated by the interface to be measured 12. Since the heating interface 11 is perpendicular to the interface to be measured 12, the traditional transmission matrix method cannot measure the interface thermal resistance of the interface to be measured 12. In addition, since the heating effect of the laser can only diffuse to a limited depth, if the position of the interface to be measured exceeds the limited depth, for example Figure 3 Since the position of the interface 12 to be measured exceeds the thermal penetration depth, the traditional transfer matrix method cannot measure the interface thermal resistance of the interface 12 to be measured. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides an interface thermal resistance measurement method and equipment, which aims to solve the problem that the existing transfer matrix method cannot measure the interface thermal resistance of the interface to be measured when the heating interface is perpendicular to the interface to be measured.

[0006] To achieve the above object, according to one aspect of the present invention, a method for measuring interface thermal resistance is provided, the method comprising the following steps:

[0007] (1) moving the heating light and the detection light from one side of the interface to be measured to the other side of the interface to be measured, while performing frequency domain thermal reflection measurement on the sample to be measured to obtain a measurement signal; the interface to be measured intersects the heating interface of the sample to be measured perpendicularly;

[0008] (2) The initial parameter values ​​and the estimated interface thermal resistance value of the sample to be tested are input into the vertical interface heat transfer model to obtain a simulation signal, and then based on the best fit, the measurement signal and the simulation signal are compared with each other to obtain the interface thermal resistance value of the interface to be tested, with the goal of minimizing the deviation between the measurement signal and the simulation signal; the vertical interface heat transfer model is obtained by integrating and summing the thermal response functions of the media on both sides of the interface to be tested and the thermal response functions generated by the heat transfer between the media on both sides.

[0009] Furthermore, it is determined whether the deviation between the measurement signal and the analog signal is less than a preset deviation threshold. If so, the estimated interface thermal resistance value is used as the interface thermal resistance value of the interface to be measured. If not, the estimated interface thermal resistance value is adjusted, and after adjustment, the process jumps to the step of obtaining the analog signal.

[0010] Furthermore, the translation stage is controlled to move from one side of the interface to be measured to the other side of the interface to be measured on the heating interface of the sample to be measured in a direction perpendicular to the interface to be measured. During the movement of the translation stage, the heating light and the detection light are used to perform frequency domain thermal reflection measurement on the sample to be measured to obtain a measurement signal.

[0011] Furthermore, after each movement of the translation stage by a preset step, frequency domain thermal reflection measurement is performed on the sample to be measured using heating light and detection light of multiple preset frequencies to obtain measurement signals corresponding to each position of the translation stage.

[0012] Furthermore, the sample to be tested is divided into two parts by the test interface, and the media of the two parts are medium 1 and medium 2 respectively; the frequency domain thermal reflection signal detected by the detection light is divided into four parts, which are the thermal response of medium 1 itself, Indicates the thermal response of medium 2 itself, using It is used to indicate the thermal response of medium 2 to heating by interface heat transfer when heating light acts on medium 1. It is expressed as, and the thermal response of medium 1 heated by interface heat transfer when heating light acts on medium 2, express.

[0013] Furthermore, the four thermal response functions are multiplied by the heating light distribution and then by the detection light distribution, and then the four product results are integrated. Finally, the four integral results are summed to obtain the vertical interface heat transfer model.

[0014] Furthermore,

[0015]

[0016] Among them, λ 2x ,λ 2y ,λ 2z They represent the thermal conductivity of medium 1 in the X, Y and Z directions respectively, C1 represents the volume heat capacity of medium 1, λ 2x ,λ 2y ,λ 2z represents the thermal conductivity of medium 2 in the X, Y and Z directions respectively, c2 represents the volume heat capacity of medium 2, G represents the interface thermal conductivity of the interface to be measured, ξ, ζ represent the Fourier variables of X and Z respectively, ω is the frequency, y′ represents the position of the virtual point source itself, and y represents the position of the virtual point source response.

[0017] Furthermore, the mathematical expression of the vertical interface heat transfer model is:

[0018]

[0019] in, and The calculation formulas are formula (6) and formula (7):

[0020]

[0021] Where y0 represents the center position of the heating light, y1 represents the center position of the detection light, and r p represents the radius of the heating light, r s represents the radius of the detection light, represents the light absorption depth of the heating light in medium 1, represents the light absorption depth of the probe light in medium 1, represents the light absorption depth of the heating light in medium 2, represents the light absorption depth of the probe light in medium 2, represents the temperature response function of the heating light in medium 1, represents the temperature response function of the heating light in medium 2, and H(ω) represents the frequency domain thermal reflection signal, that is, the vertical interface heat transfer model.

[0022] The present invention also provides an interface thermal resistance measurement system, which includes a memory and a processor. The memory stores a computer program, and the processor executes the interface thermal resistance measurement method described above when executing the computer program.

[0023] The present invention also provides a computer-readable storage medium storing machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the interface thermal resistance measurement method described above.

[0024] In general, the above technical solutions conceived by the present invention, compared with the prior art, provide the following beneficial effects of the method and device for measuring interfacial thermal resistance:

[0025] 1. The present invention can obtain a vertical interface heat transfer model that can accurately characterize the interfacial thermal resistance of the vertical interface by integrating the thermal response functions of the media on both sides of the interface to be measured and the thermal response function generated by the mutual heat transfer between the media on both sides. Even if the interface to be measured is perpendicular to the heating interface, the interfacial thermal resistance value of the interface to be measured can be accurately fitted.

[0026] 2. As long as the interface perpendicular to the interface to be measured is selected as the heating interface, the vertical interface heat transfer model of this application can be used without considering the relationship between the position of the interface to be measured and the heat penetration depth, and the application range is wider.

[0027] 3. Use heating light and detection light of multiple preset frequencies to perform frequency domain thermal reflection measurement on the sample to be measured, and obtain measurement signals corresponding to each position of the translation stage, so as to more accurately fit the interface thermal resistance.

[0028] 4. The frequency-domain thermal reflection signal detected by the detection light is not only related to the thermal response of the media on both sides of the interface to be measured, but also to the thermal response generated by the mutual heat transfer between the media on both sides. Based on this, the frequency-domain thermal reflection signal is divided into four parts, which can solve the problem of different media on both sides of the vertical interface being divided, while improving the accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of a multidimensional micro-nano device;

[0030] Figure 2 It is a schematic diagram in which the heating interface is perpendicular to the interface to be measured;

[0031] Figure 3 It is a schematic diagram showing that the position of the interface to be measured exceeds the thermal penetration depth;

[0032] Figure 4 This is a flow chart of a method for measuring interface thermal resistance provided by the present invention;

[0033] Figure 5 It is a schematic diagram of the heating light and the detection light carried by the translation stage moving on the heating interface of the sample to be measured;

[0034] Figure 6It is a schematic diagram of Green’s function partitioning;

[0035] Figure 7 is a schematic diagram of the curve of the change of reflected light intensity and the position of the translation stage;

[0036] Figure 8 It is the curve of phase and stage position change at each preset frequency;

[0037] Figure 9 It is a perspective view of modeling the uncoated geometric model;

[0038] Figure 10 This is a schematic diagram of mesh division of the uncoated model;

[0039] Figure 11 It is a structural schematic diagram of an interface thermal resistance measuring device provided by the present invention;

[0040] Figure 12 It is a structural schematic diagram of an electronic device provided by the present invention.

[0041] In all the drawings, the same figure numbers are used to represent the same elements or structures, where: 11-heating interface, 12-interface to be measured, 13-heating light, 14-detection light, 501-control module, 502-measurement module, 503-experimental module, 504-comparison module, 601-processing device, 602-ROM, 603-RAM, 604-bus, 605-input / output (I / O) interface, 606-input device, 607-output device, 608-storage device, 609-communication device. DETAILED DESCRIPTION

[0042] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0043] See also Figure 4 The present invention provides a method for measuring interface thermal resistance, which mainly includes the following steps:

[0044] S401, controlling the translation stage to move on the heating interface of the sample to be tested from one side of the interface to the other side of the interface to be tested in a direction perpendicular to the interface to be tested; the interface to be tested and the heating interface intersect perpendicularly.

[0045] In one embodiment, an interface perpendicular to the test interface in the sample to be tested can be selected as the heating interface, and the translation stage can be moved on the heating interface in a direction perpendicular to the test interface. Since the heating interface is perpendicular to the test interface, the heating interface can be divided into two parts by the test interface, with the two parts being located at one side and the other side, respectively.

[0046] like Figure 5 As shown, the sample to be tested consists of medium 1 and medium 2, which intersect at the interface to be tested 12. Under the action of the displacement stage, the heating light 13 and the detection light 14 move along the arrow direction on the heating interface 11 from one side position of the interface to be tested 12 (i.e., one part of the medium) to the other measuring position (i.e., the second part of the medium).

[0047] The steps of determining the one side position and the other side position are: controlling a microscope camera to capture an image of the heating interface, and then determining the one side position and the other side position according to the image.

[0048] Taking into account that the image positioning method can only locate the approximate positions of one side and the other side, but cannot locate them accurately, in order to avoid the need for the translation stage to move multiple times due to inaccurate positioning, in a preferred embodiment, the intersection range of the interface to be measured and the heating interface is determined according to the image; then the translation stage is controlled to move from the leftmost position of the heating interface to the rightmost position along the direction perpendicular to the interface to be measured on the heating interface; during the movement of the translation stage, the heating light and the detection light are used to perform frequency domain thermal reflection measurement on the sample to be measured, and the reflected light intensity during the measurement process is collected to generate a change curve of the reflected light intensity and the position of the translation stage; and then the position of one side and the position of the other side are determined according to the change curve.

[0049] Since the frequency domain thermal reflection measurement in this embodiment is only used for precise positioning of the interface to be measured, the frequencies of the heating light and the detection light can be kept fixed in the frequency domain thermal reflection measurement, that is, the translation stage moves one step each time, and the frequency domain thermal reflection measurement of the sample to be measured is performed with heating light and detection light of fixed frequency.

[0050] See also Figure 7 The diagram shows the curve of the change of reflected light intensity and the position of the translation stage. When the heating light and the detection light move from one side of the interface to the other, the reflected light intensity will have a sudden change when passing through the interface due to the different reflectivity of the media on both sides of the interface. Figure 7 The reflected light intensity suddenly decreases. In this embodiment, the position of the interface to be measured can be determined based on the position of the translation stage when the reflected light intensity suddenly decreases. For example, Figure 7The position of the interface to be measured is approximately 103 micrometers (μm) to 106 micrometers, and then the position on one side and the position on the other side are determined.

[0051] Compared with the image positioning method, the present invention positions the interface to be measured by measuring the curve of the reflected light intensity changing with the position of the displacement stage, and the positioning result is more accurate.

[0052] In order to verify the accuracy of the above curve positioning method, the present invention can extract the phase of the measurement signal after obtaining the measurement signal in the above step S402, and then generate the following Figure 8 The phase and stage position curves at various preset frequencies are shown. As the heating light and the detection light gradually approach the interface to be measured, the phase delay increases due to the obstruction of the interface to be measured to the heat flow. However, as the heating light and the detection light gradually approach the interface to be measured, the heat flow on the other side of the interface to be measured is transmitted to this side through the interface to be measured, which reduces the phase delay of the measurement signal. Figure 8 The position where the phase delay first increases and then decreases is approximately 102.5 μm to 105 μm, which is consistent with the above positioning results.

[0053] S402 , during the movement of the translation stage, performing frequency domain thermal reflection measurement on the sample to be measured using heating light and detection light to obtain a measurement signal.

[0054] Heating light, also known as pump light, can be applied with a waveform via an electro-optical modulator to periodically heat the surface of a physical hardware material. The surface absorbs the heat from the pump light, causing a temperature rise. Consequently, the reflectivity of the pump light varies linearly with the temperature rise. Probe light is used to detect changes in the thermal reflectivity of the physical hardware material surface, specifically the linear variation in the reflectivity of the pump light with temperature rise.

[0055] For measurement, the translation stage needs to pause while moving across the heated interface so that the heating light and probe light can be used to stably perform frequency-domain thermoreflectance measurements on the sample under test. Alternatively, the translation stage can be moved in a fixed, preset step size, with each movement resulting in a measurement. This continues until the stage moves from one position to the other, at which point the measurement is completed and all measurement signals are obtained. Here, the measurement signal refers to the frequency-domain thermoreflectance signal of the heating light, i.e., the linear variation in the reflectivity of the pump light with temperature rise. Data acquisition can be performed using a lock-in amplifier to obtain the measurement signal.

[0056] After each movement of the translation stage by a preset step, frequency domain thermal reflectance measurement is performed on the sample to be measured using heating light and detection light of multiple preset frequencies to obtain measurement signals corresponding to each position of the translation stage, wherein the measurement signal corresponding to any position of the translation stage includes the measurement signals corresponding to the multiple preset frequencies.

[0057] In one embodiment, in order to be able to fit the interface thermal resistance more accurately, preferably, each time the translation stage moves a preset step, a frequency domain thermoreflectance measurement of the sample to be tested is performed using heating light and detection light of multiple preset frequencies. For example, when the translation stage moves to position 1 (in this embodiment, the position of the translation stage is the center position of the heating light and detection light), the frequencies of the heating light and detection light are adjusted to the preset frequency 1, and the heating light and detection light at the preset frequency 1 are used to perform frequency domain thermoreflectance measurement on the sample to be tested, and measurement signal 1 is obtained; then, the frequencies of the heating light and detection light are adjusted to the preset frequency 2, and the heating light and detection light at the preset frequency 2 are used to perform frequency domain thermoreflectance measurement on the sample to be tested, and measurement signal 2 is obtained; finally, the frequencies of the heating light and detection light are adjusted to the preset frequency 3, and the heating light and detection light at the preset frequency 3 are used to perform frequency domain thermoreflectance measurement on the sample to be tested, and measurement signal 3 is obtained. After the measurement is completed, the translation stage is controlled to move a preset step to move the translation stage to position 2. The frequencies of the heating light and the detection light are then adjusted to the preset frequency 1. The heating light and the detection light at the preset frequency 1 are used to perform frequency domain thermoreflectance measurement on the sample to be measured, and a measurement signal 4 is obtained. Next, the frequencies of the heating light and the detection light are adjusted to the preset frequency 2. The heating light and the detection light at the preset frequency 2 are used to perform frequency domain thermoreflectance measurement on the sample to be measured, and a measurement signal 5 is obtained. Finally, the frequencies of the heating light and the detection light are adjusted to the preset frequency 3. The heating light and the detection light at the preset frequency 3 are used to perform frequency domain thermoreflectance measurement on the sample to be measured, and a measurement signal 6 is obtained. And so on. Each time the translation stage is moved, the detection light signal needs to be rebalanced, that is, the intensity of the heating light and the detection light needs to be adjusted to be consistent. The preset step is 0.1 micron.

[0058] S403, inputting the initial parameter values ​​and the estimated interface thermal resistance value of the sample to be tested into a vertical interface heat transfer model to obtain a simulation signal; the vertical interface heat transfer model is obtained by integrating and summing the thermal response functions of the media on both sides of the interface to be tested and the thermal response functions generated by the heat transfer between the media on both sides.

[0059] The traditional transfer matrix method is applicable to scenarios where the heating interface is parallel to the interface to be measured. The heat transfer model involved is a model generated using a layered heat transfer structure. However, for scenarios where the heating interface is perpendicular to the interface to be measured, the layered heat transfer structure no longer holds true. Therefore, the traditional transfer matrix method cannot be applied to scenarios where the heating interface is perpendicular to the interface to be measured.

[0060] In this embodiment, the steps of obtaining the analog signal are:

[0061] Inputting the initial parameter values ​​and the estimated interface thermal resistance value of the sample to be tested into the vertical interface heat transfer model to obtain the target vertical interface heat transfer model after parameter transfer;

[0062] A graphics processor is called to perform parallel calculation on the target initial vertical interface heat transfer model according to a preset number of integration nodes to obtain the simulation signal.

[0063] Preferably, the integration adopts Gauss-Legendre integration method.

[0064] In one embodiment, for a scenario where the heating interface is perpendicular to the interface to be measured, the two sides of the interface to be measured are different media, such as Figure 5 As shown, the left and right sides of the interface to be measured 12 are medium 1 and medium 2 respectively. In order to solve the problem of the vertical interface dividing the different media on both sides, the frequency domain thermal reflection signal detected by the detection light is not only related to the thermal response of the media on both sides of the interface to be measured, but also related to the thermal response generated by the heat transfer between the media on both sides. The frequency domain thermal reflection signal can be divided into four parts, namely the thermal response of medium 1 itself (using ), the thermal response of medium 2 itself (expressed by When the heating light acts on the medium 1, the thermal response of the medium 2 is generated by the interface heat transfer (expressed as ), and the thermal response of medium 1 to heat generated by interface heat transfer when the heating light acts on medium 2 (expressed as express).

[0065] Considering the distribution of heating light and interface heat transfer, the above four thermal responses can be expressed as four Green's functions. Figure 6 As shown in Figure 1, it is a schematic diagram of Green's function partitioning.

[0066] When the heating light is incident on the sample to be tested, it will show a Gaussian distribution, e.g. Figure 6 The heating light distribution is shown on the left. Figure 6 In the example, the heating light is divided by the interface 12 to be measured into the heating light in the medium 1 and the heating light in the medium 2, which directly heat the medium 1 and the medium 2 respectively, and also heat the medium on the other side through the interface. For example, see Figure 6 In the upper right subfigure, the virtual point source δ(yy′) corresponding to the heating light heats medium 2 and simultaneously heats medium 1 through interface heat transfer. Here, y′ represents the location of the virtual point source δ(yy′) itself, and y represents the location of the virtual point source response.

[0067] In Green's function, the thermal response of the heating light can be considered as the superposition of the point source response in the space of the heating light distribution, and the above four thermal responses can be obtained based on this, namely and

[0068] Among them, λ 2x ,λ 2y,λ 2z They represent the thermal conductivity of medium 1 in the X, Y and Z directions respectively, C1 represents the volume heat capacity of medium 1, λ 2x ,λ 2y ,λ 2z represents the thermal conductivity of medium 2 in the X, Y and Z directions respectively, C2 represents the volume heat capacity of medium 2, G represents the interface thermal conductivity of the interface to be measured, ζ and ξ represent the Fourier variables of X and Z respectively, ω is the frequency, y′ represents the position of the virtual point source itself, and y represents the position of the virtual point source response.

[0069] The vertical interface heat transfer model of the present invention can be obtained by integrating and summing the four thermal response functions. Specifically, the four thermal response functions are first multiplied by the heating light distribution and then by the detection light distribution. The four multiplication results are then integrated, and finally the four integrated results are summed to obtain the vertical interface heat transfer model.

[0070] In this embodiment, the calculation formula of the vertical interface heat transfer model is formula (5):

[0071]

[0072] in, and The calculation formulas are formula (6) and formula (7):

[0073]

[0074] Where y0 represents the center position of the heating light, y1 represents the center position of the detection light, and r p represents the radius of the heating light, r s represents the radius of the detection light, represents the light absorption depth of the heating light in medium 1, represents the light absorption depth of the probe light in medium 1, represents the light absorption depth of the heating light in medium 2, represents the light absorption depth of the probe light in medium 2, represents the temperature response function of the heating light in medium 1, represents the temperature response function of the heating light in medium 2, and H(ω) represents the frequency domain thermal reflection signal, that is, the vertical interface heat transfer model.

[0075] In this embodiment, the initial parameter values ​​and the estimated interface thermal resistance value of the sample to be tested may be input into the vertical interface heat transfer model to obtain a simulation signal.

[0076] The above initial parameter values ​​need to be consistent with the parameter values ​​used when obtaining the measurement signal in step S402.

[0077] Step S403 is further described in detail:

[0078] The vertical interface heat transfer model is a quadruple integral function, so the process of calculating the simulation signal based on the vertical interface heat transfer model will consume a lot of time. In order to improve the calculation speed, optionally, after the initial parameter values ​​and estimated interface thermal resistance values ​​of the sample to be tested are input into the vertical interface heat transfer model and the target vertical interface heat transfer model after parameter transfer is obtained, the graphics processor GPU can be called to perform parallel calculations on the target initial vertical interface heat transfer model to obtain the simulation signal.

[0079] Since Python has a relatively complete function library for GPU parallel computing acceleration, the torchquad function in the pytorch library can be used to implement the GPU parallel computing process.

[0080] The torchquad function supports multiple numerical integration methods, such as trapezoidal integration and Gauss-Legendre integration. The Gauss-Legendre integration method's node partitioning better matches the function's Gaussian distribution, making it suitable for GPU parallel computing. Therefore, the Gauss-Legendre integration method can optionally be used to integrate the four thermal response functions.

[0081] Optionally, the number of integration nodes when calling the GPU to perform parallel calculations on the target initial vertical interface heat transfer model can be pre-set to 70 per dimension, that is, 70 integration nodes are set for each integral in the quadruple integral.

[0082] For example, for the y-multiple integral, 70 integration nodes are set, and the GPU can calculate the y values ​​at the 70 integration nodes respectively, and then sum the 70 y values ​​as the final integration result of the y-multiple integral.

[0083] It should be noted that the above setting of 70 integration nodes is only an example and is not intended to limit the present invention. If the video memory is sufficient, more integration nodes may be divided as much as possible to reduce errors.

[0084] In this embodiment, an integral cutoff can be set to replace the above integral range of 0 to ∞. Optionally, the integral cutoffs for y, y′, ξ, and ζ can be set to 10×r S 、10×r p 、 and According to tests, the integral truncation set in this embodiment can achieve relatively good accuracy in the numerical calculation of the frequency domain thermal reflection signal (ie, analog signal).

[0085] The embodiment of the present invention can calculate the analog signal more quickly and accurately by calling the GPU and setting a suitable integration method, integration node and integration truncation, thereby improving the fitting process of the interface thermal resistance value of the interface to be measured.

[0086] S404, determine whether the deviation between the measurement signal and the simulation signal is less than a preset deviation threshold; if so, use the estimated interface thermal resistance value as the interface thermal resistance value of the interface to be measured; if not, adjust the estimated interface thermal resistance value, and jump to step S403 after adjustment.

[0087] In this embodiment, the deviation between the measurement signal and the simulation signal can be calculated. For each position where the translation stage moves, it can include measurement signals at multiple preset frequencies. Similarly, by setting the above-mentioned initial parameter values, it is also possible to make each simulated translation stage position include simulation signals at multiple preset frequencies. The deviation in this embodiment can refer to the sum of the deviations between the measurement signal and the simulation signal at all preset frequencies corresponding to all translation stage positions.

[0088] For example, for position 1, this embodiment obtains measurement signal 1 and analog signal 1 at preset frequency 1, measurement signal 2 and analog signal 2 at preset frequency 2, and measurement signal 3 and analog signal 3 at preset frequency 3; for position 2, measurement signal 4 and analog signal 4 at preset frequency 1, measurement signal 5 and analog signal 5 at preset frequency 2, and measurement signal 6 and analog signal 6 at preset frequency 3 are obtained, then the deviation of the measurement signal and the analog signal in this embodiment = (measurement signal 1-analog signal 1) + (measurement signal 2-analog signal 2) + (measurement signal 3-analog signal 3) + (measurement signal 4-analog signal 4) + (measurement signal 5-analog signal 5) + (measurement signal 6-analog signal 6).

[0089] Of course, the deviation calculation method provided above is only an example, and other methods can also be used, for example, respectively extracting the phase of the measurement signal and the analog signal and then calculating the root mean square of the phase difference based on the extracted phase as the calculated deviation, or respectively extracting the amplitude of the measurement signal and the analog signal and then calculating the root mean square of the amplitude difference based on the extracted amplitude as the calculated deviation, etc., the present invention is not limited to this.

[0090] If the above calculated deviation is greater than the preset deviation threshold, it means that the measurement signal and the simulation signal cannot fit well, and further indicates that the estimated interface thermal resistance value is very different from the actual interface thermal resistance value of the interface to be measured. In this case, the estimated interface thermal resistance value can be adjusted. For example, the estimated interface thermal resistance value is adjusted from value 1 to value 2, and then value 2 is input into the vertical interface heat transfer model. The simulation signal is calculated again and the deviation is calculated. If the deviation is less than the preset deviation threshold at this time, value 2 is used as the interface thermal resistance value of the interface to be measured. If the deviation is still greater than the preset deviation threshold at this time, the estimated interface thermal resistance value is adjusted from value 2 to value 3, and input into the vertical interface heat transfer model again. This process is repeated and so on, until an estimated interface thermal resistance value is obtained that makes the deviation between the measurement signal and the simulation signal less than the preset deviation threshold, and then it is used as the interface thermal resistance value of the interface to be measured.

[0091] Optionally, the process of continuously adjusting the estimated node thermal resistance value and comparing the deviation with a preset deviation threshold may be implemented using a minimum value search function.

[0092] The measurement method provided by the present invention first controls the translation stage to move from one side of the test interface to the other side along a direction perpendicular to the test interface on the heating interface of the test sample. During the movement, the test sample is subjected to frequency domain thermal reflection measurement using heating light and detection light to obtain a measurement signal. Then, the initial parameter value of the test sample and the estimated interface thermal resistance value are input into a vertical interface heat transfer model to obtain a simulation signal. Finally, the deviation between the measurement signal and the simulation signal is calculated and compared with a preset deviation threshold. If the calculated deviation is greater than or equal to the preset deviation threshold, the estimated interface thermal resistance value is continuously adjusted and then input into the vertical interface heat transfer model to calculate the simulation signal until the calculated deviation is less than the preset deviation threshold. The estimated interface thermal resistance value at this time is used as the interface thermal resistance value of the test interface. The present invention can obtain a vertical interface heat transfer model that can accurately characterize the interface thermal resistance of the vertical interface by integrating the thermal response functions of the media on both sides of the test interface and the thermal response function generated by the mutual heat transfer between the media on both sides. Even if the test interface is perpendicular to the heating interface, the interface thermal resistance value of the test interface can be accurately fitted. At the same time, as long as the interface perpendicular to the interface to be measured is selected as the heating interface, the vertical interface heat transfer model of the present invention can be used without considering the relationship between the position of the interface to be measured and the heat penetration depth, and the application range is wider.

[0093] A thermal reflection model can be established using COMSOL software to verify whether the interface thermal resistance value fitted by the present invention is accurate.

[0094] Specifically, a model was established in COMSOL according to specific working conditions. The surface temperature response of the sample was solved through simulation. The weighted average of the detection light intensity distribution of the temperature response was performed to simulate the reflection signal of the detection light under experimental conditions, and then the phase delay was obtained. By modifying the position of the heating light, a parametric scan was performed, and the phase and amplitude curves changing with the heating light position were calculated.

[0095] First, set the parameters of the working condition in the software. For example, the power of 2mW, frequency of 1MHz, and radius of 1μm are used to heat the sample surface. The center of the heating light moves from 3μm to the left of the interface to be measured and 3μm to the right of the interface. Set the variables: power P = 2mW, frequency f = 1MHz, heating light radius r p =1μm, detection light radius r S =1μm, heating light position x0=250, y0=500, heating light distribution expression Flux=2*p0 / pi / rp^2*exp((-2*(y-y0)^2-2*(x-x0)^2) / rp^2).

[0096] Next, a geometric model was constructed by splicing two solid blocks with length, width and height set to 500 μm to simulate the semi-infinite heat transfer situation. The material thermal properties were set to thermal conductivity λ1 = λ2 = 10 W / (m 2 ·K), density is 2500kg / m3, constant pressure heat capacity is 1000J / (kg·K). A cylinder with a radius of 5μm and a height of 2μm is set at the junction of the heating surface and the interface to be measured, such as Figure 9 A perspective view of the modeling of the uncoated geometry is shown.

[0097] The physical field settings used the COMSOL Solid Thermal Conductivity Module. The default initial values ​​were set to room temperature. Ideal thermal insulation was set for the heated surface. Convection heat flux boundary conditions were set on the four sides and bottom, with a convection heat transfer coefficient of h = 10 W / (K·m²). A thin-layer contact thermal resistance was set at the interface between the two blocks, with the interface thermal resistances set to 10⁻¹, 10⁻¹, 10⁻¹, and 1 K·m²·W⁻¹ for the four conditions. A boundary heat source was added to the cylindrical surface, set to harmonic perturbation.

[0098] The meshing of the uncoated model is as follows: Figure 10 As shown in the figure, the heating area is small and the temperature change sampling points are fine, so a more detailed temperature distribution needs to be obtained. Therefore, the cylindrical area is finely meshed, and a free quadrilateral mesh is used to generate a surface mesh with a maximum of 0.1μm and a minimum of 0.005μm on the surface. The entire cylindrical area is meshed by sweeping, and the swept mesh size is set to a maximum of 0.1μm. The remaining part simulates the semi-infinite situation, and the temperature change is small, so the free tetrahedron mesh is used for automatic division.

[0099] Set it to solve the frequency domain disturbance, and set the frequency to f = 1MHz, and you can get the temperature distribution and isothermal surface of the cylindrical area.

[0100] In order to simulate the scanning of the heating light and the detection light in the experiment and obtain the corresponding frequency domain thermal reflection signal curve, it is necessary to change the coordinates of the heating light so that it scans from -3μm to 3μm at the interface and calculate the corresponding phase and amplitude curves. The scanning and weighted averaging of the intensity distribution of the detection light are completed using the COMSOL Multiphysics 6.1 with MATLAB module. This module can realize functions such as controlling COMSOL to change parameters, run simulations, and process data through the MATLAB program. The present invention uses a program for data extraction, processing, and storage of simulation results. The program first constructs a sampling matrix to extract the temperature response of 1000×1000 points uniformly sampled in a 20μm×20μm square area around the center of the heating light. Next, the detection light intensity distribution function is set to multiply the obtained temperature distribution matrix by the detection light intensity function, and then the sum is obtained to obtain the thermal reflection signal of the point and store it. By cyclically changing the coordinates of the heated photosynthetic detection light, the 3μm area on both sides of the interface is linearly divided into 200 scanning points. The coordinates of the center position of the heating light are changed one by one and the simulation is rerun. The two hundred heating position coordinates are traversed and the frequency domain temperature response is calculated one by one to simulate the signal of the detection light reflected into the phase-locked amplifier in the experiment.

[0101] By fitting the experimental data obtained by COMSOL simulation with the measurement signal calculated by inputting the interface thermal resistance value of the interface to be measured into the vertical interface heat transfer model, the fitting results are basically consistent. This can be verified that the vertical interface heat transfer model provided by the present invention can accurately obtain the interface thermal resistance value of the interface to be measured.

[0102] See also Figure 11 The present invention also provides an interface thermal resistance measuring device, the device comprising:

[0103] The control module 501 is used to control the translation stage to move from one side of the test interface to another side of the test interface in a direction perpendicular to the test interface, wherein the test interface is perpendicular to the heating interface;

[0104] The measurement module 502 is used to perform frequency domain thermal reflection measurement on the sample to be measured using the heating light and the detection light during the movement of the translation stage to obtain a measurement signal;

[0105] Experimental module 503 is used to input the initial parameter values ​​and estimated interface thermal resistance of the sample to be tested into a vertical interface heat transfer model to obtain a simulation signal. The vertical interface heat transfer model is obtained by integrating and summing the thermal response functions of the media on both sides of the interface to be tested and the thermal response function generated by the heat transfer between the media on both sides.

[0106] The comparison module 504 is used to determine whether the deviation between the measurement signal and the simulation signal is less than a preset deviation threshold. If so, the estimated interface thermal resistance value is used as the interface thermal resistance value of the interface to be measured. If not, the estimated interface thermal resistance value is adjusted. After adjustment, the initial parameter values ​​of the sample to be measured and the estimated interface thermal resistance value are returned and input into the vertical interface heat transfer model.

[0107] When the control module determines the position on one side and the position on the other side, it may specifically be:

[0108] controlling a microscope camera to capture an image of the heating interface;

[0109] The position of one side and the position of the other side are determined based on the image.

[0110] In a possible implementation, when the control module determines the position of one side and the position of the other side according to the image, it may specifically be:

[0111] Determine the intersection range of the interface to be measured and the heating interface according to the image;

[0112] Controlling the translation stage to move from the leftmost position to the rightmost position of the heating interface along a direction perpendicular to the interface to be measured on the heating interface;

[0113] During the movement of the translation stage, the heating light and the detection light are used to perform frequency domain thermal reflection measurement on the sample to be measured. The reflected light intensity during the measurement process is collected to generate a curve of the change of the reflected light intensity and the position of the translation stage.

[0114] The position on one side and the position on the other side are determined according to the change curve.

[0115] In a possible implementation, the measurement module performs frequency domain thermal reflection measurement on the sample to be measured using heating light and detection light during the process of controlling the movement of the translation stage. When obtaining the measurement signal, the following may be performed:

[0116] Each time the translation stage moves a preset step, frequency-domain thermal reflectance measurement is performed on the sample to be measured using heating light and detection light of multiple preset frequencies to obtain measurement signals corresponding to each position of the translation stage. The measurement signal corresponding to any position of the translation stage includes measurement signals corresponding to multiple preset frequencies.

[0117] In one possible implementation, when the above experimental module inputs the initial parameter values ​​and estimated interface thermal resistance values ​​of the sample to be tested into the vertical interface heat transfer model to obtain a simulation signal, specifically:

[0118] Input the initial parameter values ​​and estimated interface thermal resistance values ​​of the sample to be tested into the vertical interface heat transfer model to obtain the target vertical interface heat transfer model after parameter transfer;

[0119] The graphics processor is called to perform parallel calculations on the target initial vertical interface heat transfer model according to a preset number of integration nodes to obtain a simulation signal.

[0120] See also Figure 12 The present invention also provides an electronic device, which may include but is not limited to fixed terminals such as mobile phones, notebook computers, PDAs (personal digital assistants), PADs (tablet computers), desktop computers, etc. Figure 12 The electronic device shown is only an example and should not limit the functions and scope of use of the embodiments of the present invention.

[0121] like Figure 12 As shown, the electronic device may include a processing device (such as a central processing unit, a graphics processing unit, etc.) 601, which can perform various appropriate actions and processes according to a program stored in a read-only memory ROM 602 or a program loaded from a storage device 608 into a random access memory RAM 603, so that the electronic device can implement the interface thermal resistance measurement method provided by any of the above embodiments. When the electronic device is powered on, various programs and data required for the operation of the electronic device are also stored in RAM 603. The processing device 601, ROM 602 and RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0122] Typically, the following devices may be connected to the I / O interface 605: an input device 606 including, for example, a touch screen, a touchpad, a keyboard, a mouse, a camera, a microphone, an accelerometer, a gyroscope, etc.; an output device 607 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 608 including, for example, a memory card, a hard disk, etc.; and a communication device 609. The communication device 609 may allow the electronic device to communicate with other devices wirelessly or by wire to exchange data.

[0123] An embodiment of the present invention further provides a computer program product including computer-readable instructions. When the computer-readable instructions are executed on an electronic device, the electronic device implements any of the interface thermal resistance measurement methods provided in the embodiments of the present invention.

[0124] An embodiment of the present invention further provides a computer-readable storage medium, which carries one or more computer programs. When the one or more computer programs are executed by an electronic device, the electronic device can implement any interface thermal resistance measurement method provided in the embodiment of the present invention.

[0125] It should also be noted that the device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present embodiment. In addition, in the drawings of the device embodiments provided by the present invention, the connection relationship between modules indicates that they have a communication connection, which can be specifically implemented as one or more communication buses or signal lines.

[0126] Through the description of the above embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general hardware, and of course can also be implemented by special hardware including application-specific integrated circuits, special CPUs, special memories, special components, etc. In general, all functions performed by computer programs can be easily implemented by corresponding hardware, and the specific hardware structures used to implement the same function can also be diverse, such as analog circuits, digital circuits or special circuits, etc. However, for the present invention, software program implementation is a better implementation method in most cases. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a readable storage medium, such as a computer's floppy disk, USB flash drive, mobile hard disk, ROM, RAM, magnetic disk or optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, training equipment, or network equipment, etc.) to execute the methods described in each embodiment of the present invention.

[0127] In the above embodiments, all or part of the embodiments may be implemented by software, hardware, firmware, or any combination thereof. When implemented by software, all or part of the embodiments may be implemented in the form of a computer program product.

[0128] The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, training device or data center to another website, computer, training device or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that a computer can store or a data storage device such as a training device or data center that includes one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a magnetic tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0129] It will be easily understood by those skilled in the art 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 in the scope of protection of the present invention.

Claims

1. A method for measuring interface thermal resistance, characterized in that: The method comprises the following steps: (1) moving the heating light and the detection light from one side of the interface to be measured to the other side of the interface to be measured, while performing frequency domain thermal reflection measurement on the sample to be measured to obtain a measurement signal; the interface to be measured intersects the heating interface of the sample to be measured perpendicularly; (2) inputting the initial parameter values ​​and the estimated interface thermal resistance value of the sample to be tested into a vertical interface heat transfer model to obtain a simulation signal, and then comparing the measurement signal with the simulation signal based on the best fit, with the minimum deviation angle between the measurement signal and the simulation signal as the goal, to obtain the interface thermal resistance value of the interface to be tested; the vertical interface heat transfer model is obtained by integrating and summing the thermal response functions of the media on both sides of the interface to be tested and the thermal response functions generated by the heat transfer between the media on both sides; The sample to be tested is divided into two parts by the test interface, and the media of the two parts are medium 1 and medium 2 respectively; the frequency domain thermal reflection signal detected by the detection light is divided into four parts, which are the thermal response of medium 1 itself, Indicates the thermal response of medium 2 itself, using Indicates that when the heating light acts on medium 1, the thermal response of medium 2 is generated by heat transfer at the interface. and the thermal response of medium 1 to medium 2 through interface heat transfer when the heating light acts on medium 1, expressed as Representation: Multiply the four thermal response functions by the heating light distribution and then by the detection light distribution, then integrate the four product results, and finally sum the four integral results to obtain the vertical interface heat transfer model.

2. The method for measuring interfacial thermal resistance according to claim 1, wherein: Determine whether the deviation between the measurement signal and the analog signal is less than a preset deviation threshold. If so, use the estimated interface thermal resistance value as the interface thermal resistance value of the interface to be measured. If not, adjust the estimated interface thermal resistance value, and after adjustment, jump to the analog signal acquisition step.

3. The method for measuring interfacial thermal resistance according to claim 1, wherein: The translation stage is controlled to move from one side of the interface to be measured to the other side of the interface to be measured along a direction perpendicular to the interface to be measured. During the movement of the translation stage, frequency domain thermal reflection measurement of the sample to be measured is performed using heating light and detection light to obtain a measurement signal.

4. The method for measuring interfacial thermal resistance according to claim 3, wherein: After each movement of the translation stage by a preset step, frequency domain thermal reflection measurement is performed on the sample to be measured using heating light and detection light of multiple preset frequencies to obtain measurement signals corresponding to each position of the translation stage.

5. The method for measuring interfacial thermal resistance according to claim 1, wherein: in, λ 1x ,λ 1y ,λ 1z They represent the thermal conductivity of medium 1 in the X, Y and Z directions respectively, C1 represents the volume heat capacity of medium 1, λ 2x ,λ 2y ,λ 2z represents the thermal conductivity of medium 2 in the X, Y and Z directions respectively, C2 represents the volume heat capacity of medium 2, G represents the interface thermal conductance of the interface to be measured, ξ,ζ represent the Fourier variables of X and Z respectively, ω is the frequency, y′ represents the position of the virtual point source itself, and y represents the position of the virtual point source response.

6. An interface thermal resistance measurement system, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the interface thermal resistance measurement method according to any one of claims 1 to 5 when executing the computer program.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the interface thermal resistance measurement method according to any one of claims 1 to 5.

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