A contact thermal conductivity measurement method

Abstract

The present invention belongs to the field of material thermal property testing, and is specifically a contact thermal conductivity measurement method. By applying an AC signal V with different heating frequencies ω at both ends of the electrode, 1ω Measure and obtain the third harmonic signal V corresponding to different heating frequencies ω 3ω , using the third harmonic signal V 3ω and temperature amplitude T 2ω The relationship between the two equations is used to calculate the electrode spectrum T 2ω ; Based on the obtained electrode spectrum T 2ω , identifying the device's sensitive frequency band for interfacial thermal resistance. Leveraging the device's insensitivity to the thermal conductivity of the sample under test at high frequencies, a finite element simulation model was used to analyze the device's interfacial thermal resistance in the frequency band sensitive to cross-sectional thermal resistance, obtaining a fitted value for the device's interfacial thermal resistance. Based on the interfacial thermal resistance, a finite element simulation model was then used to analyze the device's thermal conductivity in the 1-10 frequency band, a low-frequency band. This invention incorporates the influence of interfacial thermal resistance into the fitting range, effectively improving the measurement accuracy of thermal conductivity.

Description

Technical Field

[0001] The invention belongs to the field of material thermal property testing, and specifically relates to a contact thermal conductivity measurement method. Background Art

[0002] The 3ω method is an electrical testing method that derives the thermal conductivity of a sample by depositing a thin layer of metal electrodes on the sample surface and measuring the third harmonic (3ω signal) generated by the electrode heating signal. It is widely used to measure the thermal properties of bulk materials and thin films. This method requires the preparation of electrodes that are as narrow as possible and tightly bonded to the sample to ensure ideal heat conduction. Electrode preparation typically uses a complex photolithography process, and the test is a one-time process, requiring separate electrode preparation for each sample, making the testing process relatively cumbersome.

[0003] The contact 3ω test method uses a thin film layer wrapped around a metal electrode as a test device to contact the sample, which solves the shortcomings of the one-time test of the 3ω method, but still has the following problems: (1) Due to the differences in the surface and contact pressure of different samples, the interface thermal resistance between the sample and the contact layer has great uncertainty. To eliminate the influence of this variable, the conventional method is to fix the device as a base and apply a large pressure (about 150-200Kpa) to the sample end to reduce the interface thermal resistance to a negligible level. However, the high-pressure platform test method can only be used for solid samples and has a small scope of application. Another method is to use the interface thermal resistance as a fitting parameter and perform multi-parameter fitting together with the sample thermal conductivity. This method requires the establishment of a relatively complex mathematical model and cannot separate the effects of the interface thermal resistance and the sample thermal conductivity, resulting in a large fitting error. (2) If the introduced thin film layer is a multi-layer thin film structure, the 3ω signal of the contact method will deviate significantly from the generally applicable ideal slope analytical model. The situation of bidirectional heat conduction also makes the classic T.Borca analytical model for multi-layer structures no longer applicable, and it is difficult to obtain an accurate mathematical analytical solution.

[0004] The finite element simulation model uses mathematical approximation to divide the real physical system into small units connected to each other at the nodes, and calculate the subdomain approximate solution of the physical equation. It has good adaptability to the contact 3ω heat conduction process under multi-layer structures and complex interfaces. In the low-pressure contact fixed only with tape, the interface thermal resistance is 10 -5 (m 2 Even with a power of the order of ·K / W, a rough fit of the 3ω signal can still be performed. Currently, the application of finite element methods in contact 3ω testing is primarily focused on research. By establishing a finite element model, the effects of different test parameters (electrode width, layer thickness, etc.) on the test are analyzed.

[0005] Since it is impossible to separate the interfacial thermal resistance from the sample's thermal conductivity, it is difficult to accurately fit both parameters simultaneously using the finite element method. Therefore, the current fitting method often ignores the interfacial thermal resistance. To ensure that the interfacial thermal resistance is reduced to a negligible range, the same type of sample is usually clamped on both sides of the device, or the device is designed to be fixed to the test base, and the sample is actively pressed into contact with the base for measurement. This method has the following problems:

[0006] 1. Due to the double-sided sample clamping or base-type device design, the test flexibility is poor and measurements can only be performed by pre-preparing samples, which cannot achieve the flexibility of probe-based measurement for on-demand measurement.

[0007] 2. Cost and accuracy conflict. For fixed-base testing, extremely narrow electrodes and extremely thin contact layers can be used to approximate the mathematical model, thereby achieving higher accuracy. However, the photolithography and precision film formation processes required for narrow electrodes and thin contact layers are expensive and difficult to mass-produce. For simple double-sided support testing, the process is simple and the cost is low, but the influence of interfacial thermal resistance cannot be isolated, making it difficult to achieve ideal accuracy. Summary of the Invention

[0008] The object of the present invention is to provide a contact thermal conductivity measurement method to achieve accurate separation and measurement of the thermal conductivity and interface thermal resistance of a sample to be measured.

[0009] To achieve the above object, the present invention adopts the following technical solutions:

[0010] A contact thermal conductivity measurement method comprises the following steps:

[0011] Step 1: providing a 3ω thermal conductivity testing device, wherein the 3ω thermal conductivity testing device comprises a substrate, a metal electrode disposed on the front surface of the substrate, and a contact layer disposed on the metal electrode and completely covering the metal electrode;

[0012] Step 2: Place the sample to be tested on the upper surface of the contact layer of the device obtained in step 1 and make it fully contact with the contact layer; apply an AC signal V with different heating frequencies ω at both ends of the electrode. 1ω Measure and obtain the third harmonic signal V corresponding to different heating frequencies ω 3ω ; The value range of the heating frequency ω is 1 to 1000 Hz;

[0013] Step 3: According to the third harmonic signal V 3ω and temperature amplitude T 2ω The relationship between the third harmonic signal V measured in step 2 3ω , calculate the electrode spectrum T 2ω The third harmonic signal V 3ω and temperature amplitude T 2ωThe relationship is:

[0014]

[0015] In formula (1), R0 is the intrinsic resistance of the metal electrode, C rt is the temperature-induced resistivity of the electrode metal, I0 is;

[0016] Step 4: Establish a finite element simulation model based on the parameters of the 3ω thermal conductivity test device prepared in step 1; the parameters include: the size and thermal parameters of the polyimide film substrate, the contact layer and the electrode, and the size of the sample to be tested;

[0017] Step 5: Divide the value range of the heating frequency ω into a high frequency band and a low frequency band; Based on the spectrum T of the electrode obtained in step 3 2ω , find the sensitive frequency band of the interface thermal resistance of the device; analyze the high frequency band through the finite element simulation model to obtain the fitting value of the interface thermal resistance; the high frequency band is the 100-100 Hz frequency band, and the low frequency band is the 1-10 frequency band;

[0018] Step 6: Based on the fitting value of the interface thermal resistance obtained in step 5, the finite element simulation model is used for analysis in the low frequency band to obtain the thermal conductivity of the sample to be tested, and the final thermal conductivity of the sample to be tested is obtained.

[0019] Furthermore, the substrate is a polyimide film, the metal electrode is a gold electrode, and the contact layer is an aluminum oxide film layer.

[0020] Furthermore, the width of the metal electrode is 100-200 μm, and the thickness of the aluminum oxide film layer is less than 2 μm.

[0021] Furthermore, the finite element simulation model established in step 4 is a two-dimensional simulation model.

[0022] The present invention provides a contact thermal conductivity measurement method, which applies pressure on the back of the substrate to make the contact layer fully contact with the sample to be measured, and applies an AC signal V with different heating frequencies ω at both ends of the electrode. 1ω Measure and obtain the third harmonic signal V corresponding to different heating frequencies ω 3ω , using the third harmonic signal V 3ω and temperature amplitude T 2ω The relationship between the two equations is used to calculate the electrode spectrum T 2ω ; Based on the obtained electrode spectrum T 2ω, finding the device's sensitive frequency band for interfacial thermal resistance, which is 100-1000 Hz. Within this frequency band, the device's insensitivity to the thermal conductivity of the sample under test at high frequencies was utilized to analyze the device in the high-frequency band (100-1000 Hz) using a finite element simulation model to obtain a fitted value for the device's interfacial thermal resistance. Based on the interfacial thermal resistance, the finite element simulation model was then used to analyze the low-frequency band (1-10 Hz) to obtain the thermal conductivity of the sample under test.

[0023] Compared with the existing 3ω contact thermal conductivity measurement method combined with finite element simulation, the present invention incorporates the influence of interface thermal resistance into the fitting range, effectively improving the measurement accuracy of thermal conductivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is the thermal disturbance distribution under different thermal conductivities;

[0025] Figure 2 This is a diagram of the ω thermal conductivity test device in Example 3;

[0026] Figure 3 This is a flow chart of a thermal conductivity test of a contact thermal conductivity measurement method according to an embodiment;

[0027] Figure 4 When the sample to be tested is epoxy resin, the T generated by the electrode at a frequency of 1-1000Hz 2ω spectrum;

[0028] Figure 5 is the ratio of the contact interface thermal resistance to the sample sensitivity at a frequency range of 1-10 Hz for different metal electrode line widths in the embodiment;

[0029] Figure 6 is the fitting error of the contact thermal resistance at different estimated thermal conductivity values ​​in the 100-1000 Hz frequency range of the embodiment;

[0030] Figure 7 is the contact thermal resistance fitting error at different contact thermal resistance estimation values ​​in the 100-1000 Hz frequency range of the embodiment;

[0031] Figure 8 The thermal conductivity of the sample was fitted using the convergent value of the contact thermal resistance at 100-1000 Hz in the frequency band of Example 1-10 Hz. DETAILED DESCRIPTION

[0032] Before describing in detail the contact thermal conductivity measurement method provided by the present invention, the principle of the present invention will be described first.

[0033] The traditional 3ω test method measures the third harmonic signal V of the electrode at different frequencies. 3ω, combined with the corresponding mathematical analytical equations outside the non-finite element model, to obtain the thermal conductivity of the sample. During this process, the extent to which the thermal perturbation caused by the electrode penetrates deep into the sample is negatively correlated with the heating frequency. That is, the lower the heating frequency, the greater the extent to which the electrode can induce thermal perturbations within the sample. The thermal penetration depth q is used to characterize this thermal perturbation range:

[0034]

[0035] Where D is the thermal diffusion coefficient of the sample. Usually, a very narrow electrode line width is used to ensure that the thermal perturbation range is infinite relative to the electrode, thereby maximizing the effect of the material thermal conductivity on T 2ω The influence of this approximation T 2ω It shows a logarithmic linear relationship with the heating frequency.

[0036] The interfacial thermal resistance under contact measurement conditions will be 3-5 orders of magnitude larger than that of the atomically bonded electrode and sample interface, and it is no longer negligible. Moreover, the thicker contact layer will significantly affect the heat conduction process and cannot be simply approximated as a thin layer thermal resistance. The different thermal diffusion coefficients of each material layer also make it impossible to obtain an accurate analytical solution for q. In addition, complex boundary conditions will also make T 2ω The logarithmic linear relationship with the heating frequency is lost, making it difficult to accurately describe the heat conduction process using a mathematical model. The finite element numerical method is well applicable to this scenario.

[0037] By establishing a finite element model of the 3ω test device, the sensitive frequency band of the device to the interface thermal resistance or sample can be calculated. Based on the principle that the heating frequency is negatively correlated with the heat penetration depth, the effect of the interface thermal resistance and the thermal conductivity of the sample on T is analyzed under different heating frequencies and electrode widths. 2ω The influence of can be obtained respectively, that is, the characteristics of being sensitive to the interface thermal resistance at high frequency and the characteristics of being sensitive to the sample at low frequency. Figure 1 is the thermal disturbance distribution under different test frequencies. Figure 1 As shown in the figure, at high frequencies, the thermal disturbance generated by the electrode has not yet penetrated into the sample and remains near the interface between the contact layer and the sample. At this time, the sample has a high sensitivity to T 2ω The effect is small and is mainly affected by the interface thermal resistance. As the signal frequency decreases, the thermal disturbance penetrates into the sample layer, and the thermal conductivity of the sample begins to gradually affect T 2ω .

[0038] To characterize the effect of interface thermal resistance and sample thermal conductivity change on T 2ω The impact size is the degree to which the device responds to changes in the two. Here, the normalized sensitivity S is introduced. x :

[0039]

[0040] The subscript x represents the sensitive variable, and its sensitivity represents the change rate of the variable x and the T caused by it. 2ω The ratio of the rate of change. S R That is the interface thermal resistance sensitivity, S k is the thermal conductivity sensitivity of the sample. The S R With S k After obtaining the sensitive frequency band of the interfacial thermal resistance at high frequency, fitting is performed, and then the thermal disturbance is penetrated into the sample layer at a lower frequency to introduce the thermal conductivity of the sample as T 2ω factors to achieve accurate separation and fitting of the two variables.

[0041] In the traditional 3ω test method, the electrode line width is usually a narrow electrode below 3030um. For narrow electrodes, the heating frequency in the range of 1-1000Hz has a large S R With S k , making it difficult to distinguish the effects of interfacial thermal resistance from thermal conductivity. To address this issue, the present invention increases the electrode line width in the 3ω test device to widen the difference in this sensitive frequency band, achieving better separation and suppressing the sample's thermal conductivity response, while still retaining the device's response to the sample at low frequencies. By controlling the thickness of the alumina contact layer to within 2μm, the difference in sensitivity between the two frequencies is maintained, achieving frequency-division measurement fitting and separation.

[0042] Example 1

[0043] like Figure 3 As shown, this embodiment provides a contact thermal conductivity measurement method, comprising the following steps:

[0044] Step 1: Provide a 3ω thermal conductivity test device. Figure 2 As shown, it includes a substrate, a metal electrode provided on the front of the substrate, and a contact layer provided on the metal electrode and completely covering the metal electrode. In this embodiment, the substrate is a polyimide film, the metal electrode is a gold electrode, and the contact layer is an aluminum oxide film layer. Step 2: Place the sample to be tested on the upper surface of the contact layer of the device obtained in step 1 and make it fully contact with the contact layer. In this embodiment, the sample to be tested is epoxy resin, and an AC signal V with different heating frequencies ω is applied to both ends of the electrodes. 1ω Measure and obtain the third harmonic signal V corresponding to different heating frequencies ω 3ω ; The value range of the heating frequency ω is 1 to 1000 Hz.

[0045] Step 3: According to the third harmonic signal V 3ω and temperature amplitude T 2ω The relationship between the third harmonic signal V measured in step 2 3ω, calculate the T of the electrode on the sample 2ω Spectrum, T 2ω Spectrum Figure 4 The third harmonic signal V 3ω and temperature amplitude T 2ω The relationship is:

[0046]

[0047] In formula (1), R0 is the intrinsic resistance of the metal electrode, C rt is the temperature-induced resistivity of the electrode metal; I0 is the AC signal amplitude.

[0048] Step 4: Create a finite element simulation model based on the parameters of the 3ω thermal conductivity test device prepared in Step 1. These parameters include the dimensions and thermal parameters of the polyimide film substrate, contact layer, and electrodes, as well as the dimensions of the sample to be tested. In this example, metal electrodes with line widths of 100 μm and 200 μm are used, and the contact layer thickness is less than 2 μm.

[0049] Step 5: Figure 5 As shown, at the line width of 100um and 200um, the sensitivity of the 3ω thermal conductivity test device to the interface thermal resistance in the 100-1000Hz frequency band is significantly greater than the thermal conductivity of the sample, and the peak ratio of the two is close to one hundred times. In the 1-10Hz frequency band, the ratio of the two drops significantly to a range less than 1. At this time, the response of the device to the thermal conductivity of the sample is greater than the response to the interface thermal resistance. It can be determined that in the 100-1000Hz frequency band, the device is insensitive to the thermal conductivity of the sample to be tested. Therefore, this embodiment divides the value range of the heating frequency ω into a high frequency band and a low frequency band; the high frequency band is the 100~1000Hz frequency band, and the low frequency band is the 1-10 frequency band. The finite element simulation model is used for analysis in the high frequency band to obtain the fitting value R of the interface thermal resistance.

[0050] Step 6: Based on the fitting value R of the interface thermal resistance obtained in step 5, the finite element simulation model is used for analysis in the low frequency band to obtain the thermal conductivity of the sample to be tested, and the final thermal conductivity of the sample to be tested is obtained.

[0051] To illustrate the accuracy of the thermal conductivity of the sample to be measured obtained by the method of this embodiment, this embodiment shows the fitting curve and error convergence in the frequency bands of 1-10 Hz and 10-100 Hz, as shown in FIG. Figure 6 、 Figure 7 、 Figure 8 As shown in Figure 2, the change of thermal conductivity of the sample under test within a certain range does not affect the fitting value of the interface thermal resistance R in the frequency band of 100-1000 Hz. fit The convergence of k can also be seen from the fitting of thermal conductivity at high frequency, and its fitting error is determined by the interface thermal resistance. fitR of the fit under the estimated value fit All converge to 5E-5(m 2 ·K) / W. After fitting the interfacial thermal resistance, the thermal conductivity of the sample can be fitted separately at low frequency. Compared with k fit In the case of non-convergence, after the interface thermal resistance R is calculated, k fit That is, it converges to 1W / (m·K).

Claims

1. A contact thermal conductivity measurement method, characterized in that: The following steps are involved: Step 1: providing a 3ω thermal conductivity testing device, wherein the 3ω thermal conductivity testing device comprises a substrate, a metal electrode disposed on the front surface of the substrate, and a contact layer disposed on the metal electrode and completely covering the metal electrode; Step 2: Place the sample to be tested on the upper surface of the contact layer of the device obtained in step 1 and make it fully contact with the contact layer; apply an AC signal V with different heating frequencies ω at both ends of the electrode. 1ω Measure and obtain the third harmonic signal V corresponding to different heating frequencies ω 3ω ; The value range of the heating frequency ω is 1 to 1000 Hz; Step 3: According to the third harmonic signal V 3ω and temperature amplitude T 2ω The relationship between the third harmonic signal V measured in step 2 3ω , calculate the electrode T 2ω spectrum; Step 4: Establish a finite element simulation model based on the parameters of the 3ω thermal conductivity test device prepared in step 1; the parameters include: the size and thermal parameters of the polyimide film substrate, the contact layer and the electrode, and the size of the sample to be tested; Step 5: Divide the value range of the heating frequency ω into a high frequency band and a low frequency band; based on the T of the electrode obtained in step 3 2ω spectrum, find the sensitive frequency band of the interface thermal resistance of the device; analyze the high frequency band through the finite element simulation model to obtain the fitting value of the interface thermal resistance; the high frequency band is 100-100 Hz, and the low frequency band is 1-10 Hz; Step 6: Based on the fitting value of the interface thermal resistance obtained in step 5, the finite element simulation model is used for analysis in the low frequency band to obtain the thermal conductivity of the sample to be tested, which is used as the final thermal conductivity of the sample to be tested.

2. A contact thermal conductivity measurement method according to claim 1, characterized in that: The substrate is a polyimide film, the metal electrode is a gold electrode, and the contact layer is an aluminum oxide film layer.

3. A contact thermal conductivity measurement method according to claim 2, characterized in that: The width of the metal electrode is 100-200 μm, and the thickness of the aluminum oxide film layer is less than 2 μm.

4. A contact thermal conductivity measurement method according to any one of claims 1 to 3, characterized in that: The finite element simulation model established in step 4 is a two-dimensional simulation model.

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