Method and system for simultaneously measuring thermal conductivity, specific heat capacity and interfacial thermal resistance

Abstract

This invention relates to a method and system for simultaneously measuring thermal conductivity, specific heat capacity, and interfacial thermal resistance, belonging to the field of thermophysical property measurement technology. First, a TDTR (Transient Thermal Resonance) measurement is performed on the sample under test using a preset laser spot size and modulation frequency that meet preset criteria, obtaining a measurement signal. Then, the initial parameter values ​​of the sample are input into a heat transfer model to obtain a simulated signal. The initial parameter values ​​are continuously adjusted until the deviation between the simulated signal and the measured signal is less than a preset value. At this point, the initial parameter values ​​are used as the measured parameter values ​​of the sample. Both the measured signal and the simulated signal include a negative delay time period of -20 to -5 ps and a positive delay time period of 0.1 to 4 ns. A single TDTR measurement can simultaneously determine the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample, greatly expanding the measurement capabilities of TDTR technology.

Description

Technical Field

[0001] This invention relates to the field of thermophysical property measurement technology, and in particular to a method and system for simultaneously measuring the thermal conductivity, specific heat capacity and interfacial thermal resistance of submillimeter-sized samples using time-domain thermal reflectance technology. Background Technology

[0002] Time-domain thermal reflectometry (TDTR) is a mature and powerful thermophysical property measurement technique widely used to measure the thermal conductivity and interfacial thermal resistance of thin films and bulk materials. TDTR measurement is based on pump-probe technology. A modulated femtosecond laser pulse beam periodically heats the sample, while a delayed laser pulse beam detects the temperature response of the sample surface through thermal reflection. A photodetector converts the optical signal carried by the reflected probe light into an electrical signal, which is then extracted by a lock-in amplifier. By optimally fitting the experimental measurement signal using a heat transfer model, the thermophysical properties of the sample can be accurately obtained. Conventional TDTR measurements require knowledge of the sample's specific heat capacity to determine its thermal conductivity and interfacial thermal resistance, and the measurement error is typically 10%.

[0003] Therefore, there is an urgent need for a measurement technique that can simultaneously determine thermal conductivity, specific heat capacity, and interfacial thermal resistance. Summary of the Invention

[0004] The purpose of this invention is to provide a measurement method and system for simultaneously determining thermal conductivity, specific heat capacity and interfacial thermal resistance. By using TDTR for a single measurement, the thermal conductivity, specific heat capacity and interfacial thermal resistance of a sample can be determined simultaneously, which greatly expands the measurement capabilities of TDTR technology.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for simultaneously determining thermal conductivity, specific heat capacity, and interfacial thermal resistance, the method comprising:

[0007] The TDTR of the sample under test is measured using a preset laser spot size and modulation frequency to obtain a measurement signal; the measurement signal includes a phase signal obtained from the measurement of the negative delay time period and a phase signal obtained from the measurement of the positive delay time period;

[0008] The initial parameter values ​​of the sample to be tested are input into the heat transfer model to obtain a simulated signal; it is determined whether the deviation between the simulated signal and the measured signal is less than a preset value; if so, the initial parameter values ​​are used as the measured parameter values ​​of the sample to be tested; if not, the initial parameter values ​​are adjusted to obtain adjusted parameter values, and the adjusted parameter values ​​are used as the initial parameter values ​​for the next cycle, returning to the step of "inputting the initial parameter values ​​of the sample to be tested into the heat transfer model"; the parameter values ​​include the values ​​of thermal conductivity, specific heat capacity, and interfacial thermal resistance; the simulated signal includes the phase signal obtained by simulating the negative delay time period and the phase signal obtained by simulating the positive delay time period.

[0009] A measurement system for simultaneously determining thermal conductivity, specific heat capacity, and interfacial thermal resistance, the measurement system comprising:

[0010] The measurement module is used to perform TDTR measurement on the sample under test using a preset laser spot size and modulation frequency to obtain a measurement signal; the measurement signal includes a phase signal obtained from the measurement of the negative delay time period and a phase signal obtained from the measurement of the positive delay time period;

[0011] The simulation module is used to input the initial parameter values ​​of the sample to be tested into the heat transfer model to obtain a simulation signal; determine whether the deviation between the simulation signal and the measurement signal is less than a preset value; if so, the initial parameter values ​​are used as the measurement parameter values ​​of the sample to be tested; if not, the initial parameter values ​​are adjusted to obtain adjusted parameter values, and the adjusted parameter values ​​are used as the initial parameter values ​​for the next cycle, returning to the step of "inputting the initial parameter values ​​of the sample to be tested into the heat transfer model"; the parameter values ​​include the values ​​of thermal conductivity, specific heat capacity, and interfacial thermal resistance; the simulation signal includes a phase signal obtained by simulation during a negative delay time period and a phase signal obtained by simulation during a positive delay time period.

[0012] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0013] This invention provides a method and system for simultaneously measuring thermal conductivity, specific heat capacity, and interfacial thermal resistance. First, a TDTR (Digital Transmission Torque Measurement) is performed on the sample under test using a preset laser spot size and modulation frequency to obtain a measurement signal. Then, the initial parameter values ​​of the sample are input into a heat transfer model to obtain a simulated signal. The initial parameter values ​​are continuously adjusted until the deviation between the simulated signal and the measured signal is less than a preset value. At this point, the initial parameter values ​​are used as the measured parameter values ​​of the sample. A single TDTR measurement can simultaneously determine the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample, greatly expanding the measurement capabilities of TDTR technology. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart of the measurement method provided in Embodiment 1 of the present invention;

[0016] Figure 2 This is a block diagram illustrating the principle of the measurement method provided in Embodiment 1 of the present invention;

[0017] Figure 3 This is a schematic diagram showing the ratio of the sensitivity coefficients of the TDTR phase signal of the 100nm Al / Si sample provided in Example 1 of the present invention to the specific heat capacity and longitudinal thermal conductivity of the Si substrate material at different delay times, as a function of the laser spot radius and thermal penetration depth.

[0018] Figure 4 This is a structural block diagram of the TDTR system provided in Embodiment 1 of the present invention;

[0019] Figure 5 This is a schematic diagram showing the measurement signal, sensitivity analysis, and error analysis of the measurement results of the single-crystal silicon sample, thermal conductivity, specific heat capacity, and interfacial thermal resistance provided in Embodiment 1 of the present invention.

[0020] Figure 6 This is a system block diagram of the measurement system provided in Embodiment 2 of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] The purpose of this invention is to provide a measurement method and system for simultaneously determining thermal conductivity, specific heat capacity and interfacial thermal resistance. By using TDTR for a single measurement, the thermal conductivity, specific heat capacity and interfacial thermal resistance of a sample can be determined simultaneously, which greatly expands the measurement capabilities of TDTR technology.

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] Example 1:

[0025] The pump light modulation frequency of a TDTR is typically limited to the range of 0.5–12 MHz. In the high-frequency range of ~10 MHz, the phase signal measured by the TDTR is mainly affected by the longitudinal heat dissipation rate of the sample. k z The longitudinal thermal conductivity of the sample (where C is the sample's volumetric specific heat capacity) is affected, while in the low-frequency range of ~1MHz, the phase signal measured by TDTR is also affected by the sample's lateral thermal diffusivity (α). r =k r / C,k r This is due to the influence of the sample's surface thermal conductivity. Therefore, for isotropic materials, k... r =k z Existing technologies have proposed the variable frequency TDTR method, which can simultaneously determine thermal conductivity and specific heat capacity by fitting phase signals measured at different frequencies. However, the variable frequency TDTR method requires that the thermal conductivity measured by TDTR should not depend on the modulation frequency. In reality, when measuring the thermal conductivity of many samples (such as semiconductor alloys and two-dimensional layered materials), the thermal conductivity measured by TDTR depends on the modulation frequency, which greatly limits the application of the variable frequency TDTR method.

[0026] Existing techniques propose a two-step fitting method for TDTR (Diverterless Transmission Time). When measuring isotropic materials using appropriate modulation frequencies and laser spot sizes, the normalized amplitude signal within a delay time of 0.1–8 ns exhibits similar sensitivity to the sample's thermal conductivity and specific heat capacity, while the phase signal shows different sensitivities. Therefore, fitting the normalized amplitude signal within the 0.1–8 ns delay time yields the heat dissipation rate of the isotropic sample, and fitting the phase signal provides the thermal conductivity and specific heat capacity. While theoretically feasible, this two-step TDTR fitting method presents practical difficulties due to its stringent requirements for experimental setup perfection. Even minute changes in the laser spot position and size during TDTR experiments, caused by the movement of the delay stage, affect the measured amplitude, making accurate amplitude measurement difficult and unsuitable for fitting analysis.

[0027] Based on the deficiencies of the existing technology, this embodiment provides a measurement method for simultaneously determining thermal conductivity, specific heat capacity, and interfacial thermal resistance, such as... Figure 1 and Figure 2 As shown, the measurement method includes:

[0028] S1: TDTR measurement is performed on the sample under test using a preset laser spot size and modulation frequency to obtain a measurement signal; the measurement signal includes a phase signal obtained from the measurement of the negative delay time period and a phase signal obtained from the measurement of the positive delay time period;

[0029] The sample to be tested in this embodiment can be a sub-millimeter sample.

[0030] S2: Input the initial parameter values ​​of the sample to be tested into the heat transfer model to obtain a simulated signal; determine whether the deviation between the simulated signal and the measured signal is less than a preset value; if yes, use the initial parameter values ​​as the measured parameter values ​​of the sample to be tested; if no, adjust the initial parameter values ​​to obtain adjusted parameter values, and use the adjusted parameter values ​​as the initial parameter values ​​for the next cycle, returning to the step of "inputting the initial parameter values ​​of the sample to be tested into the heat transfer model"; the parameter values ​​include the values ​​of thermal conductivity, specific heat capacity, and interfacial thermal resistance; the simulated signal includes the phase signal obtained by simulating the negative delay time period and the phase signal obtained by simulating the positive delay time period.

[0031] The measurement method provided in this embodiment can simultaneously determine the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample in a single measurement. Compared with the variable frequency TDTR method, it eliminates the need for repeated measurements with different frequencies, simplifying the measurement process and significantly improving accuracy and reliability. This method only requires acquiring phase signals during the negative and positive delay time periods. Compared to the two-step fitting method of TDTR, signal acquisition is simpler and more reliable, operation is easier, and measurement accuracy is higher.

[0032] Experiments revealed that when using appropriate laser spot size and modulation frequency for TDTR measurement, within a short delay period (0.1–4 ns), heat transfer is primarily one-dimensional longitudinal. In this case, the TDTR phase signal is mainly affected by the longitudinal heat dissipation rate of the sample. The effect; however, after a sufficiently long time (delay time ~12.5 ns), heat transfer becomes three-dimensional, at which point the phase signal of the TDTR is simultaneously affected by the longitudinal heat dissipation rate of the sample. In-surface thermal diffusivity k r / C influence. Therefore, if the phase signal of the entire delay time period from 0.1 to 12.5 ns can be fitted simultaneously, the thermal conductivity and specific heat capacity of isotropic materials can be determined simultaneously. However, a longer delay time requires a longer mechanical displacement stage, making the optical system more complex and prone to errors. Since the TDTR signal is periodic, with one period of 12.5 ns (corresponding to a laser pulse repetition frequency of 80 MHz), the signal with a long delay time of 12.48 ns is the same as the signal with a negative delay time of -20 ps. Fitting the signal with a negative delay time of -20 ps is equivalent to fitting the signal with a long delay time of 12.48 ns. Therefore, this embodiment proposes that by simultaneously fitting the phase signals of the positive delay time period (0.1 to 4 ns) and the negative delay time period (~-20 ps), multiple parameters such as the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample can be effectively decoupled, thereby achieving the effect of simultaneously fitting the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample in a single TDTR measurement.

[0033] As mentioned above, when using appropriate laser spot size and modulation frequency for TDTR measurement, the heat transfer in the sample gradually changes from one-dimensional longitudinal transfer to three-dimensional transfer as the delay time progresses. Therefore, the longitudinal heat dissipation rate of the sample can be determined simultaneously by fitting the phase signals of the positive and negative delay time periods. In-surface thermal diffusivity k r / C. So, what laser spot size and modulation frequency should be chosen for TDTR measurement to ensure that heat transfer is one-dimensional longitudinally at a delay time of 0.1 ns and three-dimensional at a delay time of -20 ps? To answer this question, such as... Figure 3 As shown in the figure, the TDTR phase signals of the 100nm Al / Si sample were plotted in this embodiment at t d =100ps and -20ps for specific heat capacity C and longitudinal thermal conductivity k of Si substrate material z The ratio of the sensitivity coefficients The laser spot radius w0 and the thermal penetration depth d vary with the laser beam radius w0 and the thermal penetration depth d. p Schematic diagram of the change, thermal penetration depth d p Defined as This embodiment focuses on The region represents the specific heat capacity C and longitudinal thermal conductivity k of the TDTR phase signal relative to the substrate material. z The sensitivities are essentially equal, at which point heat transfer is approximately one-dimensional longitudinal. Figure 3 It can be observed that in t d =100ps, using a large spot size w0≥3d p TDTR measurements allow for approximate one-dimensional longitudinal heat transfer. In this case, the TDTR phase signal correlates with the specific heat capacity C and longitudinal thermal conductivity k of the substrate material. zThe sensitivities are basically equal; however, if we want to achieve the same sensitivity in t d If heat transfer remains one-dimensional longitudinally at -20 ps (or 12.48 ns), a larger light spot w0 ≥ 15d is required. p TDTR measurement is performed. Therefore, if a suitable laser spot size and modulation frequency are used, 3D... p ≤w0≤15d p The phase signal of TDTR will be at t d =100ps only for longitudinal heat dissipation rate of the sample Sensitive, and in t d Longitudinal heat dissipation rate of the sample at -20 ps In-surface thermal diffusivity k r Both C and P are sensitive, so by simultaneously fitting the phase signals of the positive and negative delay time periods, the longitudinal heat dissipation rate of the sample can be determined at the same time. In-surface thermal diffusivity k r / C. This embodiment was also repeated for other different samples. Figure 3 Sensitivity analysis revealed that the above conclusions remained unchanged; therefore, 3d p ≤w0≤15d p The principles are universal.

[0034] Based on this, in S1, the preset laser spot size and modulation frequency meet the preset criteria, which are: 3d p ≤w0≤15d p Where w0 is the laser spot radius, which is 1 / e of the pump light and probe light on the sample surface. 2 The root mean square value of the radius; d p The thermal penetration depth is determined by the modulation frequency.

[0035] Specifically, the formula for calculating thermal penetration depth is: Where k is the thermal conductivity of the sample under test; f is the modulation frequency; and C is the volumetric specific heat capacity of the sample under test.

[0036] Therefore, before performing TDTR measurement on the sample, S1 needs to estimate the thermal conductivity and volumetric specific heat capacity of the sample based on the sample material and literature reference values ​​or experience. This allows for the selection of a suitable laser spot size and modulation frequency using preset criteria to perform TDTR measurement and obtain the negative delay time (t). d =-20 to -5 ps) and positive delay time period (t) d The phase signal obtained by measurement (=0.1~4ns).

[0037] In S1, performing TDTR measurement on the sample under test may include: using a TDTR system to perform TDTR measurement on the sample under test. The TDTR system includes: a pump light transmission component, a probe light transmission component, and a probe component. The pump light transmission component generates pump light at a preset modulation frequency and transmits it to the sample under test to periodically heat the sample. The probe light transmission component generates probe light and transmits it to the sample under test to detect the temperature response of the sample surface and generate response light. The probe component receives the response light and extracts the thermal response signal of the sample under test. The measurement signal is obtained from the thermal response signal. Obtaining the measurement signal from the thermal response signal may include: calculating the ratio of the in-phase signal to the out-of-phase signal in the thermal response signal, and inverting the ratio to obtain the measurement signal.

[0038] More specifically, such as Figure 4 As shown, a laser (which can be a Ti:Sapphire laser) emits a laser pulse beam with a pulse width of 150 femtoseconds and a repetition frequency of 80MHz. The laser wavelength of the pulse beam is adjusted by an optical parametric oscillator, outputting a pump beam with a wavelength of 825nm and a probe beam with a wavelength of 785nm. The pump beam is first modulated by an electro-optic modulator (EOM) to produce a square wave signal with a frequency in the range of 0.5–12MHz. Then, a delay stage changes the optical path difference between the pump beam and the probe beam. Finally, it is reflected by a dichroic mirror mounted in a gimbal into the microscope objective and focused on the sample surface for periodic heating. The probe beam is reflected by a mirror into the same microscope objective, focused on the sample surface, and used to detect the temperature response of the sample surface. The reflected response light is received by a detector, the optical signal is converted into an electrical signal, and finally, a lock-in amplifier extracts the thermal response signal of the sample at the heating frequency. The thermal response signal includes an in-phase signal (V0). in ) and an out-of-phase signal (V out In this embodiment, the measurement signal is the fitted signal R = -V. in / V out The thermophysical parameters of the sample to be tested are extracted based on the measurement signal.

[0039] It should be noted that this embodiment uses an optical parametric oscillator to obtain two pulsed laser beams with different wavelengths. The advantage of this setup is that by adding a filter at the detector inlet, the pump light can be easily filtered out, and only the response light generated by the probe light is received.

[0040] In step S2, the initial values ​​of the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample to be tested are input into the heat transfer model. Phase signals corresponding to all delay time points included in the measurement signal are obtained, resulting in a simulated signal. The measured signal and the simulated signal are compared to determine whether the deviation between the measured phase signal and the simulated phase signal during the negative delay time period is less than a preset value, and whether the deviation between the measured phase signal and the simulated phase signal during the positive delay time period is less than a preset value. The thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample to be tested are continuously adjusted until the deviation between the measured signal and the simulated signal during different delay time periods is less than the preset value, thereby obtaining the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample. The heat transfer model in this embodiment is prior art and will not be described in detail here.

[0041] In S2, the initial parameter values ​​can be adjusted manually or automatically using MATLAB, such as using MATLAB's fminsearch function. It should be noted that MATLAB's automatic adjustment can also automatically calculate the deviation, determine if the deviation is less than the preset value, and adjust the initial parameter values ​​based on the difference between the deviation and the preset value.

[0042] After obtaining the measurement parameter values ​​of the sample to be tested, the measurement method in this embodiment also includes estimating the error of the input parameters, that is, using the error propagation analysis model to determine the error and correlation coefficient of the values ​​of thermal conductivity, specific heat capacity and interfacial thermal resistance.

[0043] The error propagation analysis model in this embodiment is: the criterion for simultaneous best fitting of multiple sets of measurement signals is... The value of R is the smallest. j (t d，i ) indicates that during the delay time t d，i The j-th measurement signal R, g at point j This represents the j-th simulated signal estimated by the heat transfer model. There are a total of M signals, where M is 2 in this embodiment, including signals with positive delay time periods and signals with negative delay time periods. The j-th signal has N signals in total. j There are 10 data points, where U and P are column vectors of unknown and control parameters, respectively. The unknown parameters include thermal conductivity, specific heat capacity, and interfacial thermal resistance. The control parameters include the thermal conductivity, specific heat capacity, and thickness of the aluminum film deposited on the sample surface, as well as the laser spot size. RMS j This represents the root mean square deviation between the j-th group of measured signals and the j-th group of analog signals.

[0044] In the best-fit case, the gradient of ψ should be zero for every vector in U, that is:

[0045]

[0046] Since the input parameters are uncertain, let P be... * U is a random set of possible control parameter vectors. * Let U be the corresponding unknown parameter vector for achieving the best fit. Through a series of mathematical derivations, we finally obtain U. * The covariance matrix Var[U * ]for:

[0047]

[0048] Each unknown parameter u l Uncertainty variable u i and u j The correlation coefficient between them can also be determined as The error in the values ​​of thermal conductivity, specific heat capacity, and interfacial thermal resistance can be determined using the covariance matrix described above. and correlation coefficient This error analysis considers not only the uncertainties of all input parameters, but also the fitting quality of experimental data and errors caused by experimental noise. The measurement method in this embodiment proposes an error estimation method that simultaneously fits multiple sets of signals to extract multiple parameters, achieving a more effective estimation of multi-parameter errors.

[0049] Conventional TDTR (Time-Domain Thermal Reflectance) technology requires repeated measurements with varying pump light modulation frequencies to determine the thermal conductivity and specific heat capacity of a sample. The measurement method provided in this embodiment, by selecting an appropriate laser spot size and modulation frequency for TDTR measurement and simultaneously fitting the phase signals of the negative delay time period (-20 to -5 ps) and the positive delay time period (0.1 to 4 ns), effectively decouples multiple parameters such as thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample. This allows for the simultaneous determination of these parameters in a single TDTR measurement. This novel measurement method based on time-domain thermal reflectance technology disclosed in this embodiment can simultaneously determine the thermal conductivity, specific heat capacity, and interfacial thermal resistance of sub-millimeter-sized samples in a single TDTR measurement. This method significantly expands the measurement capabilities of TDTR technology, simplifies TDTR measurement, and improves measurement accuracy.

[0050] Whether the target parameter can be extracted by fitting the experimental signal can be determined through sensitivity analysis. In the TDTR experiment, the sensitivity coefficient is used to measure the sensitivity of the experimental signal R to the parameter ξ. The sensitivity coefficient is defined as the ratio of the percentage change in the experimental signal R to the percentage change in the parameter ξ.

[0051]

[0052] Here, parameter ξ refers to any relevant parameters, including sample thickness, thermal conductivity, specific heat capacity, interfacial thermal conductivity, laser spot size, etc. For example, Sξ =-0.5 indicates that when the parameter ξ increases by 1%, the signal R decreases by 0.5%. The experimental signal needs to exhibit different trends in sensitivity to each measured parameter with varying delay times in order to extract multiple different parameters simultaneously by fitting this set of experimental signals.

[0053] Figure 5 (a) and Figure 5 (b) Shows the experimental signal R = -V of a 100 nm Al / Si sample measured by TDTR during delay periods of 0.1–4 ns and -20–-10 ps, ​​respectively. jn / V out The corresponding heat transfer model calculation results are shown. The modulation frequency used for the measurement is 10.6MHz, and the laser spot radius is 9.7μm. The symbols in the figure represent the measurement signals, and the curves represent the model calculation values. Figure 5 (c) and Figure 5 (d) shows the R signal for each fitted parameter (including the in-plane thermal conductivity k of Si). r Longitudinal thermal conductivity k z The sensitivity coefficients of the TDTR phase signal to the specific heat capacity C and the longitudinal thermal conductivity k of the Al / Si interface are shown to change with the delay time. It can be seen that within the delay time range of 0.1–4 ns, the TDTR phase signal is sensitive to the specific heat capacity C and longitudinal thermal conductivity k of the substrate material. z The sensitivities are basically the same, while the in-plane thermal conductivity k of the substrate material is also similar. r The sensitivity to this signal is essentially zero, indicating that the signal is primarily sensitive to the longitudinal heat dissipation rate of the substrate material. Sensitive. During the negative delay period (~-20 ps), the TDTR phase signal is simultaneously affected by the longitudinal heat dissipation rate of the sample. In-surface thermal diffusivity k r / C influences the phase signal, affecting the thermal conductivity k of the substrate material. r and k z Both are sensitive, but the sensitivity to C is canceled out. Therefore, for isotropic materials k r =k z The thermal conductivity k = k can be determined by first fitting the phase signal during the negative delay time period. r =k z Then, by fitting the phase signal during the positive delay time, the specific heat capacity C of the sample can also be determined. The thermal conductivity G at the Al / Si interface mainly affects the slope of the phase signal as a function of the delay time from 0.1 to 4 ns. Its influence is different from that of other parameters. Therefore, G can also be determined by fitting this set of signals.

[0054] By analyzing the fitting Figure 5 (a) Figure 5 The two sets of signals shown in (b) indicate that the thermal conductivity of the Al / Si interface is G.Al / Si =150±9MW / (m 2 ·K), the thermal conductivity of silicon is k Si =135±8.7W / (m·K), and the specific heat capacity of silicon is C. Si =1.61±0.11J / (cm) 3 ·K), with relative errors of 6%, 6.4%, and 6.8%, respectively, such as Figure 5 (e)- Figure 5 As shown in (g), the thermal conductivity and specific heat capacity of silicon agree well with the reference values, with errors of less than 7%. Conventional TDTR data processing methods only fit signals with positive delay time periods, and therefore can only fit the thermal conductivity G at the Al / Si interface. Al / Si And the thermal conductivity k of silicon Si The specific heat capacity C of silicon needs to be increased. Si As a known input parameter, the error in measuring the thermal conductivity of the sample is generally greater than 10%. It is evident that the new data processing method can not only fit more parameters, but also produce accurate measurement results with less uncertainty compared to the conventional TDTR data processing method.

[0055] This embodiment proposes a novel TDTR data processing method. By simultaneously fitting the phase signals of negative delay time periods (~-20 ps) and positive delay time periods (0.1~4 ns), the thermal conductivity, specific heat capacity, and interfacial thermal resistance of a sample can be determined from a single TDTR measurement. This method was validated by measuring 100 nm Al / Si samples, with measurement errors all less than 7%, indicating that the novel method proposed in this embodiment can not only fit more parameters and simplify the experiment but also improve measurement accuracy. This embodiment suggests, through sensitivity analysis, that samples meeting the 3d... p ≤w0≤15d p Only by performing TDTR measurements on the laser spot size and modulation frequency under certain conditions can the new data processing method proposed in this embodiment be guaranteed to simultaneously measure the thermal conductivity, specific heat capacity, and interfacial thermal resistance of the sample.

[0056] Example 2:

[0057] This embodiment provides a measurement system for simultaneously determining thermal conductivity, specific heat capacity, and interfacial thermal resistance, such as... Figure 6 As shown, the measurement system includes:

[0058] The measurement module M1 is used to perform TDTR measurement on the sample under test using a preset laser spot size and modulation frequency to obtain a measurement signal; the measurement signal includes a phase signal obtained from the measurement of the negative delay time period and a phase signal obtained from the measurement of the positive delay time period;

[0059] The simulation module M2 is used to input the initial parameter values ​​of the sample to be tested into the heat transfer model to obtain a simulation signal; determine whether the deviation between the simulation signal and the measurement signal is less than a preset value; if so, use the initial parameter values ​​as the measurement parameter values ​​of the sample to be tested; if not, adjust the initial parameter values ​​to obtain adjusted parameter values, and use the adjusted parameter values ​​as the initial parameter values ​​for the next cycle, returning to the step of "inputting the initial parameter values ​​of the sample to be tested into the heat transfer model"; the parameter values ​​include the values ​​of thermal conductivity, specific heat capacity, and interfacial thermal resistance; the simulation signal includes the phase signal obtained by simulating the negative delay time period and the phase signal obtained by simulating the positive delay time period.

[0060] Each embodiment in this specification focuses on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be found in the method section.

[0061] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A measurement method for simultaneously measuring thermal conductivity, specific heat capacity, and interfacial thermal resistance, characterized by, The measurement method comprises: The TDTR measurement on the sample to be measured comprises: using a TDTR system to perform TDTR measurement on the sample to be measured; The TDTR system comprises: a pump light transmission component, a probe light transmission component and a probe component; the pump light transmission component is used to generate pump light of a preset modulation frequency and transmit the pump light to the sample to be measured to periodically heat the sample to be measured; the probe light transmission component is used to generate probe light and transmit the probe light to the sample to be measured to detect the temperature response of the surface of the sample to be measured and generate response light; the probe component is used to receive the response light and extract a thermal response signal of the sample to be measured; the measurement signal is obtained according to the thermal response signal.

2. The measurement method according to claim 1, characterized in that, The preset laser spot size and modulation frequency satisfy a preset criterion; the preset criterion is: 3d p ≤ w0≤ 15d p ; wherein, d p is a thermal penetration depth, which is determined by the modulation frequency; w0is a laser spot radius.

3. The measurement method according to claim 2, characterized in that, The calculation formula of the thermal penetration depth is: Wherein, k is the thermal conductivity of the sample to be measured; f is the modulation frequency; C is the volumetric heat capacity of the sample to be measured.

4. The measurement method according to claim 1, characterized by, The measurement signal obtained according to the thermal response signal specifically comprises: calculating the ratio of an in-phase signal in the thermal response signal and an anti-phase signal in the thermal response signal, and taking the inverse of the ratio to obtain the measurement signal. The negative delay time period is -20 to -5 ps, and the positive delay time period is 0.1 to 4 ns.

5. The measurement method according to claim 4, characterized in that, The judgment on whether the deviation of the simulation signal and the measurement signal is less than a preset value specifically comprises:

6. The measurement method of claim 1, wherein, The judgment on whether the deviation of the simulation signal and the measurement signal is less than a preset value specifically comprises:

7. The method of claim 1, wherein, The adjustment of the initial parameter value comprises manual adjustment and automatic adjustment using MATLAB. After obtaining the measurement parameter value of the sample to be measured, the measurement method further comprises: determining the error and the correlation coefficient of the values of the thermal conductivity, the specific heat capacity and the interfacial thermal resistance by using an error propagation analysis model.

8. The method of claim 1, wherein, The measurement system comprises:

9. The method of claim 1, wherein, The measurement module is used to perform TDTR measurement on the sample to be measured by using a preset laser spot size and modulation frequency to obtain a measurement signal; the measurement signal comprises a measured phase signal in a negative delay time period and a measured phase signal in a positive delay time period; 10. A measurement system for simultaneously measuring thermal conductivity, specific heat capacity and interfacial thermal resistance, characterized in that, ​ ​ Analog module, for inputting initial parameter value of the sample to be measured into heat transfer model, obtaining analog signal; judging whether the deviation between the analog signal and the measured signal is less than preset value; if yes, taking the initial parameter value as the measured parameter value of the sample to be measured; if no, adjusting the initial parameter value to obtain adjusted parameter value, and taking the adjusted parameter value as initial parameter value of next cycle, returning to the step of inputting initial parameter value of the sample to be measured into heat transfer model; the parameter value includes the values of thermal conductivity, specific heat capacity and interfacial thermal resistance; the analog signal includes phase signal simulated in negative delay time period and phase signal simulated in positive delay time period.

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