CN113419120B - Method and system for measuring thermal resistance of dielectric film and metal interface - Google Patents
Method and system for measuring thermal resistance of dielectric film and metal interface Download PDFInfo
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Abstract
The invention relates to a method and a system for measuring thermal resistance of a dielectric film and a metal interface, wherein a thermal pulse experiment is carried out after the dielectric film and a metal foil are tightly attached to obtain an actually measured thermal response current signal curve; and establishing a heat transfer simulation model of the dielectric film and the metal foil, and when the fitting degree of a theoretical thermal response signal current curve and an actually measured thermal response current signal curve of the simulation model meets a preset convergence condition, taking the interface thermal resistance value of the simulation model as the interface thermal resistance of the dielectric film and the metal foil. Compared with the prior art, the method has the advantages that the implementation process is simple, the heat transfer simulation model is established after the actually measured thermal response current is obtained, the interface thermal resistance value of the simulation model is continuously adjusted until the fitting degree of the actually measured thermal response current and the theoretical thermal response current of the simulation model meets the convergence condition, the measurement speed is high, the accuracy is high, the operation is convenient, the dielectric film is not damaged, and the interface thermal resistance between the independent dielectric film material with the thickness of several micrometers and metal can be measured at high precision.
Description
Technical Field
The invention relates to the field of measurement of interface thermal resistance, in particular to a method and a system for measuring the interface thermal resistance of a dielectric film and metal.
Background
In an electronic device, the safety and stability of the device operation are generally ensured by mounting a heat sink, a heat dissipation plate, and the like to transfer internal heat. The dielectric film is widely used as a functional material for microelectronics, electrical insulation and energy storage capacitors, so that it is very important to accurately master thermal resistance information between the dielectric film and a metal heat sink to effectively manage the heat of an electronic device. The classical theoretical calculation model of the interface thermal resistance is as follows:
R 12 k/σ＝c(H/p) n
wherein R is 12 The contact thermal resistance of two contact materials is shown, k is the thermal conductivity harmonic mean value of the material 1 and the material 2, sigma is the surface roughness, H is the microhardness of the material, p is the contact pressure, and c and n are empirical constants. According to the formula, the theoretical calculation of the thermal resistance model is complex, a plurality of variables which are difficult to determine exist, and the interface thermal resistance is difficult to determine through the theoretical calculation, so that various experimental measurements for representing the interface thermal resistance are provided at present.
The experimental measurement is roughly classified into a steady-state method and a transient method. A steady-state method: maintaining a certain temperature difference on the two contact samples, measuring the axial temperature values of the two samples, and extrapolating the temperature values to the contact interface by the Fourier law so as to obtain the temperature difference on the interface; steady state method D5470-06 multipurpose according to ASTM standardIn bulk materials, the measurable range is 10 -7 ～10 -6 m 2 K/W, the measurement accuracy is good, but the time consumption is long, and the method is not suitable for medium films with the thickness of only a few micrometers. The transient measurement method mainly comprises a laser flash method, a heat reflection method, a TPS method and the like, most of the transient methods directly detect the temperature distribution of a sample to reversely deduce the interface thermal resistance, but for a dielectric film with the thickness of only a few micrometers, the accurate detection of the temperature in the thickness direction has certain difficulty, and the problem of insufficient precision of a detected temperature signal is difficult to avoid.
Therefore, how to measure the interface thermal resistance between the dielectric film and the metal heat sink and meet the requirement of measurement accuracy becomes an urgent problem to be solved.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a method and a system for measuring the thermal resistance of a medium film and a metal interface, the method and the system are simple in implementation process, a metal foil is selected as a heat sink, a heat transfer simulation model is established after the actually measured thermal response current of the medium film and the metal foil in a thermal pulse experiment is measured, the interface thermal resistance value in the heat transfer simulation model is continuously adjusted until the fitting degree of the theoretical thermal response current and the actually measured thermal response current of the heat transfer simulation model meets a convergence condition, the interface thermal resistance value of the heat transfer simulation model is used as the interface thermal resistance of the medium film and the metal foil, the measurement speed is high, the accuracy is high, the operation is convenient, the medium film is not damaged, and the high-accuracy measurement can be carried out on the interface thermal resistance between an independent medium film material with the thickness of several micrometers and the metal.
The purpose of the invention can be realized by the following technical scheme:
a method for measuring thermal resistance of a dielectric film and a metal interface comprises tightly attaching the dielectric film and a metal foil, performing a heat pulse experiment, and measuring to obtain an actually measured thermal response current signal curve; establishing a heat transfer simulation model of the dielectric film and the metal foil; and adjusting the interface thermal resistance value of the heat transfer simulation model, calculating to obtain a theoretical thermal response signal current curve, and taking the interface thermal resistance value of the heat transfer simulation model as the actual interface thermal resistance value of the dielectric film and the metal foil when the fitting degree of the actually measured thermal response current signal curve and the theoretical thermal response signal current curve meets the preset convergence condition.
Further, obtaining the measured thermal response current signal curve comprises the following steps:
a1: after the medium film is subjected to metallization treatment, the medium film is tightly attached to the metal foil, and direct-current voltages are externally connected to two sides of the medium film, so that an electric field which is uniformly distributed exists in the medium film;
a2: installing the dielectric film and the metal foil in a shielding box, applying pulse laser to heat the dielectric film, and collecting the actually measured thermal response current of the dielectric film;
a3: and converting the actually measured thermal response current into a frequency domain signal through fast Fourier transform to obtain an actually measured thermal response current signal curve.
Furthermore, the signal of the thermal response current is affected by the external dc voltage circuit and the pre-current amplifier, in step A3, distortion compensation is performed on the measured thermal response current to obtain a calibrated measured thermal response current, and then the calibrated measured thermal response current is converted into a frequency domain signal to obtain a measured thermal response current signal curve, where the formula is as follows:
I m～ (f)＝I 0～ (f)*H ～ (f)
wherein, I m～ (f) Representing the collected measured thermally responsive current, I 0～ (f) Represents the thermal response current in the ideal case, H ～ (f) Is a transfer function determined from the effect of the external circuit and amplifier bandwidth limitations on the thermally responsive current.
Further, establishing a heat transfer simulation model of the dielectric film and the metal foil specifically comprises: the method comprises the steps of obtaining initial temperature distribution, thickness, thermal diffusion coefficient, thermal conductivity coefficient, relative dielectric coefficient, temperature coefficient and thermal expansion coefficient of the relative dielectric coefficient of a dielectric film, obtaining initial temperature distribution, thickness, thermal diffusion coefficient and thermal conductivity coefficient of a metal foil, obtaining parameters of laser pulse and electric field in a thermal pulse experiment process, establishing a double-layer structure of the dielectric film and the metal foil in simulation software to serve as a heat transfer simulation model, initializing interface thermal resistance values of the heat transfer simulation model, and simulating disturbance of an externally applied direct current electric field and laser pulse in the double-layer structure in the simulation software.
Further, the step of obtaining the theoretical thermal response current signal curve comprises the following steps:
b1: establishing a one-dimensional heat conduction equation of a double-layer structure of a heat transfer simulation model:
the boundary conditions are as follows:
the initial conditions were:
θ 1 ＝T 1 (x)(0＜x＜x 1 )(t＝0)
θ 2 ＝T 2 (x)(x 1 ＜x＜x 2 )(t＝0)
wherein, theta 1 Is the temperature distribution of the dielectric film, a 1 Is the thermal diffusion coefficient, θ, of the dielectric film 2 Is the temperature distribution of the metal foil, a 2 Is the thermal diffusion coefficient of the metal foil, and x is the thickness direction from the dielectric film to the metal foilPosition of, x 1 Equal to the thickness, x, of the dielectric film 2 Is equal to the sum of the thicknesses of the dielectric film and the metal foil, t is time, k 1 Is the thermal conductivity, k, of the dielectric film 2 Is the thermal conductivity of the metal foil, h 12 Is the heat exchange coefficient, T, of the dielectric film and the metal foil 1 (x) Is the initial temperature distribution, T, of the dielectric film 2 (x) Is the initial temperature distribution of the metal foil, eta is the absorption coefficient of the pulse laser, q is the energy of the pulse laser, and delta (t) is the Gaussian distribution function of the pulse laser;
b2: solving the one-dimensional heat conduction equation to obtain the theoretical calculation of the temperature distribution of the dielectric film
Theoretical calculation of temperature distribution based on dielectric film
Obtaining the temperature change inside the dielectric film, and calculating according to the following formula to obtain the theoretical thermal response current:
g(x)＝ε 0 ε r (α ε -α x )E(x)
wherein I (t) represents a thermal response current, A represents an area of the dielectric film irradiated by the laser, d represents a thickness of the dielectric film, Δ θ represents a temperature change inside the dielectric film, g (x) represents a distribution function, E (x) represents an electric field distribution inside the dielectric film, and ε (t) 0 Denotes the vacuum dielectric constant,. Epsilon r Denotes the relative dielectric coefficient, alpha, of the dielectric film ε Temperature coefficient, alpha, representing the relative dielectric coefficient x Represents the thermal expansion coefficient of the dielectric film;
b3: and performing fast Fourier transform on the theoretical thermal response current and converting the theoretical thermal response current into a frequency domain signal to obtain a theoretical thermal response current signal curve.
Further, adjusting the interface thermal resistance value of the heat transfer simulation model and determining the actual interface thermal resistance value of the dielectric thin film and the metal foil specifically comprises:
c1: obtaining a theoretical thermal response current signal curve based on the current interface thermal resistance value of the heat transfer simulation model;
c2: fitting the theoretical thermal response current signal curve and the actually measured thermal response current signal curve, if the fitting degree does not meet the preset convergence condition, adjusting the interface thermal resistance value in the heat transfer simulation model, and repeating the step C1, otherwise, executing the step C3;
c3: and taking the interface thermal resistance value of the heat transfer simulation model as the actual interface thermal resistance value of the dielectric film and the metal foil.
Further, in step C2, a Nelder-Mead simplex algorithm is used to fit the theoretical thermal response current signal curve to the measured thermal response current signal curve.
Further, the preset convergence condition is a default convergence condition in the Nelder-Mead simplex algorithm.
A system for measuring thermal interface resistance of a dielectric film and a metal comprises:
the actual measurement module is used for tightly attaching the dielectric film to the metal foil, performing a heat pulse experiment and measuring to obtain an actual measurement heat response current signal curve;
the modeling module is used for establishing a double-layer structure of the dielectric film and the metal foil according to the parameters of the dielectric film and the metal foil and the parameters of the heat pulse experiment;
the calculation module is used for calculating a theoretical thermal response current signal curve of the heat transfer simulation model;
and the fitting module is used for fitting the actually measured thermal response current signal curve and the theoretical thermal response current signal curve and judging whether the fitting degree meets the preset convergence condition or not.
Furthermore, in the actual measurement module, the actual measurement thermal response current of the thermal pulse experiment is obtained, distortion compensation is performed on the actual measurement thermal response current to obtain a calibrated actual measurement thermal response current, and then the calibrated actual measurement thermal response current is converted into a frequency domain signal to obtain an actual measurement thermal response current signal curve.
Compared with the prior art, the invention has the following beneficial effects:
(1) The method has the advantages that the realization process is simple, after the actually measured thermal response current of the dielectric film and the metal foil in the thermal pulse experiment is measured, the heat transfer simulation model is established, the interface thermal resistance value in the heat transfer simulation model is continuously adjusted until the fitting degree of the theoretical thermal response current and the actually measured thermal response current of the heat transfer simulation model meets the convergence condition, the interface thermal resistance value of the heat transfer simulation model is used as the interface thermal resistance of the dielectric film and the metal foil, the measurement speed is high, the accuracy is high, the operation is convenient, the dielectric film is not damaged, and the interface thermal resistance between the independent dielectric film material with the thickness of several micrometers and the metal can be measured with high accuracy.
(2) The influence of the pre-current amplifier on the actually measured thermal response current when the external direct current voltage and the thermal response current are collected is considered, distortion compensation is carried out on the actually measured thermal response current measured in the thermal pulse experiment, and more accurate measurement is achieved.
(3) Establishing a heat transfer simulation model, simulating a heat pulse experiment in simulation software, calculating the temperature distribution of the medium film through the established heat conduction equation, calculating by using a first class of Fredholm integral equation according to the temperature distribution to obtain theoretical thermal response current, and calculating the theoretical thermal response current of the heat transfer simulation model under different interface thermal resistances.
Drawings
FIG. 1 is a flow chart of a method for measuring thermal resistance at the interface between a dielectric film and a metal;
fig. 2 is a fitting result of a measured thermal response current signal curve and a theoretical thermal response signal current curve.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
Example 1:
a method for measuring thermal resistance of a dielectric film and a metal interface belongs to a transient measurement method, is convenient to operate, has high measurement speed, does not damage a sample, and can effectively measure the thermal resistance of the interface between the dielectric film and a metal foil, and comprises the following main steps as shown in figure 1:
tightly attaching the dielectric film and the metal foil, performing a heat pulse experiment and measuring to obtain an actually measured thermal response current signal curve;
establishing a heat transfer simulation model of the dielectric film and the metal foil;
and adjusting the interface thermal resistance value of the heat transfer simulation model, calculating to obtain a theoretical thermal response signal current curve, and taking the interface thermal resistance value of the heat transfer simulation model as the actual interface thermal resistance value of the dielectric film and the metal foil when the fitting degree of the actually measured thermal response current signal curve and the theoretical thermal response signal current curve meets the preset convergence condition.
A system for measuring thermal interface resistance of a dielectric film and a metal comprises:
the actual measurement module is used for tightly attaching the dielectric film to the metal foil, performing a heat pulse experiment to obtain an actual measurement thermal response current of the heat pulse experiment, performing distortion compensation on the actual measurement thermal response current to obtain a calibrated actual measurement thermal response current, and then converting the calibrated actual measurement thermal response current into a frequency domain signal to obtain an actual measurement thermal response current signal curve;
the modeling module is used for establishing a double-layer structure of the dielectric film and the metal foil according to the parameters of the dielectric film and the metal foil and the parameters of the heat pulse experiment;
the calculation module is used for calculating a theoretical thermal response current signal curve of the heat transfer simulation model;
and the fitting module is used for fitting the actually measured thermal response current signal curve and the theoretical thermal response current signal curve and judging whether the fitting degree meets the preset convergence condition or not.
In this embodiment, the dielectric film is a BOPP dielectric film with a thickness of 5.8 μm, the metal foil is a copper foil with a thickness of 2mm, related parameters (thermal conductivity, thermal diffusivity, etc.) of the dielectric film can be measured in advance, for example, the multilayer dielectric films are stacked to measure the related parameters, the metal foil is a copper foil or a copper sheet, the related parameters of which can be directly obtained by looking up the parameters of the metal copper, and obtaining the actually measured thermal response current signal curve includes the following steps:
a1: after the medium film is subjected to metallization treatment, the medium film is tightly attached to the metal foil, and direct-current voltages are externally connected to two sides of the medium film, so that an electric field which is uniformly distributed exists in the medium film;
a2: installing the dielectric film and the metal foil in a shielding box, applying short pulse laser (25ns, 1Hz) to heat the dielectric film, and collecting the actually measured thermal response current of the dielectric film through a signal collection device of a thermal pulse experiment;
the thermal pulse method generates thermal disturbance by applying thermal pulse to the dielectric film, the temperature distribution of the dielectric film is changed, the thermal pulse drives electric charge in the internal propagation process of the dielectric film to trigger a measurable thermal response current, and the characteristics of the thermal response current can effectively represent the information of the temperature distribution in the dielectric film.
The heat flow flows into the metal foil after passing through the medium film, air with low heat conductivity is reserved due to an air gap between the medium film and the metal foil, heat transfer of the heat flow between two material interfaces is blocked, and interface thermal resistance R is formed. The air gap not only hinders heat conduction, but also affects electrical contact between an external power source and the dielectric film, resulting in poor signal-to-noise ratio in response to current. Therefore, during experimental measurement, thermal interface materials such as a thermal coupling agent and the like need to be added between the metal foil and the dielectric film to reduce thermal resistance and improve signal to noise ratio so as to obtain effective measurement data, and therefore, the interface thermal resistance value of the dielectric film and the metal foil finally obtained by the application is the interface thermal resistance value of the dielectric film, the thermal interface materials and the metal foil, and the interface thermal resistance value R int The model of (a) is expressed as:
R int ＝R contact1 +R cond +R contact2
R cond ＝d g /k Tims
thermal interface resistance R int Mainly comprises an upper interface contact thermal resistance R contact1 Lower interface thermal contact resistance R contact2 And self thermal resistance R of thermal interface material cond ，d g Is the thickness of the thermal interface material, k Tims Is the thermal conductivity of the thermal interface material.
And (3) while acquiring a measured thermal response current signal curve, recording parameters of laser pulse and electric field in a thermal pulse experiment, if the laser is pulse laser, the frequency is 1Hz, the pulse width is 25ns, and the electric field intensity E in the dielectric film in the thermal pulse experiment is 34.5k V/mm, so that preparation is made for subsequently establishing a heat transfer simulation model.
A3: and converting the actually measured thermal response current into a frequency domain signal through fast Fourier transform to obtain an actually measured thermal response current signal curve.
The signal of the thermal response current can be influenced by an external direct-current voltage circuit and a front-end current amplifier, in order to realize more accurate determination, step A3 further comprises distortion compensation of the measured thermal response current to obtain the calibrated measured thermal response current, and then the calibrated measured thermal response current is converted into a frequency domain signal to obtain a measured thermal response current signal curve, wherein the formula is as follows:
I m～ (f)＝I 0～ (f)*H ～ (f)
wherein, I m～ (f) Representing the collected measured thermally responsive current, I 0～ (f) Represents the thermal response current in the ideal case, H ～ (f) Is a transfer function determined according to the influence of the external circuit and the amplifier bandwidth limitation on the thermal response current, the transfer function H ～ (f) Distortion compensation transfer functions commonly used by those skilled in the art may be used.
The establishment of the heat transfer simulation model of the dielectric film and the metal foil comprises the following specific steps: the method comprises the steps of obtaining parameters such as initial temperature distribution, thickness, thermal diffusion coefficient, thermal conductivity, relative dielectric coefficient, temperature coefficient and thermal expansion coefficient of a dielectric film, obtaining parameters such as initial temperature distribution, thickness, thermal diffusion coefficient and thermal conductivity coefficient of a metal foil, obtaining parameters of laser pulse and electric field in a thermal pulse experiment process, establishing a double-layer structure of the dielectric film and the metal foil in simulation software to serve as a heat transfer simulation model, initializing interface thermal resistance of the heat transfer simulation model, and simulating disturbance of an externally applied direct current electric field and the laser pulse in the double-layer structure in the simulation software.
In the heat transfer simulation model, the interface thermal resistance value is first set according to experience, in this embodimentThe interface thermal resistance value is initially set to 1 x 10 empirically -6 K·m 2 And W, continuously adjusting the interface thermal resistance value according to the fitting degree of the theoretical thermal response current signal curve and the actually measured thermal response current signal curve.
In this example, the dielectric film had a thickness of 5.8 μm and a density of 910kg/m 3 The specific heat capacity is 1900J/(kg.K), the thermal conductivity, i.e., the thermal conductivity is 0.165W/(m.K), and the thermal diffusivity is 0.95X 10 -7 m 2 (s) the relative dielectric constant (60 Hz) of the dielectric thin film was 2.2, and the temperature coefficient of the relative dielectric constant of the dielectric thin film was 3.31X 10 -4 1/K, coefficient of thermal expansion of the dielectric film is 1.35 multiplied by 10 -4 1/K；
The metal foil has a thickness of 2mm and a density of 8960kg/m 3 The specific heat capacity is 384.6J/(kg.K), the thermal conductivity, i.e., the thermal conductivity is 401W/(m.K), and the thermal diffusivity is 1.16X 10 -4 m 2 /s。
The method for acquiring the theoretical thermal response current signal curve comprises the following steps:
b1: establishing a one-dimensional heat conduction equation of a double-layer structure of a heat transfer simulation model:
the boundary conditions are as follows:
the initial conditions were:
θ 1 ＝T 1 (x)(0＜x＜x 1 )(t＝0)
θ 2 ＝T 2 (x)(x 1 ＜x＜x 2 )(t＝0)
wherein, theta 1 Is the temperature distribution of the dielectric film, a 1 Is the thermal diffusion coefficient, θ, of the dielectric film 2 Is the temperature distribution of the metal foil, a 2 Is the thermal diffusion coefficient of the metal foil, x is the position from the dielectric film to the thickness direction of the metal foil, x 1 Equal to the thickness, x, of the dielectric film 2 Equal to the sum of the thicknesses of the dielectric film and the metal foil, wherein x =0 is the upper surface of the dielectric film, and x = x 1 Where is the lower surface of the dielectric film, or the upper surface of the metal foil, x = x 2 Where is the lower surface of the metal foil, t is time, k 1 Is the thermal conductivity, k, of the dielectric film 2 Is the thermal conductivity of the metal foil, h 12 Is the heat exchange coefficient between the dielectric film and the metal foil, which is determined based on the interface thermal resistance value, T 1 (x) Is the initial temperature distribution, T, of the dielectric film 2 (x) Is the initial temperature distribution of the metal foil, eta is the absorption coefficient of the pulse laser, q is the energy of the pulse laser, and delta (t) is the Gaussian distribution function of the pulse laser;
the temperature distribution refers to the temperature distribution of different thicknesses and different time, the initial temperature distribution can be measured in advance, the temperature of each thickness of the dielectric film and the metal foil is room temperature, and after the laser pulse heating is applied, the temperature of the dielectric film at different thicknesses can change until the thermal equilibrium is reached and then the temperature is kept unchanged.
B2: the principal methods for solving the one-dimensional heat conduction equation include separation variable method, green function method, laplace transform, finite element method, etc., and the theoretical calculation of the temperature distribution of the obtained dielectric film
Theoretical calculation of temperature distribution based on dielectric film
Obtaining the temperature change in the medium film, wherein the heat diffusion depth of the laser in the medium of the medium film is far less than the radius of the laser light target, the heat conduction problem can be approximated to a one-dimensional heat conduction problem, the medium film is a non-polar medium, and the calculation of the thermal response current relates to a first Fredholm integral equation as follows:
g(x)＝ε 0 ε r (α ε -α x )E(x)
wherein I (t) represents a thermal response current, A represents an area of the dielectric film irradiated with the laser, d represents a thickness of the dielectric film, Δ θ represents a temperature change inside the dielectric film, g (x) represents a distribution function, E (x) represents an electric field distribution inside the dielectric film, ε 0 Represents a vacuum dielectric constant of 8.8537 × 10 -12 F/m，ε r Denotes the relative dielectric coefficient, alpha, of the dielectric film ε Temperature coefficient, α, representing the relative dielectric coefficient x Represents the thermal expansion coefficient of the dielectric film;
b3: and performing fast Fourier transform on the theoretical thermal response current and converting the theoretical thermal response current into a frequency domain signal to obtain a theoretical thermal response current signal curve.
Adjusting the interface thermal resistance value of the heat transfer simulation model and determining the actual interface thermal resistance value of the dielectric film and the metal foil specifically as follows:
c1: obtaining a theoretical thermal response current signal curve based on the current interface thermal resistance value of the heat transfer simulation model;
c2: fitting a theoretical thermal response current signal curve and an actually measured thermal response current signal curve by using a Nelder-Mead simplex algorithm, wherein the preset convergence condition is a default convergence condition in the Nelder-Mead simplex algorithm, if the fitting degree does not meet the preset convergence condition, the interface thermal resistance value in the heat transfer simulation model is adjusted, the step C1 is repeated, and otherwise, the step C3 is executed;
c3: and taking the interface thermal resistance value of the heat transfer simulation model as the actual interface thermal resistance value of the dielectric film and the metal foil.
The Nelder-Mead simplex algorithm can process the minimum solving problem of a multivariable function, fitting a theoretical thermal response current signal curve and an actually measured thermal response current signal curve and adjusting interface thermal resistance are carried out, the theoretical thermal response current signal curve closest to the actually measured thermal response current signal curve and the interface thermal resistance value of the theoretical thermal response current signal curve can be quickly and accurately found, MATLAB is provided with an fmisearch () function, the fmisearch () function is directly used for solving to obtain the interface thermal resistance value, and the default convergence condition in the algorithm is used as the convergence condition.
In the whole heat transfer process, the thermal resistance has the function of preventing heat flow from being rapidly transferred to the metal foil and slowing down the heat dissipation of the medium film, so that the interface thermal resistance R int The main contribution of (1) is mainly reflected in the process of cooling a dielectric film sample, the action on time domain response current is mainly reflected in the characteristic that the thermal response current is attenuated to a negative value region from a peak value, the signal characteristic of a relatively low frequency band is mainly concerned in a frequency domain, the fitting result is shown in figure 2, the fitting of a real part and an imaginary part of an actually measured thermal response current signal curve and a theoretical thermal response current signal curve is considered, finally, a theoretical thermal response current signal curve with the highest fitting degree with the actually measured thermal response current signal curve is found, and the interface thermal resistance value corresponding to the theoretical thermal response current signal curve is 7.39 multiplied by 10 -6 K·m 2 W, the actual interface thermal resistance value of the dielectric film and the metal foil is 7.39 multiplied by 10 -6 K·m 2 /W。
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (8)
1. A method for measuring thermal resistance of a dielectric film and a metal interface is characterized in that the dielectric film is tightly attached to a metal foil, a heat pulse experiment is carried out, and an actually measured thermal response current signal curve is obtained through measurement; establishing a heat transfer simulation model of the dielectric film and the metal foil; adjusting the interface thermal resistance value of the heat transfer simulation model, calculating to obtain a theoretical thermal response signal current curve, and taking the interface thermal resistance value of the heat transfer simulation model as the actual interface thermal resistance value of the dielectric film and the metal foil when the fitting degree of the actually measured thermal response current signal curve and the theoretical thermal response signal current curve meets the preset convergence condition;
the establishment of the heat transfer simulation model of the dielectric film and the metal foil specifically comprises the following steps: the method comprises the steps of obtaining initial temperature distribution, thickness, thermal diffusion coefficient, thermal conductivity coefficient, relative dielectric coefficient, temperature coefficient and thermal expansion coefficient of the relative dielectric coefficient of a dielectric film, obtaining initial temperature distribution, thickness, thermal diffusion coefficient and thermal conductivity coefficient of a metal foil, obtaining parameters of laser pulse and electric field in a thermal pulse experiment process, establishing a double-layer structure of the dielectric film and the metal foil in simulation software as a heat transfer simulation model, initializing interface thermal resistance values of the heat transfer simulation model, and simulating disturbance of an externally applied direct current electric field and laser pulse in the double-layer structure in the simulation software;
the method for acquiring the theoretical thermal response current signal curve comprises the following steps:
b1: establishing a one-dimensional heat conduction equation of a double-layer structure of a heat transfer simulation model:
the boundary conditions are as follows:
the initial conditions were:
θ 1 ＝T 1 (x)(0＜x＜x 1 )(t＝0)
θ 2 ＝T 2 (x)(x 1 ＜x＜x 2 )(t＝0)
wherein, theta 1 Is the temperature distribution of the dielectric film, a 1 Is the thermal diffusion coefficient, θ, of the dielectric film 2 Is the temperature distribution of the metal foil, a 2 Is the thermal diffusion coefficient of the metal foil, x is the position from the dielectric film to the thickness direction of the metal foil, x 1 Equal to the thickness, x, of the dielectric film 2 Is equal to the sum of the thicknesses of the dielectric film and the metal foil, t is time, k 1 Is the thermal conductivity, k, of the dielectric film 2 Is the thermal conductivity of the metal foil, h 12 Is the heat exchange coefficient, T, of the dielectric film and the metal foil 1 (x) Is the initial temperature distribution, T, of the dielectric film 2 (x) Is the initial temperature distribution of the metal foil, eta is the absorption coefficient of the pulse laser, q is the energy of the pulse laser, and delta (t) is the Gaussian distribution function of the pulse laser;
b2: solving the one-dimensional heat conduction equation to obtain the theoretical calculation of the temperature distribution of the dielectric film
Temperature based on dielectric filmDegree distribution theoretical calculation
Obtaining the temperature change inside the dielectric film, and calculating according to the following formula to obtain the theoretical thermal response current:
g(x)＝ε 0 ε r (α ε -α x )E(x)
wherein I (t) represents a thermal response current, A represents an area of the dielectric film irradiated with the laser, d represents a thickness of the dielectric film, Δ θ represents a temperature change inside the dielectric film, g (x) represents a distribution function, E (x) represents an electric field distribution inside the dielectric film, ε 0 Denotes the vacuum dielectric constant,. Epsilon r Denotes the relative dielectric coefficient, alpha, of the dielectric film ε Temperature coefficient, alpha, representing the relative dielectric coefficient x Represents the thermal expansion coefficient of the dielectric film;
b3: and performing fast Fourier transform on the theoretical thermal response current and converting the theoretical thermal response current into a frequency domain signal to obtain a theoretical thermal response current signal curve.
2. The method for measuring thermal interface resistance between a dielectric film and a metal as claimed in claim 1, wherein obtaining a measured thermal response current signal curve comprises the steps of:
a1: after the medium film is subjected to metallization treatment, the medium film is tightly attached to the metal foil, and direct current voltage is externally connected to two sides of the medium film, so that an electric field which is uniformly distributed exists in the medium film;
a2: applying pulse laser to heat the medium film, and collecting the actually measured thermal response current of the medium film;
a3: and converting the actually measured thermal response current into a frequency domain signal through fast Fourier transform to obtain an actually measured thermal response current signal curve.
3. The method for measuring thermal resistance of a dielectric film and metal interface according to claim 2, wherein in the step A3, distortion compensation is performed on the measured thermal response current to obtain a calibrated measured thermal response current, and then the calibrated measured thermal response current is converted into a frequency domain signal to obtain a measured thermal response current signal curve, wherein the formula is as follows:
I m～ (f)＝I 0～ (f)*H ～ (f)
wherein, I m～ (f) Representing the collected measured thermally responsive current, I 0～ (f) Represents the thermal response current in the ideal case, H ～ (f) Is a transfer function determined from the effect of the external circuit and amplifier bandwidth limitations on the thermally responsive current.
4. The method for measuring the thermal resistance of the interface between the dielectric film and the metal as claimed in claim 1, wherein the step of adjusting the interface thermal resistance value of the heat transfer simulation model and determining the actual interface thermal resistance value of the dielectric film and the metal foil is specifically as follows:
c1: obtaining a theoretical thermal response current signal curve based on the current interface thermal resistance value of the heat transfer simulation model;
c2: fitting the theoretical thermal response current signal curve and the actually measured thermal response current signal curve, if the fitting degree does not meet the preset convergence condition, adjusting the interface thermal resistance value in the heat transfer simulation model, and repeating the step C1, otherwise, executing the step C3;
c3: and taking the interface thermal resistance value of the heat transfer simulation model as the actual interface thermal resistance value of the dielectric film and the metal foil.
5. The method as claimed in claim 4, wherein the Nelder-Mead simplex algorithm is used to fit the theoretical thermal response current signal curve to the measured thermal response current signal curve in step C2.
6. The method as claimed in claim 5, wherein the predetermined convergence condition is a default convergence condition in a Nelder-Mead simplex algorithm.
7. A system for measuring the thermal interface resistance between a dielectric film and a metal, which is based on the method for measuring the thermal interface resistance between the dielectric film and the metal as claimed in any one of claims 1 to 6, and comprises:
the actual measurement module is used for tightly attaching the dielectric film to the metal foil, performing a heat pulse experiment and measuring to obtain an actual measurement heat response current signal curve;
the modeling module is used for establishing a double-layer structure of the dielectric film and the metal foil according to the parameters of the dielectric film and the metal foil and the parameters of the heat pulse experiment;
the calculation module is used for calculating a theoretical thermal response current signal curve of the heat transfer simulation model;
and the fitting module is used for fitting the actually measured thermal response current signal curve and the theoretical thermal response current signal curve and judging whether the fitting degree meets the preset convergence condition or not.
8. The system for measuring thermal resistance of a dielectric film and a metal interface as claimed in claim 7, wherein the actual measurement module obtains an actual measurement thermal response current of a thermal pulse experiment, performs distortion compensation on the actual measurement thermal response current to obtain a calibrated actual measurement thermal response current, and then converts the calibrated actual measurement thermal response current into a frequency domain signal to obtain an actual measurement thermal response current signal curve.
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