CN114384118B - Thermal diffusion coefficient measuring method and device for dielectric film with substrate - Google Patents
Thermal diffusion coefficient measuring method and device for dielectric film with substrate Download PDFInfo
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Abstract
The invention relates to a thermal diffusion coefficient measuring method and a device for a dielectric film with a substrate, wherein the method comprises the following steps: preparing a sample with a substrate, depositing a dielectric film on the surface of the substrate, and carrying out metallization treatment; generating an electric field uniformly distributed in the dielectric film; applying laser pulse to the dielectric film, and collecting thermal response current generated by the dielectric film; constructing a thermal conduction model of the dielectric film-substrate; and adjusting the thermal diffusion coefficient of the dielectric film in the thermal conduction model, and calculating to obtain a corresponding simulation response current until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and taking the thermal diffusion coefficient of the dielectric film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the dielectric film. Compared with the prior art, the invention can rapidly and accurately measure the thermal diffusion coefficient of the dielectric film with the substrate material from submicron to micron, and provides a simple and effective transient measurement means.
Description
Technical Field
The invention relates to the technical field of measurement of thermophysical properties of dielectric films, in particular to a method and a device for measuring a thermal diffusion coefficient of a dielectric film with a substrate.
Background
Currently, the rapid progress of new science and technology represented by information, power electronics, computers, etc. has driven the development of electrical devices to integrate, thin, compact, and multifunctional, microelectronic mechanical devices (MES), microelectronic devices, etc. have been increasingly used, and polymer films of micrometer and nanometer dimensions are often selected as the main interface materials and packaging materials. The rapid growth of the microfabrication industry presents a significant challenge to the heat dissipation problem inside the device. In practical application, for electric or power electronic equipment, the internal temperature of the equipment is continuously increased along with the accumulation of device loss when the equipment is operated at high frequency and high pressure for a long time, so that the internal dielectric material can be aged in advance, destroyed or even melted to cause thermal breakdown and the like, and the safe operation of the equipment is directly affected. In fact, in the microelectronics industry, the problem of heat accumulation caused by high-density electronic packaging has become a bottleneck in industrial development, and is a major problem that must be overcome in the development path of high-transmission power and high-frequency operation microprocessors. In general, high integration and high-density assembly of industrial electrical equipment are achieved, and meanwhile, the problem of heat dissipation inside a device package is increasingly emphasized. The polymer film is used as a key link which is not negligible in the heat dissipation design of the electric device, and whether the heat conduction performance of the polymer film can meet the insulation heat dissipation requirement in the industrial field has important significance for reducing the working temperature of heating components and chips, prolonging the service life of equipment and improving the use precision.
In determining the thermophysical properties of polymer films, the thermal conductivity or thermal diffusivity of the polymer is affected by factors such as the molecular structure, crystalline and oriented structure, density, porosity, electrical conductivity, temperature and pressure of the material, and all theoretical calculation equations have great limitations. Thus, the thermal conductivity or thermal diffusivity of most materials to date has been determined by means of experimental instrumentation. However, films with thicknesses approaching submicron or even nanometer are generally adhered to a substrate with a semi-infinite thickness for use, and many methods commonly used at present, such as a flash method, a transient heat source method and a hot wire method, have obvious limitations for measuring the thermal diffusivity of the film. Therefore, there is a need for a simple, accurate, and fast method for measuring the thermal diffusivity of a polymer film with a substrate.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method and a device for measuring the thermal diffusivity of a dielectric film with a substrate.
The aim of the invention can be achieved by the following technical scheme:
a thermal diffusion coefficient measuring method of a dielectric film with a substrate comprises the following steps:
preparing a sample with a substrate, depositing a dielectric film on the surface of the substrate, and carrying out metallization treatment;
applying direct current voltage to two sides of a dielectric film in a sample with a substrate, and generating an electric field uniformly distributed in the dielectric film;
applying laser pulse to the dielectric film, and collecting thermal response current generated by thermal disturbance in the sample with the substrate through a measuring circuit;
constructing a medium film-substrate heat conduction model according to the structure of the sample with the substrate, wherein the heat conduction model is used for calculating the temperature distribution change in the medium film;
and adjusting the thermal diffusion coefficient of the medium film in the thermal conduction model by taking the thermal diffusion coefficient of the medium film as a unique unknown variable to obtain the temperature distribution change of the medium film under the thermal diffusion coefficient, calculating the corresponding simulation response current based on the temperature distribution change until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and taking the thermal diffusion coefficient of the medium film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the medium film.
Further, the established heat conduction model is specifically:
simplifying a heat conduction model of a sample with a substrate into a double-layer structure, wherein the heat conduction model comprises a film layer and a substrate layer, subscripts i=1 and 2 respectively refer to the film layer and the substrate layer, the conduction of laser pulses as heat pulses in the thickness direction of a medium film accords with a one-dimensional heat conduction equation, and the material of an ith layer has the following heat conduction equation:
wherein z represents a spatial position along the thickness direction of the dielectric thin film, t represents time, and D i Is the thermal diffusivity, deltaT, of the material of the i-th layer i (z, t) means the temperature distribution change in the material of the ith layer, z i-1 、z i The space coordinates of the front and rear boundary surfaces of the layer material in the thickness direction are respectively z 0 Thickness d of i-th layer material =0 i ＝z i -z i-1 ；
The boundary conditions are:
wherein k is i Is the heat conductivity coefficient of the material of the i layer, the z=0 point is the incident plane of the laser pulse, and the thickness of the dielectric film is equal to z 1 -0, the thickness of the substrate being equal to z 2 -z 1 F (t) is a laserTime function of heat flux density generated at z=0 after the pulse is absorbed.
Further, by combining a Laplace variation method and a numerical method, the respective temperature distribution variation of the film layer and the substrate layer is obtained in the Laplace domain, and inverse Laplace transformation is performed by using the numerical method to obtain an accurate time domain numerical solution, so as to obtain the temperature distribution variation in the dielectric film, which is specifically as follows:
the Laplace transformation is carried out on the heat transfer equation, and the method can be obtained:
wherein s is the Laplacian,an expression indicating the temperature distribution change of the i-th layer material in the Lawster domain, and obtaining a general solution of the temperature distribution change of the film layer and the basal layer in the Lawster domain:
wherein A is i 、B i As a constant to be solved for,substituting the general solution of the temperature distribution change of the film layer and the basal layer in the Lawster domain into the boundary condition to obtain an equation set:
the equation set is combined to obtain a constant term A of the temperature distribution change of the film layer 1 、B 1 Is represented by the expression:
wherein f(s) is the Laplace transform function of f (t); alpha=k 1 λ 1 /k 2 λ 2 Will A 1 、B 1 The expression of (2) is replaced into an equation set to obtain the expression of the change of the film layer temperature distribution in the Lawster domainThen the temperature distribution change delta T of the film layer can be obtained by a numerical method 1 (z，t)。
Further, if the heat conduction performance of the substrate is far higher than that of the dielectric film, the temperature distribution of the film layer changes by delta T 1 (z, t) is:
wherein DeltaT 1_0 ＝q/c 1 ρ 1 Ad 1 The physical meaning is the average temperature rise inside the film in a short time, c 1 Represents the specific heat, ρ, of the dielectric film 1 The film density of the dielectric film is represented, and a represents the irradiation area of the dielectric film receiving the laser pulse.
Further, fitting the simulated response current and the thermal response current is specifically as follows:
obtaining a thermal response current spectrum in the frequency domainAnd a simulated response current spectrum i sim (f) The error function between the two is expressed as the sum of the complex difference magnitudes of the two currents at each frequency point multiplied by the proportional term:
wherein F (D) 1 ) Representation ofAnd i sim (f) Error function between->Representing the frequency point f l Amplitude of upper thermal response current spectrum, i sim (f l ，D 1 ) Indicating that the thermal diffusivity of the dielectric film is set to D 1 Time-frequency point f l Upper simulation response to the magnitude of the current spectrum, if F (D 1 ) If the value of (2) is smaller than the preset threshold value, the fitting degree of the simulation response current and the thermal response current reaches the preset value.
Further, the simulation response current spectrum i sim (f) The acquisition of (1) is specifically as follows: calculating simulation response current i according to temperature distribution change in dielectric film sim (t) to i in time domain sim (t) Fourier transforming to obtain a simulation response current spectrum i sim (f) Wherein i is sim The calculation formula of (t) is as follows:
wherein A represents the irradiation area of the medium film for receiving laser pulse, d p Represents the thickness of the dielectric film, χ is a constant term, χ= (α) ε -α z )ε 0 ε r ，α ε Is the temperature coefficient of dielectric constant, alpha z Is the coefficient of thermal expansion, ε 0 For vacuum dielectric constant, ε r The relative permittivity of the dielectric thin film, E (z), is the electric field distribution inside the dielectric thin film, Δt (z, T) is the temperature distribution change inside the dielectric thin film, z represents the spatial position along the thickness direction of the dielectric thin film, and T represents time.
Further, a thermal response current spectrum is obtainedThe method comprises the following steps:
collecting thermal response current i generated by thermal disturbance in sample with substrate through measuring circuit exp (t) the measuring circuit comprises an isolation capacitor, an amplifier and an oscilloscope, wherein the current generated by thermal disturbance in the sample with the base flows through the isolation capacitor and is amplified by the amplifier to form a thermal response current i exp (t) and is acquired and recorded by an oscilloscope; i in time domain exp (t) after Fourier transformation, performing distortion compensation in a frequency response calibration mode to obtain a thermal response current spectrum
Further, the preparation of the base-carrying sample is specifically:
and (3) obtaining a material with a smooth and flat surface as a substrate, and sequentially carrying out metallization treatment, dielectric film deposition and metallization treatment if the substrate is an insulator, or sequentially carrying out dielectric film deposition and metallization treatment if the substrate is a conductor.
Further, the deposition thickness of the dielectric film is in a micron level, the metal thickness of the metallization treatment is in a nanometer level, and the thickness of the substrate is semi-infinite relative to the dielectric film.
A thermal diffusivity measurement device for a film of a substrate-bearing medium, comprising:
a substrate-carrying sample comprising a substrate and a dielectric film deposited on a surface of the substrate;
the direct current power supply is connected to the substrate-carrying sample and is used for applying direct current voltage to two sides of the dielectric film in the substrate-carrying sample;
a pulse light source for applying a laser pulse to the dielectric thin film;
the measuring circuit is used for collecting thermal response current generated by thermal disturbance in the sample with the substrate;
a heat conduction model unit for constructing a heat conduction model of the dielectric thin film-substrate according to the structure of the sample with the substrate, wherein the heat conduction model is used for calculating the temperature distribution change in the dielectric thin film;
and the fitting unit is used for adjusting the thermal diffusion coefficient of the dielectric film in the thermal conduction model by taking the thermal diffusion coefficient of the dielectric film as a unique unknown variable to obtain the temperature distribution change of the dielectric film under the thermal diffusion coefficient, calculating the corresponding simulation response current based on the temperature distribution change until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and taking the thermal diffusion coefficient of the dielectric film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the dielectric film.
Compared with the prior art, the invention has the following beneficial effects:
(1) The structure of the dielectric film-substrate is analyzed, a thermal conduction model is established to obtain theoretical simulation response current, when the fitting degree of the actually measured thermal response current and the simulation response current meets the requirement, the thermal diffusion coefficient in the thermal conduction model can be used as a measurement result, the thermal diffusion coefficient of the dielectric film with the substrate material from submicron to micron can be measured rapidly and accurately, and a simple and effective transient measurement means is provided.
(2) The heat conduction model is built, the heat conduction model of the sample with the substrate is simplified into a double-layer structure, the heat conduction model comprises a film layer and a substrate layer, the laser pulse is used as the heat pulse to conduct in the thickness direction of the dielectric film, the one-dimensional heat conduction equation is met, and the number of the boundaries is increased by considering the double-layer plane, so that the temperature distribution change in the dielectric film can be obtained through boundary conditions.
(3) Aiming at the special heat conduction model, the Laplace change method and the numerical method are combined, the respective temperature distribution change of the film layer and the substrate layer is obtained in the Laplace domain, and the numerical method is applied to carry out inverse Laplace transformation to obtain an accurate time domain numerical solution, so that the temperature distribution change in the medium film is obtained.
(4) The dielectric film sample is deposited on a substrate material, the substrate material has no excessively high requirement, and the substrate can be a conductive material or an insulating material, so that the application range is wide.
Drawings
FIG. 1 is a schematic illustration of a dielectric film-substrate structure;
FIG. 2 is a graph showing the fitting of the simulated response current and the thermal response current in the frequency domain;
reference numerals: 1. laser pulse 2, dielectric film 3 and substrate.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
In the drawings, like structural elements are referred to by like reference numerals and components having similar structure or function are referred to by like reference numerals. The dimensions and thickness of each component shown in the drawings are arbitrarily shown, and the present invention is not limited to the dimensions and thickness of each component. Some of the elements in the drawings are exaggerated where appropriate for clarity of illustration.
Example 1:
a thermal diffusion coefficient measuring method of a dielectric film with a substrate comprises the following steps:
preparing a sample with a substrate, depositing a dielectric film on the surface of the substrate, and carrying out metallization treatment;
applying direct current voltage to two sides of a dielectric film in a sample with a substrate, and generating an electric field uniformly distributed in the dielectric film;
applying laser pulse to the dielectric film, and collecting thermal response current generated by thermal disturbance in the sample with the substrate through a measuring circuit;
constructing a medium film-substrate heat conduction model according to the structure of the sample with the substrate, wherein the heat conduction model is used for calculating the temperature distribution change in the medium film;
and adjusting the thermal diffusion coefficient of the medium film in the thermal conduction model by taking the thermal diffusion coefficient of the medium film as a unique unknown variable to obtain the temperature distribution change of the medium film under the thermal diffusion coefficient, calculating the corresponding simulation response current based on the temperature distribution change until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and taking the thermal diffusion coefficient of the medium film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the medium film.
Under the combined action of external direct-current voltage and laser pulse (heat pulse), the non-polarized dielectric film changes the induction electric charge quantity on the surface electrode to generate a thermal response current which can be measured by an external circuit, and the thermal response current is also called displacement current, and the expression is as follows:
wherein A represents the irradiation area of the medium film for receiving laser pulse, d p Represents the thickness of the dielectric film, χ is a constant term, χ= (α) ε -α z )ε 0 ε r ，α ε Is the temperature coefficient of dielectric constant, alpha z Is the coefficient of thermal expansion, ε 0 For vacuum dielectric constant, ε r The relative permittivity of the dielectric thin film, E (z), is the electric field distribution inside the dielectric thin film, Δt (z, T) is the temperature distribution change inside the dielectric thin film, z represents the spatial position along the thickness direction of the dielectric thin film, and T represents time.
When the electric field in the dielectric film is uniformly distributed, the electric field strength is a constant, and the displacement current is simplified to be:
accordingly, if a uniform electric field is applied across the dielectric film, the thermal response current is primarily dependent on the temperature distribution variation within the dielectric film.
According to the principle, the invention provides a simulation method for measuring the thermal diffusion coefficient of the polymer film with the substrate, other thermal physical parameters in the sample with the substrate are known except the thermal diffusion coefficient of the dielectric film, a heat transfer simulation model can be constructed, and the thermal diffusion coefficient of the dielectric film is the only unknown variable in the simulation model. Setting a thermal diffusion coefficient, and calculating corresponding temperature distribution change according to a simulation model so as to calculate theoretical thermal response current. And continuously adjusting the thermal diffusion coefficient of the dielectric film in the simulation model to ensure that the theoretical thermal response current is consistent with the actually measured thermal response current, and taking the thermal diffusion coefficient of the dielectric film in the simulation model as a final measurement result.
Specifically, the method for measuring the thermal diffusion coefficient of the dielectric film with the substrate comprises the following steps:
(1) Preparing a sample with a substrate, depositing a dielectric film on the surface of the substrate, and carrying out metallization treatment;
and (3) obtaining a material with a smooth and flat surface as a substrate, and sequentially carrying out metallization treatment, dielectric film deposition and metallization treatment if the substrate is an insulator, or sequentially carrying out dielectric film deposition and metallization treatment if the substrate is a conductor.
(1) According to practical application requirements, a piece of material with a smooth and flat surface is taken as a substrate material, a dielectric film sample with a micrometer thickness is deposited on one surface of the substrate material by evaporation, tape casting or spin coating, and meanwhile, the thickness of the substrate material is approximately half infinite thickness relative to the deposited dielectric film. (2) If the substrate material is not a conductor, before depositing the dielectric film, the surface of the substrate should be metallized as a pressurizing electrode (substrate electrode), and the thickness of the metallization is controlled to be tens of nanometers; if the base material is a conductor, no metallization is required, and the base material itself acts as a pressurizing electrode (base electrode). (3) After deposition of the dielectric film sample, the surface of the dielectric film sample is metallized to serve as a grounding electrode (film electrode) and a laser light target.
(2) Applying direct current voltage to two sides of a dielectric film in a sample with a substrate, and generating an electric field uniformly distributed in the dielectric film;
and placing the tested sample with the base into an electromagnetic shielding box, and connecting the electromagnetic shielding box into an external circuit in series, wherein the electromagnetic shielding box comprises a direct current power supply and a measuring circuit. The direct current power supply is connected with the film electrode and the substrate electrode, direct current voltage is applied to the dielectric film sample between the film electrode and the substrate electrode, an electric field which is uniformly distributed is generated in the dielectric film, the voltage obtained by dividing the substrate is zero, and no electric field is distributed in the substrate. The measuring circuit comprises an isolation capacitor, an amplifier and an oscilloscope and is used for collecting thermal response current.
(3) Applying laser pulse to the dielectric film, and collecting thermal response current generated by thermal disturbance in the sample with the substrate through a measuring circuit;
the laser heat pulse acts on the medium film sample, the heat pulse is conducted to the substrate after passing through the medium film, after the laser pulse energy is absorbed, the heat pulse is conducted inside the polymer film, the medium film sample is caused to generate instantaneous temperature change in sequence along the thickness direction, the instantaneous temperature change of the medium film induces weak thermal response current on the external circuit, and the current flows through the blocking capacitor and is amplified by the amplifier to form a time domain signal i exp (t) acquired and recorded by an oscilloscope.
Taking into account the limitation of the external circuit and the bandwidth of the amplifier, the acquired time domain signal i exp (t) is a distorted signal, thus, the time domain signal i exp (t) obtaining i by Fourier transform exp (f) Distortion compensation is carried out in a frequency response calibration mode, and a calibrated thermal response current spectrum is obtainedThe calibration formula is as follows:
where H (f) is a transfer function determined from the effect of the external circuit and the amplifier bandwidth limitations on the thermal response current.
(4) Constructing a heat conduction model of the medium film 2-substrate 3 according to the structure of the sample with the substrate, wherein the heat conduction model is used for calculating the temperature distribution change in the medium film 2;
as is clear from the formula (2), for the structure of the dielectric thin film 2-substrate 3, the characteristic of the thermal response current mainly depends on the temperature distribution variation of the dielectric thin film 2, and the temperature distribution variation in the dielectric thin film 2 is mainly determined by a plurality of known parameters (for example, the thermal conductivity of the substrate 3, the energy parameter of the laser pulse 1, etc.) and unknown parameters (the thermal diffusivity of the dielectric thin film 2). Therefore, a thermal conduction model of the structure of the dielectric film 2-substrate 3 is established, so that theoretical thermal response current is obtained, and the thermal diffusion coefficient of the dielectric film 2 is obtained in a current fitting mode.
The actual structure of the sample with the substrate is composed of a metal coating-a dielectric film 2- (metal coating) -a substrate 3, the thickness of the metal coating is generally tens of nanometers in the experimental process, and the heat conductivity coefficient of the metal coating is 3-4 orders of magnitude higher than that of the dielectric film 2 and the insulating substrate 3, so that the heat resistance of the metal coating is far smaller than that of the dielectric film 2 and the substrate 3 only by considering heat transfer, and the heat conduction model of the multilayer structure is simplified into a double-layer structure for the convenience of fitting and the reduction of the calculated amount, as shown in fig. 1:
the laser pulse laser device comprises a film layer 2 and a substrate layer 3, wherein subscripts i=1 and 2 respectively refer to the film layer 2 and the substrate layer 3, the film layer 2 can be represented by a symbol subscript p, the substrate layer 3 is represented by a symbol subscript sub, the conduction of the laser pulse 1 as a heat pulse in the thickness direction of the dielectric film 2 accords with a one-dimensional heat conduction equation, and the following heat conduction equation exists for an ith layer material:
wherein z represents a spatial position along the thickness direction of the dielectric thin film 2, t represents time, D i Is the thermal diffusivity, deltaT, of the material of the i-th layer i (z, t) means the temperature distribution change in the material of the ith layer, z i-1 、z i The space coordinates of the front and rear boundary surfaces of the layer material in the thickness direction are respectively z 0 Thickness d of i-th layer material =0 i ＝z i -z i-1 ；
Since the number of boundaries increases in consideration of the double-layer plane, at z=0,at z=z 1 At DeltaT p ＝ΔT sub ，/>At z=z 2 At (I) a part of>Therefore, the temperature distribution variation inside the film 2 and the substrate 3 can be found from the following boundary conditions:
wherein k is i Is the heat conductivity coefficient of the material of the i layer, the incident surface of the laser pulse 1 is at the position of z=0, and the thickness of the dielectric film 2 is equal to z 1 -0, the thickness of the substrate 3 being equal to z 2 -z 1 F (t) is a function of time of the heat flux density generated at z=0 after the laser pulse 1 is absorbed;
the solution of the temperature rise distribution of the double-layer medium in the time domain is much more complex than that of the single-layer medium, and for the existing common heat conduction solution mathematical methods, such as a separation variable method, a green formula method, a Laplace transformation method and the like, the analytic solution in the time domain cannot be obtained when most of the multi-layer composite heat conduction models are analyzed, and the numerical method needs to be turned to. In order to solve the heat conduction problem of the double-layer model, the invention combines a Laplace change method and a numerical method, obtains respective temperature distribution changes of a film layer 2 and a substrate layer 3 in a Laplace domain, and applies the numerical method to carry out inverse Laplace transformation to obtain an accurate time domain numerical solution, thereby obtaining the temperature distribution changes in the medium film 2, and specifically comprises the following steps:
the Laplace transformation is carried out on the heat transfer equation in the formula (3), and the following can be obtained:
wherein s is the Laplacian,an expression indicating the temperature distribution change of the i-th layer material in the Lawster domain, gives a general solution of the temperature distribution change of the thin film layer 2 and the base layer 3 in the Lawster domain:
wherein A is i 、B i As a constant to be solved for,substituting the general solution of the temperature distribution change of the film layer 2 and the substrate layer 3 in the Lawster domain into the boundary condition, namely substituting the formula (6) to the formula (7) into the formula (4), so as to obtain an equation set:
the equation set is combined to obtain constant term A of temperature distribution change of film layer 2 1 、B 1 Is represented by the expression:
wherein f(s) is the Laplace transform function of f (t); alpha=k 1 λ 1 /k 2 λ 2 Will A 1 、B 1 The expression of (2) is replaced by the expression (6) to obtain the expression of the temperature distribution change of the film layer 2 in the Lawster domainThe temperature distribution change delta T of the film layer 2 can be obtained by a numerical method 1 (z，t)。
For a substrate 3 of semi-infinite thickness, if the thermal conductivity of the substrate 3 is much higher than that of the film 2, the presence of the substrate 3 corresponds to the placement of a heat sink on one side of the film 2, and after absorption of the laser pulse 1 energy, the temperature rise inside the polymer film 2 caused by the diffusion of the heat pulse will decay at a very rapid rate. The substrate 1 has extremely strong heat dissipation capability, no temperature rise in the substrate is visible, the temperature distribution and heat flow at the interface of the film 2 and the substrate 3 are continuous, the heat conduction model can be further simplified, and the temperature distribution of the film layer 2 changes by delta T 1 (z, t) is:
wherein DeltaT 1_0 ＝q/c 1 ρ 1 Ad 1 The physical meaning is the average temperature rise inside the film 2 in a short time (numerically equal to the overall average temperature rise after the adiabatic film 2 tends to be thermally stable), c 1 Represents the specific heat ρ of the dielectric thin film 2 1 The film density of the dielectric film 2 is represented, and a represents the irradiation area of the dielectric film 2 to receive the laser pulse 1.
(5) And adjusting the thermal diffusion coefficient of the medium film in the thermal conduction model by taking the thermal diffusion coefficient of the medium film as a unique unknown variable to obtain the temperature distribution change of the medium film under the thermal diffusion coefficient, calculating to obtain a corresponding simulation response current until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and taking the thermal diffusion coefficient of the medium film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the medium film.
Calculating time domain signal i according to temperature distribution change in dielectric film sim (t) time-domain signal i sim (t) Fourier transforming to obtain a simulation response current spectrum i sim (f) Wherein the time domain signal i sim The calculation formula of (t) is as follows:
wherein A represents the irradiation area of the medium film for receiving laser pulse, d p Represents the thickness of the dielectric film, χ is a constant term, χ= (α) ε -α z )ε 0 ε r ，α ε Is the temperature coefficient of dielectric constant, alpha z Is the coefficient of thermal expansion, ε 0 For vacuum dielectric constant, ε r The relative permittivity of the dielectric thin film, E (z), is the electric field distribution inside the dielectric thin film, Δt (z, T) is the temperature distribution change inside the dielectric thin film, z represents the spatial position along the thickness direction of the dielectric thin film, and T represents time.
Fitting the simulation response current and the thermal response current specifically comprises the following steps:
obtaining a thermal response current spectrum in the frequency domainAnd a simulated response current spectrum i sim (f) The error function between the two is expressed as the sum of the complex difference magnitudes of the two currents at each frequency point multiplied by the proportional term:
wherein F (D) 1 ) Representation ofAnd i sim (f) Error function between->Representing the frequency point f l Amplitude of upper thermal response current spectrum, i sim (f l ，D 1 ) Indicating that the thermal diffusivity of the dielectric film is set to D 1 Time-frequency point f l Upper simulation response to the magnitude of the current spectrum, if F (D 1 ) If the value of (2) is smaller than the preset threshold value, the response current and the thermal response current are simulatedThe fitting degree reaches a preset value.
Set D 1 Calculating the temperature distribution variation and thus the simulated response current spectrum i sim (f) And error function F (D 1 ) If F (D) 1 ) If the value of (2) is not less than the preset threshold value, continuing to adjust D 1 Up to a set value of D 1 The fitting degree of the simulation response current and the thermal response current can reach a preset value, and D is the same time 1 The final measurement result is the measurement of the thermal diffusivity of the dielectric film.
In experimental verification, the substrate is made of organic glass, the dielectric film is made of PVDF-TrEE (80/20) with the thickness of 1.4 mu m, the thermal diffusion coefficient measuring method provided by the invention is used for measuring, the fitting result of the simulated response current signal and the thermal response current signal on the frequency domain is shown as figure 2, and the experimental curve, the experimental calibration curve and the simulated fitting curve are i respectively exp (f)、And i sim (f) The final measured thermal diffusivity of the film was 9.32X10 -8 m 2 And/s, which is close to a reference value of a literature, proves that the measurement accuracy of the invention can meet the requirement.
Example 2:
a thermal diffusivity measurement device for a film of a substrate-bearing medium, comprising:
a tape substrate sample comprising a substrate and a dielectric film deposited on a surface of the substrate;
the direct current power supply is connected to the substrate-carrying sample and is used for applying direct current voltage to two sides of the dielectric film in the substrate-carrying sample;
a pulse light source for applying a laser pulse to the dielectric thin film;
the measuring circuit is used for collecting a thermal response current signal generated by thermal disturbance in the sample with the substrate;
the heat conduction model unit is used for constructing a heat conduction model of the medium film-substrate according to the structure of the sample with the substrate, and the heat conduction model is used for calculating the temperature distribution change in the medium film;
and the fitting unit is used for adjusting the thermal diffusion coefficient of the dielectric film in the thermal conduction model by taking the thermal diffusion coefficient of the dielectric film as a unique unknown variable to obtain the temperature distribution change of the dielectric film under the thermal diffusion coefficient, calculating to obtain a corresponding simulation response current signal until the fitting degree of the simulation response current signal and the thermal response current signal reaches a preset value, and taking the thermal diffusion coefficient of the dielectric film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the dielectric film.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (8)
1. The method for measuring the thermal diffusivity of the dielectric film with the substrate is characterized by comprising the following steps of:
preparing a sample with a substrate, depositing a dielectric film on the surface of the substrate, and carrying out metallization treatment;
applying direct current voltage to two sides of a dielectric film in a sample with a substrate, and generating an electric field uniformly distributed in the dielectric film;
applying laser pulse to the dielectric film, and collecting thermal response current generated by thermal disturbance in the sample with the substrate through a measuring circuit;
constructing a medium film-substrate heat conduction model according to the structure of the sample with the substrate, wherein the heat conduction model is used for calculating the temperature distribution change in the medium film;
the thermal diffusion coefficient of the medium film in the thermal conduction model is adjusted by taking the thermal diffusion coefficient of the medium film as the only unknown variable, the temperature distribution change of the medium film under the thermal diffusion coefficient is obtained, the corresponding simulation response current is calculated based on the temperature distribution change, the steps are repeated until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and the thermal diffusion coefficient of the medium film set in the thermal conduction model at the moment is taken as a measurement result, so that the thermal diffusion coefficient of the medium film is obtained;
the established heat conduction model is specifically as follows:
simplifying a heat conduction model of a sample with a substrate into a double-layer structure, wherein the heat conduction model comprises a film layer and a substrate layer, subscripts i=1 and 2 respectively refer to the film layer and the substrate layer, the conduction of laser pulses as heat pulses in the thickness direction of a medium film accords with a one-dimensional heat conduction equation, and the material of an ith layer has the following heat conduction equation:
wherein z represents a spatial position along the thickness direction of the dielectric thin film, t represents time, and D i Is the thermal diffusivity, deltaT, of the material of the i-th layer i (z, t) means the temperature distribution change in the material of the ith layer, z i-1 、z i The space coordinates of the front and rear boundary surfaces of the layer material in the thickness direction are respectively z 0 Thickness d of i-th layer material =0 i ＝z i -z i-1 ；
The boundary conditions are:
wherein k is i Is the heat conductivity coefficient of the material of the i layer, the z=0 point is the incident plane of the laser pulse, and the thickness of the dielectric film is equal to z 1 -0, the thickness of the substrate being equal to z 2 -z 1 F (t) is a function of time of the heat flux density generated at z=0 after the laser pulse is absorbed;
combining Laplace variation method and numerical method, obtaining respective temperature distribution variation of the film layer and the substrate layer in Laplace domain, and applying numerical method to carry out inverse Laplace transformation to obtain accurate time domain numerical solution, thereby obtaining temperature distribution variation in the medium film, which comprises the following specific steps:
the Laplace transformation is carried out on the heat transfer equation, and the method can be obtained:
wherein s is the Laplacian,an expression indicating the temperature distribution change of the i-th layer material in the Lawster domain, and obtaining a general solution of the temperature distribution change of the film layer and the basal layer in the Lawster domain:
wherein A is i 、B i As a constant to be solved for,substituting the general solution of the temperature distribution change of the film layer and the basal layer in the Lawster domain into the boundary condition to obtain an equation set:
the equation set is combined to obtain a constant term A of the temperature distribution change of the film layer 1 、B 1 Is represented by the expression:
wherein f(s) is the Laplace transform function of f (t); alpha=k 1 λ 1 /k 2 λ 2 Will A 1 、B 1 The expression of (2) is replaced into an equation set to obtain the expression of the change of the film layer temperature distribution in the Lawster domainThen the temperature distribution change delta T of the film layer can be obtained by a numerical method 1 (z,t)。
2. The method for measuring thermal diffusivity of a dielectric film having a substrate as set forth in claim 1, wherein if the thermal conductivity of the substrate is far higher than that of the dielectric film, the temperature distribution of the film layer varies by ΔT 1 (z, t) is:
wherein DeltaT 1_0 ＝q/c 1 ρ 1 Ad 1 The physical meaning is the average temperature rise inside the film in a short time, c 1 Represents the specific heat, ρ, of the dielectric film 1 The film density of the dielectric film is represented, and a represents the irradiation area of the dielectric film receiving the laser pulse.
3. The method for measuring the thermal diffusivity of a dielectric film with a substrate according to claim 1, wherein fitting the simulated response current and the thermal response current is specifically as follows:
obtaining a thermal response current spectrum in the frequency domainAnd a simulated response current spectrum i sim (f) The error function between the two is expressed as the complex difference amplitude of two currents at each frequency pointMultiplying by the sum of the proportional terms:
wherein F (D) 1 ) Representation ofAnd i sim (f) Error function between->Representing the frequency point f l Amplitude of upper thermal response current spectrum, i sim (f l ,D 1 ) Indicating that the thermal diffusivity of the dielectric film is set to D 1 Time-frequency point f l Upper simulation response to the magnitude of the current spectrum, if F (D 1 ) If the value of (2) is smaller than the preset threshold value, the fitting degree of the simulation response current and the thermal response current reaches the preset value.
4. The method for measuring the thermal diffusivity of a dielectric film with a substrate according to claim 3, wherein the simulated response current spectrum i sim (f) The acquisition of (1) is specifically as follows: calculating simulation response current i according to temperature distribution change in dielectric film sim (t) to i in time domain sim (t) Fourier transforming to obtain a simulation response current spectrum i sim (f) Wherein i is sim The calculation formula of (t) is as follows:
wherein A represents the irradiation area of the medium film for receiving laser pulse, d p Represents the thickness of the dielectric film, χ is a constant term, χ= (α) ε -α z )ε 0 ε r ，α ε Is the temperature coefficient of dielectric constant, alpha z Is the coefficient of thermal expansion, ε 0 For vacuum dielectric constant, ε r E (z) is the electric field distribution in the dielectric film, deltaT 1 (z, t) is a temperature distribution change in the dielectric thin film, z represents a spatial position in the thickness direction of the dielectric thin film, and t represents time.
5. The method for measuring thermal diffusivity of a dielectric film with a substrate as set forth in claim 3, wherein a thermal response current spectrum is obtainedThe method comprises the following steps:
collecting thermal response current i generated by thermal disturbance in sample with substrate through measuring circuit exp (t) the measuring circuit comprises an isolation capacitor, an amplifier and an oscilloscope, wherein the current generated by thermal disturbance in the sample with the base flows through the isolation capacitor and is amplified by the amplifier to form a thermal response current i exp (t) and is acquired and recorded by an oscilloscope; i in time domain exp (t) after Fourier transformation, performing distortion compensation in a frequency response calibration mode to obtain a thermal response current spectrum
6. The method for measuring the thermal diffusivity of a film of a substrate medium according to claim 1, wherein the preparation of the sample with substrate is specifically:
and (3) obtaining a material with a smooth and flat surface as a substrate, and sequentially carrying out metallization treatment, dielectric film deposition and metallization treatment if the substrate is an insulator, or sequentially carrying out dielectric film deposition and metallization treatment if the substrate is a conductor.
7. The method of claim 6, wherein the deposited thickness of the dielectric film is in the order of micrometers, the metallized metal thickness is in the order of nanometers, and the thickness of the substrate is semi-infinite relative to the thickness of the dielectric film.
8. A device for measuring a thermal diffusivity of a film of a base medium, characterized in that it comprises:
a substrate-carrying sample comprising a substrate and a dielectric film deposited on a surface of the substrate;
the direct current power supply is connected to the substrate-carrying sample and is used for applying direct current voltage to two sides of the dielectric film in the substrate-carrying sample;
a pulse light source for applying a laser pulse to the dielectric thin film;
the measuring circuit is used for collecting thermal response current generated by thermal disturbance in the sample with the substrate;
a heat conduction model unit for constructing a heat conduction model of the dielectric thin film-substrate according to the structure of the sample with the substrate, wherein the heat conduction model is used for calculating the temperature distribution change in the dielectric thin film;
and the fitting unit is used for adjusting the thermal diffusion coefficient of the dielectric film in the thermal conduction model by taking the thermal diffusion coefficient of the dielectric film as a unique unknown variable to obtain the temperature distribution change of the dielectric film under the thermal diffusion coefficient, calculating the corresponding simulation response current based on the temperature distribution change until the fitting degree of the simulation response current and the thermal response current reaches a preset value, and taking the thermal diffusion coefficient of the dielectric film set in the thermal conduction model at the moment as a measurement result to obtain the thermal diffusion coefficient of the dielectric film.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2009034787A1 (en) * | 2007-09-11 | 2009-03-19 | National Institute Of Advanced Industrial Science And Technology | Thin film thermophysical property measuring method and thin film thermophysical property measuring apparatus |
| CN101975794A (en) * | 2010-09-09 | 2011-02-16 | 复旦大学 | 3 omega thermal conductivity measurement scheme suitable for metal film material |
| CN109557129A (en) * | 2018-10-29 | 2019-04-02 | 同济大学 | A kind of measurement method of film thermal diffusion coefficient |
| CN109765270A (en) * | 2018-12-26 | 2019-05-17 | 西安交通大学 | A method of the system and measurement noncrystal membrane phase transformation of measurement noncrystal membrane phase transformation |
| CN111024754A (en) * | 2019-12-29 | 2020-04-17 | 北京工业大学 | Method for measuring thermal conductivity of thin film material |
| CN112415046A (en) * | 2020-10-30 | 2021-02-26 | 同济大学 | System and method for measuring longitudinal thermal diffusion coefficient of film based on medium detector |
| CN113533424A (en) * | 2021-07-29 | 2021-10-22 | 东南大学 | Nondestructive testing method for testing thermophysical properties of multilayer thin film structure |
-
2022
- 2022-01-28 CN CN202210105344.3A patent/CN114384118B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2009034787A1 (en) * | 2007-09-11 | 2009-03-19 | National Institute Of Advanced Industrial Science And Technology | Thin film thermophysical property measuring method and thin film thermophysical property measuring apparatus |
| CN101975794A (en) * | 2010-09-09 | 2011-02-16 | 复旦大学 | 3 omega thermal conductivity measurement scheme suitable for metal film material |
| CN109557129A (en) * | 2018-10-29 | 2019-04-02 | 同济大学 | A kind of measurement method of film thermal diffusion coefficient |
| CN109765270A (en) * | 2018-12-26 | 2019-05-17 | 西安交通大学 | A method of the system and measurement noncrystal membrane phase transformation of measurement noncrystal membrane phase transformation |
| CN111024754A (en) * | 2019-12-29 | 2020-04-17 | 北京工业大学 | Method for measuring thermal conductivity of thin film material |
| CN112415046A (en) * | 2020-10-30 | 2021-02-26 | 同济大学 | System and method for measuring longitudinal thermal diffusion coefficient of film based on medium detector |
| CN113533424A (en) * | 2021-07-29 | 2021-10-22 | 东南大学 | Nondestructive testing method for testing thermophysical properties of multilayer thin film structure |
Non-Patent Citations (1)
| Title |
|---|
| "拉曼闪光法测量纳米薄膜热扩散率的理论分析";胡玉东;《工程热物理学报》;第36卷(第10期);全文 * |
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