CN115165956A - Method and device for measuring thermal conductivity of thin film based on frequency domain photo-thermal radiation - Google Patents
Method and device for measuring thermal conductivity of thin film based on frequency domain photo-thermal radiation Download PDFInfo
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Abstract
The invention discloses a method and a device for measuring the thermal conductivity of a film based on frequency domain photothermal radiation, wherein the measuring method comprises the following steps: firstly, preparing a film to be measured on a substrate, preparing a heating layer on the film to obtain a sample to be measured, and preparing the heating layer on the substrate to obtain a reference sample; measuring a measured sample and a reference sample by using a measuring device; carrying out Fourier transform on the acquired signals, taking the frequency spectrum amplitude with the frequency greater than 0, and dividing the frequency spectrum amplitude of the reference sample by the amplitude of the sample Fu Pinpu to be detected to obtain dimensionless PTR data; fitting the PTR data to obtain coefficients a and b; and measuring the thicknesses of the film layers and the substrate, and calculating to obtain the thermal conductivity of the measured film. The invention uses a non-contact measuring method, avoids the damage to the surface of the measured film, can calculate the thermophysical property parameter of the measured film by only one-time measurement, obtains a measuring signal with better signal-to-noise ratio by adjusting the duty ratio and the period of the rectangular pulse, and reduces the difficulty of infrared signal detection.
Description
Technical Field
The invention relates to the technical field of non-contact optical measurement, in particular to a method and a device for measuring the thermal conductivity of a film based on frequency domain photothermal radiation.
Background
With the continuous improvement of the integration level of photoelectric devices, the application of semiconductors, metals, organic matters and nano-doped films is more and more extensive. The thermal properties of various films with nanometer-scale thicknesses determine the heat conduction and dissipation of the device. Techniques for accurately measuring the thermal properties of thin films have attracted attention in recent years. However, the currently used nano-film thermophysical property measurement technology still has some defects. For example, when the thermal conductivity is measured by a 3 ω method, a patterned metal electrode needs to be manufactured on the surface of a measured sample, and at this time, the photoetching process often damages an organic film; in addition, the preparation process of the metal electrode is complex and the cost is high.
Photothermal radiometry (PTR) belongs to a non-contact, non-destructive measurement technique, first proposed by Nordal and Kanstada in 1979. This technique is based on the photothermal effect, i.e., the intensity of surface infrared radiation increases as the sample absorbs an increase in incident light temperature. Thus, heating the sample with periodically modulated intensity of light will result in a periodic variation of the temperature of the sample surface, thereby radiating a periodically varying infrared signal. The infrared radiation signal contains thermophysical information of the sample. The thermal characteristic parameters of the sample can be obtained by inversion calculation by comparing the amplitude or phase of the radiation signal collected by the infrared detector with the amplitude or phase of the original modulation signal. The PTR method has been proven to be an effective technique for measuring thermophysical properties.
However, the existing PTR measuring devices all use a light source that is sinusoidally modulated in the time domain to heat the surface of the sample to be measured, and the modulation signal is a single frequency signal. In order to obtain infrared radiation data under heating of light sources with different modulation frequencies, the frequency of a sinusoidal modulation signal needs to be changed within a certain frequency range and in a certain step length, measurement is repeatedly carried out, a relation curve of amplitude/phase difference and modulation frequency is drawn through data processing, and then thermophysical property parameters of a measured sample are obtained through curve fitting and inversion. In order to ensure the accuracy of measuring the thermophysical parameters, the change step length of the frequency modulation frequency cannot be too large; therefore, the data volume required to be measured is large, and the experimental process is complicated. In addition, when the thermal conductivity of the sample to be measured is high, the light source needs to be modulated at high frequency. When external modulation techniques are used, high requirements are placed on the bandwidth of the modulator. Meanwhile, under the irradiation of a high-frequency modulation light source, the temperature rise of the surface of a detected sample is often low, so that an infrared radiation signal is weak, and a phase-locked amplification technology is required to detect the weak signal. These problems have made the application of the PTR measurement method rather limited.
Disclosure of Invention
The invention aims to provide a method and a device for measuring the thermal conductivity of a film based on frequency domain photothermal radiation, wherein a non-contact measuring method is used, the damage to the surface of the film to be measured is avoided, a rectangular pulse heating light and frequency domain signal processing technology is used, the thermophysical property parameter of the film to be measured can be calculated by only one-time measurement, a measuring signal with better signal-to-noise ratio is obtained by adjusting the duty ratio and the period of the rectangular pulse, and the difficulty in infrared signal detection is reduced.
In order to achieve the purpose, the invention provides a method for measuring the thermal conductivity of a film based on frequency domain photothermal radiation, which comprises the following steps:
s1, firstly preparing a tested sample and a reference sample: preparing a film to be measured on a substrate, preparing a heating layer on the film to obtain a sample to be measured, and preparing the heating layer on the substrate to obtain a reference sample;
s2, measuring the tested sample and the reference sample by adopting a measuring device;
s3, carrying out Fourier transform on the acquired signals, taking the frequency spectrum amplitude with the frequency greater than 0, and dividing the frequency spectrum amplitude of the reference sample by the amplitude of the sample Fu Pinpu to be detected to obtain dimensionless PTR data;
s4, fitting the PTR data to obtain coefficients a and b;
and S5, measuring the thicknesses of the film layers and the substrate, and calculating to obtain the thermal conductivity of the measured film.
Preferably, the step S3 of obtaining the dimensionless PTR data specifically includes, according to a PTR measurement principle, when the surface of the sample to be measured is irradiated by using a rectangular pulse light source, after the sample to be measured absorbs photon energy, changing the surface temperature of the sample by a photothermal effect, radiating energy outwards, and detecting by an infrared detector to obtain a thermal radiation signal, thereby obtaining temperature change information of the surface of the sample to be measured;
according to the heat conduction characteristic, if the light spot of the heating light is uniform and has a size smaller than the heat diffusion length, and the radiation signal collected by the detector comes from the central area of the heating light, the heat conduction of the sample is described by a one-dimensional model:
when the film to be measured is prepared on the substrate and the surface is prepared with the heating layer, in the above formula, k eq Is the equivalent thermal conductivity of the sample being measured (ρ Cp) eq D is the product of equivalent heat capacity and density of the sample to be measured, d is the total thickness of the sample to be measured, T is the temperature rise of the sample to be measured, when the sample is composed of three materials, the thicknesses are d respectively 1 、d 2 、d 3 Equivalent thermal conductivity of the measured sample:
wherein R is 12 、R 23 The total thickness of the tested sample is as follows for the interface thermal resistance among different materials:
d＝d 1 +d 2 +d 3 (3)；
when the heating light is a rectangular pulse, in one heating period, the heating light is regarded as an external heat source described by a piecewise function, thereby introducing piecewise boundary conditions, which are defined as a heating segment and a heat dissipation segment, and the initial conditions and the boundary conditions of formula (1) in the two segments can be expressed as:
q is heating power density, and is related to heating light power density, light absorption coefficient of the heating layer, area of heating light spot and thickness of the heating layer; τ is the rectangular pulse duration; tau is 0 For the rectangular pulse period, the temperature rise of the sample to be measured (hereinafter, equivalent parameter k in the formula) can be obtained from the formula (1) and the above boundary conditions eq And (ρ Cp) eq With k and ρ Cp substituted):
t is more than or equal to 0 and less than or equal to tau in the heating section;
t is more than or equal to t and less than or equal to t in heat dissipation section 0 ；
For the heating section, the temperature rise over time at z = d is obtained from equation (4):
obtaining the radiation intensity of the surface of the tested sample:
wherein, T 0 Is the initial temperature of the sample,. Epsilon.is the surface emissivity of the sample to be measured,. Sigma.is the Stefan-Boltzmann constant, and when the surface temperature T (T) is T (T) + T 0 ≈T 0 And then, the above formula is simplified as follows:
setting eta 0 For detecting coefficients for infrared optical systems：
Wherein D is the aperture of the optical system, f is the focal length of the optical system, eta is the transmittance of the optical system, S is the area of the photosensitive surface of the detector, and the vertical axis magnification of the beta optical system is used for obtaining the output voltage of the infrared detector:
wherein, for the responsivity of the detector, it is fourier transformed to:
in order to eliminate the influence of errors of the parameters on the measurement result, in the actual measurement, a reference sample consisting of a substrate and a heating layer is prepared, the frequency ω of the circle is greater than 0 spectral amplitude, and the spectral amplitude of the measured sample is divided by the spectral amplitude of the reference sample to obtain a dimensionless quantity PTR:
wherein A is a constant coefficient, namely the ratio of the thickness of the measured sample to the thickness of the reference sample.
Preferably, the step S4 of fitting the PTR data to obtain the coefficients a and b is to perform curve fitting on the measurement results processed in the same way by using formula (12), so as to obtain the coefficients a and b, where a and b are respectively:
wherein the lower subscripts s, r represent the measured sample and the reference sample, respectively.
Preferably, the thicknesses of the film layers and the substrate are measured in the step S5, and the thermal conductivity of the measured film is calculated and obtained, specifically, the equivalent thermal diffusion efficiency and coefficient of the measured sample and the reference sample:
when the thicknesses of the substrate, the measured film and the heating layer are known, the equivalent thermal diffusion coefficient alpha can be calculated according to the fitted a and b s And alpha r ；
In the one-dimensional model, the equivalent heat capacity density product (ρ Cp) eq Expressed as:
when the interface thermal resistance between each layer of the tested sample is neglected, the thermal conductivity k of the tested film can be calculated according to the formula (2) and the known thickness of each layer 2 。
The utility model provides a film thermal conductivity measuring device based on frequency domain light and heat radiation, measuring device includes heating light source, sets up acousto-optic modulator, the setting of heating light source rear end are in the heating light convergence optical system, the setting of acousto-optic modulator rear end are in the sample platform, the setting of heating light convergence optical system rear end are in the infrared optical system, the setting of sample platform rear end are in the infrared detector and the setting of infrared optical system rear end are in the signal acquisition processing module of infrared detector rear end, be connected with signal generator on the acousto-optic modulator.
Therefore, the method and the device for measuring the thermal conductivity of the film based on the frequency domain photothermal radiation have the following beneficial effects:
(1) The method comprises the steps of irradiating the surface of a film to be detected by adopting a light source with a rectangular pulse time domain waveform, carrying out Fourier transform on data after detecting an infrared radiation signal on the surface of a sample under the excitation of a rectangular light pulse, wherein the rectangular pulse signal can be regarded as linear combination of sinusoidal signals with different frequencies, and after the Fourier transform, the amplitude/phase value of a radiation signal frequency domain is the amplitude/phase value of an output signal after different frequency components pass through the sample (which can be regarded as a system), so that the frequency domain information of the response of the film to be detected under the heating of the light source with different frequencies can be obtained by only one-time measurement, and the change curve of the amplitude/phase along with the frequency can be directly obtained.
(2) And fitting the measurement result by adopting a theoretical expression of system response in the frequency domain to obtain the thermophysical property parameters of the measured sample. In addition, as the duty ratio and the period of the rectangular pulse are controllable, more appropriate surface temperature rise can be obtained by adjusting the two parameters, so that the detection difficulty caused by the undersize signal-to-noise ratio of the radiation signal is avoided.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a schematic illustration of a test sample used in the invention;
FIG. 2 is a schematic view of a measuring device according to the present invention;
FIG. 3 is a schematic view of a measuring apparatus in the embodiment operating step S2;
FIG. 4 is a graph showing the temperature change of the surface of the sample in operation S3 in the examples, wherein (a) is a sample to be measured and (b) is a reference sample;
fig. 5 shows the dimensionless PTR data and the fitting result in operation S3 of the embodiment.
Detailed Description
The invention provides a method for measuring the thermal conductivity of a film based on frequency domain photothermal radiation, which comprises the following steps:
s1, firstly preparing a tested sample and a reference sample: preparing a film to be tested on a substrate, preparing a heating layer on the film to obtain a sample to be tested, and preparing the heating layer on the substrate to obtain a reference sample.
And S2, measuring the tested sample and the reference sample by adopting a measuring device.
S3, carrying out Fourier transform on the acquired signals, taking a frequency spectrum amplitude value with the frequency being more than 0, dividing the frequency spectrum amplitude value of the reference sample by the amplitude value of the sample to be detected Fu Pinpu to obtain dimensionless PTR data, irradiating the surface of the sample to be detected by using a rectangular pulse light source according to the PTR measuring principle, changing the surface temperature of the sample through the photothermal effect after the sample to be detected absorbs photon energy, radiating the energy outwards, detecting by using an infrared detector to obtain a thermal radiation signal, and obtaining the temperature change information of the surface of the sample to be detected;
according to the heat conduction characteristic, if the light spot of the heating light is uniform and has a size smaller than the thermal diffusion length, and the radiation signal collected by the detector comes from the central area of the heating light, the heat conduction of the sample is described by a one-dimensional model:
when the film to be measured is prepared on the substrate and the surface is prepared with the heating layer, in the above formula, k eq Is the equivalent thermal conductivity of the sample being measured (ρ Cp) eq Is the product of equivalent heat capacity and density of the tested sample, d is the total thickness of the tested sample, T is the temperature rise of the tested sample, when the sample is composed of three materials, the thicknesses are d 1 、d 2 、d 3 Equivalent thermal conductivity of the measured sample:
wherein R is 12 、R 23 The total thickness of the tested sample is as follows for the interface thermal resistance among different materials:
d＝d 1 +d 2 +d 3 (3)；
when the heating light is a rectangular pulse, in one heating period, the heating light is regarded as an external heat source described by a piecewise function, thereby introducing piecewise boundary conditions, which are defined as a heating segment and a heat dissipation segment, and the initial conditions and the boundary conditions of formula (1) in the two segments can be expressed as:
q is heating power density, and is related to heating light power density, light absorption coefficient of the heating layer, area of heating light spot and thickness of the heating layer; τ is the rectangular pulse duration; tau is 0 For the rectangular pulse period, the temperature rise of the sample to be measured (hereinafter, equivalent parameter k in the formula) can be obtained from the formula (1) and the above boundary conditions eq And (ρ Cp) eq With k and ρ Cp replaced):
t is more than or equal to 0 and less than or equal to tau in the heating section;
t is more than or equal to t and less than or equal to t in heat dissipation section 0 ；
For the heating section, the temperature rise over time at z = d is obtained from equation (4):
obtaining the radiation intensity of the surface of the tested sample:
wherein, T 0 Is the initial temperature of the sample,. Epsilon.is the surface emissivity of the sample to be measured,. Sigma.is the Stefan-Boltzmann constant, and when the surface temperature T (T) is T (T) + T 0 ≈T 0 Then, the above formula is simplified as:
setting eta 0 Detection coefficients for the infrared optical system:
wherein D is the aperture of the optical system, f is the focal length of the optical system, eta is the transmittance of the optical system, S is the area of the photosensitive surface of the detector, and the vertical axis magnification of the beta optical system is used for obtaining the output voltage of the infrared detector:
wherein, for the responsivity of the detector, it is fourier transformed to:
in order to eliminate the influence of errors of the parameters on the measurement result, in the actual measurement, a reference sample consisting of a substrate and a heating layer is prepared, the frequency ω of the circle is greater than 0 spectral amplitude, and the spectral amplitude of the measured sample is divided by the spectral amplitude of the reference sample to obtain a dimensionless quantity PTR:
wherein A is a constant coefficient, namely the ratio of the thickness of the measured sample to the thickness of the reference sample.
S4, fitting the PTR data to obtain coefficients a and b; the measurement results after the same treatment are subjected to curve fitting by using the formula (12), so that coefficients a and b are obtained, wherein the coefficients a and b are respectively:
wherein the lower subscripts s, r represent the measured sample and the reference sample, respectively.
S5, measuring the thickness of each film layer and the substrate, and calculating to obtain the thermal conductivity of the measured film, the equivalent thermal diffusion efficiency and coefficient of the measured sample and the reference sample:
when the thicknesses of the substrate, the measured film and the heating layer are known, the equivalent thermal diffusion coefficient alpha can be calculated according to the fitted a and b s And alpha r ；
In the one-dimensional model, the equivalent heat capacity density product (ρ Cp) eq Expressed as:
when the interface thermal resistance between each layer of the tested sample is neglected, the thermal conductivity k of the tested film can be calculated according to the formula (2) and the known thickness of each layer 2 。
FIG. 1 is a schematic structural view of a sample to be measured, in which "1" in (a) denotes a heating layer, "2" denotes a thin film to be measured, and "3" denotes a substrate; in (b), "1" denotes a heating layer, and "3" denotes a substrate. Wherein the heating layer '1' has the function of absorbing incident heating light as a heating body and radiating an infrared signal with a certain infrared emissivity. To reduce the impact on the thermal conductivity measurement, the heating layer is required to have a thermal conductivity much greater than that of the film being measured.
As shown in FIG. 2, the measuring device comprises a heating light source 1, an acousto-optic modulator 2 arranged at the rear end of the heating light source 1, a heating light converging optical system 3 arranged at the rear end of the acousto-optic modulator 2, a sample stage 4 arranged at the rear end of the heating light converging optical system 3, an infrared optical system 5 arranged at the rear end of the sample stage 4, an infrared detector 6 arranged at the rear end of the infrared optical system 5 and a signal acquisition processing module 7 arranged at the rear end of the infrared detector 6, wherein the acousto-optic modulator 2 is connected with a signal generator 8. The method comprises the steps that firstly, a signal generator is used for generating a rectangular pulse signal, the generated rectangular pulse signal is used for modulating output light of a heating light source by a modulator to obtain rectangular pulse heating light, the rectangular pulse heating light reaches a sample table through a heating light converging optical system (a sample is placed in the sample table, the sample table is vacuumized to reduce the influence of convection heat on a measurement result), a heating layer on the surface of the sample absorbs incident light to generate temperature rise, so that the lower-layer film to be measured is heated, infrared signals are radiated outwards, the radiated infrared signals are received by an infrared optical system and converged to a photosensitive surface of an infrared detector, the infrared detector converts the received infrared radiation signals into electric signals, and finally the electric signals are collected by a signal collecting module and transmitted to a signal processing module to process and calculate the measurement result, so that the heat conductivity of the film to be measured is obtained.
The technical solution of the present invention is further illustrated by the accompanying drawings and examples.
Examples
The specific steps for measuring the thermal conductivity of the Polyimide (PI) film are as follows:
the method comprises the following steps: the sample schematic diagram is shown in fig. 1, a PI film (polyimide) 2 with the thermal conductivity to be measured is spin-coated on a quartz substrate 3, and a Cr metal layer 1 is prepared on the PI film 2 by utilizing a magnetron sputtering technology to obtain a measured sample; sputtering a Cr metal layer '1' on a quartz substrate '3' to obtain a reference sample; wherein the thickness of the quartz substrate 3 layer is 400 μm, and the product of heat capacity and density is 730 × 2200J/(kg × m) 3 ) The thickness of PI film "2" is 200nm, and the product of heat capacity density is 1100 × 1300J/(kg × m) 3 ) The thickness of the Cr metal layer '1' is 100nm, and the product of heat capacity and density is 448X 7150J/(kg m) 3 ) The emissivity was 0.31.
Step two: as shown in FIG. 3, the thermal conductivity measuring apparatus has a heating light source of 532nm continuous output laser 11, a laser output power of 2W, and an emergent spot radius of 1mm. The heating light converging optical system is composed of lenses 12, 14 having a focal length of 100 mm. A lens 12 is arranged 50mm behind a laser 11 to converge laser into an acousto-optic modulator 13, a signal generator 16 generates a rectangular pulse signal with the period of 100ms and the duty ratio of 0.1, the acousto-optic modulator 13 is controlled to work, modulation of 532nm laser is achieved, and rectangular pulse heating light (the heating time is 10 ms) is obtained. A lens 14 is arranged behind the acousto-optic modulator 13, the distance between the lens 14 and the lens 12 is 200mm, and the light beam is collimated to enable the radius of a light spot to be 1mm. The collimated heating light is incident on the sample stage 18 through the reflecting mirror 15, and heats the surface of the sample 17. Then, an infrared optical system consisting of two parabolic metal reflectors 19 and 20 with a focal length of 50.8mm, a reflectivity of 96% and a caliber of 50.8mm (wherein the distance between the parabolic metal reflector 19 and the surface of the sample 17 is 50mm, the distance between the parabolic metal reflector 20 and an infrared detector 21 is 50 mm) is used for collecting the infrared radiation of the heating area of the sample 17, the infrared radiation reaches a photosensitive surface (the radius of the photosensitive surface is 0.5 mm) of the infrared detector 21, the infrared detector 21 (the responsivity of the detector is 40000V/W) converts the received infrared radiation signal into an electric signal, and the electric signal is collected by a signal collection card 22 and then transmitted to a computer 23 for subsequent processing.
Step three: the data obtained by the acquisition are as shown in fig. 4 (wherein the abscissa represents time in ms and the ordinate represents voltage in V, where (a) is the sample to be measured and (b) is the reference sample), and the data are acquired a plurality of times and averaged to reduce the influence of noise; the mean value data was fourier transformed and the spectral amplitude with a frequency greater than 0 was taken, and dimensionless PTR data was obtained by dividing the measured sample Fu Pinpu amplitude by the spectral amplitude of the reference sample, as shown in fig. 5 (a) (where the abscissa is frequency, the unit is Hz, and the ordinate is signal amplitude), and it was observed that the curve had a peak with a corresponding frequency of 29270Hz.
Step four: fitting the PTR data using equation (12), as shown in fig. 5 (b), results in parameters a =1.001, a =13.3461, b =13.4388;
step five: substituting the calculated a and b into the formulas (13) - (16), and calculating the thermal conductivity k =0.1086 of the PI film to be measured by combining the thickness of the substrate, the PI and the metal Cr layer and the product of the heat capacity and the density without considering the interface thermal resistance.
Therefore, the method and the device for measuring the thermal conductivity of the film based on the frequency domain photothermal radiation are adopted, a non-contact measuring method is used, the damage to the surface of the film to be measured is avoided, the rectangular pulse heating light is combined with the frequency domain signal processing technology, the thermophysical property parameters of the film to be measured can be calculated by only one-time measurement, the measurement signal with better signal-to-noise ratio is obtained by adjusting the duty ratio and the period of the rectangular pulse, and the difficulty in infrared signal detection is reduced.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.
Claims (5)
1. A method for measuring the thermal conductivity of a film based on frequency domain photothermal radiation is characterized by comprising the following steps:
s1, firstly preparing a tested sample and a reference sample: preparing a film to be measured on a substrate, preparing a heating layer on the film to obtain a sample to be measured, and preparing the heating layer on the substrate to obtain a reference sample;
s2, measuring the tested sample and the reference sample by adopting a measuring device;
s3, carrying out Fourier transform on the acquired signals, taking the frequency spectrum amplitude with the frequency greater than 0, and dividing the frequency spectrum amplitude of the reference sample by the amplitude of the sample Fu Pinpu to be detected to obtain dimensionless PTR data;
s4, fitting the PTR data to obtain coefficients a and b;
and S5, measuring the thicknesses of the film layers and the substrate, and calculating to obtain the thermal conductivity of the measured film.
2. The method for measuring the thermal conductivity of the thin film based on the photothermal radiation in the frequency domain as claimed in claim 1, wherein: the step S3 of obtaining dimensionless PTR data specifically includes, according to a PTR measurement principle, when a rectangular pulse light source is used to irradiate the surface of a sample to be measured, after the sample to be measured absorbs photon energy, changing the surface temperature of the sample through a photothermal effect, radiating energy outwards, and detecting by an infrared detector to obtain a thermal radiation signal, thereby obtaining temperature change information of the surface of the sample to be measured;
according to the heat conduction characteristic, if the light spot of the heating light is uniform and has a size smaller than the heat diffusion length, and the radiation signal collected by the detector comes from the central area of the heating light, the heat conduction of the sample is described by a one-dimensional model:
when the film to be measured is prepared on the substrate and the surface is prepared with the heating layer, in the above formula, k eq Is the equivalent thermal conductivity of the sample to be measured (p Cp) eq Is the product of equivalent heat capacity and density of the tested sample, d is the total thickness of the tested sample, T is the temperature rise of the tested sample, when the sample is composed of three materials, the thicknesses are d 1 、d 2 、d 3 Equivalent thermal conductivity of the measured sample:
wherein R is 12 、R 23 The total thickness of the tested sample is as follows for the interface thermal resistance among different materials:
d＝d 1 +d 2 +d 3 (3)；
when the heating light is a rectangular pulse, in one heating period, the heating light is regarded as an external heat source described by a piecewise function, thereby introducing piecewise boundary conditions, which are defined as a heating segment and a heat dissipation segment, and the initial conditions and the boundary conditions of formula (1) in the two segments can be expressed as:
the heating section is
The heat dissipation section is
q is heating power density, and is related to heating light power density, light absorption coefficient of the heating layer, area of heating light spot and thickness of the heating layer; τ is the rectangular pulse duration; tau is 0 For the rectangular pulse period, the temperature rise of the sample to be measured (equivalent parameter k in the following formula) can be obtained from the formula (1) and the above boundary conditions eq And (ρ Cp) eq With k and ρ Cp replaced):
t is more than or equal to 0 and less than or equal to tau in the heating section;
t is more than or equal to t and less than or equal to t in heat dissipation section 0 ；
For the heating section, the sample surface is obtained from equation (4), i.e. the temperature rise at z = d as a function of time:
obtaining the radiation intensity of the surface of the tested sample:
wherein, T 0 Is the initial temperature of the sample,. Epsilon.is the surface emissivity of the sample to be measured,. Sigma.is the Stefan-Boltzmann constant, and when the surface temperature T (T) is T (T) + T 0 ≈T 0 And then, the above formula is simplified as follows:
setting eta 0 Detection coefficients for the infrared optical system:
wherein D is the aperture of the optical system, f is the focal length of the optical system, eta is the transmittance of the optical system, S is the area of the photosensitive surface of the detector, and the vertical axis magnification of the beta optical system is used for obtaining the output voltage of the infrared detector:
wherein, for the responsivity of the detector, it is fourier transformed to:
in order to eliminate the influence of errors of the parameters on the measurement result, in the actual measurement, a reference sample consisting of a substrate and a heating layer is prepared, the frequency ω of the circle is greater than 0 spectral amplitude, and the spectral amplitude of the measured sample is divided by the spectral amplitude of the reference sample to obtain a dimensionless quantity PTR:
wherein A is a constant coefficient, namely the ratio of the thickness of the measured sample to the thickness of the reference sample.
3. The method for measuring the thermal conductivity of the thin film based on the photothermal radiation in the frequency domain as claimed in claim 1, wherein: in the step S4, fitting the PTR data to obtain the coefficients a and b specifically includes fitting a curve of the measurement result processed in the same way by using the formula (12), to obtain the coefficients a and b, where a and b are:
wherein the lower subscripts s, r represent the measured sample and the reference sample, respectively.
4. The method for measuring the thermal conductivity of the thin film based on the photothermal radiation in the frequency domain as claimed in claim 1, wherein: in the step S5, the thicknesses of the film layers and the substrate are measured, and the thermal conductivity of the measured film is calculated and obtained, specifically, the equivalent thermal diffusion efficiency and coefficient of the measured sample and the reference sample:
when the thicknesses of the substrate, the measured film and the heating layer are known, the equivalent thermal diffusion coefficient alpha can be calculated according to the fitted a and b s And alpha r ；
In the one-dimensional model, the equivalent heat capacity density product (ρ Cp) eq Expressed as:
when the interface thermal resistance among all layers of the tested sample is neglected, the thermal conductivity k of the tested film can be calculated according to the formula (2) and the known thickness of each layer 2 。
5. The utility model provides a film thermal conductivity measuring device based on frequency domain light and heat radiation which characterized in that: the measuring device comprises a heating light source, an acoustic-optical modulator arranged at the rear end of the heating light source, a heating light convergence optical system arranged at the rear end of the acoustic-optical modulator, a sample stage arranged at the rear end of the heating light convergence optical system, an infrared optical system arranged at the rear end of the sample stage, an infrared detector arranged at the rear end of the infrared optical system and a signal acquisition and processing module arranged at the rear end of the infrared detector, wherein the acoustic-optical modulator is connected with a signal generator.
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| CN117288129A (en) * | 2023-11-27 | 2023-12-26 | 承德华实机电设备制造有限责任公司 | Method for detecting thickness of irradiation material contained in tray |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117288129A (en) * | 2023-11-27 | 2023-12-26 | 承德华实机电设备制造有限责任公司 | Method for detecting thickness of irradiation material contained in tray |
| CN117288129B (en) * | 2023-11-27 | 2024-02-02 | 承德华实机电设备制造有限责任公司 | Method for detecting thickness of irradiation material contained in tray |
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