CN115266812B - Method for measuring anisotropic thermal conductivity of solid material - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity
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Abstract
The invention provides a method for measuring anisotropic thermal conductivity of a solid material. A wide first heating electrode, a narrow second heating electrode and a detection electrode are arranged on the surface, far away from the substrate, of the insulating layer, alternating current is sequentially connected to the first heating electrode and the second heating electrode, direct current is simultaneously connected to the detection electrode, and anisotropic heat conductivity of the material is further solved by measuring alternating current thermal response signals of the detection electrode. The method of the invention has the following advantages: (1) The alternating-current thermal response signal of the detection electrode is only sensitive to the heat conductivity of the substrate, so that measurement errors caused by the heat conductivity of the insulating layer, the interface thermal resistance between the insulating layer and the electrode and the interface thermal resistance between the insulating layer and the substrate are eliminated; (2) The anisotropic heat conductivity of the base material is calculated by a method for solving a binary nonlinear equation set, so that a multi-parameter fitting algorithm is avoided, and the solving precision is improved.
Description
Technical Field
The invention relates to the field of semiconductor industry, in particular to a method for measuring anisotropic thermal conductivity of a solid material.
Background
The single electrode 3 omega method is a testing method for representing the thermophysical property of a solid material sample material by measuring the third harmonic component (3 omega signal) of the voltage of a strip-shaped metal electrode, wherein a strip-shaped metal film with a certain shape is processed on the sample to be tested through a photoetching technology and an evaporation/sputtering technology to be used as a testing electrode, and four bonding pads are respectively used as a voltage signal output interface and a heating current input interface at two ends of the testing electrode and are connected with an external testing circuit through a wire bonding technology. An alternating current with a frequency of 1 ω is supplied to the test electrode from the outermost pad, which alternating current signal will generate a temperature fluctuation with a frequency of 2 ω on the electrode and inside the sample due to joule heating effect. In the case of small temperature changes, the resistance of the metal and the temperature satisfy a linear relationship, so that the electrode resistance also fluctuates at the frequency of 2ω, and finally under the combined action of the alternating current of 1ω and the fluctuation of the resistance of 2ω, a voltage signal with the frequencies of 1ω and 3ω simultaneously exists on the electrode. Wherein, the 1 omega voltage signal reflects electrode resistance information, and the 3 omega voltage signal can be used for measuring the thermal conductivity of the material. However, this method has the following disadvantages: (1) The method can only derive the average value of the thermal conductivity of the measured material sample in all directions, and can not distinguish the normal direction and the facing component of the thermal conductivity; (2) The method is based on the semi-infinite assumption of the measured material, and is not applicable to samples with the thickness t s smaller than 50 mu m; (3) The measurement signal of the method is sensitive to the thermal conductivity of the insulating layer, the thermal interface resistance between the insulating layer and the electrodes and the thermal interface resistance between the insulating layer and the substrate, so that the measurement error of the thermal conductivity of the substrate is large.
A double-electrode 3 omega method is provided on the basis of the traditional single-electrode 3 omega method, and two parallel test electrodes with different widths are formed on a solid material sample to be tested through a photoetching technology and an evaporation/sputtering technology. The normal direction component and the facing component of the thermal conductivity of the measured material are derived by measuring the change trend of the 3 omega voltage signals of the two test electrodes along with the frequency and adopting a fitting algorithm. This method has the following disadvantages: (1) The method relies on a multi-parameter fitting algorithm, so that the algorithm convergence is difficult to ensure, and the solving precision is low; (2) The measuring signal of the method is sensitive to the heat conductivity of the insulating layer, the interface thermal resistance between the insulating layer and the electrodes and the interface thermal resistance between the insulating layer and the substrate, so that the measuring error of the anisotropic heat conductivity of the substrate is large.
Thus, current methods for measuring the anisotropic thermal conductivity of solid material samples still require further improvements.
Disclosure of Invention
The present invention aims to solve at least one of the technical problems in the related art to some extent. The invention aims to provide a method for measuring the anisotropic thermal conductivity of a solid material, which can realize high-precision measurement of the anisotropic thermal conductivity of a single solid material.
According to the method for measuring the anisotropic thermal conductivity of the solid material, a measured solid material sample comprises a substrate and an insulating layer which are arranged in a laminated manner;
The method comprises the following steps:
Step S1, a first heating electrode h1, a second heating electrode h2 and a detection electrode S are arranged on at least part of the surface of the insulating layer far away from the substrate, wherein the width of the first heating electrode h1 is larger than that of the second heating electrode h 2;
Step S2, a first alternating current heating current is connected to the first heating electrode h1, a first direct current detection current is connected to the detection electrode S, and a first alternating current thermal response signal DeltaT AC-S1 of the detection electrode S is calculated according to the working parameter of the detection electrode S under the first direct current detection current;
step S3, a second alternating current heating current is connected to the second heating electrode h2, a second direct current detection current is connected to the detection electrode S, and a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode S is calculated according to the working parameter of the detection electrode S under the second direct current detection current;
Step S4, in the finite element simulation, a three-dimensional finite element simulation model comprising the first heating electrode h1, the second heating electrode h2 and the detection electrode S is established, wherein the three-dimensional finite element simulation model has the same size as an actually measured solid material sample;
Step S5, setting simulation working parameters of the first heating electrode h1 in finite element simulation to be the same as actual working parameters of the first heating electrode h1 in actual experimental measurement;
taking a first alternating-current thermal response signal DeltaT AC-S1 of the detection electrode s as a known quantity, according to the relation among a first set normal thermal conductivity k cross, a first set facing thermal conductivity k in and the first alternating-current thermal response signal DeltaT AC-S1, taking one of the first set normal thermal conductivity k cross and the first set facing thermal conductivity k in as an independent variable and the other as a dependent variable, acquiring a first variation curve corresponding to the first heating electrode h 1;
Setting simulation working parameters of the second heating electrode h2 in finite element simulation to be the same as actual working parameters of the second heating electrode h2 in actual experimental measurement;
Taking a second alternating-current thermal response signal DeltaT AC-S2 of the detection electrode s as a known quantity, according to the relation among a second set normal thermal conductivity k 'cross, a second set facing thermal conductivity k' in and the second alternating-current thermal response signal DeltaT AC-S2, taking one of the second set normal thermal conductivity k 'cross and the second set facing thermal conductivity k' in as an independent variable and the other as a dependent variable, obtaining a second variation curve corresponding to the second heating electrode h 2;
and step S6, calculating the actual normal thermal conductivity and the actual facing thermal conductivity of the measured solid material sample based on the first change curve and the second change curve.
According to one embodiment of the present invention, in step S5, specifically, the method includes:
Setting the heating power and the frequency of the first heating electrode h1 in finite element simulation to be respectively the same as the heating power and the frequency of the first heating electrode h1 in actual experimental measurement;
Continuously changing a first set normal thermal conductivity k cross in finite element simulation by taking a first alternating current thermal response signal DeltaT AC-S1 of the detection electrode s as a known quantity, solving a unitary nonlinear equation to obtain a first set thermal conductivity facing k in corresponding to each first set normal thermal conductivity k cross, and finally obtaining a first change curve k in(kcross; the unitary nonlinear equation is obtained through a calculation relation among a first set normal thermal conductivity k cross, a first set surface thermal conductivity k in and a first alternating-current thermal response signal DeltaT AC-S1;
setting the heating power and the heating frequency of the second heating electrode h2 in finite element simulation to be respectively the same as the heating power and the heating frequency of the second heating electrode h2 in actual experimental measurement;
Continuously changing a second set normal thermal conductivity k 'cross in finite element simulation by taking a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode s as a known quantity, solving a unitary nonlinear equation to obtain a second set thermal conductivity facing k' in corresponding to each second set normal thermal conductivity k 'cross, and finally obtaining a second change curve k' in(k′cross); the unitary nonlinear equation is obtained through a calculation relation among a second set normal thermal conductivity k 'cross, a second set surface thermal conductivity k' in and a second alternating-current thermal response signal DeltaT AC-S2.
According to one embodiment of the present invention, in step S6, specifically, the method includes:
Solving the intersection point coordinates of the intersection point between the first change curve k in(kcross) and the second change curve k' in(k′cross), wherein the intersection point coordinates are the actual normal thermal conductivity and the actual surface thermal conductivity of the measured solid material sample.
According to one embodiment of the present invention, the step of calculating the first ac thermal response signal Δt AC-S1 of the detection electrode s according to the operating parameter of the detection electrode s at the first dc detection current specifically includes:
According to the formula Calculating a first alternating-current thermal response signal DeltaT AC-S1 of the detection electrode s, wherein I s1 is a current value of a first direct-current detection current, R el-s is a resistance of the detection electrode s, beta s is a temperature coefficient of resistance of the detection electrode s, and V 2ω-s1 is a second harmonic component of voltages at two ends of the detection electrode s under the first direct-current detection current;
And/or, the step of calculating a second ac thermal response signal Δt AC-S2 of the detection electrode s according to the working parameter of the detection electrode s at the second dc detection current specifically includes:
According to the formula And calculating a second alternating-current thermal response signal DeltaT AC-S2 of the detection electrode s, wherein I s2 is a current value of a second direct-current detection current, R el-s is the resistance of the detection electrode s, beta s is the temperature coefficient of resistance of the detection electrode s, and V 2ω-s2 is a second harmonic component of the voltage at two ends of the detection electrode s under the second direct-current detection current.
According to one embodiment of the present invention, the width W h1 of the first heating electrode h1 is 15 μm to 50 μm.
According to one embodiment of the invention, the width W h2 of the second heating electrode h2 is 1 μm to 10 μm.
According to one embodiment of the invention, the width W s of the detection electrode s is 200nm to 5 μm.
According to one embodiment of the invention, the distance d h1 between the first heater electrode h1 and the detector electrode s is 5 μm to 30 μm.
According to one embodiment of the invention, the distance d h2 between the second heating electrode h2 and the detection electrode s is 500nm to 5 μm.
According to one embodiment of the invention, the method further comprises:
And arranging a plurality of groups of electrode groups in a plurality of mutually different directions of the insulating layer on at least part of the surface of the insulating layer far away from the substrate, wherein each group of electrode groups comprises a first heating electrode h1, a second heating electrode h2 and a detection electrode S, and repeating the steps S2, S3, S4, S5 and S6 for each group of electrode groups to obtain the actual normal thermal conductivity and the actual facing thermal conductivity of the measured solid material sample in a plurality of mutually different directions.
In summary, the method for measuring anisotropic thermal conductivity of a solid material according to the embodiment of the invention has the following advantages: (1) The alternating-current thermal response signal of the detection electrode is only sensitive to the heat conductivity of the substrate, so that measurement errors caused by the heat conductivity of the insulating layer, the interface thermal resistance between the insulating layer and the electrode and the interface thermal resistance between the insulating layer and the substrate are eliminated; (2) The anisotropic heat conductivity of the base material is calculated by a method for solving a binary nonlinear equation set, so that a multi-parameter fitting algorithm is avoided, and the solving precision is improved.
Drawings
In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for measuring anisotropic thermal conductivity of a solid material provided by the invention;
FIG. 2 is a schematic diagram of the structure of a sample to be tested when tested using the method for measuring anisotropic thermal conductivity of a solid material according to the present invention;
FIG. 3 is a second schematic diagram of the structure of a sample to be tested when tested using the method for measuring anisotropic thermal conductivity of a solid material according to the present invention.
Reference numerals:
1. a substrate; 2. an insulating layer; 3. a first heating electrode; 4. a second heating electrode; 5. and detecting the electrode.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, a method for measuring anisotropic thermal conductivity of a solid material according to an embodiment of the present invention, in which a solid material sample to be measured includes a substrate 1 and an insulating layer 2 which are stacked, includes steps S1 to S6.
In step S1, a first heating electrode 3, a second heating electrode 4 and a detecting electrode 5 are disposed on at least a portion of the surface of the insulating layer 2 away from the substrate 1, wherein the width of the first heating electrode 3 is greater than the width of the second heating electrode 4.
In step S2, a first ac heating current is connected to the first heating electrode 3, a first dc detection current is connected to the detection electrode 5, and a first ac thermal response signal Δt AC-S1 of the detection electrode 5 is calculated according to the operating parameter of the detection electrode 5 at the first dc detection current.
And S3, switching on a second alternating current heating current to the second heating electrode 4, switching on a second direct current detection current to the detection electrode 5, and calculating to obtain a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode 5 according to the working parameter of the detection electrode 5 under the second direct current detection current.
In step S4, in the finite element simulation, a three-dimensional finite element simulation model including the first heating electrode 3, the second heating electrode 4, and the detecting electrode 5 is established, and the three-dimensional finite element simulation model has the same size as the solid material sample actually measured.
Step S5, setting the simulation operation parameters of the first heating electrode 3 in the finite element simulation to be the same as the actual operation parameters of the first heating electrode 3 in the actual experimental measurement. With the first ac thermal response signal Δt AC-S1 of the probe electrode 5 as a known quantity, a first variation curve corresponding to the first heating electrode 3 is acquired with one of the first set normal thermal conductivity k cross and the first set thermal conductivity k in as an independent variable and the other as a dependent variable, based on the relationship among the first set normal thermal conductivity k cross, the first set thermal conductivity k in, and the first ac thermal response signal Δt AC-S1.
The simulation operating parameters of the second heater electrode 4 in the finite element simulation are set to be the same as the actual operating parameters of the second heater electrode 4 in the actual experimental measurement. With the second alternating-current thermal response signal Δt AC-S2 of the probe electrode 5 as a known quantity, a second variation curve corresponding to the second heating electrode 4 is acquired from the relationship among the second set normal thermal conductivity k 'cross, the second set facing thermal conductivity k' in, and the second alternating-current thermal response signal Δt AC-S2, with one of the second set normal thermal conductivity k 'cross and the second set facing thermal conductivity k' in as an independent variable and the other as a dependent variable.
Step S6, calculating the actual normal thermal conductivity and the actual surface thermal conductivity of the measured solid material sample based on the first change curve and the second change curve.
According to one embodiment of the invention, step S5 comprises: the heating power and frequency of the first heating electrode 3 in the finite element simulation are set to be the same as the heating power and frequency of the first heating electrode 3 in the actual experimental measurement, respectively. Continuously changing the first set normal thermal conductivity k cross in finite element simulation by taking a first alternating current thermal response signal DeltaT AC-S1 of the detection electrode 5 as a known quantity, solving a unitary nonlinear equation to obtain a first set thermal conductivity facing k in corresponding to each first set normal thermal conductivity k cross, and finally obtaining a first change curve k in(kcross); the unitary nonlinear equation is obtained through a calculation relation among the first set normal thermal conductivity k cross, the first set surface thermal conductivity k in and the first alternating-current thermal response signal DeltaT AC-S1.
Step S5 further includes: the heating power and frequency of the second heating electrode 4 in the finite element simulation are set to be the same as the heating power and frequency of the second heating electrode 4 in the actual experimental measurement, respectively. Continuously changing the second set normal thermal conductivity k 'cross in finite element simulation by taking a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode 5 as a known quantity, solving a unitary nonlinear equation to obtain a second set thermal conductivity facing k' in corresponding to each second set normal thermal conductivity k 'cross, and finally obtaining a second change curve k' in(k′cross); wherein, the unitary nonlinear equation is obtained through the calculation relation among the second set normal thermal conductivity k 'cross, the second set surface thermal conductivity k' in and the second alternating current thermal response signal DeltaT AC-S2.
According to one embodiment of the present invention, in step S6, specifically, the method includes: solving the intersection point coordinate of the intersection point between the first change curve k in(kcross) and the second change curve k' in(k′cross), wherein the intersection point coordinate is the actual normal thermal conductivity and the actual surface thermal conductivity of the measured solid material sample.
According to an embodiment of the present invention, the step of calculating the first ac thermal response signal Δt AC-S1 of the detection electrode 5 according to the operating parameter of the detection electrode 5 at the first dc detection current specifically includes:
According to the formula The first ac thermal response signal Δt AC-S1 of the detection electrode 5 is calculated, where I s1 is a current value of the first dc detection current, R el-s is a resistance of the detection electrode 5, β s is a temperature coefficient of resistance of the detection electrode 5, and V 2ω-s1 is a second harmonic component of a voltage across the detection electrode 5 at the first dc detection current.
According to an embodiment of the present invention, the step of calculating the second ac thermal response signal Δt AC-S2 of the detection electrode 5 according to the operating parameter of the detection electrode 5 at the second dc detection current specifically includes:
According to the formula The second ac thermal response signal Δt AC-S2 of the detection electrode 5 is calculated, where I s2 is a current value of the second dc detection current, R el-s is a resistance of the detection electrode 5, β s is a temperature coefficient of resistance of the detection electrode 5, and V 2ω-s2 is a second harmonic component of a voltage across the detection electrode 5 at the second dc detection current.
It should be explained that in the context of the present invention the detection electrode 5 is represented by s, the first heating electrode 3 by h1 and the second heating electrode 4 by h 2.Δt AC-S1 refers to the first AC thermal response signal of the detection electrode 5, where "s1" represents the detection electrode 5 to which a first dc detection current is applied, "AC" represents an alternating current (here, an alternating current refers to an alternating current applied to the first heating electrode 3), Δt AC-S2 refers to the second AC thermal response signal of the detection electrode 5, where "s2" represents the detection electrode 5 to which a second dc detection current is applied, and "AC" represents an alternating current (here, an alternating current refers to an alternating current applied to the second heating electrode 4); r el-s refers to the resistance of the detection electrode 5, where "el" is an abbreviation for the English word of the current, and "s" represents the detection electrode 5; v 2ω-s1 denotes a second harmonic component of the voltage across the detection electrode 5 at the first dc detection current, where "2ω" denotes the second harmonic and "s1" represents the detection electrode 5 that is fed with the first dc detection current; v 2ω-s2 refers to the second harmonic component of the voltage across the detection electrode 5 at the second dc detection current, where "2ω" refers to the second harmonic and "s2" represents the detection electrode 5 that is fed with the first dc detection current. The reason for naming R el-s and beta s is similar to the above, and will not be repeated here.
In addition, k in(kcross) refers to a first curve on the abscissa of k cross and on the ordinate of k in, and k ' in(k′cross) refers to a second curve on the abscissa of k ' cross and on the ordinate of k ' in.
One specific embodiment of the method for measuring anisotropic thermal conductivity of a solid material according to the present invention is described below, wherein the specific test method comprises:
In step S1, a first heating electrode 3, a second heating electrode 4 and a detecting electrode 5 are disposed on at least a portion of the surface of the insulating layer 2 away from the substrate 1, wherein the width of the first heating electrode 3 is greater than the width of the second heating electrode 4.
Step S2, switching on a first alternating heating current to the first heating electrode 3, switching on a first direct detection current to the detection electrode 5, according to the formulaA first ac thermal response signal Δt AC-S1 of the detection electrode 5 is calculated.
Wherein I s1 is a current value of the first dc detection current, R el-s is a resistance of the detection electrode 5, β s is a temperature coefficient of resistance of the detection electrode 5, and V 2ω-s1 is a second harmonic component of a voltage across the detection electrode 5 at the first dc detection current.
Step S3, switching on a second AC heating current to the second heating electrode 4, switching on a second DC detection current to the detection electrode 5, and according to the formulaA second ac thermal response signal Δt AC-S2 of the detection electrode 5 is calculated.
Wherein I s2 is the current value of the second dc detection current, R el-s is the resistance of the detection electrode 5, β s is the temperature coefficient of resistance of the detection electrode 5, and V 2ω-s2 is the second harmonic component of the voltage across the detection electrode 5 at the second dc detection current.
In step S4, in the finite element simulation, a three-dimensional finite element simulation model including the first heating electrode 3, the second heating electrode 4, and the detecting electrode 5 is established, and the three-dimensional finite element simulation model has the same size as the solid material sample actually measured.
Step S5, the heating power and frequency of the first heating electrode 3 in the finite element simulation are set to be the same as the heating power and frequency of the first heating electrode 3 in the actual experimental measurement, respectively. Continuously changing the first set normal thermal conductivity k cross in finite element simulation by taking a first alternating current thermal response signal DeltaT AC-S1 of the detection electrode 5 as a known quantity, solving a unitary nonlinear equation to obtain a first set thermal conductivity facing k in corresponding to each first set normal thermal conductivity k cross, and finally obtaining a first change curve k in(kcross); the unitary nonlinear equation is obtained through a calculation relation among the first set normal thermal conductivity k cross, the first set surface thermal conductivity k in and the first alternating-current thermal response signal DeltaT AC-S1.
The heating power and frequency of the second heating electrode 4 in the finite element simulation are set to be the same as the heating power and frequency of the second heating electrode 4 in the actual experimental measurement, respectively. Continuously changing the second set normal thermal conductivity k 'cross in finite element simulation by taking a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode 5 as a known quantity, solving a unitary nonlinear equation to obtain a second set thermal conductivity facing k' in corresponding to each second set normal thermal conductivity k 'cross, and finally obtaining a second change curve k' in(k′cross); wherein, the unitary nonlinear equation is obtained through the calculation relation among the second set normal thermal conductivity k 'cross, the second set surface thermal conductivity k' in and the second alternating current thermal response signal DeltaT AC-S2.
And S6), solving the intersection point coordinates of the intersection point between the first change curve k in(kcross) and the second change curve k' in(k′cross), wherein the intersection point coordinates are the actual normal thermal conductivity and the actual surface thermal conductivity of the measured solid material sample.
For the convenience of understanding, the following is a brief description of the advantageous effects of the method of the present invention and the principles for achieving the advantageous effects:
The invention provides a three-electrode 2 omega method, and referring to fig. 1 to 3, the specific steps of the three-electrode 2 omega method are as follows: (1) A wide heating electrode (e.g., a first heating electrode 3), a narrow heating electrode (e.g., a second heating electrode 4), and a detection electrode 5 are respectively disposed on a surface of the insulating layer 2 away from the substrate 1; (2) Firstly, switching on alternating current heating current to the wide heating electrode, switching on direct current detection current to the detection electrode 5, measuring and calculating to obtain an alternating current thermal response signal of the detection electrode 5, wherein the alternating current thermal response signal is more sensitive to a normal component of the thermal conductivity of the substrate 1; (3) Switching on alternating heating current to the narrow heating electrode, switching on direct current detection current to the detection electrode 5, measuring and calculating to obtain an alternating thermal response signal of the detection electrode 5, wherein the alternating thermal response signal is more sensitive to the facing component of the thermal conductivity of the substrate 1; (4) In the finite element simulation, a three-dimensional finite element simulation model which comprises a wide heating electrode, a narrow heating electrode and a detection electrode 5 and has the same size as an actual sample is established, and then the heating power of the wide heating electrode and the corresponding detection electrode 5 signal when the wide electrode is heated are respectively taken as known quantities. Solving a unitary nonlinear equation by continuously changing normal thermal conductivity set values in finite element simulation to obtain a thermal conductivity-oriented corresponding to each normal thermal conductivity set value; (5) According to the calculation result of the step (4), two non-parallel curves of change of the thermal conductivity facing to the thermal conductivity along with the normal thermal conductivity can be obtained, and the coordinate of the intersection point of the two curves is solved, wherein the coordinate is the final result of the normal thermal conductivity and the thermal conductivity facing to the measured material.
Thus, the three-electrode 2ω method proposed by the present invention has at least the following advantages: (1) The high-precision measurement of the anisotropic thermal conductivity of a single solid material sample is realized; (2) The alternating-current thermal response signal of the detection electrode 5 is only sensitive to the heat conductivity of the substrate 1, so that measurement errors caused by the heat conductivity of the insulating layer 2, the interface thermal resistance between the insulating layer 2 and the electrodes and the interface thermal resistance between the insulating layer 2 and the substrate 1 are eliminated; (3) The anisotropic heat conductivity of the substrate 1 material is calculated by a method for solving a binary nonlinear equation set, so that a multi-parameter fitting algorithm is avoided, and the solving precision is improved.
Since the method for measuring the anisotropic thermal conductivity of the solid material according to the embodiment of the invention realizes measurement based on the three-electrode 2ω method, the method for measuring the anisotropic thermal conductivity of the solid material provided by the invention also has the advantages of the three-electrode 2ω method.
It should be specifically noted here that finite element simulation means: and constructing a model with the same structure as the actual sample in a computer, setting the same heat flow and temperature boundary conditions, and simulating the actual condition of the measured sample, thereby obtaining the corresponding thermophysical parameters by calculation.
According to some embodiments of the present invention, if the insulation of the material of the substrate 1 is good, the wide heating electrode, the narrow heating electrode, and the detection electrode 5 may be directly disposed on the surface of the substrate 1; if the material forming the substrate 1 has good conductivity, the insulating layer 2 may be provided on the surface of the substrate 1, thereby preventing electrode crosstalk and leakage.
According to some embodiments of the present invention, the number of electrodes on the surface of the sample to be measured is not particularly limited, a wide heating electrode, a narrow heating electrode and a detection electrode 5 may be disposed on the surface of the insulating layer 2 away from the substrate 1, where the surface of the insulating layer 2 away from the substrate 1 is of a simple crystal structure, and when only three electrodes are disposed for detection on the substrate 1 with a complex crystal structure, the accuracy of measurement results is poor, and multiple groups of electrodes may be disposed on the surface of the insulating layer 2 away from the substrate 1 in different directions, where each group of electrodes includes a wide heating electrode, a narrow heating electrode and a detection electrode 5, so as to obtain thermal response signals in more directions, and improve the accuracy of measurement of anisotropic thermal conductivity of the substrate 1 with a complex crystal structure.
In one embodiment, if it is desired to measure anisotropic thermal conductivity in multiple directions, the method further comprises:
At least part of the surface of the insulating layer 2 far away from the substrate 1, a plurality of groups of electrode groups are arranged in a plurality of mutually different directions of the insulating layer 2, each group of electrode groups comprises a first heating electrode 3, a second heating electrode 4 and a detection electrode 5, and the steps S2, S3, S4, S5 and S6 are repeated for each group of electrode groups, so that the actual normal thermal conductivity and the actual surface thermal conductivity of the measured solid material sample in the plurality of mutually different directions are obtained.
According to some embodiments of the present invention, referring to fig. 2 and 3, the width W h1 of the first heating electrode 3 may be 15 μm to 50 μm, specifically, 15μm、16μm、17μm、18μm、19μm、20μm、21μm、22μm、23μm、24μm、25μm、26μm、27μm、28μm、29μm、30μm、31μm、32μm、33μm、34μm、35μm、36μm、37μm、38μm、39μm、40μm、41μm、42μm、43μm、44μm、45μm、46μm、47μm、48μm、49μm and 50 μm, etc., whereby the accuracy of measurement may be improved. It should be noted that, if the width of the first heating electrode 3 is too small, the sensitivity of the ac thermal response signal of the detecting electrode 5 to the normal thermal conductivity of the substrate 1 may be affected to some extent; if the width of the first heating electrode 3 is too large, the measurement error of the alternating-current thermal response signal of the detection electrode 5 may be increased to some extent.
According to some embodiments of the present invention, referring to fig. 2 and 3, the width W h2 of the second heating electrode 4 may be 1 μm to 10 μm, specifically, may be 1 μm, 1.5 μm, 2 μm, 2.5 μm, 3 μm, 3.5 μm, 4 μm, 4.5 μm, 5 μm, 5.5 μm, 6 μm, 6.5 μm, 7 μm, 7.5 μm, 8 μm, 8.5 μm, 9 μm, 9.5 μm, 10 μm, etc., whereby the accuracy of measurement may be improved. It should be noted that, if the width of the second heating electrode 4 is too small, the heat conduction process will deviate from fourier heat conduction, and the system error will be increased to some extent; if the width of the second heating electrode 4 is too large, the sensitivity of the probe electrode 5 to the thermal conductivity of the substrate 1 facing the alternating thermal response signal will be reduced.
According to some embodiments of the present invention, referring to fig. 2 and 3, the width W s of the probe electrode 5 may be 200nm to 5 μm, specifically, 0.2μm、0.5μm、0.7μm、1μm、1.2μm、1.4μm、1.6μm、1.8μm、2μm、2.2μm、2.4μm、2.6μm、2.8μm、3μm、3.2μm、3.4μm、3.6μm、4μm、4.2μm、4.4μm、4.6μm、4.8μm and 5 μm, etc., whereby the accuracy of measurement may be improved. It should be noted that, if the width of the detection electrode 5 is too small, the process requirement is high in the process of preparing the detection electrode 5; if the width of the detection electrode 5 is excessively large, the ac thermal response signal measurement error of the detection electrode 5 may be increased to some extent.
According to some embodiments of the present invention, referring to fig. 2 and 3, the distance d h1 between the first heating electrode 3 and the detection electrode 5 is 5 μm to 30 μm, specifically, 5μm、6μm、7μm、8μm、9μm、10μm、11μm、12μm、13μm、14μm、15μm、16μm、17μm、18μm、19μm、20μm、21μm、22μm、23μm、24μm、25μm、26μm、27μm、28μm、29μm and 30 μm, etc., thereby improving the accuracy of measurement. It should be noted that, if the distance between the first heating electrode 3 and the detecting electrode 5 is too small, the risk of occurrence of crosstalk or electric leakage between the electrodes may be increased to some extent; if the distance between the first heating electrode 3 and the detecting electrode 5 is too large, the ac thermal response signal measurement error of the detecting electrode 5 may be increased to some extent.
According to some embodiments of the present invention, referring to fig. 2 and 3, the distance d h2 between the second heating electrode 4 and the detection electrode 5 is 500nm to 5 μm, specifically, may be 0.5 μm, 1 μm, 1.5 μm,2 μm, 2.5 μm, 3 μm, 3.5 μm, 4 μm, 4.5 μm, 5 μm, etc., whereby the accuracy of measurement may be improved. It should be noted that, if the distance between the second heating electrode 4 and the detecting electrode 5 is too small, the risk of occurrence of crosstalk or electric leakage between the electrodes may be increased to some extent; if the distance between the second heating electrode 4 and the detecting electrode 5 is too large, the ac thermal response signal measurement error of the detecting electrode 5 may be increased to some extent.
According to some embodiments of the present invention, the thicknesses of the first heating electrode 3, the second heating electrode 4 and the detecting electrode 5 are not limited, and those skilled in the art can design themselves according to actual needs, for example, the thicknesses of the first heating electrode 3, the second heating electrode 4 and the detecting electrode 5 may be 100nm. It should be understood by those skilled in the art that the positions of the first heating electrode 3, the second heating electrode 4 and the detecting electrode 5 are not particularly limited, and the test process can be completed by providing these three electrodes on the surface of the insulating layer 2 remote from the substrate 1, and preferably, the detecting electrode 5 is located in the middle of the first heating electrode 3 and the second heating electrode 4, so that the connection is easier and the operation is more convenient.
According to some embodiments of the present application, the materials of the first heating electrode 3, the second heating electrode 4, and the detection electrode 5 are not particularly limited, and are selected from electrode materials commonly used in the art, for example, the first heating electrode 3, the second heating electrode 4, and the detection electrode 5 in the present application are at least one selected from Au, pt, pd, ag, cr, ni, ti, cu and Al, each independently. The materials used for the three electrodes (i.e., the first heating electrode 3, the second heating electrode 4 and the detecting electrode 5) may be the same or different, if the materials forming the three electrodes are the same, it may be ensured that the sensitivity of the three electrodes to temperature is the same, and the measurement accuracy is improved to a certain extent.
According to some embodiments of the present invention, the material of the substrate 1 is not particularly limited, and the hard solid material may be tested by the above method, and specifically to the present invention, the material of the substrate 1 includes at least one of a non-radioactive inorganic non-metal solid material, a non-radioactive inorganic metal solid material, a non-radioactive organic non-metal solid material, and a non-radioactive organic metal solid material, and specifically the substrate 1 is selected from at least one of gallium nitride, aluminum nitride, tantalum nitride, gallium oxide, aluminum germanium, aluminum oxide, sapphire, silicon, germanium, silicon germanium alloy, silicon dioxide, quartz, silicon carbide, silicon nitride, diamond, graphite, highly oriented pyrolytic graphite, boron arsenide, gallium arsenide, indium gallium arsenide, aluminum phosphide, gallium phosphide, indium phosphide, zinc oxide, hafnium dioxide, titanium nitride, magnesium oxide, lithium niobate, strontium titanate, strontium ruthenate, and mica, and composite materials thereof. According to some embodiments of the present invention, the thickness of the substrate 1 is not particularly limited, and for example, the thickness of the substrate 1 may be 10 μm to 1cm. Thereby, the thickness of the substrate 1 is prevented from being excessively thin, and the measurement accuracy of the alternating-current thermal response signal of the detection electrode 5 is prevented from being affected.
According to some embodiments of the present application, the material of the insulating layer 2 is not particularly limited, and in particular, the insulating layer 2 is selected from at least one of silicon dioxide, hafnium oxide, zirconium dioxide, aluminum oxide, gallium oxide, and silicon nitride, and one skilled in the art can select the method of the present application to test the anisotropic thermal conductivity of the substrate 1 of the sample according to actual needs.
One embodiment of the method for measuring anisotropic thermal conductivity of a solid material according to the present invention is described below in conjunction with specific experimental data.
An insulating layer 2 is arranged on the surface of a monocrystalline beta-gallium oxide substrate 1 with a main positioning edge perpendicular to the [100] crystal direction, a secondary positioning edge perpendicular to the [010] crystal direction and a bare crystal face (001) orientation, the insulating layer 2 is made of SiO 2, and the thickness is 40nm. On the surface of the insulating layer 2 remote from the monocrystalline beta-gallium oxide substrate 1, a set of electrodes is provided, comprising a first heating electrode 3, a second heating electrode 4 and a detection electrode 5. Wherein the width of the first heating electrode 3 is 30 μm, the width of the second heating electrode 4 is 5 μm, the width of the detecting electrode 5 is 1 μm, the distance between the first heating electrode 3 and the detecting electrode 5 is 24 μm, the distance between the second heating electrode 4 and the detecting electrode 5 is 2 μm, and the anisotropic thermal conductivity of the substrate 1 is calculated by using the method for measuring anisotropic thermal conductivity of a solid material (i.e., the three-electrode 2ω method) of the present invention, the specific procedure is as follows:
(1) An alternating current heating current with an effective value of 5mA and a frequency of 585Hz is connected to the first heating electrode 3, a direct current detection current I s1 with 5mA is connected to the detection electrode 5, and the formula is adopted The first ac thermal response signal Δt AC-S1 of the probe electrode 5 was calculated to be 0.026K. Wherein R el-s＝185.6Ω,βs＝1.9×10-3K-1,V2ω-s1 = 32.3 μv.
(2) An effective value of 2mA and an alternating current heating current with the frequency of 1285Hz are connected to the second heating electrode 4, a direct current detection current I s2 with the frequency of 2mA is connected to the detection electrode 5, and the formula is adoptedThe second ac thermal response signal Δt AC-S2 of the probe electrode 5 was calculated to be 0.019K. Wherein R el-s＝185.6Ω,βs＝1.9×10-3K-1,V2ω-s2 = 9.4 μv.
(3) In the finite element simulation, a three-dimensional finite element simulation model including the first heating electrode 3, the second heating electrode 4, and the detection electrode 5 and having the same size as the actual sample is established. Firstly, setting the heating power and the frequency of the first heating electrode 3 to be the same as the actual conditions in experiments, taking an alternating-current thermal response signal DeltaT AC-S1 =0.026K of the detection electrode 5 as a known quantity, solving a unitary nonlinear equation to obtain a thermal conductivity facing K in corresponding to each K cross by continuously changing a material normal thermal conductivity set value K cross in finite element simulation, and finally obtaining a curve K in(kcross corresponding to the first heating electrode 3 in a K cross-kin relation diagram. Next, the heating power and frequency of the second heating electrode 4 are set to be the same as the actual conditions in the experiment, and the alternating-current thermal response signal Δt AC-S2 =0.019K of the detecting electrode 5 is taken as a known quantity, the thermal conductivity facing K ' in corresponding to each K ' cross is obtained by continuously changing the material normal thermal conductivity set value K ' cross in finite element simulation, and finally a curve K ' in(k′cross corresponding to the second heating electrode 4 is obtained in a K ' cross-k′in relation diagram.
(4) Solving the intersection point coordinates of the k in(kcross) and the k' in(k′cross), wherein the coordinates are the final measured values of the normal thermal conductivity k cross and the facing thermal conductivity k in of the measured material.
The final measurement results are shown in the following table 1:
TABLE 1
In summary, through the experimental results shown in the above table 1, it can be seen that the method provided by the application can realize accurate measurement of anisotropic thermal conductivity in different directions in a single sample, and the measurement result accords with the reference value range of the literature, thereby proving the practicability and reliability of the method.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A method for measuring anisotropic thermal conductivity of solid material is characterized in that,
The measured solid material sample comprises a substrate and an insulating layer which are arranged in a laminated manner;
The method comprises the following steps:
Step S1, a first heating electrode h1, a second heating electrode h2 and a detection electrode S are arranged on at least part of the surface of the insulating layer far away from the substrate, wherein the width of the first heating electrode h1 is larger than that of the second heating electrode h 2;
Step S2, a first alternating current heating current is connected to the first heating electrode h1, a first direct current detection current is connected to the detection electrode S, and a first alternating current thermal response signal DeltaT AC-S1 of the detection electrode S is calculated according to the working parameter of the detection electrode S under the first direct current detection current;
step S3, a second alternating current heating current is connected to the second heating electrode h2, a second direct current detection current is connected to the detection electrode S, and a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode S is calculated according to the working parameter of the detection electrode S under the second direct current detection current;
Step S4, in the finite element simulation, a three-dimensional finite element simulation model comprising the first heating electrode h1, the second heating electrode h2 and the detection electrode S is established, and the size of the three-dimensional finite element simulation model is the same as the size of the solid material sample to be actually measured;
Step S5, setting simulation working parameters of the first heating electrode h1 in finite element simulation to be the same as actual working parameters of the first heating electrode h1 in actual experimental measurement;
taking a first alternating-current thermal response signal DeltaT AC-S1 of the detection electrode s as a known quantity, according to the relation among a first set normal thermal conductivity k cross, a first set facing thermal conductivity k in and the first alternating-current thermal response signal DeltaT AC-S1, taking one of the first set normal thermal conductivity k cross and the first set facing thermal conductivity k in as an independent variable and the other as a dependent variable, acquiring a first variation curve corresponding to the first heating electrode h 1;
Setting simulation working parameters of the second heating electrode h2 in finite element simulation to be the same as actual working parameters of the second heating electrode h2 in actual experimental measurement;
Taking a second alternating-current thermal response signal DeltaT AC-S2 of the detection electrode s as a known quantity, according to the relation among a second set normal thermal conductivity k 'cross, a second set facing thermal conductivity k' in and the second alternating-current thermal response signal DeltaT AC-S2, taking one of the second set normal thermal conductivity k 'cross and the second set facing thermal conductivity k' in as an independent variable and the other as a dependent variable, obtaining a second variation curve corresponding to the second heating electrode h 2;
and step S6, calculating the actual normal thermal conductivity and the actual facing thermal conductivity of the measured solid material sample based on the first change curve and the second change curve.
2. The method for measuring anisotropic thermal conductivity of solid material according to claim 1, characterized in that in step S5, it comprises in particular:
Setting the heating power and the frequency of the first heating electrode h1 in finite element simulation to be respectively the same as the heating power and the frequency of the first heating electrode h1 in actual experimental measurement;
Continuously changing a first set normal thermal conductivity k cross in finite element simulation by taking a first alternating current thermal response signal DeltaT AC-S1 of the detection electrode s as a known quantity, solving a unitary nonlinear equation to obtain a first set thermal conductivity facing k in corresponding to each first set normal thermal conductivity k cross, and finally obtaining a first change curve k in(kcross; the unitary nonlinear equation is obtained through a calculation relation among a first set normal thermal conductivity k cross, a first set surface thermal conductivity k in and a first alternating-current thermal response signal DeltaT AC-S1;
setting the heating power and the heating frequency of the second heating electrode h2 in finite element simulation to be respectively the same as the heating power and the heating frequency of the second heating electrode h2 in actual experimental measurement;
Continuously changing a second set normal thermal conductivity k 'cross in finite element simulation by taking a second alternating current thermal response signal DeltaT AC-S2 of the detection electrode s as a known quantity, solving a unitary nonlinear equation to obtain a second set thermal conductivity facing k' in corresponding to each second set normal thermal conductivity k 'cross, and finally obtaining a second change curve k' in(k′cross); the unitary nonlinear equation is obtained through a calculation relation among a second set normal thermal conductivity k 'cross, a second set surface thermal conductivity k' in and a second alternating-current thermal response signal DeltaT AC-S2.
3. The method for measuring anisotropic thermal conductivity of solid material according to claim 2, characterized in that in step S6, it comprises in particular:
Solving the intersection point coordinates of the intersection point between the first change curve k in(kcross) and the second change curve k' in(k′cross), wherein the intersection point coordinates are the actual normal thermal conductivity and the actual surface thermal conductivity of the measured solid material sample.
4. A method for measuring anisotropic thermal conductivity of solid materials according to any of claims 1 to 3, characterized in that said step of calculating a first ac thermal response signal Δt AC-S1 of said detection electrode s from the operating parameters of said detection electrode s at said first dc detection current, comprises in particular:
According to the formula Calculating a first alternating-current thermal response signal DeltaT AC-S1 of the detection electrode s, wherein I s1 is a current value of a first direct-current detection current, R el-s is a resistance of the detection electrode s, beta s is a temperature coefficient of resistance of the detection electrode s, and V 2ω-s1 is a second harmonic component of voltages at two ends of the detection electrode s under the first direct-current detection current;
And/or, the step of calculating a second ac thermal response signal Δt AC-S2 of the detection electrode s according to the working parameter of the detection electrode s at the second dc detection current specifically includes:
According to the formula And calculating a second alternating-current thermal response signal DeltaT AC-S2 of the detection electrode s, wherein I s2 is a current value of a second direct-current detection current, R el-s is the resistance of the detection electrode s, beta s is the temperature coefficient of resistance of the detection electrode s, and V 2ω-s2 is a second harmonic component of the voltage at two ends of the detection electrode s under the second direct-current detection current.
5. The method for measuring anisotropic thermal conductivity of solid material according to claim 1, wherein the width W h1 of the first heating electrode h1 is 15 μm to 50 μm.
6. The method for measuring anisotropic thermal conductivity of solid material according to claim 1, wherein the width W h2 of the second heating electrode h2 is 1 μm to 10 μm.
7. The method for measuring anisotropic thermal conductivity of solid material according to claim 1, wherein the width W s of the probe electrode s is 200nm to 5 μm.
8. The method for measuring anisotropic thermal conductivity of solid materials according to claim 1, wherein the distance d h1 between the first heating electrode h1 and the detection electrode s is 5 μm to 30 μm.
9. The method for measuring anisotropic thermal conductivity of solid materials according to claim 1, wherein the distance d h2 between the second heating electrode h2 and the detection electrode s is 500nm to 5 μm.
10. The method of measuring anisotropic thermal conductivity of a solid material according to any of claims 5 to 9, further comprising:
And arranging a plurality of groups of electrode groups in a plurality of mutually different directions of the insulating layer on at least part of the surface of the insulating layer far away from the substrate, wherein each group of electrode groups comprises a first heating electrode h1, a second heating electrode h2 and a detection electrode S, and repeating the steps S2, S3, S4, S5 and S6 for each group of electrode groups to obtain the actual normal thermal conductivity and the actual facing thermal conductivity of the measured solid material sample in a plurality of mutually different directions.
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