JP7093944B2 - Thermophysical property measurement method - Google Patents

Description

The present invention relates to a thin plate and a method for measuring thermophysical properties in the thickness direction of a thin plate and a thin film on the thin plate.

As a method for measuring thermal conductivity (thermal diffusivity) in the thickness direction of a sample, a steady method (JIS A 1412) and a flash method (JIS R 1611) are known. Further, as a method for measuring physical properties in the thickness direction of a thin film, a measuring method using the 2ω method disclosed in Patent Document 1 is known.

Japanese Unexamined Patent Publication No. 2009-300686

In recent years, there has been a demand for a method for evaluating the thermal conductivity in the thickness direction of a thin plate having a high thermal conductivity (for example, a silicon wafer having a thickness of 200 μm). However, in the stationary method and the flash method, it is difficult to measure the thermal conductivity in the thickness direction of a thin plate having high thermal conductivity due to the measurement principle and the configuration of the measuring device.

The measuring method of Patent Document 1 is intended to measure the thermophysical properties of a thin film formed on a substrate whose thickness is assumed to be semi-infinite. That is, the measuring method of Patent Document 1 is a heat transfer model on the condition that heat does not reach the back surface of the substrate. Therefore, the measuring method of Patent Document 1 cannot be applied to the above-mentioned measurement of the thermal conductivity of a thin plate having a finite thickness.

The present invention has been made in consideration of such circumstances, and an object of the present invention is to provide a thermophysical characteristic measuring method capable of accurately obtaining a thermophysical characteristic value in the thickness direction of a thin plate.

In the thermophysical property measuring method according to the present invention, in order to solve the above-mentioned problems, a second thin film having an unknown thermal conductivity and a first thin film are laminated in order on a thin plate having an unknown thermal conductivity. (A) The temperature on the surface of the first thin film by measuring the temperature response on the surface of the first thin film due to periodic heating to the surface of the first thin film. The steps of obtaining the change amplitude A and the phase difference θ, and (b) the thermal conductivity λ ₁ of the first thin film, the volume specific heat capacity C ₁ and the film thickness d ₁ , the thermal conductivity λ ₂ of the second thin film, and the volume. It includes the specific heat capacity C ₂ and the film thickness d ₂ , and the thermal conductivity λ ₃ of the thin plate, the volume specific heat capacity C ₃ and the film thickness d ₃ , and determines the time dependence of the temperature change on the surface of the first thin film. The step of deriving the first function shown, (c) the second function showing the time dependence of the temperature change on the surface of the first thin film including the amplitude A and the phase difference θ, and the first function. The thin plate comprises a step of obtaining the heat conductivity λ ₃ of the thin plate and the heat conductivity λ ₂ of the second thin film, wherein the thin plate has a surface facing the second thin film and the surface. It has a back surface that is the opposite surface of the surface facing the second thin film, and the first function is such that at least a part of the heat flow accompanying the heating of the first thin film is from the first thin film toward the back surface of the thin plate. It is characterized in that it is derived by using a one-dimensional heat transfer model that flows vertically on the back surface and flows in the direction of the first thin film .

According to the present invention, the thermophysical property value in the thickness direction of the thin plate can be accurately obtained.

The block diagram which shows the thermophysical characteristic measuring apparatus for carrying out the thermophysical characteristic measuring method which concerns on this invention. Top view to explain the sample. FIG. 2 is a cross-sectional view taken along the line III-III of FIG. Top view of the sample installed on the XY stage. FIG. 4 is a cross-sectional view taken along the line VV of FIG. Sectional drawing along the VI-VI line of FIG. (A) is a graph showing the measurement result when the thermophysical characteristic measurement method according to the embodiment of the present invention is applied, and (B) is a graph showing the measurement result when the thermophysical characteristic measurement method as a comparative example is applied.

An embodiment of the thermophysical characteristic measurement method according to the present invention will be described with reference to the accompanying drawings. In the present embodiment, an example in which the thermophysical characteristic measuring method according to the present invention is applied to the method for measuring with the thermophysical characteristic measuring device 1 shown in FIG. 1 will be described.

FIG. 1 is a block diagram showing a thermophysical characteristic measuring device 1 for carrying out the thermophysical characteristic measuring method according to the present invention.

The thermophysical characteristic measuring device 1 has a measuring chamber 3 partitioned by a case 2. The measuring chamber 3 is in a vacuum state by removing the air inside. An XY stage 23 is provided on the inner bottom surface of the measurement chamber 3. The XY stage 23 is made of, for example, copper. The XY stage 23 has a jig 23a. The jig 23a is made of copper and forms a heat insulating layer 3a with the sample 40 (thin plate back surface 41a).

The XY stage 23 holds the sample 40 on a flat surface. The XY stage 23 is an example of a means of transportation for moving the sample 40. The XY stage 23 is connected to a movement control device 25 arranged outside the measurement chamber 3. When the movement control device 25 is driven, the XY stage 23 moves in the horizontal plane while holding the sample 40.

An AC power supply 21 is provided outside the measurement chamber 3. The AC power supply 21 is connected to the probes 24 ₁ and ₂₄₂ . When the AC power supply 21 is started after the probes 24 ₁ and ₂₄₂ come into contact with the sample 40, an AC voltage having a frequency (angular frequency) ω is applied to the sample 40.

A laser irradiation device 12 and a light detection device 13 are arranged above the inside of the measurement chamber 3. The laser irradiation device 12 is an example of irradiation means. The laser irradiation device 12 includes a laser light source 4, a condenser lens 5, a prism, a lock-in amplifier, and a power amplifier. When the laser light source 4 is activated to emit light, the laser light is divided into irradiation light and reference light by a prism. After the irradiation light is focused by the condenser lens 5, the laser beam is spotted at a predetermined position on the surface of the XY stage 23. The reflected light and the reference light after irradiation are detected by separate detectors via a prism, and the difference between the detected signals is sent to the signal input terminal of the lock-in amplifier.

The photodetector 13 is an example of a photodetector. The photodetector 13 includes a condenser lens 6, an optical filter 7, and a light receiving device 8. The reflected light is collected by the condenser lens 6, and after the optical noise is removed by the optical filter 7, the reflected light is received by the light receiving device 8. The light receiving device 8 includes a PIN photodiode and an IV amplifier. The reflected light is converted into a current by this PIN photodiode, voltage-converted by an IV amplifier, and then amplified to generate a voltage having a magnitude corresponding to the intensity of the reflected light. The light receiving device 8 is connected to a measuring device 22 arranged outside the measuring chamber 3. The voltage corresponding to the intensity of the reflected light is output to the measuring device 22.

The measuring device 22 is an example of measuring means. The measuring device 22 includes a synchronous detector 33, a signal generator 34, and an arithmetic unit 35. A voltage having a magnitude corresponding to the intensity of the reflected light is output to the synchronous detector 33. A sinusoidal AC signal having a frequency of 2ω is output from the signal generator 34 to the synchronous detector 33. By multiplying this AC signal with a voltage having a magnitude corresponding to the intensity of the reflected light, a component having a frequency of 2ω is extracted from the voltage having a magnitude corresponding to the intensity of the reflected light and output to the arithmetic unit 35. .. The arithmetic unit 35 obtains the temperature of the metal thin film 43 according to the input voltage from the input voltage.

FIG. 2 is a plan view for explaining the sample 40.
FIG. 3 is a cross-sectional view taken along the line III-III of FIG.

The sample 40 has a thin plate 41, an insulating thin film 42, and a metal thin film 43. The sample 40 is formed by sequentially laminating an insulating thin film 42 as a second thin film and a metal thin film 43 as a first thin film on a thin plate 41 having an unknown thermal conductivity. ing.
The thin plate 41 is, for example, a silicon substrate (silicon wafer) having a thickness of 200 μm or less, a thin plate made of SUS (Steel Use Stainless) having a thickness of 10 to 100 μm (and a material having a thermal diffusivity equivalent thereto), and a thickness of 20 μm. It is a sheet made of carbon graphite of the degree. The insulating thin film 42 is formed on the surface of the thin plate 41 and has an insulating property so that electricity does not flow to the thin plate 41. Further, the insulating thin film 42 is made of a material having a low thermal conductivity in order to improve the measurement sensitivity. The insulating thin film 42 is made of, for example, a polymethyl methacrylate resin (PMMA) having a thickness of 0.6 μm. The metal thin film 43 is formed on the surface of the insulating thin film 42 and is used for applying an AC voltage and detecting a temperature change. The metal thin film 43 is made of, for example, gold having a length of 4 mm, a width of 2 mm, and a thickness of 0.2 μm.

A method for obtaining the thermal conductivity of a thin plate (thermophysical property measuring method) using the thermophysical property measuring device 1 having such a configuration will be described below.
The method for determining the thermal conductivity of the thin plate is as follows: (a) The amplitude of the temperature change on the surface of the metal thin film 43 by measuring the temperature response on the surface of the metal thin film 43 due to periodic heating to the surface of the metal thin film 43. The steps of obtaining A and the phase difference θ, and (b) the thermal conductivity λ1 of the metal thin film 43, the volume specific heat capacity C1 and the film thickness d1, the thermal conductivity λ2 of the insulating thin film 42, the volume specific heat capacity C2 and the film thickness d2, and , Derived the first function showing the time dependence of the temperature change on the surface of the metal thin plate 43, including the thermal conductivity λ3 of the thin plate 41, the volume specific heat capacity C3 and the film thickness d3, and considering that the thin plate 41 is finite. The thermal conductivity of the thin plate 41 is based on (c) the second function showing the time dependence of the temperature change on the surface of the metal thin film 43 including the amplitude A and the phase difference θ, and the first function. It includes a step of obtaining λ3 and a thermal conductivity λ2 of the insulating thin film 42.
Hereinafter, steps (a) to (c) will be specifically described.

The sample 40 is placed in the measurement chamber 3 and placed on the surface of the XY stage 23 with the thin plate 41 on the lower side and the metal thin film 43 on the upper side. Since the thin plate 41 is placed on the jig 23a, a part of the thin plate 41 on the back surface 41a side is in contact with the jig 23a, and the other part is in contact with the heat insulating layer 3a. The heat insulating layer 3a is provided at a position corresponding to the range in which the irradiation light of the metal thin film 43 is irradiated. The heat insulating layer 3a is formed, for example, by creating a vacuum inside the case 2 (inside the measuring chamber 3).

Here, FIG. 4 is a plan view of the sample 40 installed on the XY stage 23. FIG. 5 is a cross-sectional view taken along the line VV of FIG. Next, the probes 24 ₁ and 242 _are erected at _both ends in the length direction of the metal thin film 43, and the probes 24 ₁ and 242 come into contact with the surface of the metal thin film 43. The AC power supply 21 is activated, and an AC voltage having a frequency ω is applied to the metal thin film 43.

Here, FIG. 6 is a cross-sectional view taken along the line VI-VI of FIG. Joule heat is generated in the metal thin film 43 due to the electric resistance of the metal thin film 43. This Joule heat is generated AC by AC voltage. The temperature of the metal thin film 43 rises due to Joule heat, but the heat flow 70 is transmitted from the metal thin film 43 to the thin plate 41 through the insulating thin film 42. Therefore, the temperature change of the metal thin film 43 depends on the heat conduction state of the thin plate 41 and the insulating thin film 42. The heat flow 70 that reaches the back surface 41a of the thin plate 41 facing the heat insulating layer 3a is reflected by the back surface 41a of the thin plate 41.

Next, the laser light source 4 is made to emit light, and the laser beam 80 is irradiated toward the surface (metal thin film 43) of the XY stage 23. At this time, the spot diameter on the surface of the metal thin film 43 of the laser beam 80 is set to be one tenth or less (for example, 100 μm) of the width of the metal thin film 43. The XY stage 23 is horizontally moved, and the laser beam 80 is irradiated to a predetermined position substantially at the center of the metal thin film 43.

The laser beam 80 thus irradiated is reflected by the metal thin film 43, and the reflectance of the metal thin film 43 changes depending on the temperature of the metal thin film 43. The intensity of the reflected light also changes due to the change in the reflectance. The reflected light is reflected in the direction of the photodetector 13 arranged above the inside of the measurement chamber 3. The photodetector 13 generates a voltage of a magnitude corresponding to the intensity that changes according to the temperature of the received reflected light.

The metal thin film 43 is stabilized at a substantially constant temperature without rising above a predetermined temperature by a cooler (not shown), so that the thermal system becomes a steady state. When the thermal system becomes a steady state and the temperature of the metal thin film 43 stabilizes at a substantially constant value, the arithmetic unit 35 obtains the temperature of the metal thin film 43.

The arithmetic unit 35 analyzes the heat conduction state of the sample 40 based on the temperature of the obtained metal thin film 43. In this sample 40, the width of the metal thin film 43 is wide, and the place where the temperature change is measured by irradiating the laser beam 80 is a very narrow region of the metal thin film 43, and is substantially at the center of the metal thin film 43. It is an area. Therefore, at this measurement point, it is considered that the heat flow 70 of Joule heat flows vertically from the metal thin film 43 toward the back surface 41a of the thin plate 41 (and is reflected vertically by the back surface 41a and flows in the direction of the metal thin film 43). Well, the heat flow 70 can be said to flow one-dimensionally. Therefore, a one-dimensional heat transfer model can be used for the analysis of the heat conduction state of the sample 40.

The parameters of each layer are as follows. Here, the interfacial thermal resistance between the metal thin film 43 and the insulating thin film 42 and the interfacial thermal resistance between the insulating thin film 42 and the thin plate 41 are set to 0 [m ² · K · W ^-1 ]. It should be noted that λ ₂ and λ ₃ are unknown.

The periodic heating will be described here assuming that the metal thin film 43 is uniformly energized and heated by intensity-modulating the voltage at a frequency f [Hz]. That is, the case where the temperature change on the surface of the metal thin film 43 due to the periodic heating of a plurality of frequencies ω by electrical or optical periodic heating is measured by the thermoreflectance method will be described.
Since the amount of heat Q (t) [W] applied to the metal thin film 43 per unit time depends on the frequency 2f [Hz], the amount of heat Q (t) per unit time applied at the angular frequency 2ω [s ^-1 ]. [W] is as shown in the following equation.

Note that q is a constant other than 0, and ω = 2πf.

ｎ＝１（金属薄膜）、ｎ＝２（絶縁薄膜）、ｎ＝３（薄板） Assuming that the reciprocal of the thermal diffusivity at frequencies 2f [Hz] of each layer 41 to 43 is k [m ^-1 ], k is expressed by the following equation.

n = 1 (metal thin film), n = 2 (insulating thin film), n = 3 (thin plate)

ｍ＝１（金属薄膜）、ｍ＝２（絶縁薄膜）、ｍ＝３（薄板） Here, the time dependence T of the temperature change on the surface by the one-dimensional heat transfer model as the first function showing the time dependence of the temperature change on the surface of the metal thin film 43 considering that the thin plate is finite ( 0, t)
[K] is the following equation.

m = 1 (metal thin film), m = 2 (insulating thin film), m = 3 (thin plate)

尚、ｘ及びｙ中には、未知数であるλ_２及びλ_３が含まれている。 The following (Equation 6) is obtained by simplifying the above (Equation 3).

It should be noted that x and y include λ ₂ and λ ₃ which are unknowns.

On the other hand, the temperature on the surface is time-dependent T (0, t) of the temperature change on the surface of the metal thin film 43 including the amplitude A and the phase difference θ when the amplitude A [K] and the phase difference θ [deg] are used. ) The following equation, which is an equation as a second function indicating [K].

Comparing (Equation 7) and (Equation 3), the following relationships (Equation 8) and (Equation 9) are established.

Then, λ ₂ and λ ₃ can be obtained by fitting the known quantities λ ₁ , C ₁ , C ₂ , C ₃ and d ₁ , d ₂ and d ₃ with the values substituted into (Equation 3). ..
Specifically, the amplitude A and the phase difference θ of the temperature change on the surface of the metal thin film 43 are measured by measuring the temperature response on the surface of the metal thin film 43 for each of the plurality of frequencies f. The amplitude A and the phase difference θ are obtained at each frequency (step (a)). Then, based on the first function and the second function, the thermal conductivity λ ₃ of the thin plate 41 and the thermal conductivity λ ₂ of the insulating thin film 42 are obtained (steps (b) and (c)). Further, the fitting is performed by correcting or approximating the obtained value of the amplitude A so as to be close to or minimize the relationship of (Equation 8). Further, in addition to the amplitude A, fitting is performed so that the value of the phase difference θ is close to or minimizes the relationship of (Equation 9). This is because the accuracy can be further improved.
As a method for approximating or minimizing, a known method such as the least squares method can be used.

By fitting as described above, the thermal conductivity λ ₃ of the thin plate 41 can be measured with extremely small error.

The method for measuring thermal physical characteristics in the present embodiment is, for example, a SUS having a thickness of 10 to 100 μm or a high thermal conductive sheet made of a material having a thermal diffusivity (4 × 10 ^-6 [m ² · s ^-1 ]) corresponding to SUS. It is suitably used for evaluating the thermal conductivity in the thickness direction of. Further, the method for measuring thermal physical characteristics in the present embodiment is also suitably used for evaluating the thermal conductivity in the thickness direction of the carbon graphite sheet. In the carbon graphite sheet, the thermal diffusivity in the in-plane direction is 100 times larger than the thermal diffusivity in the thickness direction, so that the thermal diffusivity in the in-plane direction is attracting attention. On the other hand, there is no measuring method for obtaining the thermal diffusivity in the thickness direction of about 20 μm. Therefore, in the heat dissipation design when the carbon graphite sheet is used for heat dissipation of the device, it is useful to use the measured data in the thickness direction of the sheet obtained by using the thermophysical characteristic measurement method in the present embodiment.

The above-mentioned device is only one embodiment of the present invention, and the measuring device and measuring method are not particularly limited as long as they can be periodically heated to measure the temperature response. It is preferable to use the tongue method.
Further, in the present embodiment, the spot diameter of the laser beam 80 on the surface of the sample 40 is 100 μm, but the spot diameter of the laser beam of the present invention is not limited to this, and is not more than one tenth of the width of the metal thin film 43. It should be.

Further, by providing the XY stage 23 and moving the sample 40 with respect to the laser irradiation device 12 and the photodetector 13, the position where the laser light 80 is irradiated on the surface of the sample 40 is changed. The position where the laser beam 80 is irradiated may be changed by moving the laser irradiation device 12 or the photodetector 13 without moving the sample 40.

Next, as an embodiment of the present invention, the results of measurement under the conditions shown in Table 2 below will be described using the apparatus described in the embodiment of the present invention.
The dimensions of the thin plate were 7 mm in length and 5 mm in width, and the metal thin film was formed in the central portion on the insulating thin film in a length of 4 mm and a width of 2 mm.

The amplitude A and the phase difference θ were measured by measuring the temperature response by uniformly and periodically energizing and heating the metal thin film by intensity-modulating the voltage at the frequency f.

FIG. 7A is a graph showing a case where the measurement result is applied to the heat transfer model of the thermophysical characteristic measurement method according to the embodiment of the present invention, and FIG. 7B is a heat transfer model using the measurement result as a comparative example. It is a graph which shows the measurement result when the fitting is applied in. The heat transfer model as a comparative example was carried out using the thermophysical characteristic measurement method disclosed in Patent Document 1.

Here, the amplitude A and the phase difference θ at each frequency were calculated from the measurement results, and in FIGS. 7A and 7B, the amplitude A was plotted as “◯” and the phase difference θ was plotted as “Δ”. The vertical axis on the left side is the amplitude A normalized by (2ω) ^{-1 / 2} = 0.0154, and the vertical axis on the right side is the phase difference θ. The horizontal axis of FIG. 7 is (2ω) ^{-1 / 2} [s ^1/2 ].

Each plotted value was fitted using each parameter in Table 2 based on the one-dimensional heat transfer model described in the above embodiment. In FIGS. 7A and 7B, the result of fitting the amplitude A (◯) is shown by a solid line, and the result of fitting the phase difference θ (Δ) is shown by a dotted line.

When the thermophysical characteristic measurement method is used as a comparative example, the measurement result shown in FIG. 7 (B) is theoretically not valid in the range of 200 to 10000 Hz (ω- ^{1 / 2} > 0.012). there were. In the heat transfer model as a comparative example in which the heat flow reaches the back surface of the thin plate due to the low frequency and the thin plate is assumed to be semi-infinite, the thickness used in the examples cannot be ignored (the thickness is finite). It turns out that it is not applicable to.

On the other hand, when the thermophysical characteristic measurement method according to the present invention is used, the measurement result shown in FIG. 7A is a calculated value in the range of 200 to 10000 Hz (ω- ^{1 / 2} > 0.012). It matched. The sample was set again, multiple measurements were taken, and fitting was performed based on the obtained measurement results. As a result, the thermal conductivity of the thin plate λ _Si is 147 [W ・ m ^-1・ K ^-1 ], and the thermal conductivity of the insulating thin film λ _PMMA is 0.17 [W ・ m ^-1・ K ^-1 ]. _Si was within 10% of the theoretical value of 148 [W ・ m ^-1・ K ^-1 ].

1 Thermophysical property measuring device 2 Case 3 Measuring room 3a Insulation layer 4 Laser light source 5, 6 Condensing lens 7 Optical filter 8 Light receiving device 12 Laser irradiation device 13 Light detection device 21 AC power supply 22 Measuring device 23 XY stage 23a Jig 24 ₁ , ₂₄₂ probe 25 movement control device 33 synchronous detector 34 signal generator 35 arithmetic device 40 sample 41 thin plate 42 insulating thin film 43 metal thin film

Claims (4)

For a sample formed by sequentially laminating a second thin film and a first thin film having an unknown thermal conductivity on a thin plate having an unknown thermal conductivity.
(A) By measuring the temperature response on the surface of the first thin film due to periodic heating to the surface of the first thin film, the amplitude A and the phase difference θ of the temperature change on the surface of the first thin film are obtained. Process and
(B) Thermal conductivity λ ₁ of the first thin film, volume specific heat capacity C ₁ and film thickness d ₁ , thermal conductivity λ ₂ of the second thin film, volume specific heat capacity C ₂ and film thickness d ₂ , and the above. A step of deriving a first function showing the time dependence of the temperature change on the surface of the first thin film, including the thermal conductivity λ ₃ of the thin plate, the volume specific heat capacity C ₃ and the film thickness d ₃ .
(C) The thermal conductivity of the thin plate based on the second function showing the time dependence of the temperature change on the surface of the first thin film including the amplitude A and the phase difference θ and the first function. Includes a step of obtaining λ ₃ and the thermal conductivity λ ₂ of the second thin film.
The thin plate has a back surface that is an opposite surface of a surface facing the second thin film and a surface facing the second thin film.
In the first function, at least a part of the heat flow accompanying the heating of the first thin film flows from the first thin film toward the back surface of the thin film, is reflected vertically on the back surface, and flows toward the first thin film. A method for measuring thermophysical properties , which is derived by using a heat transfer model . For the temperature response of the first thin film in the step (a), the temperature change on the surface of the first thin film due to periodic heating of a plurality of frequencies ω by electrical or optical periodic heating is measured by a thermoreflectance method. The method for measuring thermophysical properties according to claim 1, wherein the method is characterized by the above. The method for measuring thermophysical properties according to claim 1 or 2, wherein the periodic heating of the surface of the first thin film is performed by forming a heat insulating layer on the back surface side of the thin plate. The first function is represented by the following (Equation 3), (Equation 4), and (Equation 5).
The method for measuring thermophysical properties according to any one of claims 1 to 3, wherein the second function is represented by the following (Equation 7).

However, m = 1 (first thin film), m = 2 (second thin film), m = 3 (thin plate), and the first
The interfacial thermal resistance between the thin film and the second thin film and the interfacial thermal resistance between the second thin film and the thin plate are 0 [m]. ² ・ K ・ W ^-1 ].

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