JP7060378B2 - Thermal conductivity measurement method for metal film - Google Patents

Description

The present invention relates to a method for measuring thermal conductivity of a metal film.

There is a steady-state method as a typical method for measuring thermal conductivity (see, for example, Patent Document 1). In the stationary method, the sample is sandwiched between two insulated electrodes (a thermocouple is incorporated inside), and the temperature difference between the top and bottom of the sample ΔT (electrode) when heat is passed through the sample from above the electrodes. This is a method of measuring the temperature difference of the sample including the thermal resistance of the contact between the sample and the sample) and converting it into thermal conductivity. In the stationary method, heat is passed from the electrode side and passed through the sample, so that the sample itself does not generate heat.

Japanese Unexamined Patent Publication No. 2016-024083

At present, it is difficult to measure the thermal conductivity of the resistor film, which is the constituent material of the flat chip resistor, and the resistor film is printed and fired on the alumina substrate (base material), which is close to the actual product shape. It is especially difficult to measure the thermal conductivity in.

As shown in Patent Document 1, when the resistance film (thick film) is measured by utilizing the conventional steady-state method, the contact thermal resistance between the device electrode and the film becomes unstable and the measurement itself becomes difficult. Become. The reason why measurement is difficult is that it is difficult to prepare a sample. When the resistor paste is fired by itself to prepare a sample, the sample after firing is greatly deformed, and as a result, the thermal resistance of contact between the electrode and the sample is not stable, and correct measurement results cannot be obtained.

An object of the present invention is to accurately measure the thermal conductivity of a resistor film printed and fired on a substrate by using an infrared radiation thermometer.

The present invention is a method of measuring and calculating the thermal conductivity of a metal film formed on a plate body, in which the plate body is fixed to a cooling plate and heat is applied to the metal film until thermal equilibrium is obtained. The method comprising the step of measuring the thermal conductivity of the metal film from the surface temperature of the metal film and the reference temperature which is the surface temperature of the plate body or the lower surface temperature of the metal film. Further, the step of measuring the thermal conductivity of the metal film may include a step of measuring the surface temperature of the metal film with an infrared radiation thermometer. Further, the surface temperature of the plate may be used as a reference temperature.

According to the present invention, it is possible to accurately measure the thermal conductivity of a metal film such as a resistor film printed and fired on a substrate by using an infrared radiation thermometer.

It is a figure which shows one structural example of the model by this embodiment. It is a figure which shows the temperature distribution inside a resistor film in a thermal state. It is a figure which shows one configuration example of the measuring jig by this embodiment. It is a figure which shows the structural example of the sample used for the evaluation of thermal conductivity. It is a figure which shows the heat dissipation from other than the lower part of an alumina substrate.

Hereinafter, the technique for measuring the thermal conductivity of the metal film of the electronic component according to the embodiment of the present invention will be described in detail with reference to the drawings.

In recent years, the miniaturization of electronic devices and the high-density mounting of electronic components have progressed, and the heat generation density on the substrate has increased. Under such circumstances, the importance of thermal analysis in electronic device design is increasing. In order to improve the accuracy of thermal analysis, it is necessary to grasp the correct thermal physical characteristic value of each material, and the technique for measuring the thermal physical characteristic value is important.

The inventors have studied a measurement method using transient heat measurement in order to measure the thermal conductivity of a metal film, for example, a resistor film required for heat transfer analysis of a resistor. However, in many cases, comparative data cannot be obtained for the measured values, and in such cases, the validity of the measurement could not be determined. Therefore, we propose a simple method using an infrared radiation thermometer as a method for measuring the thermal conductivity of the resistor film used in the resistor. Specifically, the measurement target is a resistor film having a thickness of several tens of μm formed on an alumina substrate. In this embodiment, the thermal conductivity of the resistor film material was measured and verified by using a measurement method using an infrared radiation thermometer.

In the present invention, the temperature difference ΔT [K] between the upper and lower surfaces of the resistor film (thick film) when the steady temperature rises is measured by an infrared radiation thermometer, and the measured ΔT [K] is used to measure the resistor film (thick film). It is a method of calculating the thermal conductivity of. At this time, the resistance film (thick film) is a volume heating element that can generate a temperature distribution in the film while the entire film constantly generates heat. The temperature difference ΔT (x) from the upper surface of the resistor film (thick film) to the distance X is the shape of the film (L: dimension / W: dimension / thickness t), the distance X from the upper surface of the film, and the thermal conductivity of the film. It is determined by λ and the amount of heat Q given to the film, and the relational expression (1) holds. ΔT (X) is a function proportional to the square of the distance X from the upper surface of the film.

When the distance X from the upper surface of the film in the relational expression (1) is the film thickness t, it can be expressed as the temperature difference ΔT between the upper and lower surfaces of the film, and the temperature difference between the upper and lower surfaces of the resistor film (thick film) obtained from the actual measurement. It can be compared with ΔT by the relational expression (2).

By substituting ΔT measured by an infrared thermometer, the film shape (L: dimension / W: dimension / thickness t) obtained from the sample size survey, and the total calorific value Q of the resistor film into the relational expression (2). The thermal conductivity λ can be calculated.

According to one aspect of the present invention, it is a method of measuring the thermal conductivity of a metal film formed on a plate body, in which the plate body is fixed to a cooling plate and the metal film is subjected to heat equilibrium until thermal equilibrium is obtained. A method of applying heat and measuring the thermal conductivity of a metal film from the surface temperature T ₀ of the metal film and the reference temperature T _t which is the surface temperature of the substrate or the bottom surface temperature of the metal film is provided.

The steps for measuring the thermal conductivity of the metal film are the step of measuring the temperature difference (T ₀ −T _t ) between the surface temperature T ₀ and the reference temperature T _t with an infrared radiation thermometer, and the thermal conductivity λ. It is preferable to have a step of obtaining the above by the following formula.

Here, Q is the calorific value of the resistor film, and L (vertical), W (horizontal), and t (depth) are the dimensions of the resistor film, respectively. According to the above method, the thermal conductivity of the metal film can be obtained by using an ammeter, a voltmeter, and a dimensional measuring instrument.

It is preferable to measure the surface temperature T ₀ of the metal film with a thick metal film and measure the surface temperature T _t of the plate body in place of the thin film metal film.

According to the present invention, it is possible to accurately measure the thermal conductivity of a metal film such as a resistor film printed and fired on a substrate by using an infrared radiation thermometer.
Hereinafter, the principle and measurement results of thermal conductivity measurement using an infrared radiation thermometer will be described.

When the resistor is energized, the resistor film self-heats and the temperature rises. The heat generated by the resistor film flows toward the lower part of the substrate on which the resistor film is formed, and a temperature distribution peculiar to a self-heating element is formed inside the resistor film that has reached a thermal equilibrium state. In this embodiment, we focused on the relationship between the temperature distribution in the resistor film and the thermal conductivity, and applied it to the measurement of the thermal conductivity of the resistor film.

FIG. 1 is a perspective view showing a configuration example of a physical model according to the present embodiment. FIG. 1A shows the overall structure of this model. A pair of electrodes 5a and 5b and a resistor film (metal film) 3 for conducting between the electrodes 5a and 5b are formed on a ceramic substrate (also referred to as an alumina substrate or a plate) 1 made of alumina. .. The electrodes 5a and 5b are made of a conductive metal such as silver, and the resistor film 3 is made of a conductive metal such as ruthenium oxide, but the resistance film 3 is not limited thereto. It has the same structure as a so-called chip-type fixed resistor. The alumina substrate 1 is mounted on the cooling plate 7 with the grease 4 having good thermal conductivity interposed therebetween. By connecting the wiring to the electrodes 5a and 5b and energizing with the DC power supply 6, the current 8 flows through the resistor film 3 and self-heats. FIG. 1B is an enlarged view of the laminated portion of the resistor film 3 and the alumina substrate 1 shown by the broken line portion of FIG. 1A. Grease 4 is omitted in FIG. 1 (B).

Here, each parameter is defined as follows.
λ: Thermal conductivity of resistor film [W / (m ・ K)]
L, W, t: Dimensions of resistor film [m]
Q: Calorific value of the entire resistor film [W]
q _X : Heat flux passing through a minute interval d _X [W / m ² ]
T ₀ : Surface temperature of resistor film [° C]
T _t : Surface temperature of alumina substrate [° C]
x: Distance from the surface of the resistor film [m]
dx: Small interval at the position of distance x [m]
dR: Thermal resistance of minute section dx [K / W]
dT: Temperature difference generated in a minute interval dx [K]

As in the physical model shown in FIG. 1, when the resistor film 3 is energized while the lower surface of the alumina substrate 1 is cooled by the cooling plate 7, the temperature rises due to self-heating. The heat generated in the resistor film flows toward the lower part of the alumina substrate 1 as shown by the white arrow 9 indicated by reference numeral 9, and the temperature distribution peculiar to the self-heating element is inside the resistor film that has reached the thermal equilibrium state. Can be done. Hereinafter, the relational expression between the temperature inside the resistor film and the thermal conductivity will be derived for the case where the heat of the total calorific value Q is generated from the entire resistor film. First, consider the heat flux q _X passing through the minute interval dx at the position of the distance x in the + x direction. If the cooling from the lower part of the alumina substrate is sufficient, the heat flux q _X can be expressed by the equation (1) obtained by dividing the total calorific value from the section 0 to x by the area of the resistor film. Further, since the thermal resistance dR of the minute section dx can be expressed by the equation (2), the temperature generated in the minute interval dx by taking the product of the equations (1) and (2) and the area of the resistor film. The difference can be expressed by Eq. (3).

The temperature difference between the surface of the resistor film and the surface of the alumina substrate can be obtained by integrating Eq. (3) from x = 0 to t, and can be expressed as Eq. (4).

The temperature difference between the surface of the resistor film and the surface of the alumina substrate is determined by the thermal conductivity λ of the resistor film, the dimensions L, W, t and the total calorific value Q, and a parabolic temperature distribution is formed inside the resistor film. .. The temperature distribution shown in FIG. 2 from X = 0 to 40 μm is the temperature distribution when the thermal conductivity λ of the resistor film, the total calorific value Q of the dimensions L, W, t, and the surface temperature T ₀ are the values in Table 1. Is.

In the embodiment, the equation (5), which is a modification of the equation (4) with respect to the thermal conductivity, is used.

The surface temperature T ₀ of the resistor film and the surface temperature T _t of the alumina substrate in the thermal equilibrium state are measured by an infrared radiation thermometer. Further, the total calorific value Q of the resistor film is calculated by an ammeter and a voltmeter, and the dimensions L, W, and t of the resistor film are obtained by dimensional measurement. In this method, the thermal conductivity can be derived from a relatively small number of parameters as shown in the equation (5).

Next, the experimental method will be described with reference to FIG. A sample A in which the resistor film 3 and the metal terminals (electrodes) 5a and 5b are formed on the upper surface of the alumina substrate 1 is prepared. Both ends of the sample A are pressed by the plates 31a and 31b which are fixtures, and attached to the cooling plate 7 by the bolts 33a and 33b. A grease 4 having good heat conduction is interposed between the alumina substrate 1 and the cooling plate 7.

While the lower part of the alumina substrate 1 of the measurement sample A is cooled by the cooling plate 7, the temperature is raised by energizing the resistor film 3. Grease with a thermal conductivity of 2.95 W / (m · K) is applied between the lower part of the alumina substrate and the cooling plate to stabilize the contact thermal resistance between the lower part of the alumina substrate and the cooling plate. By using a grease having good thermal conductivity, the variation in contact thermal resistance is suppressed to about 10% of the total thermal resistance, and the surface temperatures T ₀ and T _t of the resistor film and the alumina substrate are stabilized. The variation in contact thermal resistance is the result of evaluation by transient heat measurement. When a sufficient time has elapsed and the measurement sample A has reached a thermal equilibrium state, the surface temperatures T ₀ and T _t of the resistor film 3 and the alumina substrate 1 are measured with an infrared radiation thermometer. For the measurement of the surface temperature T ₀ , a sample obtained by forming a resistor film to be measured for thermal conductivity (hereinafter referred to as “T ₀ sample”) is used. Further, for the measurement of the surface temperature T _t , a sample in which only the resistor film is changed to a metal thin film among the T ₀ samples (hereinafter referred to as “T _t sample”) is used.

Since the metal thin film has high thermal conductivity and the film thickness is as thin as 0.15 μm, the temperature difference between the upper and lower surfaces of the film is so small that it can be ignored. Therefore, the surface temperature of the metal thin film and the surface temperature of the alumina substrate can be treated as equivalent. That is, the surface temperature of the alumina substrate 1 can be regarded as the lower surface temperature (reference temperature) of the metal film. The structural image of the sample used for the measurement is shown in FIG. 4, and the dimensions of the resistor film and the emissivity ε on the surface are shown in Table 2. The emissivity is a value measured based on the reference (NEC Sanei Co., Ltd. "TH31-402 Data Capture Program Instruction Manual" (1999) Chapter 6, p.5-6), and the temperature is measured with an infrared thermometer. It was set as the setting value when Further, the total calorific value Q of the resistor film is calculated by using an ammeter and a voltmeter.

Table 3 shows the measurement results of the thermal conductivity of the resistor film. From the measurement, a thermal conductivity of 0.74 to 0.80 W / (m · K) was obtained, and the thermal conductivity of general soda glass was close to 1.03 W / (m · K). The film is mainly a composite material of SiO ₂ and a metal oxide, and since the main component is SiO ₂ , it is considered that the film has a thermal conductivity close to that of glass.

As a consideration for the thermal conductivity measurement error due to heat leakage, in this embodiment, it is a precondition that all the heat generated in the resistor film flows toward the lower part of the alumina substrate. However, in reality, heat leaks from the sample and harness surface due to heat dissipation due to natural convection and radiation. If the rate of this heat leakage is large, the measurement error becomes large. Here, the ratio of heat leakage to the total calorific value Q of the resistor film was evaluated by thermal analysis, and the measurement error due to heat leakage was considered (FIG. 5). FIG. 5 shows a thermal analysis model, and harnesses 51a and 51b are fixed to electrodes 5a and 5b in the structure shown in FIG. Heat dissipation due to natural convection and radiation was considered by the average heat transfer coefficient shown in equations (6) and (7). Natural convection is assumed to be heat radiation to air at 25 ° C, and radiation is assumed to be heat radiation to a 25 ° C environment where there is no reflection from the surroundings.

Here, the definition of the parameter is as follows.
h _con : Average heat transfer coefficient of natural convection [W / (m ² K)]
h _rad : Average heat transfer coefficient of radiation [W / (m ² K)]
C: Coefficient determined by dimensions and installation conditions [-]
S: Surface area of sample and wire harness [m ² ]
K: Representative length [m]
σ: Stefan-Boltzmann coefficient [W / (m ² · K ⁴ )]
ε: Emissivity [-]
T _cell : Surface temperature in degrees Celsius [° C]
T _ad : Absolute surface temperature [K]

From the analysis results, the heat leakage Qs from the sample surface and the heat leakage Qw from the harness surface are shown in Table 4. It was found that the ratio of the total heat leakage amount Qs + Qw to the total calorific value Q was as small as 0.15%, and the influence on the measurement error was also small.

As a result of measuring the thermal conductivity of the resistor film by using the measurement method using the infrared radiation thermometer described above, a thermal conductivity of 0.74 to 0.80 W / (m · K) was obtained. rice field.

According to this embodiment, it is possible to measure the thermal conductivity of the resistor film, which is very close to the actual product printed and fired on the alumina substrate.
The temperature difference between the upper and lower surfaces of the resistor film when the steady temperature rises is measured with an infrared radiation thermometer. A method is adopted in which the temperature of the upper surface of the film is measured using a sample of the target resistor film (thick film), and the temperature of the upper surface of the substrate is measured using the sample in which the resistor film (thin film) is formed.
The temperature difference between the upper and lower surfaces of the resistor film (thick film), which is a volume heating element, can be expressed by the relational expression (2), and the thermal conductivity can be easily calculated by using this relational expression.
It is possible to improve the measurement accuracy by devising the sample mounting conditions (selection of thermal paste 4, torque control when fixing the sample, type of base material, surface roughness on the cooling plate side, etc.) at the time of measurement.

The arithmetic processing and control described above are software processing by CPU (Central Processing Unit) and GPU (Graphics Processing Unit), ASIC (Application Specific Integrated Circuit), and FPGA (Field Programmable) hardware implementation by FPGA (Field Programmable). Can be done.

In the above embodiment, the configuration and the like shown in the illustration are not limited to these, and can be appropriately changed within the range in which the effect of the present invention is exhibited. In addition, it can be appropriately modified and implemented as long as it does not deviate from the scope of the object of the present invention.
In addition, each component of the present invention can be arbitrarily selected, and an invention having the selected configuration is also included in the present invention.

Further, the program for realizing the function described in the present embodiment is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read into the computer system and executed to process each part. May be done. The term "computer system" as used herein includes hardware such as an OS and peripheral devices.
For example, the object of the present invention may be a program for causing a computer to execute the thermal conductivity measuring method described above, or may be a computer-readable recording medium for recording the program.

INDUSTRIAL APPLICABILITY The present invention can be used as a method for measuring the thermal conductivity of an electronic component film.

1 Alumina substrate 3 Resistor film 4 Thermal grease 5a, 5b Metal terminals (electrodes)
7 Cooling plate 21 Infrared radiation thermometer

Claims (3)

It is a method of measuring and calculating the thermal conductivity of a metal film formed on a plate.
The plate is fixed to the cooling plate and
The metal film is energized to generate heat by itself until thermal equilibrium is obtained.
The method comprising the step of measuring the thermal conductivity of the metal film from the surface temperature of the metal film and the reference temperature which is the surface temperature of the plate body or the bottom surface temperature of the metal film. The step of measuring the thermal conductivity of the metal film is
The method according to claim 1, comprising the step of measuring the surface temperature of the metal film with an infrared radiation thermometer. The method according to claim 1 or 2, wherein the surface temperature of the plate is set as a reference temperature.

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