JPH0479411B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method and apparatus for measuring thermal diffusivity using AC calorimetry for determining the thermal diffusivity in a direction perpendicular to the thickness of a thin sample plate having a thickness of, for example, 0.5 mm or less.

Conventionally, various methods have been devised to measure thermal diffusivity, but it has been impossible to determine the thermal diffusivity in a direction perpendicular to the thickness of a thin sample plate with a thickness of 0.5 mm or less. However, in recent years, with advances in electronics technology, it has become common for semiconductor materials to be deposited on thin electrical insulators, such as ceramic plates, to a thickness of 0.5 mm or less. It has become necessary to know the nature of

An object of the present invention is to provide a method and apparatus for measuring thermal diffusivity by AC calorimetry that satisfies such requirements. With the part covered with a covering member, heat energy of a constant amplitude is repeatedly and intermittently irradiated on one side at a frequency f, and temperature waves are generated at points at various distances from the end of the covering member in the shielded part of the sample plate to be measured. The amplitude T _ac is measured, the slope value k of the characteristic line of the logarithm of the temperature wave amplitude T _ac is determined using the distance as a variable, and the thermal diffusivity in the direction perpendicular to the thickness of the sample plate to be measured is calculated from the following formula k=√. The second invention is characterized in that D is obtained, and the second invention includes a cover member that covers a part of one side of a thin sample plate to be measured with a constant thickness, and thermal energy of a constant amplitude is applied from the upper part of the cover member to the sample plate to be measured. A heat source equipped with a chopper that irradiates intermittently at a frequency f on one side, a thermocouple fixed to the shielded part of the sample plate to be measured, and changes in the distance between the end of the covering member and the thermocouple fixing point are measured. The thermocouple is characterized in that it is comprised of a micrometer and a lock-in amplifier that amplifies the AC output of the thermocouple.

Embodiments of the present invention will be described below with reference to the drawings. 1 and 2 show an embodiment of the measuring device of the present invention. In the same figure, 1 has a thickness of 0.1 to 0.5 mm, for example.
A cover plate 2 that covers a part of one side of the sample plate 1 is arranged on the top of the sample plate 1 so as to be movable along the surface of the sample plate 1. A heat source such as a tungsten lamp with a chopper 3 attached thereto was placed. As shown in the second figure, the chopper 3 is comprised of a semicircular plate that is rotatably supported at its diametrical center and rotated at a predetermined number of revolutions by a motor (not shown). 5 is the cover plate 2
6 is a distance L from the end of the cover plate 2 on the surface of the sample plate 1 to be measured that is shielded from the thermal energy irradiation of the heat source 4 by the cover plate 2.
With a thermocouple spot-welded to the point, the thermocouple 6 is connected to a lock-in amplifier 8 that uses the output of a sensor 7 made of, for example, a phototransistor as a reference signal, and the AC output of the thermocouple 6 is amplified by the lock-in amplifier 8. I did it like that. The heat source 4 equipped with the chopper 3, the thermocouple 6 spot-welded to the sample plate 1, and the lock-in amplifier 8 connected to the thermocouple 6 and using the output of the sensor 7 as a reference signal are the well-known AC calorimetry device. Although not shown, there is also a heat bath in which the sample plate 1 is placed. In AC calorimetry, the object to be measured is placed in a heat bath (not shown) (a hollow metal block that has a large heat capacity and is kept at a constant temperature) and is connected to the heat bath with a predetermined thermal resistance. The sample plate 1 is repeatedly subjected to intermittent heat using a chipper or the like at a constant frequency, for example, 0.1 to 10 Hz, and with the same thermal energy over the irradiation range.
A method for determining the specific heat of the sample plate 1 based on the principle that when heated in an alternating current manner, the alternating current component of the temperature of the sample plate 1 is inversely proportional to the specific heat of the sample plate 1,
The thickness of the sample plate 1 to be measured is significantly thinner than the wavelength of the temperature wave, and is selected to be, for example, 0.3 to 0.5 mm.

Next, the method and apparatus for measuring thermal diffusivity according to the present invention will be explained.

Based on the measurement principle of AC calorimetry mentioned above,
The exposed portion of one side of the sample plate 1 to be measured is irradiated with intermittent heat, which is converted into alternating current by a chopper 3, and the thermal energy is uniformly repeated over the irradiation area with an amplitude Q per unit area. As mentioned above, the thickness of the sample plate 1 to be measured is made significantly thinner than the wavelength of the temperature wave, so that the phase and amplitude of the temperature wave on one side of the sample plate 1 to be measured are the same as on the other side, Further, the thermal resistance is made large enough to prevent the heat from escaping into the heat bath when the heat of the sample plate 1 to be measured is conducted from the end of the cover plate 2 in the surface direction of the sample plate 1 to be measured.

Assuming that the sample plate 1 to be measured is infinitely long,
The temperature wave amplitude T _ac detected by the thermocouple 6 is given by the following equation as a function of the distance L by solving a differential equation of heat conduction.

However, f (=ω/2π) is the AC frequency of the thermal energy Q due to the chopper, c is the specific heat per unit volume of sample (1), d is the thickness of sample (1), and D is the frequency perpendicular to the thickness of sample (1). Thermal diffusivity τ _e is the relaxation time required for heat to escape from the sample (1) to the heat bath. When the relaxation time is increased, equation (1) becomes as follows.

T _ac =Q/2ωcde ^-kL-i(kL+ 〓 ²⁾ ...(2) k=√...(3) k is the reciprocal of the thermal diffusion length.

As is clear from equation (2), the absolute value of the temperature wave amplitude T _ac of the measured sample (1) at distance L |T ac | is |T _{ac |} =Q/2ωcd・e ^-KL ……(4) This value is measured by amplifying the output signal of the thermocouple (6) with a lock-in amplifier 8. In other words, the lock-in amplifier 8 uses the output of the sensor 7 as a reference signal to amplify the AC output of the thermocouple (6) and converts it into DC output, that is, outputs it as a temperature wave amplitude, so by measuring this value, The temperature wave amplitude |T _ac | can be determined. Transforming equation (4), log | T _ac | = logQ/2ωcd−KL ...(5) Equation (5) is a linear equation regarding L, and k is the gradient of the function log | T _ac | with L as a variable. It is.

Assuming that the sample plate (1) to be measured has a finite length, the temperature wave amplitude T _ac detected by the thermocouple (6) can be determined by solving the differential equation of heat conduction, and the distance L
It is given by the following equation as a function of

T _ac = QR/cosh[kL(1+i)]+RSk(1+i)sinh[
kL(1+i)]...(1') However, kL≧1 RSk＞1 S is the thermal conductivity in the direction perpendicular to the thickness of sample (1) k=√ k is the inverse of the thermal diffusion length However, f is the heat due to the chopper AC frequency of energy D is thermal diffusivity in the direction perpendicular to the thickness of sample (1) When the thermal resistance R is increased and the AC frequency is increased, equation (1') becomes as follows.

T _ac √2Q/Sk・e ^-kL-i(kL+ 〓 ⁴⁾ ...(2') As is clear from this equation, the absolute value of the AC temperature T _ac of the measured sample (1) at the distance L | T _ac | is |T _ac |=√2Q/Sk・e ^-kL ……(4′), and by transforming equation (4′), log|T _ac |=log√2Q/Sk−kL ……(5 ') Equation (5') is a linear equation regarding L, and k is the gradient of the function log|T _ac | with L as a variable.

As is clear from comparing equations (5) and (5′),
Although the assumptions for the sample plate (1) to be measured are different, in both cases, k is a function log |T _ac | with the distance L as a variable.
There is no change in the fact that the slope is .

Thus, when the cover member (2) is slightly moved a number of times using the micrometer (5), and the temperature wave amplitude T _ac for each movement is determined from the output of the lock-in amplifier (8) and plotted, a straight line is obtained as shown in Figure 3. Therefore, k is determined from the slope of this straight line. The thermal diffusivity D is obtained by substituting this k value into equation (2) or equation (2'). The characteristics shown in Figure 3 are the AC frequency f for Al ₂ O ₃ with a thickness of 0.1 mm.
= 10Hz, L = 0.7mm,
By substituting k obtained from this into equation (2) or (2'), the obtained thermal diffusivity D was 0.0798 cm ² /sec. In order to measure the temperature wave amplitude at a distance L from the end of the cover plate 2, the distance L may be measured and a thermocouple 6 may be attached to the distance L. This requires a lot of work, and since the effective heat capacity of the sample plate 1 to be measured tends to change each time it is attached, measurement errors are likely to occur.

In contrast, as described above, the thermocouple 6 was fixed to the shielded part of the sample plate 1 to be measured, and the distance between the end of the cover plate 2 and the fixed point of the thermocouple 6 was measured using a micrometer. Therefore, even if the distance L changes, there is no need to change the thermocouple, and handling is easy.Also, even if the effective thermocapacitance of the sample plate 1 to be measured changes due to the installation of the thermocouple, it will not be affected by the distance L. Since the effective heat capacity is constant, the above (4),
As is clear from equation (4') or equation (5) (5'), no measurement error occurs.

According to the present invention, the thickness may be, for example,
It has the effect of being able to obtain the thermal diffusivity in the direction perpendicular to the thickness of a thin sample plate of 0.5 mm or less.

Moreover, there is an effect that a measuring device can be obtained which can measure thermal diffusivity without requiring any trouble and with less error.

[Brief explanation of drawings]

Fig. 1 is a diagram of an embodiment of the device of the present invention, Fig. 2 is a plan view excluding the heat source and lock-in amplifier, and Fig. 3 is the logarithm of the temperature wave amplitude of the sample plate with respect to the movement of the cover plate. The characteristic diagram is shown. 1... Sample plate to be measured, 2... Covering member, 3...
Chiyotupa, 4...Heat source, 5...Micrometer,
6...Thermocouple, 7...Sensor, 8...Lock-in amplifier.

Claims (1)

[Scope of Claims] 1. One side of a thin sample plate to be measured with a constant thickness is covered with a covering member, and thermal energy of a constant amplitude is repeatedly and intermittently irradiated to the one side at a frequency f, and the sample plate to be measured is Measure the temperature wave amplitude T _ac at various distances from the end of the cover member in the shielded part of the plate, and find the slope value k of the characteristic line of the logarithm of the temperature wave amplitude T _ac with the distance as a variable. , a method for measuring thermal diffusivity by AC calorimetry, characterized in that the thermal diffusivity D in a direction perpendicular to the thickness of the sample plate to be measured is obtained from the following equation k=√. 2. A cover member that covers a part of one side of a thin sample plate to be measured with a constant thickness, and thermal energy of a constant amplitude is applied from the top of the cover member to one side of the sample plate to be measured at a frequency f.
a heat source equipped with a chopper that irradiates intermittently, a thermocouple fixed to a shielded portion of the sample plate to be measured, and a micrometer that measures changes in the distance between the end of the covering member and the thermocouple fixing point; and a lock-in amplifier for amplifying the AC output of the thermocouple.