JPH0654299B2 - Thermal conductivity measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention relates to a thermal conductivity measuring method in the field of surface treatment such as thin film coating, and in the field of electronics such as semiconductor devices.

[Conventional technology]

Conventionally, as a method for measuring the thermal conductivity of a thin film, a thin film conductivity measuring method using radiative cooling (7th Japan Thermophysical Property Symposium, 1986 P227-230, Funamoto et al.) And AC
Law (Rev. Sci. Instrument., 1985,
56, 1643, Hatta et al.).

In the thin film thermal conductivity measurement method using radiative cooling, the thin film to be measured with both ends fixed to a holder is placed in a vacuum, heated from both ends with heaters, and the heat is radiated from the surface of the thin film to be measured to the surroundings. This is a method of measuring the film surface temperature distribution by a radiation thermometer when the amount of heat that escapes is balanced by the amount of heat that flows in from both ends and is in a steady state, and the thermal conductivity of the thin film is determined from that distribution.

In the AC method, while periodically heating the surface of the thin film to be measured with a light, the thin film to be measured is masked to create a place to be exposed to light and a place to be shaded. taking measurement. This is a method for obtaining the thermal conductivity from the thermal diffusivity, specific heat and density obtained from the mask movement amount and temperature amplitude in this state.

[Problems to be Solved by the Invention]

Generally, in the conventional thermal conductivity measuring method, the thermal conductivity cannot be measured unless the thin film to be measured is a single layer. For example, when a thin film to be measured that cannot exist as a single layer is formed on a substrate to measure thin film thermal conductivity using radiative cooling, the second factor is a factor that determines the surface temperature distribution of the thin film to be measured. As shown in the figure, the heat flow passing through the substrate 2 and the heat flow passing through the thin film 1 to be measured coexist, and the thermal conductivity measured from this is the combined thermal conductivity of the thin film 1 to be measured and the substrate 2.
When the thermal conductivity is measured by using the AC method, the temperature is measured on the side of the thermocouple A6, and as shown in FIG.
The temperature amplitude of the heat conducted inside is measured, and the measured thermal conductivity is the combined thermal conductivity of the thin film 1 to be measured and the substrate 2. Even if the position of the thermocouple is changed to the side of the thermocouple B7, the electric current flowing from the substrate 2 exists, so that the substrate 2
Can not remove the effect of. Therefore, it is difficult to measure the thermal conductivity of the thin film to be measured 1 which cannot exist as a single layer by the conventional method without removing the influence of the substrate 2.

[Means for Solving the Problems]

According to the present invention, the micro heater 3 is embedded between the thin film 1 to be measured on the substrate 2 at a constant gap interval, and the micro heater 3 generates heat at several K to several tens of kHz, so that the thin film 1 to be measured and the substrate 2 are heated. The effect of heat is separated, the phase of the temperature amplitude on the gap of the heater embedded from the surface of the thin film 1 to be measured is measured using a radiation thermometer, the phase difference from the phase of the micro-heater heating is calculated, and the heat is calculated from the phase difference. The diffusivity is calculated and multiplied by the heat capacity per unit volume of the measured thin film 1 to obtain the thermal conductivity by the following formula (1).

α = λ / C (1) where α is the thermal diffusivity, λ is the thermal conductivity, and C is the heat capacity per unit volume.

As another means, after separating the thermal effects of the thin film 1 to be measured and the substrate 2, a radiation thermometer is used to measure the temperature amplitude on the micro heater 3 and the gap between the micro heaters from the surface of the thin film 1 to be measured. The temperature diffusivity is measured, the thermal diffusivity is calculated from the amplitude ratio and the thin film thickness to be measured, and the thermal conductivity of the thin film 1 to be measured is obtained by using the equation (1).

[Action]

As shown in FIG. 1, microheaters 3 are continuously embedded in parallel between the thin film 1 to be measured and the substrate 2, and these are simultaneously heated to generate heat flow 4 in the substrate 2 as in the conventional method. Will not go around in the longitudinal direction and affect the surface of the measured thin film 1. Regarding the heat flow 4 flowing from the substrate 2 through the gap of the heater to the thin film 1 to be measured, the gap length was set sufficiently short to make it difficult to flow.

Next, a method for obtaining the thermal conductivity from the phase of the measured thin film surface temperature amplitude on the heater gap will be described.

Equations (2), (3), and (4) show approximate equations for this heat conduction phenomenon.

Where k is the reciprocal of the thermal diffusion length, f is the frequency, T is the surface temperature, x is half the gap length, ω is the angular frequency, t is the time,
Q is the generated thermal energy, and d is the measured thin film thickness.

The imaginary part of the equation (3) represents the phase, and the phase difference Δφ between the phase of the temperature amplitude on the heater gap and the heating phase of the microheater is represented by the equation (5).

Δφ = kx + π / 2 (5) Equation (6) is obtained from Equations (2) and (5), and the thermal diffusivity of the measured thin film 1 can be obtained from this.

α = πfx ² / (Δφ−π / 2) ² (6) From this thermal diffusivity, the thermal conductivity is calculated using the equation (1).

Next, as another method, a method of obtaining the thermal conductivity from the amplitude ratio of the surface temperature amplitude on the micro heater and the surface temperature amplitude on the gap of the heater will be shown.

In order to obtain the thermal diffusivity from the temperature amplitude ratio, the system is complicated and it is difficult to solve it with a theoretical approximation formula, so a computer simulation was performed. As a result, an analytical solution as shown in FIG. 4 was obtained. Here, 1 is a half of the pitch of the micro-heaters arranged in parallel, Tg is the surface temperature amplitude on the heater gap, and To is the surface temperature amplitude on the micro-heater 3.

From this solution, the thermal diffusivity of the thin film 1 to be measured can be calculated, and the thermal conductivity is calculated using the equation (1).

〔Example〕

In the following, the results of measuring the thermal conductivity of a ceramic film having the same composition by five methods as examples are shown.

Embodiment-1 Hereinafter, an embodiment of the present invention will be described with reference to the drawings. A heating resistor 12 is formed as a film on the glass 10 by sputtering, and is patterned by photoetching so as to have a dot size of 69 μm and a pitch of 85 μm. Then, Al is sputtered on the Al electrode 11 by a photo process to form a pattern. The prepared one was prepared (Fig. 5). Using this as a substrate for the thin film 1 to be measured, a ceramic layer 13 of this substrate was formed into a film having a thickness of 5 μm by sputtering to prepare a sample 1 (FIG. 6).

A pulse generator was connected to the Al electrode 11 of the prepared sample 1, and the energy amplitude was 0.2 W and the frequency was 5000.
Periodic heating at Hz was performed. As a result of preparing the radiation thermometer and measuring the surface temperature amplitude phase during heating, the phase difference from the heating energy phase is 0.56π, and the thermal diffusivity is calculated using equation (2). It becomes 83 × 10 ⁻⁵ m ² / sec, and the heat capacity per unit volume is 2.32 from the equation (1).
When multiplied by × 10 ⁶ J / m ³ k, the thermal conductivity is 66 W / m.
It became K.

Example-2 As in Example 1, the heating resistor 12 is formed on the glass 10.
A film was formed by sputtering, and this time, it was patterned by photoetching so as to have a dot size of 69 μm and a pitch of 170 μm. Then, Al was sputtered thereon, and an Al electrode 11 pattern was prepared by a photo process. On this substrate, the same ceramic layer 1 as in Example 1 was used.
Sample 3 was prepared by sputtering 3 to a thickness of 5 μm.

A pulse generator was connected to the Al electrode 11 of the prepared sample 2, and the same energy amplitude as in Example 1 was 0.2 W and periodic heating was performed at a frequency of 5000 Hz. As a result of measuring the phase difference using the radiation thermometer, the phase difference is 0.88π, and the thermal diffusivity is calculated using the formula (6) to be 2.81 × 1.
The value was 0 ⁻⁵ m ² / sec, and when the heat capacity per unit volume was multiplied by the equation (1), the thermal conductivity was 65 W / mK.

Next, when the heating frequency was reduced to 2500 Hz and the phase difference was measured, it was 0.77π. Similarly, when the thermal diffusivity is calculated by using the equation (6), 2.78 × 10 ⁻⁵ m ² / se
c, and by multiplying this by the heat capacity per unit volume according to formula (1), the thermal conductivity was 64 W / mK.

Example-3 Sample 1 was subjected to periodic heating with an energy amplitude of 0.2 W and a frequency of 5000 Hz using a pulse generator. Using a radiation thermometer, the temperature amplitude on the micro heater and the temperature amplitude between the micro heaters were measured, and the ratio was calculated to be 0.85. When the thermal diffusivity was calculated from the analysis diagram of FIG. 4, it was 2.82 × 10 ⁻⁵ m ² / sec, and by multiplying the heat capacity per unit volume by the equation (1),
The thermal conductivity was 65 W / mK.

Example 4 The same substrate as in Example 1 was prepared, and the same ceramic layer 13 as in Example 1 was sputtered on the substrate to a thickness of 2.5 μm to prepare Sample 3.

As with Example 3, this sample was subjected to periodic heating with an energy amplitude of 0.2 W and a frequency of 5000 Hz. A radiation thermometer was used to measure the temperature amplitude on the micro heater and the temperature amplitude between the micro heaters, and the ratio was calculated to be 0.76. When the thermal diffusivity was calculated from the analysis diagram of Fig. 4, it was 2.89 × 10 ^-5 m ² / sec, and (1)
From the formula, when multiplied by the heat capacity per unit volume, the thermal conductivity was 67 W / mK.

Example-5 The same substrate as in Example 1 was prepared, and the same ceramic layer 13 as in Example 1 was sputtered on the substrate to a thickness of 7 μm to prepare Sample 4.

As with Example 3, this sample was subjected to periodic heating with an energy amplitude of 0.2 W and a frequency of 5000 Hz. A radiation thermometer was used to measure the temperature amplitude on the micro heater and the temperature amplitude between the micro heaters, and the ratio was calculated to be 0.89. When the thermal diffusivity was calculated from the analysis diagram of Fig. 4, it was 2.95 × 10 ^-5 m ² / sec, and (1)
From the formula, when multiplied by the heat capacity per unit volume, the thermal conductivity was 68 W / mK.

Table 1 below shows a list of the measurement results shown in the examples. The thermal conductivity of the ceramic layer 13 could be accurately determined by either of the methods of phase difference and temperature amplitude ratio. In addition, the thermal conductivity could be obtained without affecting the measurement parameters and changes in film thickness.

As described above, according to the present invention, it is possible to accurately measure the thermal conductivity of a thin film that cannot exist as a single layer. It is possible to make a great use for the analysis of, and the design of a heat sink of a semiconductor device.

[Brief description of drawings]

FIG. 1 is an explanatory view showing a heat flow in a measurement sample of the present invention, and FIG.
FIG. 4 is an explanatory diagram showing the heat flow in the sample of the thermal conductivity measurement method using radiative cooling, FIG. 3 is an explanatory diagram showing the heat flow in the sample of the AC method, FIG. 4 is an explanatory diagram of analysis by simulation, and FIG. FIG. 6 is a sectional view of the measurement sample substrate of the present invention, and FIG. 6 is a sectional view of the measurement sample substrate of the present invention. 1 ... Measured thin film 2 ... Substrate 3 ... Micro heater 4 ... Heat flow 5 ... Heater 6 ... Thermocouple A 7 ... Thermocouple B 8 ... Light 9 ... Mask 10 ... Glass layer 11 ... … Al electrode 12 …… Heating resistor 13 …… Ceramic layer

 ─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Sanchio Yamamoto 6-31-1, Kameido, Koto-ku, Tokyo Seiko Electronics Co., Ltd. Examiner Kohei Sakurai

Claims (3)

[Claims] 1. A heat source is continuously arranged in parallel between a thin film to be measured and a layer serving as a substrate thereof at a constant interval, and a temperature change on the surface of the thin film to be measured is measured in a state where the heat source periodically generates heat. The thermal conductivity measuring method is characterized in that the thermal influence of the thin film to be measured and the substrate can be measured separately. 2. The thermal conductivity measuring method according to claim 1, wherein the thermal conductivity of the thin film to be measured is obtained based on the phase of the temperature amplitude of the surface of the thin film to be measured and the heating phase of the heat source. 3. The thermal conductivity measuring method according to claim 1, wherein the thermal conductivity is determined based on the surface temperature amplitude of the thin film to be measured.