JP2846764B2 - Thermophysical property measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a sample having a specific heat of volume (ρ
If one of the three thermophysical constants of C), thermal conductivity (K), and thermal expansion coefficient (α) is known, the other two unknown thermophysical constants are calculated using one measurement principle. And a method for obtaining the same from the one known thermophysical property constant.

[0002]

2. Description of the Related Art Thermal volume specific heat, thermal conductivity, and coefficient of thermal expansion of a sample as described above are all important physical constants in thermal design, and are conventionally measured by the following methods.
The thermal conductivity (K) and the specific heat (C) are measured by, for example, a laser flash thermal constant measuring method. This is a method in which a laser beam is instantaneously irradiated and heated on the front surface of a sample held at a predetermined temperature, and the temperature change on the back surface of the sample from that moment is measured using a thermocouple or infrared detector. It is.
The outline of the measuring device is shown in FIG. The measured temperature of the back surface of the sample changes as shown in FIG. The thermal diffusivity D is obtained from the above-mentioned temperature change curve and equation (1) which is a solution of the one-dimensional heat conduction equation.
The specific heat C and the thermal conductivity K are calculated from the weight M and the density ρ of the sample, which are known in advance, using the equation (2). D = 1.37 (L / π) ² / (t) ^0.5 (1) C = Q / (M · ΔT), K = C · D · ρ (2) where t is the measurement time and L Is the thickness of the sample, ΔT is the temperature rise, and Q is the absorbed energy. The coefficient of thermal expansion α is
It is measured by a so-called minute constant load thermal expansion method in which a balance as shown in FIG. 9 is used and the expansion and contraction of the detection rod caused by heating the sample is detected by a differential transformer.

[0003]

As described above, although the thermal conductivity K and the thermal expansion coefficient α are both important physical constants in the thermal design, they are measured separately in the above-mentioned prior art. It is measured by the device, ie using different measurement principles, and cannot be obtained simultaneously in one measurement principle. Therefore, the consistency between the thermal constants is poor, and different data must be used for the measurement accuracy. As described above, since the measurement principles of the thermal conductivity K and the coefficient of thermal expansion α are different, it is necessary to separately process the sample into a shape suitable for each measurement principle, and the processing error of the sample may cause a variation in the measured data. As well as increase processing costs. Further, it is difficult to measure a thin material such as a semiconductor wafer by the above-described measurement principle. In the method of measuring the thermal conductivity K and the coefficient of thermal expansion α described above, only the average value of the entire processed sample is obtained, and even if K and α fluctuate in the sample, they must be measured finely. Can not.

[0004]

In order to solve the above-mentioned problems, the present invention provides three thermophysical properties of a sample such as volume specific heat (ρC), thermal conductivity (K), and thermal expansion coefficient (α). If one of the constants is known, the other two thermophysical constants are
In the method of obtaining from the one known thermophysical property constant using one measurement principle, a step of intermittently irradiating the sample with intensity-modulated excitation light and measuring the amplitude of thermal expansion vibration generated on the sample surface at that time includes the steps of: It is repeated at least three times using pump lights of different modulation frequencies, and the relationship between the obtained three or more sets of modulation frequencies and the thermal expansion amplitude is expressed as one relational expression where the volume specific heat, thermal conductivity, and thermal expansion coefficient are unknown. The method is configured as a method for measuring a thermophysical constant characterized by determining a relational expression between a known thermophysical property and an unknown thermophysical property by substituting, and obtaining an unknown thermophysical constant from the known thermophysical constant.

[0005]

The principle of measurement according to the present invention will be described with reference to FIG. Excitation light is intensity-modulated at a modulation angular frequency ω onto a sample as shown in FIG. The radius of the excitation light is r, and the power is P ₀ . Further, K is the thermal conductivity of the sample, α is the coefficient of thermal expansion, ρ is the density, and C is the specific heat. FIG. 5 shows the intensity modulation state of the excitation light as described above. The excitation light as described above penetrates into the sample by a depth d determined by the complex refractive index of the sample, as shown in FIG. The intrusion state is indicated by oblique lines. The heat generated therefrom has a heat diffusion length μ (= (2K
/ ΩρC) ^0.5 ) to increase the temperature of the heat diffusion region of the volume A by ΔT. One irradiation pulse (Fig. 5
Since the energy of the hatched portion is πP ₀ / ω and the heat capacity of the heat diffusion region is AρC, ΔT = πP ₀ / (AρC · ω) (3) Also, the amount of thermal expansion (2PA, PA in FIG. 4) Represents the amplitude of the thermal expansion vibration) 2PA = ααΔT ・ (d + μ) (4) From FIG. 4, A = π (r + μ) ² (d + μ) ... (5) Substituting equation (5) into equation (4) and rearranging yields equation (6). 2PA = αP ₀ / (2K + r (8ρCK · ω) ^0.5 + ρCr ² ω) (6) In order to evaluate the validity of the equation (6), α, C, ρ, K Four types of copper-based samples known to have been measured were compared with theoretical values obtained from the above equation (6). FIG. 6 shows the result, and shows that the theoretical value and the measured value match. Thus, the validity of the above equation (6) is understood. If K, α, and ρC in the above equation (6) are set as unknowns, and equation (6) is modified as 1 / (2PA) = y, ω = x ² to obtain these relational equations, Become like y = 2K / (αP ₀ ) + (r (8ρCK) ^0.5 / (αP ₀ )) x + (ρCr ² / (αP ₀ )) x ² (7) The above equation (7) expresses the above K, α, Since the three unknowns of ρC are included, the sample is irradiated intermittently with excitation light whose intensity is modulated at the modulation frequency ω (x = ω ² ) as shown in FIG. 5, and the amplitude of the thermal expansion vibration (2PA ) (2PA = 1 /
Each coefficient can be determined by repeating the step of measuring y) at least three times using pump lights having different modulation frequencies and determining the relationship between three sets of x and y. As a result, if P ₀ , r, etc., which are known in advance, are also included in the determined coefficients, K / α = X (8) (ρC · K) ^0.5 / α = Y (9) ρC / α = Z (10) X, Y, and Z are coefficients (constants) calculated by substituting the modulation frequency and the amount of thermal expansion obtained by the above three measurements into the equation (7). From the above equations (8) and (10), α = ρC / Z (11) K = (X / Z) · ρC (12) is obtained. Here, for example, if ρC is measured in advance, α and K can be obtained simultaneously from the above equations (11) and (12). In the above description, ρC is known and the remaining unknowns α and K are obtained from equations (8), (9), and (10). Similarly, for example, ρC and K are obtained with α already known, It is also possible to obtain ρC and α as known. As described above, according to this method, when one of the three thermophysical constants, that is, the volume specific heat (ρC), the thermal conductivity (K), and the thermal expansion coefficient (α) of the sample is known, The method of obtaining the two thermophysical constants from one of the above three thermophysical constants using one measurement principle expressed by the equation (7), wherein the excitation light intensity-modulated on the sample as described above Is intermittently illuminated, and the measurement process of measuring the amplitude (2PA) generated on the sample surface at that time in combination with the modulation frequency (ω) is repeated at least three times using the excitation light having different modulation frequencies. The known thermophysical properties and unknown thermophysical properties are obtained by substituting the relationship between the modulation frequency and the thermal expansion amplitude into one relational expression (Equation (7)) where the volume specific heat, thermal conductivity, and thermal expansion coefficient are unknowns. Are obtained (Equations (8), (9), and (10)), and By substituting the thermal property constants, and requests unknown thermal properties constant from these known thermal physical constants.

[0006]

EXAMPLE Next, three measurements were performed using the apparatus shown in FIG. 1 while changing the modulation frequency, and one of the three thermophysical constants was determined using the data obtained from these measurements. An example in which the remaining two unknown thermophysical property constants are obtained from one known thermophysical property constant will be described to provide an understanding of the present invention. In the case of the device shown in FIG.
2 and the driver 11 irradiate a laser beam intensity-modulated at a modulation frequency of 30 to 200 KHz as shown by a broken line. The laser beam irradiates a spot light having a diameter of several microns on the sample 16 by the dichroic mirror 5 and the lens 15 (FIG. 4). The thermal expansion vibration of the sample surface caused by this laser beam irradiation is caused by a heterodyne composed of a helium neon laser 1, a polarization beam splitter 2, a frequency shifter 18, a reference mirror 3, a quarter-wave plate 4, and a polarizer 6. It is measured with a type displacement measuring instrument. F ₁ in FIG. 1 is the carrier frequency, F _b is the beat frequency.
The light reflected by the mirror 3 and the light reflected by the sample 16 are combined by the polarization beam splitter 2, and the interference light is detected by the photodetector 7 and photoelectrically converted. The transition signal thus replaced with the electric signal is subjected to a signal processing circuit including a band-pass filter 8, a low-pass filter 9, a multiplier 13, and a lock-in amplifier 14 to remove noise therefrom. It is converted to amplitude (PA). FIG. 2 shows the amplitudes of the thermal expansion vibrations when the modulation frequency (ω / 2π) is changed to six types using a 0.5 mm thick silicon wafer as a sample using the measuring apparatus shown in FIG. PA), and these values agree with the theoretical values calculated from the above equation (6). FIG.
Is obtained by transforming the data of FIG. 2 into an equation of y = １ ／ PA and x = (ω) ^0.5 used to transform the equation (6).
And y. By substituting the three measured values in FIG. 3 obtained in this way into equation (7) and solving these three simultaneous equations, the coefficients X and Z are determined in advance using equations (8) and (10). When calculated from the values P ₀ (power of the excitation light) and r (spot radius), X = 7.0 × 10 ⁷ [W / m] and Z = 6.9 × 10 ¹¹ [J / m ³ ] are obtained. Was done.

By substituting these values into equations (8) and (10), the density ρ = 23
30 [kg / m ³ ], specific heat C = 772.4 [J / kg ·
K], the specific heat of volume ρC = 1.8 × 10 ⁶ [J / m
Since the ³ K], (11) from the equation, α = (ρC) / Z = (1.8 × 10 6) / (6.9 × 10 11) = 2.6 × 10 -6 [/ K] K = (X / Z) · ρC = ((7.0 × 10 ⁷ ) / (6.9 × 10 ¹¹ )) × (1.8 × 10 ⁶ ) = 182 [W / mK] This value is based on the literature value (α = 2.5 × 10 ⁻⁶ [/
K], K = 170 [W / mK]).
As described above, in this embodiment, the volume specific heat of the sample (ρ
C), thermal conductivity (K), and thermal expansion coefficient (α), one of the three thermophysical constants (specific heat of volume) is known, and the other two thermophysical constants (thermal conductivity, thermal expansion) The coefficient of thermal expansion (α) is unknown, but if the coefficient of thermal expansion (α) is known, the value of α is substituted into equation (8) to determine the thermal conductivity (K), and the equation (10) Can be obtained by the same method by substituting α into the above equation to obtain the volume specific heat (ρC). Further, if the thermal conductivity (K) is known, the thermal expansion coefficient (α) is obtained by substituting K into the equation (8), and α and K already obtained in the equation (9).
Can be substituted to obtain ρC, or α obtained from the above equation (8) can be substituted into the equation (10) to determine ρC. In short, the modulation frequency of the intensity modulation obtained by the measurement and the amplitude of the thermal expansion vibration corresponding thereto are substituted for the equation (7) in the above embodiment, and the relational equation between the known thermophysical property constant and the unknown thermophysical property constant ( (8), (9), and (10) are obtained, and the remaining unknown thermophysical constants can be obtained by substituting the known thermophysical constants into these equations. In the above example, in order to obtain the relationship between the three unknowns from equation (7), the results of the three measurements are substituted into equation (7) to determine the constants as the respective coefficients. Then, the relationship between PA and ω (that is, y and x) may be obtained, and each coefficient may be calculated from them using the least squares method. Thereby, the accuracy is further improved.

[0008]

The present invention is constructed as described above, so that the sample has a specific volumetric heat (ρC), thermal conductivity (K),
If one of the three coefficients of thermal expansion (α) is known, the other two can be obtained based on one measurement principle, so the degree of variation between the obtained thermophysical constants is homogenized, and the data Reliability is improved.

[Brief description of the drawings]

FIG. 1 is a block diagram of a thermal expansion vibration measuring device to which the present invention can be applied.

FIG. 2 is a graph showing a relationship between a modulation frequency and a thermal expansion vibration amount obtained by the measurement device of FIG. 1;

FIG. 3 is a graph obtained by modifying FIG. 2;

FIG. 4 is a conceptual diagram for explaining the theory of the present invention.

FIG. 5 is a graph showing an irradiation state of the excitation light shown in FIG.

FIG. 6 is a graph showing a relationship between a theoretical value and an actually measured value for evaluating the validity of the equation (6).

FIG. 7 is a schematic diagram of a conventional apparatus for measuring thermal conductivity and specific heat.

FIG. 8 is a graph showing a temperature change obtained by the apparatus of FIG. 7;

FIG. 9 is a principle view showing a conventional apparatus for measuring a coefficient of thermal expansion.

[Explanation of symbols]

10 semiconductor laser (excitation light laser) 1 helium neon laser (reference light source) 7 photodetector

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Hirofumi Imanaka 1-5-5 Takatsukadai, Nishi-ku, Kobe Kobe Steel, Ltd. Kobe Research Institute (58) Field surveyed (Int. Cl. ⁶ , DB name) G01N 25/00-25/72 JICST file (JOIS)

Claims (1)

(57) [Claims] 1. When one of three thermophysical constants of a sample, ie, volume specific heat (ρC), thermal conductivity (K), and coefficient of thermal expansion (α), is known, the other two thermophysical constants are known. Irradiating the sample with an intensity-modulated excitation light intermittently and measuring the amplitude of thermal expansion vibration generated on the surface of the sample at that time. Is repeated at least three times using pump light of different modulation frequencies, and the relationship between the obtained three or more sets of modulation frequencies and the thermal expansion amplitude is defined as the volume specific heat, thermal conductivity, and thermal expansion coefficient as unknowns.
A method for measuring a thermophysical property constant, comprising: obtaining a relational equation between a known thermophysical property property and an unknown thermophysical property property by substituting into two relational equations; and obtaining an unknown thermophysical property constant from the known thermophysical property constant.