JP2009257846A - Evaluation method of heat permeability - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an evaluation method of heat permeability using a thermal probe. <P>SOLUTION: A temperature in the thermal probe at the time of the contact of a sample to be measured with a probe rod is evaluated at a plurality of points using a thermophysical value measuring instrument equipped with the thermal probe composed of a probe block and a probe rod and compared with the result of a sample known in heat permeability using the temperature difference between adjacent measuring places to lead out the heat permeability of an unknown sample. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for evaluating the thermal permeability of a sample, and more particularly to a method for evaluating the thermal permeability of a substance using a measuring device using a thermal probe.

  When designing a semiconductor substrate such as a CPU, it is important to design the heat so that the temperature rise of the semiconductor substrate due to heat generated during operation is minimized, and the thermal conductivity of the material used Evaluation is necessary. In the case of thermoelectric conversion materials that may be useful for environmental problems in terms of converting waste heat into electricity and reusing it, materials with low thermal conductivity must be developed to improve the performance of thermoelectric conversion. I must.

  Conventionally, the thermal conductivity is measured by a laser flash method or a steady method.

  In general measurement methods, measurement must be performed using a bulk material, and the shape of the measurable bulk material is limited. For example, the shape is limited to a shape of diameter 10 mm × thickness 1 mm, angle 25 mm × thickness 1 mm, and only the thermophysical values of the entire bulk can be measured.

  Moreover, the sample produced in the development stage of the thermoelectric conversion material may have a non-homogeneous material or a sample shape that cannot be measured by a general measurement method. Accordingly, there is a need for development of an apparatus that can verify the homogeneity of a sample and can evaluate a sample that cannot be evaluated by a general measurement method, and an evaluation method thereof.

  As a technique related to the measurement of thermophysical properties in a minute region, for example, a method of measuring the thermal permeability by applying a periodic heating method and a thermoreflectance technique (see, for example, Non-Patent Document 1 and Patent Document 1), AFM STHM technology that measures thermal images using the technology (see, for example, Non-Patent Document 2) and STP method that collects temperature information on the sample surface using a thermocouple with a thin tip as well as a cantilever and uses it for surface shape measurement ( For example, the nonpatent literature 3 reference) etc. are proposed. A plurality of thermophysical property measurement methods using thermal probes have been proposed (see, for example, Non-Patent Documents 4 and 5, Patent Documents 2 and 3).

  In the case of Non-Patent Documents 4 and 5, a thermal probe is used as a sheath thermocouple, and measurement is performed using the temperature of the sheath thermocouple. Use of a sheathed thermocouple is not suitable for measurements other than thermal conductivity. On the other hand, in the case of Patent Document 3, the temperature at a plurality of points in the thermal probe is measured by a thermocouple. Although the thermal conductivity is converted based on the time dependence of the temperature change, it has not been theoretically verified and is determined by an empirical formula.

JP 2000-121585 A JP 2004-003872 A JP 2008-057144 A Thermal effusivity distribution measurements using a thermo- reflectance technique; in Proceeding of 10th International Conference of Photo-acoustic and Photothermal Phenomena, pp. 315-317 (1999); N. Taketoshi, M. Ozawa, H. Ohta, and T. Baba . Scanning Near-Field Optical Microscopy and Scanning Thermal Microscopy; Jpn. J. Appl. Phys. Vol. 33, p.p.3785-3790 (1994); R. J. Pylkki, P. J. Moyer, and P. E. West. Scanning Thermal Profiler; Appl. Phys. Lett., Vol. 49, No23, pp. 1587-1589 (1986); C. C. Williams and H. K. Wickamasinghe. Measurement method of three-constant thermal solids using a point contact temperature probe (measurement theory); Thermophysical properties, 13, 4, pp.246-251; Ichiro Takahashi, Masami Sasamori. Measurement method of three-state solid heat using a point contact temperature probe (examination of measured object shape and measurement conditions); Thermophysical properties, 13, 4, pp.252-257; Ichiro Takahashi, Masami Sasamori.

  Conventionally, when performing thermal conductivity evaluation based on measuring the temperature at a plurality of points in a thermal probe, it is based on an experimental formula and has not been theoretically verified using a heat transfer model.

  An object of the present invention is to solve the above-described problems of the prior art, and a method for directly measuring the temperature in a thermal probe and evaluating the thermal permeability of a substance by a method that matches the heat transfer model. It is to provide.

  When evaluating the heat permeability of a minute region, the present inventors use a measuring device equipped with a thermal probe to accurately measure the temperature at a plurality of points in the thermal probe, and the heat of an unknown material. It was noticed that the penetration rate could be accurately evaluated, and the present invention was completed.

  The thermal permeability evaluation method of the present invention uses a thermophysical property measuring apparatus equipped with a thermal probe composed of a probe block and a probe rod to determine the temperature in the thermal probe when the sample to be measured and the probe rod are in contact with each other. It is characterized by deriving the thermal permeability of an unknown sample by evaluating at a plurality of points and comparing the result of a sample with a known thermal permeability using the temperature difference between adjacent measurement locations.

  The temperature in the thermal probe at the time of the contact is measured either by directly contacting a thermocouple with the tip of the probe rod or by measuring a thermocouple made of a material different from the probe rod at the tip of the probe rod. It is.

  At the time of contact between the known sample and the probe rod tip, the temperature of a plurality of measurement locations in the probe rod is measured, the temperature difference between adjacent measurement locations is calculated, and heat penetration is performed based on the calculated temperature difference of the known sample. A calibration formula for the rate is derived, and the thermal penetration rate of the unknown sample is evaluated using this calibration formula.

  According to the present invention, by accurately measuring a temperature difference in the thermal probe, a calibration formula based on a heat transfer model of a heat permeability and a temperature difference of a sample with a known heat permeability is prepared. The thermal permeability can be evaluated from the measurement results for unknown samples using the calibration formula. Since the calibration formula verified by the heat transfer model is used, the evaluation accuracy of the thermal permeability of the unknown sample can be improved. When the present invention is applied, there is an effect that it is easy to obtain a thermal permeability distribution measurement of a sample having a shape that cannot be generally measured or a heat permeability.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  According to the present invention, a thermal probe at the time of contact between a sample to be measured placed on a sample stage and the tip of the probe rod using a thermophysical property measuring apparatus provided with a thermal probe comprising a probe block and a probe rod. The temperature inside is evaluated at multiple points. By using the temperature difference between adjacent measurement locations and comparing the result with a sample with a known thermal permeability, the thermal permeability of an unknown sample can be accurately derived.

(About thermophysical property measuring device)
The thermophysical property measuring device used in the present invention can be used in a measuring device including a thermal probe provided with a heating means such as a heater and probe rods capable of measuring temperatures at a plurality of points.

  An example of a typical thermophysical property value measuring apparatus is shown below. Here, as a typical example of the probe rod, a probe of a method for measuring a plurality of voltages and / or temperatures according to a patent application filed on the same day as the present patent application is used. A configuration diagram of a measuring apparatus using this representative example is shown in FIG.

  In FIG. 1, 1 is a sample stage made of material C (for example, copper), 2 is a thermal probe, and 21 and 22 are probes made of material A (for example, constantan). Block and probe rod.

The thermal probe 2 is integrally formed of the same material from the probe block 21 and the probe rod 22, and the probe block 21 and the probe rod 22 move together during measurement. The temperature (T _pb ) of the probe block 21 and the temperature (T _sb ) of the sample stage 1 are configured to be kept at a constant temperature during measurement by a temperature control means (not shown).

Before the measurement using the above-described apparatus, the temperature (T _pb ) of the probe block 21 and the sample _stage 1 are measured while the sample S with the known thermal permeability and the tip of the probe rod 22 of the thermal probe 2 are not in contact with each other. The temperature is controlled with _{respect to the} temperature (T _sb ). However, control is performed so as to satisfy the relationship of T _pb ≧ T _sb + 10 ° C. This is to make the tip of the probe rod sufficiently higher than the sample temperature. The measurement is performed by contacting the probe rod 22 and the sample S to be measured. During the contact, the temperature in the probe rod 22 is measured. After contact for a certain time, the tip of the probe rod 22 of the thermal probe 2 is separated from the sample S.

The temperature in the probe rod 22 is measured at three points T ₁ , T ₂ , and T ₃ . From T ₁ , T _2, and T ₃ in the probe rod 22, voltage / temperature measurement lines (material B: for example, chromel) 22 a, 22 b, and 22 c are drawn out for measurement, respectively. However, the measuring instrument is connected to the probe reference measurement line 2a (material A: constantan, for example). Therefore, in the above temperature measurement, the temperatures of T ₁ , T ₂ and T ₃ can be measured as an E thermocouple of chromel-constantan.

After contact with the sample S to be measured, the temperature difference between two adjacent measurement points in the probe rod 22 is T _1b −T _2b , T _2b −T _3b , (T _1b , T _2b and T _3b is the temperature of T ₁ , T ₂ and T ₃ after contact, respectively).

Before and after the contact, the temperature at T ₁ , T ₂ and T ₃ in the probe rod 22 changes. This temperature change is related to the amount of heat transferred to the sample. For this point, see the heat conduction equation (1) below.

  In the above formula, q is the heat flux, Q is the amount of heat, A is the cross-sectional area, λ is the thermal conductivity, dT is the temperature change, and dx is the distance change.

The temperature change in the probe rod 22 depends on the sample. When the control temperature (T _sb ) of the sample stage 1 and the control temperature (T _tb ) of the probe block 21 are kept constant, and the temperature of a plurality of samples is measured, the sample dependence of the temperature change in the probe rod 22 is systematized. It is thought that it can be evaluated.

(Theory by heat transfer model)
In the measurement of thermal permeability, the reliability of the measurement method using a thermal probe can be improved by combining with the theoretical background. From this viewpoint, first, the theory based on the heat transfer model will be described with reference to FIGS. 2 (a) and 2 (b), and the time dependence of the temperature in the probe rod based on the theory is shown in FIGS. 3 (a) and 3 (b). Next, the data obtained by measuring the temperature in the probe rod in order to verify the theory will be described with reference to FIGS. 4 (a) and 4 (b). In FIGS. 3A and 3B and FIGS. 4A and 4B, the horizontal axis represents elapsed time (t / s), and the vertical axis represents temperature (T / ° C.).

  Assuming that the temperature in the probe rod before the contact between the sample to be measured and the probe rod of the thermal probe is one-dimensional heat transfer model from the temperature controller toward the tip,

（上記式中、ｑ_beforeは接触前の熱流束、λはプローブ棒の熱伝導率、ｄＴは温度変化、ｄｘは距離変化を表す。）
温度制御部からの距離によって直線的に温度変化するとしてプローブ棒内の温度を計算する（図２（ａ））。

(In the above formula, q _before represents the heat flux _before contact, λ represents the thermal conductivity of the probe rod, dT represents the temperature change, and dx represents the distance change.)
The temperature in the probe rod is calculated assuming that the temperature changes linearly with the distance from the temperature control unit (FIG. 2A).

When a steady state is reached after contact between the sample to be measured and the probe rod of the thermal probe, the temperature at the contact point (T _cp ) corresponds to the temperature when two kinds of semi-infinite solids are in contact, and the temperature inside the probe rod Assumes that a one-dimensional heat transfer model is established from the temperature controller to the tip,

（上記式中、ｑ_{ａｆｔｅｒ}は接触後の熱流束、λはプローブ棒の熱伝導率、ｄＴは温度変化、ｄｘは距離変化を表す。）
温度制御部からの距離によって直線的に温度変化するとしてプローブ棒内の温度を計算する（図２（ｂ））。

(In the above formula, q _after is the heat flux _after contact, λ is the thermal conductivity of the probe rod, dT is the temperature change, and dx is the distance change.)
The temperature in the probe rod is calculated assuming that the temperature changes linearly with the distance from the temperature control unit (FIG. 2B).

In this model, the material A (e.g., constantan, etc.) are produced by a thermal probe temperature probe rod tip is T _4, made of a material D (e.g., copper), the control temperature is T _sb sample A case consisting of a table was assumed. Assuming that a steady state is reached after contact, the temperature inside the probe rod assumes that a one-dimensional heat transfer model is established from the temperature controller to the contact portion, and the probe rod is assumed to change linearly with the distance from the temperature controller. Calculate the temperature inside. (Fig. 2 (b))

(Verification of theory using samples with known thermal permeability)
The material of the thermal probe was constantan, and the known sample was SiO ₂ glass and Si. The set temperature of the probe block was 60 ° C., and the set temperature of the sample stage was 30 ° C.

  Detailed setting conditions in the above are shown in Table 2 below.

In the above, SiO ₂ glass having low thermal conductivity and low thermal permeability and Si having good thermal conductivity and high thermal permeability are used as known samples, and probe rod temperatures T ₁ and T ₂ are used. ₃ and FIG. 3B show the calculation results using the model for T ₃ and T ₃ . 3A and 3B show the cases of SiO ₂ glass and Si, respectively. Moreover, the actual measurement results, Fig. 4 in the case of SiO ₂ glass (a), also shows the case of Si in Figure 4 (b).

  As apparent from FIGS. 3 (a) and 3 (b) and FIGS. 4 (a) and 4 (b), when the tip of the probe rod and the known sample are brought into contact with each other in 1.5 seconds, a temperature change appears and gradually Decrease. The measurement results were qualitatively consistent with the calculation results using the model.

Using Vespel, BiTe, Pyrex 7740, SiO ₂ glass, Macor, stabilized zirconia, SUS304, Ge, MgO, Ta, Si, and Cu as known samples, as described above, two adjacent points in the probe bar Calculation and measurement of temperature differences T _1b -T _2b and T _2b -T _3b between the measurement locations were performed. The same method was used for calculation and measurement for determining the temperature used to use the temperature difference. The values in Table 3 below were used as thermophysical values of known samples.

Regarding the temperature difference dependence of the thermal permeability of a known sample, the calculation result using a model is shown in FIG. 5, and the measurement result is shown in FIG. 5 and 6, the horizontal axis represents the thermal permeability b (Js ^−0.5 m ⁻² K ⁻¹ ), and the vertical axis represents the temperature difference ΔT (° C.). From the calculation result when the model of FIG. 5 is used, the thermal permeability b can be expressed by the temperature difference ΔT by the following equation.

上記式中、ｃ_１、ｃ_２、ｃ_３は定数である。

In the above formula, c ₁ , c ₂ , and c ₃ are constants.

  Similarly to the above equation, the measurement results are fitted to the relationship between the thermal permeability b and the temperature difference ΔT as shown in FIG. 6, and the measurement results can also be fitted. Therefore, a calibration equation can be derived by measuring the temperature difference using a sample with a known thermal permeability.

(Evaluation of unknown sample)
For unknown samples, the temperature inside the probe rod can be measured using the same thermophysical property measuring instrument as above, and the thermal permeability of the unknown sample can be evaluated from the temperature difference in the probe rod using this calibration formula. it can.

  Further, if the volume specific heat capacity C (density and specific heat capacity) of an unknown sample is measured by a known method, a conversion formula from a known heat permeability b to a heat conductivity λ.

に基づいて、未知試料について測定された熱浸透率から未知試料の熱伝導率を推定することができる。従って、実際の装置としては、その変換式を組み込むことにより、未知試料の熱伝導率として表示することもできる。

The thermal conductivity of the unknown sample can be estimated from the thermal permeability measured for the unknown sample. Therefore, as an actual apparatus, it is possible to display the thermal conductivity of an unknown sample by incorporating the conversion formula.

Measurement was performed according to the above method using p-SiGe as a sample under the same conditions as when the above calibration equation was derived. The obtained thermal permeability is 3100 ± 300 Js ^−0.5 m ⁻² K ⁻¹ , and when the volume specific heat capacity is 1.6 × 10 ⁶ Jm ⁻³ K ⁻¹ , the thermal conductivity is 5. The value was 9 ± 1.1 Wm ⁻¹ K ⁻¹ , and a value comparable to the literature value was obtained.

  According to the present invention, by accurately evaluating the thermal permeability of an unknown sample by a method that matches the heat transfer model, the accuracy of evaluating the thermal permeability of the thermoelectric conversion material can be increased. It can be used when developing a material useful in the technical field that uses a thermoelectric conversion material with good thermoelectric conversion efficiency.

The typical block diagram of the measurement system for demonstrating the method to evaluate the temperature in the thermal probe at the time of sample contact. It is a schematic diagram for demonstrating the theory by a heat-transfer model, (a) is the case before a contact, (b) shows the case after a contact. Temperature _T 1, _{T 2} and _{T 3} in the probe rod is a graph showing the calculation results using a model, illustrates the use of a (a) in the case of using the SiO ₂ glass, (b) the Si . Temperature _T 1, _{T 2} and _{T 3} in the probe rod is a graph showing an actual measurement result, (a) shows the case of using the SiO ₂ glass, (b) shows the case of using Si. The graph which shows the calculation result using a model about the temperature difference dependence of a thermal osmosis rate. The graph which shows a measurement result about the temperature difference dependence of a thermal osmosis rate.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Sample stand 2 Thermal probe 2a Probe reference measurement line 21 Probe block 22 Probe rod 22a, 22b, 22c Voltage / temperature measurement line S Sample

Claims (2)

Using a thermophysical property measuring device equipped with a thermal probe consisting of a probe block and a probe rod, the temperature inside the thermal probe at the time of contact between the sample to be measured and the probe rod is evaluated at multiple points, and A method of evaluating a thermal osmosis rate, wherein the thermal osmosis rate of an unknown sample is derived by comparing the result of a sample with a known thermal osmosis rate using a temperature difference. At the time of contact between the known sample and the probe rod tip, the temperature of a plurality of measurement locations in the probe rod is measured, the temperature difference between adjacent measurement locations is calculated, and heat penetration is performed based on the calculated temperature difference of the known sample. 2. The thermal osmosis rate evaluation method according to claim 1, wherein a calibration equation for the rate is derived and the thermal osmosis rate of the unknown sample is evaluated using the calibration equation.

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