JPH0479535B2 - - Google Patents
Info
- Publication number
- JPH0479535B2 JPH0479535B2 JP59130044A JP13004484A JPH0479535B2 JP H0479535 B2 JPH0479535 B2 JP H0479535B2 JP 59130044 A JP59130044 A JP 59130044A JP 13004484 A JP13004484 A JP 13004484A JP H0479535 B2 JPH0479535 B2 JP H0479535B2
- Authority
- JP
- Japan
- Prior art keywords
- sample plate
- points
- measured
- thermal diffusivity
- frequency
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Lifetime
Links
- 238000007707 calorimetry Methods 0.000 claims description 6
- 238000000034 method Methods 0.000 claims description 6
- 238000000691 measurement method Methods 0.000 description 4
- 230000003321 amplification Effects 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 230000001678 irradiating effect Effects 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 229910052751 metal Inorganic materials 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 239000000615 nonconductor Substances 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
- WFKWXMTUELFFGS-UHFFFAOYSA-N tungsten Chemical compound [W] WFKWXMTUELFFGS-UHFFFAOYSA-N 0.000 description 1
- 229910052721 tungsten Inorganic materials 0.000 description 1
- 239000010937 tungsten Substances 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity
Landscapes
- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Investigating Or Analyzing Materials Using Thermal Means (AREA)
Description
本発明は、肉薄な試料板の厚さ方向の熱拡散率
を求める交流カロリメトリによる熱拡散率測定方
法に関する。
従来、熱拡散の測定には種々の方法が考案され
ているが、厚さが0.5mm以下の肉薄の試料の厚さ
方向の熱拡散率を求めることは不可能であつた。
しかし近年、エレクトロニクスの技術の進歩にと
もない、薄い電気絶縁物、たとえばセラミツク板
の上に半導体材料を0.5mm以下の膜厚に蒸着する
ことが多くなつており、これ等の肉薄板状材料の
熱的性質も知ることが必要になつてきた。
本発明は、肉薄な試料板の厚さ方向の熱拡散率
を測定する交流カロリメトリによる熱拡散率測定
方法を提供することをその目的としたもので、そ
の第１発明は楔形の被測定試料板の表面に一定振
幅の熱エネルギを種々の周波数で断熱照射し、該
試料板の裏面の厚さが異なる２つの点の温度波の
振幅比の対数の特性線からその勾配ｍを求め、次
式
但し、ltは２点の厚さの差
より前記被測定試料板の厚さ方向の熱拡散率Dt
を得ることを特徴とし、第２発明は楔形の被測定
試料板の表面に一定振幅の熱エネルギを種々の周
波数で断熱照射し、該試料板の裏面の厚さが異な
る２つの点の温度波の位相差の特性線からその勾
配ｍを求め、次式
但し、ltは２点の厚さの差
より前記被測定試料板の厚さ方向の熱拡散率Dt
を得ることを特徴とする。
以下本発明の実施例を図面につき説明する。
第１図及び第２図は、被測定試料板の厚さ方向
の熱拡散率Dtを求めるために使用する測定装置
の一例を示す。
同図において、１は厚さに対して十分に長い楔
形の被測定試料板で、第３図に拡大して示すよう
に、該被測定試料板１の裏面の厚さLt1、Lt2の個
所にそれぞれ熱電対２1，２2を取着した。３は被
測定試料板１の上部に配置した例えばタングステ
ンランプのような熱源、４は被測定試料板１に照
射する熱源３の熱エネルギーを断続するチヨツパ
で、該チヨツパ４は第２図示のように直径上の中
心で回転自在に軸支され、図示されないモータに
より種々の回転数で回転される半円形板から成
る。５は、例えばフオトトランジスタからなるセ
ンサ６の出力を参照信号とし、切換スイツチ７を
介して入力する熱電対２1，２2の交流出力を増幅
するロツクイン増幅器である。
尚、第１図及び第２図では図示しないが、被測
定試料板１は熱浴中に配置し、該試料板１から外
へ熱が逃げるときの熱抵抗を大とした。
以上の、試料板１に取着した熱電対２1，２2、
熱源３、チヨンパ４及びクロツクイン増幅器５は
周知の交流カロリメトリ装置を構成するものであ
る。
交流カロリメトリは、図示しない熱浴（大きな
熱容量をもち一定温度に保たれている中空の金属
などのブロツク）中に、熱浴に対して所定の熱抵
抗で接続された状態で配置された被測定試料板１
にチヨツパなどで一定周波数の熱波を与えて該試
料板１を交流的に加熱したとき、該試料板１の温
度波の振幅が該試料板１の比熱を求める方法であ
り、被測定試料板１の厚さは、熱波の波長に対し
て著しく短く選定されている。次に、第１図及び
第２図に示す測定装置を用いて被測定試料板と厚
さ方向への熱拡散率Dtを測定する本発明の第１
の測定方法について説明する。
第１図に示すように、楔形の被測定試料板１の
表面に、単位面積当り振幅Ｑの熱エネルギをチヨ
ツパ４により設定した周波数で断続して照射す
る。
このとき、試料板１の裏面の厚さLtにおける温
度波Tacは次式で与えられる。
Tac＝QR／cosh〔ktLt（１＋ｉ）〕＋RStkt（１＋ｉ）si
nh〔ktLt（１＋ｉ）〕……(1)
但し、Ｒは試料板１から外へ熱が逃げるときの
熱抵抗
Stは試料板１の厚さ方向へ熱伝動率
また、ktの逆数は熱拡張長であり、
kt＝√t ……(2)
但し、ｆはチヨツパによる熱エネルギの交流周
波数
Dtは試料１の厚さ方向への熱拡散率
前記熱抵抗Ｒを大きくし、また交流周波数を高く
すると(1)式は次のようになる。
Tac＝√2Q／Stkte−ktLt−ｉ（ktLt＋π／４） ……(3)
この式から明らかなように、厚さLtにおける被測
定試料板１の温度波Tacの振幅地｜Tac｜は
｜Tac｜＝√2Q／Stkt・e−ktLt ……(4)
である。
かくて、比測定試料板１の厚さがLt1、Lt2の個
所の２点の温度波Tacの振幅が｜Tac1｜、｜Tac2｜
の比をとると
｜Tac1｜／｜Tac2｜＝e−kt（Lt1−Lt2）……(5)
(5)式を変形すると
(6)式から明らかなように、関数log｜Tac1｜／｜Tac2｜
は変
数√の１次式であり、
The present invention relates to a thermal diffusivity measurement method using AC calorimetry for determining the thermal diffusivity in the thickness direction of a thin sample plate. Conventionally, various methods have been devised to measure thermal diffusion, but it has been impossible to determine the thermal diffusivity in the thickness direction of thin samples 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 properties of An object of the present invention is to provide a thermal diffusivity measurement method using AC calorimetry for measuring the thermal diffusivity in the thickness direction of a thin sample plate. The surface of the sample plate is adiabatically irradiated with thermal energy of a constant amplitude at various frequencies, and its slope m is determined from the characteristic line of the logarithm of the amplitude ratio of the temperature wave at two points with different thicknesses on the back surface of the sample plate, and the slope m is calculated using the following formula. However, l t is the thermal diffusivity D t in the thickness direction of the sample plate to be measured based on the difference in thickness between the two points.
The second invention is characterized in that the surface of a wedge-shaped sample plate to be measured is adiabatically irradiated with thermal energy of a constant amplitude at various frequencies to generate temperature waves at two points with different thicknesses on the back surface of the sample plate. Find the slope m from the characteristic line of the phase difference, and use the following formula However, l t is the thermal diffusivity D t in the thickness direction of the sample plate to be measured based on the difference in thickness between the two points.
It is characterized by obtaining. Embodiments of the present invention will be described below with reference to the drawings. FIGS. 1 and 2 show an example of a measuring device used to determine the thermal diffusivity D t in the thickness direction of a sample plate to be measured. In the figure, reference numeral 1 denotes a wedge-shaped sample plate to be measured that is sufficiently long relative to its thickness, and as shown in an enlarged view in FIG . Thermocouples 2 1 and 2 2 were attached to each location. 3 is a heat source such as a tungsten lamp placed above the sample plate 1 to be measured, and 4 is a chopper that cuts off the thermal energy of the heat source 3 irradiating the sample plate 1 to be measured, and the chopper 4 is as shown in the second figure. It consists of a semicircular plate that is rotatably supported at its diametrical center and rotated at various rotational speeds by a motor (not shown). Reference numeral 5 denotes a lock-in amplifier that amplifies the alternating current outputs of the thermocouples 2 1 and 2 2 input via the changeover switch 7, using the output of a sensor 6 made of, for example, a phototransistor as a reference signal. Although not shown in FIGS. 1 and 2, the sample plate 1 to be measured was placed in a heat bath to increase the thermal resistance when heat escapes from the sample plate 1 to the outside. The above thermocouples 2 1 , 2 2 attached to the sample plate 1,
The heat source 3, the selector 4, and the clock-in amplifier 5 constitute a well-known AC calorimetry device. 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. Sample plate 1
This is a method for determining the specific heat of the sample plate 1 based on the amplitude of the temperature wave of the sample plate 1 when the sample plate 1 is heated in an alternating current manner by applying a heat wave of a constant frequency to the sample plate 1. 1 is chosen to be significantly shorter than the wavelength of the heat wave. Next, in the first aspect of the present invention, the thermal diffusivity D t in the thickness direction of the sample plate to be measured is measured using the measuring apparatus shown in FIGS. 1 and 2.
The measurement method will be explained. As shown in FIG. 1, the surface of a wedge-shaped sample plate 1 to be measured is intermittently irradiated with thermal energy having an amplitude Q per unit area at a set frequency using a chopper 4. At this time, the temperature wave T ac at the thickness L t of the back surface of the sample plate 1 is given by the following equation. T ac = QR/cosh [k t L t (1+i)] + RS t k t (1+i) si
nh [k t L t (1+i)]...(1) However, R is the thermal resistance when heat escapes from the sample plate 1, S t is the thermal conductivity in the thickness direction of the sample plate 1, and k t The reciprocal of is the thermal expansion length, k t = √ t ...(2) However, f is the AC frequency of thermal energy by the chopper D t is the thermal diffusivity in the thickness direction of sample 1 However, if the AC frequency is increased, equation (1) becomes as follows. Tac=√2Q/S t k te −k t L t −i (k t L t +π/4) ...(3) As is clear from this equation, the temperature of the sample plate 1 to be measured at the thickness L t The amplitude of the wave T ac |T ac | is |T ac |=√2Q/S t k t・e −k t L t ……(4). Thus, the amplitudes of the temperature waves T ac at the two points where the thickness of the ratio measurement sample plate 1 is L t1 and L t2 are |T ac1 |, |T ac2 |
Taking the ratio of |T ac1 |/|T ac2 |= e −k t (L t1 −L t2 )……(5) Transforming equation (5), As is clear from equation (6), the function log | T ac1 | / | T ac2 |
is a linear expression of variable √,
【式】
（但しlt＝Lt1−Lt2）
は該一次式の勾配ｍである。
かくて試料板１の裏面の厚さLt1、Lt2における
２点の種々の周波数での温度波の振幅｜Tac1｜、
｜Tac2｜をその２点にそれぞれ取着させた熱電対
２1，２2の出力を増幅するロツクイン増幅器５の
出力から求める。それから周波数の平方根√を
変数とする厚さLt1、LtDの２点の温度波Tac1、
Tac2の振幅比の対数の特性線を描き、その直線の
勾配ｍを求め、
から試料板１の厚さ方向の熱拡散率Dtを得る。
次に、前記被測定試料板１の厚さ方向へ熱拡散
率Dtを測定する本発明の第２測定方法について
説明する。
被測定試料板１の厚さLtにおける温度波Tacは
前述のように３式が成立するから、厚さLt1、Lt2
における２点の温度波Tacの位相差（Lt1）−
（Lt2）は、(3)式より
但し、[Formula] (where l t =L t1 -L t2 ) is the slope m of the linear equation. Thus, the amplitude of the temperature wave at various frequencies at two points in the thicknesses L t1 and L t2 of the back surface of the sample plate 1 |T ac1 |,
|T ac2 | is determined from the output of the lock-in amplifier 5 that amplifies the output of the thermocouples 2 1 and 2 2 attached to the two points, respectively. Then, the temperature wave T ac1 at two points with thickness L t1 and L tD with the square root of the frequency as a variable,
Draw a characteristic line of the logarithm of the amplitude ratio of T ac2 , find the slope m of the straight line, The thermal diffusivity D t in the thickness direction of the sample plate 1 is obtained from Next, a second measuring method of the present invention for measuring the thermal diffusivity D t in the thickness direction of the sample plate 1 to be measured will be explained. The temperature wave T ac at the thickness L t of the sample plate 1 to be measured satisfies the three equations as described above, so the thicknesses L t1 , L t2
The phase difference between the temperature waves T ac at two points (L t1 ) −
(L t2 ) is from equation (3) however,
【式】
が得られる。
かくて、試料板１の裏面の厚さLt1、Lt2におけ
る２点の種々の周波数での温度波の位相差をその
２点にそれぞれ取着された熱電対２1，２2の出力
を増幅するロツクイン増幅器５の出力から求め
る。
それから、(7)式にもとづき、周波数の平方根√
ｆを変数とする厚さLt1、Lt2の２点の温度波
Tac1、Tac2の位相差の特性線を描き、その直線勾
配ｍを求め、
（但し、ltはLt1−Lt2）から、試料板１の厚み方
向への熱拡散率Dtを得る。以上の本発明の第１
及び第２の測定方法の実施例では、いずれも周波
数の平行根√を変数とする厚さの異なる２点の
温度波の振幅比の対数の特性線と周波数の平行根
を変数とする厚さの異なる２点の温度波の位相差
を特性線を描き、その直線の勾配を求めて熱拡散
率を得たが、該特性線を紙上に描くことなくその
他の手段で勾配を求めてもよい。
上述の説明から明らかなように、本発明の第１
及び第２方法によれば肉薄な試料板の厚さ方向の
熱拡散率しを容易に得ることができる効果を有す
る。[Formula] is obtained. Thus, the phase difference of the temperature waves at various frequencies at two points at the thicknesses L t1 and L t2 of the back surface of the sample plate 1 can be expressed as the outputs of the thermocouples 2 1 and 2 2 respectively attached to the two points. It is determined from the output of the lock-in amplifier 5 for amplification. Then, based on equation (7), the square root of the frequency √
Temperature wave at two points with thickness L t1 and L t2 with f as a variable
Draw a characteristic line of the phase difference between T ac1 and T ac2 and find its linear slope m, (However, L t is L t1 −L t2 ) to obtain the thermal diffusivity D t in the thickness direction of the sample plate 1. The first aspect of the present invention
In the example of the second measurement method, the characteristic line of the logarithm of the amplitude ratio of temperature waves at two points with different thicknesses with the parallel root of the frequency as a variable and the thickness with the parallel root of the frequency as a variable. Thermal diffusivity was obtained by drawing a characteristic line representing the phase difference between two temperature waves at different points and determining the slope of the line; however, the slope may be determined by other means without drawing the characteristic line on paper. . As is clear from the above description, the first aspect of the present invention
According to the second method, the thermal diffusivity in the thickness direction of a thin sample plate can be easily obtained.
第１図は本発明の実施に使用する測定装置の線
図、第２図は熱源及びロツクイン増幅器を除いた
第１図示のものの平面図、第３図は本発明の実施
に使用する被測定試料の斜視図を示す。
１……被測定試料板、２1，２2……熱電対、３
……熱源、４……チヨツパ、５……ロツクイン増
幅器、６……センサ、７……切換スイツチ。
Fig. 1 is a diagram of the measuring device used in the practice of the present invention, Fig. 2 is a plan view of the device shown in Fig. 1 excluding the heat source and lock-in amplifier, and Fig. 3 is the sample to be measured used in the practice of the present invention. A perspective view of the figure is shown. 1... Sample plate to be measured, 2 1 , 2 2 ... Thermocouple, 3
... Heat source, 4 ... Chipper, 5 ... Lock-in amplifier, 6 ... Sensor, 7 ... Changeover switch.
Claims (1)
ネルギを種々の周波数で断熱照射し、該試料板の
裏面の厚さが異なる２つの点の温度波の振幅を当
該交流周波数で測定し、該周波数の平方根を変数
とする前記２つの点の温度波の振幅比の対数の特
性線からその勾配ｍを求め、次式 但し、ltは２点の厚さの差 より前記被測定試料板の厚さ方向の熱拡散率Dt
を得ることを特徴とする交流カロリメトリによる
熱拡散率測定方法。 ２ 楔形の被測定試料板の表面に一定振幅の熱エ
ネルギを種々の周波数で断熱照射し、該試料板の
裏面の厚さが異なる２つの点の温度波の振幅を当
該交流周波数で測定し、該周波数の平方根を変数
とする２つの点の温度波の位相差の特性線からそ
の勾配ｍを求め、次式 但し、ltは２点の厚さの差 より前記被測定試料板の厚さ方向の熱拡散率Dt
を得ることを特徴とする交流カロリメトリによる
熱拡散率測定方法。[Claims] 1. The surface of a wedge-shaped sample plate to be measured is adiabatically irradiated with thermal energy of a constant amplitude at various frequencies, and the amplitude of the temperature wave at two points with different thicknesses on the back surface of the sample plate is The slope m is determined from the characteristic line of the logarithm of the amplitude ratio of the temperature wave at the two points, measured at the AC frequency and using the square root of the frequency as a variable, and the slope m is calculated using the following formula. However, l t is the thermal diffusivity D t in the thickness direction of the sample plate to be measured based on the difference in thickness between the two points.
A method for measuring thermal diffusivity by alternating current calorimetry, characterized by obtaining the following properties: 2. The surface of a wedge-shaped sample plate to be measured is adiabatically irradiated with thermal energy of a constant amplitude at various frequencies, and the amplitude of the temperature wave at two points with different thicknesses on the back side of the sample plate is measured at the AC frequency, Find the slope m from the characteristic line of the phase difference of the temperature wave at two points with the square root of the frequency as a variable, and use the following formula: However, l t is the thermal diffusivity D t in the thickness direction of the sample plate to be measured based on the difference in thickness between the two points.
A method for measuring thermal diffusivity by alternating current calorimetry, characterized by obtaining the following properties:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP13004484A JPS6110752A (en) | 1984-06-26 | 1984-06-26 | Measurement for diffusitivity of heat by intermittent heating |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP13004484A JPS6110752A (en) | 1984-06-26 | 1984-06-26 | Measurement for diffusitivity of heat by intermittent heating |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS6110752A JPS6110752A (en) | 1986-01-18 |
| JPH0479535B2 true JPH0479535B2 (en) | 1992-12-16 |
Family
ID=15024730
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP13004484A Granted JPS6110752A (en) | 1984-06-26 | 1984-06-26 | Measurement for diffusitivity of heat by intermittent heating |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPS6110752A (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DK2119472T3 (en) * | 2004-02-12 | 2014-10-13 | Proventure Far East Ltd | Skin / hårbehandlingssystem |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5772052A (en) * | 1980-10-24 | 1982-05-06 | Nippon Telegr & Teleph Corp <Ntt> | Measuring method for heat transmission factor of thin film |
-
1984
- 1984-06-26 JP JP13004484A patent/JPS6110752A/en active Granted
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5772052A (en) * | 1980-10-24 | 1982-05-06 | Nippon Telegr & Teleph Corp <Ntt> | Measuring method for heat transmission factor of thin film |
Also Published As
| Publication number | Publication date |
|---|---|
| JPS6110752A (en) | 1986-01-18 |
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