Minute heat conductivity measurement device and measurement method

Abstract

To provide a new heat transport evaluation method within STEM based on the phase measurement of temperature waves, which is relatively unaffected by a change in an endothermic quantity caused by differences in sample thickness or material type.SOLUTION: A minute heat conductivity measurement device includes: a thermocouple that contacts a sample; a heating device that heats a heating point on the sample by using a pulsed electron beam with a prescribed frequency (f); and a device that detects the output of the thermocouple in response to the temperature rise of a contact point caused by the heating by the pulsed electron beam with the prescribed frequency and measures a phase component of the temperature waves corresponding to a heating position of the heating point with the prescribed frequency. The minute heat conductivity measurement device uses a phase component (θ) of the temperature waves by the pulsed electron beam to obtain a thermal diffusivity (α) between the heating point and the contact point on the basis of a distance (L) from the heating point to the contact point of the thermocouple on the sample by the following the equation: α=πf / (θ / L)2.SELECTED DRAWING: Figure 2C

Description

[Technical field]

[0001] The present invention relates to an apparatus for measuring temperature, relative heat flow and thermal resistance on the nano- and micro-scale, and more specifically to a measurement apparatus and method suitable for use in nano-scale heat transport evaluation in a transmission electron microscope using an electron beam pulse and a micro-thermocouple. [Background technology]

[0002] In recent years, there has been a demand for the development of a new nanoscale thermal transport evaluation method for controlling the thermal properties of thermoelectric materials and for developing materials and devices for precise thermal control. The present inventor has been developing a scanning transmission electron microscope (STEM)-based thermal analytical microscopy (STAM) method that combines a nanothermocouple produced by electrolytic polishing with a local heating method using electron beam irradiation (see Patent Document 1 and Non-Patent Document 1). Here, electrolytic polishing refers to a method in which a product is placed on the positive side, a direct current is passed through an electrolyte, and the metal surface is dissolved to obtain a polishing effect. The STAM method utilizes the temperature rise caused by plasmon excitation during electron beam irradiation, and has the advantage of being able to evaluate the heat passing through the sample based on Fourier's law by two-dimensionally recording the steady-state temperature (thermoelectromotive force) corresponding to each heating position during STEM scanning.

[0003] On the other hand, it is known that temperature wave thermal analysis is effective for measuring the thermal diffusivity of small amounts of thin materials, mainly thin polymeric materials (see Patent Document 2 and Non-Patent Documents 2 and 3). In temperature wave thermal analysis, a weak temperature wave with an amplitude of 1°C or less is applied to a sample, its propagation is analyzed, and the thermal conductivity λ is obtained from the temperature amplitude attenuation, and the thermal diffusivity α is obtained from the phase delay measurement. Known methods of applying thermal stimuli include pulse (flash method), step (hot wire method), alternating current (temperature wave method), constant temperature rise (DSC), etc. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 6164735 Claim 17 [Patent Document 2] Patent No. 5489789 [Non-patent literature]

[0005] [Non-Patent Document 1] N. Kawamoto et al., Nano Energy, 52 323-328 (2018). [Non-Patent Document 2] Junko Morikawa, Toshimasa Hashimoto, "Measurement of Thermal Diffusivity and Thermal Conductivity Using Temperature Waves," Network Polymer, Vol. 34, No. 2 (2013) [Non-Patent Document 3] Toshimasa Hashimoto and Junko Morikawa, "Fourier Transform Temperature Wave Thermal Analysis", Thermal Measurements Vol. 27 No. 3, 141-151 (2000) Summary of the Invention [Problem to be solved by the invention]

[0006] In conventional micro-thermal conductivity measuring devices as shown in Patent Document 1 and Non-Patent Document 1, the temperature in a steady state where the temperature has risen to the maximum is recorded two-dimensionally at the nano thermocouple contact point (fixed) for each heating point. When performing thermal conductivity analysis based on Fourier's law using a conventional micro-thermal conductivity measuring device, it is necessary to prepare a sample in which a reference material with a known thermal conductivity and a measurement sample are arranged in series, and the sample is required to be rod-shaped and have as uniform a thickness as possible, which causes a problem that sample preparation takes time. In other words, with the STAM method, the amount of heat input by electron beam irradiation depends on differences in sample thickness and the plasmon mean free path of the irradiated material, and therefore heat transport evaluation poses challenges such as the need to prepare samples with as uniform a thickness as possible and to take into account the amount of heat input during analysis.

[0007] In addition, although temperature wave thermal analysis is used to measure the thermal diffusivity of small amounts of thin materials, mainly thin polymeric materials, there are no known examples of its application to nanoscale heat transport evaluation inside a transmission electron microscope. The present invention aims to solve the above-mentioned problems and to provide a new method for evaluating heat transport in a STEM based on temperature wave phase measurement that is relatively unaffected by changes in the amount of heat absorption due to differences in sample thickness and type of material. [Means for solving the problem]

[0008] [1] According to the micro-thermal conductivity measuring device of the present invention, as shown in FIG. 1, for example, there is a thermocouple (23, 24) in contact with a sample 21, a heating device (10, 22) for heating at least one heating point on the sample using a pulsed electron beam of a predetermined frequency (f), and a device 50 for detecting the output of the thermocouple in response to the temperature rise of the contact point due to heating by the pulsed electron beam of the predetermined frequency and measuring the phase component of the temperature wave corresponding to the heating position of the heating point by the predetermined frequency, and using the phase component (θ) of the temperature wave by the pulsed electron beam, the thermal diffusivity (α) between the heating point and the contact point is calculated based on the distance (L) from the heating point to the contact point of the thermocouple on the sample by the following equation. α=πf / (θ / L) 2

[0009] [2] In the micro-thermal conductivity measuring device [1] of the present invention, it is preferable that the sample is contained in a transmission electron microscope (TEM) or a scanning transmission electron microscope (STEM) so that a TEM image or a STEM image can be observed, and that the heating device that irradiates the focused electron beam to the heating point is an electron gun of the TEM or STEM. [3] In the micro thermal conductivity measuring device [1] of the present invention, the heating points on the sample are preferably a plurality of heating points having different distances (L) to the contact points of the thermocouple on the sample. [4] In the present invention, the predetermined frequency is preferably a plurality of frequencies selected from the range of 1 Hz to 500 kHz. The predetermined frequency is selected and used depending on the material and the length of the measurement section. [5] In the micro thermal conductivity measuring device [1] of the present invention, preferably, the pulsed electron beam of the predetermined frequency (f) has an on-off duty ratio selected between 1:9 and 9:1, and a pulse on-time width selected between 100 ns and 1 sec. The pulse on-time width is determined by the characteristics of the heating device. For example, in the case of EDM, the minimum pulse on-time width is set to 100 ns. [6] In the micro thermal conductivity measuring device [1] of the present invention, preferably, the thermocouple is a joint of needle-shaped objects made of two types of non-magnetic materials. [7] In the micro thermal conductivity measuring device [6] of the present invention, preferably, the two types of materials are chromel and constantan. [8] In the micro thermal conductivity measuring device [6] of the present invention, preferably, the diameter of the tip of the needle-like object is 100 nm or less. [9] In the micro thermal conductivity measuring device [1] of the present invention, it is preferable that the sample is attached to the base via a material having a higher thermal resistance than the thermocouple.

[10] In the micro thermal conductivity measuring devices [1] to [9] of the present invention, it is preferable that the measurement timing of the device that measures the phase component of the temperature wave is a state in which the temperature is oscillating with a small amplitude at a temperature that has been raised to an almost steady state by the pulsed electron beam.

[11] In the micro thermal conductivity measuring device [1] to

[10] of the present invention, it is preferable to further include an analytical computer 60, and the analytical computer 60 may use the phase component (θ) of the temperature wave generated by the pulsed electron beam to determine the thermal diffusivity (α) between the heating point and the contact point of the thermocouple on the sample based on the distance (L) from the heating point to the contact point of the thermocouple on the sample, using the following equation. α=πf / (θ / L) 2

[0010]

[12] According to the method for measuring micro-thermal conductivity of the present invention, for example, as shown in FIG. 4, a thermocouple is brought into contact with a sample (S404), a heating point on the sample is heated using a pulsed electron beam of a predetermined frequency (f) (S406), a plurality of outputs of the thermocouple are detected in response to the temperature rise of the contact point due to heating by the pulsed electron beam of the predetermined frequency (S408), and the phase components of the temperature wave corresponding to the heating positions of the heating point by the predetermined frequency are measured (S410). Using the phase component (θ) of the temperature wave by the pulsed electron beam, the thermal diffusivity (α) between the heating point and the contact point is calculated based on the distance (L) from the heating point to the contact point of the thermocouple on the sample by the following equation (S412). α=πf / (θ / L) 2

[0011]

[13] In the micro thermal conductivity measurement method

[12] of the present invention, it is preferable that the sample is placed in a TEM or STEM so that its TEM image or STEM image can be observed (S402), and the electron beam is irradiated by an electron gun of the TEM or STEM.

[14] In the micro-thermal conductivity measuring method

[12] of the present invention, it is preferable to detect a plurality of calibration outputs from the thermocouple corresponding to the heating positions of the plurality of heating points while releasing the contact between the sample and the thermocouple, and to cancel out the influence of secondary electrons caused by irradiation of the electron beam on the plurality of heating points on the output of the thermocouple by the plurality of calibration outputs.

[15] In the micro thermal conductivity measurement method

[12] of the present invention, preferably, the heating points on the sample are a plurality of heating points having different distances (L) to the contact points of the thermocouple on the sample.

[16] In the method for measuring micro-thermal conductivity of the present invention

[12] , the predetermined frequencies are preferably a plurality of frequencies selected from the range of 1 Hz to 500 kHz.

[17] In the microthermal conductivity measuring method

[12] of the present invention, preferably, the pulsed electron beam of the predetermined frequency (f) has an on-off duty ratio selected from the range of 1:9 or more and 9:1 or less, and the pulse on-time width selected from the range of 100 ns or more and 1 sec or less.

[18] In the micro thermal conductivity measurement methods

[12] to

[17] of the present invention, the timing for measuring the phase component of the temperature wave is preferably a state in which the temperature is oscillating with a small amplitude at a temperature that has been raised to an almost steady state by the pulsed electron beam. Effect of the Invention

[0012] According to the micro thermal conductivity measuring device and method of the present invention, the thermal diffusivity (α) is measured using the temperature wave phase method, so that the sample only needs to be a sample consisting of the composition to be measured, and there is no need to further prepare a composition with known properties for comparison reference as in the conventional method, which simplifies sample preparation. In addition, when measuring thermal diffusivity (α) using the temperature wave phase method, the shape of the test piece sample can be a rod-like sample, and there is an advantage that the thickness and type of the measurement sample do not need to be taken into consideration. [Brief description of the drawings]

[0013] [Figure 1] 1 is an overall configuration diagram of a micro thermal conductivity measuring device according to the present invention. [Figure 2A] A photograph of the TEM holder with the nano thermocouple attached. [Figure 2B] TEM image showing nano thermocouple in contact with sample [Figure 2C] FIG. 2 is a diagram for explaining the propagation of a temperature wave when a heating point of a sample is heated by an electron beam. [Figure 3A] FIG. 2 is an explanatory diagram of the principle of the temperature wave method used in the present invention, showing the frequency method. [Figure 3B] FIG. 1 is an explanatory diagram of the principle of the thermal wave method used in the present invention, showing the distance method of the heating position. [Figure 4] 1 is a flowchart illustrating a method for measuring thermal conductivity at a low temperature according to the present invention. [Diagram 5] FIG. 1 is a conceptual diagram showing a model of a configuration example that can determine the absolute value of the thermal conductivity of a conventional device. [Figure 6A] FIG. 2 is a conceptual diagram showing a model of a configuration example that can determine a relative value of thermal conductivity using the micro thermal conductivity measuring device of the present invention. [Figure 6B] This is an enlarged image of the thermocouple part taken with a STEM-HAADF (High-angle Annular Dark Field Scanning TEM). [Figure 6C] FIG. 2 is an explanatory diagram of heating by a pulsed electron beam of a predetermined frequency, showing an on-off waveform of the electron beam. [Figure 7] FIG. 2 is an explanatory diagram of heating by a pulsed electron beam of a predetermined frequency according to the frequency method, showing a temperature wave waveform measured by a thermocouple. [Figure 8] FIG. 1 is an explanatory diagram of heating by a pulsed electron beam of a predetermined frequency according to the frequency method, showing a phase image of a temperature wave measured by a thermocouple. [Figure 9] The relationship for evaluating thermal diffusivity is shown by the ratio of the phase delay θ of the temperature wave to the distance L from the heating position. [Figure 10] (A) is an explanatory diagram of heating by a pulsed electron beam of a specific frequency by the frequency method, showing the amplitude image of the temperature wave measured by a thermocouple. (B) shows the result of evaluating the amplitude of the temperature wave using the amplitude Q of the temperature wave and the distance L from the heating position. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] The following definitions are given for the academic terms used in this specification. Fourier's law describes the relationship between the amount of heat transferred in conductive heat transfer and is expressed by the following equation.

number

[0015] Thermal conductivity is a coefficient that determines the speed at which thermal energy is transferred due to a temperature gradient. Specifically, when the amount of heat flowing per unit cross-sectional area per unit time (i.e., heat flux) is proportional to the temperature gradient, the thermal conductivity is the coefficient λ when the relationship between the heat flux J and the temperature (T) gradient is expressed by the following equation (2). J = -λgradT (2) If we express the relationship between temperature and heat in a material more generally using Gauss's divergence theorem, we can derive the following heat conduction equation. ∂q / ∂t=∇ 2 λT (3) Here, q is the amount of heat per unit volume, and it is assumed that there is no heat absorption or heat generation within the material. If the thermal conductivity λ is constant regardless of position or time, then equation (3) becomes ∂q / ∂t=λ∇ 2 T (4) It becomes.

[0016] Thermal diffusivity is a coefficient that determines the speed at which temperature travels through a temperature gradient; specifically, it is the proportionality coefficient α in the heat diffusion equation (equation (5)) derived by converting the heat quantity q to temperature T in equation (4). ∂T / ∂t=α∇ 2 T (5) The relationship between thermal conductivity λ and thermal diffusivity α is λ=α Cp ρ (6) These are related as follows, and together with ρ (density) and Cp (specific heat capacity at constant pressure), they are called the four thermal constants. When measuring, it is common to calculate either thermal conductivity or thermal diffusivity and convert it using equation (6). As with material diffusion, the longer the diffusion distance and the smaller the thermal diffusivity, the longer it takes to homogenize.

[0017] Temperature wave is a method of measuring amplitude attenuation and phase delay by applying a weak AC stimulus of thermal energy to a sample. In order to popularize the measurement method, it was certified as standard in the field of thermal conductivity of plastics (TC-61) in 2008 as ISO22007-3 (phase analysis type for thin films), and further certified as amplitude analysis type as ISO-22007-6. In the case of an alternating temperature wave, the thermal diffusion length μ is defined as the following equation as a measure of the distance required for the temperature to be uniform. μ=√2α / ω (7)

[0018] Next, the principle of the present invention will be described in detail. The micro thermal conductivity measuring device and method of the present invention measures thermal diffusivity (α) using a temperature wave phase method, and is based on the following one-dimensional heat conduction equation.

number

number

[0019] In detecting the amplitude and phase of the temperature wave, the phase change Δθ occurring between the heating positions is given by the following equation:

number

[0020] FIG. 1 is a diagram showing the overall configuration of a micro thermal conductivity measuring device according to the present invention. In the figure, the micro thermal conductivity measuring device comprises a transmission electron microscope 10, a temperature wave generating section 20, a lock-in amplifier 30, a signal processing section 40, an electron beam control and image processing system 50, and an analytical computer 60. The transmission electron microscope 10 includes an electrostatic shutter 12, a shutter driver 13, an electrostatic dose modulator (EDM) 14, a synchronization signal generator 15, an attenuation adjustment knob 16, and a control software unit 18. The temperature wave generating unit 20 is an enlarged view of the electron beam irradiated area of ​​the transmission electron microscope 10 shown in Fig. 1. The temperature wave generating unit 20 includes a sample 21, a pulsed electron beam 22, a constantan probe 23, and a chromel probe 24. Details will be described with reference to Figs. 2(A) and (B). In the lock-in amplifier 30, a constantan probe 23 and a chromel probe 24 of a thermocouple are connected to an input terminal, and a synchronization signal generating unit 15 is connected to a reference terminal.

[0021] The signal processing unit 40 includes an amplifier circuit, a filter circuit, and an attenuation circuit. The electron beam control and image processing system 50 may be, for example, a DigiScan (trademark) system provided by Gatan, Inc., a member company of the Electronic Instruments Business Group of AMETEK Corporation. An electron beam control signal and an image signal processed by a signal processing unit 40 are sent to an input terminal of the system, and an analysis computer 60 is connected to an output terminal. The electron beam control and image processing system 50 can measure the phase component of a temperature wave corresponding to the heating position of a heating point by a predetermined frequency using a STEM image obtained by the transmission electron microscope 10. The analytical computer 60 inputs the amplitude and phase of the temperature wave measured by the electron beam control and image processing system 50 and calculates the thermal conductivity of the sample 21. For such calculation, for example, a Gatan digital micrograph (trademark) may be used, in which a script for dividing the position information is actually written and converted into a thermal diffusivity image. Also, instead of using the analytical computer 60, a line profile of the phase image of the rod-shaped sample may be taken and the thermal diffusivity α may be calculated in Excel (trademark) according to the following formula: α=πf / (θ / L) 2 (16) The signal processing unit 40, the electron beam control and image processing system 50, and the analysis computer 60 are well known to those skilled in the art, or can be constructed by those skilled in the art without exerting any special inventive effort based on the descriptions in this specification and the drawings, and therefore detailed explanations and illustrations thereof will be omitted.

[0022] The Electrostatic Dose Modulator (EDM) 14 is a high-speed beam blanking system with electrostatic deflectors before the sample, including electronics and software control. With the EDM, the beam can be switched on or off in less than 50 ns, for example. This blanking speed is on the order of 10,000 to 100,000 times faster than the opening and closing speed of conventional electrostatic shutters 12, thus instantly improving the clarity of data acquired with fast exposure times. The EDM can also attenuate the electron irradiation without affecting the imaging conditions, thus giving TEM and STEM users great control over the dose to the sample. With the EDM, advanced applications such as time-dose structuring and STEM synchronization are available through state-of-the-art electronics and software add-ons.

[0023] The electron beam control and image processing system 50 can be connected to a STEM device, and a common user interface allows flexible setting of scan conditions and digitization tones to obtain an image suitable for an experiment. For example, the DigiScan (trademark) system allows up to four channels of synchronous input as standard, and is equipped with a function for setting the number of pixels in the X and Y directions up to a maximum of 32k x 32k pixels using analog or pulse input, but is not limited to this number of channels or pixels. The pixel dwell time can be set within the range of 50ns to 400ms per pixel. "Dwell time" refers to the time that the electron beam stays at one pixel when acquiring a STEM image by electron beam scanning. Dwell time is an index of the scanning speed of the electron beam. When the retention time is multiplied by the number of scan pixels in one horizontal line scan and the flyback time is added, the scan time for one horizontal line scan is obtained. When this scan time is multiplied by the number of vertical scans (horizontal scan lines), the acquisition time for one scanned image is calculated.

[0024] Figure 2A is a photograph of a TEM holder with a nanothermocouple attached, and Figure 2B is a TEM image showing the state where the nanothermocouple is in contact with the sample. As shown in paragraph numbers 0013 to 0019 of Patent Document 1, H 3 PO 4 Cu fabricated by an electrolytic polishing method using an aqueous solution 55 Ni 45 (mass%) (Constantan (trademark)) probe and Cr 10 Ni 90 (mass%) (Chromel (trademark)) probe were combined to fabricate a constantan-chromel nanothermocouple. As a result, the operating temperature range could be significantly expanded to -200°C < T < 800°C. In addition, low thermal conductivity, large thermoelectric power, linear responsiveness, high resolution of the measured temperature reaching 10 -2 K, high responsiveness with a micro-junction realized, and since the thermocouple material is a combination of non-magnetic materials, it can be introduced into a strong magnetic field space such as inside a transmission electron microscope, and the performance could be improved in various aspects. Also, in this manufacturing method, depending on the application, nanothermocouples can be fabricated using other thermocouple materials.

[0025] [Manufacturing method of nanothermometer] By an electrolytic polishing method, Cu-Ni and Cr-Ni wires were respectively fabricated into micro-probes with a tip diameter sharpened to 100 nm or less. Specifically, by precisely controlling the position of the micro-probes using a piezo element inside a transmission electron microscope (TEM) and bringing the tip portions of these micro-probes into contact with each other, and passing a current of about 10 μA between the probes, a junction with an extremely small contact resistance between the constantan wire and the chromel wire shown in Figure 2(B) was formed, and a nanothermocouple, that is, a nanothermometer, was fabricated. In the micro thermal conductivity measuring device configured in this manner, the sample 21 is irradiated with a focused electron beam, thereby applying heat to a nanoscale region on the sample 21, and the location and amount of heat applied can be controlled.

[0026] Figure 2(A) shows a photograph of a holder for mounting the nanothermocouple thus fabricated to measure the temperature of a minute region on a target sample in a TEM. Figure 2(A) also shows a schematic voltmeter for measuring the thermoelectromotive force generated in the nanothermocouple in this holder. What is important here is that since a large magnetic field (for example, 2 T in this embodiment) is applied to the sample position in the TEM, the holder material, and especially the nanothermocouple, must be made of a nonmagnetic material. In this embodiment, this condition is satisfied by using chromel and constantan as the nano thermocouple material. 2 O 3 (hereinafter simply referred to as alumina) is used as the sample, but it is of course possible to use various other materials as the sample to be measured.

[0027] [Heat application and temperature measurement at the nanoscale] The holder with the nanothermocouple attached as described above is placed inside the TEM, and the tip (junction) of the nanothermocouple is brought into contact with the sample as shown in FIG. 2(B). Here, an electron beam is irradiated near the tip of the thermocouple, and the thermoelectromotive force generated in the nanothermocouple changes depending on whether the electron beam is turned on or off. The electron gun used to irradiate the electron beam can be the same as that used in TEMs. In addition, the position where the nanothermocouple is brought into contact with the sample and the irradiation position of the focused electron beam can be accurately determined by observation using a TEM. In this way, the irradiation position can be determined by referring to the TEM image, allowing for a higher degree of freedom in measurements compared to methods in which the position where heat is applied is determined in advance and a specialized sample is prepared for that purpose.

[0028] An important point is that the location where heat is applied by the electron beam does not need to be spatially coincident with the location where the temperature is measured, and the electron beam may be irradiated to any point on the sample other than the contact point of the nano thermocouple, allowing the analysis of the thermal conduction in a desired section on the sample.

[0029] FIG. 2C is a diagram for explaining the propagation of a temperature wave when a heating point of a sample is heated by an electron beam. In a one-dimensional sample 21, the position where a thermocouple, a constantan probe 23 and a chromel probe 24, are connected to one end of the sample 21 is set as the origin, x=0, and the coordinate of the irradiation position of the pulsed electron beam 22 is x 0 , x 1 , x 2 In this case, the temperature wave T(x i , t) (i=0, 1, 2), the amplitude attenuates with distance, but the following equation holds for the phase lag θ: θ 1 =k(x 1 -x 0 ) (11) θ 2 =k(x 2 -x 0 ) (12)

[0030] FIG. 3A is an explanatory diagram of the principle of the temperature wave method used in the present invention, showing the frequency control method, where (A) shows the heating position of the sample using a pulsed electron beam and the thermocouple attachment position, and (B) shows the phase delay θ, with the horizontal axis showing the square root of frequency (√f) and the vertical axis showing the phase. In Figure 3A, T M indicates the position where the thermocouple is attached to the sample, and the distance L indicates the distance between the heating position of the sample by the pulsed electron beam and the thermocouple attachment position. The phase lag θ increases at the rate of the square root of the frequency (√f) as the frequency f increases.

[0031] FIG. 3B is an explanatory diagram of the principle of the temperature wave method used in the present invention, showing the heating position distance method (Heating position control), in which (A) shows the heating position of the sample by the pulsed electron beam and the thermocouple attachment position, and (B) shows the phase delay θ, with the horizontal axis showing the square root of frequency (√f) and the vertical axis showing the distance L between the heating position of the sample by the pulsed electron beam and the thermocouple attachment position. In Fig. 3B(A), the heating position of the sample by the pulsed electron beam moves from a position close to the thermocouple attachment position to the other end of the sample. The phase lag θ increases in proportion to the increase in the distance L between the heating position of the sample by the pulsed electron beam and the thermocouple attachment position.

[0032] FIG. 4 is a flow chart illustrating the method for measuring thermal conductivity at a low temperature according to the present invention. First, the sample 21 is placed in a TEM or STEM so that its TEM image or STEM image can be observed (S402). Next, the thermocouples (23, 24) are brought into contact with the sample 21 (S404). Next, at least one heating point on the sample 21 is heated using a pulsed electron beam of a predetermined frequency (f) (S406). The signal processing unit 40 detects multiple outputs of the thermocouples (23, 24) in response to the temperature rise at the contact point due to heating by the pulsed electron beam of a predetermined frequency (S408). If necessary, the positional and temporal relationship between the multiple output signals of the thermocouples (23, 24) by the signal processing unit 40 and the electron beam irradiated by the transmission electron microscope 10 is linked by the electron beam control and image processing system 50. The electron beam control and image processing system 50 measures the phase components of the temperature waves corresponding to the heating positions of the heating points at a predetermined frequency (S410). Using the phase component (θ) of the temperature wave generated by the pulsed electron beam, analytical computer 60 determines the thermal diffusivity (α) between the heated point and the contact point of the thermocouples (23, 24) on sample 21 from the distance (L) from the heated point to the contact point of the thermocouples (23, 24) on sample 21 using the following equation (S412). α=πf / (θ / L) 2

[0033] Preferably, the reliability of the micro thermal conductivity measuring method of the present invention can be improved by performing a calibration operation at regular intervals or when deemed necessary. In the calibration operation, a plurality of calibration outputs corresponding to the heating positions of a plurality of heating points from the thermocouples (23, 24) are detected in a state where the contact between the sample 21 and the thermocouples (23, 24) is released, and the influence of secondary electrons caused by the irradiation of the electron beam 22 on the plurality of heating points on the output of the thermocouples (23, 24) is cancelled by the plurality of calibration outputs.

[0034] A specific example of the device thus configured will be described. In Fig. 5, (A) is a conceptual diagram modeling an example of a configuration that can obtain the absolute value of thermal conductivity of a conventional device, and (B) is a line graph showing the relationship between the distance from the tip of the thermocouple to the electron beam irradiation position and the temperature rise at the tip of the thermocouple due to the irradiation. In Fig. 5(A), the sample 21 has a measured sample portion 212, a standard material portion 214, electron beam heat conversion portions 216a, 216b, and 216c, a thermal resistance portion 218, and a base portion 219. The measured sample portion 212 is a portion for measuring the thermal conductivity k of the sample. The standard material portion 214 is a standard material having a known thermal conductivity k. The electron beam heat conversion portions 216a, 216b, and 216c are "same sample" made of a heavy element (e.g., tungsten W) that has a high thermal conversion rate and a relatively large heat input when irradiated with an electron beam, and are provided in three separate locations to sandwich the standard sample portion 214 and the measured sample portion 212. The irradiation portions of the pulsed electron beam 22 are the electron beam heat conversion portions 216a, 216b, and 216c so that all the electron beam irradiation points are made of the same material so that the amount of heat absorbed when irradiated with an electron beam is the same at all irradiation points. The thermal resistance portion 218 is made of, for example, epoxy resin, and has a sufficiently large thermal resistance at the end opposite to the end that contacts the thermocouples 23 and 24. The base portion 219 supports the entire sample 21, and supports the electron beam heat conversion portions 216a, 216b, 216c, etc. and the thermocouples 23 and 24 via the thermal resistance portion 218.

[0035] In the apparatus thus configured, the electron beam is irradiated to points on the electron beam heat conversion parts 216a, 216b, and 216c on the sample placed in the TEM, whereby heat is applied to the points, causing the temperature to rise. A heat flow occurs due to the temperature gradient created by this. In FIG. 5(A), heat flow may occur to both the left and right sides of the electron beam irradiation point. However, the heat flow to the right side is almost blocked by the low thermal conductivity (i.e., high thermal resistance) of the thermal resistance part 218 (epoxy resin) for bonding the sample 21 to the pedestal part 219, and most of the heat flow flows to the left side of FIG. 5, and finally reaches the thermocouples 23 and 24 at the left end, causing a temperature change at this position. By providing the electron beam heat conversion parts 216a, 216b, and 216c, it is also possible to measure the thermal conductivity of a sample made of a light element that is difficult to convert into heat when irradiated with an electron beam, in which the measured sample part 212 is irradiated with an electron beam. Even if the measured sample part 212 is made of a light element such as carbon, which is a material that is more transparent to electron beams, such as carbon nanotubes, graphene, or epoxy resin, the sample is not directly irradiated with an electron beam, and therefore it is possible to overcome the problem of not being able to input a sufficient amount of heat due to poor heat absorption, which occurs when irradiating the sample directly with an electron beam.

[0036] In the configuration shown in FIG. 5(A), among the electron beam irradiation points (1) to (6), (2) and (3) are determined near the measurement sample on the upstream and downstream sides of the measurement sample portion 212 in terms of the direction of heat flow. Similarly, (4) and (5) are determined near the upstream and downstream sides of the standard material portion 214 in terms of the direction of heat flow. By irradiating this configuration with electron beams in the manner described above and measuring the temperature change at the left end portion with a thermocouple, the graph shown in FIG. 5(B) is obtained. Here, the electron beams are all irradiated to the portion made of tungsten, so the amount of heat absorbed by the sample by each irradiation is the same. In addition, the heat flow path length in the measurement sample and the standard material can be measured by observation with a TEM or the like. Therefore, it is possible to calculate ΔT sample / Δx sample, which is the slope of the line segment of the graph between (2) and (3), and ΔT standard material / Δx standard material, which is the slope of the line segment of the graph between (4) and (5) on this graph.

[0037] Now, using the known thermal conductivity k of the standard material, the thermal conductivity k of the sample can be expressed as k standard material = αk sample (13) Where: α = (ΔT sample / Δx sample) / (ΔT standard material / Δx standard material) (14) Since the numerator and denominator of the fractional expression representing α can be calculated as described above, the absolute value of the thermal conductivity k of the sample can also be calculated.

[0038] In this way, by estimating the heat energy generated during electron beam irradiation using a standard material with known thermal conductivity, it becomes possible to estimate the absolute value. That is, in order to make the heat flow pass through a material with known thermal conductivity (standard material part 214), the standard material part 214 sandwiched between electron beam heat conversion parts 216a, 216b, and 216c is provided in the passage of the heat flow.

[0039] In addition, in the above description, when the thermal conductivity of the electron beam thermal conversion parts 216a, 216b, and 216c sandwiching the measured sample part 212 in the relevant usage environment is known, the standard material part 214 can be made of the same material as the electron beam thermal conversion parts 216a, 216b, and 216c. In this way, when the standard material part 214 is also made of the same material as the electron beam thermal conversion parts 216a, 216b, and 216c, the structure on the left side of (3) in Figure 5(A) is simplified to an integrated structure made only of the same material as the electron beam thermal conversion parts 216a, 216b, and 216c. The above-mentioned formula for calculating the absolute value of the thermal conductivity can also be modified accordingly.

[0040] 6A is a conceptual diagram modeling an example of a configuration in which the relative value of thermal conductivity can be obtained by the micro thermal conductivity measuring device of the present invention. The sample 21 is formed into a very narrow or very thin shape (for example, as described above, it is processed to a thickness of 500 nm or less using a FIB (Focused Ion Beam)) and supported by a pedestal 219, so that there is no non-uniformity inside the sample. By configuring as shown in Fig. 6A, the one-dimensional heat flow model explained with reference to Fig. 5 is established. That is, not only is the end opposite to the end where the thermocouple is in contact thermally insulated by a means having a sufficiently large thermal resistance (for example, epoxy resin or vacuum, etc.), but also, in order to make the heat flow almost one-dimensional, it is necessary to surround the periphery with a material having a large thermal resistance, a vacuum, etc. so that there is practically no path of the heat flow in other directions (in Fig. 5(A) , the heat flow does not leak in the up and down directions in the middle of the path). Furthermore, the condition that the heat flow flows in the inside of the sample in the one-dimensional direction is satisfied (that is, the inside of the sample has a one-dimensional structure in terms of thermal conductivity, and the heat flow does not meander or detour in an unpredictable manner inside the sample).

[0041] As another aspect in which the one-dimensional heat flow model is valid, even if there are regions with different thermal conductivities inside the sample, the last condition can be considered to be substantially satisfied if the distribution pattern of the regions is sufficiently uniform in comparison with the measurement resolution, or if, when focusing on a region through which most of the heat flow passes because the thermal conductivity is sufficiently greater than that of other regions, such a region provides a substantially uniform one-dimensional heat flow path.

[0042] 6B is an enlarged view of the thermocouple portion taken with a STEM-HAADF (High-angle Annular Dark Field Scanning TEM). A constantan probe 23 and a chromel probe 24, which are thermocouples, are connected to the ends of the sample 21. 6C is an explanatory diagram of heating by a pulsed electron beam of a predetermined frequency, showing the on-off waveform of the electron beam. Here, the frequency is 333 Hz, and the duty ratio of the on-off waveform is 1:1 (50%). Note that the predetermined frequency is not limited to 333 Hz, and an appropriate frequency f is selected and used depending on the material of the sample 21 and the length L of the measurement section, and may be, for example, a plurality of frequencies selected between 1 Hz and 500 kHz. Furthermore, the on-off duty ratio of the pulsed electron beam of a predetermined frequency (f) is not limited to 1:1, but may be selected, for example, between 1:9 and 9:1, and the pulse on-time width may be selected between 100 ns and 1 sec. The pulse on-time width is determined by the characteristics of the heating device, and for example, in the case of EDM, the minimum pulse on-time width is set to 100 ns.

[0043] Fig. 7 is an explanatory diagram of heating by a pulsed electron beam of a specific frequency by the frequency method, showing the temperature wave waveform measured by a thermocouple. Here, the cases of frequencies of 1 kHz, 5 kHz, 10 kHz, and 20 kHz are shown. As the frequency f increases, the phase delay θ increases. The signal-to-noise ratio decreased with increasing frequency f. Here, the phase delay θ is given by the following equation: θ=L√(πf / α) (15) Here, L is the distance from the heating position to the thermocouple, and α is the thermal diffusivity.

[0044] Figure 8 is an explanatory diagram of heating by a pulsed electron beam of a specific frequency by the frequency method, showing a phase image of a temperature wave measured by a thermocouple. Here, the cases of frequencies of 5 kHz, 10 kHz, and 20 kHz are shown, and for reference, a STEM image of a sample without heating by a pulsed electron beam is also shown. Here, the phase delay θ is represented by shading. Line profiles were acquired to quantitatively investigate the thermal diffusivity of the samples, as shown in Figure 8. The line profile provides information on the slope of the graph of phase delay θ versus distance L. That is, the ratio of θ to L was identified for each frequency of the irradiated pulsed electron beam. Here, in the case of 5 kHz, the phase lag θ at the heating point was 39°, and the phase lag θ at the sample end near the thermocouple was 18.5°. In the case of 10 kHz, the phase lag θ at the heating point was 54.5°, and the phase lag θ at the sample end near the thermocouple was 24°. In the case of 20 kHz, the phase lag θ at the heating point was 68°, and the phase lag θ at the sample end near the thermocouple was 25.5°.

[0045] Figure 9 shows the relationship for evaluating thermal diffusivity α based on the ratio of the temperature wave phase lag θ to the distance L from the heating position. Here, thermal diffusivity α is given by the following equation, which is a modification of equation (15). α=πf / (θ / L) 2 (16) In the case of 5 kHz, the regression equation is y = 0.0474x - 0.3666, θ / L = 0.0474, and the square of the correlation coefficient R is 2 The correlation coefficient R is 0.9975, which indicates a high correlation between the two variables x and y. In the case of 10 kHz, the regression equation is y = 0.0688x - 0.5183, θ / L = 0.0688, and the squared correlation coefficient R is 2 The correlation coefficient R is 0.9987, which shows a high correlation between the two variables x and y. In the case of 20 kHz, the regression equation is y = 0.0953x - 0.7280, θ / L = 0.0953, and the squared correlation coefficient R is 2 shows a high correlation between the two variables x and y, at 0.9977. As a result, the thermal diffusivity α(m 2 / s) is 6.99x10 at 5kHz -6 , 6.64x10 at 10kHz -6 , 6.92x10 at 20kHz -6 The values ​​are roughly equal to

[0046] FIG. 10(A) is an explanatory diagram of heating by a pulsed electron beam of a predetermined frequency by the frequency method, and shows the amplitude image of the temperature wave measured by a thermocouple. Here, the amplitude of the temperature wave in the case of 5 kHz was 8.0 μV when the heating point was at the thermocouple attachment position, 6.0 μV when the heating point was at the tip of the sample, and 6.7 μV when the heating point was at the midpoint between the thermocouple attachment position and the sample tip. The amplitude of the temperature wave in the case of 10 kHz was 6.1 μV when the heating point was at the thermocouple attachment position, 3.9 μV when the heating point was at the tip of the sample, and 4.6 μV when the heating point was at the midpoint between the thermocouple attachment position and the sample tip. The amplitude of the temperature wave in the case of 20 kHz was 4.0 μV when the heating point was at the thermocouple attachment position, 2.3 μV when the heating point was at the tip of the sample, and 3.1 μV when the heating point was at the midpoint between the thermocouple attachment position and the sample tip. Here, the amplitude T(x) of the temperature wave is given by the following equation:

number

[0047] Figure 10(B) shows the results of evaluating the amplitude of the temperature wave using the amplitude Q of the temperature wave and the distance L from the heating position. The theoretical values ​​and measured values ​​were compared for frequencies of 5 kHz, 10 kHz, and 20 kHz when the distance L from the thermocouple attachment position to the heating position ranged from 0 μm to 6 μm. When the frequency was 5 kHz and L was 0 μm, the amplitude of the temperature wave was maximum, with a theoretical value of 0.14 K and a measured value of 0.13 K. As the frequency decreased, the amplitude of the temperature wave became smaller, and when the frequency was 20 kHz and L was 8 μm, the amplitude of the temperature wave was minimum, with a theoretical value of 0.035 K and a measured value of 0.04 K.

[0048] As described above, the micro thermal conductivity measuring device and method of the present invention measure thermal diffusivity by combining a nanoscale heat application method using electron beam irradiation or the like with temperature measurement with nanoscale spatial resolution, and various modified embodiments are conceivable within the scope of obviousness to those skilled in the art. For example, it is possible to measure thermal diffusivity and simultaneously perform electromagnetic property and elemental analysis by combining the micro thermal conductivity measuring device and method of the present invention with conventional electron microscope methods such as microstructure evaluation and elemental analysis (EDS, EELS), electromagnetic field observation, electrical transport measurement, and stress measurement. [Industrial Applicability]

[0049] In addition, the micro-thermal conductivity measuring device and method of the present invention can be applied to the evaluation of thermal resistance at voids, grain boundaries, and contact interfaces within materials, and can be used to measure heat transport and specific heat of insulators, semiconductors, metals, nanowires, nanotubes, particles, thermally conductive fillers, composite heat dissipation materials, etc. [Explanation of symbols]

[0050] 10 Transmission Electron Microscopy (STEM) 12 Electrostatic Shutter 14 Electrostatic Dose Modulator (EDM) 20 Temperature wave generator 21 Sample 22 Pulsed electron beam 23 Constantan probe (thermocouple) 24 Chromel probe (thermocouple) 30 Lock-in amplifier 40 Signal Processing Section 50 Electron beam control and image processing system (DigiScan) 60 Analysis Computer

Claims

1. A thermocouple that contacts the sample at the contact point, A heating device that heats at least one heating point on the sample using a pulsed electron beam of a predetermined frequency (f), The device includes a mechanism for detecting the output of the thermocouple in response to the temperature rise at the contact point due to heating by a pulsed electron beam of a predetermined frequency, and for measuring the phase component of the temperature wave corresponding to the heating position at the heating point at the predetermined frequency. A minute thermal conductivity measuring device that uses the phase component (θ) of the temperature wave produced by the pulsed electron beam to determine the thermal diffusivity (α) between the heating point and the contact point based on the distance (L) from the heating point to the contact point using the following formula. α=π / (θ / L) ２

2. The sample is housed in a transmission electron microscope (TEM) or a scanning transmission electron microscope (STEM) so that a TEM image or STEM image can be observed, The heating device that irradiates the heated point with the focused electron beam is the electron gun of the TEM or STEM. The device for measuring minute thermal conductivity according to claim 1.

3. The minute thermal conductivity measuring device according to claim 1, wherein the heating points on the sample are a plurality of heating points on the sample that differ in distance (L) from the contact point of the thermocouple.

4. The minute thermal conductivity measuring device according to claim 1, wherein the predetermined frequency is a plurality of frequencies selected between 1 Hz and 500 kHz.

5. The minute thermal conductivity measuring device according to claim 1, wherein the pulsed electron beam of a predetermined frequency (f) has an on-off duty cycle selected between 1:9 and 9:1, and the on-time width of the pulse is selected between 100 ns and 1 sec.

6. The minute thermal conductivity measuring device according to claim 2, wherein the thermocouple is a joint of needle-shaped objects made of two non-magnetic materials.

7. The minute thermal conductivity measuring device according to claim 6, wherein the two types of materials are chromel and constantan.

8. The minute thermal conductivity measuring device according to claim 6, wherein the diameter of the tip of the needle-shaped object is 100 nm or less.

9. The minute thermal conductivity measuring device according to any one of claims 1 to 8, wherein the sample is attached to the base via a material with a higher thermal resistance than the thermocouple.

10. The minute thermal conductivity measuring device according to any one of claims 1 to 8, wherein the measurement timing of the device for measuring the phase component of the temperature wave is when the temperature is oscillating with a small amplitude at a temperature that has risen to a nearly steady state by the pulsed electron beam.

11. Furthermore, it is equipped with an analysis computer, The aforementioned analysis computer uses the phase component (θ) of the temperature wave produced by the pulsed electron beam to determine the thermal diffusivity (α) between the heating point and the contact point, based on the distance (L) from the heating point to the contact point of the thermocouple on the sample, using the following formula: A device for measuring minute thermal conductivity according to any one of claims 1 to 8. α=π / (θ / L) ２

12. A thermocouple is brought into contact with the sample at the contact point. The heating point on the sample is heated using a pulsed electron beam of a predetermined frequency (f). Multiple outputs of the thermocouple in response to the temperature rise of the contact point due to heating by the pulsed electron beam of the predetermined frequency are detected, and the phase component of the temperature wave corresponding to the heating position of the heating point at the predetermined frequency is measured. A method for measuring minute thermal conductivity, which uses the phase component (θ) of the temperature wave produced by the pulsed electron beam to determine the thermal diffusivity (α) between the heating point and the contact point based on the distance (L) from the heating point to the contact point, using the following formula. α=π / (θ / L) ２

13. The sample is placed in a TEM or STEM so that its TEM image or STEM image can be observed. The electron beam irradiation is performed by the electron gun of the TEM or STEM. The method for measuring minute thermal conductivity according to claim 12.

14. With the contact between the sample and the thermocouple released, multiple calibration outputs corresponding to the heating positions of the multiple heating points are detected from the thermocouple. The influence of secondary electrons produced by the irradiation of the electron beam to the plurality of heating points on the output of the thermocouple is canceled out by the plurality of calibration outputs. The method for measuring minute thermal conductivity according to claim 12.

15. The method for measuring minute thermal conductivity according to claim 12, wherein the heating points on the sample are a plurality of heating points on the sample that differ in distance (L) from the contact point of the thermocouple.

16. The predetermined frequency is one of several frequencies selected between 1 Hz and 500 kHz. The method for measuring minute thermal conductivity according to claim 12.

17. The method for measuring minute thermal conductivity according to claim 12, wherein the pulsed electron beam of a predetermined frequency (f) has an on-off duty cycle selected between 1:9 and 9:1, and the on-time width of the pulse is selected between 100 ns and 1 sec.

18. The timing for measuring the phase component of the temperature wave is when the temperature is oscillating with a small amplitude at a temperature that has risen to a nearly steady state by the pulsed electron beam, according to any one of claims 12 to 17.

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