Method for evaluating the thermal conductivity of diamond

Abstract

To provide a method for easily evaluating thermal conductivity of diamond.SOLUTION: A method for evaluating thermal conductivity of gas-phase synthesized diamond includes acquiring thermal conductivity from hydrogen concentration in diamond.SELECTED DRAWING: Figure 1

Description

[Technical Field] 【0001】 This invention relates to a method for evaluating the thermal conductivity of diamond. [Background technology] 【0002】 Diamonds possess several excellent physical properties, making them suitable for a wide range of applications. For example, their high hardness—the hardest of all naturally occurring materials—makes them ideal for use as cutting tools, and their high refractive index and dispersion rate make them highly valued as gemstones. Furthermore, compared to Si, SiC, and GaN, diamonds have a larger band gap, carrier mobility, and dielectric breakdown voltage, making them promising for applications in power devices. 【0003】 Furthermore, in recent years, its use as a heat dissipation material, taking advantage of its high thermal conductivity, has attracted attention. While greases mixed with diamond powder, such as diamond grease, have traditionally been used as heat dissipation materials, in recent years, there has been research into lowering the operating temperature of devices and improving their performance by bonding or depositing diamond films onto them. 【0004】 For diamonds used for heat dissipation, thermal conductivity is an important indicator. There are several methods for evaluating the thermal conductivity of diamond, but the laser flash method is often used to measure the thermal conductivity of bulk diamonds, while the pulsed light heating thermoreflectance method is often used to measure the thermal conductivity of thin films. 【0005】 The laser flash method is a method for evaluating thermal conductivity by heating a sample with a metal film attached to its surface using a pulsed laser, and then measuring the temperature change on the back surface. 【0006】 The pulsed light heating thermoreflectance method is a method for measuring thermal conductivity by heating a metal film deposited on a diamond with a pulsed laser and measuring the change in reflectivity due to the temperature change of the metal film with another pulsed laser. There are two methods: one in which the metal film is deposited only on the surface of the diamond, the surface is heated, and the temperature change of the surface is measured (surface heating / surface temperature measurement); and another in which the metal film is deposited on both the front and back surfaces of the diamond thin film, the back surface is heated, and the temperature change of the surface is measured (back surface heating / surface temperature measurement). Back surface heating / surface temperature measurement can measure thermal conductivity with higher accuracy than surface heating / surface temperature measurement, but it requires the deposition of metal films on both the front and back surfaces of the diamond thin film. 【0007】 Prior art will be mentioned. Patent Document 1 states that a low hydrogen content in diamond film material is an indicator of fewer defects and less non-diamond carbon. Patent Document 2 lists the hydrogen concentration and thermal conductivity of single-crystal diamond in Table 1. Patent Document 3 states that the most important impurities for lowering thermal conductivity are nitrogen, hydrogen, and 13 It is stated that it is a 1C isotope. [Prior art documents] [Patent Documents] 【0008】 [Patent Document 1] Japanese Patent Application Publication No. 06-263590 [Patent Document 2] Japanese Patent Publication No. 2005-162525 [Patent Document 3] Japanese Patent Publication No. 2021-119602 [Overview of the project] [Problems that the invention aims to solve] 【0009】 As mentioned above, the thermal conductivity of diamond has been evaluated. However, conventional methods such as the laser flash method and the pulsed light heating thermoreflectance method require a metal film to be attached to the diamond, which has the problem of contaminating the sample. 【0010】 Furthermore, conventional technologies have not included the idea of ​​determining thermal conductivity from the impurity concentration in diamond, nor have they provided specific instructions for doing so. For example, Patent Documents 1 and 3 state that hydrogen concentration in diamond is one of the factors that reduce thermal conductivity, but they do not describe a method for determining thermal conductivity from hydrogen concentration. Also, while Table 1 of Patent Document 2 lists the hydrogen concentration and thermal conductivity of single-crystal diamond, it does not describe the idea of ​​determining thermal conductivity from hydrogen concentration, nor does it describe a method for doing so. 【0011】 As mentioned above, conventional techniques have the problem of contaminating samples when evaluating the thermal conductivity of diamond, and a new method is needed that is simpler to evaluate the thermal conductivity of diamond. 【0012】 This invention has been made in view of the problems of the prior art described above, and aims to provide a simple method for evaluating the thermal conductivity of diamond. [Means for solving the problem] 【0013】 To solve the above problems, the present invention provides a method for evaluating the thermal conductivity of gas-phase synthesized diamond, characterized in that the thermal conductivity is determined from the hydrogen concentration in the diamond. 【0014】 This method for evaluating the thermal conductivity of diamond allows for a simple and convenient assessment of its properties. 【0015】 Furthermore, it is preferable to determine the thermal conductivity of the diamond from the hydrogen concentration in the diamond using the following formula (1). 【number】 (Here, K is the thermal conductivity of the diamond we are looking for, K0 is the thermal conductivity of defect-free diamond, [H] is the hydrogen concentration in the diamond, and a and b are constants.) 【0016】 By using such an equation, the thermal conductivity can be obtained more accurately. 【Advantages of the Invention】 【0017】 As described above, according to the present invention, it becomes possible to simply evaluate the thermal conductivity of diamond. 【Brief Description of the Drawings】 【0018】 [Figure 1] It is a diagram showing the flow of the method for evaluating the thermal conductivity of diamond of the present invention. [Figure 2] It is the result of calculating the relationship between the film thickness and the thermal conductivity of single crystal diamond. [Figure 3] It is the relationship between the hydrogen concentration and the thermal conductivity. The solid line is the result of fitting the mathematical formula (1). [Figure 4] It is the relationship between the nitrogen concentration and the thermal conductivity. The solid line is the result of fitting the mathematical formula (4). [Figure 5] It is the relationship between the thermal conductivity obtained from the hydrogen concentration in Example 1 and the measured thermal conductivity. [Figure 6] It is the relationship between the thermal conductivity obtained from the nitrogen concentration in Comparative Example 1 and the measured thermal conductivity. 【Modes for Carrying Out the Invention】 【0019】 As described above, there has been a demand for a method for simply evaluating the thermal conductivity of diamond without contaminating the sample. 【0020】 As a result of intensive studies on the above problems, the present inventor has found a method for evaluating the thermal conductivity of vapor-grown diamond, which is a method for evaluating the thermal conductivity of diamond characterized by obtaining the thermal conductivity from the hydrogen concentration in diamond, and can simply evaluate the thermal conductivity without contaminating the sample, and has completed the present invention. 【0021】 The present invention will be described in detail below, but the present invention is not limited to these descriptions. 【0022】 I will explain by referring to the drawings. Figure 1 shows the evaluation flow of the thermal conductivity of diamond according to the present invention. 【0023】 S11 in Figure 1 is the process of preparing vapor-phase synthesized diamond (first step). 【0024】 This explains the vapor phase synthesis method for diamond. 【0025】 Prepare a substrate that will serve as the base for the vapor-phase synthesis of diamond. This substrate can be diamond, semiconductor materials such as Si, SiC, or GaN, or even cutting tool components such as cemented carbide or ceramics. 【0026】 If the substrate is not diamond, a diamond nucleus is formed before the diamond is synthesized in the vapor phase. There are several methods for diamond nucleation, but for example, one method is to use diamond powder, and another is to perform BEN (Bias Enhanced Nucleation) treatment. 【0027】 In methods using diamond powder, diamond nuclei are formed on the substrate by rubbing the diamond powder onto the substrate, ultrasonically cleaning it with a solution containing diamond powder, or by adhering the diamond powder to the substrate. This method allows for the synthesis of polycrystalline diamond on dissimilar materials. 【0028】 BEN treatment is a method used in microwave plasma CVD (Chemical Vapor Deposition) equipment under conditions of a high methane / hydrogen ratio in the source gas and a high bias voltage. By treating under such conditions, high-energy ions are irradiated onto the substrate, forming diamond nuclei. This method allows for the synthesis of single-crystal diamond on dissimilar materials. 【0029】 There are several methods for vapor-phase synthesis of diamond, but two examples can be used: microwave plasma CVD and hot filament CVD. In both methods, hydrogen and methane are used as raw material gases. Gases containing nitrogen, oxygen, argon, boron, and phosphorus can also be added to the raw material gases. In microwave plasma CVD, these raw material gases are decomposed by plasma generated by microwaves to form a film. In hot filament CVD, a high-melting-point metal is heated, and the raw material gas is decomposed by the heat to form a film. 【0030】 At pressures below atmospheric pressure, which are used in the CVD process, graphite is more stable than diamond. Therefore, while diamond grows due to carbon sources such as CH3 produced by the decomposition of the raw material gas, graphite is also formed at the same time. 【0031】 On the other hand, hydrogen atoms dissociated from hydrogen molecules etch graphite more easily than diamond, so by introducing hydrogen atoms, it is possible to selectively grow only diamond. In the gas-phase synthesis method, synthesis is carried out in a high-hydrogen atmosphere where hydrogen accounts for 80% or more of the raw material gas in order to suppress the formation of graphite. Hydrogen is incorporated into the diamond and segregates at grain boundaries and dislocations. In addition, hydrogen also bonds with interstitial diamond, vacancies, impurity atoms, and dopant atoms. 【0032】 For microwave plasma CVD systems, microwave frequencies such as 915 MHz and 2.45 GHz can be used. These frequencies allow for the preparation of a microwave source with sufficient power for diamond synthesis. 【0033】 When generating plasma using a single resonant mode, the area where a uniform plasma can be generated is approximately half the wavelength of the microwave. Therefore, synthesis can be performed in an area with a diameter of approximately 2 inches (50 mm) when using 2.45 GHz, and in an area with a diameter of approximately 6 inches (150 mm) when using 915 MHz. When generating plasma by superimposing multiple resonant modes, diamond synthesis can be performed over a larger area. 【0034】 Lower microwave frequencies and larger diamond sizes require higher microwave output during diamond synthesis. For example, using 2.45 GHz allows for an output of 1 kW to 30 kW, while using 915 MHz allows for an output of 5 kW to 100 kW. 915 MHz has lower plasma generation efficiency than 2.45 GHz, requiring greater power to generate the plasma. Since microwave output is limited by the maximum output of the microwave source, it is possible to synthesize diamonds with even higher output by using a microwave source capable of higher output. 【0035】 Diamond synthesis can be carried out under conditions such as a temperature of 600°C to 1300°C, a pressure of 1 kPa to 50 kPa, a methane concentration of 0.1% to 10%, and a bias voltage of 0V to 300V. Nitrogen, oxygen, and argon can be added during diamond synthesis to accelerate the growth rate. Additionally, gases containing dopants such as boron and phosphorus can be added. 【0036】 Diamond synthesis using a hot filament CVD apparatus can be performed, for example, by using W, Ta, Mo, and Re as the filament material, setting the filament temperature to 1700°C or higher and 2400°C or lower, the substrate temperature to 600°C or higher and 1300°C or lower, the distance between the substrate and filament to 5 mm or higher and 30 mm or lower, the pressure to 1 kPa or higher and 50 kPa or lower, and the methane concentration to 0.1% or higher and less than 20%. 【0037】 There are no particular restrictions on the thickness or size of the diamond. 【0038】 Step S12 in Figure 1 is the second step (measurement of hydrogen concentration in gas-phase synthesized diamond). Methods for measuring hydrogen concentration include, for example, SIMS (Secondary Ion Mass Spectrometry) and FTIR (Fourier Transform Infrared Spectroscopy). 【0039】 Using SIMS, it is possible to measure hydrogen concentration at any location and depth. Although the surface of vapor-phase synthesized diamond is rough, hydrogen concentration can still be measured even on rough surfaces. 【0040】 FTIR measured 3100cm -1 Because hydrogen absorption is observed in the vicinity, the hydrogen concentration can be quantified from its absorbance. FTIR allows for the quantification of hydrogen concentration without damaging the diamond. 【0041】 S13 in Figure 1 is the process of calculating the thermal conductivity from the hydrogen concentration (third step). 【0042】 This explains the factors that reduce the thermal conductivity of diamond. As stable isotopes of diamond, 12 C and 13 C is present, with natural abundances of 98.93% and 1.07%. 12 Contains in C 13 Because carbon has a different mass, it acts as a phonon scattering source, which reduces thermal conductivity. In addition, impurity atoms in diamond also affect the base material. 12 Although impurity atoms can act as phonon scattering sources due to their different mass from carbon, the influence of phonon scattering by impurity atoms is considered to be small because impurity atoms generally do not make up a percentage-order amount. 【0043】 On the other hand, dislocations and grain boundaries present in diamond act as phonon scattering sources, contributing to a decrease in thermal conductivity. The inventors hypothesized that impurity atoms in diamond tend to segregate at dislocations and grain boundaries, and therefore, the longer the dislocation and the larger the grain boundary area, the greater the amount of impurity atoms. Consequently, they hypothesized that the greater the amount of impurity atoms, the stronger the effect of phonon scattering by dislocations and grain boundaries, leading to a decrease in thermal conductivity. In other words, they hypothesized that thermal conductivity could be determined from the concentration of impurity atoms. After investigating such impurity atoms, it was found that hydrogen is preferable. As mentioned earlier, hydrogen is always used in the gas-phase synthesis of diamond, so hydrogen segregates if there are dislocations or grain boundaries. Since hydrogen is present in larger quantities than nitrogen or oxygen, it is considered the most suitable. 【0044】 This section explains the formula for calculating thermal conductivity from hydrogen concentration. The relationship between grain boundaries and thermal conductivity is given by the following equation (2): 【number】 This is the result. Here, K is the thermal conductivity of the diamond we are looking for, K0 is the thermal conductivity of defect-free diamond, R is the thermal resistance of the grain boundary, and d is the grain boundary size. Assuming that the hydrogen concentration is related to the grain boundary size d, we thought that by making the denominator of equation (2) a function of the hydrogen concentration, we could obtain a formula to calculate the thermal conductivity from the hydrogen concentration. After diligent research by the inventors, the relationship between hydrogen concentration and thermal conductivity is given by the following equation (1) 【number】 It was found that this is the case. Here, [H] is the hydrogen concentration in the diamond, and a and b are constants. 23.25 is the density of diamond, 1.763 × 10⁻⁶. 23 This is the common logarithm of . 【0045】 Since non-diamond carbon has a lower thermal conductivity than diamond, the presence of non-diamond carbon in diamond causes a decrease in thermal conductivity. Because non-diamond carbon is more likely to incorporate hydrogen than diamond, even if non-diamond carbon is mixed in diamond, the thermal conductivity can be calculated by measuring the hydrogen concentration. 【0046】 The grain boundary size can be measured by EBSD (Electron BackScatter Diffraction) analysis. However, in addition to the fact that EBSD analysis cannot be performed unless the surface of the diamond is mirror-like, there is a problem that a more complex analysis requiring more time than the measurement of the hydrogen concentration is needed. Also, in EBSD analysis, there are problems that the grain boundary size cannot be known when it is small or about the depth direction of the grain boundary. On the other hand, since hydrogen is considered to be uniformly present at the grain boundaries, the hydrogen concentration is considered to have a good positive correlation with the grain boundary area, which is more accurate than the grain boundary size and is considered to be a better indicator of thermal conductivity than the grain boundary size analyzed by EBSD. 【0047】 As the thermal conductivity K0 of defect-free diamond, for example, 2200 W / m·K can be used for naturally occurring diamond, 12 and for C diamond, for example, 3400 W / m·K, which is greater than 2200 W / m·K, can be used. 【0048】 The thermal conductivity decreases due to phonon scattering at the surface as the film becomes thinner (Figure 2). Therefore, from the relationship between the film thickness and the thermal conductivity shown in Figure 2, the ideal thermal conductivity of single-crystal diamond with a desired film thickness can be obtained and used as the thermal conductivity K0 of defect-free diamond. By doing so, the thermal conductivity of not only bulk diamond but also thin-film diamond can be accurately calculated. 【0049】 The ideal thermal conductivity of a thin film of single-crystal diamond can be calculated, for example, using the free software P-TRANS developed at the University of Tokyo. For diamond film thicknesses between 10 nm and 100 μm, the following formula (3) applies. 【number】 The thermal conductivity K0 of a defect-free diamond can be calculated using the following formula, where x is the common logarithm of the diamond's film thickness (μm). 【0050】 Equation (3) was obtained by varying the thickness of a single-crystal diamond film within the range of 10 nm to 100 μm, calculating the vertical thermal conductivity of the diamond film using P-TRANS, and then correcting the bulk thermal conductivity by multiplying it by 1.13 to match the thermal conductivity of naturally occurring single-crystal diamond (2200 W / m·K) before fitting the corrected value using the least squares method. Higher-order functions can also be used. The solid line in Figure 2 shows the calculation results of equation (3). 【0051】 When the diamond film thickness is greater than 100 μm, the thermal conductivity of bulk single-crystal diamond, 2200 W / m·K, can be used. 12 In the case of C diamonds, 12 The thermal conductivity of diamond can be corrected by applying a coefficient. For example, defect-free 12 If the thermal conductivity of single-crystal diamond C is 3400 W / m·K, the value obtained by multiplying the thermal conductivity calculated using formula (3) by 1.55 can be used. [Examples] 【0052】 The present invention will be described in detail below with reference to examples and comparative examples, but this is not intended to limit the present invention. 【0053】 [Example 1] (Formation of a diamond film) A 10mm square Si substrate with a thickness of 5mm was ultrasonically cleaned for 15 minutes in a methanol solution containing diamond powder to induce diamond nucleation. Subsequently, polycrystalline diamond was deposited using microwave plasma CVD. The pressure in the chamber was set to 19kPa. The microwave frequency was set to 2.45GHz, the microwave output to 4kW, and the bias voltage to 0V. CH4 and H2 were used as gases. Nine samples were prepared: five samples with a CH4 / H2 ratio of 1% and substrate temperatures of 950, 960, 990, 1005, and 1020°C, and four samples with a substrate temperature of 1020°C and CH4 / H2 ratios of 1.5, 2, 2.5, and 3%. In all cases, the polycrystalline diamond film thickness was 340μm. After depositing the polycrystalline diamond, the Si substrate was polished to remove it, and then 30μm of the polycrystalline diamond on the side that was in contact with the Si substrate was polished to remove the transition layer with low thermal conductivity. 【0054】 (Measurement of hydrogen concentration in diamond film) The hydrogen concentration in the polycrystalline diamond film was measured using SIMS. The measurement was performed from the surface to a depth of 5 μm. After polishing the surface of the polycrystalline diamond to a depth of 10 μm, Ti was deposited on both sides of the polycrystalline diamond, and the thermal conductivity of the polycrystalline diamond at room temperature was measured using the laser flash method. After irradiating the surface of the polycrystalline diamond with a pulsed laser, the temperature rise on the back side of the polycrystalline diamond was measured using an infrared detector. 【0055】 (Calculation of a and b in formula (1)) First, the thermal diffusivity was determined from the measured temperature profile. The thermal conductivity was calculated by multiplying the thermal diffusivity by the specific heat capacity and density of the diamond. Next, we determine a and b in equation (1) using five samples with varying substrate temperatures. The relationship between hydrogen concentration and thermal conductivity for the five samples is shown by the black circles in Figure 3. The average value of the hydrogen concentration at 4-5 μm from the surface was used. It can be seen that the lower the hydrogen concentration, the higher the thermal conductivity. The solid black line in Figure 3 is the result of calculations using equation (1) with the thermal conductivity K0 of defect-free diamond set to 2200 W / m·K, a set to 4750, and b set to 6.66. a and b were obtained by fitting the experimental results to equation (1). 【0056】 (Estimation of thermal conductivity in a diamond film) Next, we demonstrate that thermal conductivity can be estimated using equation (1) with four levels of samples, each with a different CH4 / H2 ratio. Figure 5 shows the relationship between the thermal conductivity estimated by substituting hydrogen concentration into equation (1) (horizontal axis) and the thermal conductivity measured by the laser flash method (vertical axis). As is clear from Figure 5, there is a positive correlation between the data from the four levels of samples, and it can be seen that the actual thermal conductivity can be estimated from the thermal conductivity obtained from hydrogen concentration. 【0057】 [Comparative Example 1] A diamond film was formed under the same conditions as in Example 1, but unlike Example 1, the nitrogen concentration in the polycrystalline diamond was measured by SIMS. The measurement was performed from the surface to a depth of 5 μm. On the other hand, the thermal conductivity was measured under the same conditions as in Example 1, using the laser flash method. Subsequently, a correlation diagram between nitrogen concentration and thermal conductivity in the diamond film was created using five samples with varying substrate temperatures, and a formula for estimating thermal conductivity from nitrogen concentration was derived. 【0058】 Figure 4 shows the relationship between nitrogen concentration and thermal conductivity. The average nitrogen concentration was measured at a depth of 4-5 μm from the surface. Figure 4 differs significantly from Figure 3, which shows the relationship between hydrogen concentration and thermal conductivity; lower nitrogen concentrations result in lower thermal conductivity. For example, equation (4) below illustrates this trend. 【number】 Let us assume the following. Here, [N] is the nitrogen concentration in the diamond, and a and b are constants. Assuming K0 is the same as above at 2200 W / m·K, and fitting a and b to the experimental results, a is 1.02 × 10 16 b was 1.01. Next, the thermal conductivity was estimated from the nitrogen concentration using four levels of samples with varying CH4 / H2 ratios. Figure 6 shows the relationship between the thermal conductivity estimated by substituting the nitrogen concentration into equation (4) (horizontal axis) and the thermal conductivity measured by the laser flash method (vertical axis). As is clear from Figure 6, there is no correlation between the data of the four levels of samples, and it can be seen that the actual thermal conductivity cannot be estimated from the thermal conductivity obtained from the nitrogen concentration. 【0059】 As described above, the embodiments of the present invention demonstrate that the thermal conductivity can be determined from the hydrogen concentration in diamond. 【0060】 As described above, the present invention provides a method for evaluating the thermal conductivity of gas-phase synthesized diamond, which involves determining the thermal conductivity of diamond from the hydrogen concentration in the diamond, allowing for a simple evaluation of thermal conductivity. 【0061】 Furthermore, it is preferable to determine the thermal conductivity of diamond from the hydrogen concentration in the diamond using the above formula (1). 【0062】 By using such a formula, the thermal conductivity can be determined more accurately. 【0063】 It should be noted that the present invention is not limited to the embodiments described above. The embodiments described above are illustrative, and any configuration that has substantially the same technical idea as described in the claims of the present invention and achieves similar effects is included within the technical scope of the present invention. [Explanation of symbols] 【0064】 S11...first process, S12...second process, S13...third process

Claims

[Claim 1] A method for evaluating the thermal conductivity of vapor-phase synthesized diamond, wherein the thermal conductivity is determined from the hydrogen concentration in the diamond. A method for evaluating the thermal conductivity of diamond, characterized in that the thermal conductivity of the diamond is determined from the hydrogen concentration in the diamond using the following formula (1). [Math 1] (Here, K is the thermal conductivity of the diamond we are looking for, K0 is the thermal conductivity of a defect-free diamond, [H] is the hydrogen concentration in the diamond, and a and b are constants.)

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