Method for producing aluminum nitride single crystals and aluminum nitride single crystals

The liquid phase growth of aluminum nitride single crystals using a composite melt and controlled temperature gradient addresses the challenges of high costs and slow growth rates, producing high-quality, transparent crystals with improved luminescence efficiency.

JP7832630B2Active Publication Date: 2026-03-18TOHOKU UNIV +1
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Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Filing Date
2024-08-07
Publication Date
2026-03-18

AI Technical Summary

Technical Problem

Conventional methods for producing aluminum nitride single crystals face challenges such as high production costs, slow crystal growth rates, and the need for expensive seed crystals that exhibit discoloration, leading to reduced luminescence efficiency in ultraviolet light-emitting devices.

Method used

A method involving a liquid phase growth process using a composite melt of Fe, Ni, and Co, or Fe-Cr, with a controlled temperature gradient, allows for the growth of aluminum nitride single crystals on an AlN template substrate, enabling easy peeling and achieving high crystal growth rates, while minimizing impurities and threading dislocations.

Benefits of technology

This method enables the production of thick, transparent aluminum nitride single crystals with improved crystal quality and ease of separation from the substrate, enhancing luminescence efficiency by reducing absorption in the deep ultraviolet range.

✦ Generated by Eureka AI based on patent content.

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Abstract

To simply provide a transparent and thick aluminium nitride single crystal capable of manufacturing the aluminium nitride single crystal having a large crystal growth rate and easily peeled from a sapphire substrate.SOLUTION: A method for manufacturing an aluminium nitride single crystal comprises steps of: preparing a raw material melt obtained by melting Al and N in the saturation state of aluminium nitride at a predetermined temperature in an alloy melt; and growing an aluminium nitride single crystal on the AlN layer side of an AlN template substrate by bringing the AlN template substrate into contact with the raw material melt to cool at least the periphery of the AlN template substrate to a temperature lower than the predetermined temperature. The AlN layer of the AlN template substrate has a half value width of 300 arcsec or less in the X-ray rocking curve of the (10-12) plane of a C plane AlN single crystal.SELECTED DRAWING: Figure 3
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Description

[Technical Field]

[0001] This invention relates to a method for producing aluminum nitride single crystals and to aluminum nitride single crystals. [Background technology]

[0002] Ultraviolet light-emitting diodes (UV-LEDs) are next-generation light sources expected to be used in a wide range of applications, including germicidal light sources, high-brightness white light sources combined with phosphors, high-density information recording light sources, and resin curing light sources. These UV-LEDs are made from AlGaN-based nitride semiconductors.

[0003] Candidate substrate materials for AlGaN-based nitride semiconductors include SiC, GaN, and AlN (aluminum nitride) due to their high lattice matching with AlGaN. However, SiC and GaN absorb light with higher energy than 380 nm and 365 nm, respectively, limiting the wavelength range from which light can be extracted. On the other hand, AlN has a wider band gap than AlGaN and does not have the wavelength range limitations of SiC and GaN, making it the most suitable substrate material for ultraviolet light-emitting devices. However, AlN exhibits a high dissociation pressure at high temperatures and therefore does not become molten under normal pressure. For this reason, it is extremely difficult to produce AlN single crystals from its own molten state, as is the case with silicon single crystals.

[0004] Therefore, conventional methods have attempted to produce bulk AlN single crystals by sublimation (see, for example, Non-Patent Document 1). However, the sublimation method for producing AlN crystals requires high temperatures exceeding 2448K in the raw material stage, making it difficult to produce crystals of a size and cost suitable for practical use.

[0005] To solve this problem, the present inventors have developed a liquid phase growth method for AlN single crystals, which involves contacting a gas containing nitrogen with the surface of an Al-containing alloy solution to grow crystals on the surface of the molten metal (see, for example, Patent Document 1). This method does not use a template substrate, and therefore can prevent the occurrence of threading dislocations, misfit dislocations, and strains in the grown AlN crystal.

[0006] Furthermore, the present inventors have developed an AlN single crystal growth method to increase the growth rate of AlN single crystals, which includes a heating step in which a Ni-Al composite solution is heated to a temperature in which AlN becomes thermodynamically unstable while in contact with an AlN-containing sintered body such as a crucible that holds the melt, thereby dissolving a portion of the AlN sintered body into the melt, and a crystallization step in which AlN crystals are crystallized in the composite solution by lowering the temperature of the composite solution to a thermodynamically stable temperature after the heating step (see, for example, Patent Document 2).

[0007] Furthermore, the inventors have also developed an AlN single crystal growth method that allows for the continuous production of AlN single crystals without the need for heating and crystallization steps, by providing a temperature gradient in a Ni-Al composite liquid, holding an AlN sintered body in the high-temperature section, and crystallizing AlN crystals in the low-temperature section (see, for example, Non-Patent Document 2).

[0008] Furthermore, the first and second-order interaction coefficients of Al, N, and Cr in Fe melt and Fe-Cr compound liquid have been disclosed as functions of temperature (see, for example, Non-Patent Documents 3 and 4). In addition, the equilibrium constant for the reaction in which AlN is produced in Fe melt has also been disclosed as a function of temperature (see, for example, Non-Patent Documents 3 or 5). [Prior art documents] [Non-patent literature]

[0009] [Non-Patent Document 1] Carsten Hartmann et. al., “Preparation of Bulk AlN Seeds by Spontaneous Nucleation of Freestanding Crystals”, Jpn. J. Appl. Phys., 2013, 52, 08JA06 [Non-Patent Document 2] Rintaro Miyata, Makoto Otsuka, Masayoshi Adachi, Hiroyuki Fukuyama, “Growth of AlN on Sapphire Template Substrate Using Ni-Al Melts”, Transactions of the Japan Institute of Metals, 2022 Spring Meeting, The 170th Meeting Preprint Collection, [Searched on February 9, 2023], Internet <URL:https: / / confit.atlas.jp / guide / event / jim2022spring / subject / 2ISIJ107-12-03 / advanced> [Non-Patent Document 3] Wan-Yi KIM, et. al., “Thermodynamics of Aluminum, Nitrogen and AlN formation in Liquid Iron”, ISIJ International, 2007, Vol.47, No.7, p.945-954 [Non-Patent Document 4] Jong-Oh JO, et. al., “Thermodynamic Interaction between Chromium and Aluminum in Liquid Fe-Cr Alloys Containing 26 mass% Cr”, ISIJ International, 2011, Vol. 51, No.2, p.208-213 [Non-Patent Document 5] Mitsutaka Hino and Kimihisa Ito, “THERMODYNAMIC DATA FOR STEELMAKING”, Tohoku University Press, 2010 [Patent Document]

[0010] [Patent Document 1] Japanese Patent Publication No. 2019-194133 [Patent Document 2] Japanese Patent Publication No. 2022-37713 [Overview of the project] [Problems that the invention aims to solve]

[0011] The liquid-phase growth methods for aluminum nitride single crystals described in Patent Documents 1 and 2 can produce very high-quality aluminum nitride single crystals inexpensively, but the crystal growth rate is somewhat slow. Furthermore, aluminum nitride single crystals produced by methods such as HVPE or sublimation, which are available as seed crystals, are expensive and exhibit discoloration. When discoloration is observed with the naked eye, the transmittance to deep ultraviolet light tends to be low; for example, an amber-colored aluminum nitride single crystal has an absorption coefficient α of 50 cm² at a wavelength of 265 nm. -1 It was known that the degree was high. In ultraviolet light-emitting devices using such aluminum nitride single crystals, there is a risk of reducing the luminescence efficiency when light is emitted from the substrate side.

[0012] This invention was made in view of these problems, and aims to provide a simple way to manufacture thick aluminum nitride single crystals with a high crystal growth rate, and to easily peel them off from a sapphire substrate, thereby providing transparent aluminum nitride single crystals. [Means for solving the problem]

[0013] (1) A step of preparing a raw material melt by dissolving Al and N in a saturated aluminum nitride state in a composite liquid consisting of at least one element from Fe, Ni, and Co, and at least one element from Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf at a predetermined temperature. The process includes bringing an AlN template substrate, on which an AlN layer has been formed on the surface of a sapphire substrate, into contact with the molten raw material, and cooling at least the area around the AlN template substrate to a temperature lower than the predetermined temperature, thereby growing an aluminum nitride single crystal on the AlN layer side of the AlN template substrate. The AlN layer of the AlN template substrate has a full width at half maximum of 300 arcsec or less for the (10-12) plane X-ray rocking curve of the C-plane AlN single crystal. A method for manufacturing an aluminum nitride single crystal, wherein after growing the aluminum nitride single crystal, a void is formed between the sapphire substrate and the aluminum nitride single crystal.

[0014] (2) The method for producing an aluminum nitride single crystal according to (1), wherein the compounding solution is an Fe-Cr compounding solution or an Fe-Cr-Ni compounding solution.

[0015] (3) A method for producing an aluminum nitride single crystal according to (1) or (2), further comprising the step of peeling the aluminum nitride single crystal from the sapphire substrate after growing the aluminum nitride single crystal.

[0016] (4) A method for producing an aluminum nitride single crystal according to any one of (1) to (3), wherein a substance containing aluminum nitride is brought into contact with the compounding solution, and the raw material melt is prepared by holding it at the predetermined temperature for a predetermined time so that Al and N dissolve from the substance into the compounding solution and the aluminum nitride becomes saturated at the predetermined temperature, and then the AlN template substrate is brought into contact with the raw material melt.

[0017] (5) An aluminum nitride single crystal formed on an AlN template substrate having an AlN layer deposited on the surface of a sapphire substrate, The AlN layer of the AlN template substrate has a full width at half maximum of 300 arcsec or less for the (10-12) plane X-ray rocking curve of the C-plane AlN single crystal. A void is formed between the sapphire substrate and the aluminum nitride single crystal. At least one of the elements Fe, Ni, and Co, A single crystal of aluminum nitride containing at least one of the following elements as an impurity element: Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf.

[0018] (6) An aluminum nitride single crystal formed on an AlN template substrate having an AlN layer deposited on the surface of a sapphire substrate, The AlN layer of the AlN template substrate has a through-dislocation density of 1 × 10⁻¹⁶ as measured by a cross-sectional TEM image. 9 / cm 2 The following: A void is formed between the sapphire substrate and the aluminum nitride single crystal. At least one of the elements Fe, Ni, and Co, A single crystal of aluminum nitride containing at least one of the following elements as an impurity element: Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf. [Effects of the Invention]

[0019] According to the present invention, it is possible to manufacture thick aluminum nitride single crystals with a high crystal growth rate, and it is also possible to easily peel them off from a sapphire substrate and provide transparent aluminum nitride single crystals in a simple manner. [Brief explanation of the drawing]

[0020] [Figure 1A] This graph illustrates the method for producing aluminum nitride single crystals according to the present invention, and shows the relationship between the amount of Al dissolved and the amount of N dissolved in a Fe-16mass%Cr molten state at various temperatures. [Figure 1B] This is a schematic diagram illustrating states (1) and (2) in Figure 1A. [Figure 2] This is a front view showing one aspect of the overall configuration of an aluminum nitride single crystal growth apparatus applicable to the method for producing aluminum nitride single crystals according to the present invention. [Figure 3] This is a cross-sectional SEM image of the AlN template substrate after growing an aluminum nitride single crystal in Example 1. [Figure 4] This is a cross-sectional SEM image of the AlN template substrate after growing an aluminum nitride single crystal in Example 2. [Figure 5] This is a cross-sectional SEM image of the AlN template substrate after growing an aluminum nitride single crystal in Example 3. [Modes for carrying out the invention]

[0021] (Method for manufacturing aluminum nitride single crystals) The embodiments of the present invention will be described below based on drawings and examples. In a method for producing an aluminum nitride single crystal according to one embodiment of the present invention, an aluminum nitride (AlN) single crystal can be produced by following the steps of preparing a raw material melt and growing an aluminum nitride single crystal as follows.

[0022] <Process for preparing the raw material melt> Specifically, first, in a nitrogen-containing atmosphere, a compounding solution is prepared in a container such as a crucible, consisting of at least one element from Fe, Ni, and Co, and at least one element from Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf. The alloy raw materials may be added to the crucible and heated to form the compounding solution, or the metal raw materials may be added and heated to form the compounding solution within the crucible. The alloy constituting the compounding solution does not contain any other elements except for unavoidable impurities. Furthermore, before dissolving Al and before heating, the alloy does not contain Al except for unavoidable impurities. Note that Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf are elements that increase the solubility product of Al and N. It is particularly preferable to select at least one element from Cr and Nb as the element that increases the solubility product of Al and N. Then, in this compounding liquid, Al and N are dissolved in a saturated state of aluminum nitride (AlN) at a predetermined temperature to prepare the raw material melt.

[0023] The amounts of Al and N dissolved in a Fe-16mass%Cr compound solution will be specifically explained using this as a concrete example. Figures 1A and 1B are graphs and schematic diagrams showing the relationship between the amounts of Al and N dissolved in a Fe-16mass%Cr compound solution at various temperatures. The amounts of Al and N dissolved are points on the equilibrium concentration curve at a given temperature, as shown in Figure 1A. In the graph of Figure 1A and the schematic diagram of Figure 1B, (1) refers to the preparation process of the raw material melt, and (2) refers to the process of growing aluminum nitride single crystals. The compound solution preferably contains at least one element from Fe, Ni, and Co as its main component, with at least one of these elements present in an amount of 50% by mass or more.

[0024] Here, the predetermined temperature is any temperature at which Al and N dissolve at saturation solubility according to the curve shown in Figure 1A at a predetermined pressure of supplied nitrogen, so that the raw materials become molten. It is preferable that this temperature is above the melting point of the alloy constituting the composite solution used, but is also preferable that it is lower than the temperature of 2448K used in the sublimation method. By raising the temperature to the predetermined temperature as shown by the arrow to (1) in Figure 1A, Al and N dissolve in the composite solution to the saturation state of aluminum nitride. The pressure of the supplied nitrogen is arbitrary, but is preferably 0.1 to 1 bar, for example, it can be 1 bar.

[0025] Figures 1A and 1B described above will be explained in more detail. The reaction in which AlN is produced from Al and N dissolved in the raw material melt is shown by the following equation (1). Al + N → AlN(s) (1)

[0026] Furthermore, the equilibrium constant K for the reaction in equation (1) is given by equation (2) below, since the activity of AlN is considered to be 1.

number

[0027] Here, f Al and f N [mass%Al] and [mass%N] are the activity coefficients of Al and N based on 1 mass% (mass%) in at least one of the elements Fe, Ni, and Co, and [mass%Al] and [mass%N] are the mass percentage concentrations (amount dissolved) of Al and N in the raw material melt. If the raw material melt contains at least one of the elements Fe, Ni, and Co, Al, and N, as well as one or more elements X that increase the solubility product of Al and N, then f Al and f N These are represented by equations (3) and (4) below, respectively.

[0028]

number

[0029] Here, e i j is the first-order interaction coefficient of component j on component i, and r i j,k is the second-order interaction coefficient of component j and component k on component i. For example, when the raw material melt consists of Fe, Al, N, and Cr, and the element X is Cr, the interaction coefficients in equations (3) and (4) are shown in Non-Patent Document 3 and Non-Patent Document 4 as functions of temperature, and f Al and f N can be obtained using those values.

[0030] Also, the equilibrium constant K of equation (2) is shown in Non-Patent Document 3 and Non-Patent Document 5 as a function of temperature. Substituting the obtained f Al and f N into equation (2), the product (solubility product) of the dissolved amount of Al [mass%Al] and the dissolved amount of N [mass%N] at each temperature can be obtained. For example, FIG. 1A shows the relationship between the equilibrium concentrations of Al and N obtained from the solubility products of Al and N at various temperatures in an Fe-16mass%Cr alloy melt. As shown in FIG. 1A, it can be seen that the solubility product of Al and N decreases as the temperature of the raw material melt decreases.

[0031] In this embodiment, the composite financial solution is more preferably an Fe-Cr composite financial solution or an Fe-Cr-Ni composite financial solution. Commercially available stainless steel (such as SUS304 or SUS430) may be used as a raw material for the composite financial solution. In the case of an Fe-Cr composite financial solution, it is preferable that the solution contains 50% to 90% by mass of Fe and 10% to 50% by mass of Cr, and that the predetermined temperature is within the range of 1773K to 2073K. In the case of an Fe-Cr-Ni composite financial solution, it is preferable that the solution contains 50% to 90% by mass of Fe and 10% to 50% by mass of Cr and Ni combined, that the value of Cr content / (Cr content + Ni content) is greater than 0 and less than 1 on a mass basis, and that the predetermined temperature is within the range of 1673K to 2073K. It is preferable that the composite financial solution contains a large amount of elements that increase the AlN solubility product ([mass%Al][mass%N]). Therefore, it is preferable that the Cr content be between 16% by mass and 50% by mass, and more preferably between 18% by mass and 50% by mass.

[0032] The predetermined temperature is preferably 1773K to 1973K, and more preferably 1773K to 1873K, in both the case of Fe-Cr composite solution and Fe-Cr-Ni composite solution. Depending on the partial pressure of nitrogen, if the temperature of the composite solution is 1873K or lower at 1 bar of nitrogen, it is possible to prevent changes such as partial decomposition from occurring in the aluminum nitride of the AlN template substrate waiting on the composite solution. Furthermore, it is preferable to increase the temperature range (temperature range ΔT for crystal growth) during cooling while crystal growth occurs, from the predetermined temperature which is higher than the melting point of the composite solution for dissolving Al and N in the composite solution, to the temperature at which the composite solution begins to solidify (freezing point), because this allows for a longer crystal growth time. For example, it is preferable to have a temperature range ΔT for crystal growth of 50K or more, and more preferably 100K or more. To achieve this, depending on the predetermined temperature, for example, the melting point (freezing point) of the alloy constituting the composite liquid is preferably 1773K or lower, and more preferably 1723K or lower.

[0033] In a composite financial solution comprising at least one element from Fe, Ni, and Co, and at least one element from Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf, to increase the AlN solubility product while lowering the melting point of the alloy compared to the aforementioned Fe-Cr composite financial solution, it is preferable to use, for example, an Fe-Cr-Ni composite financial solution (a ternary composite financial solution of Fe, Cr, and Ni). Alternatively, Ni-Cr composite financial solutions or Co-Cr-Mo composite financial solutions may be selected as appropriate.

[0034] In this case, a method for preparing the raw material melt by dissolving Al and N in the compounding solution is to, for example, bring a substance such as a sintered body containing aluminum nitride into contact with the compounding solution placed in a container, and then hold it in that state at a predetermined temperature for a predetermined time. As a result, Al and N dissolve from the sintered body or other substance into the compounding solution, reaching a saturated state of AlN, and the raw material melt can be prepared. Note that the substance brought into contact with the compounding solution is not limited to a sintered body containing aluminum nitride, but can be any substance such as a crystal containing aluminum nitride, as long as Al and N dissolve in the compounding solution.

[0035] Another method for preparing the raw material melt is to supply Al to the alloying liquid from a crucible containing the alloying liquid, and an Al-containing sintered body can be used as the crucible. For example, it is preferable to use an aluminum nitride crucible or an alumina crucible. For example, the alloying liquid is placed in a crucible made of an aluminum nitride sintered body, and it is held at a predetermined temperature for a predetermined time. As a result, Al and N dissolve from the crucible into the alloying liquid, reaching a saturated state of AlN, and the raw material melt can be prepared. Alternatively, the alloying liquid may be placed in the crucible after preparation, or the alloying raw materials may be placed in the crucible and heated to create the alloying liquid within the crucible. Furthermore, the crucible may be made of an Al-containing sintered body, and as described above, an Al nitride-containing sintered body or crystal fragments may be placed in the crucible as raw materials for aluminum nitride single crystals. Furthermore, when using a crucible that does not contain nitrogen, such as an alumina crucible, it is preferable to either include a sintered body or crystal fragments containing aluminum nitride as a raw material for aluminum nitride single crystals, or to supply nitrogen separately from an atmospheric gas or the like.

[0036] The state in which Al and N in the compounding solution reach the saturation solubility of AlN at a predetermined temperature is called the raw material melt. After preparing the raw material melt, a seed crystal is brought into contact with the raw material melt in a nitrogen-containing atmosphere and cooled to a temperature lower than the predetermined temperature, at least around the seed crystal. As a method of lowering the temperature at least around the seed crystal to a temperature lower than the predetermined temperature, the seed crystal may be cooled by controlling the temperature of the member supporting the seed crystal, or a part or all of the raw material melt may be cooled to a temperature lower than the predetermined temperature by controlling the temperature of a heater, or a combination of these cooling methods may be used. As a result, the temperature of the raw material melt near the seed crystal, or the temperature of the raw material melt as a whole, decreases, and the solubility product of Al and N in the cooled range of the raw material melt decreases, for example, as shown by the (2) arrow in the graph in Figure 1A. Due to the difference caused by this decrease in solubility product, the Al and N that were dissolved in the raw material melt in a saturated state of AlN become supersaturated, and an aluminum nitride single crystal can be deposited on the surface of the seed crystal. In this way, an aluminum nitride single crystal can be grown by the deposition of the aluminum nitride single crystal.

[0037] The cooling rate after contacting the seed crystal with the molten raw material is arbitrary and can be adjusted, for example, within the range of 0.1 K / min to 10 K / min. The thickness and flatness of the resulting crystal can be adjusted by the predetermined temperature, the temperature range ΔT for crystal growth, and the cooling rate.

[0038] <Process for growing aluminum nitride single crystals> The method for producing an aluminum nitride single crystal according to an embodiment of the present invention involves continuously growing an aluminum nitride single crystal by maintaining a seed crystal at a temperature lower than a predetermined temperature of the raw material melt, or by continuously cooling the entire raw material melt so that a state of supersaturation of Al and N persists. The seed crystal used in this growth process is an AlN template substrate. As is generally known, an AlN template substrate is a sapphire substrate on which an AlN layer has been deposited. In this specification, the AlN layer of the single crystal on the AlN template substrate is simply referred to as the AlN layer. In the present invention, by growing an aluminum nitride single crystal on the AlN template substrate (on the AlN layer of the AlN template substrate), a void is formed between the sapphire substrate and the aluminum nitride single crystal after the aluminum nitride single crystal has been grown. In the present invention, the precipitation of the aluminum nitride single crystal is promoted by making the cooled range of the raw material melt supersaturated with Al and N. Therefore, compared to cases where crystal growth is carried out only on the surface of the melt, or where a temperature gradient is provided in a compounding solution containing Al, the present invention allows for the growth of aluminum nitride single crystals at a much higher growth rate. Furthermore, at the interface between the sapphire substrate, where oxygen diffusion from sapphire (Al2O3) occurs, and the aluminum nitride single crystal, components of the compounding solution are included as impurities and diffuse. Moreover, as the aluminum nitride single crystal thickens, stress concentrates at this interface. These phenomena are thought to cause delamination at the interface between the AlN layer of the AlN template substrate and the sapphire substrate, creating a void at that interface. This delamination is thought to occur during the cooling process after the growth of the aluminum nitride single crystal. The average thickness of the aluminum nitride single crystal to be grown is preferably 30 μm or more, and more preferably 80 μm or more.

[0039] The AlN template substrate used in this invention is an AlN template substrate in which a C-plane AlN layer is epitaxially grown on a C-plane sapphire substrate, and the full width at half maximum of the X-ray rocking curve of the (10-12) plane of the AlN layer is 300 arcsec or less. Furthermore, the thickness of the AlN layer on the sapphire substrate is more preferably 0.3 μm or more and 1.2 μm or less, and the full width at half maximum of the X-ray rocking curve of the (0002) plane of the AlN layer is more preferably 150 arcsec or less. The X-ray rocking curve is measured by ω scanning with an X-ray diffractometer (e.g., D8 DISCOVER AUTOWAFS; manufactured by Bruker AXS). The detector side of the X-ray diffractometer is an open slit, and the aperture width of the detector is 0.5°.

[0040] Furthermore, the AlN template substrate used in this invention has a through-dislocation density of 1 × 10⁻¹⁶ as determined by cross-sectional TEM imaging. 9 / cm 2 The following is preferable: 2 × 10 8 / cm 2 The following is more preferable: The penetration dislocation density can be determined by measuring the number of scotomas in the cross-sectional TEM image and calculating the density of scotomas per unit area.

[0041] By using an AlN template substrate in which the full width at half maximum (FWHM) of the X-ray rocking curve of the (10-12) plane of the AlN layer grown on a sapphire substrate is 300 arcsec or less, the crystal quality of the AlN single crystal produced by the manufacturing method of the present invention can be improved. By using such an AlN template substrate, the FWHM of the X-ray rocking curve of the (10-12) plane of the aluminum nitride single crystal formed on the AlN template substrate can be made 450 arcsec or less. Furthermore, when the AlN template substrate is immersed in the raw material melt to grow an AlN single crystal in the liquid phase, the decomposition and disappearance of the AlN layer on the surface of the AlN template substrate due to etching can be suppressed. However, if the AlN layer in contact with the raw material melt is polycrystalline, or even if it is a single crystal, if the FWHM of the X-ray rocking curve of the (10-12) plane is greater than 300 arcsec, the AlN layer is prone to decomposition, and the AlN layer may disappear when immersed in the raw material melt.

[0042] Furthermore, the penetration dislocation density obtained from the cross-sectional TEM image was 1 × 10⁻⁶ 9 / cm 2 By using the following AlN template substrate, it is possible to prevent the occurrence of threading dislocations, misfit dislocations, and strains in the grown AlN crystal.

[0043] The sapphire substrate used for the AlN template substrate is preferably a surface with a chamfered edge that is inclined at an off-angle of 0.05° to 0.55°.

[0044] An AlN template substrate in which a C-plane AlN layer is epitaxially grown on a C-plane sapphire substrate and the full width at half maximum of the X-ray rocking curve of the (10-12) plane of the AlN layer is 300 arcsec or less can be obtained by subjecting the AlN template substrate grown by MOCVD to a dislocation reduction treatment by annealing in a nitrogen atmosphere at 1823K or higher (e.g., 1873K). Along with the dislocation reduction treatment, the amount of oxygen diffusion from sapphire (Al2O3) to the AlN layer may be increased, and a region of high oxygen concentration or an AlON layer may be present at the interface.

[0045] Furthermore, as a method for growing the AlN layer, it is preferable to use the MOCVD method, which uses trimethylaluminum (TMA) and ammonia as raw material gases.

[0046] In AlN template substrates, the AlN layer formed using the MOCVD method is transparent to the naked eye. Its transmittance in the deep ultraviolet region is also higher than that of seed crystals colored amber or similar by other methods; for example, its absorption coefficient α at a wavelength of 265 nm is 30 cm⁻¹. -1 The following is low. Furthermore, by using such an AlN template substrate as a seed crystal, the aluminum nitride single crystal formed on the AlN template substrate is also likely to be transparent.

[0047] Furthermore, the present invention may further include a step of peeling the aluminum nitride single crystal from the sapphire substrate after growing the aluminum nitride single crystal. According to the present invention, since there is a void between the sapphire substrate and the aluminum nitride single crystal, the peeling process is easier compared to the case where there is no void. In addition to a method of mechanically peeling using the void, there is a method of expanding the void and allowing natural peeling by adjusting the cooling rate during cooling to room temperature after separating the crystal from the bonding solution after crystal growth. By these methods, it is also possible to obtain a transparent, self-supporting aluminum nitride single crystal.

[0048] (Aluminum nitride single crystal) According to the present invention, an aluminum nitride single crystal formed on an AlN template substrate having an AlN layer deposited on the surface of a sapphire substrate has a void formed between the sapphire substrate and the aluminum nitride single crystal. This aluminum nitride single crystal contains at least one element from Fe, Ni, and Co, and at least one element from Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf as impurity elements. The thicker the aluminum nitride single crystal formed at this time, the easier it is for a void to form between the sapphire substrate and the aluminum nitride single crystal. Therefore, it is preferable that the thickness of the aluminum nitride single crystal observed as a flat plate-like portion in a cross-sectional SEM image is 27 μm or more.

[0049] Furthermore, since the crystal quality of AlN single crystals produced by the manufacturing method of the present invention can be further improved, it is preferable that the AlN layer of the AlN template substrate has a full width at half maximum of 300 arcsec or less of the X-ray rocking curve of the (10-12) plane of the C-plane AlN single crystal, and the penetration dislocation density as determined by the cross-sectional TEM image is 1 × 10 9 / cm 2 The following is preferable:

[0050] The impurity elements listed above are components of the compounding solution that are present as impurities. The amount of these impurities can be measured by SIMS analysis, which is 1 × 10⁻⁶. 15 atoms / cm 3 The above 1 x 10 19 atoms / cm 3 The following is preferable: 8 × 10 16 atoms / cm 3 It is more preferable that the above conditions are met.

[0051] In this invention, the aluminum nitride single crystal formed on the AlN template substrate is transparent to the naked eye. Its transmittance in the deep ultraviolet region is also high; for example, the absorption coefficient α at a wavelength of 265 nm is 30 cm⁻¹. -1 It is preferable that the carbon concentration of the aluminum nitride single crystal is 4 × 10 17It is preferable that the amount is less than or equal to 2 × 10 atoms / cm. 17 atoms / cm 3 The following is even more preferable: a low carbon concentration increases the likelihood of obtaining a high transmittance because it reduces the absorption coefficient in the ultraviolet region.

[0052] The following describes an embodiment of the present invention regarding a method for producing aluminum nitride single crystals and an apparatus applicable to the production of aluminum nitride single crystals.

[0053] [Manufacturing apparatus and method for aluminum nitride single crystals] In the embodiment described later, an experiment to manufacture aluminum nitride single crystals will be conducted using the apparatus shown in Figure 2. As shown in Figure 2, the apparatus for manufacturing aluminum nitride single crystals includes a reaction vessel 1, a heater 2, an insulating material 3, a gas supply pipe 4, a gas exhaust pipe 5, and a seed crystal holder 6. The heater 2 is installed inside the reaction vessel 1 so as to house a crucible 7 inside and cover the sides of the crucible 7 housed inside. The heater 2 is capable of heating the crucible 7 housed inside. The insulating material 3 is installed inside the reaction vessel 1 so as to surround the sides of the heater 2 and the crucible 7 and cover the bottom of the heater 2. The gas supply pipe 4 is installed through the ceiling of the reaction vessel 1 so as to be able to supply atmospheric gas to the inside of the reaction vessel 1. The gas exhaust pipe 5 is installed through the floor of the reaction vessel 1 so as to be able to discharge gas from inside the reaction vessel 1. The seed crystal holder 6 is installed so as to be able to slide vertically through the ceiling of the reaction vessel 1. The seed crystal holder 6 slides vertically, allowing its lower end to move back and forth between the inside and outside of the crucible 7, which is housed inside the heater 2.

[0054] First, the compounding solution 8 and the AlN sintered body 9 are placed inside the crucible 7, and the seed crystal 10 is attached to the lower end of the seed crystal holder 6 or nearby. If the crucible 7 is made of AlN sintered body, the AlN sintered body 9 does not need to be placed. At this time, the seed crystal holder 6 is held in a position where the seed crystal 10 does not come into contact with the compounding solution 8. In this state, the gas inside the reaction vessel 1 is discharged from the gas exhaust pipe 5, and the inside of the reaction vessel 1 is evacuated. After evacuating, atmospheric gas is supplied from the gas supply pipe 4, and the reaction vessel 1 is filled with atmospheric gas.

[0055] Subsequently, the heater 2 is energized to heat the compounding solution 8 to a predetermined temperature, dissolving Al and N from the AlN sintered body 9 into the compounding solution 8. The compounding solution 8 is held at a predetermined temperature for a predetermined time until the amount of dissolved Al and N reaches the saturation point and equilibrium is reached, thereby preparing the raw material melt. After that, aluminum nitride single crystals can be manufactured by employing the following two cooling methods.

[0056] <Local cooling method> While maintaining a constant temperature of the prepared raw material melt, the seed crystal holder 6, which is set to a temperature lower than that of the raw material melt, is slid downward to bring the seed crystal 10 into contact with the surface of the raw material melt. The seed crystal 10 is then held in this state, and an aluminum nitride single crystal is grown on the surface of the seed crystal 10.

[0057] <Uniform cooling method> After preparing the raw material melt, the seed crystal holder 6 is slid downward to bring the seed crystal 10 into contact with the surface of the raw material melt. With the seed crystal 10 still in place, the raw material melt is cooled at a predetermined rate by temperature control using the heater 2, and an aluminum nitride single crystal is grown on the surface of the seed crystal 10.

[0058] In any of the above methods, after the growth of the aluminum nitride single crystal, the seed crystal holder 6 is slid upward to separate the seed crystal 10 and the grown aluminum nitride single crystal from the molten raw material. After cooling the reaction vessel 1, the grown aluminum nitride single crystal is recovered together with the seed crystal 10.

[0059] The above apparatus and methods are illustrative examples. Local cooling and uniform cooling methods may be combined, and various modifications can be made, such as changing the manufacturing equipment for temperature control necessary for single crystal growth, or adding equipment that allows for the recovery of the grown aluminum nitride single crystals and the renewal of raw materials and seed crystals. [Examples]

[0060] (Example 1) First, an AlN template substrate was fabricated. Specifically, an AlN layer was formed on a 2-inch diameter, 430 μm thick C-plane sapphire substrate (off-angle 0.11° in the M-plane direction) using the MOCVD method with trimethylaluminum (TMA) and ammonia as source gases. The growth temperature was 1613 K and the growth pressure was 13.3 mbar. The AlN layer grown on the C-plane sapphire substrate was a C-plane AlN single crystal with a thickness of 0.5 μm. Furthermore, after growing the AlN single crystal using the MOCVD method, a dislocation reduction treatment was performed by annealing in a nitrogen atmosphere at 1873 K for 4 hours. The full width at half maximum (FWHM) of the X-ray rocking curve of the (10-12) plane of the C-plane AlN layer on the surface of the fabricated AlN template substrate was measured and found to be 265 arcsec. Similarly, the FWHM of the X-ray rocking curve of the (0002) plane of the C-plane AlN layer was measured and found to be 49 arcsec. Furthermore, the penetration dislocation density measured using cross-sectional TEM images was 2 × 10⁻⁶ 8 / cm 2 That was the case.

[0061] Refer again to the apparatus shown in Figure 2. An aluminum nitride sintered body was used as the crucible 7, and Fe-18mass%Cr-8mass%Ni (SUS304L (low carbon)) was used as the compounding solution 8. In addition, 1 bar of N2 gas (nitrogen gas) was used as the atmospheric gas. Furthermore, an AlN template substrate prepared as described above was used as the seed crystal 10. Note that, unlike in Figure 2, the AlN sintered body 9 was not placed into the crucible 7 because an aluminum nitride sintered body was used as the crucible 7. In the experiment, heater 2 was used to heat the material from room temperature to 1873K over 160 minutes. The material was then held at 1873K for 4 hours to prepare a raw material melt in which Al and N dissolved in a saturated AlN state.

[0062] After preparing the raw material melt, the seed crystal holder 6 was slid into contact with the AlN template substrate. The heating temperature of the heater 2 was then adjusted to lower the temperature of the raw material melt to 1723K over 1.25 hours at a cooling rate of 2K / min, allowing an aluminum nitride single crystal to grow on the AlN layer on the surface of the AlN template substrate. After that, the seed crystal holder 6 was slid upward to separate the AlN template substrate from the melt, and the temperature was lowered to room temperature at a cooling rate of 10K / min. During the experiment, the inside of the reaction vessel 1 was replaced with N2 gas, and N2 gas was continuously supplied into the reaction vessel 1 at a flow rate of 0.1 L / min until the inside of the reaction vessel 1 cooled back to room temperature, while the pressure inside the reaction vessel 1 was maintained at atmospheric pressure.

[0063] Figure 3 shows a cross-sectional SEM image of the AlN template substrate after the deposition of aluminum nitride single crystals. From Figure 3, it was confirmed that there were AlN single crystals with a thickness of 41-43 μm on the sapphire. Note that the thickness of 43 μm shown in Figure 3 is the value at the location with the greatest thickness. The thickness of the grown AlN single crystal was relatively uniform. Since the film thickness of the AlN layer on the AlN template substrate before growth was 0.5 μm, it was found that the aluminum nitride single crystal grew to 40.5-42.5 μm in 1.25 hours in this example.

[0064] Figure 3 shows a gap, indicated by a black line, at the interface between the sapphire substrate (bottom of Figure 3) and the aluminum nitride single crystal (top of Figure 3). Except for a portion enclosed by a dashed line, the aluminum nitride single crystal has delaminated from the sapphire substrate. In other words, a void exists between the sapphire substrate and the aluminum nitride single crystal. This suggests that the delamination is occurring at the interface between the AlN layer of the AlN template substrate and the sapphire substrate. It is also expected that if the aluminum nitride single crystal is grown to a greater thickness, the void observed in Figure 3 will expand, causing the aluminum nitride single crystal to delaminate from the sapphire substrate.

[0065] Furthermore, the AlN layer on the AlN template substrate was observed to be transparent with the naked eye. The aluminum nitride single crystal in this embodiment 1 had high transmittance.

[0066] Furthermore, SIMS analysis revealed that the aluminum nitride single crystal contains 1 × 10⁻⁶ Fe and Cr. 17 atoms / cm 3 The above elements were found to be present, and it was also confirmed that Ni was present. Note that the AlN layer in the AlN template substrate before crystal growth did not contain these metal elements, and the carbon concentration was 4 × 10⁻⁶. 17 atoms / cm 3 That is the case.

[0067] (Example 2) In Example 2, the material was heated from room temperature to 1833K over 160 minutes using heater 2. The material was held at 1833K for 4 hours to prepare a raw material melt in which Al and N dissolved in a saturated state of AlN. After preparing the raw material melt, the seed crystal holder 6 was slid to bring the AlN template substrate into contact with the raw material melt. Then, the heating temperature of heater 2 was adjusted to lower the temperature of the raw material melt to 1783K over 0.83 hours (50 minutes) at a cooling rate of 1K / min. The aluminum nitride single crystal of Example 2 was grown under the same conditions as in Example 1.

[0068] (Example 3) In Example 3, the material was heated from room temperature to 1873K over 160 minutes using heater 2. The material was held at 1873K for 4 hours to prepare a raw material melt in which Al and N dissolved in a saturated state of AlN. After preparing the raw material melt, the seed crystal holder 6 was slid to bring the AlN template substrate into contact with the raw material melt. Then, the heating temperature of heater 2 was adjusted to lower the temperature of the raw material melt to 1823K over 0.83 hours (50 minutes) at a cooling rate of 1K / min. The aluminum nitride single crystal of Example 3 was grown under the same conditions as in Example 1.

[0069] Figures 4 and 5 show cross-sectional SEM images of the AlN template substrates after the deposition of aluminum nitride single crystals in Example 2 and Example 3, respectively. From Figures 4 and 5, it was confirmed that in Example 2, an AlN single crystal with a thickness of 27 μm was present on the sapphire, and in Example 3, an AlN single crystal with a thickness of 32 μm was present. The crystal growth rate, which is the value obtained by dividing the thickness of the grown AlN single crystal by the time taken to cool, was 32 μm / hour and 38 μm / hour, respectively. In both cases, a gap observed as a black area was confirmed at the interface between the sapphire substrate (bottom of the figure) and the aluminum nitride single crystal (top of the figure), indicating that at least a portion of the aluminum nitride single crystal had peeled off from the sapphire substrate. In other words, it was found that there was a void between the sapphire substrate and the aluminum nitride single crystal. Furthermore, it was possible to peel off a portion of the aluminum nitride single crystal from the sapphire substrate using tweezers.

[0070] Furthermore, when the full width at half maximum (FWHM) of the X-ray rocking curve of the (10-12) plane was examined for the obtained aluminum nitride single crystals, Example 2 showed 331 arcsec and Example 3 showed 418 arcsec, indicating that crystals with a FWHM of 450 arcsec or less were obtained. It was confirmed that the obtained aluminum nitride single crystals inherited the high-quality crystallinity of the (10-12) plane of the AlN layer of the AlN template substrate.

[0071] (Comparative Example 1) As the seed crystal 10, a substrate of aluminum nitride single crystal (thickness 455 μm) was used, which was molded to be thin along the c-axis direction and had two c-planes. The experiment was conducted by attaching the seed crystal 10 c-plane to the lower end surface of the seed crystal holder 6 with the aluminum polar surface of the c-plane in contact with the raw material melt, except that the experiment was carried out in the same manner as in Example 1.

[0072] In cross-sectional observation, no voids were observed at the expected interface between the seed crystal and the aluminum nitride single crystal grown on it.

[0073] Furthermore, the seed crystal was observed to be amber-colored with the naked eye. The aluminum nitride single crystal that precipitated after the seed crystal was also a light amber color.

[0074] (Comparative Example 2) In this example, Fe-16mass%Cr(SUS430) was used as the compounding solution 8, instead of the compounding solution used in Example 1. Furthermore, as the seed crystal 10, a substrate (455 μm thick) of aluminum nitride single crystal, molded thinly along the c-axis so that two of its surfaces were c-planes, was used, similar to Comparative Example 1. The seed crystal 10 was then attached to the lower end surface of the seed crystal holder 6 with its c-plane facing the aluminum polar surface, so that the aluminum polar surface of the c-plane was in contact with the raw material molten liquid. Also, similar to Example 1, an aluminum nitride sintered body was used as the crucible 7, and N2 gas (nitrogen gas) was used as the atmospheric gas. In the experiment, the compounding solution 8 was heated to 1773K using heater 2 and held for 2 hours, then heated to 1967K over 9 hours. It was held at 1967K for 4 hours to prepare a raw material melt in which Al and N were dissolved in a saturated state of AlN.

[0075] After preparing the raw material melt, the seed crystal holder 6 was slid to bring the seed crystal 10 into contact with the raw material melt. The seed crystal holder 6 was then cooled to maintain the seed crystal 10 at a temperature lower than the predetermined temperature, and this state was maintained for a further 4 hours to grow an aluminum nitride single crystal on the surface of the seed crystal 10. After that, the seed crystal holder 6 was slid upward to separate it from the melt, and then the temperature was lowered to room temperature. During the experiment, the inside of the reaction vessel 1 was replaced with N2 gas, and N2 gas was continuously supplied into the reaction vessel 1 at a flow rate of 0.1 L / min until the inside of the reaction vessel 1 cooled back to room temperature, while the pressure inside the reaction vessel 1 was maintained at atmospheric pressure.

[0076] The thickness of the aluminum nitride single crystals after precipitation ranged from 522 μm to 667 μm, showing variation depending on the location. It was found that the aluminum nitride single crystal film grew by 67 μm to 212 μm in 4 hours.

[0077] In cross-sectional observation, no voids were observed at the expected interface between the seed crystal and the aluminum nitride single crystal grown on it.

[0078] The seed crystal, upon visual observation, appeared amber in color. The aluminum nitride single crystal that precipitated after the seed crystal was also a light amber color.

[0079] Furthermore, SIMS analysis revealed that the aluminum nitride single crystals in the precipitated region contained Fe at a concentration of 7 × 10⁻⁶. 17 atoms / cm 3 and Cr is 3 × 10 17 atoms / cm 3 It was confirmed that it was present. Furthermore, in the aluminum nitride single crystal seed crystal, Fe and Cr were below the detection limit. The carbon concentration of the seed crystal was 4 × 10⁻⁶. 19 atoms / cm 3 The carbon concentration of the precipitated aluminum nitride single crystal is 6 × 10 17 atoms / cm 3 That was the case.

[0080] (Comparative Example 3) As the compounding solution 8, a Ni-20mol%Al alloy was used, and the Ni-20mol%Al alloy was placed in a crucible 7 made of an aluminum nitride sintered body. After evacuating the inside of the reaction vessel, the inside of the reaction vessel was replaced with N2 by supplying N2 gas from a gas supply pipe, creating an N2 gas atmosphere in the reaction vessel at 1 bar. As the seed crystal 10, an AlN template substrate similar to that in Example 1 was used, and this template substrate was placed on the side of a seed crystal holder 6 with a double-tube structure equipped with a cooling mechanism. Next, with the seed crystal holder, which consists of a double tube holding the AlN template substrate, held so as not to come into contact with the raw material melt, the raw material melt was heated by energizing a heater 2 consisting of a high-frequency coil to heat the susceptor, until the temperature of the interface between the crucible 7 and the raw material melt reached 1852K. Then, Ar gas was introduced into the inner tube of the seed crystal holder at a flow rate of 10 L / min as a cooling gas to cool it, while the seed crystal holder 6 was immersed in the raw material melt. This was done for 7 hours, maintaining the temperature of the high-temperature part of the melt while keeping the area around the holder in the melt at a lower temperature, and allowing aluminum nitride single crystals to precipitate on the AlN template substrate. After that, the holder was removed from the raw material melt and cooled to room temperature.

[0081] In Comparative Example 3, the aluminum nitride single crystal grew only 3.7 μm in 7 hours, which was a slower crystal growth rate compared to Example 1. Furthermore, no voids were observed at the interface between the sapphire substrate and the aluminum nitride single crystal grown on it.

[0082] From the above results, it can be seen that, according to this embodiment, by applying the manufacturing method according to the present invention, a thick aluminum nitride single crystal with a thickness of 30 μm or more can be manufactured in a short time, and a transparent aluminum nitride single crystal having a void at the interface with the sapphire substrate can be easily provided. [Industrial applicability]

[0083] According to the present invention, it is possible to manufacture thick aluminum nitride single crystals with a high crystal growth rate, and it is also possible to easily peel them off from a sapphire substrate and provide transparent aluminum nitride single crystals in a simple manner. [Explanation of symbols]

[0084] 1. Reaction vessel 2 Heater 3. Insulation 4. Gas supply pipe 5. Gas exhaust pipe 6 types of crystal holders 7 Crucible 8 Joint financial liquid 9 AlN sintered body 10 seed crystals

Claims

1. A step of preparing a raw material melt by dissolving Al and N in a saturated aluminum nitride state in a composite liquid consisting of at least one element from Fe, Ni, and Co, and at least one element from Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf at a predetermined temperature. The process includes bringing an AlN template substrate, on which an AlN layer has been formed on the surface of a sapphire substrate, into contact with the molten raw material, and cooling at least the area around the AlN template substrate to a temperature lower than the predetermined temperature, thereby growing an aluminum nitride single crystal on the AlN layer side of the AlN template substrate. The AlN layer of the AlN template substrate has a full width at half maximum of 300 arcsec or less of the X-ray rocking curve of the (10-12) plane of the C-plane AlN single crystal. A method for manufacturing an aluminum nitride single crystal, wherein after growing the aluminum nitride single crystal, a void is formed between the sapphire substrate and the aluminum nitride single crystal.

2. The method for producing an aluminum nitride single crystal according to claim 1, wherein the composite financial solution is an Fe-Cr composite financial solution or an Fe-Cr-Ni composite financial solution.

3. A method for producing an aluminum nitride single crystal according to claim 1, further comprising the step of peeling the aluminum nitride single crystal from the sapphire substrate after growing the aluminum nitride single crystal.

4. A method for producing an aluminum nitride single crystal according to claim 1, comprising: preparing the raw material melt by contacting a substance containing aluminum nitride with the compounding liquid and holding it at the predetermined temperature for a predetermined time so that Al and N dissolve from the substance into the compounding liquid and the aluminum nitride becomes saturated at the predetermined temperature; and then contacting the AlN template substrate with the raw material melt.

5. An aluminum nitride single crystal formed on an AlN template substrate having an AlN layer deposited on the surface of a sapphire substrate, The AlN layer of the AlN template substrate has a full width at half maximum of 300 arcsec or less of the X-ray rocking curve of the (10-12) plane of the C-plane AlN single crystal. A void is formed between the sapphire substrate and the aluminum nitride single crystal. At least one of the elements Fe, Ni, and Co, It contains at least one of the following elements as an impurity element: Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf. An aluminum nitride single crystal in which the amount of the aforementioned impurity element is between 1 × 10¹⁵ atoms / cm³ and 1 × 10¹⁹ atoms / cm³.

6. An aluminum nitride single crystal formed on an AlN template substrate having an AlN layer deposited on the surface of a sapphire substrate, The AlN layer of the AlN template substrate has a through-dislocation density of 1 × 10⁻¹⁶ as determined by a cross-sectional TEM image. 9 / cm 2 The following: A void is formed between the sapphire substrate and the aluminum nitride single crystal. At least one of the elements Fe, Ni, and Co, It contains at least one of the following elements as an impurity element: Mn, Cr, V, Ti, Te, Mo, Nb, Zr, Re, W, Ta, and Hf. An aluminum nitride single crystal in which the amount of the aforementioned impurity element is between 1 × 10¹⁵ atoms / cm³ and 1 × 10¹⁹ atoms / cm³.

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