Method for manufacturing gallium arsenide single crystal, method for manufacturing gallium arsenide single crystal substrate, gallium arsenide single crystal substrate, and gallium arsenide single crystal

Abstract

This method for producing a gallium arsenide monocrystal comprises a step for growing a gallium arsenide monocrystal from a seed crystal by using a gallium arsenide monocrystal production device. A growth-side surface of the seed crystal has an off angle of 4-20° from the (100) plane of the gallium arsenide monocrystal. The gallium arsenide monocrystal production device comprises: a crucible having a portion that is cylindrical; a crucible holding base for holding the crucible; and a heating element for heating the crucible. The crucible includes a seed crystal accommodation part, a diameter-increase part connected to the seed crystal accommodation part, and a straight body part connected to the diameter-increase part on the side opposite to the seed crystal accommodation part side. The diameter-increase part has a truncated cone shape in which the diameter is larger upward in the axial direction, and is connected to the seed crystal accommodation part on the small diameter side of the diameter-increase part. The straight body part has a hollow cylindrical shape and is connected to the large diameter side of the diameter-increase part. The crucible holding base holds the diameter-increase part. The diameter-increase part comprises an upper region and a lower region. The upper region is separated from the crucible holding base, and the lower region is in contact with the crucible holding base.

Description

[Technical Field]

[0001] The present disclosure relates to a method for producing a gallium arsenide single crystal, a method for producing a gallium arsenide single crystal substrate, a gallium arsenide single crystal substrate, and a gallium arsenide single crystal. [Background technology]

[0002] International Publication No. 2006 / 106644 (Patent Document 1) discloses a silicon (Si)-doped gallium arsenide single crystal ingot (hereinafter also referred to as a "GaAs single crystal ingot") that is applied to a gallium arsenide single crystal substrate (hereinafter also referred to as a "GaAs single crystal substrate"). The GaAs single crystal ingot has an average dislocation density of 50 cm -2 When the carrier concentration in the portion with a solidification rate of 0.1 is C0.1 and the carrier concentration in the portion with a solidification rate of 0.8 is C0.8, the relationship C0.8 / C0.1<2.0 is satisfied. Furthermore, Patent Document 1 discloses that the carrier concentration of the GaAs single crystal ingot is 1.0×10 17 cm -3 Over 1.0 x 10 19 cm -3 International Publication No. 2021 / 251349 (Patent Document 2) discloses that the average dislocation density is 500 cm -2 The atomic concentration of Si is 2.0×10 or less. 17 cm -3 Over 1.5 x 10 19 cm -3 and the carrier concentration is 5.5×10 17 cm -3 The following GaAs single crystal ingot is disclosed:

[0003] Japanese Patent Laid-Open No. 2011-148693 (Patent Document 3) and Japanese Patent Laid-Open No. 2011-148694 (Patent Document 4) both disclose Si-doped n-type GaAs single crystal substrates. The GaAs single crystal substrates each have an average dislocation density of 40 to 100 cm -2 and 15-30 cm -2 and the atomic concentration of Si is 5.0×10 16 cm-3 Over 5.0 x 10 17 cm -3 and 5.0×10 16 cm -3 Over 5.0 x 10 17 cm -3 JP 2011-527280 A (Patent Document 5) and Sasanabe et al., "Low Dislocation Density GaAs Wafers Using the VGF Method Suitable for Mass Production of Semiconductor Lasers," Hitachi Cable, No. 20, August 2001, pp. 33-36 (Non-Patent Document 1) disclose a measurement method in which a mass having a predetermined size is formed on a main surface and dislocations present in the mass are counted to determine the dislocation density. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2006 / 106644 [Patent Document 2] International Publication No. 2021 / 251349 [Patent Document 3] Japanese Patent Application Laid-Open No. 2011-148693 [Patent Document 4] Japanese Patent Application Laid-Open No. 2011-148694 [Patent Document 5] Special Publication No. 2011-527280 [Non-patent literature]

[0005] [Non-Patent Document 1] Sasane et al., "Low Dislocation Density GaAs Wafers by the VGF Method Suitable for Mass Production of Semiconductor Lasers," Hitachi Cable, No. 20, August 2001, pp. 33-36 Summary of the Invention

[0006] A method for producing a gallium arsenide single crystal according to the present disclosure is a method for producing a cylindrical gallium arsenide single crystal. The method includes growing a gallium arsenide single crystal from a seed crystal using a gallium arsenide single crystal production apparatus. The growth-side surface of the seed crystal is a plane having an off-angle of 4° or more and 20° or less from the (100) plane of the gallium arsenide single crystal. The gallium arsenide single crystal production apparatus includes a partially cylindrical crucible, a crucible holder for holding the crucible, and a heating element for heating the crucible. The crucible includes a seed crystal housing portion, an increasing diameter portion connected to the seed crystal housing portion, and a straight body portion connected to the increasing diameter portion on the side opposite the seed crystal housing portion. The seed crystal housing portion has a cylindrical cavity that opens to the side connected to the increasing diameter portion and has a bottom wall formed on the opposite side. The increasing diameter section has a truncated cone shape that expands axially upward and is connected to the seed crystal accommodation section at the smaller diameter side of the increasing diameter section. The straight body section has a hollow cylindrical shape and is connected to the larger diameter side of the increasing diameter section. The crucible holder holds the increasing diameter section. The increasing diameter section consists of an upper region and a lower region. The upper region is spaced apart from the crucible holder and the lower region is in contact with the crucible holder. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 is a flowchart shown as an example of a method for producing a gallium arsenide single crystal and a method for producing a gallium arsenide single crystal substrate according to this embodiment. [Figure 2] FIG. 2 is a vertical cross-sectional view illustrating a gallium arsenide single crystal manufacturing apparatus used in the step of growing a gallium arsenide single crystal in the manufacturing method of the gallium arsenide single crystal according to this embodiment. [Figure 3] FIG. 3 is an enlarged view of a main part of FIG. [Figure 4] FIG. 4 is a plan view illustrating a main surface of a gallium arsenide single crystal substrate according to this embodiment and a measurement point (measurement region) for measuring the carrier concentration in the substrate. [Figure 5]FIG. 5 is an explanatory diagram illustrating a virtual lattice created on the main surface of the gallium arsenide single crystal substrate shown in FIG. 4, in which squares with sides of 2 mm are arranged in parallel in the greatest number possible without overlapping each other, in order to determine the dislocation density on the main surface. [Figure 6] FIG. 6 is an explanatory diagram illustrating a sample for Hall measurement fabricated using the gallium arsenide single crystal substrate shown in FIG. [Figure 7] FIG. 7 is a perspective view for schematically explaining the gallium arsenide single crystal according to this embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0008] [Problem to be solved by this disclosure] In recent years, as disclosed in the above-mentioned Patent Documents 1 to 5 and Non-Patent Document 1, research and development has been underway with the aim of producing GaAs single crystals with good crystallinity and then obtaining GaAs single crystal substrates from the GaAs single crystals with extremely low average dislocation densities on their main surfaces. This is because semiconductor devices can be produced from such substrates with high yields. However, when GaAs single crystal substrates with large diameters (approximately 8 inches) and main surfaces with an off-angle of 4° or more from the (100) plane of the GaAs single crystal are obtained using the methods disclosed in the above-mentioned Patent Documents 1 to 5 and Non-Patent Document 1, the GaAs single crystal substrates tend to have high average dislocation densities on their main surfaces, adversely affecting the yield of semiconductor devices. Therefore, a large-diameter GaAs single crystal substrate with extremely low average dislocation densities on its main surfaces with a relatively large off-angle has not yet been realized, and its development is eagerly awaited.

[0009] In view of the above circumstances, the present disclosure has an object to provide a method for manufacturing a gallium arsenide single crystal for obtaining a large-diameter gallium arsenide single crystal substrate having an extremely small average value of dislocation density, etc., on a main surface having a relatively large off-angle. The present disclosure also has an object to provide a method for manufacturing the gallium arsenide single crystal substrate, the gallium arsenide single crystal substrate, and the gallium arsenide single crystal.

[0010] [Effects of the Present Disclosure] According to the present disclosure, there is provided a method for manufacturing a gallium arsenide single crystal for obtaining a gallium arsenide single crystal substrate having a large diameter, in which the average value of the dislocation density on the main surface having a relatively large off-angle is extremely small. Further, there are provided the method for manufacturing the gallium arsenide single crystal substrate, the gallium arsenide single crystal substrate, and the gallium arsenide single crystal.

[0011] [Outline of Embodiment] First, the outline of the embodiment of the present disclosure will be described. The inventor has intensively studied to solve the above problems. The inventor has focused on manufacturing a gallium arsenide single crystal with good crystallinity while controlling the thermal environment of a gallium arsenide single crystal manufacturing apparatus (hereinafter, also referred to as "GaAs single crystal manufacturing apparatus") so that the thermal distribution inside the crystal growing in the crucible becomes more uniform. Specifically, in the GaAs single crystal manufacturing apparatus used in the step of growing a gallium arsenide single crystal, the enlarged diameter portion is divided into an upper region and a lower region, the upper region is separated from the crucible holding table, and the lower region is brought into contact with the crucible holding table. As a result, the thermal environment in the above step is represented by a heat flux q from the inside of the crucible toward the crucible holding table, the upper region is A1, the lower region is A2, the amount of the heat flux passing through the upper region is q(A1), and the amount of the heat flux passing through the lower region is q(A2), and is controlled so as to satisfy the relationship q(A1) < q(A2). As a result, the inventor has found that the generation of thermal fluctuations inside the crystal during growth is suppressed, and the thermal distribution becomes uniform, so that even a large single crystal having a diameter of about 8 inches can minimize the thermal strain inside the crystal. Thus, the inventor has reached a manufacturing method for manufacturing a GaAs single crystal substrate having a relatively large off-angle and an extremely small average value of the dislocation density on the main surface and a large diameter using a GaAs single crystal as a material. In addition, the inventor has also reached a method for manufacturing a GaAs single crystal for obtaining the GaAs single crystal substrate, and completed the present disclosure.

[0012] Next, the embodiments of the present disclosure will be described by listing them. [1] A method for producing a gallium arsenide single crystal according to one embodiment of the present disclosure is a method for producing a cylindrical gallium arsenide single crystal. The method includes growing a gallium arsenide single crystal from a seed crystal using a gallium arsenide single crystal production apparatus. The growth-side surface of the seed crystal is a plane having an off-angle of 4° to 20° from the (100) plane of the gallium arsenide single crystal. The gallium arsenide single crystal production apparatus includes a partially cylindrical crucible, a crucible holder for holding the crucible, and a heating element for heating the crucible. The crucible includes a seed crystal housing, an increasing diameter section connected to the seed crystal housing, and a straight body section connected to the increasing diameter section on the side opposite the seed crystal housing. The seed crystal housing has a cylindrical cavity that opens to the side connected to the increasing diameter section and has a bottom wall formed on the opposite side. The increasing diameter section has a truncated cone shape that expands axially upward and is connected to the seed crystal accommodation section at the smaller diameter side of the increasing diameter section. The straight body section has a hollow cylindrical shape and is connected to the larger diameter side of the increasing diameter section. The crucible holder holds the increasing diameter section. The increasing diameter section consists of an upper region and a lower region. The upper region is spaced apart from the crucible holder and the lower region is in contact with the crucible holder.

[0013] The method for producing a gallium arsenide single crystal having these characteristics can produce a gallium arsenide single crystal with extremely small thermal strain inside the crystal. As a result, the gallium arsenide single crystal obtained by the above-mentioned production method has an extremely small average value of dislocation density on a main surface having a relatively large off-angle, and can be used as a material for producing a large-diameter gallium arsenide single crystal substrate.

[0014] [2] The increased diameter portion preferably satisfies the following formula I, where S(A1) is the surface area of ​​the upper region and S(A2) is the surface area of ​​the lower region. 0.2≦S(A2) / (S(A1)+S(A2))≦0.6 Formula I In this case, a gallium arsenide single crystal having the above-mentioned characteristics can be easily obtained.

[0015] [3] The upper region preferably faces the crucible holder in a direction perpendicular to the growth direction of the gallium arsenide single crystal, making it easy to obtain a gallium arsenide single crystal having the above-mentioned characteristics.

[0016] [4] The crucible holder is preferably made of a single material, which makes it easier to obtain gallium arsenide single crystals having the above-mentioned characteristics.

[0017] [5] The material is preferably made of quartz, which makes it easier to obtain gallium arsenide single crystals having the above-mentioned characteristics.

[0018] [6] The material is preferably opaque, which makes it easier to obtain gallium arsenide single crystals having the above-mentioned characteristics.

[0019] [7] A method for manufacturing a gallium arsenide single crystal substrate according to one embodiment of the present disclosure is a method for manufacturing a gallium arsenide single crystal substrate having a circular main surface. The manufacturing method includes a step of cutting the gallium arsenide single crystal obtained by the method for manufacturing a gallium arsenide single crystal into a disk shape and processing it to obtain a gallium arsenide single crystal substrate. The method for manufacturing a gallium arsenide single crystal substrate having these characteristics can produce a gallium arsenide single crystal substrate with a large diameter and with an extremely small average dislocation density on the main surface having a relatively large off-angle. As a result, semiconductor devices can be obtained from the gallium arsenide single crystal substrate with a high yield, even when a semiconductor layer is formed on the main surface.

[0020] [8] A gallium arsenide single crystal substrate according to one embodiment of the present disclosure is a gallium arsenide single crystal substrate having a circular main surface. The diameter of the gallium arsenide single crystal substrate is 200 mm or more and 210 mm or less. The main surface is a plane having an off-angle of 4° or more and 20° or less from the (100) plane of the gallium arsenide single crystal. The off-axis direction of the plane having the off-axis angle is any of the [01-1], [0-1-1], [0-11], and

[0011] directions. The average dislocation density of the main surface is 0 cm -2More than 3.77cm -2 In a virtual lattice formed by arranging as many squares, each 2 mm on a side, as possible in parallel without overlapping on the main surface, the ratio of the number of squares without dislocations to the total number of squares constituting the lattice is 98.04% or more. The gallium arsenide single crystal substrate contains silicon. The silicon concentration is 1.0×10 18 cm -3 Over 5.0 x 10 19 cm -3 The carrier concentration of the gallium arsenide single crystal substrate is 0.8×10 18 cm -3 Over 4.0 x 10 18 cm -3 A gallium arsenide single crystal substrate having such characteristics has a large diameter and a very small average dislocation density on a main surface having a relatively large off-angle. As a result, even when a semiconductor layer is formed on the main surface, semiconductor devices can be obtained from the gallium arsenide single crystal substrate with a high yield.

[0021] [9] The gallium arsenide single crystal substrate preferably contains boron. The boron concentration is 1.0×10 18 cm -3 Over 1.0 x 10 19 cm -3 In this case, the gallium arsenide single crystal substrate has fewer dislocations.

[0022]

[10] A gallium arsenide single crystal according to one embodiment of the present disclosure is a cylindrical gallium arsenide single crystal. The diameter of the circular plane forming the surface of the gallium arsenide single crystal is 200 mm or more and 210 mm or less. The circular plane is a plane having an off-angle of 4° or more and 20° or less from the (100) plane of the gallium arsenide single crystal. The off-axis direction of the plane having the off-axis angle is any of the [01-1], [0-1-1], [0-11], and

[0011] directions. The average dislocation density in the circular plane is 0 cm -2 More than 3.77cm -2In a virtual lattice formed by arranging as many squares, each 2 mm on a side, as possible in parallel without overlapping on the circular surface, the ratio of the number of squares without dislocations to the total number of squares constituting the lattice is 98.04% or more. The gallium arsenide single crystal contains silicon. The silicon concentration is 1.0 × 10 18 cm -3 Over 5.0 x 10 19 cm -3 The carrier concentration of the gallium arsenide single crystal is 0.8 × 10 18 cm -3 Over 4.0 x 10 18 cm -3 A gallium arsenide single crystal having these characteristics has extremely small thermal strain inside the crystal. As a result, the gallium arsenide single crystal has an extremely small average value of dislocation density on a main surface having a relatively large off-angle, and is provided as a material for producing a large-diameter gallium arsenide single crystal substrate.

[0023]

[11] The axial length of the cylindrical shape is preferably 40 mm or more and 110 mm or less, in which case a large number of gallium arsenide single crystal substrates having the above-mentioned characteristics are provided.

[0024]

[12] and

[13] The carrier concentration at one end of the gallium arsenide single crystal is 0.8 × 10 18 cm -3 Over 1.5 x 10 18 cm -3 The carrier concentration at the other end of the gallium arsenide single crystal is 1.5×10 18 cm -3 Over 3.5 x 10 18 cm -3 In this case, a large number of gallium arsenide single crystal substrates having the above-mentioned characteristics are provided.

[0025] [Details of the embodiment] An embodiment according to the present disclosure (hereinafter also referred to as "the present embodiment") will be described in further detail below, but the present disclosure is not limited thereto. The following description may be made with reference to the drawings, and the same or corresponding elements in the present specification and drawings will be designated by the same reference numerals, and the same description will not be repeated. The drawings are shown with the scale adjusted appropriately to facilitate understanding of each component, and the scale of each component shown in the drawings does not necessarily match the scale of the actual component.

[0026] In this specification, the expression "A to B" means the upper and lower limits of a range (i.e., A or more and B or less), and when no unit is specified for A and only a unit is specified for B, the unit of A and the unit of B are the same. Furthermore, when a compound or the like is expressed in a chemical formula in this specification, the chemical formula is intended to include any known atomic ratio when the atomic ratio is not particularly limited, and is not necessarily limited to only those within a stoichiometric range.

[0027] As used herein, "device yield" refers to the yield obtained by multiplying the processing yield, which indicates the percentage of wafers (e.g., microLED (Light Emitting Diode, μLED)-formed wafers) obtained from a gallium arsenide single crystal substrate without cracks, chips, or the like occurring during processing of the substrate, by the performance yield, which indicates the percentage of μLEDs obtained from the wafers that meet the required performance. The "device yield" is expressed as a percentage. The "processing yield" is expressed as the percentage of the substrates that do not crack, chip, or the like during a series of processes from the process of epitaxially growing a semiconductor layer on the gallium arsenide single crystal substrate to the process of forming a μLED-formed wafer. The "performance yield" is expressed as the percentage of non-defective μLEDs obtained from the wafers, which are subjected to a burn-in accelerated degradation test and evaluated for quality based on the degree of degradation after the test. An example of a wafer in which a semiconductor layer is formed on the substrate is a vertical cavity surface emitting laser (VCSEL) wafer. In this case, the "processing yield" is expressed as the percentage of the substrate that does not crack or chip in the series of processes from the process of epitaxial growth to form a semiconductor layer on a gallium arsenide single crystal substrate to the process of forming a VCSEL wafer. The "performance yield" is expressed as the percentage of non-defective VCSELs obtained from the wafer, which are subjected to a burn-in accelerated degradation test and judged as good or bad based on the degree of degradation after the test.

[0028] In this specification, the "main surface" of a gallium arsenide single crystal substrate refers to both of the two circular faces of the substrate. A gallium arsenide single crystal substrate falls within the scope of the present invention if at least one of the two faces satisfies the scope of the claims of the present disclosure. An epitaxial film may be disposed on the "main surface" of the gallium arsenide single crystal substrate. Furthermore, in this specification, the "face" used in the term "in-plane" refers to the "main surface." In this specification, when the diameter of a gallium arsenide single crystal substrate is described as "8 inches," this means that the diameter is within the range of 200 mm to 210 mm. The diameter is measured using a known outer diameter measuring instrument such as a vernier caliper.

[0029] As used herein, the "circular surface forming the surface" of a gallium arsenide single crystal refers to both of the two circular surfaces included in the surface of the single crystal having a cylindrical shape. A gallium arsenide single crystal falls within the scope of the present invention if at least one of the two circular surfaces satisfies the scope of the claims of the present disclosure. As used herein, when the diameter of the "circular surface forming the surface" of a gallium arsenide single crystal is described as "8 inches," this means that the diameter is within the range of 200 mm to 210 mm. The diameter of the gallium arsenide single crystal is also measured using a known outer diameter measuring device such as a vernier caliper.

[0030] In the crystallographic descriptions in this specification, individual orientations are represented by [], collective orientations by <>, individual planes by (), and collective planes by {}. A negative index in crystallographic terms is usually represented by placing a "- (bar)" before the number, but in this specification, a negative sign is placed before the number.

[0031] [Method for producing gallium arsenide single crystals] A method for producing a gallium arsenide single crystal (GaAs single crystal) according to this embodiment is a method for producing a cylindrical gallium arsenide single crystal. The method includes growing a GaAs single crystal from a seed crystal using a gallium arsenide single crystal production apparatus (GaAs single crystal production apparatus). The growth-side surface of the seed crystal is a plane having an off-angle of 4° to 20° from the (100) plane of the gallium arsenide single crystal. The GaAs single crystal production apparatus includes a partially cylindrical crucible, a crucible holder for holding the crucible, and a heating element for heating the crucible. The crucible includes a seed crystal housing portion, an increasing diameter portion connected to the seed crystal housing portion, and a straight body portion connected to the increasing diameter portion on the side opposite to the seed crystal housing portion. The seed crystal housing portion has a cylindrical cavity that opens to the side connected to the increasing diameter portion and has a bottom wall formed on the opposite side. The increasing diameter section has a truncated cone shape that expands axially upward and is connected to the seed crystal accommodation section at the smaller diameter side of the increasing diameter section. The straight body section has a hollow cylindrical shape and is connected to the larger diameter side of the increasing diameter section. The crucible holder holds the increasing diameter section. The increasing diameter section consists of an upper region and a lower region. The upper region is spaced apart from the crucible holder and the lower region is in contact with the crucible holder.

[0032] Specifically, the manufacturing method preferably includes steps such as those shown in the flowchart of FIG. 1. FIG. 1 is a flowchart shown as an example of a method for manufacturing a gallium arsenide single crystal and a method for manufacturing a gallium arsenide single crystal substrate according to this embodiment. According to FIG. 1, the method for manufacturing a GaAs single crystal includes a step S10 (first step: preparation step) of preparing a GaAs single crystal growth apparatus, a seed crystal, and a chunk of gallium arsenide (hereinafter also referred to as "bulk GaAs"), and a step S20 (second step: GaAs single crystal obtaining step) of growing a GaAs single crystal from the seed crystal using the GaAs single crystal manufacturing apparatus. Furthermore, according to FIG. 1, the method for manufacturing a GaAs single crystal substrate preferably includes a step S30 (third step: GaAs single crystal substrate obtaining step) of cutting the GaAs single crystal obtained by the GaAs single crystal manufacturing method into a disk shape and processing it to obtain a GaAs single crystal substrate.

[0033] The step S20 of obtaining a GaAs single crystal includes a step of accommodating a seed crystal in a seed crystal accommodating portion and accommodating massive GaAs together with silicon in an enlarged diameter portion and a straight cylindrical portion (raw material loading step S21), and heating a crucible with a heating element to melt a part of the seed crystal and the massive GaAs into a gallium arsenide melt (hereinafter also referred to as "GaAs melt"), and bringing the GaAs melt into contact with the remaining portion of the seed crystal (raw material melting step S22), and a step of growing a GaAs single crystal from the GaAs melt on the remaining portion of the seed crystal (GaAs single crystal growth step S23).

[0034] Particularly, in the GaAs single crystal growth step S23, when the heat flux in the direction from the inside of the crucible toward the crucible holding table is q, the upper region is A1, the lower region is A2, the amount of the heat flux passing through the upper region is q(A1), and the amount of the heat flux passing through the lower region is q(A2), the thermal environment of the GaAs single crystal growth apparatus is controlled so as to satisfy the relationship of q(A1) < q(A2). That is, in the GaAs single crystal growth step S23, it is always controlled so that the amount of the heat flux passing through the lower region (q(A2)) is larger than the amount of the heat flux passing through the upper region (q(A1)).

[0035] In order to solve the above problems, the inventor of the present invention focused on executing the step S20 of obtaining a GaAs single crystal while satisfying the relationship of q(A1) < q(A2) by controlling the thermal environment of a GaAs single crystal growth apparatus for growing a GaAs single crystal as a raw material of a GaAs single crystal substrate. Specifically, along with the control of the heat output in the heating element, studies were advanced on the structure of the enlarged diameter portion of the crucible constituting the apparatus and the structure of the crucible holding table for holding the crucible. Particularly, the enlarged diameter portion was distinguished into an upper region and a lower region, and a structure was conceived in which the upper region is separated from the crucible holding table and the lower region is brought into contact with the crucible holding table.

[0036] Furthermore, regarding the diameter increasing portion, when the surface area of the upper region constituting this is denoted as S(A1) and the surface area of the lower region is denoted as S(A2), we tried to adopt a structure that satisfies the following formula I. Here, both the surface area (S(A1)) of the upper region and the surface area (S(A2)) of the lower region mean the area of the surface on the side of the crucible holding table in the diameter increasing portion. 0.2 ≦ S(A2) / (S(A1)+S(A2)) ≦ 0.6 Formula I

[0037] Alternatively, regarding the relationship between the above-mentioned diameter increasing portion and the above-mentioned crucible holding table, we tried to oppose the above-mentioned upper region to the above-mentioned crucible holding table in a direction perpendicular to the growth direction of the GaAs single crystal. Through these trial and errors, as a result of controlling the heat flux in the direction from the inside of the crucible toward the above-mentioned crucible holding table so as to satisfy q(A1) < q(A2), we found that the heat distribution inside the GaAs single crystal growing in the crucible can be made uniform. Thereby, in the GaAs single crystal substrate obtained from the above-mentioned GaAs single crystal, the average value of the dislocation density on the main surface having a relatively large off-angle was made extremely small. In addition, by obtaining the effect of reducing the dislocation density by silicon doping, a GaAs single crystal substrate with extremely low dislocations or no dislocations was achieved. From the above, the inventor has completed a method for manufacturing a GaAs single crystal for obtaining a GaAs single crystal substrate having a large diameter with an extremely small average value of the dislocation density etc. on the main surface having a relatively large off-angle. Even when a semiconductor layer is formed on the above-mentioned main surface, the above-mentioned GaAs single crystal substrate can obtain semiconductor devices with a good yield. Regarding the structure of the above-mentioned diameter increasing portion, when the surface area of the upper region is denoted as S(A1) and the surface area of the lower region is denoted as S(A2), it is reasonable to adopt a structure that satisfies the relationship of 0.1 < S(A2) / (S(A1)+S(A2)) < 0.8.

[0038] In the step S20 of obtaining a GaAs single crystal, when the relationship between q(A1) and q(A2) does not satisfy the relationship q(A1) < q(A2) and becomes a relationship such as q(A1) ≥ q(A2), there is a possibility that a GaAs single crystal similar to that disclosed in the above patent documents or the like may be manufactured. In this case, when attempting to obtain a GaAs single crystal substrate having a large diameter of about 8 inches of GaAs and a main surface having an off-angle of 4° or more from the (100) plane of the GaAs single crystal, the average value of the dislocation density of the main surface deteriorates, which may have an adverse effect on the device yield. Alternatively, when the relationship between q(A1) and q(A2) does not satisfy the relationship q(A1) < q(A2) and becomes a relationship such as q(A1) ≥ q(A2), there is also a possibility that it cannot be grown as a single crystal.

[0039] Here, the inventor further found that there are the following concerns when manufacturing a GaAs single crystal by the methods disclosed in the above patent documents 1 to 5 and non-patent document 1 in the process of repeated studies to solve the above problems. That is, when a GaAs single crystal substrate having a main surface composed of a surface having a large diameter of about 200 mm and an off-angle of 4° or more from the (100) plane of the GaAs single crystal is obtained by the method disclosed in the above prior art documents or the like, it was found that the carrier concentration distribution in the plane of the main surface varies. Due to the variation in the carrier concentration distribution, there is a concern that the GaAs single crystal substrate frequently cracks and chips during its processing. Based on this finding, the inventor carried out the step S20 of obtaining the above-described GaAs single crystal using a seed crystal having a crystal surface with an off-angle of 4° or more and 20° or less from the (100) plane of the GaAs single crystal on the surface. As a result, when a GaAs single crystal substrate was obtained from the GaAs single crystal thus produced, it was suggested that the carrier concentration distribution on the main surface of the substrate is extremely uniform, thereby having a favorable effect on the device yield. Therefore, the GaAs single crystal obtained by the method for manufacturing a GaAs single crystal according to the present disclosure has an extremely small average value of the dislocation density and the like on the main surface having a relatively large off-angle, and is provided as a material for obtaining a large-diameter gallium arsenide single crystal substrate.

[0040] Hereinafter, by referring to FIGS. 2 and 3, the outline of the above GaAs single crystal growth apparatus and each step included in the method for manufacturing the above GaAs single crystal will be described respectively. FIG. 2 is a longitudinal sectional view schematically explaining a gallium arsenide single crystal manufacturing apparatus used in the step of growing a gallium arsenide single crystal with respect to the method for manufacturing a gallium arsenide single crystal according to the present embodiment. FIG. 3 is an enlarged view of the main part of FIG. 2. The method for manufacturing a GaAs single crystal according to the present embodiment is a method for manufacturing a GaAs single crystal having a cylindrical shape. The above manufacturing method includes, for example, a step of growing a GaAs single crystal (step S20 of obtaining a GaAs single crystal) using the GaAs single crystal growth apparatus 10 shown in FIG. 2. The GaAs single crystal growth apparatus 10 includes a crucible 5 partially having a cylindrical shape, a crucible holding table 6 for holding the crucible 5, and a heating element 7 for heating the crucible 5. The GaAs single crystal growth apparatus 10 can grow a GaAs single crystal by a vertical boat method using a crucible. Hereinafter, the vertical boat method is abbreviated as the VB method. The VB method includes a vertical Bridgman method and a vertical temperature gradient solidification method.

[0041] <GaAs single crystal growth apparatus> (Crucible) As shown in FIG. 2 , the crucible 5 in the GaAs single crystal growth apparatus 10 has a partially cylindrical structure. Specifically, the crucible 5 includes a cylindrical seed crystal accommodating portion 51, an increasing diameter portion 52 connected to the seed crystal accommodating portion 51, and a straight body portion 53 connected to the increasing diameter portion 52 on the side opposite the seed crystal accommodating portion 51. The seed crystal accommodating portion 51 has a cavity that opens to the side connected to the increasing diameter portion 52 and has a bottom wall formed on the side opposite the increasing diameter portion 52. The seed crystal accommodating portion 51 can accommodate and hold a seed crystal 8 a in the cavity. The increasing diameter portion 52 has a truncated cone shape that expands upward in the axial direction of the crucible 5 and is connected to the seed crystal accommodating portion 51 on the smaller diameter side of the increasing diameter portion 52. The straight body portion 53 has a hollow cylindrical shape and is connected to the larger diameter side of the increasing diameter portion 52. The increasing diameter portion 52 and the straight body portion 53 function to hold bulk GaAs (specifically, polycrystalline gallium arsenide) therein. Furthermore, as will be described later, the increasing diameter portion 52 and the straight body portion 53 function to solidify GaAs melt 82, which is a molten state of bulk GaAs or the like, to grow GaAs single crystal 81 as a crystalline solid. Various materials that can withstand the temperature of GaAs melt 82 are used for the crucible 5. For example, pyrolytic boron nitride (pBN) is used as the material for the crucible 5. The inner diameter of the straight body portion 53 corresponds to the diameter of the GaAs single crystal 81 to be grown, and is, for example, 200 mm or more and 215 mm or less. The increasing diameter portion 52 will be described in more detail below with reference to FIG. 3 .

[0042] (increased diameter part) As shown in FIG. 3, the diameter increasing portion 52 consists of an upper region 521 and a lower region 522. The upper region 521 is separated from the crucible holding table 6, and the lower region 522 is in contact with the crucible holding table 6. The upper region 521 means the region on the upper side in the axial direction in the diameter increasing portion 52. The lower region 522 means the region on the lower side in the axial direction than the upper region 521 in the diameter increasing portion 52. Also, the region of the diameter increasing portion 52 where the heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6 is mainly based on radiation is defined as the upper region 521. The region of the diameter increasing portion 52 where the heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6 is mainly based on radiation and heat conduction is defined as the lower region 522. The boundary between the upper region 521 and the lower region 522 is determined by the structural difference of whether it is separated from or in contact with the crucible holding table 6. Regarding the boundary between the upper region 521 and the lower region 522, it is also determined by the way heat is transmitted that constitutes the heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6.

[0043] The GaAs single crystal growth apparatus 10 can make the heat distribution inside the GaAs single crystal grown in the crucible uniform because the upper region 521 and the lower region 522 have the structures described above. Specifically, due to the structures of the upper region 521 and the lower region 522 described above, the heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6 in the upper region 521 can be mainly based on radiation. The heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6 in the lower region 522 can be mainly based on radiation and heat conduction. Thereby, the GaAs single crystal growth apparatus 10 can make the heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6 in the lower region 522 larger than that in the upper region 521 by the amount of heat conduction, and can easily satisfy the relationship of q(A1) < q(A2).

[0044] Particularly, according to the structure that is separated from the crucible holding table 6 in the upper region 521, the heat flux in the direction from the inside of the crucible 5 in the upper region 521 toward the crucible holding table 6 can be mainly based on radiation. Therefore, the GaAs single crystal growth apparatus 10 can make the heat distribution inside the growing GaAs single crystal 81 sufficiently uniform by the above structure. Further, according to the structure that contacts the crucible holding table 6 in the lower region 522, although heat fluctuations occur inside the growing GaAs single crystal 81 based on the above-described heat conduction in the GaAs single crystal growth apparatus 10, due to the structure of the crucible 5, the direction of heat conduction can be set to the direction toward the seed crystal accommodating portion 51. Therefore, the GaAs single crystal growth apparatus 10 can significantly suppress the amount of the above-described heat fluctuations. Thus, the GaAs single crystal growth apparatus 10 can make the thermal strain inside the GaAs single crystal 81 extremely small based on the above-described structure.

[0045] When the diameter increasing portion 52, for example, has the surface area of the upper region 521 as S(A1) and the surface area of the lower region 522 as S(A2), it is preferable to satisfy the following formula I. 0.2 ≦ S(A2) / (S(A1) + S(A2)) ≦ 0.6 Formula I With such a structure of the diameter increasing portion 52, the GaAs single crystal growth apparatus 10 can easily adjust the relationship between the amount of heat flux in the direction from the inside of the crucible 5 in the upper region 521 toward the crucible holding table 6 and the amount of heat flux in the direction from the inside of the crucible 5 in the lower region 522 toward the crucible holding table 6 so as to satisfy q(A1) < q(A2). Note that the amount of heat flux in the direction from the inside of the crucible 5 in the upper region 521 toward the crucible holding table 6 means the amount of heat flux passing through the upper region 521, and the amount of heat flux in the direction from the inside of the crucible 5 in the lower region 522 toward the crucible holding table 6 means the amount of heat flux passing through the lower region 522. [[ID=IO]]

[0046] The above formula I is preferably the following formula I'. Further, S(A2) / (S(A1) + S(A2)) is more preferably 0.5. 0.3 ≦ S(A2) / (S(A1) + S(A2)) ≦ 0.5 Formula I'[[ID=IS]] If S(A2) / (S(A1)+S(A2)) is less than 0.2 or more than 0.6, the heat distribution inside the growing GaAs single crystal 81 may not be sufficiently uniform, and the effect of extremely reducing the average value of dislocation density may not be sufficient. In particular, if S(A2) / (S(A1)+S(A2)) is, for example, 0.1 or less, the lower region 522 held by the crucible holder 6 is too small, making it difficult to grow the GaAs single crystal 81 while keeping the crucible 5 stable, which may adversely affect the growth of the GaAs single crystal 81. If (A2) / (S(A1)+S(A2)) is, for example, 0.8 or more, the lower region 522 held by the crucible holder 6 will be too large, and the relationship between the above q(A1) and q(A2) will become q(A1)≧q(A2), etc., which may have an adverse effect on the growth of the GaAs single crystal.

[0047] Upper region 521 preferably faces crucible holder 6 in a direction perpendicular to the growth direction of GaAs single crystal 81. Due to the above-described structure of upper region 521, the heat flux in upper region 521 in the direction from inside crucible 5 toward crucible holder 6 is mainly due to radiation. As a result, in step S20 of obtaining a GaAs single crystal, GaAs single crystal growth apparatus 10 can suppress the occurrence of thermal fluctuations inside GaAs single crystal 81 during growth, making the heat distribution uniform and reducing thermal strain inside GaAs single crystal 81.

[0048] (crucible holding stand) The GaAs single crystal growth apparatus 10 includes a crucible holder 6 for holding the diameter-increasing portion 52. The crucible holder 6 may have, for example, a cylindrical shape. The crucible holder 6 is preferably made of a single material. Examples of such materials include quartz, alumina, and silicon carbide. The material is preferably quartz. It is particularly preferable that the material is opaque. When the crucible holder 6 is made of an opaque material with poor heat dissipation, the lower region 522 is in contact with the crucible holder 6. This allows the direction of heat conduction constituting the heat flux in the lower region 522 to be axially downward (toward the seed crystal accommodation portion 51). In this case, the crucible holder 6 can significantly reduce the amount of thermal fluctuation described above. The outer diameter of the crucible holder 6 can correspond to or be the same as the outer diameter of the straight body portion 53, for example, 215 mm to 230 mm.

[0049] In this specification, "opaque" refers to a transmittance of 10% or less for light with a wavelength of 1600 to 2400 nm. Whether the material constituting the crucible holder 6 is opaque or not is evaluated using, for example, a recording spectrophotometer (product name (product number): "U-4000", manufactured by Hitachi, Ltd.). Specifically, the transmittance of the member used as the material for the crucible holder 6 and parallel plate samples with the same shape are prepared, and the samples are measured with the recording spectrophotometer to evaluate whether they are opaque or not.

[0050] (heating element) The GaAs single crystal growth apparatus 10 includes a heating element 7 for heating the crucible 5. The heating element 7 may consist of two elements. In this case, the two elements are arranged so as to surround the outer periphery of the crucible 5. Each heating element 7 is divided into multiple sections perpendicular to the axis of the crucible. This allows each heating element 7 to be configured in multiple stages. Furthermore, the output of each heating element 7 can be controlled independently for each element and for each section. Therefore, the temperature at the interface between the GaAs single crystal 81 and the GaAs melt 82 is precisely controlled. For example, a known electric heater may be used as the heating element 7.

[0051] The GaAs single crystal growth apparatus 10 can include a thermocouple 75 capable of measuring the temperature of the crucible 5 heated by the heating element 7. A plurality of thermocouples 75 may be arranged outside the crucible 5 and along the axial direction. In this case, it is preferable that at least a plurality of thermocouples 75 are arranged near the height corresponding to the interface between the GaAs single crystal 81 and the GaAs melt 82 in the crucible 5, outside the crucible 5 and in the axial direction. Based on the temperatures measured by each of the thermocouples 75, the temperatures at various locations of the GaAs single crystal 81 growing in the crucible 5 are estimated. In particular, based on the temperatures measured by each of the thermocouples 75, the radial temperature distribution at the above interface is estimated, whereby the uniformity of the heat distribution inside the GaAs single crystal 81 during crystal growth is indirectly evaluated. In other words, while the structures of the diameter increasing portion 52 and the crucible holding base 6 described above are adopted, the heat output of the heating element 7 is controlled, so that the temperatures measured by each of the thermocouples 75 are optimized. Thereby, the heat distribution inside the GaAs single crystal 81 during crystal growth becomes more uniform.

[0052] <Each process included in the method for manufacturing a GaAs single crystal> (Step 1: Preparation step S10) As shown in FIG. 1, in the method for manufacturing a GaAs single crystal substrate according to the present embodiment, first, as the first step, a preparation step S10 is executed. In the preparation step S10, the above-described GaAs single crystal growth apparatus 10, the seed crystal 8a, and the bulk GaAs for manufacturing the above GaAs single crystal are respectively prepared. The seed crystal 8a is made of a GaAs single crystal. The seed crystal 8a and the bulk GaAs may be prepared by known methods or may be prepared by obtaining commercially available ones.

[0053] The seed crystal 8a preferably has a cylindrical shape that can be accommodated in the seed crystal accommodation portion 51. The growth-side surface of the seed crystal is a plane having an off-angle of 4° to 20° from the (100) plane of the gallium arsenide single crystal. Specifically, the crystal plane of the circular plane that forms the cylindrical surface of the seed crystal 8a is a plane inclined from the (100) plane of the GaAs single crystal by an angle selected from an angle range of 4° to 20°. In this case, the inclined plane is preferably inclined in any of the [01-1], [0-1-1], [0-11], and

[0011] directions of the GaAs single crystal. When the method for producing a GaAs single crystal according to this embodiment is performed using the seed crystal 8a having such crystal plane characteristics, the GaAs single crystal substrate obtained from the GaAs single crystal produced by the method has an extremely uniform carrier concentration distribution on its main surface.

[0054] (Second step: Step S20 of obtaining GaAs single crystal) Next, in the method for manufacturing a GaAs single crystal substrate according to this embodiment, step S20 is performed in which a GaAs single crystal is grown using the GaAs single crystal manufacturing apparatus. Step S20 for obtaining a GaAs single crystal includes the following steps: raw material loading step S21, raw material melting step S22, and GaAs single crystal growing step S23. These steps are performed in this order in step S20 for obtaining a GaAs single crystal.

[0055] 1) Raw material charging process S21 The raw material charging step S21 is a step of placing a seed crystal 8a in the seed crystal accommodating portion 51, and placing chunks of GaAs together with silicon in the increasing diameter portion 52 and the straight body portion 53. The raw material charging step S21 includes a seed crystal charging step and a gallium arsenide charging step. The raw material charging step S21 may further include a sealant placement step. As shown in FIG. 2 , in the seed crystal charging step, a seed crystal 8a made of a GaAs single crystal is charged into the hollow portion of the seed crystal accommodating portion 51 of the crucible 5. The seed crystal 8a can be charged into the seed crystal accommodating portion 51 by, for example, a known method. In the gallium arsenide charging step, a plurality of chunks made of polycrystalline GaAs are charged as chunks of GaAs and stacked in the increasing diameter portion 52 and the straight body portion 53 of the crucible 5. Furthermore, in the gallium arsenide charging step, the silicon concentration of the GaAs single crystal obtained by this manufacturing method is 1.0×10 18 cm -3 Over 5.0 x 10 19 cm -3 A predetermined amount of silicon is added to the increased diameter portion 52 and the body portion 53 of the crucible 5 as follows: In the sealant placement step, a sealant known in the VB method (for example, a solid sealant made of B2O3 (boron oxide)) is preferably placed on the above-mentioned mass.

[0056] 2) Raw material melting process S22 In the raw material melting step S22, the crucible 5 is heated by the heating element 7 to melt a portion of the seed crystal 8a and the bulk GaAs into a GaAs melt 82, and the GaAs melt 82 is brought into contact with the remainder of the seed crystal 8a. In this step, the seed crystal 8a and the GaAs melt 82 are brought into contact with each other to obtain a GaAs single crystal 81. This allows the GaAs single crystal 81 to grow on the remainder of the seed crystal 8a in the next step of this manufacturing method. Specifically, in the raw material melting step S22, the crucible 5 containing the seed crystal 8a, the bulk GaAs, and preferably a solid sealant therein is supported by the crucible holder 6. As described above, the upper region 521 of the increased diameter portion 52 of the crucible 5 is spaced from the crucible holder 6, and the lower region 522 is in contact with the crucible holder 6. Thereafter, a current is supplied to the heating element 7 to heat the crucible 5. As a result, the mass melts to form a GaAs melt 82. Then, a portion of the seed crystal 8a also melts, and the remainder of the seed crystal 8a comes into contact with the GaAs melt 82 at the interface. If a solid sealant is placed on the mass in the raw material loading step S21, it is preferable that the mass melts to form the GaAs melt 82 and the sealant also melts to form a liquid sealant (not shown in FIG. 4 ).

[0057] 3) GaAs single crystal growth process S23 The GaAs single crystal growth step S23 is a step of growing a GaAs single crystal 81 from the GaAs melt 82 on the remaining portion of the seed crystal 8a. In the GaAs single crystal growth step S23, for example, the crucible 5 is gradually lowered along its axis (toward the seed crystal accommodation portion 51) relative to the heating element 7, thereby forming a temperature gradient in the crucible 5 such that the temperature on the seed crystal 8a side is lower and the temperature on the GaAs melt 82 side is higher. This causes the GaAs melt 82 in contact with the seed crystal 8a to solidify, and a GaAs single crystal 81 is continuously grown from the GaAs melt 82 on the remaining portion of the seed crystal 8a. The speed at which the crucible 5 is lowered along its axis is not particularly limited, but is, for example, 1 to 5 mm / hour.

[0058] The GaAs single crystal growth process S23 is carried out while controlling the thermal environment in the GaAs single crystal manufacturing apparatus based on the structure in which the upper region 521 in the enlarged diameter portion 52 of the crucible 5 is separated from the crucible holding table 6 and the lower region 522 is brought into contact with the crucible holding table 6 as described above, and the structure of the crucible holding table 6. Specifically, the heat flux in the direction from the inside of the crucible 5 in the upper region 521 toward the crucible holding table 6 is mainly based on radiation. Further, the heat flux in the direction from the inside of the crucible 5 in the lower region 522 toward the crucible holding table 6 is mainly based on radiation and heat conduction. Thereby, in the GaAs single crystal growth process S23, when the heat flux in the direction from the inside of the crucible 5 toward the crucible holding table 6 is q, the upper region 521 is A1, the lower region 522 is A2, the amount of the heat flux passing through the upper region 521 is q(A1), and the amount of the heat flux passing through the lower region 522 is q(A2), it is carried out while satisfying the relationship of q(A1) < q(A2).

[0059] In particular, in order to easily satisfy the above relationship of q(A1) < q(A2), when the surface area of the upper region 521 is S(A1) and the surface area of the lower region 522 is S(A(2)) for the enlarged diameter portion 52, it is preferable to satisfy the following formula I. 0.2 ≦ S(A2) / (S(A1)+S(A2)) ≦ 0.6 Formula I Furthermore, in order to easily satisfy the above relationship of q(A1) < q(A2), it is also preferable that the upper region 521 faces the crucible holding table 6 in a direction perpendicular to the growth direction of the GaAs single crystal 81.

[0060] In the GaAs single crystal growth process S23, the crucible 5 is continuously pulled downward along its axis with respect to the heating element 7, so that the interface between the GaAs single crystal 81 and the GaAs melt 82 rises toward the liquid sealant side and the GaAs melt 82 solidifies. Thereby, the GaAs single crystal growth process S23 can crystal-grow the GaAs single crystal 81 upward along the axis of the crucible 5. The crystal growth of the GaAs single crystal 81 continues until the solidification of the GaAs melt 82 remaining in the straight barrel portion 53 of the crucible 5 is completed. Thus, an ingot of the GaAs single crystal 8) is obtained.

[0061] Here, the carrier concentration of the ingot of the GaAs single crystal 81 is 0.8×10 when the solidification rate is 0.3. 18 cm -3 Over 1.5 x 10 18 cm -3 The carrier concentration of the ingot of the GaAs single crystal 81 is preferably 2.5×10 when the solidification rate is 0.85. 18 cm -3 Over 3.5 x 10 18 cm -3 or less. In this specification, the term "solidification rate" refers to the ratio of the mass of a cylinder formed from the end of the ingot on the seed crystal side to the cut surface to the total mass of the ingot when the ingot is cut in a direction perpendicular to its growth direction to produce a cylinder. In other words, the term "solidification rate" refers to a parameter indicating the extent to which solidification has progressed accompanying the growth of the ingot during the process of growing an ingot of GaAs single crystal 81, starting with solidification of GaAs melt 82 from the side in contact with seed crystal 8a in GaAs single crystal growth step S23. Accordingly, a solidification rate of 0 indicates that the entire GaAs melt 82 is in a molten state, a solidification rate of 1 indicates that the entire GaAs melt 82 has solidified, and a solidification rate of 0.5 indicates that solidification, which progresses from the seed crystal 8a side, has progressed to 50 mass% of the entire GaAs melt 82. The method for measuring the carrier concentration of the GaAs single crystal and the GaAs single crystal substrate will be described later.

[0062] <Action and effect> According to the GaAs single crystal manufacturing method of this embodiment, in the GaAs single crystal obtaining step S20 (particularly the GaAs single crystal growing step S23), the thermal environment of the GaAs single crystal growth apparatus 10 is controlled and the GaAs single crystal 81 is grown. This suppresses thermal fluctuations within the GaAs single crystal 81 during growth, resulting in uniform heat distribution, minimizing thermal strain within the crystal even for large single crystals with diameters of approximately 8 inches. As a result, a GaAs single crystal is produced that has extremely small average values ​​of dislocation density on its main surface with a relatively large off-angle and is suitable for obtaining large-diameter GaAs single crystal substrates. Therefore, even when a semiconductor layer is formed on the main surface, semiconductor devices can be fabricated from the GaAs single crystal substrate with a high yield.

[0063] In the above manufacturing method, the growth direction of the GaAs single crystal 81 is preferably normal to the circular plane forming the cylindrical surface of the seed crystal 8a. That is, the growth direction of the GaAs single crystal 81 is preferably normal to a plane tilted from the (100) plane of the GaAs single crystal by an angle selected from the range of 4° to 20° toward any of the [01-1], [0-1-1], [0-11], and

[0011] directions of the GaAs single crystal. Furthermore, the GaAs single crystal substrate according to this embodiment can be obtained by cutting the GaAs single crystal ingot as described above, using as its main surface a plane tilted from the (100) plane of the GaAs single crystal by an angle selected from the range of 4° to 20°. Here, the cutting may be performed in a direction perpendicular to the growth direction of the GaAs single crystal 81. This results in a highly uniform carrier concentration distribution within the main surface of the GaAs single crystal substrate fabricated by the above manufacturing method. If the growth direction of the GaAs single crystal 81 is set to a normal direction at an angle exceeding 20° from the (100) plane of the GaAs single crystal, it may not be possible to grow a GaAs single crystal having the desired low average value of dislocation density described above.

[0064] [Method for manufacturing GaAs single crystal substrate] <Third step: Step S30 of obtaining a GaAs single crystal substrate> The method for manufacturing a gallium arsenide single crystal substrate (GaAs single crystal substrate) according to this embodiment is a method for manufacturing a GaAs single crystal substrate having a circular main surface. As shown in FIG. 1 , the manufacturing method includes a step of cutting a GaAs single crystal obtained by the GaAs single crystal manufacturing method into a disk shape and processing it to obtain a GaAs single crystal substrate (GaAs single crystal substrate obtaining step S30). Specifically, the GaAs single crystal substrate obtaining step S30 includes a cutting step of cutting the GaAs single crystal obtained by the GaAs single crystal manufacturing method into a disk shape to obtain a GaAs single crystal substrate precursor, and an outer periphery grinding step of processing the GaAs single crystal substrate precursor by grinding the outer periphery to obtain a GaAs single crystal substrate having a circular main surface. The GaAs single crystal substrate obtaining step S30 includes the following cutting step, outer periphery grinding step, and, if necessary, a polishing step described below, which may be performed in this order.

[0065] The cutting step is a step of slicing the ingot made of GaAs single crystal 81 removed from the crucible 5 into wafers having a predetermined thickness to obtain a disk-shaped GaAs single crystal substrate precursor. Furthermore, the periphery grinding step is a step of grinding the periphery of the GaAs single crystal substrate precursor to obtain a GaAs single crystal substrate having a circular main surface. The cutting step and the periphery grinding step may use known cutting and periphery grinding methods. Furthermore, the polishing step is a step of mirror-finishing the main surface. For the polishing step, known polishing methods may be used.

[0066] <Action and effect> By carrying out the above steps, a GaAs single crystal substrate having a circular main surface is manufactured. According to the GaAs single crystal substrate manufacturing method of this embodiment, a GaAs single crystal substrate is manufactured from a low-dislocation or dislocation-free GaAs single crystal produced by the GaAs single crystal manufacturing method described above, thereby providing a GaAs single crystal substrate that can improve device yield.

[0067] [Gallium arsenide single crystal substrate] FIG. 4 is a plan view illustrating the main surface of a gallium arsenide single crystal substrate according to this embodiment and a measurement location (measurement region) for measuring the carrier concentration in the substrate. As shown in FIG. 4, the gallium arsenide single crystal substrate (GaAs single crystal substrate) 1 according to this embodiment is a GaAs single crystal substrate having a circular main surface 11. The diameter of the GaAs single crystal substrate 1 is 200 mm or more and 210 mm or less. The main surface 11 is a plane having an off-angle of 4° or more and 20° or less from the (100) plane of the GaAs single crystal. The off-axis direction of the plane having the off-axis angle is any of the [01-1], [0-1-1], [0-11], and

[0011] directions. The average dislocation density of the main surface 11 is 0 cm -2 More than 3.77cm -2 In a virtual lattice formed by arranging as many squares, each 2 mm on a side, as possible in parallel without overlapping on the main surface 11, the ratio of the number of squares without dislocations to the total number of squares constituting the lattice is 98.04% or more. The GaAs single crystal substrate 1 contains silicon. The concentration of the silicon is 1.0×10 18 cm -3 Over 5.0 x 10 19 cm -3 The carrier concentration of the GaAs single crystal substrate 1 is 0.8×10 18 cm -3 Over 4.0 x 10 18 cm -3 The GaAs single crystal substrate 1 having these characteristics has an extremely small average dislocation density on the main surface 11 having a relatively large off-angle. This allows the GaAs single crystal substrate 1 to produce semiconductor devices with a high yield even when a semiconductor layer is formed on the main surface 11.

[0068] The reason why the GaAs single crystal substrate 1 can improve device yield is as follows. Specifically, the GaAs single crystal substrate 1 is obtained from a GaAs single crystal produced, for example, by the GaAs single crystal manufacturing method described above, or preferably produced by the GaAs single crystal substrate manufacturing method described above. Therefore, even if the GaAs single crystal substrate 1 is a large single crystal with a diameter of approximately 8 inches, as described above, it can be made of a low-dislocation or dislocation-free GaAs single crystal produced so as to minimize thermal distortion within the crystal. In addition, the GaAs single crystal substrate 1 is preferably made of a GaAs single crystal grown from a seed crystal whose cylindrical surface is inclined at an angle selected from the range of 4° to 20° from the (100) plane of the GaAs single crystal. The GaAs single crystal substrate 1 with these characteristics has an extremely low average in-plane dislocation density on the main surface 11 and an extremely uniform carrier concentration distribution. This prevents cracking, chipping, and other problems from occurring during processing. Furthermore, many semiconductor devices having semiconductor layers formed on the GaAs single crystal substrate 1 can satisfy predetermined performance requirements. From the above, it is believed that semiconductor devices can be fabricated with a good yield even when semiconductor layers are formed on the main surface of a GaAs single crystal substrate 1 having a large diameter and a relatively large off-angle (specifically, 4° to 20°).

[0069] <Main surface> As described above, the GaAs single crystal substrate 1 has a circular main surface 11. In this specification, the term "circular shape" used to describe the shape of the main surface includes not only a geometrically circular shape but also a shape in which the main surface does not form a geometrically circular shape due to the presence of at least one of a notch, an orientation flat (hereinafter also referred to as "OF"), and an index flat (hereinafter also referred to as "IF") on the periphery of the main surface. Here, "a shape in which the main surface does not form a geometrically circular shape" refers to a shape in which, among line segments extending from any point on the periphery of the main surface to the center of the main surface, the lengths of line segments extending from any point on the notch, OF, or IF to the center of the main surface are shorter. Furthermore, "a shape in which the main surface does not form a geometrically circular shape" also includes a shape in which the lengths of all line segments extending from any point on the periphery of the main surface to the center of the main surface are not necessarily the same due to the shape of the GaAs single crystal used to form the GaAs single crystal substrate. In this case, the center of the main surface refers to the position of the center of gravity. The diameter of a GaAs single crystal substrate refers to the length of the longest line segment extending from any point on the periphery of the GaAs single crystal substrate, passing through the center of the main surface, to another point on the periphery.

[0070] The surface roughness of the main surface 11 is preferably 0.3 nm or less in terms of surface roughness Sa as defined in JIS B 0681-2:2018. This allows the main surface 11 of the GaAs single crystal substrate 1 to have a mirror-like surface, which contributes to improving device characteristics. The surface roughness Sa of the main surface 11 is more preferably 0.2 nm or less, and even more preferably 0.1 nm or less. The surface roughness Sa of the main surface 11 is measured using an intermittent contact mode of a known atomic force microscope (e.g., trade name: "Dimension 3000" manufactured by Bruker). More specifically, the surface roughness Sa of the main surface 11 is measured by using the atomic force microscope to correspond the 512 × 512 pixel size for calculating the surface roughness Sa to any square area of ​​0.2 μm length × 0.2 μm width on the main surface 11. This allows the surface roughness Sa of that area to be determined.

[0071] The surface roughness Sa does not need to be 0.3 nm or less in all of the regions measured on the main surface 11, but it is sufficient that the surface roughness Sa measured in at least one of the multiple regions set on the main surface 11 of the GaAs single crystal substrate 1 is 0.3 nm or less. As the regions on the main surface 11 for measuring the surface roughness Sa, for example, a total of five regions can be selected, with the center O of the GaAs single crystal substrate 1 and any four points (not shown) on a circumference 5 mm inward from the outer edge of the GaAs single crystal substrate 1 as the centers of the measurement range.

[0072] (off angle and off direction) The main surface 11 is a plane having an off-angle of 4° to 20° from the (100) plane of the GaAs single crystal. The off-axis direction of the plane having the off-axis angle is any of the [01-1], [0-1-1], [0-11], and

[0011] directions. In other words, the [01-1], [0-1-1], [0-11], and

[0011] directions of the GaAs single crystal are four directions equivalent to the [01-1] direction of the GaAs single crystal, and are crystallographically <110> It is expressed as a direction.

[0073] The main surface 11 is preferably a plane having an off-angle of 6° or more and 15° or less from the (100) plane of the GaAs single crystal. In this case, the GaAs single crystal substrate 1 can further improve device yield. A GaAs single crystal substrate having an off-angle of the main surface of less than 4° from the (100) plane of the GaAs single crystal may be able to achieve the above-mentioned effects of the present disclosure even by using other means. A GaAs single crystal substrate having an off-angle of the main surface of more than 20° from the (100) plane of the GaAs single crystal may have difficulty achieving the above-mentioned effects of the present disclosure as long as it is based on the GaAs single crystal manufacturing method according to the present embodiment.

[0074] In the present disclosure, the crystal plane of main surface 11 is assumed to have an accuracy error of ±0.5°. For example, when it is said that main surface 11 is "a plane having an off-angle of 6° from the (100) plane of GaAs single crystal," this means that main surface 11 may be a plane having an off-angle of 5.5° to 6.5° from the (100) plane. The off-angle of main surface 11 of GaAs single crystal substrate 1 from the (100) plane is measured using a known crystal orientation measurement device (for example, product name (product number): "2991G2" manufactured by Rigaku Corporation).

[0075] <diameter> The diameter of the GaAs single crystal substrate 1 is 200 mm or more and 210 mm or less. This allows for an improved device yield in a large-diameter GaAs single crystal substrate 1 having a diameter of 200 mm or more and 210 mm or less. Here, the diameter of the GaAs single crystal substrate 1 is determined based on the circular shape before the OF, IF, etc. are formed, even if the main surface does not have a geometrically circular shape due to the influence of the OF, IF, etc. Furthermore, as described above, the diameter of the GaAs single crystal substrate 1 is measured using a known outer diameter measuring instrument such as a vernier caliper.

[0076] <Dislocation density> The average dislocation density of the main surface 11 is 0 cm -2 More than 3.77cm -2 or less. Furthermore, in a virtual lattice formed by arranging as many squares, each 2 mm on a side, as possible in parallel without overlapping on the main surface 11, the ratio of the number of squares in which dislocations are not present to the total number of squares constituting the lattice (hereinafter also referred to as the "dislocation-free rate") is 98.04% or more. The average dislocation density of the main surface 11 and the dislocation-free rate are specifically determined by counting the number of etching pits (hereinafter also referred to as "etch pits") that appear on the main surface 11 after etching the main surface 11 with molten potassium hydroxide. In other words, the GaAs single crystal substrate 1 according to this embodiment has an average number of etch pits of 0 cm -2 More than 3.77cm -2The dislocation-free rate is 98.04% or more, and the upper limit of the dislocation-free rate is 100%. Although etch pits are not academically synonymous with dislocations, they are considered to be equivalent to dislocations in this technical field.

[0077] (Method for calculating the number of etch pits) Fig. 5 is an explanatory diagram illustrating how a virtual lattice is set up on the main surface of the gallium arsenide single crystal substrate shown in Fig. 4, in which squares with sides of 2 mm are arranged in parallel as many times as possible without overlapping each other, in order to determine the dislocation density on the main surface. Hereinafter, a specific method for calculating the number of etch pits will be described with reference to Fig. 5.

[0078] First, the main surface 11 of the GaAs single crystal substrate 1 is immersed in molten potassium hydroxide at 500°C for 10 minutes. The GaAs single crystal substrate 1 is then removed from the molten potassium hydroxide. A known method is used to immerse the GaAs single crystal substrate 1. Next, as shown in FIG. 5 , a virtual lattice G is established on the main surface 11 of the GaAs single crystal substrate 1 by arranging as many 2 mm squares as possible in parallel without overlapping each other. Each square constituting the virtual lattice G is then observed with a known optical microscope (e.g., the trade name "ECLIPSE (registered trademark) LV150N" manufactured by Nikon Corporation), and the number of etch pits appearing in one field of view of the optical microscope is counted. In this case, the observation with the optical microscope is performed at a magnification of 50x. As a result, one field of view of the optical microscope is 2 mm × 2 mm in size, corresponding to the size of the square. Therefore, the number of etch pits per field of view is calculated as the number of dislocations per square constituting the virtual lattice G. Note that when the area is 100 μm 2 Only etch pits that are confirmed to be equal to or greater than this shall be counted in the number of etch pits.

[0079] Finally, the etch pits counted for each square constituting the virtual lattice G were 1 cm 2The dislocation density for each square is then calculated. The sum of the dislocation densities is then divided by the number of squares to determine the average dislocation density for the main surface. The dislocation-free rate is then calculated by determining the ratio of the number of squares that are free of dislocations to the total number of squares that make up the virtual lattice G. In this specification, the phrase "laying the squares so as to maximize the number of parallel squares without overlapping each other" on the main surface 11 means that when the squares are laid out parallel to the main surface 11 without overlapping each other, and the squares overlap the periphery of the main surface 11 and its outside, the squares are excluded from the elements that make up the virtual lattice G. This is because the number of dislocations in the region near the periphery, including the periphery of the main surface 11 of the GaAs single crystal substrate 1, varies greatly from substrate to substrate, and is typically not used as a material for semiconductor devices.

[0080] The average dislocation density of the main surface 11 is 0 cm -2 More than 3cm -2 Preferably less than 0 cm -2 More than 2.88cm -2 The dislocation-free rate is preferably 99.0% or more, and more preferably 99.45% or more, which makes it possible to provide GaAs single crystal substrates with improved device yields.

[0081] <Dopant> The GaAs single crystal substrate 1 according to this embodiment contains silicon (Si). The atomic concentration of the Si is 1.0×10 18 cm -3 Over 5.0 x 10 19 cm -3 The atomic concentration of Si is 1.4×10 18 cm -3 Over 1.0 x 10 19 cm -3 Preferably, it is 1.8 x 10 or less. 18 cm -3 Over 5.0 x 10 18 cm -3It is more preferable that the following is true: In this case, n-type (electron-donating) conductivity is imparted to the GaAs single crystal substrate 1, and the effect of reducing dislocation density is obtained.

[0082] The GaAs single crystal substrate 1 preferably contains boron (B). In this case, the atomic concentration of B is 1.0×10 18 cm -3 Over 1.0 x 10 19 cm -3 The atomic concentration of B is preferably 1.5×10 or less. 18 cm -3 Over 5.0 x 10 18 cm -3 or less. In this case, the GaAs single crystal substrate 1 has fewer dislocations. The atomic concentrations of Si and B in the GaAs single crystal substrate 1 are both measured using glow discharge mass spectrometry (GDMS). When the GaAs single crystal substrate 1 is obtained through the GaAs single crystal manufacturing method described above, the B is produced by a reaction between silicon added to the raw material gallium arsenide and boron oxide, which functions as a sealant. As a result, the B may be contained in the GaAs single crystal substrate 1.

[0083] <Carrier concentration> The carrier concentration of the GaAs single crystal substrate 1 is 0.8×10 18 cm -3 Over 4.0 x 10 18 cm -3 The carrier concentration is 1.2 × 10 18 cm -3 Over 3.8 x 10 18 cm -3 Preferably, it is 1.4 × 10 or less. 18 cm -3 Over 3.6 x 10 18 cm -3or less. In this case, the GaAs single crystal substrate 1 is given n-type (electron-donating) conductivity. The carrier concentration of the GaAs single crystal substrate 1 is determined by performing Hall measurement using the Van der Pauw method on a rectangular slice obtained by cleaving the GaAs single crystal substrate 1 at room temperature of 25°C. The rectangular slice has dimensions of, for example, 4 mm length × 4 mm width × 600 μm thickness. A method for measuring the carrier concentration of the GaAs single crystal substrate 1 will be described below with reference to FIGS. 4 and 6. FIG. 6 is an explanatory diagram illustrating a Hall measurement sample prepared using the gallium arsenide single crystal substrate shown in FIG. 4.

[0084] First, a GaAs single crystal substrate 1 to be measured is prepared from a GaAs single crystal obtained by the GaAs single crystal manufacturing method described above. Next, as shown in FIG. 4 , four intersections are defined for this GaAs single crystal substrate 1, where the circumference 5 mm inward from its outer edge intersects with half lines extending from the center O of the main surface 11 of the GaAs single crystal substrate 1 in the [01-1], [0-1-1], [0-11], and

[0011] directions of the GaAs single crystal. Furthermore, rectangular slices 11a, each measuring 4 mm long, 4 mm wide, and 600 μm thick, are prepared with their centers at each of the four intersections. Next, as shown in FIG. 6 , electrodes 21 made of an alloy containing gold, nickel, and germanium are formed at the four corners of the rectangular slice 11a, thereby obtaining four Hall measurement samples. The shape of the electrodes 21 is not limited to the rectangular shape shown in the figure; they may be sector-shaped or circular. The carrier concentration is determined by applying Hall measurement by the Van der Pauw method to four Hall measurement samples equipped with such electrodes 21 in an atmosphere at 25°C. In this specification, the "carrier concentration of the GaAs single crystal substrate" refers to the average value of the carrier concentrations obtained from the four Hall measurement samples. Furthermore, the value obtained by subtracting the minimum value from the maximum value of the carrier concentrations obtained from the four Hall measurement samples and dividing the result by the average value is defined as the second carrier concentration ([max-min] / average) of the GaAs single crystal substrate. The second carrier concentration represents the variation in carrier concentration on the main surface 11 of the GaAs single crystal substrate 1, and the smaller this value, the more uniform the carrier concentration distribution on the main surface 11 is evaluated to be.

[0085] [Gallium arsenide single crystal] FIG. 7 is a perspective view schematically illustrating a gallium arsenide single crystal according to this embodiment. As shown in FIG. 7, a gallium arsenide single crystal (GaAs single crystal) 100 according to this embodiment is a GaAs single crystal having a cylindrical shape. The diameter of a circular face 110 forming the surface of the GaAs single crystal 100 is 200 mm or more and 210 mm or less. The circular face 110 is a face having an off-angle of 4° or more and 20° or less from the (100) face of the GaAs single crystal. The off-direction of the face having the off-angle is any one of the [01-1], [0-1-1], [0-11], or

[0011] directions. The average dislocation density on the circular face 110 is 0 cm -2 More than 3.77cm -2 In a virtual lattice formed by arranging as many squares, each 2 mm on a circular surface 110, in parallel as possible without overlapping, the ratio of the number of squares without dislocations to the total number of squares constituting the lattice is 98.04% or more. The GaAs single crystal 100 contains silicon. The concentration of silicon is 1.0×10 18 cm -3 Over 5.0 x 10 19 cm -3 The carrier concentration of the GaAs single crystal 100 is 0.8 × 10 18 cm -3 Over 4.0 x 10 18 cm -3 The GaAs single crystal 100 having these characteristics has extremely small thermal strain inside the crystal. Therefore, the GaAs single crystal 100 has an extremely small average dislocation density on the main surface having a relatively large off-angle, and is provided as a material for producing large-diameter GaAs single crystal substrates.

[0086] In particular, in the GaAs single crystal 100, the axial length of the cylindrical shape is preferably 40 mm or more and 110 mm or less. When the axial length of the cylindrical shape is 40 mm or more, a larger number of GaAs single crystal substrates with high device yields can be provided. When the axial length of the cylindrical shape is 110 mm or less, GaAs single crystal substrates with little variation in carrier concentration between product lots can be provided.

[0087] The reason why the GaAs single crystal 100 can provide a GaAs single crystal substrate with improved device yield is the same as the reason why the above-described GaAs single crystal substrate 1 can improve the device yield, so overlapping explanations will not be repeated.

[0088] <Circular surface forming the surface of the GaAs single crystal> The GaAs single crystal 100 has a cylindrical shape. As a result, the GaAs single crystal 100 has a circular surface 110 that forms its surface. In this specification, the shape of the circular surface 110 includes not only a geometric circular shape but also a shape when a geometric circular shape is not formed. Here, the "shape when a geometric circular shape is not formed" of the circular surface 110 refers to a shape where the lengths of all line segments extending from an arbitrary point on the outer periphery of the circular surface 110 to the center of the circular surface 110 are not necessarily the same. In this case, the center of the circular surface 110 is the position of the centroid. The diameter of the circular surface 110 is the length of the longest line segment among the line segments extending from an arbitrary point on the outer periphery of the circular surface 110 through the center of the circular surface 110 to another point on the outer periphery.

[0089] (Off-angle and off-direction) The circular surface 110 is a surface having an off-angle of 4° or more and 20° or less from the (100) plane of the GaAs single crystal. The off-direction of the surface having the above off-angle is any one of the [01-1], [0-1-1], [0-11], or

[0011] directions. Regarding the characteristics of the off-angle and off-direction of the circular surface 110 in the GaAs single crystal 100, they are the same as the characteristics of the off-angle and off-direction of the "main surface 11" of the above-described GaAs single crystal substrate 1, so overlapping explanations will not be repeated. In addition, the preferred range of the off-angle in the circular surface 110 is also the same as the preferred range of the off-angle in the main surface 11. In the present disclosure, the crystal plane of the circular surface 110 has an accuracy error of ±0.5°, similar to the main surface 11 of the GaAs single crystal substrate 1.

[0090] <Diameter> The diameter of circular surface 110 forming the surface of GaAs single crystal 100 is not less than 200 mm and not more than 210 mm. As described above, the diameter of circular surface 110 forming the surface of GaAs single crystal 100 is measured using a known diameter measuring device such as a vernier caliper.

[0091] <Dislocation density> The average dislocation density of the circular surface 110 is 0 cm -2 More than 3.77cm -2 The following is true. Furthermore, in a virtual lattice formed by arranging as many 2-mm-side squares as possible in parallel on the circular surface 110 without overlapping, the ratio of the number of squares without dislocations to the total number of squares constituting the lattice (dislocation-free rate) is 98.04% or more. The characteristics and effects of the average dislocation density and dislocation-free rate of the circular surface 110 are the same as those of the average dislocation density and dislocation-free rate of the main surface 11 of the GaAs single crystal substrate 1 described above, and therefore will not be repeated. The preferred ranges of the average dislocation density and dislocation-free rate of the circular surface 110 are also the same as those of the main surface 11. The method for calculating the number of etch pits on the circular surface 110 is the same as that for the main surface 11. Therefore, the number of etch pits on the circular surface 110 can be determined by replacing the term "main surface 11" used in the explanation of the method for calculating the number of etch pits on the main surface 11 with the term "circular surface 110" and applying the above calculation method.

[0092] <Dopant> The GaAs single crystal 100 contains silicon (Si). The atomic concentration of Si is 1.0×10 18 cm -3 Over 5.0 x 10 19 cm -3The characteristics and effects of the dopant in GaAs single crystal 100 are the same as those of the dopant in GaAs single crystal substrate 1 described above, and therefore redundant explanations will not be repeated. Note that GaAs single crystal 100 preferably contains boron (B) as a dopant, and the range of the B content (atomic concentration) in this case is also the same as that of GaAs single crystal substrate 1. The dopant concentration in GaAs single crystal 100 is also determined by the same measurement method as that for GaAs single crystal substrate 1.

[0093] <Carrier concentration> The carrier concentration of GaAs single crystal 100 is 0.8 × 10 18 cm -3 Over 4.0 x 10 18 cm -3 The characteristics and effects of the carrier concentration of GaAs single crystal 100 are the same as those of GaAs single crystal substrate 1 described above, and therefore redundant explanations will not be repeated. The carrier concentration and second carrier concentration of GaAs single crystal 100 can also be determined by the same measurement method as that of GaAs single crystal substrate 1. Therefore, the carrier concentration and second carrier concentration of GaAs single crystal 100 can be determined by applying the above measurement method, substituting the term "circular surface 110" for the term "major surface 11" used in the description of the method for measuring the carrier concentration and second carrier concentration of GaAs single crystal substrate 1.

[0094] In particular, the carrier concentration at one end of the GaAs single crystal 100 is 0.8×10 18 cm -3 Over 1.5 x 10 18 cm -3 The carrier concentration at the other end of the GaAs single crystal 100 is preferably 1.5×10 18 cm -3 Over 3.5 x 10 18 cm -3 In this case, the GaAs single crystal 100 is appropriately given n-type (electron-donating) conductivity characteristics.

[0095] Furthermore, the carrier concentration of the GaAs single crystal 100 is 0.8×10 when the solidification rate is 0.3. 18 cm -3 Over 1.5 x 10 18 cm -3 The carrier concentration of the GaAs single crystal 100 is preferably 2.5×10 or less when the solidification rate is 0.85. 18 cm -3 Over 3.5 x 10 18 cm -3 or less. In this case, good epitaxial growth is achieved on a GaAs single crystal substrate obtained from GaAs single crystal 100. As used herein, the term "solidification rate" refers to the ratio of the mass of a cylindrical body formed from the seed crystal end of GaAs single crystal 100 to the total mass of GaAs single crystal 100 when GaAs single crystal 100 is cut in a direction perpendicular to its growth direction to produce the cylindrical body. [Example]

[0096] The present disclosure will be described in more detail below with reference to examples, but the present disclosure is not limited to these examples. In these examples, the inventors used a GaAs single crystal growth apparatus such as that shown in Figure 2 to produce GaAs single crystals for each sample by the vertical Bridgeman method, and obtained GaAs single crystal substrates from the GaAs single crystals for each sample. In the following description, Samples 11 to 18 and Samples 21 to 25 are examples, and Samples 101 to 103 and Samples 201 to 203 are comparative examples.

[0097] [First Example] [Manufacturing GaAs single crystal substrates] The GaAs single crystal substrates of Samples 11 to 18 and Samples 101 to 103, each having a diameter of 205 mm, were manufactured in the following manner.

[0098] <Sample 101> (1st step: Preparation step S10) A known GaAs single crystal growth apparatus using the vertical Bridgeman method was prepared. A seed crystal and bulk GaAs consisting of GaAs polycrystals were each produced by a known method. The GaAs single crystal growth apparatus was configured so that the entire surface of the increasing diameter section facing the crucible holder was in contact with the crucible holder. Therefore, the heat flux from the inside of the crucible toward the crucible holder in the increasing diameter section of the GaAs single crystal growth apparatus was primarily due to radiation and conduction throughout the entire section. Therefore, the entire increasing diameter section was considered to be the lower region. In this case, the value of S(A2) / (S(A1)+S(A2)) in the increasing diameter section, as shown in Equation I above, was 1. The inner diameter of the straight body of the crucible in the GaAs single crystal growth apparatus was 210 mm. The seed crystal was cylindrical, and the circular crystal plane forming the surface of the cylindrical shape was a plane having an off angle of 4° in the

[0011] direction from the (100) plane.

[0099] (Second step: Step S20 of obtaining GaAs single crystal) 1) Raw material charging process S21 Using a known method, a seed crystal was placed in the hollow portion of the seed crystal holder of a crucible installed in a GaAs single crystal growth apparatus. Multiple GaAs blocks made of polycrystalline GaAs were then placed in the diameter-enhancing portion and the body portion of the crucible and stacked. A trace amount of silicon (Si) was also added. A sealant made of B2O3 was then placed on the GaAs blocks.

[0100] 2) Raw material melting process S22 An electric current was supplied to the heating element to heat the crucible, thereby converting the sealant into a liquid sealant and converting the bulk GaAs charged into a GaAs melt in the diameter-increasing portion and the body portion. Furthermore, by controlling the heating element that heats the seed crystal receiving portion, a portion of the seed crystal received in the cavity was also melted. This caused the remaining portion of the seed crystal to come into contact with the GaAs melt.

[0101] 3) GaAs single crystal growth process S23 The power of the heating element that heated the crucible was controlled, and the crucible was gradually pulled downward (towards the seed crystal housing portion) along its axis relative to the heating element, creating a temperature gradient in the crucible such that the temperature on the seed crystal side was lower and the temperature on the GaAs melt side was higher. This resulted in continuous crystal growth of GaAs single crystals from the GaAs melt on the remaining part of the seed crystal. The speed at which the crucible was pulled downward along its axis was 2 mm / hour.

[0102] In the GaAs single crystal growth step S23, the output of the heating element for heating the crucible was controlled, and the crucible was pulled downward along its axis relative to the heating element, solidifying the GaAs melt and causing a GaAs single crystal to grow upward along the axis of the crucible. Thereafter, crystal growth of the GaAs single crystal continued until solidification of the GaAs melt remaining in the body of the crucible was completed, thereby obtaining a GaAs single crystal ingot.

[0103] In the preparation of the GaAs single crystal substrate of sample 101, the entire surface of the increasing diameter portion facing the crucible holder is in contact with the crucible holder, and therefore the entire increasing diameter portion is considered to be the lower region. In this case, the heat flux in the increasing diameter portion from the inside of the crucible toward the crucible holder is mainly composed of radiation and thermal conduction throughout the entire region. Therefore, in the GaAs single crystal growth step S23, it was difficult to sufficiently suppress the occurrence of thermal fluctuations inside GaAs single crystal 81 during growth.

[0104] (Third step: Step S30 of obtaining a GaAs single crystal substrate) Using known cutting and periphery grinding methods, a GaAs single crystal substrate having a predetermined thickness and a circular main surface was obtained from the GaAs single crystal ingot removed from the crucible. The main surface of the GaAs single crystal substrate was then polished by a known method to a mirror finish. Thus, the GaAs single crystal substrate of sample 101 was obtained. The crystal plane of the main surface of the GaAs single crystal substrate had an off-angle of 4° from the (100) plane in the

[0011] direction. Furthermore, the surface roughness Sa of the main surface of the GaAs single crystal substrate measured by the above-mentioned measurement method was 0.15 nm.

[0105] <Sample 102> In preparation step S10, a GaAs single crystal substrate of sample 102 was obtained in the same manner as sample 101, except that a cylindrical seed crystal was prepared in which the circular crystal plane forming the surface of the cylindrical shape was a plane having an off-angle of 6° in the

[0011] direction from the (100) plane. Therefore, in the GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 102, the value of S(A2) / (S(A1)+S(A2)) shown in formula I above was 1. In addition, in GaAs single crystal growth step S23, the entire diameter-increasing section was the lower region, and the heat flux in the direction from the inside of the crucible toward the crucible holder in the diameter-increasing section was mainly composed of radiation and thermal conduction, making it difficult to sufficiently suppress the occurrence of thermal fluctuations inside GaAs single crystal 81 during growth. The crystal plane of the main surface of the GaAs single crystal substrate of sample 102 was a plane having an off-angle of 6° in the

[0011] direction from the (100) plane. The surface roughness Sa of the main surface of the GaAs single crystal substrate measured by the above-mentioned measuring method was 0.15 nm.

[0106] <Sample 11> In preparation step S10, a GaAs single crystal growth apparatus employing the vertical Bridgeman method, as shown in Figure 2, was prepared. A cylindrical seed crystal was prepared, with the growth surface being a plane with a 4° off-angle in the

[0011] direction from the (100) plane of the GaAs single crystal. The GaAs single crystal substrate of sample 11 was obtained in the same manner as sample 101, except that the GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 11 had a crucible with an increased diameter consisting of an upper region and a lower region, with the upper region separated from the crucible holder and the lower region in contact with the crucible holder. Furthermore, the value of S(A2) / (S(A1)+S(A2)) shown in the above formula I was 0.5. The crystal plane of the main surface of the GaAs single crystal substrate of sample 11 was a plane having an off-angle of 4° in the

[0011] direction from the (100) plane. The surface roughness Sa of the main surface of the GaAs single crystal substrate measured by the above-mentioned measuring method was 0.15 nm.

[0107] <Samples 12 to 18, and Sample 103> In preparation step S10, GaAs single crystal substrates 12 to 18 and 103 were obtained in the same manner as sample 11, except that a cylindrical seed crystal was prepared in which the circular crystal plane forming the surface of the cylindrical shape was tilted at an angle of 6 to 22° from the (100) plane in the

[0011] direction as shown in Table 1 below. The crystal planes of the main surfaces of the GaAs single crystal substrates of samples 12 to 18 and 103 had an off-angle of 6 to 22° from the (100) plane in the

[0011] direction as shown in Table 1 below. The surface roughness Sa of the main surfaces of the GaAs single crystal substrates measured by the above-mentioned measurement method was 0.15 nm.

[0108] Here, samples 12 and 13 are GaAs single crystal substrates obtained from the same GaAs single crystal ingot with an off-angle of 6°. However, sample 12 is a GaAs single crystal substrate obtained from a portion of the ingot where the solidification rate was 0.27, while sample 13 is a GaAs single crystal substrate obtained from a portion of the ingot where the solidification rate was 0.89. Samples 16 and 17 are GaAs single crystal substrates obtained from the same GaAs single crystal ingot with an off-angle of 15°. However, sample 16 is a GaAs single crystal substrate obtained from a portion of the ingot where the solidification rate was 0.27, while sample 17 is a GaAs single crystal substrate obtained from a portion of the ingot where the solidification rate was 0.89.

[0109] <Characteristics evaluation> The above-described measurement or calculation methods were performed on the GaAs single crystal substrates of Samples 11 to 18 and Samples 101 to 103, and the silicon atomic concentration, carrier concentration, second carrier concentration, boron atomic concentration, average dislocation density, and dislocation-free rate were determined for each sample. The results are shown in Table 1. Table 1 also shows the off-angle of the main surface of the GaAs single crystal substrate of each sample, the structure of the increased diameter portion (presence or absence of an upper region and a lower region), and the value of S(A2) / (S(A1)+S(A2)) shown in the above formula I.

[0110] <Element yield> VCSELs were fabricated using the GaAs single crystal substrates of Samples 11 to 18 and Samples 101 to 103 according to the method disclosed in Japanese Patent Application Laid-Open No. 2008-283137. The device yield (%) was calculated by multiplying the processing yield, which indicates the percentage of VCSEL-formed wafers containing multiple VCSEL portions obtained from the GaAs single crystal substrates without cracking or chipping during processing, by the performance yield, which indicates the percentage of VCSELs obtained from the wafers that met the required performance. The "performance yield" was evaluated using the following accelerated degradation test. The "VCSEL portion" refers to the device-like portion on the VCSEL-formed wafer that can function as a VCSEL after being divided and packaged. The VCSEL portions were divided into VCSELs measuring 500 μm long and 500 μm wide.

[0111] Before conducting the accelerated degradation test, initial characteristics of each VCSEL portion on the VCSEL-formed wafer fabricated for each sample were evaluated in the on-wafer state. In the initial characteristic evaluation, VCSEL portions with an optical output of 4 mW or more at an operating current of 9 mA were deemed to be non-defective. VCSEL portions with an optical output of less than 4 mW at an operating current of 9 mA were marked as defective on the wafer. Next, the wafer was divided into chips. Next, 40 non-defective chips (i.e., unmarked chips) were randomly selected from the chips and mounted to obtain VCSELs. Furthermore, an accelerated degradation test was conducted on the VCSELs by applying an applied current of 18 mA at an ambient temperature of 80°C for 100 hours. After that, each VCSEL was returned to room temperature, and its optical output at an operating current of 9 mA was evaluated. In the above evaluation, VCSELs whose optical output had decreased by less than 10% of the level before the accelerated degradation test (i.e., optical output of 3.6 mW or more) were deemed to be non-defective, and the ratio of non-defective VCSELs to the 40 samples was deemed to be the performance yield. The results are shown in Table 1. In Table 1, samples with an element yield of 90% or more were rated A, samples with an element yield of 80% or more but less than 90% were rated B, and samples with an element yield of less than 80% were rated C.

[0112] [Table 1]

[0113] <Consideration> In the GaAs single crystal substrates of Samples 11 to 18, the off-angle of the main surface is 4 to 20°, and the average dislocation density of the main surface is 0 cm -2 More than 3.77cm -2 The dislocation-free rate was 98.04% or more. Furthermore, the silicon atomic concentration was 1.0 × 10 18 cm -3 Over 5.0 x 10 19 cm -3 The carrier concentration is 0.8×10 18 cm -3 Over 4.0 x 10 18 cm-3 Furthermore, the device yield of these GaAs single crystal substrates was 89.8% or more, and they were judged to be A or B. In contrast, the GaAs single crystal substrates of samples 101 and 102 had an off-angle of 4 to 6° on their main surfaces, but the average dislocation density on the surface was 3.77 cm -2 The dislocation-free rate exceeded 98.04%, and the dislocation-free rate was less than 98.04%. The GaAs single crystal substrates of Samples 101 and 102 were produced using a GaAs single crystal manufacturing apparatus with a structure in which the entire surface of the diameter increasing portion contacts the crucible holder. In this case, the device yield for these GaAs single crystal substrates was less than 80%, and they were judged to be C. The GaAs single crystal substrate of Sample 103 had an off-angle of 22° on its main surface, and the average dislocation density on the main surface was 3.77 cm -2 In this case, the device yield of the GaAs single crystal substrate of sample 103 was less than 80%, and was judged as C.

[0114] [Second Example] [Manufacturing GaAs single crystal substrates] GaAs single crystal substrates of Samples 21 to 25 and Samples 201 to 203, each having a diameter of 205 mm, were fabricated in the following manner.

[0115] <Sample 201> The GaAs single crystal substrate of the sample 102 described above was obtained as the GaAs single crystal substrate of the sample 201.

[0116] <Sample 202> In preparation step S10, a GaAs single crystal growth apparatus was prepared, the diameter-increasing section of which consisted of an upper region and a lower region, with the upper region separated from the crucible holder and the lower region in contact with the crucible holder. The value of S(A2) / (S(A1)+S(A2)) in the diameter-increasing section of the crucible, as shown in formula I above, was 0.1. Otherwise, a GaAs single crystal substrate (sample 202) was obtained in the same manner as sample 12. The crystal plane of the main surface of the GaAs single crystal substrate (sample 202) was a plane with an off-angle of 6° in the

[0011] direction from the (100) plane. Furthermore, the surface roughness (Sa) of the main surface of the GaAs single crystal substrate, measured by the above-mentioned measurement method, was 0.15 nm.

[0117] <Samples 21 to 23, Sample 25, and Sample 203> In preparation step S10, GaAs single crystal substrates of samples 21 to 23, sample 25, and sample 203 were each obtained in the same manner as sample 202, except that a GaAs single crystal growth apparatus having an increased diameter section structure as described below was prepared. The GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 21 had a value of S(A2) / (S(A1)+S(A2)) shown in formula I above at the increased diameter section of the crucible of 0.2. The GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 22 had a value of S(A2) / (S(A1)+S(A2)) shown in formula I above at the increased diameter section of the crucible of 0.3. The GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 23 had a value of S(A2) / (S(A1)+S(A2)) shown in formula I above at the increased diameter part of the crucible of 0.4. The GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 25 had a value of S(A2) / (S(A1)+S(A2)) shown in formula I above at the increased diameter part of the crucible of 0.6. The GaAs single crystal growth apparatus used to produce the GaAs single crystal substrate of sample 203 had a value of S(A2) / (S(A1)+S(A2)) shown in formula I above at the increased diameter part of the crucible of 0.8.

[0118] <Sample 24> The GaAs single crystal substrate of Sample 12 described above was obtained as the GaAs single crystal substrate of Sample 24.

[0119] <Characteristics evaluation> The above-described measurement or calculation methods were performed on the GaAs single crystal substrates of Samples 21 to 25 and Samples 201 to 203, and the silicon atomic concentration, carrier concentration, second carrier concentration, boron atomic concentration, average dislocation density, and dislocation-free rate were determined for each sample. The results are shown in Table 2. Table 2 also shows the off-angle of the main surface of the GaAs single crystal substrate of each sample, the structure of the increased diameter portion (presence or absence of an upper region and a lower region), and the value of S(A2) / (S(A1)+S(A2)) shown in the above formula I.

[0120] <Element yield> The GaAs single crystal substrates of samples 21 to 25 and samples 201 to 203 were subjected to the same method as that for determining the device yield in Example 1 to determine the device yield (%) of these samples. The results are shown in Table 2. In Table 2, as in Table 1, samples with a device yield of 90% or more were judged as A, samples with a device yield of 80% or more but less than 90% were judged as B, and samples with a device yield of less than 80% were judged as C.

[0121] [Table 2]

[0122] <Consideration> In the GaAs single crystal substrates of Samples 21 to 25, the off-angle of the main surface is 6°, and the average dislocation density of the main surface is 0 cm -2 More than 3.77cm -2 The dislocation-free rate was 98.04% or more. Furthermore, the silicon atomic concentration was 1.0 × 10 18 cm -3 Over 5.0 x 10 19 cm -3 The carrier concentration is 0.8×10 18 cm -34.0 × 10 above 18 cm -3 or less. Furthermore, the device yield in these GaAs single crystal substrates was 89.5% or more, and they were determined to be A or B. On the other hand, for the GaAs single crystal substrate of Sample 201, although the off-angle of the main surface was 6°, the average value of the dislocation density on the surface exceeded 3.77 cm -2 and the dislocation-free rate was less than 98.04%. Also, the GaAs single crystal substrate of Sample 201 was produced by a GaAs single crystal manufacturing apparatus having a structure in which the entire surface of the diameter-expanded portion contacts the crucible holding table. In that case, the device yield in the GaAs single crystal substrate of Sample 201 was less than 80% and was determined to be C. For the GaAs single crystal substrates of Sample 202 and Sample 203, although the off-angle of the main surface was 6°, the average value of the dislocation density on the surface exceeded 3.77 cm -2 and the dislocation-free rate was less than 98.04%. Also, the GaAs single crystal substrates of Sample 202 and Sample 203 did not satisfy the relationship of 0.1 < S(A2) / (S(A1)+S(A2)) < 0.8. In that case, the device yield in these GaAs single crystal substrates was less than 80% and was determined to be C. In particular, for the GaAs single crystal substrate of Sample 202, the lower region held by the crucible holding table was too small, making it difficult to grow a GaAs single crystal in a stable state of the crucible, and it is presumed that it had an adverse effect on the growth of the GaAs single crystal. For the GaAs single crystal substrate of Sample 203, the lower region held by the crucible holding table was too large, and it is presumed that the relationship between q(A1) and q(A2) became a relationship such as q(A1) ≥ q(A2), which had an adverse effect on the growth of the GaAs single crystal.

[0123] As described above, the embodiments and examples of the present disclosure have been explained. However, it has also been planned from the beginning to appropriately combine the configurations of the above-described embodiments and examples.

[0124] The embodiments and examples disclosed this time should be considered as illustrative in all respects and not restrictive. The scope of the present invention is shown not by the above-described embodiments and examples but by the claims, and it is intended that all modifications within the meaning and scope equivalent to the claims are included. [Explanation of symbols]

[0125] S10 preparation step, S20 step of obtaining a GaAs single crystal, S21 raw material charging step, S22 raw material melting step, S23 GaAs single crystal growth step, S30 step of obtaining a GaAs single crystal substrate, 10 GaAs single crystal growth apparatus, 5 crucible, 51 seed crystal accommodation section, 52 diameter increasing section, 521 upper region, 522 lower region, 53 straight body section, 6 crucible holder, 7 heating element, 75 thermocouple, 8a seed crystal, 81 gallium arsenide single crystal (GaAs single crystal), 82 gallium arsenide melt (GaAs melt), 1 gallium arsenide single crystal substrate (GaAs single crystal substrate), 11 main surface, 11a rectangular slice, 21 electrode, G virtual lattice, O center, 100 gallium arsenide single crystal (GaAs single crystal), 110 circular surface.

Claims

1. A method for producing a cylindrical gallium arsenide single crystal, comprising: The manufacturing method includes a step of growing a gallium arsenide single crystal from a seed crystal using a gallium arsenide single crystal manufacturing apparatus, the growth-side surface of the seed crystal is a plane having an off-angle of 4° or more and 20° or less from the (100) plane of the gallium arsenide single crystal, The gallium arsenide single crystal manufacturing apparatus includes a crucible having a partially cylindrical shape, a crucible holder that holds the crucible, and a heating element that heats the crucible; The crucible includes a seed crystal accommodating portion, an increasing diameter portion connected to the seed crystal accommodating portion, and a straight body portion connected to the increasing diameter portion on an opposite side to the seed crystal accommodating portion, the seed crystal accommodation portion has a cylindrical hollow portion that opens to a side connected to the diameter increasing portion and has a bottom wall formed on the opposite side, the increasing diameter portion has a truncated cone shape that increases in diameter axially upward, and is connected to the seed crystal accommodation portion at a small diameter side of the increasing diameter portion; The straight body portion has a hollow cylindrical shape and is connected to the large diameter side of the increased diameter portion, the crucible holder holds the increased diameter portion, the increased diameter section comprises an upper region and a lower region; the upper region is spaced apart from the crucible holder; The method for producing a gallium arsenide single crystal, wherein the lower region is in contact with the crucible holder.

2. 2. The method for producing a gallium arsenide single crystal according to claim 1, wherein the increased diameter portion satisfies the following formula I, where S(A1) is the surface area of ​​the upper region and S(A2) is the surface area of ​​the lower region. 0.2≦S(A2) / (S(A1)+S(A2))≦0.6 Formula I

3. 3. The method for producing a gallium arsenide single crystal according to claim 1, wherein the upper region faces the crucible holder in a direction perpendicular to the growth direction of the gallium arsenide single crystal.

4. 3. The method for producing a gallium arsenide single crystal according to claim 1, wherein the crucible holder is made of a single material.

5. The method for producing a gallium arsenide single crystal according to claim 4 , wherein the material is made of quartz.

6. The method for producing a gallium arsenide single crystal according to claim 4, wherein the material is opaque.

7. A method for manufacturing a gallium arsenide single crystal substrate having a circular main surface, comprising: The manufacturing method includes a step of cutting the gallium arsenide single crystal obtained by the manufacturing method of the gallium arsenide single crystal according to claim 1 or 2 into a disk shape and processing it to obtain a gallium arsenide single crystal substrate.

8. A gallium arsenide single crystal substrate having a circular main surface, the diameter of the gallium arsenide single crystal substrate is 200 mm or more and 210 mm or less; the main surface is a plane having an off angle of 4° or more and 20° or less from a (100) plane of the gallium arsenide single crystal, the off-axis direction of the plane having the off-axis angle is any one of the [01-1], [0-1-1], [0-11], and [011] directions, The average dislocation density of the main surface is 0 cm -2 3.77cm or more -2 is as follows: In a virtual lattice formed by arranging squares, each 2 mm on a side, on the main surface in such a manner that the maximum number of squares are arranged in parallel without overlapping each other, the ratio of the number of squares in which no dislocations exist to the total number of squares constituting the lattice is 98.04% or more, the gallium arsenide single crystal substrate comprises silicon; The silicon concentration is 1.0×10 18 cm -3 Above 5.0 x 10 19 cm -3 is as follows: The carrier concentration of the gallium arsenide single crystal substrate is 0.8×10 18 cm -3 Above 4.0 x 10 18 cm -3 The following is a gallium arsenide single crystal substrate.

9. the gallium arsenide single crystal substrate contains boron; The concentration of boron is 1.0×10 18 cm -3 Above 1.0 x 10 19 cm -3 9. The gallium arsenide single crystal substrate of claim 8, wherein:

10. A gallium arsenide single crystal having a cylindrical shape, the diameter of the circular surface forming the surface of the gallium arsenide single crystal is 200 mm or more and 210 mm or less; the circular surface is a surface having an off angle of 4° to 20° from the (100) plane of the gallium arsenide single crystal, the off-axis direction of the plane having the off-axis angle is any one of the [01-1], [0-1-1], [0-11], and [011] directions, The average dislocation density on the circular surface is 0 cm -2 3.77cm or more -2 is as follows: In a virtual lattice formed by arranging as many squares, each 2 mm on a side, as possible in parallel on the circular surface without overlapping each other, the ratio of the number of squares that do not have dislocations to the total number of squares that make up the lattice is 98.04% or more, the gallium arsenide single crystal contains silicon; The silicon concentration is 1.0×10 18 cm -3 Above 5.0 x 10 19 cm -3 is as follows: The carrier concentration of the gallium arsenide single crystal is 0.8×10 18 cm -3 Above 4.0 x 10 18 cm -3 Below is a gallium arsenide single crystal.

11. 11. The gallium arsenide single crystal according to claim 10, wherein the axial length of the cylindrical shape is 40 mm or more and 110 mm or less.

12. The carrier concentration at one end of the gallium arsenide single crystal is 0.8×10 18 cm -3 1.5 x 10 18 cm -3 is as follows: The carrier concentration at the other end of the gallium arsenide single crystal is 1.5×10 18 cm -3 3.5 x 10 18 cm -3 11. The gallium arsenide single crystal of claim 10, wherein:

13. The carrier concentration at one end of the gallium arsenide single crystal is 0.8×10 18 cm -3 1.5 x 10 18 cm -3 is as follows: The carrier concentration at the other end of the gallium arsenide single crystal is 1.5×10 18 cm -3 3.5 x 10 18 cm -3 12. The gallium arsenide single crystal of claim 11, wherein:

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