Patent Publication Number: US-2013243680-A1

Title: Group 13 nitride crystal and group 13 nitride crystal substrate

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority to and incorporates by reference the entire contents of Japanese Patent Application No. 2012-062235 filed in Japan on Mar. 19, 2012. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a group 13 nitride crystal and a group 13 nitride crystal substrate. 
     2. Description of the Related Art 
     Gallium nitride (GaN) based semiconductor materials are used for semiconductor devices, such as blue light-emitting diodes (LEDs), white LEDs, and laser diodes (LDs). White LEDs are used for backlights of mobile phone screens and liquid crystal displays and for lighting, for example. Blue LEDs are used for traffic lights and other illuminations, for example. Blue-violet LDs are used as light sources for Blu-ray discs. These days, most of GaN-based semiconductor devices used as ultraviolet, violet-blue-green light sources, are produced by performing crystal growth on a sapphire or silicon carbide (SiC) substrate with metal organic chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE), for example. 
     If sapphire or SiC is used as a substrate, crystal defects increase because of large difference in the coefficient of thermal expansion and in the lattice constant from a group 13 nitride. Such defects have negative effects on device characteristics, thereby making it difficult to extend the life of a light-emitting device or increasing operating power, for example. To address these problems, a GaN substrate made of the same material as that of the crystal growing on the substrate is most suitably used. 
     These days, a free-standing GaN substrate is manufactured by: growing GaN thickly on a dissimilar substrate, such as a sapphire substrate and a gallium arsenide (GaAs) substrate, by hydride vapor phase epitaxy (HVPE) using a growth method for reducing the dislocation density, such as epitaxial lateral overgrowth (ELO); and separating the GaN thick film from the dissimilar substrate. The dislocation density of the GaN substrate manufactured in this manner is reduced to approximately 10 6  cm 2 . Furthermore, such a GaN substrate having a size of 2 inches is put into practical use and is mainly used for laser devices. Recently, to reduce cost of white LEDs and apply a substrate to electronic devices, designing of a substrate with a larger diameter of 4 inches or 6 inches is required. 
     However, warpage and a crack occurring because of difference in the coefficient of thermal expansion and in the lattice constant between the dissimilar substrate material and the GaN prevent designing of a large-diameter substrate. Furthermore, the dislocation density described above still remains. In addition, because a GaN substrate is manufactured by separating one GaN thick film from one dissimilar substrate and polishing the GaN thick film, it costs a lot to manufacture the GaN substrate. 
     By contrast, a flux method of dissolving nitrogen from a vapor phase into a mixed melt of an alkali metal and a group 13 metal to grow a GaN crystal has been researched and developed as one of methods for realizing a GaN substrate by liquid phase growth. 
     In the flux method, by heating a mixed melt containing an alkali metal, such as sodium (Na) and potassium (K), and a group 13 metal, such as gallium (Ga), to approximately 600 degrees C. to 900 degrees C. under an atmosphere at nitrogen pressure of equal to or lower than 10 MPa, nitrogen is dissolved from a vapor phase. Subsequently, by causing the nitrogen to react with the group 13 metal in the mixed melt, a group 13 nitride crystal is grown. The flux method enables crystal growth at a lower temperature and a lower pressure than other liquid phase growth. In addition, the crystal thus grown advantageously has a dislocation density of lower than 10 6  cm 2 . 
     Chemistry of Materials Vol. 9 (1997) pp. 413-416 reports the fact that a GaN crystal was grown by placing sodium azide (NaN 3 ) and metal Ga serving as raw materials in a reaction container made of a stainless steel (inner dimension of the container: an inside diameter of 7.5 mm and a length of 100 mm) and sealing up the container under a nitrogen atmosphere, and maintaining the reaction container at a temperature from 600 degrees C. to 800 degrees C. for 24 hours to 100 hours. 
     Proc. 21st Century COE Joint Workshop on Bulk Nitrides IPAP Conf. Series 4 pp. 14-20 reports a dislocation and a tilt grain boundary generated when GaN is grown on a sapphire substrate by the MOCVD and the HVPE. 
     Japanese Patent Application Laid-open No. 2010-100449 discloses a method of growing a GaN crystal from a base substrate by the flux method. Japanese Patent No. 4588340 discloses a method of forming a mask film patterned on a base substrate and selectively growing GaN by the flux method. Japanese Patent Application Laid-open No. 2008-94704 discloses a method of using a needle crystal of aluminum nitride (AlN) as a seed crystal and growing a columnar crystal of GaN as a method for producing a large crystal of GaN. Japanese Patent Application Laid-open No. 2006-045047 discloses a method for producing a needle crystal of AlN serving as a seed crystal. Japanese Patent Application Laid-open No. 2010-254576 discloses a method for manufacturing a GaN substrate having a low dislocation by slicing a GaN crystal grown from a base substrate along a plane parallel to a growth direction. 
     In the conventional technology, however, it is difficult to provide a high-quality bulk crystal because of influences of a threading dislocation of a c-plane and a basal plane dislocation. 
     Therefore, there is a need to provide a group 13 nitride crystal applicable to a high-quality group 13 nitride semiconductor substrate and a group 13 nitride crystal substrate. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to at least partially solve the problems in the conventional technology. 
     According to an embodiment, there is provided a group 13 nitride crystal having a hexagonal crystal structure containing a nitrogen atom and at least one type of metal atom selected from the group consisting of B, Al, Ga, In, and Ti. The group 13 nitride crystal includes a basal plane dislocation in a plurality of directions, wherein dislocation density of the basal plane dislocation is higher than dislocation density of a threading dislocation of a c-plane. 
     According to another embodiment, there is provided a group 13 nitride crystal substrate including the group 13 nitride crystal according to the above embodiment. 
     The above and other objects, features, advantages and technical and industrial significance of this invention will be better understood by reading the following detailed description of presently preferred embodiments of the invention, when considered in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic perspective view of a structure of a group 13 nitride crystal; 
         FIG. 2  is an exemplary sectional view of the group 13 nitride crystal along a section parallel to a c-axis and an a-axis; 
         FIG. 3  is an exemplary sectional view of the group 13 nitride crystal along a c-plane (0001); 
         FIG. 4  is a schematic perspective view of another structure of the group 13 nitride crystal; 
         FIG. 5  is a schematic perspective view of still another structure of the group 13 nitride crystal; 
         FIG. 6  is a sectional view of a seed crystal along the c-axis; 
         FIG. 7  is a schematic sectional view of a structure of the seed crystal; 
         FIG. 8  is a schematic sectional view of another structure of the seed crystal; 
         FIG. 9  is a schematic sectional view of still another structure of the seed crystal; 
         FIG. 10  is a graph of an example of an emission spectrum caused by electron beam excitation or ultraviolet light excitation; 
         FIG. 11  is a schematic sectional view of a crystal producing apparatus that produces a seed crystal; 
         FIG. 12  is a schematic sectional view of a crystal producing apparatus that produces a group 13 nitride crystal; 
         FIG. 13  is a view schematically illustrating a dislocation on a section parallel to the c-axis and the a-axis in the group 13 nitride crystal; 
         FIG. 14  is a schematic of processing performed on the group 13 nitride crystal; 
         FIG. 15  is a schematic of another processing performed on the group 13 nitride crystal; 
         FIG. 16A  is a schematic of an example of a group 13 nitride crystal substrate; 
         FIG. 16B  is a schematic of another example of the group 13 nitride crystal substrate; 
         FIG. 16C  is a schematic of still another example of the group 13 nitride crystal substrate; 
         FIG. 17  is a schematic of a process in which the group 13 nitride crystal grows from the seed crystal; 
         FIG. 18  is a schematic of another process in which the group 13 nitride crystal grows from the seed crystal; 
         FIG. 19  is a schematic of still another process in which the group 13 nitride crystal grows from the seed crystal; 
         FIG. 20  is a schematic illustrating the relationship between the shape of the seed crystal and L/d; 
         FIG. 21  is a view of a mapping image of spectral intensity of photoluminescence from 360 nm to 370 nm; 
         FIG. 22  is a view of a mapping image of spectral intensity of photoluminescence from 500 nm to 800 nm; 
         FIG. 23  is a view schematically illustrating emission distribution of photoluminescence in an example; and 
         FIGS. 24A and 24B  are views schematically illustrating a group 13 nitride crystal in a comparative example. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Exemplary embodiments of a group 13 nitride crystal and a group 13 nitride crystal substrate according to the present invention are described below with reference to the accompanying drawings. In the description below, the drawings only schematically illustrate shapes, sizes, and arrangement of components so as to understand the present invention and are not intended to limit the present invention. Furthermore, similar components illustrated in a plurality of drawings are represented by the same reference numerals, and a duplicated explanation thereof may be omitted. 
     A group 13 nitride crystal according to an embodiment of the present invention is a group 13 nitride crystal having a hexagonal crystal structure containing at least one type of metal atom selected from the group consisting of B, Al, Ga, In, and Tl, and a nitrogen atom. The group 13 nitride crystal according to the present embodiment has a basal plane dislocation in a plurality of directions, and the dislocation density of the basal plane dislocation is higher than the dislocation density of a threading dislocation of a c-plane. 
     The basal plane dislocation (BPD) is a dislocation in a direction parallel to the c-plane (a plane perpendicular to a c-axis). In the group 13 nitride crystal according to the present embodiment, the BPD is present not in one direction but in a plurality of directions different from one another on a plane parallel to the c-plane. As a result, occurrence of warpage and distortion is suppressed compared with the case where a dislocation in a direction parallel to the c-plane is present in one direction. 
     Furthermore, in the group 13 nitride crystal according to the present embodiment, the dislocation density of the BPD is higher than the dislocation density of the threading dislocation of the c-plane. The threading dislocation of the c-plane is a dislocation in a direction threading through the c-plane. Thus, the dislocation in a direction threading through the c-plane is suppressed. 
     Therefore, it is possible to provide a group 13 nitride crystal of high quality. 
     Detailed description will be made below. 
     [1] Group 13 Nitride Crystal 
     As described above, the group 13 nitride crystal according to the present embodiment is a group 13 nitride crystal having a hexagonal crystal structure containing at least one type of metal atom selected from the group consisting of B, Al, Ga, In, and Ti, and a nitrogen atom. The group 13 nitride crystal according to the present embodiment preferably contains at least one of Ga and Al as the metal atom and more preferably contains at least Ga. 
       FIG. 1  to  FIG. 3  illustrate an example of a group 13 nitride crystal  19  according to the present embodiment. In more detail,  FIG. 1  is a schematic perspective view of an example of a structure of the group 13 nitride crystal  19  according to the present embodiment.  FIG. 2  is a sectional view of the group 13 nitride crystal  19  along a section parallel to the c-axis and an a-axis.  FIG. 3  is a sectional view of the group 13 nitride crystal  19  along a c-plane cross-section (a cross-section parallel to the c-plane). 
     As illustrated in  FIG. 3 , the c-plane cross-section of the group 13 nitride crystal  19  is a hexagon. In the present embodiment, examples of the hexagon include a regular hexagon and hexagons other than the regular hexagon. The side surface of the group 13 nitride crystal  19  corresponding to a side of the hexagon is mainly formed of a {10-10} m-plane of the hexagonal crystal structure. 
       FIG. 1  illustrates the group 13 nitride crystal  19  in a columnar shape with a hexagonal pyramid, having a bottom surface on the c-plane (0001) and a central axis along the c-axis, provided on a hexagonal columnar crystal having a bottom surface on the c-plane (0001) and a central axis along the c-axis (that is, a &lt;0001&gt; direction). However, the group 13 nitride crystal  19  simply needs to have a hexagonal crystal structure and is not limited to a columnar crystal. The group 13 nitride crystal  19 , for example, may have a shape with the c-plane formed at the apex of the hexagonal pyramid of the group 13 nitride crystal  19  illustrated in  FIG. 1 . 
       FIG. 4  and  FIG. 5  are schematics of an example of the group 13 nitride crystal  19  in a shape with the c-plane formed at the apex of the hexagonal pyramid. As illustrated in  FIG. 4  and  FIG. 5 , the group 13 nitride crystal  19  has a hexagonal crystal structure and may be in a shape with the c-plane formed at the apex of the hexagonal pyramid of the group 13 nitride crystal  19  illustrated in  FIG. 1 . 
     Referring back to  FIG. 1 , the group 13 nitride crystal  19  according to the present embodiment is a single crystal and includes a first area  21  and a second area  27 . The first area  21  is an area provided to the inner side of the c-plane cross-section in the group 13 nitride crystal  19 . The first area  21  is a seed crystal, and the second area  27  is an area grown from the seed crystal. The first area  21  and the second area  27  have different crystallinities. The first area  21  and the second area  27  will be described later in detail. The group 13 nitride crystal  19  simply needs to be a crystal including the second area  27 . 
     As described above, the group 13 nitride crystal  19  according to the present embodiment has a BPD in a plurality of directions different from one another. Furthermore, the dislocation density of the BPD is higher than the dislocation density of a dislocation in a direction threading through the c-plane in the group 13 nitride crystal  19 . 
     In the group 13 nitride crystal  19 , the dislocation density of the BPD simply needs to be higher than the dislocation density of the threading dislocation of the c-plane. More specifically, the dislocation density of the BPD is preferably equal to or more than 100 times higher than the dislocation density of the threading dislocation of the c-plane and more preferably equal to or more than 1000 times higher than the dislocation density of the threading dislocation of the c-plane. 
     In the group 13 nitride crystal  19 , the dislocation density of the BPD and the dislocation density of the threading dislocation of the c-plane are measured by the following method. 
     For example, by etching the outermost surface of a measurement target surface, an etch pit is formed; subsequently, a micrograph of a structure of the measurement target surface thus etched is captured using an electron microscope; and the etch-pit density is calculated from the micrograph thus obtained. 
     Examples of the method for measuring the dislocation density include a method of measuring the measurement target surface by cathodoluminescence (CL). 
     The c-plane, the m-plane {10-10}, and an a-plane {11-20} are used as the measurement target surface, for example. 
       FIG. 3  is a schematic illustrating the case where the c-plane (c-plane cross-section) of the group 13 nitride crystal  19  is used as the measurement target surface. 
     As illustrated in  FIG. 3 , the c-plane cross-section of the group 13 nitride crystal  19  is etched as described above and is observed with the electron microscope or by CL. As a result, a plurality of dislocations are found. By counting a linear dislocation as a BPD P among the dislocations found on the c-plane cross-section, the dislocation density of the BPD P is calculated. By contrast, by counting a dot dislocation as a threading dislocation Q among the dislocations found on the c-plane cross-section, the dislocation density of the threading dislocation Q is calculated. In the case of CL, a dislocation is found as a dark dot or a dark line. 
     In respect to the dot dislocation, if the ratio of a major axis of a dot dislocation thus found to a minor axis thereof is equal to or larger than 1 and equal to or smaller than 1.5, the dislocation is counted as a “dot” dislocation in the present embodiment. Thus, the dot dislocation is not limited to a perfect circle, and an elliptically shaped dislocation is also counted as a dot dislocation. More specifically, a dislocation having a major axis of equal to or smaller than 0.5 μm in a sectional shape thus found is counted as the dot dislocation in the present embodiment. 
     By contrast, in respect to the linear dislocation, if the ratio of a major axis of a linear dislocation thus found to a minor axis thereof is equal to or larger than 4, the dislocation is counted as a “linear” dislocation in the present embodiment. More specifically, a dislocation having a major axis of larger than 2 μm in a sectional shape thus found is counted as the linear dislocation in the present embodiment. 
       FIG. 4  is a schematic illustrating the case where the side surface (m-plane {10-10}) in the hexagonal group 13 nitride crystal  19  is used as the measurement target surface. 
     As illustrated in  FIG. 4 , the m-plane {10-10} of the group 13 nitride crystal  19  is etched as described above and is observed with the electron microscope or by CL. As a result, a plurality of dislocations are found. By counting a dot dislocation as the BPD P among the dislocations found on the m-plane {10-10}, the dislocation density of the BPD P is calculated. A linear dislocation in a direction perpendicular to the c-axis is also counted as the BPD P. By contrast, among the dislocations found on the m-plane {10-10}, a linear dislocation extending in the c-axis direction can be counted as the threading dislocation Q. 
     The definitions of the dot dislocation and the linear dislocation are the same as those described above. 
       FIG. 5  is a schematic illustrating the case where an m-plane parallel to the a-axis and the c-axis in the hexagonal group 13 nitride crystal  19  is used as the measurement target surface.  FIG. 5  illustrates a cross-section parallel to the c-axis and passing through the first area  21 , which is the seed crystal, in the group 13 nitride crystal  19 . 
     As illustrated in  FIG. 5 , the m-plane {10-10} of the group 13 nitride crystal  19  is etched as described above and is observed with the electron microscope or by CL. As a result, a plurality of dislocations are found. Among the dislocations found on the m-plane {10-10} in  FIG. 5 , a linear dislocation extending in a direction parallel to the a-axis can be counted as the BPD P. By contrast, a linear dislocation extending in a direction parallel to the c-axis can be counted as the threading dislocation Q. The definitions of the dot dislocation and the linear dislocation are the same as those described above. 
     Referring back to  FIG. 3 , the BPDs P in the group 13 nitride crystal  19  according to the present embodiment include a dislocation extending in a direction from the first area  21  to the second area  27 . In other words, as illustrated in  FIG. 3 , the BPD P is present on a plane parallel to the c-plane as a dislocation extending in a direction outward in the second area  27 , which is an area grown from the seed crystal. 
     The dislocation density of the BPD in the group 13 nitride crystal  19  is higher than the density of grain boundary on the c-plane. 
     The grain boundary is an interface between crystals and can be considered as an aggregate of dislocations. The dislocation density of the BPD in the group 13 nitride crystal  19  simply needs to be higher than the density of grain boundary on the c-plane. More specifically, the dislocation density of the BPD in the group 13 nitride crystal  19  is preferably equal to or more than 10 times higher than the density of grain boundary on the c-plane and more preferably equal to or more than 100 times higher than the density of grain boundary on the c-plane. 
     The density of grain boundary is measured by the following method. 
     The density of grain boundary can be measured by a well-known crystal analysis method. By using the measurement target surface etched in the etching for measurement of the dislocation density, for example, the density of grain boundary can be measured by an analysis method, such as X-ray diffraction, X-ray topography, simple light reflection, CL, and a micro-level analysis of an atomic image captured by a transmission electron microscope. 
     By comparing an image obtained by white X-ray topography using radiated light with an appearance of a crystal, the number of grain boundaries can be determined. If the appearance of the crystal and the external form of the image obtained by the topography are similar to each other, it is determined that a small number of grain boundaries are present. By contrast, if the external form of the image obtained by the topography is significantly distorted or only a part of the crystal is shown in the image, it is determined that a large number of grain boundaries are present. 
     The density of grain boundary of a cross-section intersecting the c-plane is preferably higher than the density of grain boundary on the c-plane in the group 13 nitride crystal  19  according to the present embodiment. 
     The density of grain boundary of the cross-section intersecting the c-plane in the group 13 nitride crystal  19  is more preferably equal to or more than 10 times higher than the density of grain boundary on the c-plane and particularly preferably equal to or more than 100 times higher than the density of grain boundary on the c-plane. 
     The number of grain boundaries per 1 cm 2  on the c-plane of the group 13 nitride crystal  19  is preferably equal to or less than 1 and is particularly preferably 0. 
     The grain boundary and the density of grain boundary may be measured by the method described above. 
     The first area  21  that is a seed crystal and the second area  27  that is a growth area where crystal has grown from the seed crystal in the group 13 nitride crystal  19  will now be described in detail. 
     The second area  27  is provided in a manner covering at least a part of the outer circumference of the first area  21  on the c-plane cross-section in the group 13 nitride crystal  19 . The second area  27  simply needs to be provided in a manner covering at least a part of the outer circumference of the first area  21  and may be provided in a manner covering the entire outer circumference of the first area  21 . In the group 13 nitride crystal  19  illustrated in  FIG. 3 , the second area  27  is provided in a manner covering the entire outer circumference of the first area  21 . 
     The thickness of the second area  27  on the c-plane cross-section is larger than the maximum diameter of the first area  21 . The thickness of the second area  27  is the maximum length, that is, the maximum thickness of the second area  27  in a direction from the center of the first area  21  to the outer edge of the group 13 nitride crystal  19  on the c-plane cross-section. In the example of  FIG. 3 , the thickness of the second area  27  is represented by a length L 2 . 
     The maximum diameter of the first area  21  is the maximum value of the diameter of the first area  21  and is represented by a length L 1  in the example of  FIG. 3 . 
     The relationship between the thickness of the second area  27  and the maximum diameter of the first area  21  on the c-plane cross-section of the group 13 nitride crystal  19  according to the present embodiment is not particularly restricted as long as it satisfies the relationship described above. More specifically, the thickness of the second area  27  is preferably equal to or more than 5 times larger than the maximum diameter of the first area  21  and is more preferably equal to or more than 10 times larger than the maximum diameter of the first area  21 . 
     The carrier concentration of the second area  27  is higher than the carrier concentration of the first area  21 . In the group 13 nitride crystal  19  according to the present embodiment, the relationship between the carrier concentrations of the first area  21  and the second area  27  is not particularly restricted as long as it satisfies the relationship described above. More specifically, the carrier concentration of the second area  27  is preferably equal to or more than 5 times higher than the carrier concentration of the first area  21  and more preferably equal to or 10 times higher than the carrier concentration of the first area  21 . 
     Furthermore, the relationship between the carrier concentrations of the first area  21  and the second area  27  is not particularly restricted as long as it satisfies the relationship described above. More specifically, the carrier concentration of the first area  21  is preferably equal to or lower than 2×10 18 /cm 3  or equal to or lower than 8×10 17 /cm 3 . The carrier concentration of the second area  27  is preferably equal to or higher than 4×10 18 /cm 3  or equal to or higher than 8×10 18 /cm 3 . 
     In the present embodiment, the carrier corresponds to an electron, and the carrier concentration corresponds to the electron carrier concentration. 
     The carrier concentrations of the first area  21  and the second area  27  are measured by the following measuring method. 
     The carrier concentrations of the first area  21  and the second area  27  are measured by converting the carrier density using Raman spectroscopy. To convert the carrier concentration, “Journal of the Spectroscopical Society of Japan 49 (2000) Characterization of GaN and Related Nitrides by Raman Scattering: Hiroshi Harima” is used. As a measuring device, a laser Raman spectroscopic device is used for the measurement. 
     The carrier concentrations of the first area  21  and the second area  27  are controlled so as to satisfy the relationship described above by controlling production conditions in a production method of the group 13 nitride crystal  19 , which will be described later. Furthermore, the size of the first area  21  and the second area  27  (the thickness and the diameter) are also controlled so as to satisfy the relationship described above by controlling production conditions in the production method of the group 13 nitride crystal  19 , which will be described later. 
     The first area  21  of the group 13 nitride crystal  19  according to the present embodiment may be formed of a plurality of areas. As illustrated in  FIG. 6  to  FIG. 8 , for example, a first area  21 A may be used instead of the first area  21 . 
       FIG. 6  to  FIG. 8  illustrate an example of a crystal having a hexagonal crystal structure formed of the first area  21 A. In more detail,  FIG. 6  is a view of a cross-section parallel to the c-axis and the a-axis in the hexagonal crystal formed of the first area  21 A.  FIG. 7  and  FIG. 8  are sectional views of the c-plane cross-section in the hexagonal crystal formed of the first area  21 A. 
     A third area  29   a  is provided inside of the first area  21 A on the c-plane cross-section. Furthermore, a fourth area  29   b  is provided in a manner covering at least a part of the outer circumference of the third area  29   a.    
     The fourth area  29   b  simply needs to be provided in a manner covering at least a part of the outer circumference of the third area  29   a . Therefore, the fourth area  29   b  may be provided in a manner covering the entire outer circumference of the third area  29   a  (refer to  FIG. 8 ). Alternatively, a part of the outer circumference of the third area  29   a  may have a portion to which the fourth area  29   b  is not provided (refer to  FIG. 7 ). 
     Similarly to the example described above, the first area  21 A simply needs to include the third area  29   a  and the fourth area  29   b  on at least one of cross-sections intersecting the c-axis, and the cross-section is not limited to the c-plane cross-section strictly. 
     While the thickness of the fourth area  29   b  is not restricted, the thickness is preferably equal to or larger than 100 nm, for example. 
     If a group 13 nitride crystal is grown by the flux method using a GaN crystal as a seed crystal, melt-back of the seed crystal may possibly occur. In terms of melt-back, it is known that the amount of dissolution (amount of melt-back) increases if the seed crystal is poor in quality, particularly, if an affected layer remains in the seed crystal. 
     To address this, the fourth area  29   b  that is a crystal layer of higher quality than that of the third area  29   a  is provided by a thickness of equal to or larger than 100 nm at the outer side of the crystal. Therefore, even if melt-back occurs in a process of growing the seed crystal, the fourth area  29   b  is likely to remain, thereby facilitating growth of the second area  27  of higher quality. 
     While the c-plane cross-section of the group 13 nitride crystal  19  and the cross-sections of the areas are shown as regular hexagons in  FIG. 3 ,  FIG. 7 ,  FIG. 8 , and other figures, these figures are given just as schematics, and each of the cross-sections is not limited to a regular hexagon. The c-plane cross-section of the group 13 nitride crystal  19  and the c-plane cross-sections of the areas are each formed in a nearly hexagonal shape by the cross-section of the group 13 nitride crystal  19  having a hexagonal crystal structure. If other structures are formed at the inside or the boundary of the cross-sections in the process of crystal growth, the outline of each hexagon may possibly be deformed by the boundaries of the other structures. 
     Furthermore, the group 13 nitride crystal  19  is not necessarily formed only of the areas described above (the first area  21  or the first area  21 A, and the second area  27 ). The group 13 nitride crystal  19  may further include other structures and other areas (e.g., the N-th area (N represents an integer equal to or more than 5 in the present embodiment)) having optical characteristics. 
       FIG. 9  is a view of an example of a crystal having a hexagonal crystal structure formed of a first area  21 B. In more detail,  FIG. 9  is a sectional view of the c-plane cross-section in the hexagonal crystal formed of the first area  21 B. 
     As illustrated in  FIG. 9 , the third area  29   a  is provided in the first area  21 B. Furthermore, a fourth area  29   b   1  and a fourth area  29   b   2  may be provided in a manner covering at least a part of the outer circumference of the third area  29   a.    
     Properties Of Each Area 
     Crystal properties of the first area  21  (the first area  21 A and the first area  21 B) and the second area  27  of the group 13 nitride crystal  19  will now be described. 
     Light Emission Property 
     The peak intensity of a first peak including band-edge emission of GaN in an emission spectrum caused by electron beam excitation or ultraviolet light excitation in the third area  29   a  and the fourth area  29   b  on the c-plane cross-section of the group 13 nitride crystal  19  according to the present embodiment and the peak intensity of a second peak on the longer-wavelength side than the first peak have the following relationship. 
     Specifically, the peak intensity of the first peak in the third area  29   a  is lower than the peak intensity of the second peak, and the peak intensity of the first peak in the fourth area  29   b  is higher than the peak intensity of the second peak. 
     The peak intensity of the first peak and the peak intensity of the second peak in the third area  29   a  and the fourth area  29   b  are not restricted as long as they satisfy the relationship described above. More specifically, the peak intensity of the first peak in the fourth area  29   b  is preferably higher than the peak intensity of the first peak in the third area  29   a . Furthermore, the peak intensity of the second peak in the fourth area  29   b  is preferably lower than the peak intensity of the second peak in the third area  29   a.    
     The first peak is light emission including band-edge emission (hereinafter, simply referred to as band-edge emission) of GaN in the measurement target area of the group 13 nitride crystal  19  and is a peak of an emission spectrum appearing in a wavelength range of approximately 364 nm in measurement at room temperature. The band-edge emission of GaN is light emission due to recombination of a hole at the upper edge of a valence band and an electron at the bottom of a conduction band in the group 13 nitride crystal  19  and is emission of light having energy (wavelength) equal to the band gap. In other words, the first peak is a peak caused by binding (a binding state) of nitrogen and gallium and a periodic structure of the crystal in the group 13 nitride crystal  19 . The first peak may include the band-edge emission and emission from the vicinity of the band edge. 
     The second peak is at least one peak appearing on the longer-wavelength side than the first peak and is a peak including light emission caused by impurities and defects, for example. 
     More preferably, the second peak falls within a wavelength range from 450 nm to 650 nm in an emission spectrum caused by electron beam excitation or ultraviolet light excitation in measurement at room temperature. 
     Still more preferably, the second peak falls within a wavelength range from 590 nm to 650 nm in an emission spectrum caused by electron beam excitation or ultraviolet light excitation in measurement at room temperature. 
       FIG. 10  is a graph of an example of an emission spectrum caused by electron beam excitation or ultraviolet light excitation in the third area  29   a  and the fourth area  29   b.    
     In the emission spectrum in the third area  29   a , the peak intensity of the second peak is higher than the peak intensity of the first peak. This indicates that the third area  29   a  contains a relatively large number of impurities and defects. By contrast, in the emission spectrum in the fourth area  29   b , the peak intensity of the first peak is higher than the peak intensity of the second peak. This indicates that the fourth area  29   b  contains a relatively small number of impurities and defects and that the crystal of the fourth area  29   b  is excellent in quality. 
     Therefore, in the production method of the group 13 nitride crystal  19 , which will be described later, if the crystal formed of the first area  21 A is used as the seed crystal, it is possible to facilitate production of the group 13 nitride crystal  19  of higher quality compared with the case where the crystal formed of the first area  21  is used as the seed crystal. This is because crystal growth can be performed on the fourth area  29   b  having less impurities and defects by using the seed crystal formed of the first area  21 A provided with the fourth area  29   b  having less impurities and defects on the outer side thereof. 
     Furthermore, in the production of a larger group 13 nitride crystal  19  by using the seed crystal formed of the first area  21 A, the crystal growth can be performed from an area abutting on the fourth area  29   b  having less impurities, defects, and the like than the third area  29   a . Thus, it is possible to obtain the second area  27  that is excellent in crystal quality and larger in size. 
     Examples of the impurities in the present embodiment include B, Al, 0, Ti, Cu, Zn, Si, Na, K, Mg, Ca, W, C, Fe, Cr, Ni, and H. 
     In the fourth area  29   b  illustrated in  FIG. 9 , the emission intensity of the first peak in the fourth area  29   b   2  is lower than the emission intensity of the first peak in the fourth area  29   b   1 , which is not illustrated. 
     Boron Concentration 
     The boron concentration of the third area  29   a  is higher than the boron concentration of the fourth area  29   b . Specifically, for example, the boron concentration of the third area  29   a  is preferably equal to or higher than 4×10 18  atms/cm 3 , and the boron concentration of the fourth area  29   b  positioned outside of the third area  29   a  is preferably lower than 4×10 18  atms/cm 3 . 
     More preferably, the boron concentration of the third area  29   a  is equal to or higher than 6×10 18  atms/cm 3 , and the boron concentration of the fourth area  29   b  is lower than 1×10 18  atms/cm 3 . 
     In the production of the group 13 nitride crystal  19  by crystal growth from the seed crystal of the first area  21 A provided with the fourth area  29   b  outside of the third area  29   a , if the boron concentrations satisfy the relationship described above, it is possible to start the crystal growth mainly from the outer circumferential surface of the fourth area  29   b  with a low boron concentration and high quality. Therefore, even in the production of the group 13 nitride crystal  19  having a longer dimension in the c-axis direction using the seed crystal of the first area  21 A elongated in the c-axis direction by a boron addition process, it is possible to produce the group 13 nitride crystal  19  of high quality. 
     Production Method 
     The production method of the group 13 nitride crystal  19  will now be described. 
     The group 13 nitride crystal  19  is produced by using the seed crystal of the first area  21 , the seed crystal of the first area  21 A, or the seed crystal of the first area  21 B, and performing crystal growth from the seed crystal. 
     The seed crystal of the first area  21  and the seed crystals of the first area  21 A and the first area  21 B have a hexagonal crystal structure and are elongated in the c-axis direction. In the seed crystal of the first area  21  and the seed crystals of the first area  21 A and the first area  21 B, a cross-section (c-plane cross-section) perpendicular to the c-axis is a hexagon. The side surface of the seed crystal corresponding to a side of the hexagon is mainly formed of the m-plane of the hexagonal crystal structure. 
     The production method will be described in detail. 
     [2] Crystal Production Method of a Seed Crystal 
     Crystal Producing Apparatus 
       FIG. 11  is a schematic sectional view of a crystal producing apparatus  1  that produces a seed crystal  30  serving as the seed crystal of the first area  21  and the seed crystal of the first area  21 A according to the present embodiment. In the description below, the seed crystal of the first area  21  and the seed crystals of the first area  21 A and the first area  21 B may be collectively referred to as the seed crystal  30 . 
     As illustrated in  FIG. 11 , the crystal producing apparatus  1  has a dual structure: an inner container  11  is arranged in an outer pressure-resistant container  28  made of a stainless steel; and the inner container  11  houses a reaction container  12 . The inner container  11  is attachable to and detachable from the outer pressure-resistant container  28 . 
     The reaction container  12  is a container that contains therein a mixed melt  24  in which raw materials and additives are melted to provide the seed crystal  30 . The configuration of the reaction container  12  will be described later. 
     Gas supply pipes  22  and  32  are connected to the outer pressure-resistant container  28  and the inner container  11 , respectively. The gas supply pipes  22  and  32  supply a nitrogen (N 2 ) gas, which is a raw material of a group 13 nitride crystal, and a diluent gas for adjusting the total pressure to an internal space  33  of the outer pressure-resistant container  28  and an internal space  23  of the inner container  11 , respectively. A gas supply pipe  14  is bifurcated into a N 2  supply pipe  17  and a diluent gas supply pipe  20 , and these pipes can be separated from the gas supply pipe  14  by valves  15  and  18 , respectively. 
     While an argon (Ar) gas, which is an inert gas, is preferably used as the diluent gas, the diluent gas is not limited thereto. Other inert gasses, such as helium (He), may be used as the diluent gas. 
     The N 2  gas is supplied from the N 2  supply pipe  17  connected, for example, to a gas cylinder of the N 2  gas. After the pressure of the N 2  gas is controlled by a pressure control device  16 , the N 2  gas is supplied to the gas supply pipe  14  through the valve  15 . By contrast, the diluent gas (e.g., an Ar gas) is supplied from the diluent gas supply pipe  20  connected, for example, to a gas cylinder of the diluent gas. After the pressure of the diluent gas is controlled by a pressure control device  190 , the diluent gas is supplied to the gas supply pipe  14  through the valve  18 . The N 2  gas and the diluent gas whose pressure is controlled in this manner are supplied to the gas supply pipe  14  and mixed. 
     The mixed gas of the N 2  gas and the diluent gas is supplied to the outer pressure-resistant container  28  and the inner container  11  through valves  31  and  29 , respectively, from the gas supply pipe  14 . The inner container  11  can be detached from the crystal producing apparatus  1  at the portion of the valve  29 . 
     The gas supply pipe  14  is provided with a pressure gauge  220 . Therefore, it is possible to control the pressure in the outer pressure-resistant container  28  and the inner container  11  while monitoring the total pressure in the outer pressure-resistant container  28  and the inner container  11  with the pressure gauge  220 . 
     In the present embodiment, by controlling the pressure of the N 2  gas and the diluent gas in this manner with the valves  15  and  18  and the pressure control devices  16  and  190 , respectively, the partial pressure of N 2  can be controlled. Furthermore, because the total pressure in the outer pressure-resistant container  28  and the inner container  11  can be controlled, evaporation of an alkali metal (e.g., sodium) in the reaction container  12  can be suppressed by setting the total pressure in the inner container  11  higher. In other words, it is possible to control the partial pressure of N 2  serving as a raw material for nitrogen affecting crystal growth conditions of GaN and the total pressure affecting suppression of evaporation of sodium separately. 
     As illustrated in  FIG. 11 , a heater  13  is arranged around the inner container  11  in the outer pressure-resistant container  28 . The heater  13  can heat the inner container  11  and the reaction container  12 , thereby enabling control of the temperature of the mixed melt  24 . 
     In the present embodiment, the seed crystal  30  is produced by the flux method. An explanation will be made of the case where the seed crystal of the first area  21 A (including the third area  29   a  and the fourth area  29   b ) or of the first area  21 B is produced as the seed crystal  30 . 
     To produce the seed crystal of the first area  21 A or the first area  21 B as the seed crystal  30 , the following processes are performed: a boron dissolution process for dissolving boron into the mixed melt  24 ; a boron incorporation process for, during the growth of the GaN crystal, incorporating boron into the crystal; and a boron reduction process for lowering the boron concentration in the mixed melt  24  along with the crystal growth so as to perform crystal growth with different boron concentrations for the inner side of the crystal and the outer side of the crystal in the seed crystal  30 . 
     To produce the seed crystal of the first area  21 , a method may be employed in which the boron dissolution process and the boron incorporation process are performed and the boron reduction process is not performed. For this reason, an explanation will be made of the method for producing the seed crystal of the first area  21 A as the seed crystal  30 . The method for producing the seed crystal of the first area  21 B is the same as that for producing the first area  21 A. 
     In the boron dissolution process, boron is dissolved into the mixed melt  24  from boron nitride (BN) contained in the inner wall of the reaction container  12  or a BN member arranged in the reaction container  12 . The dissolved boron is then incorporated into a growing crystal (the boron incorporation process). Subsequently, along with the crystal growth, the amount of boron incorporated into the crystal is gradually reduced (the boron reduction process). 
     In the boron reduction process, if the seed crystal  30  grows while growing the m-plane ({10-10} plane), the boron concentration in the outer side area can be made lower than the boron concentration in the inner side area on a cross-section intersecting the c-axis. As a result, the concentration of boron that is an impurity and the dislocation density possibly caused by impurities in the crystal are reduced in the outer circumferential surface (six side surfaces of the hexagonal column) formed of the m-plane of the seed crystal  30 . Thus, it is possible to form the outer circumferential surface of the seed crystal  30  with a crystal of excellent quality compared with the inner side area of the seed crystal  30 . 
     In the method for producing the group 13 nitride crystal  19  (specifically, the second area  27 ) by performing crystal growth from the seed crystal  30 , which will be described later in [3], the group 13 nitride crystal  19  grows mainly from the side surface (the outer circumferential surface formed of the m-plane) of the seed crystal  30  serving as a starting point of the crystal growth. Therefore, if the outer circumferential surface formed of the m-plane of the seed crystal  30  is excellent in quality as described above, the crystal growing therefrom is also excellent in quality. Thus, according to the present embodiment, it is possible to grow the seed crystal  30  that is large in size and excellent in quality and to provide the group 13 nitride crystal  19  (specifically, the second area  27 ) of high quality as a result of the crystal growth. 
     The boron dissolution process, the boron incorporation process, and the boron reduction process will now be described more specifically. 
     (1) Method for Causing the Reaction Container  12  to Contain BN 
     In an example of the boron dissolution process, the reaction container  12  made of a sintered compact of BN (a BN sintered compact) may be used as the reaction container  12 . While the reaction container  12  is being heated to a crystal growth temperature, boron is melted from the reaction container  12  and dissolved into the mixed melt  24  (the boron dissolution process). In the growth process of the seed crystal  30 , the boron in the mixed melt  24  is incorporated into the seed crystal  30  (the boron incorporation process). Subsequently, along with the growth of the seed crystal  30 , the boron in the mixed melt  24  is gradually reduced (the boron reduction process). 
     While the reaction container  12  made of a BN sintered compact is used in the description above, the structure of the reaction container  12  is not limited thereto. Preferably, a substance containing BN (e.g., a BN sintered compact) is used at least a part of the inner wall having contact with the mixed melt  24  in the reaction container  12 . For the other parts of the reaction container  12 , a nitride such as pyrolytic BN (P-BN), an oxide such as alumina and yttrium aluminum garnet (YAG), and a carbide such as SIC may be used, for example. 
     (2) Method for Arranging a Member Containing BN in the Reaction Container  12   
     In another example of the boron dissolution process, a member containing BN may be arranged in the reaction container  12 . A member made of a BN sintered compact may be arranged in the reaction container  12 , for example. Similarly to (1), the material of the reaction container  12  is not particularly restricted. 
     In this method, while the reaction container  12  is being heated to the crystal growth temperature described above, boron is gradually dissolved into the mixed melt  24  from the member arranged in the reaction container  12  (the boron dissolution process). 
     In the methods of (1) and (2), a crystal nucleus of a GaN crystal is likely to be formed on the surface of the member containing BN and having contact with the mixed melt  24 . Therefore, if the crystal nucleus of GaN is formed on the surface of BN (that is, the inner wall surface or the surface of the member described above) and the surface is gradually covered with the crystal nucleus, the amount of boron dissolved into the mixed melt  24  from the BN thus covered is gradually reduced (the boron reduction process). Furthermore, along with the growth of the GaN crystal, the surface area of the crystal increases, whereby the density of incorporation of boron into the GaN crystal decreases (the boron reduction process). 
     While the explanation has been made of the case where boron is dissolved into the mixed melt  24  by using a substance containing boron in (1) and (2), the method for dissolving boron into the mixed melt  24  is not limited thereto. Other methods, such as addition of boron to the mixed melt  24 , may be employed. Also for the method for reducing the boron concentration in the mixed melt  24 , other methods may be employed. The crystal production method according to the present embodiment simply needs to include the boron dissolution process, the boron incorporation process, and the boron reduction process described above. 
     Adjustment of Raw Material and the Like and Crystal Growth Conditions 
     Input of a raw material and the like to the reaction container  12  is performed by placing the inner container  11  in a glove box under an inert gas, such as an argon gas, atmosphere. 
     To produce the seed crystal  30  by the method of (1), the substance containing boron described in (1), a substance to be used as a flux, and the raw material are input to the reaction container  12  with the structure described in (1). 
     To produce the seed crystal  30  by the method of (2), the member containing boron described in (2), the substance to be used as a flux, and the raw material are input to the reaction container  12  with the structure described in (2). 
     While sodium or a sodium compound (e.g., sodium azide) is used as the substance to be used as a flux, the other alkali metals, such as lithium and potassium, and a compound of such an alkali metal may be used, for example. Alternatively, an alkaline earth metal, such as barium, strontium, and magnesium, and a compound of such an alkaline earth metal may be used. Furthermore, a plurality of types of alkali metals or alkaline earth metals may be used. 
     While gallium is used as the raw material, the other group 13 elements, such as boron, aluminum, indium, and a mixture of these elements may be input to the reaction container  12  as the raw material. 
     While the explanation has been made of the case where the reaction container  12  has a structure containing boron in the present embodiment, the structure is not limited thereto. The reaction container  12  may have a structure containing at least one of B, Al, O, Ti, Cu, Zn, and Si. 
     After setting the raw material and the like in this manner, the heater  13  is turned ON to heat the inner container  11  and the reaction container  12  inside thereof to the crystal growth temperature. As a result, the substance to be used as a flux and the raw material and the like are melted together to form the mixed melt  24 . By bringing N 2  at the partial pressure described above into contact with the mixed melt  24  and dissolving the N 2  into the mixed melt  24 , it is possible to supply the N 2  serving as the raw material of the seed crystal  30  to the mixed melt  24 . Furthermore, boron is dissolved into the mixed melt  24  as described above (the boron dissolution process) (a mixed melt formation process). 
     On the inner wall of the reaction container  12 , a crystal nucleus of the seed crystal  30  is formed from the raw material and the boron dissolved in the mixed melt  24 . Subsequently, the raw material and the boron in the mixed melt  24  are supplied to the crystal nucleus to grow the crystal nucleus, whereby the seed crystal  30  in a needle shape is grown. In the crystal growth process of the seed crystal  30 , the boron in the mixed melt  24  is incorporated into the crystal as described above (the boron addition process). As a result, the third area  29   a  having a higher boron concentration is likely to be formed on the inner side of the seed crystal  30 , and the seed crystal  30  is likely to be elongated in the c-axis direction. As the boron to be incorporated into the crystal is reduced along with reduction in the boron concentration in the mixed melt  24  (the boron reduction process), the fourth area  29   b  having a lower boron concentration is likely to be formed on the outside of the third area  29   a . As a result, the seed crystal  30  is less likely to be elongated in the c-axis direction and likely to grow in an m-axis direction. 
     The partial pressure of N 2  in the inner container  11  preferably falls within a range from 5 MPa to 10 Mpa. 
     The temperature (crystal growth temperature) of the mixed melt  24  preferably falls within a range from 800 degrees C. to 900 degrees C. 
     More preferably, the ratio of the number of moles of an alkali metal (e.g., sodium) to the total number of moles of gallium and the alkali metal falls within a range from 75% to 90%, the crystal growth temperature of the mixed melt  24  falls within a range from 860 degrees C. to 900 degrees C., and the partial pressure of N 2  falls within a range from 5 MPa to 8 Mpa. 
     Still more preferably, the molar ratio of gallium to the alkali metal is 0.25:0.75, the crystal growth temperature falls within a range from 860 degrees C. to 870 degrees C., and the partial pressure of N 2  falls within a range from 7 MPa to 8 Mpa. 
     By performing the processes described above, the seed crystal of the first area  21 A serving as the seed crystal  30  used for production of the group 13 nitride crystal  19  can be obtained. As described above, by performing the first process for growing the third area  29   a  of the GaN crystal containing boron without performing the second process, the seed crystal of the first area  21  can be obtained. 
     [3] Production Method of a Group 13 Nitride Crystal 
     The group 13 nitride crystal  19  is produced by using the seed crystal  30  described in [2] and enlarging the cross-sectional area of the c-plane of the seed crystal  30  with the flux method. 
     Crystal Producing Apparatus 
       FIG. 12  is a schematic sectional view of an exemplary configuration of a crystal producing apparatus  2  used for growing the second area  27  from the seed crystal  30  to produce the group 13 nitride crystal  19 . The crystal producing apparatus  2  has a dual structure: an inner container  51  is arranged in an outer pressure-resistant container  50  made of a stainless steel; and the inner container  51  houses a reaction container  52 . The inner container  51  is attachable to and detachable from the outer pressure-resistant container  50 . An explanation will be made of the case where the seed crystal of the first area  21 A is used as the seed crystal  30 . 
     The reaction container  52  is a container that contains therein the seed crystal  30  and the mixed melt  24  of an alkali metal and a substance containing at least a group 13 element to perform crystal growth of the second area  27  from the seed crystal  30  (note that growth of a bulk crystal from a seed crystal is referred to as seed growth (SG)). 
     The material of the reaction container  52  is not particularly restricted, and a nitride such as a BN sintered compact and P-BN, an oxide such as alumina and YAG, and a carbide such as SiC may be used as the material, for example. The inner wall surface of the reaction container  52 , that is, the portion of the reaction container  52  having contact with the mixed melt  24  is preferably made of a material less likely to react with the mixed melt  24 . In the production of the second area  27  as a GaN crystal, examples of the material that enables crystal growth of GaN include a nitride such as BN, P-BN, and aluminum nitride, an oxide such as alumina and YAG, and a stainless steel (SUS). 
     Gas supply pipes  65  and  66  are connected to the outer pressure-resistant container  50  and the inner container  51 , respectively. The gas supply pipes  65  and  66  supply a N 2  gas, which is a raw material of the group 13 nitride crystal  19 , and a diluent gas for adjusting the total pressure to an internal space  67  of the outer pressure-resistant container  50  and an internal space  68  of the inner container  51 , respectively. A gas supply pipe  54  is bifurcated into a N 2  supply pipe  57  and a gas supply pipe  60 , and these pipes can be separated from the gas supply pipe  54  by valves  55  and  58 . 
     While an Ar gas, which is an inert gas, is preferably used as the diluent gas, the diluent gas is not limited thereto. Other inert gasses, such as He, may be used as the diluent gas. 
     The N 2  gas is supplied from the N 2  supply pipe  57  connected to a gas cylinder of the N 2  gas, for example. After the pressure of the N 2  gas is controlled by a pressure control device  56 , the N 2  gas is supplied to the gas supply pipe  54  through the valve  55 . By contrast, the gas for adjusting the total pressure (e.g., an Ar gas) is supplied from the gas supply pipe  60  for adjusting the total pressure connected to a gas cylinder of the gas for adjusting the total pressure, for example. After the pressure of the gas for adjusting the total pressure is controlled by a pressure control device  59 , the gas for adjusting the total pressure is supplied to the gas supply pipe  54  through the valve  58 . The N 2  gas and the gas for adjusting the total pressure whose pressure is controlled in this manner are supplied to the gas supply pipe  54  and mixed. 
     The mixed gas of the N 2  gas and the diluent gas is supplied to the outer pressure-resistant container  50  and the inner container  51  through a valve  63  and the gas supply pipe  65 , and a valve  61  and the gas supply pipe  66 , respectively, from the gas supply pipe  54 . The inner container  51  can be detached from the crystal producing apparatus  2  at the portion of the valve  61 . The gas supply pipe  65  is connected to the outside via a valve  62 . 
     The gas supply pipe  54  is provided with a pressure gauge  64 . Therefore, it is possible to control the pressure in the outer pressure-resistant container  50  and the inner container  51  while monitoring the total pressure in the outer pressure-resistant container  50  and the inner container  51  with the pressure gauge  64 . 
     In the present embodiment, by adjusting the pressure of the N 2  gas and the diluent gas in this manner with the valves  55  and  58  and the pressure control devices  56  and  59 , respectively, the partial pressure of N 2  can be controlled. Furthermore, because the total pressure in the outer pressure-resistant container  50  and the inner container  51  can be controlled, evaporation of an alkali metal (e.g., sodium) in the reaction container  52  can be suppressed by setting the total pressure in the inner container  51  higher. In other words, it is possible to control the partial pressure of N 2  serving as a raw material for nitrogen affecting crystal growth conditions of GaN and the total pressure affecting suppression of evaporation of sodium separately. 
     As illustrated in  FIG. 12 , a heater  53  is arranged around the inner container  51  in the outer pressure-resistant container  50 . The heater  53  can heat the inner container  51  and the reaction container  52 , thereby controlling the temperature of the mixed melt  24 . 
     Adjustment Of Raw Material and the Like and Crystal Growth Conditions 
     Input of a raw material including the seed crystal  30 , Ga, Na, an additive such as C, and a dopant such as Ge, for example, to the reaction container  52  is performed by placing the inner container  51  in a glove box under an inert gas, such as an argon gas, atmosphere. This can be done with the reaction container  52  placed in the inner container  51 . 
     The seed crystal  30  described in [2] is arranged in the reaction container  52 . Furthermore, a substance containing at least a group 13 element (e.g., gallium) and a substance to be used as a flux are input to the reaction container  52 . 
     While sodium or a sodium compound (e.g., sodium azide) is used as the substance to be used as a flux, the other alkali metals, such as lithium and potassium, and a compound of such an alkali metal may be used, for example. Alternatively, an alkaline earth metal, such as barium, strontium, and magnesium, and a compound of such an alkaline earth metal may be used. Furthermore, a plurality of types of alkali metals or alkaline earth metals may be used. 
     While gallium, which is an element of group 13, is used as the substance containing at least a group 13 element serving as the raw material, for example, the other group 13 elements, such as boron, aluminum, indium, and a mixture of these elements may be used. 
     While the molar ratio between the substance containing a group 13 element and the alkali metal is not particularly restricted, the molar ratio of the alkali metal to the total number of moles of the group 13 element and the alkali metal is preferably set to 40% to 90%. 
     After setting the raw material and the like in this manner, the heater  53  is turned ON to heat the inner container  51  and the reaction container  52  inside thereof to the crystal growth temperature. As a result, the substance containing a group 13 element serving as the raw material, the alkali metal, the additives and the like are melted together to form the mixed melt  24 . By bringing N 2  at the partial pressure described above into contact with the mixed melt  24  and dissolving the N 2  into the mixed melt  24 , it is possible to supply the N 2  serving as the raw material of the group 13 nitride crystal  19  to the mixed melt  24  (the mixed melt formation process). 
     Subsequently, the raw material dissolved in the mixed melt  24  is supplied to the outer circumferential surface of the seed crystal  30 , whereby the second area  27  is grown from the outer circumferential surface of the seed crystal  30  with the raw material (the crystal growth process). 
     As described above, by growing the second area  27  from the outer circumferential surface of the seed crystal  30 , it is possible to produce the group 13 nitride crystal  19  including the seed crystal  30 . 
     Preferably, the partial pressure of the N 2  gas in the internal space  68  of the inner container  51  and the internal space  67  of the outer pressure-resistant container  50  is at least equal to or higher than 0.1 MPa. More preferably, the partial pressure of the N 2  gas in the internal space  68  of the inner container  51  and the internal space  67  of the outer pressure-resistant container  50  falls within a range from 2 MPa to 5 MPa. 
     Preferably, the temperature (crystal growth temperature) of the mixed melt  24  is at least equal to or higher than 700 degrees C. More preferably, the crystal growth temperature falls within a range from 850 degrees C. to 900 degrees C. 
     The conditions of the single crystal growth process can be selected appropriately depending on the group 13 nitride crystal  19  to be produced. 
     The seed crystal of the first area  21  and the seed crystal of the first area  21 A obtained by production of the seed crystal  30  are produced mainly by being grown in the c-axis direction. By contrast, the group 13 nitride crystal  19  produced by the crystal growth of the second area  27  from the seed crystal  30  is produced mainly by being grown in a direction perpendicular to the c-axis. Thus, the crystal growth direction of the first area  21  (or the first area  21 A) is different from that of the second area  27 . Because difference in the crystal growth direction leads to difference in the way of incorporating impurities, the first area  21  (or the first area  21 A) and the second area  27  are different in the way of incorporating impurities. Therefore, the second area  27  obtained by the crystal growth in a direction perpendicular to the c-axis with the production method described above has a higher carrier concentration than the first area  21  (or the first area  21 A) obtained by the crystal growth in the c-axis direction. 
     Furthermore, because the crystal of the first area  21  or the first area  21 A is used as the seed crystal, the thickness of the second area  27  becomes larger than the maximum diameter of the first area  21  or the first area  21 A on the c-plane cross-section in the group 13 nitride crystal  19  thus produced, and the second area  27  is formed as a large area. Therefore, by using the second area  27 , it is possible to provide the group 13 nitride crystal  19  that is excellent in quality and suitably applicable to a low-resistance conductive device, for example. 
     Examples of the conductive device include a semiconductor laser and a light-emitting diode. 
     Furthermore, if the group 13 nitride crystal  19  is produced by growing the second area  27  from the seed crystal  30  using the production method described above, the dislocation density of the second area  27  grown mainly from the outer circumferential surface formed of the m-plane of the seed crystal  30  is affected by the quality of the outer circumferential surface formed of the seed crystal  30 . 
     As described in [2], if the seed crystal of the first area  21 A is used as the seed crystal  30 , the outer circumferential surface formed of the m-plane of the seed crystal  30  has a low dislocation density and high quality. Thus, by growing the second area  27  using the seed crystal  30 , dislocations propagated from the seed crystal  30  to the second area  27  can be reduced. As a result, it is possible to keep the dislocation density of the group 13 nitride crystal  19  thus produced, more specifically, the dislocation density of the second area  27  lower. This makes it possible to facilitate production of the group 13 nitride crystal  19  that is large in size and excellent in quality. 
     In the present embodiment, the group 13 nitride crystal  19  produced by the production method described above grows in the m-axis direction (that is, a direction in which the c-plane cross-section of the hexagon becomes larger) from the m-plane serving as the outer circumferential surface of the seed crystal  30  (the first area  21 , the first area  21 A, or the first area  21 B). Therefore, the group 13 nitride crystal  19  showing the dislocation described above can be obtained. 
       FIG. 13  is a view schematically illustrating a dislocation on a cross-section parallel to the c-axis and the a-axis in the group 13 nitride crystal  19 .  FIG. 13  is an enlarged view of a portion on the right side of the first area  21 A in the cross-section parallel to the c-axis and the a-axis in the group 13 nitride crystal  19 . 
     Typically, even if crystal growth is performed by any one of the flux method, the HVPE, and other methods, not a few dislocations occur in the group 13 nitride crystal  19 . Furthermore, if a dislocation (a line defect or a point defect) is present on the outer circumferential surface of the first area  21 A or the first area  21  (not illustrated in  FIG. 13 ), the dislocation may possibly be propagated to the second area  27  when the second area  27  is grown form the outer circumferential surface of the seed crystal of the areas. It is considered that the dislocation is caused by difference in the coefficient of thermal expansion and in the lattice constant between the seed crystal and the second area  27  grown from the seed crystal and defects such as a strain and a crack of the crystal on the surface of the seed crystal, for example. 
     By contrast, in the present embodiment, the second area  27  is grown from the seed crystal of the first area  21 A, that is, the fourth area  29   b . Therefore, it is possible to facilitate reduction in the dislocation density of the second area  27  in the group 13 nitride crystal  19 . 
     Typically, a dislocation (a line defect) extending parallel to the crystal growth direction continues to extend without vanishing during the crystal growth. By contrast, a line defect extending in a direction not parallel to the crystal growth direction frequently vanishes during the crystal growth. The group 13 nitride crystal  19  grows in the m-axis direction (that is, a direction in which the c-plane cross-section of the hexagon becomes larger) from the m-plane serving as the outer circumferential surface of the seed crystal  30 . Therefore, the number of dislocations occurring from the growth interface of the seed crystal is larger in a &lt;11-20&gt; direction parallel to the crystal growth direction and smaller in a &lt;11-23&gt; direction not parallel to the crystal growth direction. 
     Thus, in the group 13 nitride crystal  19  according to the present embodiment, the number of threading dislocations threading through the c-plane is smaller than the number of BPDs, which are dislocations parallel to the c-plane. The fact that the number of BPDs is larger than the number of threading dislocations indicates that the group 13 nitride crystal  19  is produced by being grown in a direction in which the c-plane cross-section becomes larger. 
     As described above, the group 13 nitride crystal  19  according to the present embodiment is produced by being grown from the seed crystal  30  in a direction in which the hexagon of the c-plane cross-section becomes larger. Therefore, the BPDs of the group 13 nitride crystal  19  thus produced include dislocations in directions parallel to the c-plane and different from one another (refer to  FIG. 13 ). 
     If a group 13 crystal substrate is manufactured by using a group 13 nitride crystal in which the BPD, which is a dislocation in a direction along the c-plane, extends in one direction alone, the group 13 crystal substrate has large distortion and warpage. By contrast, in the group 13 nitride crystal  19  according to the present embodiment, the BPD extends not in one direction but in a plurality of directions. Therefore, the group 13 nitride crystal  19  according to the present embodiment is applicable to manufacturing of a group 13 crystal substrate in which distortion and warpage are suppressed. 
     Furthermore, the group 13 nitride crystal  19  produced by the production method described above is produced by being grown in a direction in which the c-plane cross-section becomes larger. Therefore, the group 13 nitride crystal  19  according to the present embodiment can suppress generation of a grain boundary in a direction not parallel to the c-plane. 
     In the group 13 nitride crystal  19 , no grain boundary is present on the c-plane of the second area  27  that is an area grown from the seed crystal  30  in the m-axis direction. However, a grain boundary may possibly be present between the first area  21  (the first area  21 A or the first area  21 B) serving as the seed crystal  30  and the second area  27 . 
     As described above, the group 13 nitride crystal  19  according to the present embodiment has the BPD extending in directions different from one another. In the group 13 nitride crystal  19 , the dislocation density of the BPD is preferably higher than the density of grain boundary on the c-plane as described above. Furthermore, in the group 13 nitride crystal  19 , the density of grain boundary of a cross-section intersecting the c-plane is preferably higher than the density of grain boundary on the c-plane. Moreover, in the group 13 nitride crystal  19 , the number of grain boundaries per 1 cm 2  on the c-plane is preferably equal to or less than 1. 
     Therefore, if a group 13 nitride crystal substrate having the principal surface formed of the c-plane is manufactured from the group 13 nitride crystal  19 , the group 13 nitride crystal substrate can be of high quality. 
     In the crystal production method according to the present embodiment, the same material (e.g., GaN) may be used for the seed crystal  30  and the second area  27  grown from the seed crystal  30 . In this case, unlike the case where a seed crystal made of a dissimilar material, such as aluminum nitride (AlN), is used, the lattice constants and the coefficients of thermal expansion of the seed crystal  30  and the second area  27  can agree with each other. As a result, it is possible to suppress occurrence of a dislocation due to lattice mismatch and difference in the coefficient of thermal expansion. 
     Furthermore, because the seed crystal  30  and the second area  27  are produced by the same crystal growth method (flux method), the agreement of the lattice constants and the coefficients of thermal expansion therebetween can be improved compared with the case where the seed crystal  30  and the second area  27  are produced by methods different from each other. As a result, it is possible to facilitate suppression of occurrence of a dislocation. 
     By performing the processes described above, it is possible to produce the group 13 nitride crystal  19  in practical size and of high quality. 
     While the explanation has been made of the crystal production method using the flux method, the crystal production method is not particularly restricted. The crystal growth may be performed by vapor phase epitaxy, such as the HVPE, or a liquid phase method other than the flux method. In terms of production of the group 13 nitride crystal  19  of high quality, the flux method is preferably used. Specifically, production of the group 13 nitride crystal  19  by the flux method enables growth of the second area  27  of higher quality. Therefore, it is possible to obtain the group 13 nitride crystal  19  of higher quality. 
     The position of the first area  21  or the first area  21 A, which is an area used as the seed crystal, in the group 13 nitride crystal  19  produced by the production method described in [3] simply needs to be inside of the group 13 nitride crystal  19 . The position may be a position threading through the center of the c-plane cross-section of the group 13 nitride crystal  19  along the c-axis direction or a position deviated from the position threading through the center along the c-axis direction. 
     While the explanation has been made of the case where the group 13 nitride crystal  19  is a needle crystal obtained by providing, on a hexagonal columnar crystal, a hexagonal pyramid whose bottom surface is the upper surface of the hexagonal column in the present embodiment, the present invention is not limited to this shape. The group 13 nitride crystal  19  may have a hexagonal pyramid shape with no m-plane provided, for example. 
     [4] Group 13 Nitride Crystal Substrate 
     A group 13 nitride crystal substrate according to the present embodiment is obtained by processing the group 13 nitride crystal  19 . 
     Based on a processing direction (a cutting direction) of the group 13 nitride crystal  19 , the group 13 nitride crystal substrate having the principal surface formed of an arbitrary crystal plane, such as the c-plane, the m-plane, the a-plane, a {10-11} plane, and a {11-23} plane can be obtained. 
       FIG. 14  and  FIG. 15  are schematics illustrating a direction to slice the group 13 nitride crystal  19 .  FIG. 16A  to  FIG. 16C  are schematics of an example of a group 13 nitride crystal substrate  100  ( 100   a  to  100   c ) obtained after the slicing. 
     By slicing the group 13 nitride crystal  19  in a direction perpendicular to the c-axis of the seed crystal (the first area  21 ) as indicated by a dashed-dotted line P 1  in  FIG. 14 , for example, the group 13 nitride crystal substrate  100   a  illustrated in  FIG. 16A  is obtained. Alternatively, by slicing the group 13 nitride crystal  19  in a direction oblique to the c-axis of the seed crystal  21  as indicated by a dashed-dotted line P 2  in  FIG. 14 , the group 13 nitride crystal substrate  100   b  illustrated in  FIG. 16B  may be obtained. Still alternatively, by slicing the group 13 nitride crystal  19  in a direction parallel to the c-axis of the seed crystal  21  as indicated by a dashed-dotted line P 3  in  FIG. 14 , the group 13 nitride crystal substrate  100   c  illustrated in  FIG. 160  may be obtained. 
     After the slicing described above, various types of processing such as forming and surface treatment may be performed. 
     In the manufacturing method according to the present embodiment, the group 13 nitride crystal substrate  100  is cut out from the group 13 nitride crystal  19  elongated in the c-axis direction as described above. Therefore, it is possible to make the substrate principal surface large both in the case of cutting out the c-plane and a plane other than the c-plane. In other words, according to the present embodiment, it is possible to manufacture the large-area crystal substrate  100  having the principal surface formed of an arbitrary crystal plane, such as the c-plane, the m-plane, the a-plane, the {10-11} plane, a {20-21} plane, and a {11-22} plane. Therefore, it is possible to manufacture the group 13 nitride crystal substrate  100  in practical size that is applicable to various types of semiconductor devices. 
     In the manufacturing method according to the present embodiment, because the crystal substrate  100  whose principal surface is formed of the c-plane has a BPD extending in a plurality of directions different from one another, distortion and warpage are suppressed. Therefore, the crystal substrate  100  is more suitably used as a seed crystal substrate for various types of semiconductor devices. 
     In the manufacturing method according to the present embodiment, the group 13 nitride crystal substrate  100  is manufactured by slicing a group 13 nitride bulk crystal (the group 13 nitride crystal  19 ). Unlike the conventional technology, there is no process for separating a thick-film crystal grown on a dissimilar substrate that is significantly different in the coefficient of thermal expansion and in the lattice constant from the substrate. As a result, a crack is less likely to occur on the group 13 nitride crystal substrate  100  in the manufacturing method according to the present embodiment. Therefore, it is possible to manufacture the group 13 nitride crystal substrate  100  of higher quality than that of the conventional technology. 
     [5] Preferable Shape of the Group 13 Nitride Crystal (Bulk Crystal) 
     A preferable shape of the group 13 nitride crystal  19  will now be described.  FIG. 17  to  FIG. 19  are schematics for explaining a process in which the second area  27  is grown from the seed crystal of the first area  21 A (including the third area  29   a  and the fourth area  29   b ), the first area  21 B, or the first area  21 . In the description below, the crystal growth method is not particularly restricted.  FIG. 17  to  FIG. 19  illustrate a cross-section on a plane parallel to the c-axis and the a-axis of the group 13 nitride crystal  19 . 
     As illustrated in  FIG. 17 , the group 13 nitride crystal  19  includes an area  27   a  and an area  27   b . The area  27   a  is grown mainly in the m-axis direction (that is, a direction in which the c-plane cross-section of the hexagon becomes larger) from the m-plane serving as the outer circumferential surface of the seed crystal of the first area  21 , the first area  21 A, or the first area  21 B. The area  27   b  is grown mainly from the {10-11} plane of the seed crystal or the {10-11} plane on the upper surface of the area  27   a.    
     In the area  27   b , the rate of formation of the {10-11} plane may be limited. As a result, the group 13 nitride crystal  19  (second area  27 ) grown around the upper portion of the seed crystal is likely to have a hexagonal pyramid shape. 
       FIG. 18  is a schematic illustrating a state of crystal growth in the case where a length L of the seed crystal in the c-axis direction is short. If the length L of the seed crystal is not sufficiently long, the ratio of the hexagonal pyramid portion to the hexagonal columnar portion is made large. As a result, the volume ratio of the area  27   b  formed in a &lt;10-11&gt; direction to the area  27   a  formed in the m-axis direction is made larger. Thus, the group 13 nitride crystal  19  is likely to have the shape illustrated in  FIG. 19 . In this case, all the c-plane cross-sections include the area  27   b.    
       FIG. 19  is a schematic illustrating a state in which the crystal growth of the group 13 nitride crystal (second area  27 ) in  FIG. 18  is further promoted. As illustrated in  FIG. 19 , if the outer circumference of the seed crystal is surrounded by the area  27   b , no outer circumferential surface composed of the m-plane is formed even if further crystal growth is performed. As a result, it is frequently observed that the group 13 nitride crystal (second area  27 ) grows while the {10-11} plane is being kept as the outer circumferential surface. 
     The area  27   a  is an area that starts to grow from the outer circumferential surface of the m-plane of the seed crystal. As described above, the group 13 nitride crystal (area  27   a ) grown mainly from the m-plane of the seed crystal has a relatively small number of threading dislocations extending in the c-axis direction. Therefore, in manufacturing of the group 13 nitride crystal substrate having the principal surface formed of the c-plane, it is preferable that the group 13 nitride crystal substrate include the area  27   a  as much as possible. 
     [6] Preferable Size of the Seed Crystal 
     A preferable shape of the seed crystal used for growing the group 13 nitride crystal  19  in the preferable shape described above will now be explained. The seed crystal of the first area  21 A has a hexagonal crystal structure, and the angle formed by the a+c axis (&lt;11-23&gt; direction) and the c-plane is 58.4 degrees, for example. Furthermore, if the ratio L/d of the length L of the seed crystal of the first area  21 A in the c-axis direction to a crystal diameter d on the c-plane cross-section is 0.813, for example, the seed crystal has a hexagonal pyramid shape. 
     As described above, to obtain the group 13 nitride crystal  19  of high quality, it is preferable that the group 13 nitride crystal (second area  27 ) grow mainly from the outer circumferential surface of the m-plane of the seed crystal. Thus, the seed crystal preferably includes the m-plane as the outer circumferential surface thereof. 
       FIG. 20  is a schematic illustrating the relationship between the shape of the seed crystal of the first area  21 A and L/d. As illustrated in  FIG. 20 , if (a) L/d=0.813 is satisfied, the seed crystal has a hexagonal pyramid shape. If (b) L/d&gt;0.813 is satisfied, the upper part has a hexagonal pyramid shape and the lower part has a hexagonal columnar shape, and the outer circumferential surface (side surface) of the seed crystal includes the m-plane. If (c) L/d&lt;0.813 is satisfied, the seed crystal has a hexagonal pyramid shape not including the m-plane or a shape in which a part including the apex of the hexagonal pyramid portion is not included, the c-plane is formed on the upper surface of the crystal, and the height of the hexagonal columnar portion including the m-plane is short. 
     Therefore, the ratio L/d of the length L in the c-axis direction to the crystal diameter d on the c-plane is preferably larger than 0.813 in the seed crystal. 
     The size of the group 13 nitride crystal substrate  100  is desired to be half an inch (12.7 mm) or 2 inches (5.08 cm) for practical use. Thus, an explanation will be made of the size of the seed crystal required for making the maximum diameter of the group 13 nitride crystal substrate  100  having the principal surface formed of the c-plane equal to or larger than half an inch (12.7 mm) or equal to or larger than 2 inches. 
     In the description below, an estimation will be made of the case where the thickness of the group 13 nitride crystal substrate  100  is 1 mm as an example of the minimum thickness required to be a practical substrate. However, the required minimum thickness is not limited thereto and is arbitrarily estimated. 
     To cause the diameter of the group 13 nitride crystal substrate  100  to be 12.7 mm, that is, to cause a diameter d of the group 13 nitride crystal substrate  100  to be 12.7 mm, the second area  27  needs to grow by at least equal to or more than 6.35 mm in the radial direction (m-axis direction) assuming that the crystal diameter of the seed crystal is 0. 
     An assumption is made that a crystal growth velocity Vm in the m-axis direction is twice as fast as a crystal growth velocity Vc in the c-axis direction, for example. In this case, the group 13 nitride crystal grows by approximately 3.2 mm in the c-axis direction while growing by 6.35 mm in the m-axis direction. Because L/d&gt;0.813 is satisfied as described above, the length L in the c-axis direction (the height of the hexagonal pyramid portion) needs to be 11.9 mm to cause the crystal diameter d (the diameter of the bottom surface of the hexagonal pyramid portion) to be 12.7 mm. Therefore, it is estimated that the length of the seed crystal  30  needs to be 11.9−3.2=8.7 mm. In other words, the minimum length of the seed crystal required to obtain the group 13 nitride crystal in a hexagonal pyramid shape is 8.7 mm. Furthermore, an area in a hexagonal columnar shape is required to be formed under the hexagonal pyramid. Assuming that the thickness of the group 13 nitride crystal substrate  100  needs to be equal to or larger than 1 mm, it is estimated that the length L of the seed crystal  30  in the c-axis direction needs to be 9.7 mm. 
     As described above, the length L of the seed crystal (seed crystal of the first area  21 , the first area  21 A, or the first area  21 B) in the c-axis direction is preferably equal to or larger than 9.7 mm. 
     Preferably, the ratio L/d of the length L in the c-axis direction to the crystal diameter d on the c-plane is larger than 0.813, and the length L in the c-axis direction is equal to or larger than 9.7 mm. The ratio L/d is more preferably larger than 7 and still more preferably larger than 20. 
     As described above, according to the preferred embodiment, it is possible to manufacture the group 13 nitride crystal substrate  100  having a diameter on the c-plane of half an inch. Furthermore, because the group 13 nitride crystal  19  grown from the m-plane of the seed crystal is of high quality as described above, it is possible to manufacture the group 13 nitride crystal substrate  100  that is large in size and excellent in quality. 
     To obtain the group 13 nitride crystal substrate  100  having a diameter of 2 inches (5.08 cm), it is estimated that the length L of the seed crystal in the c-axis direction needs to be equal to or larger than 37.4 mm. 
     Therefore, the length L of the seed crystal in the c-axis direction is preferably equal to or larger than 37.4 mm. Thus, it is possible to manufacture the group 13 nitride crystal substrate  100  having a diameter of the c-plane of equal to or larger than 2 inches. Furthermore, because the group 13 nitride crystal  19  grown from the m-plane of the seed crystal is of high quality as described above, it is possible to manufacture the group 13 nitride crystal substrate  100  with a large diameter and of high quality. 
     EXAMPLES 
     While examples will be described below to explain the present invention in greater detail, the examples are not intended to limit the present invention. Reference numerals correspond to those in the configurations of the crystal producing apparatuses  1  and  2  described with reference to  FIG. 11  and  FIG. 12 . 
     Production of Seed Crystal 
     A seed crystal used for production of a group 13 nitride crystal was produced by the following production method. 
     Production Example 1 of the Seed Crystal 
     The seed crystal of the first area  21 A was produced using the crystal producing apparatus  1  illustrated in  FIG. 11 . 
     Gallium with a nominal purity of 99.99999% and sodium with a nominal purity of 99.95% were input in a molar ratio of 0.25:0.75 to the reaction container  12  with an inside diameter of 92 mm made of a BN sintered compact. 
     The reaction container  12  was placed in the pressure-resistant container  11  under a high-purity Ar gas atmosphere in a glove box. Subsequently, the valve  31  was closed to isolate the inside of the reaction container  12  from an external atmosphere, and the pressure-resistant container  11  was sealed up in a manner filled with the Ar gas. 
     Subsequently, the pressure-resistant container  11  was taken out of the glove box and incorporated into the crystal producing apparatus  1 . In other words, the pressure-resistant container  11  was placed at a predetermined position with respect to the heater  13  and connected to the gas supply pipe  14  for a N 2  gas and an Ar gas at the portion of the valve  31 . 
     After the Ar gas was purged from the inner container  11 , the N 2  gas was injected from the N 2  supply pipe  17 . The pressure of the N 2  gas was controlled by the pressure control device  16 , and the valve  15  was opened. Thus, the pressure of N 2  in the inner container  11  was set to 3.2 MPa. Subsequently, the valve  15  was closed, and the value of the pressure control device  16  was set to 8 MPa. The heater  13  was then turned ON to heat the reaction container  12  to the crystal growth temperature. In Production example 1, the crystal growth temperature was set to 870 degrees C. 
     The gallium and the sodium in the reaction container  12  are melted at the crystal growth temperature to form the mixed melt  24 . The temperature of the mixed melt  24  is equal to the temperature of the reaction container  12 . Furthermore, if the reaction container  12  is heated to this temperature, a gas in the inner container  11  is heated to cause the total pressure to be 8 MPa in the crystal producing apparatus  1  in Production example 1. 
     Subsequently, the valve  15  was opened to cause the pressure of the N 2  gas to be 8 MPa, thereby achieving the pressure equilibrium between the inside of the inner container  11  and the inside of the N 2  supply pipe  17 . 
     After the reaction container  12  was held in this state for 500 hours to perform crystal growth of GaN, the heater  13  was controlled to cool the inner container  11  to room temperature (approximately 20 degrees C.). After the pressure of the gas in the inner container  11  was reduced, the inner container  11  was opened. As a result, it was found that a large number of GaN crystals were grown in the reaction container  12 . The seed crystal  30 , which is the GaN crystal thus grown, was colorless and transparent. The crystal diameter d of the seed crystal  30  was approximately 100 to 1500 μm, the length L thereof was approximately 10 to 40 mm, and the ratio L/d of the length L to the crystal diameter d was approximately 20 to 300. The seed crystal  30 , which is the GaN crystal thus grown, was grown nearly parallel to the c-axis, and the m-plane was formed on the side surface thereof. 
     Production Example 2 of the Seed Crystal 
     Crystal growth was performed in the same manner as in Production example 1 of the seed crystal except for the following conditions: alumina was used as the material of the reaction container  12 ; a plate made of a BN sintered compact fitting into the bottom surface of the reaction container  12  was placed; the partial pressure of N 2  in the pressure-resistant container  11  at a crystal growth temperature of 870 degrees C. was maintained at 6 MPa (the partial pressure of N 2  in the pressure-resistant container  11  at room temperature is 2.8 MPa); and crystal growth time was set to 300 hours. 
     As a result, similarly to Production example 1 of the seed crystal, it was found that a large number of colorless and transparent seed crystals  30 , which are grown GaN crystals, were grown. The crystal diameter d of the seed crystal  30  was approximately 100 to 500 μm, the length L thereof was approximately 10 to 15 mm, and the ratio L/d of the length L to the crystal diameter d was approximately 30 to 500. 
     Production Example 3 of the Seed Crystal 
     Crystal growth was performed in the same manner as in Production example 1 of the seed crystal except that the crystal growth temperature was set to 860 degrees C. and the pressure of N, was set to 5 MPa. As a result, a GaN microcrystal having a size of approximately several hundred micrometers was obtained. However, no GaN single crystal having a length of equal to or larger than 3 mm was obtained. 
     Various types of measurement were performed on each seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal. The measurement results are as follows. 
     Measurement Results of Photoluminescence (PL) 
     Photoluminescence (PL) of the seed crystal produced in Production example 1 of the seed crystal and PL of the seed crystal produced in Production example 2 of the seed crystal were measured at room temperature (25 degrees C.). The PL was measured using LabRAM HR-80 manufactured by HORIBA, Ltd. A helium-cadmium (He—Cd) laser at a wavelength of 325 nm was used as an excitation light source. The PL was measured in the third area  29   a  serving as the inner side area of the seed crystal  30  and the fourth area  29   b  serving as the outer side area of the seed crystal  30 . 
       FIG. 10  illustrates an example of measurement results of an emission spectrum of the PL in the third area  29   a  and the fourth area  29   b . The abscissa axis represents wavelengths (nm) and the ordinate axis represents emission intensity. 
     As indicated by a solid line in  FIG. 10 , broad emission (the second peak) from 500 nm to 800 nm having a peak at around 600 nm was detected in the third area  29   a  in Production example 1 of the seed crystal and Production example 2 of the seed crystal. However, only extremely low emission intensity was detected in light emission (the first peak) in the vicinity of the band-edge of GaN (364 nm). 
     By contrast, as indicated by a dotted line in  FIG. 10 , high peak intensity was detected in light emission (the first peak) in the vicinity of the band-edge of GaN (364 nm) in the fourth area  29   b  in Production example 1 of the seed crystal and Production example 2 of the seed crystal. However, only extremely low emission intensity was detected in broad emission (the second peak) from 500 nm to 800 nm. 
     As described above, in terms of the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal, it was found that the peak intensity of the first peak was lower than the peak intensity of the second peak in the third area  29   a  on the inner side of the seed crystal  30 . Furthermore, it was found that the peak intensity of the first peak was higher than the peak intensity of the second peak in the fourth area  29   b  on the outer side of the seed crystal  30 . 
     An explanation will be made of emission intensity distribution of the PL measured for the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal with reference to  FIG. 21  and  FIG. 22 .  FIG. 21  and  FIG. 22  are views of examples of PL results measured on the c-plane cross-section of the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal and illustrate spectral intensity at different wavelength bands at the same measurement point on the c-plane cross-section. 
       FIG. 21  is a view of a mapping image of spectral intensity of the PL from 360 nm to 370 nm. A deeper color indicates higher spectral intensity in a range of 360 nm to 370 nm. 
       FIG. 22  is a view of a mapping image of spectral intensity of the PL from 500 nm to 800 nm. A deeper color indicates higher spectral intensity in a range of 500 nm to 800 nm. 
     Therefore according to the mapping results in  FIG. 21  and  FIG. 22 , it was found that the third area  29   a  was located on the inner side of the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal and that the fourth area  29   b  was located on the outer side thereof. 
     As a result of PL measurement performed on the c-plane cross-section of the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal, it was found that the fourth area  29   b  covered the entire outer circumference of the third area  29   a  in some seed crystals  30 . Furthermore, it was found that the fourth area  29   b  covered a part of the outer circumference of the third area  29   a  in the other seed crystals  30 . Thus, it was found that the fourth area  29   b  covered at least a part of the outer circumference of the third area  29   a  on the c-plane cross-section of the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal. 
     Measurement of Boron Concentration 
     The boron concentration in the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal was measured using a secondary ion mass spectrometer (SIMS). IMS 7f (a model designation) manufactured by CAMECA was used as the SIMS. A Cs +  ion was used as a primary ion beam. In the present measurement, the boron concentration was measured at a plurality of points in the inner side area (that is, the third area  29   a ) and the outer side area (that is, the fourth area  29   b ) on the c-plane cross-section of the seed crystal  30 . 
     While there was a little fluctuation in the measurement results depending on the positions, the boron concentration of the third area  29   a  was approximately 5×10 18  cm −3  to 3×10 19  cm −3 , and the boron concentration of the fourth area  29   b  was approximately 1×10 16  cm −3  to 8×10 17  cm −3 . 
     Thus, it was found that the boron concentration of the fourth area  29   b  on the outer side on the c-plane cross-section was lower than the boron concentration of the third area  29   a  on the inner side in the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal. 
     By the crystal production method described above, the group 13 nitride crystal  19  was produced using the seed crystal  30  produced in Production example 1 of the seed crystal and Production example 2 of the seed crystal. 
     Example A1 
     In Example A1, the second area  27  was grown from the seed crystal  30  to produce the group 13 nitride crystal  19  by the crystal producing apparatus  2  illustrated in  FIG. 12 . 
     The seed crystal  30  produced in Production example 1 of the seed crystal was used as the seed crystal  30 . The seed crystal  30  had a width of 1 mm and a length of approximately 40 mm. In the seed crystal  30  used in Example A1, the fourth area  29   b  covered the entire outer circumference of the third area  29   a  on at least a part of the c-plane cross-sections. Furthermore, it was found that a thickness t (thickness in the m-axis direction) of the fourth area  29   b  was at least equal to or larger than 10 μm on the c-plane cross-section of the seed crystal  30 . 
     The inner container  51  was detached from the crystal producing apparatus  2  at the portion of the valve  61  and put into a glove box under an Ar atmosphere. Subsequently, the seed crystal  30  was placed in the reaction container  52  made of alumina and having an inside diameter of 140 mm and a depth of 100 mm. The seed crystal  30  was held in a manner inserted into a hole with a depth of 4 mm bored on the bottom of the reaction container  52 . 
     Subsequently, sodium (Na) was heated into a liquid and input to the reaction container  52 . After the sodium solidified, gallium was input. In Example A1, the molar ratio of the gallium to the sodium was set to 0.25:0.75. 
     Subsequently, the reaction container  52  was placed in the inner container  51  under a high-purify Ar gas atmosphere in the glove box. The valve  61  was then closed to seal up the inner container  51  filled with the Ar gas, and the inside of the reaction container  52  was isolated from an external atmosphere. Subsequently, the inner container  51  was taken out of the glove box and incorporated into the crystal producing apparatus  2 . In other words, the inner container  51  was placed at a predetermined position with respect to the heater  53  and connected to the gas supply pipe  54  at the portion of the valve  61 . 
     After the Ar gas was purged from the inner container  51 , the N 2  gas was injected from the N 2  supply pipe  57 . The pressure of the N 2  gas was controlled by the pressure control device  56 , and the valve  55  was opened. Thus, the total pressure in the inner container  51  was caused to be 1.2 MPa. Subsequently, the valve  55  was closed, and the value of the pressure control device  56  was set to 3.2 MPa. 
     The heater  53  was then turned ON to heat the reaction container  52  to the crystal growth temperature. The crystal growth temperature was set to 870 degrees C. Subsequently, in the same manner as in the production in Production Example A1 of the seed crystal, the valve  55  was opened to cause the pressure of the N 2  gas to be 3.2 MPa. The reaction container  52  was held in this state hours to grow a GaN crystal. 
     As a result, crystal growth was performed from the seed crystal  30 , and the crystal diameter was increased in a direction perpendicular to the c-axis, whereby the group 13 nitride crystal  19  (single crystal) having a larger crystal diameter was grown in the reaction container  52 . The group 13 nitride crystal  19  obtained by the crystal growth was roughly colorless and transparent. The crystal diameter d was 51 mm, and the length L in the c-axis direction was approximately 54 mm including the portion of the seed crystal  30  inserted into the reaction container  52 . In the group 13 nitride crystal  19 , the upper part had a hexagonal pyramid shape and the lower part had a hexagonal columnar shape. 
     Example A2 
     In Example A2, crystal growth of the seed crystal  30  was performed to produce the group 13 nitride crystal  19  by the crystal producing apparatus  2  illustrated in  FIG. 12  under the same conditions as those in Example A1 except that the seed crystal  30  produced in Production example 2 of the seed crystal was used as the seed crystal. 
     The group 13 nitride crystal  19  obtained in Example A2 had a hexagonal pyramid shape. 
     Comparative Example A1 
     In Comparative example A1, a crystal having a defect extending in a different direction because of difference in the growth direction from Example A1 was produced. In Comparative example A1, crystal growth was performed such that the crystal was grown in the c-axis direction using the group 13 nitride crystal substrate having the principal surface formed of the c-plane and produced in Example B1 as the seed crystal. The c-plane diameter of the seed crystal was 50.8 mm, and the thickness of the substrate was 400 μm. 
     The inner container  51  was detached from the crystal producing apparatus  2  at the portion of the valve  61  and put into a glove box under an Ar atmosphere. Subsequently, the group 13 nitride crystal substrate  100  was placed in the reaction container  52  made of alumina and having an inside diameter of 140 mm and a depth of 100 mm. Subsequently, sodium (Na) was heated into a liquid and input to the reaction container  52 . After the sodium solidified, gallium was input. In Comparative example A1, the molar ratio of the gallium to the sodium was set to 0.25:0.75. 
     Subsequently, the reaction container  52  was placed in the inner container  51  under a high-purify Ar gas atmosphere in the glove box. The valve  61  was then closed to seal up the inner container  51  filled with the Ar gas, and the inside of the reaction container  52  was isolated from the external atmosphere. Subsequently, the inner container  51  was taken out of the glove box and incorporated into the crystal producing apparatus  2 . In other words, the inner container  51  was placed at a predetermined position with respect to the heater  53  and connected to the gas supply pipe  54  at the portion of the valve  61 . After the Ar gas was purged from the inner container  51 , the N 2  gas was injected from the N 2  supply pipe  57 . The pressure of the N 2  gas was controlled by the pressure control device  56 , and the valve  55  was opened. Thus, the total pressure in the inner container  51  was caused to be 1.0 MPa. Subsequently, the valve  55  was closed, and the value of the pressure control device  56  was set to 3 MPa. 
     The heater  53  was then turned ON to heat the reaction container  52  to the crystal growth temperature. The crystal growth temperature was set to 870 degrees C. Subsequently, in the same manner as the operation in Example 1, the valve  55  was opened to cause the pressure of the N 2  gas to be 2.5 MPa. The reaction container  52  was held in this state for 700 hours to grow a GaN crystal (the second area  27 ). 
     As a result, the thickness of the crystal substrate was increased in the c-axis direction, and a GaN crystal (single crystal) was grown in the reaction container  52 . A GaN crystal  84  thus grown was roughly colorless and transparent, and the length L in the c-axis direction was approximately 8 mm (refer to  FIG. 24A ). 
     Subsequently, a group 13 nitride crystal substrate was manufactured using the group 13 nitride crystal produced in Example A1 and Comparative example A1. 
     Example B1 
     The group 13 nitride crystal produced in Example A1 was subjected to external shape grinding and was sliced parallel to the c-plane. Subsequently, by polishing the surface and performing surface treatment thereon, a group 13 nitride crystal substrate having the principal surface formed of the c-plane with an external shape (φ) of 2 inches and a thickness of 400 μm and including a first area and a second area was manufactured. 
     Example B2 
     The group 13 nitride crystal produced in Example A2 was subjected to external shape grinding and was sliced parallel to the c-plane. Subsequently, by polishing the surface and performing surface treatment thereon, a group 13 nitride crystal substrate having the principal surface formed of the c-plane and including a first area and a second area was manufactured. 
     Example B3 
     The group 13 nitride crystal produced in Example A1 was subjected to external shape grinding and was sliced parallel to the m-plane. Subsequently, by polishing the surface and performing surface treatment thereon, a group 13 nitride crystal substrate  101  having the principal surface formed of the m-plane with a height of 40 mm, a width of 25 mm, and a thickness of 400 μm and a group 13 nitride crystal substrate  102  having the principal surface formed of the m-plane with a height of 40 mm, a width of 40 mm, and a thickness of 400 μm were manufactured (refer to  FIG. 4  and  FIG. 5 ). The crystal substrate  102  includes the seed crystal. 
     Comparative example B1 
     A c-plane substrate was manufactured under the same conditions as those in Example B1 except that the group 13 nitride crystal produced in Comparative Example A1 was used instead of the group 13 nitride crystal produced in Example A1.  FIG. 24B  is a schematic of an m-plane cross-section of the GaN crystal  84  produced in Comparative example A1. The c-plane substrate did not include a portion of a GaN substrate  103  serving as the seed crystal and was manufactured from the portion of the GaN crystal  84  grown from the seed crystal substrate in the c-axis direction. 
     Comparative Example B2 
     An m-plane substrate (refer to  FIG. 24B ) with a height of 7 mm, a width of 15 mm, and a thickness of 400 μm was manufactured by processing an m-plane substrate under the same conditions as those in Example B3 except that the group 13 nitride crystal produced in Comparative Example A1 was used instead of the group 13 nitride crystal produced in Example A1. 
     Evaluation 
     Evaluation Of Dislocation Density 
     Evaluation was made on the dislocation direction, the dislocation density, the grain boundary, and the density of grain boundary on each c-plane of the group 13 nitride crystal substrate serving as a c-plane substrate manufactured in Example B1, Example B2, and Comparative example B1. 
     Specifically, each c-plane surface of the group 13 nitride crystal substrate serving as a c-plane substrate manufactured in Example B1, Example 32, and Comparative example B1 was observed by CL. MERLIN manufactured by Carl Zeiss was used as a CL device, and the observation was made at an accelerating voltage of 5.0 kV, a probe current of 4.8 nA, and room temperature. 
     The threading dislocation density threading through the c-plane of the group 13 nitride crystal substrate manufactured in Example B2 was equal to or lower than 10 2  cm −2 . This value was derived by counting spots found as dark spots by CL on the c-plane. In the CL observation of the c-plane of the group 13 nitride crystal substrate, if a dislocation extending in a direction not parallel to the c-axis and the c-plane, such as the &lt;11-23&gt; direction, is present on the c-plane surface, the dislocation is found as a short dark line, for example. On the c-plane of the group 13 nitride crystal substrate manufactured in Example B2, however, no short dark line was found. Therefore, it was found that there were few dislocations not parallel to the c-axis and the c-plane in the group 13 GaN crystal according to the present embodiment. 
     In the same manner as in Example B1 and Example B2, the threading dislocation density in a direction threading through the c-plane was measured for the group 13 nitride crystal substrate manufactured in Comparative example B1 and having the principal surface formed of the c-plane. As a result, a threading dislocation density of approximately from 10 4  cm −2  to 10 5  cm −2  was found. Furthermore, the group 13 nitride crystal substrate manufactured in Comparative example B1 had an area in which dislocations were concentrated, and a grain boundary was found to be present based on contrast in the CL observation image. The density of grain boundary of Comparative example B1 was 10 to 100 cm −2 . 
     Crystallinity Evaluation 1 
     The crystallinity was evaluated for each c-plane of the group 13 nitride crystal substrate serving as a c-plane substrate and manufactured in Example B1 and Example B2. 
     Specifically, the crystallinity of each c-plane of the group 13 nitride crystal substrate serving as a c-plane substrate and manufactured in Example B1 and Example B2 was evaluated by a half width of a rocking curve in X-ray diffraction (XRD) measurement. X&#39; Pro MRD manufactured by PANalytical was used for the XRD measurement. As a result, it was found that the half width of the rocking curve of the c-plane substrate surface was high quality of 25 to 50 arcsec. 
     Thus, no grain boundary was present in the second area on the c-plane of the group 13 nitride crystal produced in Example A1 and Example A2, and a grain boundary was present only in the interface between the first area serving as a seed crystal and the second area grown from the seed crystal. The density of grain boundary was derived for the entire area on the c-plane, that is, the entire area of the first area serving as the seed crystal and the second area grown from the seed crystal. As a result, the number of grain boundaries per 1 cm 2  was 1. 
     Thus, it was found that the dislocation density of the BPD on the c-plane of the group 13 nitride crystal produced in Example A1 and Example A2 was higher than the density of grain boundary on the c-plane. Furthermore, it was found that the number of grain boundaries on the c-plane of the group 13 nitride crystal produced in Example A1 and Example A2 per 1 cm 2  was equal to or less than 1. 
     To obtain the group 13 nitride crystal substrate including no grain boundary, the group 13 nitride crystal substrate may be cut out from the group 13 nitride crystal produced in Example A1 and Example A2 such that the group 13 nitride crystal substrate includes not the first area serving as the seed crystal but the second area grown from the seed crystal alone. 
     In the same manner as described above, the crystallinity of the group 13 nitride crystal substrate manufactured in Comparative example B1 and having the principal surface formed of the c-plane was evaluated by a half width of a rocking curve in XRD measurement. As a result, it was found that the half width of the rocking curve of the c-plane substrate surface was 100 to 200 arcsec and that the group 13 nitride crystal substrate manufactured in Comparative example B1 was of lower quality than the substrates manufactured in Example B1 and Example B2. 
     Crystallinity Evaluation 2 
     The crystallinity was evaluated for the group 13 nitride crystal substrate  101  and the group 13 nitride crystal substrate  102  serving as m-plane substrates and manufactured in Example B3. 
     The dislocation density was measured for the m-plane surface serving as the principal surface of the group 13 nitride crystal substrate  101  by using CL. As a result, dislocations were mainly found as short dark lines, and the density of a dislocation threading through the m-plane surface was approximately from 10 4  cm −2  to 10 6  cm −2 . The group 13 nitride crystal substrate  101  had an area in which dislocations were concentrated, and a grain boundary was found to be present based on contrast in the CL observation image. The density of grain boundary was 10 to 100 cm −2 . 
     The m-plane surface serving as the principal surface of the crystal substrate  102  was observed by CL. As a result, a number of dislocations were found as dark lines extending in directions parallel to the c-plane. Furthermore, there was an area in which dislocations extending in directions parallel to the c-plane were concentrated in a stacked manner, and a grain boundary was found to be present in a direction parallel to the c-plane. 
     There was an area in which dislocations were concentrated around the interface between the area of the seed crystal and the area grown from the seed crystal. In the area around the interface in which dislocations were concentrated, a dislocation extending in a direction not parallel to the c-plane, such as the &lt;11-23&gt; direction, was present. 
     Furthermore, a plurality of dislocations extending in directions outward from the seed crystal were found. 
     Thus, it was found that BPDs of the group 13 nitride crystal produced in Example A2, which is a base of the group 13 nitride crystal substrate manufactured in Example B3, included dislocations extending in directions from the first area serving as the seed crystal to the second area grown from the seed crystal. 
     In the same manner as described above, the dislocation density of the BPD and the BPD were measured for the group 13 nitride crystal substrate manufactured in Example B1 and Example B2. As a result, it was found that the dislocation density of the BPD was higher than the dislocation density of the threading dislocation extending in a direction threading though the c-plane. 
     Thus, it was found that the dislocation density of the BPD in the group 13 nitride crystal produced in Example A1 and Example A2 was higher than the dislocation density of the threading dislocation extending in a direction threading though the c-plane. 
     If the BPD is present in a plurality of directions, the group 13 nitride crystal substrate can be of high quality with a little distortion and warpage. Therefore, even if the group 13 nitride crystal substrate was cut out from the group 13 nitride crystal produced in Example A1 and Example A2 such that the group 13 nitride crystal substrate includes the first area serving as the seed crystal, the group 13 nitride crystal substrate can be of high quality with a little distortion and warpage compared with the conventional group 13 nitride substrate. 
     From the evaluation results described above, it was found that the dislocation density of the BPD was higher than the density of grain boundary on the c-plane in the group 13 nitride crystal produced in Example A1 and Example A2. 
     Furthermore, it was found that a crystal substrate having lower dislocation density and a smaller grain boundary can be manufactured by processing the crystal so as to have the principal surface formed of the c-plane. 
     In the same manner as described above, the BED dislocation density was measured for the group 13 nitride crystal substrate manufactured in Comparative example B2 and having the principal surface formed of the m-plane. As a result, dislocations were found mainly as short dark lines, but the density of the dislocation threading through the m-plane surface was equal to or lower than 10 2  cm 2 . 
     Thus, it was found that the group 13 nitride crystal produced in Comparative example A1 did not satisfy the relationship between the threading dislocation and the basal plane dislocation in the group 13 nitride crystal produced in Example A1 and Example A2. 
     PL Evaluation 
     PL was measured at room temperature for the c-plane cross-section of the group 13 nitride crystal substrate manufactured in Example B1. A He—Cd laser at a wavelength of 325 nm was used as an excitation light source. 
       FIG. 23  is a view schematically illustrating emission distribution of PL in the group 13 nitride crystal substrate manufactured in Example B1. The area of the seed crystal (first area  21 B) included areas  291  to  293  (the third area  29   a  and the fourth area  29   b  (the fourth area  29   b   1  and the fourth area  29   b   2 )) having different light emission properties, such as colors and intensity of the PL. It was assumed that the difference in the light emission properties, such as emission intensity and colors, among the areas was caused by difference in impurities contained in the areas and the amount of the impurities. 
     Because the area  291  is an area exhibiting intense red light emission and emits red light, it is found that light emission from 600 to 650 nm, which is light emission from other than the vicinity of the band edge of GaN, is intense in the area  291 . In other words, the area  291  has the property of the third area  29   a.    
     Because the area  292  is an area exhibiting intense blue light emission and emits light in a blue wavelength range, it is found that the light emission is from the band edge of GaN or the vicinity of the band edge. The area  293  is an area in which the emission intensity of blue light is lower than the emission intensity of blue light in the area  292 . In the area  292  and the area  293 , no orange or red light emission is found, and light emission from other than the vicinity of the band edge of GaN is not intense. In other words, the area  292  has the property of the fourth area  29   b   1 , and the area  293  has the property of the fourth area  29   b   2 . Furthermore, it was found that the thickness t (thickness in the m-axis direction) of the fourth area  29   b  was at least equal to or larger than 10 μm on the c-plane cross-section of the seed crystal (first area  21 B). 
     The GaN crystal in the second area  27  grown around the seed crystal  21 B exhibited blue light emission. 
     As described above, from the results of the PL measurement, it was found that the c-plane of the crystal substrate  100  included the third area  29   a  and the fourth area  29   b  (the fourth area  29   b   1  and the fourth area  29   b   2 ). Furthermore, it was found that the third area  29   a  was covered by the fourth area  29   b   1  and that the fourth area  29   b   1  was covered by the fourth area  29   b   2 . 
     According to the embodiments, it is possible to provide a group 13 nitride crystal and a group 13 nitride crystal substrate of high quality. 
     Although the invention has been described with respect to specific embodiments for a complete and clear disclosure, the appended claims are not to be thus limited but are to be construed as embodying all modifications and alternative constructions that may occur to one skilled in the art that fairly fall within the basic teaching herein set forth.