Patent Publication Number: US-2022235490-A1

Title: Single crystal ingot, crystal growth die, and single crystal production method

Description:
TECHNICAL FIELD 
     The present invention relates to a single crystal ingot, a crystal growth die, and a manufacturing method of a single crystal. 
     BACKGROUND ART 
     The EFG (Edge-defined Film-fed Growth) method (refer to Patent document 1, for example) is known as a conventional single crystal growing method. Patent document 1 discloses a method for growing a flat plate-shaped β-Ga 2 O 3  single crystal by the EFG method. 
     The EFG method is a technique of growing a flat plate-shaped single crystal by immersing a lower portion of a die formed with a slit in a melt, holding, on the die, a melt that has risen up through the slit due to capillary phenomenon, bringing a seed crystal into contact with the melt thus risen up, and pulling up a resulting single crystal. Usually, a cross section, taken perpendicularly to the crystal pulling direction, of a single crystal thus pulled up is approximately the same, in shape, as the top surface of the die. 
     CITATION LIST 
     Patent Literature 
     Patent document 1: JP-A-2004-56098 
     SUMMARY OF INVENTION 
     Technical Problem 
     However, the present inventors carried out EFG crystal growth repeatedly by adding various dopants to a Ga 2 O 3  material to control resistivity and found that single crystals grown have following problems (deficit) described below depending on the kind of dopant added. 
     In crystal growth from an undoped Ga 2 O 3  material, a resulting crystal expanded until coming very close to edges of the top surface of the die and, as mentioned above, a cross section, taken perpendicularly to the crystal pulling direction, of the pulled-up single crystal was approximately the same, in shape, as the top surface of the die. On the other hand, if EFG crystal growth was carried out by adding FeO to a material to make a resulting Ga 2 O 3  single crystal semi-insulative, there was a tendency that a crystal being grown did not expand easily toward the edges of the die top surface. As a result, plural linear recesses extending in the pulling direction were formed on an as-grown surface extending in the crystal pulling direction of a single crystal being pulled up. These recesses extended as the pulling-up operation proceeded. 
     If such recesses are formed in a single crystal grown, an area from which substrates can be cut out is reduced when substrates having a desired shape are cut out from the single crystal. This results in reduction in the yield of substrate manufacture. 
     For solving the above described problems, an object of the present invention is to provide an EFG manufacturing method of a single crystal capable of decreasing the depths of the recesses even in a case that recesses are formed on an as-gown surface, extending in a crystal pulling direction, of a single crystal grown, a crystal growth die to be used in that manufacturing method, and a single crystal ingot manufactured by that manufacturing method. 
     Solution to Problem 
     To attain the above object, one aspect of the invention provides the following single crystal ingots of items [1] to [5], crystal growth dies of items [6] to [11], and manufacturing methods of a single crystal of items [12] to [15]: 
     [1] An as-grown single crystal ingot of a metal oxide containing a dopant or a pseudobinary-component compound, in which: 
     a length of a side surface, extending in a longitudinal direction that is parallel with a crystal pulling direction, in the longitudinal direction is 50 mm or larger; 
     the side surface has a linear recess that extends in the longitudinal direction from one end in the longitudinal direction; 
     among cross sections taken perpendicularly to the longitudinal direction of a portion surrounded by the side surface, a cross section at a position that is distant from the other end located on a side without the recess in the longitudinal direction by 50 mm in the longitudinal direction has an external shape such that a distance X max  that is a maximum value of distance of the recess from an ideal external shape is 5 mm or shorter in portions excluding a portion formed by an intersection line of the cross section and a facet; and the ideal external shape is a rectangle or a quadrangle having a smallest area capable of containing the external shape of the cross section. 
     [2] The single crystal ingot according to [1], in which a width of the single crystal ingot is 50 mm or larger. 
     [3] The single crystal ingot according to item [1] or [2], in which the distance X max  that is a maximum value of distance of the recess from the ideal external shape is 5 mm or shorter in all portions including the portion formed by the intersection line of the cross section and the facet. 
     [4] The single crystal ingot according to any one of items [1] to [3], in which: the metal oxide is a Ga 2 O 3 -based semiconductor; and the dopant is one or more elements selected from the group consisting of Mg, Si, Ti, Fe, Co, Ni, Cu, Zr, Nb, Hf, and Ta. 
     [5] The single crystal ingot according to any one of items [1] to [4], in which the distance X max  is 1 mm or longer. 
     [6] A crystal growth die to be used for crystal growth using an EFG method, the crystal growth die including: 
     a top surface having an opening of a slit and being flat; and 
     a drainage acceleration portion for urging drainage of a melt from the top surface, that is formed at an edge of the top surface or a position that is located in a vicinity of the edge and spaced from the slit. 
     [7] The crystal growth die according to item [6], in which the drainage acceleration portion is formed at least in a vicinity of the edge that is parallel with the slit. 
     [8] The crystal growth die according to item [6] or [7], in which the drainage acceleration portion is a chamfered portion, an R-chamfered portion, or a step portion that is formed in at least a part of the edge. 
     [9] The crystal growth die according to item [6] or [7], in which the drainage acceleration portion is a slant portion that is formed in entire or a part of an upper portion of a side surface. 
     [10] The crystal growth die according to item [6] or [7], in which the drainage acceleration portion is a groove that is formed in a side surface so as to extend downward from the top surface. 
     [11] The crystal growth die according to item [6] or [7], in which the drainage acceleration portion is a through-hole having an opening in a region located in a vicinity of the edge of the top surface. 
     [12] A manufacturing method, using an EFG method, of a single crystal of a metal oxide containing a dopant or a pseudobinary-component compound, in which: 
     the single crystal is pulled up while a melt located between a top surface of a crystal growth die and a single crystal growth interface is drained from an edge of the top surface of the crystal growth die or a portion in a vicinity of the edge. 
     [13] A manufacturing method, using an EFG method, of a single crystal of a metal oxide containing a dopant or a pseudobinary-component compound, in which: 
     a linear recess is formed in a side surface extending in a longitudinal direction that is parallel with a crystal pulling direction of the single crystal when the single crystal is pulled up; and 
     in an ingot of the single crystal grown, among cross sections taken perpendicularly to the longitudinal direction of a portion surrounded by the side surface, a cross section at a position that is distant from an end located on a side without the recess in the longitudinal direction by 50 mm in the longitudinal direction has an area of 80% or more of an area of the top surface of a crystal growth die. 
     [14] The manufacturing method of a single crystal according to item [12] or [13], in which: 
     the metal oxide is a Ga 2 O 3 -based semiconductor; and 
     the dopant is one or more elements selected from the group consisting of Mg, Si, Ti, Fe, Co, Ni, Cu, Zr, Nb, Hf, and Ta. 
     [15] The manufacturing method of a single crystal according to any one of claims  12  to  14 , in which the crystal growth die according to any one of claims  6  to  11  is used. 
     Advantageous Effects of Invention 
     The present invention can provide an EFG manufacturing method of a single crystal capable of decreasing the depths of the recesses even in a case that a dopant is added that causes recesses to be formed on an as-gown surface, extending in a pulling direction, of a single crystal grown, a crystal growth die to be used in that manufacturing method, and a single crystal ingot manufactured by that manufacturing method. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is vertical sectional view of part of an EFG single crystal growing apparatus according to a first embodiment of the present invention. 
         FIG. 2A  is a schematic diagram showing a state in the vicinity of a crystal growth interface in EFG single crystal growth using a conventional apparatus. 
         FIG. 2B  is a schematic diagram showing a state in the vicinity of a crystal growth interface in EFG single crystal growth using a conventional apparatus. 
         FIG. 3A  is a phase diagram showing a relationship between the temperature of a certain pure substance and the concentration of a dopant added to that pure substance. 
         FIG. 3B  is another phase diagram showing a relationship between the temperature of the certain pure substance and the concentration of a dopant added to that pure substance. 
         FIG. 4A  shows an appearance of a single crystal ingot grown by an EFG method using a conventional apparatus, as comparative example. 
         FIG. 4B  is a sectional view, taken perpendicularly to the crystal pulling direction, of the single crystal ingot shown in  FIG. 4A . 
         FIG. 5  is a schematic diagram showing a state in the vicinity of a crystal growth interface in EFG single crystal growth using a crystal growth die of the first embodiment of the invention. 
         FIG. 6A  is a sectional view of part of an EFG single crystal growing apparatus that employs a modification of the crystal growth die. 
         FIG. 6B  is a sectional view of part of an EFG single crystal growing apparatus that employs another modification of the crystal growth die. 
         FIG. 7A  is a perspective view showing an example structure of drainage acceleration portions of the crystal growth die of the first embodiment of the invention. 
         FIG. 7B  is a perspective view showing an example structure of drainage acceleration portions of the crystal growth die of the first embodiment of the invention. 
         FIG. 7C  is a perspective view showing an example structure of drainage acceleration portions of the crystal growth die of the first embodiment of the invention. 
         FIG. 8  is a perspective view of a crystal growth die of a case that portions of the edges of the top surface are formed with chamfered portions, respectively. 
         FIG. 9A  is a perspective view showing an example structure of drainage acceleration portions of the crystal growth die of the first embodiment of the invention. 
         FIG. 9B  is a perspective view showing an example structure of drainage acceleration portions of the crystal growth die of the first embodiment of the invention. 
         FIG. 9C  is a perspective view showing an example structure of drainage acceleration portions of the crystal growth die of the first embodiment of the invention. 
         FIG. 10  is a perspective view of a crystal growth die in which all of the edges of the top surface are formed with chamfered portions, respectively. 
         FIG. 11A  shows an appearance of a single crystal ingot of the first embodiment of the invention. 
         FIG. 11B  is an example cross section, taken perpendicularly to the longitudinal direction at a position that is distant by 50 mm from an end located on the side without recesses in the longitudinal direction, of a portion, surrounded by a side surface, of a single crystal ingot. 
         FIG. 11C  is another example cross section, taken perpendicularly to the longitudinal direction at a position that is distant by 50 mm from an end located on the side without recesses in the longitudinal direction, of a portion, surrounded by a side surface, of a single crystal ingot. 
         FIG. 12  is a phase diagram showing a relationship between the temperature and the composition of a composite oxide including an AO component and a BO component. 
         FIG. 13  is a plan view showing a plate member measuring 25 mm×15 mm that was cut out from a Ga 2 O 3  single crystal ingot by cutting it perpendicularly to a crystal pulling direction and measurement positions of a concentration measurement. 
         FIG. 14A  is a graph showing a distribution of Fe concentration in the Ga 2 O 3  single crystal plate member measured. 
         FIG. 14B  is another graph showing a distribution of Fe concentration in the Ga 2 O 3  single crystal plate member measured. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
     Although the present embodiment will be described mainly using a single crystal of a Ga 2 O 3 -based semiconductor as an example metal oxide single crystal grown, the metal oxide single crystal of the present invention is not limited to it. 
     (Configuration of EFG Single Crystal Growing Apparatus) 
       FIG. 1  is vertical sectional view of part of an EFG single crystal growing apparatus  10  according to a first embodiment of the invention. 
     The EFG single crystal growing apparatus  10  includes a crucible  11  which contains a melt  20  of a Ga 2 O 3 -based compound and a dopant(s) such as FeO; a crystal growth die  12  which is set in the crucible  11 ; a lid  13  which closes the opening of the crucible  11  so that a top surface  120  of the crystal growth die  12  is exposed; a seed crystal holding member  14  which holds a flat plate-shaped seed crystal  21  that is a single crystal of the Ga 2 O 3 -based compound; and a shaft  15  which supports the seed crystal holding member  14  in such a manner as to elevate and lower it. 
     The crucible  11  contains the melt  20  that was obtained by melting a sintered body of powder, granules, pellets, etc. of the Ga 2 O 3 -based compound. The crucible  11  is made of a material such as iridium that is so heat-resistant as to be able to contain a melt  20  of the Ga 2 O 3 -based compound. 
     The crystal growth die  12  has a slit  121  for elevating a melt  20  in the crucible  11  to the top surface  120  by capillary phenomenon. The crystal growth die  12  has, as a novel and an unprecedented structure, drainage acceleration portion for accelerating drainage, from the top surface  120 , of melts  20  in the vicinities of the edges of the top surface  120 . The drainage acceleration portions will be described later. 
     The lid  13  prevents evaporation of the high-temperature melt  20  from the crucible  11  and also prevents solidified material in which vapor of the melt  20  is condensed from sticking to portions, other than the top surface  120 , of the crystal growth die  12 . 
     The EFG single crystal growing apparatus  10  grows a flat plate-shaped growth crystal  22  by lowering the seed crystal  21  so as to bring it into contact with the top surface  120  of the crystal growth die  12  that is supplied with the melt  20  and pulling up the seed crystal  21  that have been kept in contact with the melt  20 . The crystal orientation of the growth crystal  22  is the same as that of the seed crystal  21 , and the crystal orientation of the growth crystal  22  is controlled by, for example, adjusting the surface orientation and the angle in the horizontal plane of the bottom surface of the seed crystal  21 . 
     Each of the seed crystal  21  and the growth crystal  22  are a single crystal of a Ga 2 O 3 -based compound. The Ga 2 O 3 -based compound is Ga 2 O 3  or Ga 2 O 3  added with elements such as Al and In and has, for example, a composition represented by (In x Al y Ga z ) 2 O 3  (x+y+z=1, x≥0, y≥0, and z&gt;0). Furthermore, the Ga 2 O 3 -based compound constituting the seed crystal  21  and the growth crystal  22  or the Ga 2 O 3 -based compound constituting the growth crystal  22  contains, as a dopant(s), an element that is low in volatility in the vicinity of a melting temperature of Ga 2 O 3 , such as Mg, Si, Ti, Fe, Co., Ni, Cu, Zr, Nb, Hf, or Ta. The dopant will be described later. 
     (Problem of Single Crystal Growth by EFG Method) 
       FIGS. 2A and 2B  are schematic diagrams each showing a state in the vicinity of a crystal growth interface of EFG single crystal growth using a conventional apparatus.  FIG. 2A  is a schematic diagram of a case that a growth crystal  212   a  containing no dopant is grown from a melt  210   a  containing no dopant.  FIG. 2B  is a schematic diagram of a case that a growth crystal  212   b  containing a dopant is grown from a melt  210   b  containing the dopant. A problem of the single crystal growth by the EFG method that has been found by the present inventors will be described with reference to  FIGS. 2A and 2B . 
     As shown in  FIGS. 2A and 2B , in the EFG method, the volume of a melt  210  that is directly involved in the crystal growth is restricted to that of a gap between a crystal growth surface  211  and the top surface  201  of a crystal growth die  200  and a melt  210   a  or  210   b  is supplied continuously from a slit  202  of the crystal growth die  200  to the gap. Arrow A in  FIGS. 2A and 2B  indicates a flow of the melt  210   a  or  210   b  and arrow P indicates a crystal pulling direction. 
     In the melt  210   b , the dopant exists in the form of an oxide (e.g., Fe exists in a Ga 2 O 3  melt in the form of FeO or the like). Thus, when a growth crystal  212   b  is grown, as shown in  FIG. 2B  the concentration of the dopant oxide increases in portions of a melt  210   b  that are distant from the slit  202  in the gap due to segregation. In  FIG. 2B , the gradation that is given to each of the melt  210   b  and the growth crystal  212   b  indicates, schematically, a concentration distribution of the dopant oxide; a darker gradation portion means a higher concentration. Arrows B in  FIG. 2B  indicate flows of a dopant oxide that remains in the melt  210   b  without being incorporated into the growth crystal  212   b . Since the solidification temperature of the melt  210   b  lowers as the concentration of the dopant oxide increases, crystal growth from portions distant from the slit  202  lowers. 
     As a result, growth failures occur in the vicinities of outer peripheries of a growth crystal  212   b  and plural linear recesses extending in the crystal pulling direction P are formed in a side surface (as-grown surface) extending in the crystal pulling direction P. On the other hand, where a growth crystal  212   a  containing no dopant is grown, as shown in  FIG. 2A , since no dopant is contained in the melt  210   a , a melt  210   a  in the gap between the crystal growth surface  211  and the top surface  201  of the crystal growth die  200  is uniform. As a result, the growth crystal  212   a  is not formed with linear recesses due to segregation of a dopant oxide in the melt. 
     Although segregation of a dopant in a material also occurs in crystal growth from a melt in the Czochralski method, Bridgman method, Kyropoulos method, heat exchange method (HEM), etc., since the volume of a melt involved in crystal growth is not small unlike in the EFG method, there does not occur a phenomenon that recesses are formed in the surface of a growth crystal because crystal growth is obstructed by segregation of a dopant oxide. 
     The present inventors have studied, from the viewpoint of the crystal growth engineering, about a specific mechanism of how recesses are formed in growing a Ga 2 O 3  single crystal to which Fe is added as a dopant, and have made the following analyses and judgments. 
     (1) Ga 2 O 3  is doped with Fe by adding a doping material that is an oxide such as Fe oxide (e.g., FeO or Fe 2 O 3 ) to a Ga 2 O 3  material. 
     (2) The ratio of an amount of Fe incorporated into a grown crystal to an amount of Fe added to Ga 2 O 3  is about 0.2. This ratio can be said to be a segregation coefficient of Fe in Ga 2 O 3 . 
     (3) It is considered that Fe exists in a Ga 2 O 3  melt in the form of an oxide such as FeO. When a melt that has risen up through the slit formed approximately at the center of the die from the crucible by capillary phenomenon is crystallized right over the slit, part of the Fe oxide contained in the melt is incorporated into the crystal at a ratio of about 0.2 with respect to its addition amount and the other part of the Fe oxide remains in the melt at a ratio of about 0.8. 
     (4) While part of the melt that has risen up through the slit is crystallized on the crystal side, the other part flows through the gap between the crystal growth interface and the top surface of the die toward the edges of the die top surface (i.e., the ridges formed by the top surface and the side surfaces). 
     (5) Based on items (3) and (4), it is considered that the concentration of the Fe oxide in the melt that flows through the gap between the crystal growth interface and the die top surface toward the edges of the die top surface increases toward the edges of the die top surface. 
     (6) As the pulling-up of the crystal proceeds, the amount of the Fe oxide remaining in the melt existing in the gap between the crystal growth interface and the die top surface is increased and the concentration of the Fe oxide existing in melts located in the vicinities of the edges of the die top surface becomes even higher to lower the solidification temperature (melting temperature lowers). 
     (7) As a result of the phenomenon (6), in the melt existing in the gap between the crystal growth interface and the die top surface, the portions in the vicinities of the edges of the die top surface are crystallized less easily because the crystallization temperature (solidification temperature) of those portions where the concentration of the Fe oxide is made higher than its addition concentration is lower than in the portion right over the slit of the die where the concentration of the Fe oxide remains approximately the same as its addition concentration; thus, outer peripheries of the crystal recede from the edges of the top surface of the die. As a result, plural linear recesses are formed so as to extend in the pulling direction in an as-grown surface, extending in the crystal pulling direction, of a crystal grown. 
     Furthermore, the inventors confirmed that the above-described problem of formation of linear recesses in a crystal grown does not occur in a case that an Sn oxide is used as a dopant material instead of an Fe oxide to employ Sn as dopant. The reason is considered as follows. Although the concentration of the Sn oxide is made higher in the portions of a melt in the vicinities of the edges of the die top surface as in the case of use of the Fe oxide, since Sn is high in volatility in the vicinity of the melting temperature of Ga 2 O 3 , Sn volatilizes from the edges of the die top surface and almost no decrease occurs in the crystallization temperature (solidification temperature). 
     For the above reason, it is inferred that also in the case where an least one element selected from the group consisting of Mg, Si, Ti, Fe, Co, Ni, Cu, Zr, Nb, Hf, and Ta which are low in volatility in the vicinity of the melting temperature of Ga 2 O 3  is used as a dopant(s), segregation of an oxide of the dopant would occur to cause the above-described problem that linear recesses are formed in a crystal grown. 
     Also in a case of growing a single crystal of a metal oxide other than Ga 2 O 3 , if a dopant is added that is low in volatility in the vicinity of the melting temperature of that metal oxide, segregation of an oxide of the dopant occurs in the same manner as in the case of using Fe in growing a Ga 2 O 3  single crystal to cause the above-described problem of formation of linear recesses in a crystal grown. 
     How the dopant concentration and the solidification temperature of a melt vary in a process of crystal precipitation from a melt can be understood using a phase diagram. 
       FIGS. 3A and 3B  are phase diagrams each showing a relationship between the temperature of a certain pure substance and the concentration of a dopant added to that pure substance. 
     An addition concentration of a dopant in a melt of a pure substance is represented by C L0 . First, when the temperature of the melt is lowered, as shown in  FIG. 3A  a primary crystal having a composition on a solid phase line at a temperature T 0  at which a liquid phase line is reached is precipitated. The addition concentration of the dopant (liquid phase composition C L0 ) and the concentration in the primary crystal (solid phase concentration C S0 ) have a relationship k=C S0 /C L0  and k is called a segregation coefficient. 
     Where the dopant is diffused sufficiently in the liquid phase, as shown in  FIG. 3B  the dopant concentration in the liquid phase increases and the solidification temperature lowers along the liquid phase line as the solidification of the material proceeds. In parallel with these actions, the concentration of the dopant incorporated in the crystal increases. As the dopant concentration in the liquid phase increases from C L0  to C L1 , the concentration of the dopant incorporated in the crystal increases from C S0  to C S1 . Finally, crystallization occurs at a eutectic point in the form of a mixture at a dopant concentration CE. 
       FIG. 4A  shows an appearance of a single crystal ingot  100  grown by an EFG method using a conventional apparatus, as comparative example.  FIG. 4B  is a sectional view, taken perpendicularly to the crystal pulling direction P, of the single crystal ingot  100 . The single crystal ingot  100  is an unprocessed grown crystal as pulled up, that is, an as-grown crystal. 
     The as-grown side surface (outer circumferential surface)  101 , extending in the crystal pulling direction P, of the single crystal ingot  100  has plural linear recesses  102  extending in the crystal pulling direction P. For the above-described reason, the recesses  102  are formed after the pulling-up of the crystal has proceeded to some extent and are increased in size as the pulling-up proceeds further. Thus, the recesses  102  are increased in size as their position goes away from the seed crystal  21 . Furthermore, there is a tendency that the recesses  102  start to be formed from positions near the four corners when the single crystal ingot  100  are seen from the crystal pulling direction P. 
     (Manufacturing Method of Single Crystal) 
     A manufacturing method of a single crystal according to the present embodiment that has been invented in view of the problem of the above-described EFG single crystal growth will be described below. 
       FIG. 5  is a schematic diagram showing a state in the vicinity of a crystal growth interface  220  in EFG single crystal growth using a crystal growth die  12  according to the first embodiment of the invention. In  FIG. 5 , the gradation that is given to each of a melt  20  and a growth crystal  22  indicates, schematically, a concentration distribution of a dopant oxide; a darker gradation portion means a higher concentration. 
     In the crystal growth die  12 , the top surface  120  is flat and is formed with an opening of the slit  121 . The top surface  120  has drainage acceleration portions  123  for accelerating drainage of a melt  20  from the top surface  120  at the edges of the top surface  120  (i.e., the ridges between the top surface  120  and side surfaces  122 ) or positions that are in the vicinities of the edges and are spaced from the slit  121  (i.e., not in contact with the slit  121 ). 
     As described above, the solidification temperature is low and hence the viscosity is low in portions, close to the edges of the top surface  120 , of a melt  20 . Thus, once a melt  20  remaining in the gap between the crystal growth interface  220  and the top surface  120  because of surface tension reaches the drainage acceleration portions  123 , it flows to the side surfaces  122  past the drainage acceleration portions  123 . In this manner, the drainage acceleration portions  123  can effectively urge drainage, from the top surface  120 , of melts  20  that are located in the vicinities of the edges of the top surface  120  and are high in the concentration of the dopant oxide. 
     As shown in  FIG. 1 , in the EFG single crystal growing apparatus  10  according to the embodiment, flow passages of a melt  20  from the top surface  120  of the crystal growth die  12  to inside the crucible  11  are secured and hence a melt  20  drained from the top surface  120  can return to inside the crucible  11  across the side surfaces  122 . As a result, a drained melt  20  can be reused for single crystal growth without being discarded uselessly. 
       FIGS. 6A and 6B  are sectional views of parts of EFG single crystal growing apparatuses  10  that employ crystal growth dies  12   a  and  12   b  that are modifications of the crystal growth die  12 , respectively. In the crystal growth die  12   a , each of the side surfaces is not formed with a step. In the crystal growth die  12   b , a top portion including the top surface  120  is wider than the other portion. In the case where the crystal growth die  12   a  or  12   b  is used, flow passages of a melt  20  from the top surface  120  of the crystal growth die  12  to inside the crucible  11  are secured. 
     In the embodiment, occurrence of growth failures in the outer peripheries of a growth crystal  22  can be suppressed by growing a growth crystal  22  while portions, located in the vicinities of the edges of the top surface  120  and being high in the concentration of the dopant oxide, of a melt  20  existing between the top surface  120  of the crystal growth die  12  and the crystal growth interface  220  are drained using the drainage acceleration portions  123 . 
     As a result, the depths of plural linear recesses that are formed in an as-grown surface, extending in the crystal pulling direction, of a grown single crystal ingot and extend in the crystal pulling direction can be made small. 
     The features that the top surface  120  of the crystal growth die  12  is flat and that the drainage acceleration portions  123  are provided at positions that are spaced from the slit  121  are conditions for preventing air from entering the slit  121  from the sides in the case where the slit  121  is open sideways. If air enters the slit  121  from the sides during crystal growth, a melt is not raised and no crystal grows from the portion that air entered, resulting in formation of a recess in a grown crystal  22 . 
       FIGS. 7A-7C  are perspective views showing example structures of the drainage acceleration portions  123  of the crystal growth die  12  ( 12   a ,  12   b ). 
     Chamfered portions  123   a  shown in  FIG. 7A , which are one form of the drainage acceleration portions  123 , are slant surfaces formed by chamfering the ridges between the top surface  120  and the side surfaces  122 . The manner of forming the drainage acceleration portions  123   a  is not limited to C chamfering (i.e., chamfering of an angle 45°). 
     R-chamfered portions  123   b  shown in  FIG. 7B , which are another form of the drainage acceleration portions  123 , are curved surfaces formed by R-chamfering the ridges between the top surface  120  and the side surfaces  122 . 
     Step portions  123   c  shown in  FIG. 7C , which are a further form of the drainage acceleration portions  123 , are steps formed by working the edges of the top surface  120  into step shapes, respectively. Each of the step portions  123   c  may be formed by plural steps. 
     It is preferable that the width W of the chamfered portions  123   a , the R-chamfered portions  123   b , and the step portions  123   c  be in a range of 0.1 mm or more and 2 mm or less. Draining effect for the melt  20  is exerted effectively in the case where the width W is 0.1 mm or larger. On the other hand, draining effect for the melt  20  exhibits almost no variation after the width W exceeds 2 mm. Thus, setting width W at 2 mm or smaller makes it possible to avoid size increase of the crystal growth die  12  while sufficiently exerting draining effect for the melt  20 . 
     To sufficiently exert draining effect for the melt  20 , it is preferable that the height H of the step portions  123   c  be in a range of 0.1 mm or more and 1 mm or less. 
       FIG. 8  is a perspective view of a crystal growth die  12  ( 12   a ,  12   b ) of a case that portions of the edges of the top surface  120  are formed with chamfered portions  123   a , respectively. Portions of the edges of the top surface  120  may likewise be formed with R-chamfered portions  123   b  or step portions  123   c , respectively. 
     In this case, it is also preferable that the width W of the chamfered portions  123   a , the R-chamfered portions  123   b , and the step portions  123   c  be in a range of 0.1 mm or more and 2 mm or less. The draining effect for the melt  20  is exerted effectively in the case where the width W is 0.1 mm or larger. Furthermore, where the width W is set smaller than or equal to 2 mm, the probability that the presence of the chamfered portions  123   a , the R-chamfered portions  123   b , or the step portions  123   c  becomes a cause of formation of recesses in an as-grown surface, extending in the crystal pulling direction P, of a grown crystal  22 . 
     The length L of the chamfered portions  123   a , the R-chamfered portions  123   b , and the step portions  123   c  is preferably 0.1 mm or larger. The draining effect for the melt  20  is exerted effectively in the case where the length L is 0.1 mm or larger. 
     The draining effect for the melt  20  can be enhanced by forming chamfered portion  123   a , R-chamfered portion  123   b , or step portion  123   c , each of which is provided at a part of the edge of the top surface  120 , in plural portions in such a manner that they are arranged along the edge. 
       FIGS. 9A-9C  are perspective views showing other example structures of the drainage acceleration portions  123  of the crystal growth die  12  ( 12   a ,  12   b ). 
     Slant portions  123   d  shown in  FIG. 9A , which are one form of the drainage acceleration portions  123 , are slant surfaces each of which is formed in all or part of an upper portion of a side surface  122 . An inclination angle θ of the slant portion  123   d  (i.e., an angle formed by the top surface  120  and each slant portion  123   d ) is preferably 100° or larger. The draining effect for the melt  20  is exerted effectively in the case where the inclination angle is 100° or larger. On the other hand, the draining effect for the melt  20  exhibits almost no variation after the inclination angle θ exceeds 150°. 
     Grooves  123   e  shown in  FIG. 9B , which are another form of the drainage acceleration portions  123 , are linear grooves that are formed in the side surfaces  122  so as to extend from the top surface  120  toward the bottom of the crystal growth die  12 . To enhance the draining effect for the melt  20 , it is preferable that plural grooves  123   e  be formed along the edge of the top surface  120 . 
     The depth D p  of the grooves  123   e  is preferably in a range of 0.1 mm or more and 2 mm or less. The draining effect for the melt  20  is exerted effectively in the case where the depth D p  is 0.1 mm or larger. Where the depth D p  is 2 mm or smaller, the probability that the presence of the grooves  123   e  becomes a cause of formation of recesses in an as-grown surface extending in the crystal pulling direction P of a grown crystal  22 . 
     Through-holes  123   f  shown in  FIG. 9C , which are another form of the drainage acceleration portions  123 , are through-holes having respective openings in the vicinities of the edges of the top surface  120 . Typically, as shown in  FIG. 9C , the through-holes  123   f  penetrate through a wide upper portion of the crystal growth die  12   b  from its top surface  120  to its bottom surfaces  124 . In this case, to prevent a melt  20  in the crucible  11  from rising up through the through-holes  123   f  by capillary phenomenon, it is necessary that the bottom surfaces  124  be spaced from the liquid surface of the melt  20  in the crucible  11 . Where the through-holes  123   f  penetrate from the top surface  120  to the side surfaces  122 , this structure can be applied to any of the crystal growth dies  12 ,  12   a , and  12   b  as long as the openings in the side surfaces  122  are located above the liquid surface of the melt  20  in the crucible  11 . To enhance the draining effect for the melt  20 , it is preferable that plural through-holes  123   f  be formed alongside the edge of the top surface  120 . 
     The diameter of the through-holes  123   f  is preferably in a range of 0.1 mm or more and 2 mm or less. The draining effect for the melt  20  is exerted effectively in the case where the diameter is 0.1 mm or larger. Where the diameter is 2 mm or smaller, the probability is lowered that even melt  20  that is distant from the edges of the top surface  120  to some extent and in which the concentration of the dopant oxide is relatively low is drained to impair the crystal growth. 
     The distance D between the portions, closest to the slit  121 , of the through-holes  123   f  and the edges of the top surface  120  is preferably 2 mm or shorter. Where the distance D is longer than 2 mm, even melt  20  that is distant from the edges of the top surface  120  to some extent and in which the concentration of the dopant oxide is relatively low may be drained to impair the crystal growth. 
     Where the top surface  120  is rectangular or square, it is preferable that the above-described various kinds of drainage acceleration portions  123  be formed in the vicinities of at least ones, parallel with the slit  121 , of the edges of the top surface  120  as shown in  FIGS. 7A-7C, 8, and 9A-9C . This is to effectively drain, by means of the drainage acceleration portions  123 , melt  20  that is distant to a large extent from the edges parallel with the slit  121  and has high concentration of the dopant oxide in the vicinities of edges parallel with the slit  121 . 
     To effectively drain melt  20  that is high in the concentration of the dopant oxide and thereby effectively decrease the depths of recesses formed in an as-grown surface, parallel with the crystal pulling direction P, of a grown crystal  22 , it is preferable that the drainage acceleration portions  123  be formed in the vicinities of all of the edges of the top surface  120 . 
       FIG. 10  is a perspective view of a crystal growth die  12  in which all of the edges of the top surface  120  are formed with chamfered portions  123   a , respectively. It is preferable that an R-chamfered portion  123   b , a step portion  123   c , a slant portion  123   d , grooves  123   e , and through-holes  123   f  be likewise formed at or in the vicinity of every edge of the top surface  120 . 
     The shape of the top surface  120  of the crystal growth die  12  is not limited to a rectangle and a square and may be a circle, for example. 
     (Features of Single Crystal) 
       FIG. 11A  shows an appearance of a single crystal ingot  1  according to the first embodiment of the invention. The single crystal ingot  1  is an unprocessed grown crystal  22  that is left as it is after it was pulled up, that is, an as-grown crystal  22 . Thus, the single crystal ingot  1  is, for example, a single crystal ingot of a Ga 2 O 3 -based compound and contains, as a dopant(s), one or more elements selected from the group consisting of Mg, Si, Ti, Fe, Co., Ni, Cu, Zr, Nb, Hf, and Ta which are low in volatility in the vicinity of the melting temperature of Ga 2 O 3 . 
     A side surface (outer circumferential surface)  221  extending in the longitudinal direction that is parallel with the crystal pulling direction P is an as-grown surface, and the length L of a portion, surrounded by the side surface  221 , of the single crystal ingot  1  (i.e., a portion excluding a shoulder portion that is formed in a growth initial stage) is 50 mm or longer. Where the length L is 50 mm or longer, substrates of about 2 inches in diameter can be cut out from the single crystal ingot  1  by, for example, setting the width of the single crystal ingot  1  (i.e., the length of the sides that are perpendicular to the length L direction and are not in the width direction of the slit  121  of the die  12 ) 50 mm or longer at any position. The length L and the width of the single crystal ingot  1  are preferably 60 mm or longer, even preferably 70 mm or longer. 
     The thickness of the single crystal ingot  1  (i.e., the length of the sides that are in the width direction of the slit  121  during crystal growth) is preferably 10 mm or longer at any position. It is even preferable that the thickness of the single crystal ingot  1  be 15 mm or longer. Where the grown crystal  22  is too thin, there may occur a phenomenon that the grown crystal  22  becomes insufficient for a pulling-up speed and the crystal being grown is separated from the crystal growth die  12  and the crystal growth is stopped. 
     The phenomenon that the grown crystal  22  is detached from the crystal growth die  12  in the case where the single crystal ingot  1  is thin is considered due to the following reason. (1) The horizontal gradient of the concentration of the dopant oxide tends to remain small in a melt  20  located between the top surface  120  of the crystal growth die  12  and the crystal growth interface  220  and the concentration of the dopant oxide increases in the entire area as the growth proceeds. Thus, the melting temperature lowers in the entire melt  20  located between the top surface  120  of the crystal growth die  12  and the crystal growth interface  220 , making it difficult to maintain the crystal growth. (2) When the concentration of the dopant oxide is increased, the melt  20  located between the top surface  120  of the crystal growth die  12  and the crystal growth interface  220  comes to have a eutectic composition (for example, to obtain, as a single crystal ingot  1 , an ingot of a Ga 2 O 3  single crystal containing Fe as a dopant, a melt  20  becomes a Ga 2 O 3 /Fe 2 O 3 -based stoichiometric compound rather than Ga 2 O 3  containing Fe. 
     The single crystal ingot  1  has plural linear recesses  222  that are formed in the portion surrounded by the side surface  221  so as to extend in the longitudinal direction. The recesses  222  become larger as the position goes away from the seed crystal  21 . That is, the recesses  222  are formed in the portion surrounded by the side surface  221  so as to start from one end opposite to the seed crystal  21  and extend in the longitudinal direction, that is, the crystal pulling direction. 
       FIGS. 11B and 11C  are example cross sections, taken perpendicularly to the longitudinal direction at a position that is distant from the other end located on the side without recesses  222  in the longitudinal direction (i.e., the end on seed crystal  21  side) by 50 mm in the longitudinal direction, of the portion, surrounded by the side surface  221 , of the single crystal ingot  1 .  FIG. 11B  shows an example cross section of a case that the single crystal ingot  1  has no facet and  FIG. 11C  shows an example cross section of a case that the single crystal ingot  1  has facets  230 . The term “facet” means a flat surface that appears as a surface of a crystal that has experienced facet growth. Also in the EFG method, a facet  230  may appear as a result of facet growth that has occurred in a surface surrounded by a side surface  221  depending on factors such as the concentration of a dopant oxide in a melt  20 , increase of the concentration of the dopant oxide that occurs as the growth proceeds, and the temperature conditions described above. A portion that is defined by an intersection line formed by a facet  230  and a cross section deviates inward from an ideal external shape  30  but can be discriminated because it is a flat line unlike in a case of a recess  222 . 
     As for the external shape of a cross section as shown in  FIG. 11B or 11C  taken at a position that is distant from the other end of a single crystal ingot  1  by 50 mm in the longitudinal direction, it is preferable that the maximum value (hereinafter represented by X max ) of distances X of recesses  222  from an ideal external shape  30  in portions other than portions formed by intersection lines of the cross section and facets  230  be 5 mm or smaller, even preferably 4 mm or smaller and further preferably 3 mm or smaller. Furthermore, as for the external shape of a cross section taken at a position that is distant from the other end of the single crystal ingot  1  by 80 mm in the longitudinal direction, it is preferable that the distances X max  of recesses  222  from an ideal external shape  30  be 5 mm or smaller. In the case of single crystal ingots  100  grown by an EFG method using a conventional apparatus, X max  does not become 5 mm or smaller. If X max  is small, in the case where the width of a single crystal ingot  1  is, for example, 50 mm or larger, a large number of substrates can be cut out because recesses  222  are small in a region of the single crystal ingot  1  from which substrates of about 2 inches in diameter can be cut out. 
     The term “ideal external shape  30 ” as used above is a rectangle or quadrangle having a smallest area that can contain the external shape of a cross section taken at a position that is distant from the above-mentioned other end located on the side without recesses  222  by 50 mm in the longitudinal direction. The ideal external shape  30  of a single crystal ingot  1  is approximately the same as the external shape of the top surface  120  of the crystal growth die  12 . The ideal external shape  30  is a rectangle in the case where the top surface  120  is a rectangle, and is approximately a square in the case where the top surface  120  is a square. 
     In the case of single crystal ingots  100  containing a dopant and grown by an EFG method using a conventional apparatus, X max  does not become 5 mm or smaller. X max  may become smaller if a single crystal ingot  100  is made thinner. However, if a single crystal ingot  100  is made thinner, it is highly probable that a grown crystal  212  becomes insufficient for a pulling-up speed during crystal growth and is separated from a crystal growth die  200  and the crystal growth is stopped before X max  reaches 5 mm. 
     In single crystal ingots  100  containing a dopant and grown by an EFG method using a conventional apparatus, there may occur a case that an ideal external shape  30  does not coincide with the external shape of the top surface of a crystal growth die because large recesses  102  are formed over the entire circumference. Also in that case, the maximum value X max  of distances X from an ideal external shape  30  in portions other than portions formed by intersection lines of a cross section of single crystal ingot  100  and facets does not become 5 mm or smaller. This is because recesses  102  are not formed uniformly over the entire circumference of the crystal. 
     Even if it is grown by an EFG method using a conventional apparatus, a single crystal ingot not containing a dopant does not have recesses in a side surface and hence a cross section taken perpendicularly to the crystal pulling direction has an external shape that is approximately coincide with the external shape of the top surface of the crystal growth die. 
     In the above-described manufacturing method of a single crystal according to the embodiment, the sizes of recesses  222  formed in a single crystal ingot  1  can be reduced. On the other hand, even where the method according to the embodiment is used, the distance X max  seldom becomes smaller than 1 mm. Thus, in many cases, the distance X max  is 1 mm or larger. 
     When the dopant concentration is high, crystal growth may become close to solution growth rather than melt growth and a facet(s)  230  may appear as described above. Since formation of a facet(s)  230  is also a cause of making the sectional area of a single crystal ingot  1  small, it is preferable that the external shape of a cross section taken perpendicularly to the longitudinal direction at a position that is distant from the other end located on the side without recesses  222  in the longitudinal direction by 50 mm in the longitudinal direction be such that the maximum value X max  of distances X of recesses  222  from an ideal external shape  30  of all portions including a portion(s) formed by an intersection line of the cross section and a facet(s)  230  be 5 mm or smaller, even preferably 4 mm or smaller and further preferably 3 mm or smaller. According to the above-described manufacturing method of a single crystal according to the embodiment, formation of facets  230  can be suppressed because a crystal can be grown while draining melts  20  that are located in the vicinities of the edges of the top surface  120  of the crystal growth die  12  and in which the concentration of the dopant oxide is high. 
     Furthermore, according to the above-described manufacturing method of a single crystal according to the embodiment, by reducing the sizes of recesses  222 , the area of a cross section, taken perpendicularly to the longitudinal direction at a position that is distant from the end located on the side without recesses  222  in the longitudinal direction (i.e., the end on the seed crystal  21  side) by 50 mm in the longitudinal direction, of a portion, surrounded by a side surface  221 , of a single crystal ingot  1  can be made 80% or more of the area of the top surface  120  of the crystal growth die  12 , preferably 90% or more. 
     As described above, the concentration of the dopant oxide in melts  20  located between the crystal growth interface  220  and the top surface  120  of the crystal growth die  12  increases as the position goes away from the slit  121 . For this reason, where the distance Z 1  between the edges of the top surface  120  and the slit  121  in the slit width direction (refer to  FIGS. 7A-7C, 8, 9A-9C, and 10 ) is longer than the distance Z 2  between the edges of the top surface  120  and the slit  121  in the slit direction (refer to  FIGS. 7A-7C, 8, 9A-9C, and 10 ), the concentration of the dopant oxide in melts  20  located in the vicinities of the edges of the top surface  120  in the slit width direction is higher. As a result, in this case, the maximum concentration of the dopant oxide in melts  20  located in the vicinities of the edges of the top surface  120  become higher and the maximum depth (i.e., the length of the longest one of lines drawn perpendicularly to the sides of plural recesses  222  from the sides of an ideal external shape) of the recesses  222  becomes larger as the maximum value (called a “distance Z”) of the distance Z 1  increases. That is, there exists a correlation between the distance Z and the depth of recesses  222 . According to the above-described manufacturing method of a single crystal according to the embodiment, the maximum depth of recesses  222  at a position that is distant from the end located on the side without recesses  222  in the longitudinal direction (i.e., the end on the seed crystal  21  side) by 50 mm in the longitudinal direction, of a portion, surrounded by a side surface  221 , of a single crystal ingot  1  can be made as small as Z×0.3 or less. 
     Furthermore, as described above, a single crystal ingot  1  having recesses  222  contains a dopant that is low in volatility in the vicinity of a melting point of a metal oxide as a base material. For example, where the metal oxide is a Ga 2 O 3 -based semiconductor, it contains, as a dopant(s), one or more elements selected from the group consisting of Mg, Si, Ti, Fe, Co, Ni, Cu, Zr, Nb, Hf, and Ta. 
     There are no particular limitations on the concentration of the dopant of a single crystal ingot  1 . This is because even if the concentration of the dopant of a single crystal ingot  1  (i.e., a dopant concentration in a central portion) is on the ppm order, during crystal growth the dopant concentration of melts  20  in the vicinities of the edges of the top surface  120  of the crystal growth die  12  is increased to such a level that recesses  222  can be formed. That is, recesses  222  can be formed even if a dopant material that is low in volatility in the vicinity of the melting temperature of a metal oxide as a base material is contained in a melt  20  by even a very small amount. In the case of a single crystal ingot  1  that is an ingot of a semi-insulative Ga 2 O 3  single crystal containing Fe, a typical Fe concentration is 15 to 30 ppm (weight) and a concentration of FeO in a melt  20  needs to be 100 to 200 ppm (weight) if segregation is taken into consideration. However, recesses  222  are formed even at a lower concentration than this range. 
     Second Embodiment 
     Although the first embodiment was directed to the case of growing a single crystal containing a dopant that is low in volatility in the vicinity of the melting temperature of a metal oxide as a base material, the problem of formation of recesses  222  may occur in the same mechanism also in growing a single crystal of a pseudobinary-component compound such as a composite oxide. 
     Example pseudobinary-component compounds such as a composite oxide are LiNbO 3  which is considered a composite of two kinds of metal oxides Li 2 O and Nb 2 O 5 , Y 3 Al 5 O 12 , and PbMoO 4 . 
     If a slight deviation occurs in the material composition of a pseudobinary-component compound such as a composite oxide, a difference occurs between a crystallization composition and a composition in the vicinity of a crystal interface, as a result of which the solidification temperature of melts  20  located in the vicinities of the edges of the top surface  120  of the crystal growth die  12  lowers as in the case of segregation of a dopant oxide. A case of growing a single crystal of a composite oxide ABO 2  will be described below. 
       FIG. 12  is a phase diagram showing a relationship between the temperature and the composition of a composite oxide including an AO component and a BO component. Assume that the amount of the AO component in a melt is C L0  that is slightly deviated from its amount in ABO 2 . In this case, as shown in  FIG. 12 , as crystal growth proceeds, the deviation in composition increases to cause melting temperature reduction (solidification temperature reduction). 
     That is, if the material composition of a pseudobinary-component compound such as a composite oxide has a slight deviation, the deviation of the composition of a melt increases and the solidification temperature lowers as the position goes from right over the slit  121  toward each edge on the top surface  120  of the crystal growth die  12 . 
     According to the manufacturing method of a single crystal according to the first embodiment of the invention, a crystal can be grown while draining melts  20  in the vicinities of the edges of the top surface  120  of the crystal growth die  12 . Thus, if this method is applied to this embodiment in which a single crystal of a pseudobinary-component compound such as a composite oxide is grown, a crystal can be grown while draining melts  20  that are located in the vicinities of the edges of the top surface  120  and hence have a large deviation in composition and are lowered in solidification temperature. The sizes of recesses  222  can therefore be made small. 
     Advantage of Embodiments 
     The above embodiments can provide an EFG manufacturing method of a single crystal capable of decreasing the depths of the recesses even in a case that recesses are formed in an as-gown surface, extending in a crystal pulling direction, of a single crystal grown, a crystal growth die to be used in that manufacturing method, and a single crystal ingot manufactured by that manufacturing method. 
     EXAMPLE 
     A Ga 2 O 3  single crystal containing Fe as a dopant was grown by a conventional EFG method and a distribution of Fe concentration in the single crystal was measured by a laser abrasion ICP-MS method. 
       FIG. 13  is a plan view showing a plate member  23  measuring 25 mm×15 mm that was cut out from a Ga 2 O 3  single crystal ingot by cutting it perpendicularly to a crystal pulling direction and measurement positions (M 1 -M 6 ) of the concentration measurement. 
     The Ga 2 O 3  single crystal plate member shown in  FIG. 13  was cut out from a region (indicated by a broken line in  FIG. 13 ), obtained by removing recesses  222 , of the Ga 2 O 3  single crystal ingot whose cross section taken perpendicularly to the crystal pulling direction measured 30 mm×30 mm. The surfaces of the Ga 2 O 3  single crystal plate member were polished and a distribution of Fe concentration was measured. 
       FIGS. 14A and 14B  are graphs showing a distribution of Fe concentration of the measured Ga 2 O 3  single crystal plate member. Numbers (M 1 -M 6 ) of respective data shown in  FIGS. 14A and 14B  correspond to the numbers (M 1 -M 6 ) of measurement positions shown in  FIG. 13 . The horizontal axis of  FIGS. 14A and 14B  represent the position with respect to a measurement start position and the vertical axis represents the ratio of the intensity of  56 Fe with respect to that of  71 Ga in a mass spectrometry signal. 
     As seen from  FIGS. 14A and 14B , the Fe concentration of the Ga 2 O 3  single crystal plate member increases toward the outer peripheries of the Ga 2 O 3  single crystal plate member and, in particular, increases rapidly in the vicinities of the outer peripheries. This indicates a probability that the concentration of Fe in a melt located between the top surface of a crystal growth die and a crystal growth interface increases rapidly as the position comes closer to the edges of the top surface of the die, which causes reduction of the solidification temperature. 
     Furthermore, according to observations of the present inventors, after the crystal growth residues of a high-concentration Fe oxide were found in portions of the top surface of the die where the crystal side surface receded (i.e., portions where recesses occurred). Also based on this finding, it is inferred that the expansion of a crystal to the edges of the crystal growth die was obstructed as a result of increase of the Fe concentration in the vicinities of the edges of the crystal growth die and the solidification temperature lowered there. 
     Although the embodiments and Example according to the invention have been described above, the invention is not limited to these embodiments and Example and various modifications are possible without departing from the gist and scope of the invention. 
     The above-described embodiments and Example should not be construed as restricting the claimed invention. Furthermore, it should be noted that all of the combination of the features described in the embodiments and Example is not necessarily indispensable for the means for attaining the object of the invention. 
     INDUSTRIAL APPLICABILITY 
     The present invention provides a manufacturing method, using an EFG method, of a single crystal capable of decreasing the depths of the recesses even in a case that a dopant is added that induces formation of recesses in an as-gown surface, extending in a crystal pulling direction, of a single crystal grown, a crystal growth die to be used in that manufacturing method, and a single crystal ingot manufactured by that manufacturing method. 
     DESCRIPTION OF SYMBOLS 
     
         
           1 : Single crystal ingot 
           10 : EFG single crystal growing apparatus 
           12 : Crystal growth die 
           20 : Melt 
           22 : Grown crystal 
           30 : Ideal external shape 
           120 : Top surface 
           121 : Slit 
           122 : Side surface 
           123 : Drainage acceleration portion 
           123   a : Chamfered portion 
           123   b : R-chamfered portion 
           123   c : Step portion 
           123   d : Slant portion 
           123   e : Groove 
           123   f : Through-hole 
           220 : Crystal growth interface 
           221 : Side surface 
           222 : Recess